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UBC Theses and Dissertations

Analyses of competition in binary and ternary mixtures involving a crop and three weed species Minjas, Athanasio Ndeonasia 1982

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ANALYSES OF COMPETITION IN BINARY AND TERNARY MIXTURES INVOLVING A CROP AND THREE WEED SPECIES by ATHANASIO NDEONASIA MINJAS B . S c , U n i v e r s i t y o f Dar-es-Salaam, M.Sc. U n i v e r s i t y o f Dar-es-Salaam A THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE DEPARTMENT OF PLANT SCIENCE We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA (c) September 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of P Lfl-rvJ J ^C^t t~ r^C k The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) ABSTRACT S e v e r a l models e x i s t f o r i n v e s t i g a t i n g the e f f e c t s o f p l a n t c o m p e t i t i o n w i t h i n and among s p e c i e s , i . e . i n t r a - and i n t e r - s p e c i f i c c o m p e t i t i o n . The models f o r i n t e r s p e c i f i c c o m p e t i t i o n are based upon a d d i t i v e and replacement (de Wit) s e r i e s e x p e r i m e n t s . Each approach has p r e v i o u s l y been used a l m o s t e x c l u s i v e l y t o s t u d y t h e e f f e c t s o f b i n a r y m i x t u r e s , and each has been used t o d e r i v e v a r i o u s i n d i c e s o f compet-i t i v e n e s s among s p e c i e s . S t u d i e s were und e r t a k e n i n 1980 and 1981 t o compare and e v a l u a t e the d i f f e r e n t models, and t o i n v e s t i g a t e the r e l a t i v e performance o f s p e c i e s i n t e r n a r y c o m b i n a t i o n s . M o n o c u l t u r e ( d e n s i t y ) , a d d i t i v e and rep l a c e m e n t s e r i e s e x p e r i m e n t s i n v o l v i n g b i n a r y m i x t u r e s o f b a r n y a r d g r a s s ( E c h i n o c h l o a c r u s g a l l i ) , r e d r o o t pigweed (Amaranthus r e t r o f l e x u s ) and green f o x t a i l ( S e t a r i a v i r i d i s ) were u n d e r t a k e n i n b o t h y e a r s ; monoculture ( d e n s i t y ) and rep l a c e m e n t s e r i e s i n v o l v i n g b i n a r y and t e r n a r y m i x t u r e s o f rapeseed ( B r a s s i c a napus) w i t h pigweed and f o x t a i l were a l s o i n v e s t i g a t e d i n b o t h y e a r s ; i n 1981, t h e rapeseed-pigweed-f o x t a i l e x p e r i m e n t s a l s o i n c l u d e d a d d i t i v e s e r i e s m i x t u r e s , the e x p e r i m e n t a l d e s i g n f o r which p e r m i t t e d the i n v e s t i g a t i o n o f b i n a r y r e p l a c e m e n t s e r i e s a t d i f f e r e n t t o t a l d e n s i t i e s . M o n o c u l t u r e e x p e r i m e n t s showed t h a t y i e l d o f a l l f o u r s p e c i e s was r e l a t e d t o the d e n s i t y a c c o r d i n g t o de W i t ' s - i i i -spacing formula. Additive series experiments involving barnyardgrass or rapeseed with the other two species showed that the y i e l d of the indicator species followed the Dew's relationship between y i e l d and the square root of the density of the associated species. The present studies have shown that the y i e l d of the l a t t e r (in the presence of the indicator species) can also be described by the spacing formula. In binary replacement series experiments, de Wit's r e l a t i v e crowding c o e f f i c i e n t s (k) were calculated. Estimates of y i e l d obtained from the k-values were usually found to agree well with observed y i e l d s . Dew's Index of Competition (CI) was calculated from additive series data for each combination of species tested. Relative crowding c o e f f i c i e n t s (k), Willey and Rao's Competition Ratio (CR) and McGilchrist's Aggressivity (A) were calculated from binary replacement series data. Both k- and CR- values contain components which relate to i n t r a - and i n t e r - s p e c i f i c competition. The actual r e l a t i v e contributions of i n t r a s p e c i f i c and i n t e r s p e c i f i c competition were calculated by comparing the ef f e c t on a given species of adding equal densities of i t s own kind or of a second species, to the same t o t a l density; the r a t i o of the former to the l a t t e r i s a new parameter, termed the Interference Ratio (IR), and i s related to the r e l a t i v e crowding c o e f f i c i e n t . Intercomparisons of the various measures of competitiveness showed that i n both years k-values were - i v -highly correlated with A and CR, and i n 1980 were also corre - ~ i lated with CI. However, there was only a weak co r r e l a t i o n between k and IR. In general, CR-, k- and A-values suggested that barnyardgrass and rapeseed were the most competitive species. However, IR-values indicated that the greatest competitiveness was exhibited by pigweed against f o x t a i l . Pigweed was much more sensitive to i t s own kind than to f o x t a i l . Estimates of k-values for untested combinations based upon either the use of de Wit's spacing formula or upon k-values determined for binary mixtures involving each of the untested pair with a common t h i r d species were found to be unreliable. In several mixtures, k was found to be density dependent. In ternary mixtures, the e f f e c t s on the y i e l d of a given species could not be predicted from i t s behaviour i n the presence of either of i t s competitors i n binary combinations. For example, pigweed and f o x t a i l behaved s y n e r g i s t i c a l l y against high density rapeseed, but tended to act antagonis-t i c a l l y at low rapeseed densities. Although f o x t a i l was consistently the weakest competitor i n any binary mixture, i t had the greatest e f f e c t of any species i n determining the competitive in t e r a c t i o n between the other species. In order to estimate y i e l d losses, e.g. i n crop-weed systems, only additive series data are shown to be of general a p p l i c a b i l i t y . - V TABLE OF CONTENTS A b s t r a c t i i T a b l e o f C o n t e n t s v L i s t o f T a b l e s x L i s t o f F i g u r e s xv:_ L i s t o f Appendices x v i ' i Acknowledgements x i x 1. INTRODUCTION 1 2. LITERATURE REVIEW 6 2.1 B i o l o g y o f the S p e c i e s 6 2.1.1 Green f o x t a i l ( S e t a r i a v i r i d i s L.) Beauv 7 2.1.2 B a r n y a r d g r a s s ( E c h i n n o c h l o a c r u s g a l l i L. Beauv. ) 8 2.1.3 Redroot pigweed (Amaranthus r e t r o f l e x u s L.)..10 2.1.4 Rapeseed 12 2.2 T e r m i n o l o g i e s and the meaning o f c o m p e t i t i o n . . . 1 5 2.3 C o m p e t i t i v e and n o n - c o m p e t i t i v e i n t e r a c t i o n s . . . 20 2.3.1 C o m p e t i t i v e i n t e r a c t i o n s ( i n t e r f e r e n c e ) among s p e c i e s m i x t u r e s 20 2.3.1.1 C o m p e t i t i o n ( E x p l o i t a t i o n ) 22 2.3.1.1.1 C o m p e t i t i o n f o r l i g h t 24 2.3.1.1.2 C o m p e t i t i o n f o r m i n e r a l n u t r i e n t s 27 2.3.1.1.3 C o m p e t i t i o n f o r water 30 2.3.1.4 B i o c h e m i c a l i n t e r a c t i o n s ( A l l e l o p a t h y ) 33 2.3.2 N o n - c o m p e t i t i v e i n t e r a c t i o n ( c o o p e r a t i o n ) among s p e c i e s m i x t u r e 36 2.4 M e t h o d o l o g i e s i n c o m p e t i t i o n s t u d i e s 37 2.4.1 I n v e s t i g a t i o n s i n v o l v i n g d u r a t i o n o f com-p e t i t i o n and d e n s i t i e s o f c o m p e t i t o r s i n a d d i t i v e s e r i e s 37 2.4.2 I n v e s t i g a t i o n i n v o l v i n g r e p l a c e m e n t s e r i e s . . . 4 0 - v i ; -2.5 C o m p e t i t i o n i n d i c e s 55 2.6 R e l a t i o n s between performance i n p u r e / s t a n d s and i n m i x t u r e s 61 2.7 P r e d i c t i o n s o f y i e l d s and y i e l d l o s s e s due t o c o m p e t i t i o n 6 5 MATERIALS AND METHODS 68 3.1 G e n e r a l 68 3.2 P l a n t m a t e r i a l s 69 3.3 P l o t s and p l a n t i n g 69 3.4 H a r v e s t i n g 70 3.5 E x p e r i m e n t a l d e s i g n s and t r e a t m e n t s 70 3.6 Approaches t o a n a l y s i s o f d a t a ....74 3.6.1 I n t r a s p e c i f i c i n t e r a c t i o n s 74 3.6.2 I n t e r s p e c i f i c i n t e r a c t i o n s 74 3.6.2.1 B i n a r y a d d i t i v e s e r i e s m i x t u r e s 74 3.6.2.2 B i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s 76 3.6.2.3 T e r n a r y r e p l a c e m e n t s e r i e s 78 3.6.3 S t a t i s t i c a l a n a l y s i s and cu r v e f i t t i n g 82 RESULTS AND DISCUSSION 83 4.1 Y i e l d - d e n s i t y r e l a t i o n s h i p s o f b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rapeseed 83 4.2 Y i e l d s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 89 4.2.1 Y i e l d s o f b a r n y a r d g r a s s and r e d r o o t pigweed i n a d d i t i v e s e r i e s m i x t u r e s 90 4.2.1.1 B a r n y a r d g r a s s as i n d i c a t o r s p e c i e s 90 4.2.1.2 Redroot pigweed as i n d i c a t o r s p e c i e s 95 - v i i : . -4.2.2 Y i e l d s o f b a r n y a r d g r a s s and green f o x t a i l i n a d d i t i v e s e r i e s m i x t u r e s 98 4.2.2.1 B a r n y a r d g r a s s as i n d i c a t o r s p e c i e s 98 4.2.2.2 Green f o x t a i l as i n d i c a t o r s p e c i e s 103 4.2.3 Y i e l d s o f r e d r o o t pigweed and green f o x t a i l i n a d d i t i v e s e r i e s m i x t u r e s 103 4.2.3.1 Redroot pigweed as i n d i c a t o r s p e c i e s 103 4.2.3.2 Green f o x t a i l as i n d i c a t o r s p e c i e s 109 4.2.4 C o m p e t i t i o n among b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l r e v e a l e d by a d d i t i v e s e r i e s e x p e r i m e n t s 110 4.2.5 P r e d i c t i o n s o f y i e l d , and y i e l d l o s s e s among b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l based upon a d d i t i v e s e r i e s e x p e r i m e n t s 114 4.3 Y i e l d s o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n b i n a r y a d d i t i v e s e r i e s e x p e r i -ments 117 4.3.1 Y i e l d s o f rapeseed and r e d r o o t pigweed i n a d d i t i v e s e r i e s m i x t u r e s 118 4.3.1.1 Rapeseed as i n d i c a t o r s p e c i e s 118 4.3.1.2 Redroot pigweed as i n d i c a t o r s p e c i e s 121 4.3.2 Y i e l d s o f rapeseed and green f o x t a i l i n a d d i t i v e s e r i e s m i x t u r e s 123 4.3.2.1 Rapeseed as i n d i c a t o r s p e c i e s 123 4.3.2.2 Green f o x t a i l as i n d i c a t o r s p e c i e s 126 4.3.3 Y i e l d s o f a d d i t i v e r e d r o o t pigweed and green f o x t a i l m i x t u r e s 127 4.3.3.1 Redroot pigwed as i n d i c a t o r s p e c i e s 127 4.3.3.2 Green f o x t a i l as i n d i c a t o r s p e c i e s 127 4.3.4 C o m p e t i t i o n among r a p e s e e d , r e d r o o t pigweed and green f o x t a i l r e v e a l e d by a d d i t i v e s e r i e s e x p e r i m e n t s 128 - v i i i -4.3.5 P r e d i c t i o n s o f y i e l d s and y i e l d l o s s e s among r a p e s e e d , r e d r o o t pigweed and green f o x t a i l based upon a d d i t i v e s e r i e s e x p e r i m e n t s 131 4.4 Y i e l d s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n b i n a r y r e p l a c e m e n t s e r i e s e x p e r i m e n t 133 4.4.1 Y i e l d s o f b a r n y a r d g r a s s and r e d r o o t pigweed m i x t u r e s 135 4.4.2 Y i e l d s o f b a r n y a r d g r a s s and green f o x t a i l m i x t u r e s 143 4.4.3 Y i e l d s o f r e d r o o t pigweed and green f o x t a i l m i x t u r e s 151 4.4.4 C o m p e t i t i o n among b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l based upon re p l a c e m e n t s e r i e s e x p e r i m e n t s 158 4.4.5 P r e d i c t i o n s o f y i e l d s and y i e l d l o s s e s i n b i n a r y r e p l a c e m e n t s e r i e s among b a r n y a r d -g r a s s , r e d r o o t pigweed and green f o x t a i l based upon r e p l a c e m e n t s e r i e s 167 4.5 Y i e l d s o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n b i n a r y r e p l a c e m e n t s e r i e s e x p e r i m e n t s 170 4.5.1 Y i e l d s o f b i n a r y r apeseed and r e d r o o t pigweed m i x t u r e s 173 4.5.2 Y i e l d s o f b i n a r y rapeseed and green f o x t a i l m i x t u r e s 179 4.5.3 Y i e l d s o f b i n a r y r e d r o o t pigweed and green f o x t a i l m i x t u r e s 184 4.5.4 C o m p e t i t i o n among r a p e s e e d , r e d r o o t pigweed and green f o x t a i l based upon replacement s e r i e s e x p e r i m e n t s . 188 - i-x -4.5.5 P r e d i c t i o n s o f y i e l d s and y i e l d l o s s e s i n b i n a r y r e p l a c e m e n t s e r i e s among rapeseed r e d r o o t pigweed and green f o x t a i l based upon r e p l a c e m e n t s e r i e s e x p e r i m e n t s 193 4.6 I n t e r a c t i o n s o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n t e r n a r y r e p l a c e m e n t s e r i e s m i x t u r e s 195 4.6.1 B i n a r y r e p l a c e m e n t s e r i e s a t d i f f e r e n t l e v e l s o f t h i r d s e r i e s 197 4.6.2 P s e u d o - b i n a r y r e p l a c e m e n t s e r i e s between one s p e c i e s and c o n s t a n t p r o p o r t i o n s o f two o t h e r s p e c i e s 205 4.6.3 P r e d i c t e d r e l a t i v e crowding c o e f f i c e n t s o f b i n a r y m i x t u r e s 215 5. GENERAL DISCUSSION .221 5.1 Y i e l d d e n s i t y r e l a t i o n s h i p s i n monoculture and t h e i r use i n t h e p r e d i c t i o n s o f y i e l d s i n m i x t u r e s c u l t u r e 221 5.2 E s t i m a t i o n o f y i e l d s and performance i n mixed c u l t u r e 224 5.3 E s t i m a t i o n o f y i e l d s and performance i n a d d i t i v e s e r i e s e x p e r i m e n t s 226 5.4 Measurements o f c o m p e t i t i o n s 232 5.5 I n f l u e n c e o f a t h i r d s p e c i e s on b e h a v i o u r o f b i n a r y m i x t u r e s i n replacement s e r i e s 237 6. SUMMARY AND CONCLUSIONS 2 45 LITERATURE CITED 25 2 APPENDICES 267 - X -LIST OF TABLES 3.1 D e t a i l s o f s p e c i e s c o m b i n a t i o n s (Exp.A,and A 2 ) 72 3.2 D e t a i l s o f s p e c i e s c o m b i n a t i o n s (Exp.A3) 73 4.1 Y i e l d s (g/m^) o f b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rapeseed i n m o n o c u l t u r e s 84 4.2 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f r e d r o o t pigweed i n the p resence o f b a r n y a r d g r a s s as i n d i c a t o r s p e c i e s 94 4.3 E s t i m a t e d y i e l d per p l a n t (Bft) o f b a r n y a r d g r a s s i n the presence o f r e d r o o t pigweed as i n d i c a t o r s p e c i e s 98 4.4 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f green f o x t a i l i n the presence o f b a r n y a r d g r a s s as i n d i c a t o r s p e c i e s 10 2 4.5 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f b a r n y a r d g r a s s i n the p resence o f green f o x t a i l as i n d i c a t o r s p e c i e s 106 4.6 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f green f o x t a i l i n the p resence o f r e d r o o t pigweed as i n d i c a t o r s p e c i e c 109 4.7 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f r e d r o o t pigweed i n the p resence o f green f o x t a i l as i n d i c a t o r s p e c i e s 110 4.8 R e g r e s s i o n c o e f f i c i e n t s , c o r r e l a t i o n v a l u e s and i n d i c e s o f c o m p e t i t i o n f o r b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n the absence o f monoculture d a t a '. 112 4.9 R e g r e s s i o n c o e f f i c i e n t s , c o r r e l a t i o n v a l u e s and i n d i c e s o f c o m p e t i t i o n f o r b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n t h e presence o f monoculture d a t a 113 4.10 C o r r e l a t i o n and r e g r e s s i o n c o e f f i c i e n t s between obser v e d and e s t i m a t e d y i e l d s o f competing s p e c i e s i n a d d i t i v e s e r i e s e x p e r i m e n t s i n v o l v i n g b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l . . . . 115 4.11 A c t u a l and e s t i m a t e d l o s s o f y i e l d o f b a r n y a r d -g r a s s , r e d r o o t pigweed and green f o x t a i l as i n d i c a t o r s p e c i e s 116 - x i 4.12 E s t i m a t e d y i e l d p e r p l a n t (BO) o f r e d r o o t pigweed i n the presence o f rapeseed as i n d i c a t o r s p e c i e s . . . . 1 2 1 4.13 E s t i m a t e d y i e l d p e r p l a n t (Bft) o f rapeseed i n t h e presence o f r e d r o o t pigweed as i n d i c a t o r s p e c i e s . . . . 122 4.14 E s t i m a t e d y i e l d per p l a n t (Bfi) o f green f o x t a i l i n t he presence o f rapeseed as i n d i c a t o r s p e c i e s . . . . 126 4.15 E s t i m a t e d y i e l d p e r p l a n t (Bfi) o f rapeseed i n the presence o f green f o x t a i l as i n d i c a t o r s p e c i e s 127 4.16 R e g r e s s i o n c o e f f i c i e n t s , c o r r e l a t i o n v a l u e s and i n d i c e s o f c o m p e t i t i o n f o r r a p e s e e d , r e d r o o t pigweed and green f o x t a i l w i t h o u t monoculture d a t a 1 29 4.17 R e g r e s s i o n c o e f f i c i e n t s , c o r r e l a t i o n v a l u e s and i n d i c e s o f c o m p e t i t i o n f o r r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n t h e presence o f the monoculture d a t a 130 4.18 C o r r e l a t i o n and r e g r e s s i o n c o e f f i c i e n t s between obser v e d and e s t i m a t e d y i e l d s o f competing s p e c i e s i n a d d i t i v e s e r i e s e x p e r i m e n t s i n v o l v i n g r a p e s e e d , r e d r o o t pigweed and gr e e n f o x t a i l 132 4.19 A c t u a l and e s t i m a t e d y i e l d l o s s e s o f ra p e s e e d , r e d r o o t pigweed and green f o x t a i l as i n d i c a t o r s p e c i e s 134 4.20 Mean y i e l d s (g/m 2) o f b a r n y a r d g r a s s and r e d r o o t pigweed i n b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s and t h e i r m i x t u r e y i e l d s i n c l u d i n g r e l a t i v e y i e l d t o t a l s 136 4.21 R e l a t i v e performance o f b a r n y a r d g r a s s and r e d r o o t pigweed e x p r e s s e d as r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o i t s monoculture y i e l d a t comparable d e n s i t i e s 136 4.22 Mean y i e l d s (g/m 2) o f b a r n y a r d g r a s s and green f o x t a i l i n b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s and t h e i r t o t a l m i x t u r e y i e l d s i n c l u d i n g r e l a t i v e y i e l d t o t a l s 144 4.23 R e l a t i v e performance o f b a r n y a r d g r a s s and green f o x t a i l e x p r e s s e d as r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o i t s monoculture, y i e l d a t comparable d e n s i t i e s 146 - x i i -'4 4.24 Mean y i e l d s (g/m 2) o f r e d r o o t pigweed and green f o x t a i l i n b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s and t h e i r t o t a l m i x t u r e y i e l d s i n c l u d i n g r e l a t i v e y i e l d t o t a l s 1 52 4.2 5 R e l a t i v e performance o f r e d r o o t pigweed and green f o x t a i l e x p r e s s e d as r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o i t s y i e l d m o noculture a t comparable d e n s i t i e s 154 4.26 R e l a t i v e crowding c o e f f i c i e n t s f o r b i n a r y com-b i n a t i o n s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l 161 4.27 A g g r e s s i v i t y , C o m p e t i t i o n R a t i o s , I n t e r f e r e n c e R a t i o s and R e l a t i v e crowding c o e f f i c i e n t s among b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l . . . . 165 4.28 Observed and e s t i m a t e d y i e l d s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n b i n a r y r eplacement s e r i e s m i x t u r e s 168 4.29 A c t u a l and e s t i m a t e d r e l a t i v e l o s s e s i n y i e l d i n b i n a r y replacement s e r i e s i n v o l v i n g b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l 169 4.30 Mean y i e l d s (g/m 2) o f r a p e s e e d , r e d r o o t pigweed i n b i n a r y replacement s e r i e s m i x t u r e s and t h e i r t o t a l m i x t u r e y i e l d s i n c l u d i n g r e l a t i v e y i e l d t o t a l s 171 4.3 1 R e l a t i v e performance o f rapeseed and r e d r o o t pigweed e x p r e s s e d as the r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o monoculture y i e l d a t comparable d e n s i t i e s 174 4.32 Mean y i e l d s (g/m 2) o f rapeseed and green f o x t a i l i n b i n a r y replacement s e r i e s m i x t u r e s and t h e i r t o t a l m i x t u r e y i e l d s i n c l u d i n g r e l a t i v e y i e l d t o t a l s 1 80 4.33 R e l a t i v e performance o f rapeseed and green f o x t a i l e x p r e s s e d as the r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o monoculture y i e l d a t comparable d e n s i t i e s 183 4.34 R e l a t i v e crowding c o e f f i c i e n t s f o r b i n a r y com-b i n a t i o n s o f ra p e s e e d , r e d r o o t pigweed and green f o x t a i l 189 - x i i i -4.35 A g g r e s s i v i t y , C o m p e t i t i o n R a t i o s , I n f e r e n c e R a t i o s and R e l a t i v e crowding c o e f f i c i e n t s among ra p e s e e d , r e d r o o t pigweed and green f o x t a i l 193 4.36 Observed and e s t i m a t e d y i e l d s o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n b i n a r y replacement s e r i e s m i x t u r e s 194 4.37 A c t u a l and e s t i m a t e d r e l a t i v e y i e l d l o s s e s i n b i n a r y replacement s e r i e s i n v o l v i n g r a p e s e e d , r e d r o o t pigweed and green f o x t a i l 196 4.38 Mean r e l a t i v e c rowding c o e f f i c i e n t s o f b i n a r y m i x t u r e s and t h e i r p r o d u c t s among rapeseed and green f o x t a i l a t d i f f e r e n t d e n s i t i e s o f t h e t h i r d s p e c i e s 198 4.39 Mean r e l a t i v e c rowding c o e f f i c i e n t s o f pseudo b i n a r y replacement s e r i e s m i x t u r e s among rapeseed r e d r o o t pigweed and green f o x t a i l a t d i f f e r e n t r a t i o s o f the s p e c i e s c o n s t i t u t i n g combined p a i r s 210 4.40 R e l a t i v e c rowding c o e f f i c i e n t s f o r rap e s e e d , r e d r o o t pigweed and green f o x t a i l i n pseudo-b i n a r y replacement s e r i e s . . . 212 4.4 1 C a l c u l a t e d r e l a t i v e c r o w d i n g c o e f f i c i e n t s f o r ra p e s e e d , r e d r o o t pigweed and green f o x t a i l i n p s e u d o - b i n a r y replacement s e r i e s 214 4.42 Computation o f k - v a l u e s f o r b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rapeseed f o r u n t e s t e d b i n a r y c o m b i n a t i o n s based upon t h e i r performance i n b i n a r y m i x t u r e s w i t h a t h i r d s p e c i e s 2 17 4.4 3 Computation o f k - v a l u e s f o r b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rapeseed based upon the s p a c i n g f o r m u l a 2 19 4.44 V a l u e s f o r k f o r b a r n y a r d g r a s s and rapeseed d e r i v e d from u n t e s t e d c o m b i n a t i o n s i n b i n a r y m i x t u r e s w i t h a t h r i d common s p e c i e s and from the s p a c i n g f o r m u l a 220 5.1 C o r r e l a t i o n c o e f f i c i e n t f o r the v a r i o u s measures o f c o m p e t i t i v e n e s s 234 - xiv -5.2 D i f f e r e n c e s between o b s e r v e d and e x p e c t e d y i e l d s (g/m2) o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l a t c o n s t a n t r e l a t i v e d e n s i t i e s f o r the presence o f b i n a r y replacement s e r i e s o f any p a i r o f s p e c i e s i n t e r n a r y m i x t u r e s . Expected y i e l d s are t h o s e p r o r a t e d from the i n d i v i d u a l y i e l d s i n b i n a r y m i x t u r e , assuming no i n t e r -a c t i o n between the s p e c i e s c o n s t i t u t i n g a p a i r 241 - --- X V -LIST OF FIGURES F i g . 2 .1 Scheme o f t e r m i n o l o g y r e l a t e d t o p l a n t s p e c i e s i n t e r a c t i o n s 19 F i g . 2.2 Replacement s e r i e s d i a g r a m o f s p e c i e s a and s p e c i e s b grown i n monoculture and i n m i x t u r e s a t c o n s t a n t t o t a l d e n s i t y 43 F i g . 2 .3 Replacement s e r i e s diagram based upon r e l a t i v e y i e l d s 48 F i g . 2.4 R a t i o diagrams f o r v a r i o u s b i n a r y replacement s e r i e s 50 F i g . 3.1 B i n a r y components o f t e r n a r y r e p l a c e m e n t s e r i e s a t d i f f e r e n t l e v e l s o f s p e c i e s a 80 F i g . 3 .2 Pseudo-replacement s e r i e s c o m b i n a t i o n s 81 F i g . 4.1 The y i e l d - d e n s i t y r e l a t i o n s h i p i n a s p a c i n g e x p e r i m e n t i n the b a r n y a r d g r a s s i n 1981 85 F i g . 4 .2 Mean y i e l d s (g/m 2)of b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rapeseed i n mono-c u l t u r e s 8 7 F i g . 4 .3 Mean y i e l d s (g/m 2) o f r e d r o o t pigweed i n mono-c u l t u r e and i n t h e p r e s e n c e o f t h r e e d e n s i t i e s o f b a r n y a r d g r a s s and o f b a r n y a r d g r a s s a t t h e s e d e n s i t i e s 92 F i g . 4 .4 Mean y i e l d s (g/m 2) o f b a r n y a r d g r a s s i n mono-c u l t u r e and i n the presence o f t h r e e d e n s i t i e s o f r e d r o o t pigweed and o f r e d r o o t pigweed a t thes e d e n s i t i e s 97 F i g . 4 .5 Mean y i e l d s (g/m 2) o f green f o x t a i l i n mono-c u l t u r e and i n the pr e s e n c e o f t h r e e d e n s i t i e s o f b a r n y a r d g r a s s and o f b a r n y a r d g r a s s a t t h e s e d e n s i t i e s 100 ^ F i g . 4 .6 Mean y i e l d s (g/m 2) o f b a r n y a r d g r a s s i n mono-c u l t u r e and i n the pr e s e n c e o f t h r e e d e n s i t i e s o f green f o x t a i l and o f green f o x t a i l a t the s e d e n s i t i e s 105 F i g . 4 . 7 a Mean y i e l d s (g/m 2) o f green f o x t a i l i n mono-c u l t u r e and i n t h e pr e s e n c e o f t h r e e d e n s i t i e s o f r e d r o o t pigweed and o f r e d r o o t pigweed a t th e s e d e n s i t i e s 108 - x v i -F i g . 4.7b Mean y i e l d s (g/m 2) o f r e d r o o t pigweed i n mono-c u l t u r e and i n the pr e s e n c e o f t h r e e d e n s i t i e s o f green f o x t a i l and o f green f o x t a i l a t t h e s e d e n s i t i e s 108 Fig.. 4.8a Mean y i e l d s (g/m 2) o f r e d r o o t pigweed i n mono-c u l t u r e and i n the pr e s e n c e o f t h r e e d e n s i t i e s o f rapeseed and o f rapeseed a t t h e s e d e n s i t i e s . 1 2 0 F i g . 4.8b Mean y i e l d s (g/m 2) o f rapeseed i n monoculture and i n the pr e s e n c e o f t h r e e d e n s i t i e s o f r e d r o o t pigweed and o f r e d r o o t pigweed a t thes e d e n s i t i e s 120 F i g . 4.9a Mean y i e l d s (g/m 2)of green f o x t a i l i n mono-c u l t u r e and i n t h e pr e s e n c e o f t h r e e d e n s i t i e s o f rapeseed and o f rapeseed a t the s e d e n s i t i e s . 1 2 5 F i g . 4.9b Mean y i e l d s (g/m 2) o f rapeseed i n monoculture and i n t h e pr e s e n c e o f t h r e e d e n s i t i e s o f green f o x t a i l and o f green f o x t a i l a t the s e d e n s i t i e s 125 F i g . 4.10 Replacement s e r i e s diagrams f o r b a r n y a r d g r a s s and r e d r o o t pigweed based upon r e l a t i v e y i e l d s . 1 4 1 F i g . 4.11 R a t i o diagrams f o r b a r n y a r d g r a s s and r e d r o o t pigweed a t 1 440 p l a n t s / m 2 t o t a l d e n s i t y 142 F i g . 4.12 Replacement s e r i e s diagrams f o r b a r n y a r d g r a s s and green f o x t a i l based upon r e l a t i v e y i e l d s . . . 1 4 8 F i g . 4.13 R a t i o diagrams f o r b a r n y a r d g r a s s and green f o x t a i l a t 1 440 p l a n t s / m 2 t o t a l d e n s i t y 150 F i g . 4.14 Replacement s e r i e s diagrams f o r r e d r o o t pigweed and green f o x t a i l based upon r e l a t i v e y i e l d s 157 F i g . 4.15 R a t i o diagrams f o r r e d r o o t pigweed and green f o x t a i l a t 1440 p l a n t s / m 2 t o t a l d e n s i t y 159 F i g . 4.16 Replacement s e r i e s diagrams f o r rapeseed and r e d r o o t pigweed based upon r e l a t i v e y i e l d s 176 F i g . 4.17 R a t i o diagrams f o r rapeseed and r e d r o o t pigweed a t 1440 " R P S - u n i t s " p e r square metre...178 F i g . 4.18 Replacement s e r i e s diagrams f o r rapeseed and green f o x t a i l based upon r e l a t i v e y i e l d s 186 - x v i i F i g . 4.19 R a t i o diagrams f o r rapeseed and green f o x t a i l a t 1440 " R P S - u n i t s " p e r square metre 187 F i g . 4.20 Replacement s e r i e s diagrams f o r b i n a r y com-b i n a t i o n s o f two s p e c i e s a t c o n s t a n t d e n s i t y o f the t h i r d s p e c i e s based upon r e l a t i v e y i e l d s . 1980 d a t a 201 F i g . 4.21 Replacement s e r i e s diagrams f o r b i n a r y com-b i n a t i o n s o f two s p e c i e s a t c o n s t a n t d e n s i t y o f the t h i r d s p e c i e s based upon r e l a t i v e y i e l d s 1981 d a t a 203 F i g . 4.22 Replacement s e r i e s diagrams f o r pseudo-b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s o f r a p e -seed, r e d r o o t pigweed and green f o x t a i l . 1980 d a t a 207 F i g . 4.23 Replacement s e r i e s diagrams f o r pseudo-b i n a r y r eplacement s e r i e s m i x t u r e s o f r a p e -seed, r e d r o o t pigweed and green f o x t a i l . 1981 d a t a 209 - x v i i i -L I S T O F A P P E N D I C E S 1. Monthly mean t e m p e r a t u r e s and p r e c i p i t a t i o n a t South Campus f i e l d s , U n i v e r s i t y o f B r i t i s h C olumbia ( 1 979-1981 ) 269 2. Y i e l d s (g/m 2) o f b a r n y a r d g r a s s as i n d i c a t o r and of r e d r o o t pigweed i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 270 3. Y i e l d s (g/m 2) o f r e d r o o t pigweed as i n d i c a t o r and of b a r n y a r d g r a s s i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 271 4. Y i e l d s (g/m 2) o f b a r n y a r d g r a s s as i n d i c a t o r and of green f o x t a i l i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 272 5. Y i e l d s (g/m 2) o f green f o x t a i l as i n d i c a t o r and of b a r n y a r d g r a s s i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 273 6. Y i e l d s (g/m 2) o f r e d r o o t pigweed as i n d i c a t o r and of green f o x t a i l i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 274 7. Y i e l d s (g/m 2) o f green f o x t a i l as i n d i c a t o r and o f green f o x t a i l n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 275 8. Y i e l d s (g/m 2) o f rapeseed as i n d i c a t o r and o f r e d -r o o t pigweed i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 276 9. Y i e l d s (g/m 2) o f r e d r o o t pigweed as i n d i c a t o r and of rapeseed i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s 277 10. Y i e l d s (g/m 2) o f rapeseed as i n d i c a t o r and o f green f o x t a i l i n b i n a r y a d d i t i v e s e r i e s m i x t u r e s . . . . 278 11. Y i e l d s (g/m 2) o f green f o x t a i l as i n d i c a t o r and of rapeseed i n a d d i t i v e s e r i e s m i x t u r e s 279 12. Y i e l d s (g/m 2) o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n b i n a r y r e p l a c e m e n t s e r i e s 280 13. Y i e l d s (g/m 2) o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n t e r n a r y r e p l a c e m e n t s e r i e s m i x t u r e s 281 14. L i s t o f Symbols 280 15. L i s t o f E q u a t i o n s 281 - xix -ACKNOWLEDGEMENTS I am most d e e p l y g r a t e f u l t o my s u p e r v i o s r Dr. V i c t o r C. Rune c k l e s f o r h i s w i l l i n g n e s s t o o f f e r h i s i n v a l u a b l e time t o s u p e r v i s e the c o m p l e t i o n o f t h i s r e s e a r c h a f t e r the d e p a r t u r e o f Dr. B a r r y G. Todd from the U n i v e r s i t y o f B r i t i s h Columbia f o r a new p o s i t i o n w i t h t h e Man i t o b a M i n i s t r y o f A g r i c u l t u r e . T h i s t h e s i s owes a g r e a t debt t o h i s en t h u s i a s m , u n d e r s t a n d i n g , p a t i e n c e and courage. I w i s h t o acknowledge the guid a n c e and h e l p o f my former s u p e r v i s o r Dr. B a r r y G. Todd d u r i n g the e a r l y s t a g e s o f t h i s r e s e a r c h . H i s f r i e n d s h i p d u r i n g t h e s e i n v e s t i g a t i o n s i s g r e a t l y a p p r e c i a t e d . I a l s o w i s h t o acknowledge s u g g e s t i o n s d i c u s s i o n s , and h e l p o f my committee members: Dr. P.A. J o l l i f f e and Dr. M.D. P i t t , i n making d e c i s i o n s when I found m y s e l f t i e d up i n some s c i e n t i f i c k n o t ; Dr. G.W. Eaton f o r some s t i m u l a t i n g d i s c u s s i o n s about s t a t i s t i c s , and Dr. R.A. T u r k i n g t o n , Dr. M.Y. S i d d i q i and Dr. K. Yamanaka f o r t h e i r i n t e r e s t i n my r e s e a r c h . I acknowledge the t e c h n i c a l h e l p o f D. P e a r c e , P. G a r n e t t , A. Her a t h and B. M c M i l l a n ; S. T r i t t e r f o r a s s i s t i n g i n t he l o n g h a r v e s t s r e q u i r e d t o c a r r y o u t the e x p e r i m e n t s . - X X -I g r a t e f u l l y acknowledge the s c h o l a r s h i p g r a n t e d t o me by the I n t e r n a t i o n a l Development Research C e n t r e , Ottawa t h r o u g h the I n t e r c r o p p i n g P r o j e c t , T a n z a n i a . The generous s t u d y l e a v e g r a n t e d t o me by t h e Department o f Crop S c i e n c e , U n i v e r s i t y o f Dar es Salaam, T a n z a n i a which e n a b l e d me t o do t h e s e s t u d i e s and I am g r a t e f u l . I am g r a t e f u l t o Mrs. C. van den D r i e s e n f o r her e x t r a o r d i n a r y s k i l l s and i n t e r e s t i n t y p i n g t h i s m a n u s c r i p t . L a s t but not the l e a s t , I w i s h t o thank my f a m i l y . The s u p p o r t and f o r e b e a r a n c e o f my w i f e , E m i l y and our c h i l d r e n , MacFadyen, V i o l e t , A d a j u s t i n e and J e n n i f e r , who s h o u l d e r e d the g r e a t burden o f my l o n g hours away from home w i t h g r e a t courage and p a t i e n c e ; i n many r e s p e c t s t h i s t h e s i s i s as much t h e i r s as i t i s mine. To my p a r e n t s , Ndeonasia and H o i s i a e l i , I owe an unpayable d e b t . - 1 -1. INTRODUCTION I t i s w e l l known t h a t , i n an assemblage of s p e c i e s , each has the p o t e n t i a l f o r growth, but s i n c e t h e s p e c i e s d i f f e r i n b i o l o g i c a l c h a r a c t e r i s t i c s and demand the same q u a l i t a t i v e c o n s t i t u e n t s from th e h a b i t a t , no one s p e c i e s i s s u p e r i o r t o t h e o t h e r s i n e x p l o i t i n g the r e s o u r c e s so e f f e c t i v e l y t h a t i t g a i n s e x c l u s i v e monopoly o f t h e h a b i t a t (Grubb, 1977; Harper e t a_l. , 1961). I n such s i t u a t i o n s the s p e c i e s r e a c t t o each o t h e r i n r e l a t i o n t o t h e i r r e l a t i v e p r o x i m i t y (and hence t o t h e i r r e l a t i v e d e n s i t i e s ) and the e x t e n t t o w h i c h t h e y d i f f e r i n t h e i r b i o l o g y (Harper, 1977). The outcome of t h e r e a c t i o n s o f p l a n t s p e c i e s t o each o t h e r had a l o n g h i s t o r y ( K i n g , 1966) and the d e c l i n e i n performance due t o d i s p r o p o r t i o n a t e a c q u i s i t i o n o f growth r e q u i s i t e s ( c o m p e t i t i o n ) i s perhaps th e b e s t known and most i m p o r t a n t f e a t u r e o f such r e a c t i o n s (Clements e t a l . , 1929; D onald, 1963; de W i t , 1960). The i n c r e a s e d p r o x i m i t y o f i n d i v i d u a l components i n a m i x t u r e i s t h e major f a c t o r t h a t may l e a d t o r educed growth o f components i n a m i x t u r e and hence low d r y m a t t e r p r o d u c t i o n . However, t h e r e i s i n c r e a s i n g e v i d e n c e t h a t component s p e c i e s i n c e r t a i n m i x t u r e s may e x h i b i t i n c r e a s e d growth over t h e i r pure s t a n d s (Trenbath, 1974; Andrews and Kassam, 1976; T r e n b a t h , 1976; T r e n b a t h and H a r p e r , 1973). The i n t e r a c t i v e p r o c e s s e s l e a d i n g t o a decline,.,dn'• - 2 -m i x t u r e y i e l d s have been s t u d i e d and r e v i e w e d e x t e n s i v e l y ( H i l l and Shimamoto, 1973; H a l l , 1974 and 1978; Donald, 1963; Bunce, e t a l . , 1977; Snaydon, 1979; R i c e , 1979; Mead, 1979). Two complementary t e c h n i q u e s have been used i n s t u d i e s on p l a n t i n t e r a c t i o n s , p a r t i c u l a r l y c o m p e t i t i v e i n t e r a c t i o n s . The f i r s t t e c h n i q u e i s based on one s p e c i e s , u s u a l l y r e f e r r e d t o as t h e i n d i c a t o r s p e c i e s (Welbank, 1963), b e i n g grown a t a c o n s t a n t d e n s i t y ( i n case o f a c r o p s p e c i e s , the recommended s e e d i n g r a t e ) . Mixed s t a n d s a r e produced by the a d d i t i o n o f v a r i o u s p r o p o r t i o n s o f a n o t h e r s p e c i e s t o s t a n d s o f t h e i n d i c a t o r . The t e c h n i q u e has been w i d e l y used i n crop-weed a s s o c i a t i o n s i n which the y i e l d o f t h e c r o p i n pure s t a n d i s compared t o i t s y i e l d i n t h e p r e s e n c e o f v a r i o u s weed i n f e s t a -t i o n s ( C h i s a k a , 1977). The most i m p o r t a n t c o n t r i b u t i o n o f t h i s t e c h n i q u e has been the concept o f " c o m p e t i t i o n i n d e x " w h i c h q u a n t i f i e s t h e c o m p e t i t i v e e f f e c t o f one s p e c i e s on a n o t h e r (Dew, 1972). The second t e c h n i q u e i s t h a t o f de Wit (1960). I n t h i s , b o t h pure s t a n d s and m i x t u r e s are sown a t the same o v e r a l l d e n s i t y ; m i x t u r e s are produced by v a r i o u s s u b s t i t u t i o n s o f a g i v e n p r o p o r t i o n o f p l a n t s i n t h e pure s t a n d by p l a n t s o f a n o t h e r s p e c i e s . The two t e c h n i q u e s have a c c o r d i n g l y been termed " a d d i t i v e " and "replacement" r e s p e c t i v e l y . The r e p l a c e m e n t s e r i e s approach a l l o w s the s t u d y o f e f f e c t s o f t h e r e l a t i v e d e n s i t y o f component s p e c i e s upon the i n t e r a c t i o n between them (Snaydon, 1979). T h i s approach has - 3 -been d e v e l o p e d p r i m a r i l y t h r o u g h s t u d i e s i n e s t a b l i s h e d p a s t u r e s ( H a l l , 1974; 1976; T r e n b a t h , 1974), v a r i o u s . s p e c i e s m i x t u r e s i n c r o p s (Mead and S t e r n , 1980; W i l l e y , 19 79) and r e l a t i v e l y l e s s so i n crop-weed a s s o c i a t i o n s ( M i n j a s , 1976; E l b e r s e and K r u y f , 1979; I v e n and Mlowe,1980). The most i m p o r t a n t c o n t r i b u t i o n s o f t h e rep l a c e m e n t s e r i e s a re the m a t h e m a t i c a l a n a l y s e s and t h e g r a p h i c a l d i s p l a y o f t h e d a t a ( H a l l , 1974a, de W i t , 1960), w h i c h a r e p u r p o r t e d t o r e f l e c t t h e r e l a t i v e c o m p e t i t i v e n e s s o f t h e component s p e c i e s and the p o s s i b l e mechanisms i n v o l v e d (de W i t , 1960; de Wit and van den Bergh, 1965; de Wit e t a l . , 1966; H a l l , 1974a and '! 1974b). I n c o n t r a s t , t h e a d d i t i v e s e r i e s f o c u s e s on c o m p e t i -t i v e e f f e c t s o f n e i g h b o u r i n g p l a n t s on the i n d i c a t o r s p e c i e s . I n b o t h t h e a d d i t i v e and rep l a c e m e n t s e r i e s t e c h n i -ques, c o m p e t i t i o n between component s p e c i e s i n b i n a r y m i x t u r e s i s dependent on t h e t o t a l m i x t u r e d e n s i t y ( H a l l , 1978, W i l l e y and Rao, 1980). However, i n f o r m a t i o n on t h e r e l a t i v e c o m p e t i t i v e n e s s o f t h e components i n t e r n a r y m i x t u r e s g e n e r a t e d by i n t r o d u c i n g a t h i r d s p e c i e s i n t o b i n a r y r e p l a c e m e n t s e r i e s i s s c a n t y . The few r e p o r t s on t e r n a r y m i x t u r e s ( H a i z e l , 1972; H a i z e l and Harper, 1973) i n d i c a t e t h a t t h e response o f s p e c i e s i n t e r n a r y m i x t u r e s cannot be p r e d i c t e d from t h e i r i n d i v i d u a l r e s p o n s e s i n b i n a r y m i x t u r e s . I t i s c l e a r t h a t i n a g r i c u l t u r a l s i t u a t i o n s , t h r e e t y p e s o f p l a n t i n t e r a c t i o n s may be o c c u r r i n g between c r o p and weed s p e c i e s c o n c u r r e n t l y : F i r s t , w i t h i n s p e c i e s i n t e r -- 4 -a c t i o n s i n monoculture have been shown t o e x h i b i t v a r i o u s y i e l d - d e n s i t y r e l a t i o n s h i p s ( H o l l i d a y , 1960a; W i l l e y and Heath, 1969). Second, between s p e c i e s i n t e r a c t i o n s may r e s u l t i n d e v i a t i o n s o f the y i e l d o f each s p e c i e s from t h a t i n monoculture ( A s p i n a l l , 1960; B l a c k , 1960; Mann and Barnes, 1950; H a l l , 1974a and b; T r e n b a t h , 1974). T h i r d , i n t e r a c t i o n s between d i f f e r e n t weed s p e c i e s may o c c u r (Trenbath and H a r p e r , 1973; H a i z e l and H a r p e r , 1973). The r e s u l t a n t e f f e c t s o f t h e s e i n t e r a c t i o n s i n d i v i d u a l l y and t h e i r p o s s i b l e i n t e r -r e l a t i o n s h i p s produce t h e anomalous y i e l d o f a g i v e n s p e c i e s i n a mixed s t a n d . I n t h e l i g h t o f the f o r e g o i n g , e x p e r i m e n t s were d e s i g n e d t o i n v e s t i g a t e the c o m p e t i t i v e i n t e r a c t i o n s o f r e d -r o o t pigweed ( A m a r a n t h u s , r e t r o f l e x u s L.) and green f o x t a i l ( S e t a r i a v i r i d i s (L) Beauv.) i n r e l a t i o n t o b a r n y a r d g r a s s ( E c h i n o c h l o a c r u s g a l l i (L.) Beauv.), and rapeseed ( B r a s s i c a  napus L.) i n b i n a r y m i x t u r e s based upon b o t h the a d d i t i v e and r e p l a c e m e n t s e r i e s . The r a p e s e e d experiment was m o d i f i e d t o i n c l u d e some t r e a t m e n t s c o n t a i n i n g t e r n a r y c o m b i n a t i o n s w i t h r e d r o o t pigweed, green f o x t a i l i n r e p l a c e m e n t s e r i e s . Y i e l d -d e n s i t y r e s p o n s e s were a l s o o b t a i n e d f o r each s p e c i e s i n m o n o c u l t u r e , i n o r d e r t o determine the v a l i d i t y o f t h e approach d e v e l o p e d by de Wit (1960) which i n c e r t a i n c i r c u m s t a n c e s may p e r m i t t h e b e h a v i o u r o f s p e c i e s i n b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s t o be p r e d i c t e d from t h e i r mono-c u l t u r a l c h a r a c t e r i s t i c s . Thus th e e x p e r i m e n t a l d e s i g n s used - 5 -constituted matrices of treatments incorporating monoculture/ density series, replacement series at f i v e levels of t o t a l density and additive series, with a view to comparing the d i f f e r e n t a n a l y t i c a l approaches, evaluating t h e i r i n d i v i d u a l merits, and developing additional a n a l y t i c a l approaches aimed at improving our understanding of plant competition. - 6 -2. LITERATURE REVIEW 2.1 B i o l o g y of the Species Knowledge of the b i o l o g y of i n d i v i d u a l p l a n t s i s of prime importance i n the study of p l a n t i n t e r a c t i o n s . P l a n t s r e q u i r e b a s i c a l l y the same resources from the environment on which they grow. Any p l a n t t h a t can s u r v i v e i n a mixture succeeds i n pre-empting the reso u r c e s r e q u i r e d by the other p l a n t s ; and y e t c o e x i s t e n c e among p l a n t s p e c i e s i n n a t u r a l and a g r i c u l t u r a l communities i s a common phenomenon (see f o r example, Harper e t a_l. , 1961) . The mechanisms by which p l a n t s c o e x i s t have been reviewed by Grubb (1977) and they i n c l u d e d i f f e r e n c e s i n l i f e forms (Turkington, 1975), p h e n o l o g i c a l s e p a r a t i o n (Bratton, 1976), f l u c t u a t i o n s i n the environment (Thomas and Dale, 1976), balanced mixtures ( M a r s h a l l and J a i n , 1969), and v a r i a t i o n i n co m p e t i t i v e a b i l i t y w i t h age (Watt, 1955). I d e a l l y , p l a n t a d a p t a t i o n s which permit co-e x i s t e n c e should be obtained from c l o s e l y r e l a t e d s p e c i e s l i v i n g i n the same h a b i t a t . Since t a x o n o m i c a l l y r e l a t e d p l a n t s are l e s s o f t e n found t o g e t h e r , i n f o r m a t i o n on the i n t e r a c t i o n of p a r t i c u l a r s e l e c t i v e f a c t o r s and p a r t i c u l a r p l a n t c h a r a c t e r i s t i c s has been d e r i v e d from t a x o n o m i c a l l y d i v e r s e p l a n t s of s i m i l a r ecology growing i n the same h a b i t a t (Harper, 1977) . - 7 -Much of our knowledge on the i n t e r a c t i o n s among p l a n t s has accrued from a d u l t p l a n t s (Grubb, 1977). Information on a d u l t - a d u l t p l a n t i n t e r a c t i o n s , e s p e c i a l l y i n r e l a t i o n to growth r a t e , s i z e and s t r u c t u r e of shoot and r o o t systems, together with t h a t on the r e c r u i t m e n t phase of the l i f e c y c l e (seed number, l o n g e v i t y , dormancy, germination and e s t a b l i s h -ment) i s e n l i g h t e n i n g and important. These c h a r a c t e r i s t i c s are d i s c u s s e d b r i e f l y i n r e l a t i o n to the b i o l o g y and ecology of green f o x t a i l , GFT, ( S e t a r i a . v i r i d i s (L.) Beav.), barnyard-g r a s s , BYG, ( E c h i n o c h l o a , c r u s g a l l i - (L.) Beav.), r e d r o o t pigweed, RPW, (Amaranthus r e t r o f l e x u s L.) and rape, RPS, (Bassica napus L . ) , the s p e c i e s used i n the present s t u d i e s . 2.1.1 Green F o x t a i l ( S e t a r i a v i r i d i s (L.) Beauv.) Green f o x t a i l (GFT) i s a member of the f a m i l y Poaceae. I t i s an annual which reproduces s o l e l y by seeds. Morphologi-c a l l y , GFT may develop one stem (culm) or may t i l l e r a t the base forming s e v e r a l culms which can grow over 0.9m i n h e i g h t . The leaves are glabrous and they develop a sharp p o i n t at the t i p . The r o o t system i s shallow and f i b r o u s . Green f o x t a i l i s of A s i a t i c o r i g i n ( S y l v e s t e r , 1970). I t was i n t r o d u c e d t o Canada from Europe and by 1948 the weed was widespread (Groh and Franktow, 1949; Alex e t a l . , 1972). I t grows i n a wide range of h a b i t a t s : crop lands ( i n a s s o c i a -t i o n w i t h c e r e a l s , o i l seeds, forages and other f i e l d c r o p s ) , summer f a l l o w s , wastelands, r o a d s i d e s and r a i l w a y r i g h t s of - 8 -way. I t i s a p r o l i f i c seed p r o d u c e r (Vanden B o r n , 1971); i t s seeds can remain v i a b l e i n t h e s o i l f o r up t o 13 y e a r s (Dawson and Bruns, 1975). Newly produced seeds a re dormant but t h e y r e a d i l y germinate i n t h e s p r i n g a t s o i l t e m p e r a t u r e s between 15°C and 35°C (Vanden B o r n , 1971). G e n e r a l l y , green f o x t a i l i s a weak c o m p e t i t o r (Rahman and A s h f o r d , 1972), but i n y e a r s when te m p e r a t u r e s a r e h i g h e r t h a n average a t the time o f p l a n t i n g , o r when s e e d i n g of t h e c r o p i s d e l a y e d , i t can become v e r y c o m p e t i t i v e and cause s e r i o u s c r o p l o s s e s ( B l a c k , 1968). B e i n g s h a l l o w r o o t e d , green f o x t a i l can i n t e r c e p t b r o a d c a s t f e r t i l i z e r b e f o r e i t reac h e s t h e c r o p r o o t zone and t h i s i n c r e a s e i t s c o m p e t i t i v e -n e s s . S i m i l a r l y , c o n t i n u o u s c r o p p i n g e n r i c h e s the s o i l seed bank o f green f o x t a i l and t h e r e s u l t i n g h i g h seed d e n s i t i e s i n c r e a s e i t s c o m p e t i t i v e n e s s . Looked a t i n t h i s way, green f o x t a i l i s a c t u a l l y an " o p p o r t u n i s t i c " weed wh i c h causes s u b s t a n t i a l y i e l d l o s s e s when i t o c c u r s i n h i g h d e n s i t i e s and when t h e c o n d i t i o n s a r e u n f a v o u r a b l e f o r p r o p e r e s t a b l i s h m e n t of t he c r o p (Makowski, 1980). 2.1.2 B a r n y a r d g r a s s ( E c h i n o c h l o a . ^ c r u s g a l l i (L.) Beauv.) . B a r n y a r d g r a s s (BYG) a l s o b e l o n g s t o t h e Poaceae. I t i s a summer a n n u a l t h a t r e p r o d u c e s o n l y by seeds. I t i s r o b u s t , o f t e n r o o t i n g and b r a n c h i n g a t the base, and grows up t o 1.5m t a l l . The l e a v e s a r e l i n e a r w i t h a broad base and t a p e r a t t h e t i p . C h a r a c t e r i s t i c a l l y BYG l a c k s a l i g u l e . - 9 -I t i s a n a t i v e o f Europe and I n d i a (Holm e t a l . , 1977) but i t i s now e s t a b l i s h e d i n most a r e a s o f t h e w o r l d (Brod, 1968). I t i s a p r o l i f i c seed p r o d u c e r ; i t s seeds v a r y i n dormancy among numerous e c o t y p e s ( A r a i and M i y a h a r a , 1962). V i a b i l i t y o f i t s seeds ranges from 7 y e a r s i n d r y s t o r a g e t o 3 y e a r s i n t h e s o i l (Holms e t a l . , 1977). The optimum temp e r a t u r e f o r the g e r m i n a t i o n o f b a r n y a r d g r a s s seeds i s w i t h i n t h e range 32°C t o 37°C (Brod, 1968). B a r n y a r d g r a s s i s a h y g r o p h i l o u s s p e c i e s and i t grows w e l l on medium heavy s o i l s , sandy loams or loamy sands w i t h s u f f i c i e n t water s u p p l y , but i t s development i s enhanced by h i g h f e r t i l i t y and a r i c h s u p p l y o f n i t r o g e n (Brod, 1968). Schmutz e t a_l. (1968) have r e p o r t e d a c c u m u l a t i o n o f n i t r a t e i n t h e t i s s u e s o f b a r n y a r d g r a s s p l a n t s , a t c o n c e n t r a t i o n s h i g h enough t o be t o x i c t o farm a n i m a l s ( K n o t t , 1971). B a r n y a r d g r a s s grows i n a d i v e r s e number of h a b i t a t s i n c l u d i n g c u l t i v a t e d f i e l d s , gardens, waste a r e a s , d i t c h e s , r o a d s i d e s ; . i t u s u a l l y grows on m o i s t r i c h s o i l s . I t i s a troublesome weed i n major w o r l d c r o p s i n c l u d i n g c o t t o n ( M i l l e r e t a l . , 1961), r i c e ( C h i s a k a , 1977), p o t a t o e s (Rahu e t a l . , 1968), sugar b e e t s (Dawson, 1965), soy bean (Dowson, 1977), c o r n , g r a i n sorghum, t o b a c c o e t c . (see f o r example, Holm e t a l . , 1977). The h i g h c o m p e t i t i v e a b i l i t y o f b a r n y a r d g r a s s w i t h a l a r g e number o f c r o p s can be e x p l a i n e d by i t s c h a r a c t e r i s t i c s : r a p i d r a t e o f growth (Dawson and Bruns, 1975), c l o s e resem-- 10 -b l a n c e t o some c r o p s such as r i c e (Noda, 1977), p a t t e r n o f n i t r o g e n a b s o r p t i o n which c o n t i n u e d u n t i l l a t e i n t h e growing season ( C h i s a k a , 1977), p r o l o n g e d emergence o f the seeds t o the end o f t h e growing season (Holm e t a l . , 1977), t h e l a c k o f s e l f - t h i n n i n g a t h i g h d e n s i t i e s (Yamagishi e t a l . , 1978), a b i l i t y t o m a i n t a i n a r i c h seed bank thus e n s u r i n g p o p u l a t i o n s o f h i g h d e n s i t i e s i n each season (Brod, 1968), and i t s o c c u r -rence i n a wide spectrum o f h a b i t a t s r a n g i n g from s e m i a q u a t i c t o t e r r e s t r i a l e nvironments (Noda, 1977). 2.1.3 Redroot pigweed (Amaranthus r e t r o f l e x u s L . ) . Redroot pigweed (RPW) b e l o n g s t o t h e f a m i l y Amarantha-ceae. I t i s an an n u a l r e p r o d u c i n g o n l y by seeds. The stem, 'highly b r anched, i s e r e c t and grows up t o 2m t a l l . The l e a v e s a r e ' l o n g - s t a l k e d , s p a r s e l y h a i r y w i t h prominent w h i t e v e i n s on the a b a x i a l s u r f a c e . The t a p r o o t system i s s h a l l o w and o f t e n p i n k i s h . Pigweeds o r i g i n a t e d i n t r o p i c a l A merica and t h e i r s p r e a d t h r o u g h o u t the w o r l d i s accounted f o r i n p a r t by man's e a r l y c u l t i v a t i o n o f them ( F e l t n e r , 1970) and t h r o u g h c r o p seed c o n t a m i n a t i o n . I n Canada, RPW o c c u r s i n a g r i c u l t u r a l a r e a s i n a l l p r o v i n c e s e x c e p t Newfoundland (Weaver and M c W i l l i a m s , 1980). I t grows i n a v a r i e t y o f h a b i t a t s i n c l u d i n g c u l t i v a t e d f i e l d s , w a s t e l a n d s , r o a d s i d e s , and many d i s t u r b e d h a b i t a t s . Pigweeds can grow i n s o i l s w i t h pH r a n g i n g from 4.2 - 9.1 ( F e l t n e r , 1970) b u t t h e i r growth i s markedly reduced on s o i l s w i t h a - 11 -pH 5.2 o r l e s s (Buchanan e t a_l. , 1975). G e n e r a l l y , RPW produces v e r y l a r g e numbers o f seeds t h a t can remain v i a b l e i n t he s o i l f o r up t o 40 y e a r s ( D a r l i n g t o n and S t e i n b a u e r , 1961). G e r m i n a t i o n o f f r e s h l y h a r v e s t e d seeds i s enhanced by s c a r i f i c a t i o n (Andersen, 1968); t h e y germinate b e s t a t te m p e r a t u r e s between 30°C and 40°C ( T a i l o r s o n and H e n d r i c k s , 1969) . A. r e t r o f l e x u s i s a common weed o f many c r o p s and i s known t o reduce c r o p y i e l d by c o m p e t i t i o n ( V e n g r i s e t a_l. , 1955; Senesac and M i n o t t i , 1978) . Pigweed p l a n t s a re c a p a b l e o f a c c u m u l a t i n g h i g h l e v e l s o f n i t r a t e s ( K i n g s b u r y , 1964) w i t h t h e stems and branches b e i n g the p r i m a r y s t o r a g e o r g a n s . The amount o f n i t r a t e i n t h e p l a n t t i s s u e s v a r i e s w i t h age and the h i g h e s t c o n c e n t r a t i o n i s a t t a i n e d j u s t b e f o r e f l o w e r i n g (Campbell, 1924). Pigweeds a r e drought r e s i s t a n t and have a r e l a t i v e l y low water r e q u i r e m e n t . Hence t h e y can compete f o r water when water s u p p l y i s a l i m i t i n g f a c t o r . I n a r e l a t i v e l y n e u t r a l s o i l (pH 7.5), r e d r o o t pigweed has been shown t o have a r e l a t i v e l y g r e a t e r c o m p e t i t i v e a b i l i t y than green f o x t a i l (Weaver and M c W i l l i a m s , 1980). I t s p r o l i f i c seed p r o d u c t i o n , a b i l i t y t o occupy a wide spectrum o f h a b i t a t s , the c o i n c i d e n c e o f i t s l i f e c y c l e w i t h t h a t o f warm season c r o p s , i t s a b i l i t y t o c o n c e n t r a t e n u t r i e n t s i n e x c e s s o f i t s r e q u i r e m e n t s , i t s f a s t r a t e o f growth and i t s a b i l i t y t o w i t h s t a n d drought make A. r e t r o f l e x u s one o f t h e most s e r i o u s weeds. - 12 2.1.4 Rapeseed The term "rape" was d e r i v e d from the l a t i n word "rapum" meaning t u r n i p (Downey, 1966). Rapeseed (RPS) b e l o n g s t o t h e same f a m i l y ( B r a s s i c a c e a e ) as many w e l l known vege-t a b l e s such as cabbage, t u r n i p , b r u s s e l s s p r o u t s , e t c . The two most w i d e l y grown r a p e s e e d s p e c i e s i n Western Canada are A r g e n t i n a rape ( B r a s s i c a napus L.) w h i c h i s adapted t o t h e S o u t h e r n r e g i o n s and P o l i s h o r T u r n i p rape ( B r a s s i c a c a m p e s t r i s L.) most s u i t e d f o r t h e more n o r t h e r l y r e g i o n s o f Canada. I n b o t h s p e c i e s t h e r e i s one seed t y p e and two f o d d e r t y p e s f o r each. Of t h e f o d d e r t y p e s w h i c h produce s w o l l e n r o o t s , t h a t o f B. napus i s termed t h e "swede" and t h a t o f B. c a m p e s t r i s the " t u r n i p " . The p l a n t s w h i c h y i e l d r a p e s e e d can grow up t o 1.5m h i g h . The f i r s t 3-4 l e a v e s are r e l a t i v e l y l a r g e and t h e stem i s c o n s i d e r a b l y branched near t h e t o p . Rapeseed i s a c o o l season c r o p and a l t h o u g h i t does w e l l on a wide range o f s o i l s , i t p e r f o r m s b e s t i n loam s o i l s (Bowren and P i t t m a n , 1975) . M o i s t u r e i s an i m p o r t a n t f a c t o r i n t h e growth and y i e l d o f B r a s s i c a s p e c i e s (Krogman and Hobbs, 1975). However, under drought s t r e s s c o n d i t i o n s , B. napus accumulates g r e a t e r d r y m a t t e r b e f o r e a n t h e s i s t h a n does B. c a m p e s t r i s ( R i c h a r d s and T h u r l o n g , 1978; 1 Munoz and F e r d i n a n d e z , 1978). These a u t h o r s s u ggested t h a t B. napus a v o i d s drought a t the most c r i t i c a l s t a g e and t h a t i t has enough p h o t o s y n t h e t i c r e s e r v e s t o p r o t e c t i t o v e r t h e p o s t - a n t h e s i s p e r i o d . Both s p e c i e s - 13 -respond favourably to nitrogen f e r t i l i z e r (Munoz, 1978). However, suitable moisture conditions are required for f u l l u t i l i z a t i o n of the nitrogen, and y i e l d s are highest under suitable i r r i g a t i o n schemes (Krogman and Hobbs, 1975). Once rapeseed i s established, the plants usually show a very rapid-rate of growth but the shoot dry weight declines 14 days after anthesis under f i e l d conditions (Tayo and Morgan, 1975). Rapeseed i s somewhat unusual i n that v a r i a t i o n i n seeding rates or plant populations over a wide range have very l i t t l e e f f e c t s on y i e l d s under normal conditions. Under heavy seeding rates, i n t r a s p e c i f i c competition occurs r e s u l t -ing i n fewer smaller pods concentrated on the upper part of the plant '(Anonymous, 1974; ...see also Tayo and Morgan, 19 75) . It seems- that i n Brassica substantial plant component compensation to environmental conditions or planting dates occurs (Mendhan and Scott, 1975). At low planting density for example, the plants are large, branched and spread out and the seed pods extend lower on the plant. S i m i l a r l y , delayed sowing i n B. napus re s u l t s i n fewer pods per plant but there i s no s i g n i f i c a n t change i n seed weight per pod (Thurling, 1974a and b). Rapeseed does not compete well with weeds in the early stages of growth (Anonymous, 1974) but once established, the leaves expand to cover the s o i l surface cutting o f f the l i g h t and smothering the competing weeds growing under the crop canopy. There i s much informa-- 14 -t i o n i n the l i t e r a t u r e on t h e c o m p e t i t i v e a b i l i t y o f rapeseed based on t h e a c t u a l y i e l d l o s s e s o f c r o p by weeds and t h e p o p u l a t i o n s o f weeds r e q u i r e d t o cause s i g n i f i c a n t y i e l d l o s s e s as r e p o r t e d by t h e E x p e r t Committee on Weeds-Western Canada. Weeds cause y i e l d l o s s e s i n r a p e s e e d t h r o u g h compe-t i t i o n and dockage. Because o f t h e wide spectrum o f s o i l t y p e s i n w h i c h r a p e s e e d i s grown a l a r g e number o f weeds have been r e p o r t e d i n r a p e s e e d f i e l d s . W i l d o a t s , green f o x t a i l , r e d r o o t pigweed, b a r n y a r d g r a s s , mustards, w i l d buckwheat e t c . have f r e q u e n t l y been r e p o r t e d t o o c c u r i n d i v i d u a l l y o r i n v a r i o u s c o m b i n a t i o n s w i t h RPS (Hunter e t a l . , 1975; .Anonymous, 1980; M o l b e r g and" S h e r i f f , 1971). Most c r o p p r o d u c t i o n g u i d e s s t r e s s t h a t r a p e s e e d s h o u l d not be seeded on i t s own s t u b b l e because o f t h e ,' i n c r e a s e d r i s k o f c r o p l o s s e s from d i s e a s e s and i n s e c t b u i l d up. However, t h e r e i s ample e v i d e n c e t h a t r a p e s e e d p l a c e s g r e a t demand on t h e s o i l f o r n u t r i e n t s (Loof, 1972) and t h a t i t a l s o produces water s o l u b l e compounds c a p a b l e o f r e t a r d i n g g e r m i n a t i o n and growth o f subsequent c r o p s ( K a s t i n g e t a l . , 1973). However, i n f o r m a t i o n on t h e p h y t o t o x i c e f f e c t s o f rapeseed on weeds growing e i t h e r i n a s s o c i a t i o n w i t h t h e c r o p o r i n t h e c r o p ' s s t u b b l e i s s c a n t y . R e s e a r c h and p r o d u c t i o n programs i n r a p e s e e d have expanded c o n s i d e r a b l y s i n c e t h e end o f World War I I and r a p e s e e d i s now t h e second m o s t . i m p o r t a n t c r o p ( a f t e r wheat). and i s t h e most r a p i d l y e x p a n d i n g r c r o p i n Canada (Ohlson, 15 -1972). The term. "Can o l a " has keen adopted i n Canada (Anonymous, 1980) f o r t h o s e v a r i e t i e s -of ..rape w i t h low e f u c i c a c i d (5% o f t o t a l f a t t y a c i d s ) and g l u c o s i n u l a t e (3mg/g) c o n t e n t s . 2.2 T e r m i n o l o g i e s and t h e Meaning o f C o m p e t i t i o n The t e rm " c o m p e t i t i o n " has been used i n p o p u l a t i o n b i o l o g y t o i n c l u d e t h e b i o l o g i c a l and p h y s i c a l p r o c e s s e s t h a t i n f l u e n c e t h e growth and development o f component s p e c i e s i n m i x t u r e s . A c c o r d i n g t o t h e O x f o r d E n g l i s h D i c t i o n a r y , c o m p e t i t i o n means "the a c t i o n o f e n d e a v o u r i n g t o g a i n what an o t h e r endeavours t o g a i n a t t h e same t i m e ; t h e s t r i v i n g o f two o r more f o r t h e same o b j e c t ; r i v a l r y " . I n b i o l o g i c a l p a p e r s , t h e term has o f t e n been employed w i t h o u t d e f i n i t i o n w i t h an assumption t h a t t h e meaning i s w e l l u n d e r s t o o d . T h i s has l e d t o c o n f u s i o n because c o m p e t i t i o n has been t a k e n t o mean d i f f e r e n t t h i n g s by d i f f e r e n t p e o p l e . The d e f i n i t i o n and t h e i n t e r p r e t a t i o n o f c o m p e t i t i o n i n p l a n t s have been r e v i e w e d by Clements e t a l . , (1929) and i n a n i m a l s by M i l n e (1961). " C o m p e t i t i o n i s p u r e l y a p h y s i c a l p r o c e s s . W i t h few e x c e p t i o n s , such as t h e c r o w d i n g o f t u b e r o u s p l a n t s when grown t o o c l o s e l y , an a c t u a l s t r u g g l e between competing p l a n t s never o c c u r s . C o m p e t i t i o n a r i s e s from t h e r e a c t i o n o f one p l a n t upon t h e p h y s i c a l f a c t o r s about i t and t h e e f f e c t s o f t h e m o d i f i e d f a c t o r s upon i t s c o m p e t i t o r s . I n t h e e x a c t 16 -sense, two p l a n t s , no m a t t e r how c l o s e , do not compete w i t h each o t h e r so l o n g as t h e water c o n t e n t , the n u t r i e n t mate-r i a l , t h e l i g h t and the heat a re i n e x c e s s o f the needs o f b o t h . When the immediate s u p p l y o f a s i n g l e f a c t o r f a l l s below t h e combined demands o f t h e p l a n t s , c o m p e t i t i o n b e g i n s " (Clements e t a_l. , 1929). I t i s c l e a r from t h i s i n t e r p r e t a -t i o n and from t h e O x f o r d E n g l i s h D i c t i o n a r y t h a t c o m p e t i t i o n i s p i v o t e d on growth f a c t o r s . The c o n f u s i o n t h a t has been v o i c e d i n t h e l i t e r a t u r e on t h e use o f t h e term may have a r i s e n because many b i o l o g i s t s have used i t t o embrace the v a r i o u s forms o f mutual i n f l u e n c e between p l a n t s ( s p e c i e s ) growing t o g e t h e r (Donald, 1963; R i c e , 1979) and not a c c o r d i n g t o t h e b i o l o g i c a l c o n c e p t s o f Clements. Harper (1961) a t t e m p t e d t o c l e a r up the c o n f u s i o n , by a r g u i n g t h a t t h e term c o m p e t i t i o n l a c k s independent s c i e n t i f i c meaning. He proposed t h e term " i n t e r f e r e n c e " t o embrace t h e o v e r a l l i n f l u e n c e s o f one p l a n t o r s p e c i e s on an o t h e r (see a l s o M i l l e r , 1969). I n t h i s c o n t e x t c o m p e t i t i o n i t s e l f i s but o n l y one f a c e t o f i n t e r f e r e n c e (Harper, 1964). The use o f i n t e r f e r e n c e i n p r e f e r e n c e t o c o m p e t i t i o n has r e c e i v e d wide s u p p o r t ( H a l l , 1974a and b; T r e n b a t h , 1974). Harper (1964.) used t h e term t o mean " a l l t h e r e s p o n s e s o f an i n d i v i d u a l p l a n t o r p l a n t s p e c i e s t o i t s environment as t h i s i s m o d i f i e d by the presence and/or growth o f a n o t h e r " . I n i t s s t r i c t e s t sense i n t e r f e r e n c e i n c l u d e s any a c t i v i t y o f one p l a n t o r s p e c i e s t h a t i n f l u e n c e s the o t h e r ' s a b i l i t y o r - 17 -e f f i c i e n c y t o i n t e r c e p t and/or u t i l i z e e n v i r o n m e n t a l r e s o u r c e s . H a l l (1974a) s u b d i v i d e d i n t e r f e r e n c e i n t o b o t h " c o m p e t i t i v e " and " n o n - c o m p e t i t i v e " p r o c e s s e s ; " c o m p e t i t i v e i n t e r f e r e n c e " r e f e r s t o ca s e s where "one s p e c i e s d i r e c t l y a f f e c t s t h e growth o f t h e o t h e r by competing f o r a r e s o u r c e ( s ) p o t e n t i a l l y e q u a l l y a v a i l a b l e t o b o t h " . The same d e f i n i t i o n has been used by a number o f b o t a n i s t s t o r e f e r t o " c o m p e t i t i o n e x p l o i t a t i o n " ( L e v i n e , 1976; Bunce e t a l . , 1977). " N o n - c o m p e t i t i v e i n t e r -f e r e n c e " on t h e o t h e r hand r e f e r s t o s i t u a t i o n s i n wh i c h one s p e c i e s has an i n n a t e a b i l i t y t o monopolize a r e s o u r c e t h a t i s not a v a i l a b l e t o the o t h e r s p e c i e s (at l e a s t a t some st a g e d u r i n g t h e i r r e l a t i v e development, as i n legume-grass m i x t u r e s w i t h r e s p e c t t o n i t r o g e n f i x a t i o n ) . A more s u b t l e d e v i a t i o n i n t e r m i n o l o g y t o e x p l a i n o r d e f i n e t h e mutual i n f l u e n c e s o f s p e c i e s i n m i x t u r e s was made by de Wit (1960) when he wrote " c o m p e t i t i o n f o r space", w i t h space b e i n g i n t e r p r e t e d as b i o l o g i c a l space and a composite o f a l l growth- f a c t o r s and r e s o u r c e s . Thus de -.Wit'.. (1960) d e l i b e r a t e l y d e v i a t e d from Clements e t a_l. (1929) and Donald (1963), who took the v i e w o f i d e n t i f y i n g t h e f a c t o r s f o r which c o m p e t i -t i o n o c c u r s . But he has m a i n t a i n e d t h a t t o s u b d i v i d e such a complex i n t o p a r t i c u l a r components " i s not n e c e s s a r y , always i n a c c u r a t e and t h e r e f o r e i n a d v i s a b l e " . A c c o r d i n g t o de Wit (1960), i n f l u e n c e s o f a d e t r i m e n t a l n a t u r e among s p e c i e s i n a m i x t u r e a r i s e from " c o m p e t i t i o n f o r t h e same space" i n c o n t r a s t t o " c o m p e t i t i o n f o r p a r t l y t h e same space" when th e y - 18 -a r e o f p o s i t i v e n a t u r e . These d e f i n i t i o n s are s i m i l a r t o the " c o m p e t i t i v e " and " n o n - c o m p e t i t i v e " i n t e r f e r e n c e s r e s p e c t i v e l y o f H a l l (1974a). H a l l (1974a) comments t h a t t h e use o f the term c o m p e t i t i o n f o r t h e two p r o c e s s e s by de Wit i s u n f o r t u n a t e , b u t i t i s c l e a r from t h e f o r e g o i n g t h a t t h e use o f t h e s e l f -c o n t r a d i c t o r y term " n o n - c o m p e t i t i v e i n t e r f e r e n c e " i s s i m i l a r l y u n f o r t u n a t e . I t i s i n t h i s c o n t e x t t h a t the b r o a d e r and l e s s c o n f u s i n g term " p l a n t o r s p e c i e s i n t e r a c t i o n " seems more p r e f e r a b l e . " S p e c i e s i n t e r a c t i o n " embraces a l l mutual o r r e c i p r o c a l i n f l u e n c e s o f one s p e c i e s on a n o t h e r . T r e n b a t h (1976) has r i g h t f u l l y r e s e r v e d t h e term c o m p e t i t i o n f o r i n t e r a c t i o n s i n v o l v i n g growth r e q u i s i t e s , i . e . " c o m p e t i t i v e i n t e r a c t i o n " . N o n - c o m p e t i t i v e i n t e r a c t i o n s would i n c l u d e the n o n - c o m p e t i t i v e i n t e r f e r e n c e o f H a l l (1974a), t h e c o m p e t i t i o n f o r p a r t l y t h e same space o f de Wit (1960) and t h e v a r i o u s forms o f i n t e r a c t i o n s t h a t a re o f a p r o t e c t i v e n a t u r e such as from wind (Paner, 1975), l o d g i n g (de W i t , 1978), and g r a z i n g (Harper, 1964). B i o c h e m i c a l i n t e r a c t i o n s i n c l u d e a l l the e f f e c t s o f t o x i c e xudates o f one s p e c i e s on an o t h e r ( a l l e l o -p a t h y ; MoQilsch, 1937). — For t h e sake o f c l a r i t y and t o attempt t o m i n i m i z e c o n f u s i o n i n t h e use o f v a r i o u s terms r e l a t e d t o p l a n t i n t e r -a c t i o n s a scheme i s p r e s e n t e d i n F i g u r e 2.1 t o show t h e i r i n t e r r e l a t i o n s h i p s . C o o p e r a t i o n H i l l and Shimamoto (1973) P l a n t o r S p e c i e s I n t e r a c t i o n s ( n o n - c o m p e t i t i v e i n t e r f e r e n c e ) H a l l (1974a) I n t e r f e r e n c e Crombie (1947) Harper (1961) ( c o m p e t i t i v e i n t e r f e r e n c e ) H a l l (1974a) C o m p e t i t i o n Clements e t a l . (1929) Donald.(1963) ( E x p l o i t a t i o n ) L e v i n e (1976) Bunce e t a l . (1977) A l l e l o p a t h y M o l i s c h (1937) R i c e (1979) F i g u r e 2.1 Scheme of t e r m i n o l o g y r e l a t e d t o p l a n t s p e c i e s i n t e r a c t i o n s . - 20 2.3 C o m p e t i t i v e and N o n c o m p e t i t i v e I n t e r a c t i o n s 2.3.1 C o m p e t i t i v e I n t e r a c t i o n ( I n t e r f e r e n c e ) Among S p e c i e s M i x t u r e s C o m p e t i t i v e i n t e r a c t i o n i s used t o merge t h e b a s i c schemes o f t e r m i n o l o g y r e l a t i n g t o t h e d e t r i m e n t a l o r g a n i s m i c i n t e r a c t i o n s proposed by Crombie (1947) and e l a b o r a t e d by Harper (1961), and M i l l e r (1969). I n t e r f e r e n c e as o u t l i n e d i n F i g u r e 2.1 i s used t o c o v e r a l l forms o f d e t r i m e n t a l i n t e r a c t i o n s among organisms i n c l o s e p r o x i m i t y w i t h each o t h e r , o f wh i c h c o m p e t i t i o n ( e x p l o i t a t i o n ) and a l l e l o p a t h y a r e but p a r t s . M u l l e r (1969) d i s t i n g u i s h e s c o m p e t i t i o n from a l l e l o p a t h y by l a b e l l i n g a l l i n t e r a c t i o n s w h i c h a r e d e t r i m e n t a l due t o t h e "removal o f some l i m i t e d but r e q u i r e d r e s o u r c e ( s ) by one o f t h e component s p e c i e s as c o m p e t i t i o n , w h i l e a l l e l o -p a t h y i s d e t r i m e n t a l because o f t h e a d d i t i o n o f an i n h i b i t o r y c h e m i c a l t o t h e environment." I n a m i x t u r e , d i f f e r e n c e s i n morphology and/or p h y s i o l o g y between s p e c i e s cause t h e i r i n d i v i d u a l s t o e x p e r i -ence d i f f e r e n t m i c r o - e n v i r o n m e n t s and hence d i f f e r e n t r e s o u r c e a v a i l a b i l i t y from t h o s e e x p e r i e n c e d by p l a n t s o f t h e same genotype i n pure s t a n d s . I t i s t h e s e b i o l o g i c a l d i f f e r e n c e s t h a t d etermine whether a s p e c i e s i n t h e m i x t u r e e i t h e r p a r t l y o r e x c l u s i v e l y g a i n s a t t h e expense o f i t s a s s o c i a t e s ( c o m p e t i t i v e i n t e r a c t i o n ) o r i n d e p e n d e n t l y o f the a s s o c i a t e s ( n o n - c o m p e t i t i v e i n t e r a c t i o n ) . - 21 Plants require the growth factors water, l i g h t , nutrients, carbon dioxide and oxygen for growth (Donald, 1963; Rhodes, 1 9 7 0 ) . Light and carbon dioxide are absorbed into the plant by the shoot system, and water, nutrients and oxygen by the root system (Clements et a l . , 192 9; Harper, 1961; Donald, 1963) . Competition for carbon dioxide i s more l i k e l y to occur i n closed canopies e s p e c i a l l y when the a i r within the canopy i s not well mixed (Impens et a l . 1967; Monteith, 1S63),. Greenwood (196 9) pointed out that except i n water-logged s o i l s , the d i f f u s i o n of oxygen i n s o i l s i s usually fast enough to maintain adequate supplies to a l l roots. It i s thus generally accepted that the environmental resources for which competition occurs are p r i n c i p a l l y water, l i g h t and mineral nutrients (Trenbath, 19 7 4 ) . In a newly established plant community the i n i t i a l y i e l d of the component species i s proportional to the area available to each species (de Wit, 1960) i . e . the shoot and the root systems of the component species are i n low enough density for the per plant supply, interception, and absorption of growth factors to equal that i n isol a t e d plants growing under similar conditions. The root and shoot systems of the component species come closer together as growth proceeds which leads to intergenotypic interactions in r e l a t i o n to interception and absorption of the growth requisites (Hunt, 197 8 ) . The onset of such i n t e r s p e c i f i c i nteraction i s depend-ent on the stand density and l e v e l of the resource supply, and - 22 o c c u r s e a r l i e r i n h i g h e r d e n s i t i e s ( S t e r n , 1965; Donald, 1958) and a t h i g h n u t r i e n t l e v e l s (Bazzaz and H arper, 1976). G e n e r a l l y , t h e outcome of c o m p e t i t i v e i n t e r a c t i o n may r e s u l t e i t h e r i n d e a t h of p l a n t s ( m o r t a l i t y e f f e c t ) , r e d u c t i o n i n the growth r a t e o f i n d i v i d u a l s ( p l a s t i c i t y e f f e c t ) o r b o t h . Bazzaz and Harper (1976) demonstrated t h a t , i n a m i x t u r e of S i n a p i s . a l b a (L.) Rabench and L e p i d i u m s a t i v u m L., S i n a p i s c o n t r i b u t e d most t o t h e y i e l d o f t h e m i x t u r e and l e s s t o t h e m o r t a l i t y ; the r e v e r s e was t r u e o f L e p i d i u m . Both s p e c i e s , however, s u f f e r e d g r e a t e r m o r t a l i t y i n f e r t i l e t h a n i n i n f e r t i l e s o i l (see a l s o White and H arper, 1970). T h i s i s p a r t l y because a t h i g h e r f e r t i l i t y l e v e l s t h e i n d i v i d u a l p l a n t s g e n e r a l l y grow l a r g e r and enhance i n t e r s p e c i f i c " c o n t a c t s " l e a d i n g p o s s i b l y t o g r e a t e r s h a d i n g e f f e c t s . 2.3.1.1 C o m p e t i t i o n ( e x p l o i t a t i o n ) The c o n c e p t o f c o m p e t i t i o n can be viewed i n t h r e e ways based on t h e p o i n t o f v i e w o f t h e i n v e s t i g a t o r . One s c h o o l of t hought may be i n t e r e s t e d i n c o m p e t i t i o n as a r e s u l t o f d i f f e r e n t i a l p a r t i t i o n i n g o f growth r e q u i s i t e s . I n t h i s case the i m p l i c a t i o n i s t h a t " p l a n t s compete f o r some-t h i n g " . T h i s v i e w i s h e l d by p l a n t p h y s i o l o g i s t s and t h e y i n e v i t a b l y l o o k a t c o m p e t i t i o n e f f e c t s a t t h e i n d i v i d u a l p l a n t l e v e l . The main c o n c e r n i n such p h y s i o l o g i c a l approaches i s t h e l e v e l o f t h e f a c t o r s and ways t o s e p a r a t e t h e s e f a c t o r s b o t h i n t ime and space. The e c o l o g i s t on the o t h e r hand p l a c e s emphasis on t h e e f f e c t s o f c o m p e t i t i o n on the composi-t i o n o f p l a n t c ommunities. I n t h i s case c o m p e t i t i o n i s re g a r d e d as one o f the f a c t o r s i n f l u e n c i n g community p a t t e r n s i n n a t u r e . The d e n s i t i e s o f s p e c i e s i n a community a t any one p o i n t i n ti m e a r e r e g a r d e d as t h e outcomes o f c o m p e t i t i o n . W i t h the use o f v a r i o u s ' d e n s i t y measurements a t d i f f e r e n t t i m e s c o m p e t i t i o n i s i n f e r r e d (Harper, 1961; A r e s , 1972). C o m p e t i t i o n among p o p u l a t i o n s has been the a g r o n o m i s t ' s approach because he i s i n t e r e s t e d i n the e f f e c t s o f c o m p e t i -t i o n on t h e whole c r o p o r p a s t u r e . The agr o n o m i s t m a i n l y works w i t h a known d e n s i t y o f b o t h pure and mixed st a n d s and t h e outcome o f c o m p e t i t i o n i s d e t e r m i n e d i n terms o f y i e l d p e r g i v e n a r e a . V a r i o u s a t t e m p t s have been made t o examine t h e e f f e c t s o f growth r e q u i s i t e s i n d i v i d u a l l y on t h e outcome o f c o m p e t i -t i o n among and between s p e c i e s ( A s p i n a l l , 1960; Bazzaz and Harper, 1976; H a l l , 1974b; L i t a v and I t s i , 1972; Snaydon, 1971 Donald, 1958). S i g n i f i c a n t c o m p e t i t i o n above and below ground has been demonstrated and t h e r e i s an i n t e r a c t i o n between shoot and r o o t c o m p e t i t i o n (Donald, 1963). I t i s r e a d i l y a c c e p t e d f o r example, t h a t a p l a n t shaded by i t s n e i g h b o u r s t o an e x t e n t t h a t l i g h t i s l i m i t i n g i t s growth may, by v i r t u e o f i t s r e d u c e d development, have a s m a l l e r r o o t system and hence be l e s s c o m p e t i t i v e f o r n u t r i e n t and w a t e r . S i m i l a r l y a p l a n t o b t a i n i n g s u b o p t i m a l s u p p l i e s o f n u t r i e n t s from t h e s o i l as a d i r e c t r e s u l t o f g r e a t e r uptake o f t h e s e same - 24 -n u t r i e n t s by i t s n e i g h b o u r s may show reduced a e r i a l d e v e l o p -ment and be l e s s c o m p e t i t i v e f o r l i g h t . W i t h t h i s c a u t i o n i n mind the f a c t o r s f o r which c o m p e t i t i o n o c c u r s can c o n v e n i -e n t l y be d i s c u s s e d i n d i v i d u a l l y . 2.3.1.1.1 C o m p e t i t i o n f o r l i g h t L i g h t i s among the most i m p o r t a n t r e s o u r c e s i n p l a n t c o m p e t i t i o n . C o m p e t i t i o n f o r l i g h t o c c u r s not o n l y between d i f f e r e n t s p e c i e s but a l s o between i n d i v i d u a l s o f t h e same s p e c i e s and between d i f f e r e n t l e a v e s o f the same p l a n t . Donald (1961) emphasized t h a t " l i g h t i s i n s t a n t a n e o u s l y a v a i l a b l e " and has t o be " i n s t a n t a n e o u s l y i n t e r c e p t e d " i f i t i s t o be used f o r p h o t o s y n t h e s i s . The canopy a r c h i t e c t u r e has been i d e n t i f i e d as the p l a n t component most v i t a l i n the c o m p e t i t i o n f o r l i g h t between and w i t h i n s p e c i e s (Monsi and S a e k i , 1953; Rhodes and S t e r n , 1978; S t e r n , 1962). G e n e r a l l y a shoot system w i t h i t s l e a v e s h i g h up i n t h e canopy i s a t an advantage. In a m i x t u r e , i t i s l i k e l y t h a t i f the l e a v e s a r e h o r i z o n t a l l y o r i e n t e d , the advantage i s g r e a t e r t h a n i f t h e y are e r e c t ( S t e r n and Donald, 1962a and b ) . H o r i z o n t a l l y o r i e n t e d ( p l a n o p h i l e ) l e a v e s i n t e r c e p t more l i g h t per u n i t a r e a o f t h e l e a f t h a n do e r e c t ( e r e c t o p h i l e ) l e a v e s (Kasanga and M o n s i , 1954). The c o n v e r s e i s a l s o t r u e t h a t c o m p e t i t i o n f o r l i g h t i s m i n i m i z e d when the t a l l e r component i n t h e m i x t u r e has e r e c t l e a v e s and the s h o r t e r one has a more h o r i -z o n t a l l e a f h a b i t ( T r e n b a t h , 1974). I n t h e l a t t e r case the m i x t u r e i n t e r c e p t s more l i g h t energy over time and t h e r e f o r e has h i g h e r p o t e n t i a l f o r p h o t o s y n t h e s i s t h a n t h e pure s t a n d s . Andrews and Kassam (1976) summarized t h i s by s a y i n g t h a t m i x t u r e s u t i l i z e t h e e n v i r o n m e n t a l r e s o u r c e s more f u l l y t h a n pure s t a n d s (see a l s o O s i r u and W i l l e y , 1972). C o m p e t i t i o n f o r l i g h t o c c u r s i n v a r i o u s c r o p s and p a s t u r e s e s p e c i a l l y when the h e i g h t o f one component tends t o i n c r e a s e more r a p i d l y t h a n t h e o t h e r . O s i r u and W i l l e y (1972) f o r example o b s e r v e d marked d i f f e r e n c e s i n y i e l d from m i x t u r e s o f maize and beans, and sorghum and beans, w i t h the former m i x t u r e y i e l d i n g more t h a n t h e l a t t e r . They a s c r i b e d t h i s d i f f e r e n c e t o t h e marked d i f f e r e n c e i n t h e h e i g h t between th e components o f the m i x t u r e s and hence a b e t t e r u t i l i z a t i o n o f l i g h t . B l a c k e t a l . (1969) r e p o r t e d t h a t c o m p e t i t i v e a b i l i t y depends on t h e n e t c a p a c i t y o f a p l a n t t o a s s i m i l a t e c a r b o n d i o x i d e and use p h o t o s y n t h a t e t o e x t e n d i t s f o l i a g e o r i n c r e a s e i t s s i z e . They c o n c l u d e d t h a t p h o t o s y n t h e t i c a l l y e f f i c i e n t (C 4) p l a n t s are s t r o n g e r c o m p e t i t o r s t h a n n o n - e f f i c i e n t (C^) p l a n t s . Among the s p e c i e s t h e y examined, b a r n y a r d g r a s s ( E c h i n o c h l o a , c r u s g a l l i (L.) Beauv.), r e d r o o t pigweed (Amaran-t h u s r e t r o f l e x u s L . ) , f o x t a i l m i l l e t ( S e t a r i a i t a l i c a (L.) Beauv.) and c o r n (Zea mays L.) were e f f i c i e n t and lamb's q u a r t e r s (Chenopodium- album L.) p e r e n n i a l r y e g r a s s (Lolium. perenne L.) and rape ( B r a s s i c a napus L.) were l i s t e d as i n e f f i c i e n t . K roh and Stephenson (1980) ranked v a r i o u s weeds a c c o r d i n g t o t h e i r r e l a t i v e c o m p e t i t i v e a b i l i t y (sum o f t h e 26 -r a t i o s o f mean p l a n t w e i g h t s o f each component s p e c i e s i n pure s t a n d t o t h a t from m i x t u r e ) as f o l l o w s : A. r e t r o f l e x u s > C. album >. S e t a r i a , v i r i d i s (L.) Beauv. > Panicum c a p i l l a r e L. T h i s o r d e r s u p p o r t s t h e c l a s s i f i c a t i o n o f s p e c i e s above by B l a c k , e t a l . (1969). I n c o r n / g r e e n - f o x t a i l m i x t u r e s , N i e t o and S t a n i f o r t h (1961) found t h a t t h e s i z e o f t h e compet-i n g f o x t a i l and hence t h e f i n a l y i e l d r e d u c t i o n s i n c o r n was de t e r m i n e d by t h e s h a d i n g e f f e c t s o f t h e t a l l , more e f f i c i e n t c o r n p l a n t s . Marcedo and T a l a t a l a (1977) found t h a t d r i l l e d r i c e s u f f e r e d from c o m p e t i t i o n w i t h E c h i n o c h l o a ...colonum (Lj Link 2 a t a d e n s i t y o f 80 p l a n t s / m d u r i n g t h e i n i t i a l 40 days a f t e r d r i l l i n g . They o b s e r v e d t h a t c o m p e t i t i o n was more i m p o r t a n t when the weeds were t a l l e r t h a n the c r o p . T h i r t y p e r c e n t s h a d i n g d u r i n g e a r l y growth s t a g e s reduced growth and y i e l d o f tomato and A. r e t r o f l e x u s , b u t had l i t t l e e f f e c t a t l a t e r growth s t a g e s (Mohammed and Sweet, 1976). They a l s o o b s e r v e d t h a t A. r e t r o f l e x u s e x h i b i t e d g r e a t e r s e n s i t i v i t y t o s h a d i n g t h a n tomato, and c l o s e s p a c i n g reduced weed growth more th a n wide s p a c i n g . C o m p e t i t i o n for.' l i g h t o c c u r s r e l a t i v e l y e a r l y i n h i g h d e n s i t y p o p u l a t i o n s but as t h e canopy d e v e l o p s the d e n s i t y e f f e c t on t h e l i g h t p e n e t r a t i o n i n the canopy i s c a n c e l l e d . The r e l a t i v e p e r i o d a t wh i c h p o p u l a t i o n d e n s i t y ceases t o have e f f e c t on l i g h t a t t e n u a t i o n by t h e canopy i s dependent on t h e time o f g e r m i n a t i o n and r a t e o f growth. Many c r o p s a r e poor c o m p e t i t o r s w i t h weeds i n the e a r l y s t a g e s o f growth, but - 27 -some e.g. r a p e s e e d , once e s t a b l i s h e d , grow r a p i d l y and the l e a v e s expand t o c o v e r the s o i l s u r f a c e . The weeds growing under t h e canopy may be smothered from s h a d i n g e f f e c t s (Anonymous, 1974). I n w i l d o a t s , Lee e t a l . (1980) r e p o r t e d t h a t i f l i g h t i s t h e p r i m a r y f a c t o r i n c o m p e t i t i o n , t h e damage caused may not be e v i d e n t u n t i l l a t e r i n the r e a s o n when the weeds have a t t a i n e d some h e i g h t . 2.3.1.1.2 C o m p e t i t i o n f o r m i n e r a l n u t r i e n t s Much l e s s i s known about p l a n t r e l a t i o n s h i p s below the ground s u r f a c e a l t h o u g h a consensus e x i s t s t h a t c o m p e t i -t i o n f o r water and n u t r i e n t s i s more f r e q u e n t and s e v e r e t h a n f o r l i g h t ( L i t a v and I s t i , 1972; Remison, 1979). I t i s common a g r i c u l t u r a l p r a c t i c e t o s u p p l y m i n e r a l n u t r i e n t s , e s p e c i a l l y n i t r o g e n (N), phosphorus ( P ) , p o t a s s i u m (K) and s u l p h u r ( S ) . However, s i n c e c r o p s a r e c o n t i n u a l l y i n v a d e d by weed s p e c i e s , t h e n u t r i e n t s s u p p l i e d a re bound t o be shared by b o t h t h e c r o p and weeds. Alkamper (1976) p r o v i d e d an a n a l y s i s f o r w e e d - f e r t i l i t y i n t e r a c t i o n s . The s t u d y emphasized t h a t weeds u s u a l l y absorb n u t r i e n t s f a s t e r and i n r e l a t i v e l y l a r g e r amounts th a n c r o p s and t h e r e f o r e d e r i v e g r e a t e r b e n e f i t r e l a -t i v e t o t h e c r o p p l a n t s . T h i s o b s e r v a t i o n i s f u r t h e r s u p p o r t e d by o t h e r s t u d i e s such as t h a t o f V e n g r i s e t a l . (1955) who compared t h e r e l a t i v e uptake o f n u t r i e n t s i n weed-free c o r n , c o r n i n f e s t e d w i t h A. r e t r o f l e x u s and A. r e t r o f l e x u s a l o n e , and found t h a t t h e c o n t e n t s o f N,P,K, c a l c i u m (Ca) and - 28 -magnesium (Mg) were s i g n i f i c a n t l y reduced i n w e e d - i n f e s t e d c o r n r e l a t i v e t o weed-free c o r n , and t h a t t h e K-, Ca- and Mg- c o n t e n t s o f A. r e t r o f l e x u s i t s e l f were a p p r e c i a b l y g r e a t e r t h a n i n weed-free c o r n . C h e m i c a l a n a l y s i s o f m i x t u r e components has been used t o i n f e r d i f f e r e n c e s i n c o m p e t i t i o n f o r n u t r i e n t s (Snaydoh, 1971; H a l l , 1974b). These a n a l y s e s are based on t h e assump-t i o n t h a t d i f f e r e n c e s i n c o m p e t i t i o n f o r n u t r i e n t s w i l l be r e f l e c t e d i n the n u t r i e n t c o n t e n t o f t h e component s p e c i e s . I t i s w e l l known t h a t s p e c i e s v a r y markedly i n t h e i r n u t r i e n t r e q u i r e m e n t s , the forms of n u t r i e n t s which p l a n t s can r e a d i l y a b s o r b , and t h e i r a b i l i t y t o e x t r a c t them from th e s o i l (Davies and Snaydon, 1973; W i l l i a m s , 1976). There i s ample e v i d e n c e t h a t weeds have the p o t e n t i a l t o absorb and accumulate v a r i o u s m i n e r a l elements s e l e c t i v e l y ( E r v i o , 1971). Lamb's q u a r t e r s f o r example, can remove t w i c e as much N and P, and t h r e e t i m e s as much K from th e s o i l as c o r n p l a n t s ( M a g g i t t , 1970). Hoveland e t a l . (1976) have c a t e g o r i z e d t h e r e s p o n s e s of weeds t o s o i l P and K. They o b s e r v e d t h a t P-uptake i s s p e c i f i c f o r d i f f e r e n t c o m b i n a t i o n s o f s p e c i e s as w e l l as the s t a g e of growth. S i m i l a r i n t e r a c t i o n s t o n u t r i e n t uptake and s p e c i e s have a l s o been demonstrated i n Desmodium/Setaria m i x t u r e s ( H a l l , 1974b). When the s o i l l e v e l s o f K were low, S e t a r i a was much b e t t e r a b l e t o e x t r a c t t h i s n u t r i e n t t h a n t h e a s s o c i a t e d Desmodium and grew b e t t e r t h a n th e l a t t e r i n t h e m i x t u r e . - 2 9 -Discussions on below ground resources most often involve a consideration of rooting pattern. One consideration i s that the mixture components may exploit d i f f e r e n t s o i l horizons, and thus i n t o t a l they may exploit a greater s o i l volume i n contrast to pure stands. In studies involving various weed mixtures, Kroh and Stephenson (1980) observed that Amaranthus,retroflexus, had a dominant central tap root while Chenopodium album had several robust branch roots and Setaria v i r i d i s had a shallow fibrous root system. The r e l a t i v e l y better uptake of various nutrients may be due to morphological attributes or some other factors such as high root "demand" (Drew et a l . , 1969) or the a b i l i t y to avoid roots of neighbouring plants (Baldwin et a l . , 1972). Eagles (1972) reported that for competition between natural popula-tions of Dactylis.glomerata the onset of root competition was much e a r l i e r than shoot competition for l i g h t . In t h i s way one population may exploit the nutrients in successive horizons i n advance of the other or may absorb nutrients more e f f i c i e n t l y when the roots of both populations are i n close proximity. O'Brien et a l . (1967) observed an advantage of the hybrid of t a l l fescue x ryegrass over either parent when under competition. They ascribed t h i s advantage to i t s a b i l i t y to exploit water and nutrients from deeper horizons of the s o i l . It i s clear from the foregoing that overcoming weed competition by f e r t i l i z a t i o n may not be successful. Thurston - 30 -(1956) made t h e f o l l o w i n g remarks f o r c o n d i t i o n s e n c o u n t e r e d i n E ngland ; " F e r t i l i z e r s have t h e same e f f e c t on w i l d o a t s as c u l t i v a t e d c e r e a l s , so t o p - d r e s s i n g an i n f e s t e d f i e l d may r e s u l t i n a h e a v i e r c r o p w i t h more v i g o r o u s w i l d o a t p l a n t s . " T h i s s u p p o r t s t h e e a r l i e r s tatement t h a t b o t h weeds and c r o p s respond t o f e r t i l i z e r a p p l i c a t i o n and t h a t t h e outcome o f t h e i r c o m p e t i t i v e i n t e r a c t i o n w i l l depend on t h e e f f e c t o f t h e i r r esponse t o shoot c o m p e t i t i o n . Two c u l t i v a r s o f b a r l e y were a s s e s s e d f o r t h e i r > a b i l i t y t o compete f o r . l i g h t by-Edwards and A l l a r d (196 3) b u t t h e y found t h a t t h e r e was no c o m p e t i t i o n f o r l i g h t a l t h o u g h one c u l t i v a r d i s p l a y e d a d i s t i n c t c o m p e t i t i v e advantage over th e o t h e r . However, p h e n o l o g i c a l d a t a r e v e a l e d t h a t t h e dominant c u l t i v a r began t o d e v e l o p a dense mass o f crown r o o t s a t the j o i n t i n g s t a g e and may have become more e f f i c i e n t a t g a t h e r i n g n u t r i e n t s and w a t e r . 2.3.1.1.3 C o m p e t i t i o n f o r water Water i s t h e most i m p o r t a n t r e s o u r c e f a c t o r t o competing p l a n t s under c u l t i v a t i o n . Yet i t i s t h e l e a s t r e l i a b l e o f a l l growth r e q u i s i t e s i n b o t h the t ime o f i t s a v a i l a b i l i t y and t h e p e r i o d f o r w h i c h i t w i l l c o n t i n u e t o be a v a i l a b l e . I n c o n t r a s t t o l i g h t , water and n u t r i e n t s can be s t o r e d i n t h e s o i l f o r v a r y i n g p e r i o d s and p l a n t s can draw from t h e s e s u p p l i e s and t o some e x t e n t a m e l i o r a t e t h e u n c e r t a i n a v a i l a b i l i t i e s . The i n i t i a l s t o r e s o f water i n t h e s o i l may be supplemented by r a i n f a l l o r by i r r i g a t i o n . - 31 Loss of water from the s o i l reservoirs occur through three main routes: d i r e c t evaporation from the s o i l surface; leaching as a r e s u l t of gr a v i t a t i o n a l and other physical forces; and absorption by plants which act as a "wick" connecting the s o i l and the atmosphere through the process of t r a n s p i r a t i o n . A question of agronomic interest i s what fr a c t i o n of the reservoir i s available to the crop stand? The size of the reservoir of water available to a plant at any time depends on the depth of root penetration and the amount of available water within the root zone. It i s obvious that more vigorous plants have time to develop an extensive root system and hence to tap a larger reservoir of water from the s o i l than less vigorous ones. The extent of the root zone thus varies with species, stage of develop-ment, the environmental conditions under which the plants are growing and the s o i l water management schemes (Milthorpe, 1961) . When two or more plant species are grown together there are bound to be some differences i n size and develop-. . mental stages between them including the depths and extents of t h e i r root systems. The sharp d i s t i n c t i o n s between types of root system and transpiring canopies between species growing i n mixtures were observed by Bakke and Plagge (1925) in mustards, oats and wheat. They reported that three plants of common mustard (Brassica nigra) with a t o t a l leaf area of 2 5,369 cm had a maximum water loss (through transpiration) of - 32 -68.4g per square metre o f l e a f s u r f a c e per hour i n comparison 2 2 t o 13.6 g/m f o r o a t s i n mustard and 18.0 g/m f o r wheat i n mustard. The r e m a r k a b l e d i f f e r e n c e s i n t h e amount o f water l o s t by t h e s e s p e c i e s i n m i x t u r e s suggest t h a t under c o n d i t i o n s o f m i l d water s t r e s s , mustard may use the water r e s o u r c e s and thu s d e p r i v e t h e accompanying s p e c i e s . M i l t h o r p e (1961) s t a t e d t h e g e n e r a l p r i n c i p l e t h a t t h e g r e a t e r a p l a n t ' s l e a f growth b e f o r e i t comes i n t o c o n t a c t w i t h a n o t h e r p l a n t , t h e more e x t e n s i v e w i l l be i t s r o o t system and t h e l e s s l i k e l y i t w i l l be t o s u f f e r from d r o u g h t , i . e . "the h i g h e r t h e d e n s i t y , t h e s m a l l e r t h e p l a n t a t any time i n ontogeny, and t h e h i g h e r t h e water c o n t e n t a t which s h o r t -age o f water i s e x p e r i e n c e d " . Any p l a n t ' s a b i l i t y t o s u c c e s s f u l l y compete f o r water depends on t h e r a t e and com-p l e t e n e s s w i t h which i t u t i l i z e s the s o i l water s u p p l y , a c h a r a c t e r i s t i c t h a t r e l a t e s t o a t t r i b u t e s o f t h e genotype w i t h i n a p a r t i c u l a r environment. Such a t t r i b u t e s i n c l u d e r e l a t i v e growth r a t e , c o r r e s p o n d i n g e a r l i n e s s o f water demand, and t h e r a t e o f r o o t e x t e n s i o n . L o f (1976) examined water use e f f i c i e n c y and c o m p e t i t i o n between two a r i d zone a n n u a l g r a s s e s - Hordeum murinum and P h a l a r i s minor i n w h i c h the former i s e c o n o m i c a l and t h e l a t t e r a s p e n d t h r i f t o f w a t e r . I n g e n e r a l he found t h a t P h a l a r i s s u p p r e s s e d b u t d i d not e l i m i n a t e Hordeum, wh i c h e x h i b i t s a r a p i d e a r l y growth (when c o n d i t i o n s a r e f a v o u r a b l e ) i n v e s t i n g l i t t l e i n t h e p r o d u c t i o n o f r o o t s and s p r e a d i n g t h r o u g h t h e s o i l w i t h many n e a r l y - 33 -h o r i z o n t a l t i l l e r s . F u rthermore Hordeum completes i t s p h e n o l o g i c a l c y c l e much f a s t e r t h a n P h a l a r i s and, when f l o w e r -i n g , most o f t h e p h o t o s y n t h e s i s o c c u r s i n i t s awns. P h a l a r i s produces much more d r y m a t t e r t h a n Hordeum, b u t because i t l a c k s t h e s e a d a p t i v e f e a t u r e s i t cannot r e p l a c e the " o p p o r t u n i s t i c " "Hordeum i n a community. 2.3.1.2 B i o c h e m i c a l i n t e r a c t i o n s ( A l l e l o p a t h y ) The term a l l e l o p a t h y was c o i n e d by M o l i s c h (1937) t o r e f e r t o " b i o c h e m i c a l i n t e r a c t i o n s between a l l t y p e s o f p l a n t s i n c l u d i n g m i c r o o r g a n i s m s " . The term c o v e r s b o t h d e t r i m e n t a l and b e n e f i c i a l , r e c i p r o c a l b i o c h e m i c a l i n t e r a c t i o n s . Competi-t i v e i n t e r a c t i o n s among and between p l a n t s a re d i s t i n c t from a l l e l o p a t h y i n t h a t t h e l a t t e r i n v o l v e s a r e l e a s e o f c h e m i c a l compound (by a donor) i n t o the environment w h i c h i n f l u e n c e s t h e growth o f a n o t h e r ( r e c i p i e n t ) growing i n the same e n v i r o n -ment. C o m p e t i t i o n on the o t h e r hand i n v o l v e s t h e removal o f some f a c t o r ( s ) t h a t i s a l s o r e q u i r e d by t h e o t h e r p l a n t s s h a r i n g t h e environment. The r o l e o f a l l e l o p a t h y i n a g r i c u l t u r e has a l o n g h i s t o r y . De C a n d o l l e (1832) suggested t h a t t h e s o i l s i c k n e s s p roblem i n a g r i c u l t u r e might be due t o exudates o f c r o p p l a n t s and t h a t r o t a t i o n o f c r o p s c o u l d h e l p a l l e v i a t e t h e problem. R e c e n t l y , Putman and Duke (1978) have g i v e n a comprehensive r e v i e w on t h e n a t u r e and r o l e o f a l l e l o p a t h y i n a g r i c u l t u r e . A l l e l o p a t h i c compounds can be l e a c h e d from l i v e l e a v e s by r a i n o r i r r i g a t i o n , t h e y may be a c t i v e l y s e c r e t e d by l i v e - 34 -r o o t s , o r t h e y can be l e a c h e d from decomposing shoot o r r o o t m a t e r i a l s . E xcept f o r J u g l a n s n i g r a ( R i c e , 1974) and a few o t h e r s p e c i e s , e.g. C a m e l i n a . m i c r o c a r p a (Grummer and Boye, 1960) t h e major e f f e c t s o f a l l e l o p a t h y on c r o p p r o d u c t i o n would seem t o be a r e s u l t o f r e l e a s e o f p h y t o t o x i c s u b s t a n c e s from p l a n t l i t t e r i n t o the environment ( P a t r i c k , 1971). Some o f t h e most s e r i o u s weeds have been r e p o r t e d t o have some a l l e l o p a t h i c e f f e c t s . The y i e l d r e d u c t i o n s o f c r o p s from q u a c k g r a s s (Agropyron repens (L.) Beauv.) have been a t t r i b u t e d t o c o m p e t i t i o n f o r n u t r i e n t s and w a t e r , o r t o exuda-t i o n o f t o x i c i n h i b i t o r s from t h e weed r h i z o m e s . Bandeen and B u c h h o l t z (1967) demonstrated t h a t s u b s t a n t i a l e a r l y season uptake o f N and K by q u a c k g r a s s c o n t r i b u t e d t o but was not s o l e l y r e s p o n s i b l e f o r t h e r e d u c t i o n i n growth and y i e l d o f c o r n . I t seems t h a t w i t h q u a c k g r a s s b o t h c o m p e t i t i o n and a l l e l o p a t h i c e f f e c t s o c c u r . S i m i l a r l y , y e l l o w nutsedge has been r e p o r t e d t o i n f l i c t c r o p l o s s e s i n b o t h c o r n and soy-beans t h r o u g h a l l e l o p a t h y and c o m p e t i t i o n (Drost and D o l l , 1980). Among c r o p s , r a p e s e e d has been shown t o have a l l e l o -p a t h i c e f f e c t s . Most c r o p p r o d u c t i o n g u i d e s s t a t e t h a t r a p e -seed s h o u l d never be seeded on i t s own s t u b b l e because o f i t s i n c r e a s e d r i s k o f c r o p l o s s e s from d i s e a s e s and i n s e c t b u i l d up. B e s i d e s t h e s e problems, r a p e s e e d i n a d d i t i o n t o b e i n g a heavy u s e r o f s o i l n u t r i e n t s has a l s o been shown t o c o n t a i n a w a t e r - s o l u b l e compound c a p a b l e o f r e t a r d i n g g e r m i n a t i o n and 35 growth o f subsequent c r o p s ( H o r r i c k s , 1969). H o r r i c k s (1975) r e p o r t e d t h a t where wheat o r b a r l e y i m m e d i a t e l y f o l l o w e d a rape c r o p , p l a n t s t a n d s were " t h i n " , m a t u r i t y was d e l a y e d and y i e l d s were reduced t e n t o twenty p e r c e n t . No e f f e c t was v i s i b l e a y e a r a f t e r f a l l o w i n g o r c r o p p i n g . I t seems t h a t a t o x i c s u b s t a n c e i s r e l e a s e d from decomposing s t u b b l e and s i n c e i t s e f f e c t i s not n o t i c e d a y e a r a f t e r f a l l o w i n g o r c r o p p i n g the s u b s t a n c e may not be v e r y s t a b l e i n t h e s o i l o r i t may be e a s i l y l e a c h e d i n t o deeper h o r i z o n s . In g e n e r a l t h e problem o f a l l e l o p a t h i c compounds r e l e a s e d from s t u b b l e may be f a c i n g a g r o n o m i s t s f o r some time t o come. The g e n e r a l f a r m i n g p r a c t i c e i n p r e s e n t days i s a d v a n c i n g towards l e s s d i s t u r b a n c e o f t h e s o i l and hence reduced o r minimum t i l l a g e . The reduced y i e l d s o c c a s i o n a l l y accompanying a d o p t i o n o f minimum t i l l a g e and s t u b b l e m u l c h i n g i n agronomic c r o p s have been a t t r i b u t e d , a t l e a s t i n p a r t , t o t h e r e l e a s e o f g r o w t h - i n h i b i t i n g s u b s t a n c e s from c r o p r e s i d u e s ( P a t r i c k e t a _ l . , 1964). S i m i l a r l y , w i t h the i n c r e a s -i n g use o f h e r b i c i d e s i n agronomic c r o p s , t h e r e i s a l i k e l i -hood f o r i n c r e a s i n g i n c i d e n c e s o f a l l e l o p a t h i c e f f e c t s from the weed l i t t e r . There does not appear t o be any r e s e a r c h c u r r e n t l y b e i n g conducted on t h e s e a s p e c t s -of a l l e l o p a t h y . Two r e c e n t r e s e a r c h p l a n n i n g c o n f e r e n c e s (Anonymous, 1971; 1977), i n t h e USA recommended more i n t e n s i v e i n v e s t i g a t i o n o f t h e e f f e c t s o f a l l e l o p a t h i c s u b s t a n c e s on p l a n t growth dynamics and p h y s i o l o g i c a l p r o c e s s e s . Such i n v e s t i g a t i o n s s h o u l d 36 -c o n t r i b u t e t o our u n d e r s t a n d i n g the importance o f a l l e l o p a t h y i n weed-crop r e l a t i o n s and t i l l a g e p r a c t i c e s . 2.3.2 N o n - c o m p e t i t i v e I n t e r a c t i o n ( C o o p e r a t i o n ) Among S p e c i e s M i x t u r e s Many i n s t a n c e s o f n o n - c o m p e t i t i v e i n t e r a c t i o n a r e known i n mixed p o p u l a t i o n s . There are numerous r e p o r t s o f the y i e l d advantages o f m i x t u r e s o f s p e c i e s as compared t o pure s t a n d s on t h e same l a n d a r e a (Andrew and Kassam, 1976). The y i e l d advantage o f m i x t u r e s has been th e b a s i s o f t h e m u l t i p l e - c r o p p i n g systems commonly used i n t r o p i c a l and sub-t r o p i c a l r e g i o n s . Harper (1964) c i t e s , an example o f the d i r e c t s t i m u l a t i o n o f one s p e c i e s by a n o t h e r , t h e case i n which n i t r o g e n f i x e d by a legume becomes a v a i l a b l e t o a non-legume (see a l s o H a l l , 1974a and b ) . I n a legume-grass m i x t u r e , b o t h s p e c i e s r e l y on t h e s o i l n i t r o g e n s o u r c e d u r i n g th e e a r l y s t a g e s o f growth, but w i t h time t h e legume becomes independent o f t h e s o i l n i t r o g e n and f i x e s a t m o s p h e r i c n i t r o g e n , i n most c a s e s i n e x c e s s o f i t s own needs. Hence the accompanying non-legume s p e c i e s b e n e f i t s from t h e a s s o c i a -t i o n . U n p a l a t a b l e s p e c i e s i n a p a s t u r e o r r a n g e - l a n d may p r o t e c t a n o t h e r s p e c i e s i n c l o s e p r o x i m i t y from b e i n g g r a z e d (Harper et_ al_. , 1961). T a l l , r o b u s t components i n m i x t u r e s on t h e o t h e r hand, may p r o v i d e a wind break f o r the more d e l i c a t e components (Brown and Rosenberg, 1970). N o n - l o d g i n g c e r e a l s are known t o be i n t e r c r o p p e d w i t h t y p e s s u s c e p t i b l e t o l o d g i n g i n o r d e r t o o f f e r p h y s i c a l s u p p o r t , as i n t h e case - 37 -o f o a t s and b a r l e y i n Denmark (de W i t , 1960). I t i s a l s o easy t o v i s u a l i z e t h a t the i n t e r a c t i o n between a t a l l "sun" s p e c i e s and a s h o r t "shade" s p e c i e s may be o f a p o s i t i v e n a t u r e , i . e . t h e shade s p e c i e s a c t u a l l y b e n e f i t s from b e i n g a " l o s e r " i n i t s r e l a t i v e a b i l i t y t o i n t e r c e p t l i g h t (see a l s o Paner, 1975). However, r e l a t i v e l y l i t t l e a t t e n t i o n has been a c c o r d e d t o n o n - c o m p e t i t i v e i n t e r a c t i o n s as compared t o the c o m p e t i t i v e ones. The " c o m p e t i t i o n f o r space" and " p a r t l y t h e same space" as used by de Wit (1960) seems t o be t h e c o r n e r s t o n e f o r i d e n t i f y i n g and s u b s e q u e n t l y q u a n t i f y i n g t h e p r o c e s s / phenomenon o f n o n - c o m p e t i t i v e i n t e r a c t i o n . Indeed H a l l (1974a) extended the model o f de Wit (1960) t o a n a l y z e i n t e r a c t i o n s between a legume and a g r a s s and i t was amply c l e a r t h a t the two p r o c e s s e s o f i n t e r a c t i o n were o c c u r r i n g . 2.4 Methodology i n C o m p e t i t i o n S t u d i e s 2.4.1 I n v e s t i g a t i o n s I n v o l v i n g D u r a t i o n o f C o m p e t i t i o n and D e n s i t i e s o f C o m p e t i t o r s i n A d d i t i v e S e r i e s There have been many d i f f e r e n t k i n d s o f c o m p e t i t i o n e x p e r i m e n t s because o f t h e v a s t d i v e r s i t y o f themes and o b j e c t i v e s o f r e s e a r c h e r s i n v o l v e d i n c o m p e t i t i o n . Crop a g r o n o m i s t s f o r example have aimed a t d e t e r m i n i n g the e x t e n t o f y i e l d r e d u c t i o n s due t o v a r y i n g d e n s i t i e s o f t h e c r o p and/ o r i n v a d i n g weeds. They have t h e r e f o r e d i r e c t e d t h e i r . e x p e r i m e n t s t o d e t e r m i n i n g (a) when c o m p e t i t i o n b e g i n s , 38 -(b) the length of the weed-free period required for maximum y i e l d and (c) the magnitude of the reduction i n crop y i e l d attributable to weed den s i t i e s . To answer the f i r s t question, weeds have been allowed to grow i n the crop for varying lengths of time from crop emergence to maturity. Experiments designed to answer the second question often involve keeping the crop weed-free for varying periods of time after (crop) emergence and then permitting weed growth. Dawson (1977) simulated the d i f f e r e n t periods of weed control provided by s o i l - a p p l i e d herbicides of varying persistence i n f i e l d beans by maintaining weed-free plots for varying periods (0, 2, 3, 4, 5, 7, and 10 weeks or more) after planting. By removing the beans from half of the plots after the prescribed weed-free periods so that l a t e r emerging weeds were allowed to grow with or without the crop, he was also able to integrate into the experiment the e f f e c t of the beans upon l a t e r emerging weeds. It i s possible from such experiments to pi n -point the c r i t i c a l period of weed competition. Work involv-ing weed density and/or time of removal under f i e l d conditions has been reported for giant f o x t a i l with corn and soybean (Knake and S l i f e , 1962) and smooth pigweed (Amaranthus  •hybridus E.) i n corn-'and soybeans (Mpolani et. a l . , 1964). Another view of competition by crop agronomists has been to look at competition as a difference i n a plant's e f f i c i e n c y i n securing the growth requisites for optimal growth and reproduction. Experimentation on these physiolo-- 39 -g i c a l l y o r i e n t e d a s p e c t s o f c o m p e t i t i o n has c e n t r e d i n t r y i n g t o i s o l a t e t h e c o m p e t i t i o n e f f e c t s i n the above- and below-ground environments by means o f a e r i a l and s o i l p a r t i t i o n s i n c o n t a i n e r s (Donald, 1958, Snaydon, 1971). The t e c h n i q u e has been m o d i f i e d v a r i o u s l y s i n c e i t was d e v e l o p e d (Donald, 1958) and b e s i d e s b e i n g a b l e t o accommodate a d d i t i o n and sub-s t i t u t i o n o f t h e components (Snaydon, 1979) the n a t u r e o f the i n t e r a c t i o n has been examined by c h e m i c a l a n a l y s i s o f p l a n t m a t e r i a l s f o r d i f f e r e n c e s i n n u t r i e n t c o n t e n t (Snaydon, 1971). From h i s e x p e r i m e n t s Donald (1958) c o n c l u d e d t h a t t h e r e i s an i n t e r a c t i o n between " l i g h t " and " n u t r i e n t c o m p e t i t i o n " . F u r t h e r m o r e , c o m p e t i t i o n between s p e c i e s , b o t h below and above ground, i s an a c t i v e p r o c e s s t h e outcome o f w h i c h i s dependent on the r e l a t i v e a b i l i t i e s o f t h e s p e c i e s t o c a p t u r e and u t i l i z e a v a i l a b l e r e s o u r c e s (Grime, 1977). I n a l l t h e methods o f s t u d y p r e v i o u s l y used, whether t h e y i n v o l v e p a r t i t i o n s t o s e p a r a t e r o o t and shoot c o m p e t i t i o n o r the a d d i t i o n o f v a r y i n g d e n s i t i e s o f a n o t h e r s p e c i e s t o a r e f e r e n c e s p e c i e s grown a t a c o n s t a n t d e n s i t y ( i n t h e d e n s i t y / time o f removal e x p e r i m e n t s ) , t h e r e are drawbacks t h a t must be c o n s i d e r e d . Thus, i n t h e e x p e r i m e n t s t h a t i n v o l v e r o o t and shoot p a r t i t i o n s the i n t e r a c t i o n s between p l a n t s (or s p e c i e s ) a r e r e s t r i c t e d o n l y t o l a t e r a l d i m e n s i o n s (see f o r example Snaydon, 1979). There i s a l s o the a r t i f i c i a l i t y o f r e s t r i c t i n g t h e r o o t s t o o n l y a p o r t i o n o f t h e a v a i l a b l e s o i l - 40 -i n t h e c o n t a i n e r , a c o n d i t i o n t h a t c o u l d be r a r e i n t h e f i e l d . A n other problem t h a t i s more d i f f i c u l t t o r e s o l v e i s the p o s s i b l e e f f e c t o f t h e p a r t i t i o n s on the component s p e c i e s and t h e i r m i c r o c l i m a t e s . I t i s o b v i o u s t h a t such p a r t i t i o n s can i n f l u e n c e a i r f l o w , r o o t growth and p o s s i b l y l i g h t q u a n t i t y and/or q u a l i t y . However, u s e f u l i n f o r m a t i o n can be o b t a i n e d from such e x p e r i m e n t s but i t s e x t r a p o l a t i o n t o f i e l d c o n d i -t i o n s s h o u l d be h a n d l e d w i t h c a u t i o n . S i m i l a r l y , i n d e n s i t y t y p e s o f e x p e r i m e n t the major problem has been the c o n f o u n d i n g between e f f e c t s due t o change i n t h e p r o p o r t i o n s o f t h e geno-t y p e s and t h e e f f e c t s due t o d i f f e r e n c e s i n t o t a l d e n s i t y . The d e s i g n , however, has been u s e f u l i n weed-crop s i t u a t i o n s t o d etermine such i m p o r t a n t c o n c e p t s as c r i t i c a l weed d e n s i t y f o r weeds, c r i t i c a l t i me o f r e m o v a l , economic t h r e s h o l d f o r weeds and more r e c e n t l y c o m p e t i t i o n i n d i c e s (Dew, 1972). The d e s i g n i s r e l e v a n t t o a c t u a l f i e l d s i t u a t i o n s i n w h i c h weeds in v a d e f i e l d c r o p s , w i t h v a r y i n g t i m e s o f emergence, numbers and s p e c i e s c o m p o s i t i o n . 2.4.2 I n v e s t i g a t i o n s I n v o l v i n g Replacement S e r i e s A d i f f e r e n t approach t o p l a n t i n t e r a c t i o n s was d e v e l o p e d by de Wit (1960) and h i s a s s o c i a t e s a t Wageningen. The main f e a t u r e o f t h e i r s u b s t i t u t i v e d e s i g n , r e f e r r e d t o as a r e p l a c e m e n t s e r i e s , i s t h a t t h e p r o p o r t i o n s o f t h e compo-nent s p e c i e s (a and b) i n the m i x t u r e are i n v e r s e l y v a r i e d w h i l e t h e o v e r a l l t o t a l d e n s i t y ( p l a n t s per u n i t area) remains - 41 -constant. In t h i s way substitutive designs avoid density -dependent ef f e c t s and allow precise comparisons of neighbour ef f e c t s at one constant density (Trenbath and Harper, 1973). Replacement series experiments have mainly been used to study the interactions between two species and they were used by de Wit to look at "space" re l a t i o n s between plants alone and i n mixtures. The most o r i g i n a l and c h a r a c t e r i s t i c feature of the replacement series l i e s i n the analysis of the data, both graphically and mathematically. The simple assump-tion i n the analysis, however, i s that the y i e l d of each species i n a mixture i s proportional to the share of the environmental resources i t can acquire. If t h i s sharing i s unequal then the stronger competitor w i l l acquire more and the weaker species l e s s . To f a c i l i t a t e the analysis, the two species a and b are grown i n monocultures and i n mixtures of varying propor-tions so that the f i n a l density (Z) i s kept constant: Z a ^ " ( Z a + Z b , + Z b / ( Z a + Z b ) = 1 l a * where Z and Z, are the actual densities for species a and a D a species b respectively. In terms of r e l a t i v e densities, z a and z^, equation l a can be rewritten: z +z, - 1 l b * a b where z a = { Z a ) / ( Z a + Z b > a n d zb = ( Z b ) / ( Z a + Z b > * See Appendix 14 and 15 - 42 -The component yields from the mixtures are compared with t h e i r respective monoculture y i e l d s and the differences are interpreted as revealing whether competition , i s occurring or not, and i f so which species i s the more successful. The comparison can be represented i n graphical form, with the actual y i e l d s being represented on the ordinate and the r e l a t i v e seed proportions on the abscissa, as depicted for a hypothetical example i n Figure 2.2. The y i e l d measures may be any of the growth components of plants: seed y i e l d , dry matter y i e l d , t i l l e r numbers, leaf area, plant height, etc. The example depicted i n Figure 2.2 represents one of the three cases: (a) individuals of the two species (a and b) do not i n t e r f e r e with each other; (2) interference has not yet started (either the plants are planted so far apart that i n d i v i d u a l demands for optimal growth are met or the plants are s t i l l young and no i n t e r s p e c i f i c contacts have occurred); or (3) the two species have an e f f e c t of equal magnitude on the growth of each other. The two species may make equal demands on the environment but because they may d i f f e r i n the e f f i c i e n c i e s of t h e i r " u t i l i z a t i o n " they therefore contribute d i f f e r e n t l y to the mixture y i e l d . This r e l a t i o n -ship has been termed "mutually exclusive" (de Wit, 1960). In these interpretations, i t i s important to recognize that i n cases 1 and 2, where no i n t e r s p e c i f i c interference i s occurring, the l i n e a r r e l a t i o n s h i p between y i e l d and density for each species implies that there i s no i n t r a s p e c i f i c compe-t i t i o n among the individuals of either species. 43 -Figure 2.2. Replacement series diagram of species a and species b grown i n monoculture and i n mixtures at constant t o t a l density. 44 -Perhaps t h e most comprehensive i n t e r p r e t a t i o n , o f the repla c e m e n t s e r i e s diagram i s t h a t by H i l l and Shimamoto (1973). When one s p e c i e s g a i n s i n t h e m i x t u r e a t t h e expense o f t h e o t h e r such t h a t t h e g a i n s by one s p e c i e s c o u n t e r -b a l a n c e s t h e l o s s by the o t h e r , "compensation" between t h e s p e c i e s has o c c u r r e d . I n such an i n t e r a c t i o n t h e c o n t r i b u t i o n by t h e i n d i v i d u a l components t o the t o t a l m i x t u r e y i e l d cannot be p r e d i c t e d . However, when the g a i n s and l o s s e s by t h e component s p e c i e s do not c o u n t e r b a l a n c e , t h e n "complementation" has o c c u r r e d . Complementation can be p o s i t i v e (when t h e m i x t u r e performance exceeds t h e average o f t h e component mono-c u l t u r e s ) o r n e g a t i v e (when m i x t u r e performance f a l l s below t h a t o f monoculture a v e r a g e ) . P o s i t i v e complementation o c c u r s when b o t h s p e c i e s f a i l t o s u f f e r as much y i e l d r e d u c -t i o n as would be e x p e c t e d from t h e monoculture r e s p o n s e s , p o s s i b l y because o f : (1) a s y m b i o t i c r e l a t i o n s h i p whereby one s p e c i e s a i d s t h e o t h e r (e.g. i n grass-legume m i x t u r e ) ; o r (2) t h e growth p e r i o d s o f t h e s p e c i e s do not c o i n c i d e i n t h e growing p e r i o d . I f one s p e c i e s produces a c h e m i c a l t h a t r e duces t h e growth o f t h e o t h e r s p e c i e s o r o f b o t h s p e c i e s , t h e n a n e g a t i v e complementation may o c c u r . P o s i t i v e and-."-' ,negative complementation have a l s o been d e s c r i b e d as c o -o p e r a t i o n and mutual i n h i b i t i o n r e s p e c t i v e l y ( H i l l and Shimamoto, 1973). I n g e n e r a l , however, t h e component y i e l d c u r v e s i n t h e repl a c e m e n t s e r i e s diagrams a re convex f o r t h e r e l a t i v e l y b e t t e r c o m p e t i t o r and concave f o r t h e weaker c o m p e t i t o r (see a l s o Harper and McNaughton, 1962). A d i r e c t comparison o f t h e two s p e c i e s cannot be made from t h e a b s o l u t e y i e l d s i n F i g u r e 2.2. I n o r d e r t o make comparisons between t h e s p e c i e s on an e q u a l f o o t i n g , " r e l a -t i v e y i e l d " r a t h e r t h a n a b s o l u t e y i e l d i s used, where R e l a t i v e Y i e l d (r) = Y i e l d o f Component i n M i x t u r e (0) 2 * Y i e l d o f Component i n Pure Stand (M) The r e l a t i v e y i e l d s f o r s p e c i e s a (r ) and s p e c i e s b (r, ) c l i J summed t o g e t h e r g i v e t h e " r e l a t i v e y i e l d t o t a l " (RYT) ,(de W i t , 1960) : RYT = r & + r b 3 * The RYT can the n be used t o d e s c r i b e t h e mutual i n t e r a c t i o n s t h a t o c c u r between s p e c i e s , when t h e t o t a l d e n s i t y i s s u f f i -c i e n t l y g r e a t t o ensure t h a t t h e s p e c i e s impinge upon each o t h e r , as f o l l o w s : 1. RYT = 1: T h i s s i t u a t i o n i m p l i e s t h a t each s p e c i e s i s making t h e same demand f o r "space" as t h e o t h e r . They a r e m u t u a l l y e x c l u s i v e (de Wit and Van den Bergh, 1965) . 2. RYT >: 1: T h i s can o c c u r when t h e two s p e c i e s (a) make d i f f e r e n t demands on t h e same r e s o u r c e ; (b) occupy d i f f e r e n t n i c h e s i n time 'or space; o r (c) e x h i b i t some k i n d o f s y m b i o t i c r e l a t i o n s h i p . 3. RYT < 1: T h i s s i t u a t i o n o c c u r s when one o r b o t h s p e c i e s a re s e r i o u s l y a f f e c t e d by i n t e r s p e c i f i c com-p e t i t i o n and may i n d i c a t e a l l e l o p a t h y . * See Appendix 14 and 15 46 -The model can also be used to predict y i e l d of the component species i n the mixture. When there i s no competi-t i o n , the yi e l d s of species a and are given by (de Wit, 1960): °a = { ( z a ) / ( z a + Z b ! l M a ; a n d °b = l ( zb> 1 ( za + zbK"" 4 a & b* where 0 = y i e l d i n mixture M = y i e l d i n pure stands z = r e l a t i v e seed rate (ratio of ind i v i d u a l component seed rate to that of t o t a l mixture; Equation l b ) . When the o v e r a l l spacing i s reduced i n t r a - and i n t e r s p e c i f i c competition occurs and the y i e l d of the component species i n the mixture i s no longer proportional to the r e l a t i v e density. The density i n equations 4a and b i s now weighted by a competition factor, k(de Wit, 1960): °a = KbZa> / ( kab za + zbf Ma a n d Y ' \ °b =Ka a ) / ( kba za + ZbK " — — - — 5a & b * where k ^  i s the "r e l a t i v e crowding c o e f f i c i e n t " for species a with respect to species b. The r e l a t i v e crowding c o e f f i c i e n t i s a measure of the extent to which one species infringes upon the space available to the other species. Generally, estimates of the mean k-values are obtained by substituting for Oa, and and i n equations 6a and b which are rearrangements of equations 5a and b: * See Appendix 15 kab = ( 0 a Z b ) / ( M a - ° a ) z a ; kba = ( 0 b Z a ) / ( M b - ° b ) z b 6 a & b * From the estimated k, estimates of the r e l a t i v e y i e l d s (r) for the two species can be obtained for d i f f e r e n t r e l a t i v e densities i n order to obtain smooth curves such as those shown in Figure 2.3. According to Bennett (1975) and also as described i n de Wit (1960) the curves for the in d i v i d u a l species i n such replacement diagram are obtained by an i t e r a -t i v e process i n which estimates of k may be adjusted to provide the best v i s u a l f i t to the experimental data. This approach has been j u s t i f i e d by de Wit (1960) on the grounds that i n many interactions i t has been found that RYT = 1.0. The method has been found to hold i n a wide variety of cases. Trenbath (1974) conducted a survey of 572 mixtures analyzed i n t h i s way and found that the mean values for RYT were 1.027 ± 0.006. The de Wit model was developed to i d e n t i f y cases i n which species compete for the same space. This was shown to be the case when RYT i s unity, but the same conclusion i s also obtained from the products of the crowding c o e f f i c i e n t s (K = k , x k, ) . Thus: ab ba 1. If K = 1, the species crowd for the same space; 2. If K > 1, they crowd for a space that i s par t l y the same or one species benefits from the * See Appendix 15 - 48 -1 0 Figure 2.3. Replacement series diagram base upon r e l a t i v e y i e l d s ( r ) . - 49 -presence of the other; 3. If K 1, one species hampers the growth of the other by some means other than crowding for the same space. Yet another approach to the analysis of replacement series was also developed by de Wit (I960), and u t i l i z e s the r a t i o diagram i n which the r a t i o of the yi e l d s of the compo-nent species (0 /0, ) i s plotted against the r a t i o of t h e i r a o densities (za/zj-,) > a s depicted i n Figure 2.4. In Figure 2.4a species a i s the more aggressive, since the r a t i o l i n e i s above the equilibrium l i n e . The equilibrium l i n e depicts the sit u a t i o n i n which k ^ = k^ a = 1.0, i . e . the two species are competing equally for i d e n t i c a l resources, and bisects the r a t i o diagram with a slope of 45°. In Figure 2.4b, species a i s the less aggressive, since the r a t i o l i n e i s below the equilibrium l i n e . Figure 2.4c, with a slope 1 depicts the sit u a t i o n i n which the two species either promote each other's growth, or compete or "crowd" for space and resources which are not i d e n t i c a l , while Figure 2.4d with a slope 1 is i n d i c a t i v e of a si t u a t i o n i n which one species hampers or i n h i b i t s the growth of the other by some means other than competing for the same space or resources. In the cases depicted i n Figure 2.4c and d, de Wit (1960) also showed that the curves are actually S-shaped, with t h e i r ends p a r a l l e l to the equilibrium l i n e . - 50 -Figure 2.4. Ratio diagrams for various binary replacement s e r i e s . - 51 -The de Wit model has been extended v a r i o u s l y t o o f f e r s t a t i s t i c a l a n a l y s i s (Thomas, 1970) and to e x p l a i n the mecha-nisms of t h e i n t e r a c t i o n s t h r o u g h n u t r i e n t ( H a l l , 1974b) and p l a n t a n a l y s i s ( H a l l , 1974a and b ) . The e x t e n s i o n o f t h e model, e s p e c i a l l y t h a t by H a l l (1974a and b) i n t e g r a t e s the two major approaches t o p l a n t i n t e r a c t i o n s d e v e l o p e d by Donald (1958) and de Wit (1960). The use o f r e p l a c e m e n t s e r i e s has p r o v e d u s e f u l i n u n d e r s t a n d i n g th e i n t e r a c t i o n s i n v o l v e d i n v a r i o u s s p e c i e s a s s o c i a t i o n s : (1) i n c r o p agronomy (de W i t , 1960; Baeumer and de W i t , 1968; W i l l e y and O s i r u , 1972; O s i r u and W i l l e y , 1972; W i l l e y , 1979; F i s h e r , 1979); (2) i n p a s t u r e s i n v o l v i n g grass/legume m i x t u r e s ( H a l l , 1974a and b; de Wit e_t a l . , 1966; B a k h u i s t and K l e t e r , 1965) as w e l l as. i n combina-t i o n s o f g r a s s e s ( H i l l and Shipmamoto, 1973; Haggar, 1979); and (3) i n weed-crop s i t u a t i o n s ( E l b e r s e and K r u y f , 1979; Eussen, 1979; Ivens and Mlowe, 1980; P e r k a s e n e t a l . , 1980a and b) . H a l l (1974a) i s worthy o f s p e c i a l mention because i t forms t h e backbone o f the wide a p p l i c a t i o n o f t h e r e p l a c e m e n t s e r i e s e x p e r i m e n t s . He used d a t a from V a l l i s e t a l . (1967) i n w h i c h the n i t r o g e n r e l a t i o n s o f Rhodes g r a s s ( C h l o r i s  gayana) and T o w n s v i l l e s t y l o ( S t y l o s a n t h e s h u m i l i s ) were i n v e s t i g a t e d . These c o n t r a s t i n g s p e c i e s p r o v i d e d an o p p o r t u -n i t y t o examine an a s s o c i a t i o n i n w h i c h t h e r e was a p o t e n t i a l i n b o t h c o m p e t i t i v e i n t e r f e r e n c e and c o o p e r a t i o n (see F i g u r e 2.4 a b ove). U s i n g a n a l y s i s p e r t i n e n t t o t h e r e p l a c e m e n t s e r i e s (as d i s c u s s e d above) t h e a u t h o r was a b l e t o i l l u s t r a t e - 52 -t h a t a l t h o u g h c o m p e t i t i v e i n t e r f e r e n c e was o c c u r r i n g t o the advantage o f Rhodes g r a s s , n o n - c o m p e t i t i v e i n t e r a c t i o n ( i n v o l v i n g a t m o s p h e r i c n i t r o g e n which Rhodes g r a s s c o u l d not u t i l i z e d i r e c t l y ) was a l s o o c c u r r i n g . De Wit (1960) and Baeumer and de Wit (1968) suggested t h a t t h e b i n a r y r e p l a c e m e n t s e r i e s model can be extended t o m i x t u r e s o f more th a n two s p e c i e s . De Wit (1960) proposed m a t h e m a t i c a l e x p r e s s i o n s , analogous t o t h o s e f o r b i n a r y m i x t u r e s , t o d e s c r i b e c o m p e t i t i v e i n t e r a c t i o n s i n n s p e c i e s . The e x p r e s s i o n s f o r multicomponent m i x t u r e s were a r r i v e d a t by s u p p o s i n g t h a t one o f t h e s p e c i e s i n a m i x t u r e does not grow a t a l l . Hence, i n a m i x t u r e s c o m p r i s i n g n s p e c i e s , (n-1) independent r e l a t i v e c r o w d i n g c o e f f i c i e n t s w i l l be o b t a i n e d by c u l t i v a t i n g t h e s p e c i e s i n (n-1) b i n a r y c o m b i n a t i o n s under s i m i l a r c o n d i t i o n s . The r e l a t i v e c r o w d i n g c o e f f i c i e n t s o f t h e component s p e c i e s are e x p r e s s e d w i t h r e s p e c t t o an a r b i t r a r y r e f e r e n c e s p e c i e s w h i c h i s assumed t o have a r e l a -t i v e c r o w d i n g c o e f f i c i e n t e q u a l t o one. The proposed m a t h e m a t i c a l e x p r e s s i o n s h o l d i f t h e p l a n t s grow s i m u l t a n e -o u s l y , compete f o r the same r e s o u r c e s and the growth c u r v e s f o r t h e s p e c i e s a r e o f t h e same form (de W i t , 1960). The q u a l i t a t i v e a s p e c t o f t h e model were i l l u s t r a t e d by de Wit (1960) u s i n g d a t a by H a r l a n and M a r t i n i (1938) f o r 10 c u l t i v a r s o f b a r l e y grown i n b i n a r y m i x t u r e s f o r 13 y e a r s w i t h t h e s e e d i n g r a t e s f o r each c u l t i v a r f o r each s u c c e e d i n g y e a r b e i n g p r o p o r t i o n a l t o t h e seed y i e l d o b t a i n e d i n the - 53 -p r e v i o u s y e a r . The " i n t e r m e d i a t e " c u l t i v a r g a i n e d f i r s t and l o s t i n subsequent y e a r s , w h i l e the " w i n n i n g " c u l t i v a r g a i n e d and t h e " l o s i n g " one l o s t each y e a r . The e x t e n s i o n o f t h e b i n a r y model t o t h r e e o r more s p e c i e s l e d de Wit (1960) t o p o s t u l a t e t h a t t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t s f o r t h e b i n a r y c o m b i n a t i o n s a r e i n t e r -r e l a t e d by t h e e q u a t i o n : k , = k x k , 7 ab ac cb where the s u b s c r i p t s r e f e r t o s p e c i e s a, b and c, and k i s as d e f i n e d by E q u a t i o n 6, p r o v i d e d t h a t a l l s p e c i e s are competing f o r t h e same space, and t h e r e l a t i v e y i e l d t o t a l s a r e e q u a l t o one. However, i t appears t h a t t h i s r e l a t i o n s h i p has never been t e s t e d by d i r e c t e x p e r i m e n t a t i o n . When a t h i r d s p e c i e s i s i n t r o d u c e d i n t o a b i n a r y m i x t u r e e x p e r i m e n t , t h r e e changes i n t h e o v e r a l l e x p e r i m e n t a -t i o n o c c u r : (1) t h e number o f e x p e r i m e n t a l u n i t s i n c r e a s e s r a p i d l y , (2) t h e n a t u r e o f i n t e r a c t i o n s i s m o d i f i e d t o accom-modate the impact o f t h e t h i r d s p e c i e s on each o f t h e i n i t i a l two s p e c i e s i n d i v i d u a l l y and i n c o m b i n a t i o n , and hence, (3) t h e m a t h e m a t i c a l and g r a p h i c a l a n a l y s e s o f the d a t a a r e a l s o m o d i f i e d . I n t e r n a r y r e p l a c e m e n t s e r i e s , t r e a t m e n t s i n v o l v i n g b i n a r y c o m b i n a t i o n s o f t h e component s p e c i e s and t h e i r i n d i v i d u a l m o n o c u l t u r e s must a l s o be i n c o r p o r a t e d . Hence, t h e r e l a t i v e performance o f each s p e c i e s can be s t u d i e d i n mono-54 -c u l t u r e , i n b i n a r y m i x t u r e s and i n t e r n a r y m i x t u r e s . As a r e s u l t o f t h e problem o f management, t h e number o f a d d i t i o n a l t r e a t m e n t s and f a c t o r s i n t e r n a r y r e p l a c e m e n t s e r i e s i s i n e v i t a b l y k e p t s m a l l (see H a i z e l , 1972). H a i z e l (1972) s t u d i e d i n t e r a c t i o n s between b a r l e y (Hordeum v u l g a r e L. c v . P r o c t o r ) , w h i t e mustard ( S i n a p i s a l b a L . ) , and poppy (Papaver  rhoeas L.) i n pure and mixed s t a n d s o f two and t h r e e s p e c i e s i n r e p l a c e m e n t s e r i e s a t c o n s t a n t d e n s i t y o f 36 p l a n t s per p o t . The b i n a r y m i x t u r e s were i n 2:2 r a t i o s w h i l e t h e t e r n a r y c o m b i n a t i o n s were i n the r a t i o s o f 2:1:1. The number o f v a r i a n t s i n t h e ex p e r i m e n t was l i m i t e d by the time and . <: r e s o u r c e s . H a i z e l and Harper (1973) found t h a t i n b a r l e y , w h i t e mustard and w i l d o a t s , t h e e f f e c t o f t h e weeds t o g e t h e r on the c r o p c o u l d n ot be p r e d i c t e d from t h e i r i n d i v i d u a l e f f e c t s i n b i n a r y m i x t u r e s w i t h t h e c r o p . M i x t u r e s o f mustard and w i l d o a t s i n b a r l e y , and mustard and b a r l e y i n w i l d o a t s produced l e s s e f f e c t on t h e r e f e r e n c e s p e c i e s t h a n t h e sum o f t h e i r i n d i v i d u a l e f f e c t s . Hence t h e i n t e r a c t i v e p r o c e s s e s i n b i n a r y and t e r n a r y m i x t u r e s a re not n e c e s s a r i l y t h e same and t h e y i e l d s o f t h e components i n t h e t e r n a r y m i x t u r e s may not be a c c u r a t e l y p r e d i c t e d from t h e i r m o n o c u l t u r e s o r b i n a r y m i x t u r e s (Harper, 1964; Baeumer and de W i t , 1968). - 56 -2.5 C o m p e t i t i o n I n d i c e s I n n a t u r a l communities, m u l t i p l e - c r o p p i n g s i t u a t i o n s , p a s t u r e s and i n crop-weed a s s o c i a t i o n s , s p e c i e s m i x t u r e s a r e the r u l e r a t h e r t h a n t h e e x c e p t i o n . S t u d i e s i n p a s t u r e and m u l t i p l e c r o p p i n g s i t u a t i o n s have c e n t r e d on o b t a i n i n g s p e c i e s c o m b i n a t i o n s t h a t would g i v e the b e s t y i e l d r e l a t i v e t o t h e i r pure s t a n d s o r d e s i g n i n g methods t h a t would b e s t q u a n t i f y y i e l d advantage from m i x t u r e s ( T r e n b a t h , 1974, 1976; Donald, 1963). To t h i s end RYT has been w i d e l y used t o g e t h e r w i t h the analogous "Land E q u i v a l e n t R a t i o " (LER) i n m u l t i p l e -c r o p p i n g s i t u a t i o n s ( W i l l e y and Rao, 1980). I n crop-weed s t u d i e s v a r i o u s a n a l y s e s have been d e v e l o p e d t o determine t h e c r i t i c a l d e n s i t y and the c r i t i c a l t i me f o r weeds t o cause economic l o s s e s and v a r i o u s r e g r e s s i o n e q u a t i o n s have been used ( C h i s a k a , 1977). The o n l y a s p e c t o f m i x t u r e i n t e r a c t i o n s y e t t o be e x p l o i t e d i n more d e t a i l i s a means o f q u a n t i f y i n g t h e a c t u a l c o m p e t i t i o n between and among p l a n t s p e c i e s . V a r i o u s a t t e m p t s have been made a l o n g t h e s e l i n e s (de W i t , 1960; G.A. M c l n t y r e , i n Donald, 1963; Dew, 1972). M c l n t y r e ' s approach t o q u a n t i f y i n g i n t e r s p e c i f i c c o m p e t i t i o n i s based on t h e a d d i t i v e s e r i e s d e s i g n i n wh i c h the t o t a l d e n s i t y o f t h e m i x t u r e s and o f each pure s t a n d a r e e q u a l . The y i e l d p e r p l a n t o f each s p e c i e s i n t h e pr e s e n c e and i n t h e absence o f the o t h e r a r e d i s p l a y e d g r a p h i c a l l y on a l o g - l o g s c a l e such t h a t the y i e l d d e p r e s s i o n o f a s p e c i e s i n the m i x t u r e and i n the pure s t a n d can be d e p i c t e d . The - 56 -d e n s i t y a t w h i c h t h e y i e l d per p l a n t i n t h e pure s t a n d and i n t h e m i x t u r e a r e e q u a l i s t h e pure c u l t u r e e q u i v a l e n t . M c l n t y r e p r oposed a method o f computing an i n d e x o f c o m p e t i -t i o n (CI) based on t h e pure c u l t u r e e q u i v a l e n t s and t h e a c t u a l d e n s i t y o f t h e p l a n t s i n t h e m i x t u r e a s : C I _ P r o d u c t o f Pure C u l t u r e E q u i v a l e n t s ' 8 P r o d u c t o f A c t u a l Number o f P l a n t s i n M i x t u r e M c l n t y r e ' s i n d e x o f c o m p e t i t i o n i s based on t h e assumption t h a t "the s l o p e o f t h e r e g r e s s i o n between the l o g a r i t h m o f the w e i g h t o f i n d i v i d u a l p l a n t s and t h e l o g a r i t h m o f p o p u l a -t i o n ( i n d i c a t o r + c o m p e t i t o r ) d e n s i t y i s p r o p o r t i o n a l t o t h e i n t e n s i t y o f c o m p e t i t i o n " (Harper, 1961). I n t e r p r e t a t i o n o f the i n d e x o f c o m p e t i t i o n ( E q u a t i o n 8) i s based on whether the m i x t u r e s a r e b e n e f i c i a l o r d e t r i m e n t a l . I f the mutual d e p r e s s i o n o f s p e c i e s i n m i x t u r e , i s l e s s t h a n i n pure s t a n d s , t h e m i x t u r e i s c o n s i d e r e d b e n e f i c i a l . Hence, a c o m p e t i t i o n i n d e x o f l e s s t h a n 1.0 i n d i c a t e s t h a t t h e r e i s m i n i m a l c o m p e t i t i o n , and t h e m i x t u r e s a re b e n e f i c i a l . A v a l u e o f 1.0 o r l a r g e r i n d i c a t e s a m i x t u r e o f no b e n e f i t o r one o f d e t r i -m e n t a l e f f e c t . McCown and W i l l i a m s (1968) used M c l n t y r e ' s method t o a s s e s s the i n t e r a c t i o n between s o f t - c h e s s (Bromus m o l l i s L . ) , and b r o a d l e a f f i l a r e e (Erodium b o t r y s (Cav.) B e r t r o l . ) , i n c o n t a i n e r s under low and h i g h l e v e l s o f s u l p h u r . The a u t h o r s o b t a i n e d CI < 1 under low l e v e l s and >1 under h i g h s u l p h u r , w h i c h suggested t h a t m i x t u r e s o f Bromus and Erodium were b e n e f i c i a l a t low s u l p h u r l e v e l s - 57 -and d e t r i m e n t a l a t h i g h s u l p h u r l e v e l s . However, as p o i n t e d out e a r l i e r by Donald (1963)',_ .other a p p l i c a t i o n s o f the approach y i e l d e d c o n f l i c t i n g r e s u l t s . Dew (1972) d e r i v e d a c o m p e t i t i o n i n d e x f o r w i l d o a t s i n wheat, b a r l e y and f l a x , e s s e n t i a l l y based on the a d d i t i v e s e r i e s approach. The method i s based on r e g r e s s i n g y i e l d o f t h e i n d i c a t o r s p e c i e s (crop) on t h e square r o o t o f t h e d e n s i t y o f t h e accompanying s p e c i e s , t h u s : Y = a-b N / X, 9 where Y i s the y i e l d o f the i n d i c a t o r s p e c i e s ( c r o p ) , X i s t h e d e n s i t y o f t h e accompanying s p e c i e s (weed), a i s t h e i n t e r -c e p t on the o r d i n a t e and b i s t h e r e g r e s s i o n c o e f f i c i e n t o f Y on s/ X . The c o e f f i c i e n t (b^) o b t a i n e d from th e r e g r e s -s i o n o f v a l u e s o f b and a o b t a i n e d from s e v e r a l e x p e r i m e n t s o r f i e l d o b s e r v a t i o n s ( w i t h t h e c o n s t r a i n t t h a t the r e g r e s s i o n l i n e p a sses t h r o u g h t h e o r i g i n ) i s d e f i n e d as t h e " i n d e x o f c o m p e t i t i o n " , C . I . , i . e . CI = b, = -k— , 10 x a The i n d e x was a l s o c o n f i r m e d by Hamman (197 9 ) . The method has been used t o d e t e r m i n e the i n d e x f o r v a r i o u s weeds i n c r o p s : w i l d o a t s i n rape (Dew and Keys, 1976); l a m b s q u a r t e r s and green f o x t a i l i n c o r n ( S i b u g a , 1978); and b a r n y a r d g r a s s i n r e d r o o t pigweed ( M i n j a s and Todd, 1981). The i n d e x can be used t o g e t h e r w i t h the weed-free y i e l d and the d e n s i t y o f - 58 -weed i n f e s t a t i o n t o p r e d i c t y i e l d r e d u c t i o n s from weeds (see S e c t i o n 2.7). The model d e v e l o p e d by de Wit (1960) p r o v i d e s an a l t e r n a t i v e measure of c o m p e t i t i o n , based upon th e e s t i m a t e d r e l a t i v e c r o w d i n g c o e f f i c i e n t s (k) i n b i n a r y r e p l a c e m e n t s e r i e s , as d e s c r i b e d above. S i n c e the s p e c i e s w i t h t h e g r e a t e r v a l u e o f k i s t h e b e t t e r c o m p e t i t o r i n a p a i r o f s p e c i e s grown i n a m i x t u r e , t h e i n d i v i d u a l v a l u e s o f k and t h e i r p r o d u c t (K) are used t o d e s c r i b e t h e e x t e n t and t h e n a t u r e o f i n t e r a c t i o n between t h e components grown i n a b i n a r y m i x t u r e a t c o n s t a n t t o t a l d e n s i t y . T h i s i s t h e major c o n t r a s t between de W i t ' s (1960) i n d e x o f c o m p e t i t i o n and t h e o t h e r i n d i c e s d i s c u s s e d e a r l i e r . However, W i l l e y and Rao (1980) have p o i n t e d out one d i f f i c u l t y w i t h such k - v a l u e s , namely t h a t t h e y r e a l l y r e f e r t o c o m p e t i t i v e n e s s a g a i n s t a second s p e c i e s r e l a t i v e t o t h e monoculture s i t u a t i o n s , and hence do not i n d i c a t e s o l e l y t h e i n t e r s p e c i f i c c o m p e t i t i o n w h i c h may be p r e s e n t . I n t h e s i m p l e s t r e p l a c e m e n t s e r i e s , t h e d i a l l e d ! , f o r example, t h e r e l a t i v e y i e l d s o f t h e competing s p e c i e s when p r e s e n t a t e q u a l d e n s i t y ( i . e . a 1:1 r a t i o ) a r e d e t e r m i n e d by t h e e f f e c t o f r e p l a c i n g h a l f t h e p l a n t s i n t h e monoculture by p l a n t s o f th e second s p e c i e s . However, a t any t o t a l d e n s i t y s u f f i c i e n t f o r i n t e r f e r e n c e between the i n d i v i d u a l s o f e i t h e r s p e c i e s i n m onoculture t o o c c u r , such r e p l a c e m e n t p r o v i d e s i n f o r m a t i o n w hich i s r e l a t i v e o n l y t o t h e performance i n m o n o c u l t u r e . S i n c e t h e l a t t e r a l r e a d y i n c l u d e s t h e e f f e c t s o f i n t r a -- 59 -s p e c i f i c c o m p e t i t i o n , the i n f o r m a t i o n o b t a i n e d from r e p l a c e -ment s e r i e s s t u d i e s a n a l y z e d by de W i t ' s methods i s i n e v i t a b l y confounded by t h e s i m u l t a n e o u s i n v o l v e m e n t o f b o t h i n t r a -and i n t e r - s p e c i f i c e f f e c t s . The p r e c i s e magnitude o f t h e c o m p e t i t i v e n e s s o f i n d i v i d u a l s p e c i e s i n rep l a c e m e n t s e r i e s e x p e r i m e n t s has been the o b j e c t i v e o f f u r t h e r developments. M c G i l c h r i s t (1965) proposed t h a t t h e " a g g r e s s i v e n e s s 1 1 o f a s p e c i e s c o u l d be e s t i m a t e d from, I ( o a - m a ) + | ( m b - o b ) , 11 where a l l y i e l d s a r e e x p r e s s e d on a per p l a n t b a s i s , o & and o, a r e t h e y i e l d s from 1:1 m i x t u r e s , and m and m, a r e mono-b -1 ' a b c u l t u r e y i e l d s . I n terms o f t o t a l y i e l d s , e x p r e s s i o n 11 may be r e w r i t t e n a s : (O a- 2M a) + (*M b-O b), 12 M c G i l c h r i s t and T r e n b a t h (1971) m o d i f i e d t h i s e x p r e s s i o n , i n o r d e r t o d e f i n e " a g g r e s s i v i t y " , A a b , i n 1:1 m i x t u r e s , as i °a °b A = i 13 ab m rtv a b where y i e l d s a r e a g a i n e x p r e s s e d on a per p l a n t b a s i s . On a t o t a l y i e l d b a s i s , e q u a t i o n 13 becomes A a b M M, ' ~ 1 4 a b - 60 -w h i c h r e d u c e s t o A a b = * ( r a " r b l > ~ 1 5 where r a and r ^ a r e t h e r e l a t i v e y i e l d s o f s p e c i e s a and b. H a l l (1978) p o i n t e d o u t , however, t h a t a g g r e s s i v i t y d e t e r m i n e d from s i m p l e d i a l l e l r e p l a c e m e n t s e r i e s a c c o r d i n g t o e q u a t i o n 15 f a i l s t o d i f f e r e n t i a t e between s i t u a t i o n s i n w h i c h t h e n a t u r e o f t h e c o m p e t i t i o n may be v e r y d i f f e r e n t . U s i n g two examples i n t h e f i r s t o f which r & = 0.75 and r, = 0.25, and i n t h e second, r =1.0 and r, = 0.5, he D a a p o i n t e d out t h a t b o t h g i v e c a l c u l a t e d a g g r e s s i v i t i e s o f 0.25, but i n the f i r s t c a s e , s p e c i e s a g a i n s s o l e l y a t t h e expense of s p e c i e s b, whereas i n the second case i t does n o t , because the r e l a t i v e y i e l d t o t a l s a r e q u i t e d i f f e r e n t ; RYT = 1.0 vs 1.5, r e s p e c t i v e l y . H a l l (1978) f u r t h e r p o i n t e d out t h a t t h e r e s t r i c t i o n o f r e p l a c e m e n t s e r i e s t o t h e s i m p l e d i a l l e l i s i n e f f i c i e n t , and t h a t t h e use o f r e l a t i v e r a t h e r t h a n a b s o l u t e y i e l d s may i t s e l f be m i s l e a d i n g , s i n c e , depending upon th e c o m b i n a t i o n o f s p e c i e s i n v e s t i g a t e d , r e s p o n s e s may be v e r y d i f f e r e n t i n a b s o l u t e terms. For example, i n one c o m b i n a t i o n , t h e lower y i e l d i n g s p e c i e s may be the a g g r e s s o r , w h i l e i n a n o t h e r , t h e h i g h e r y i e l d i n g s p e c i e s may be t h e a g g r e s s o r , and y e t i n b o t h c o m b i n a t i o n s , t h e i r r e l a t i v e p erformances may be i d e n t i c a l . More r e c e n t l y , W i l l e y and Rao (1980) proposed t h e use of the C o m p e t i t i o n R a t i o (CR), d e f i n e d as the r a t i o o f the - 61 -r e l a t i v e y i e l d s of two species (r and r^) grown i n mixture divided by the r a t i o of t h e i r densities, as a simple and meaningful measure of the r e l a t i v e competitive behaviour of the two species. They argued that the r a t i o provides an immediate measure of the degree of competition., i n terms of the number of times that one species i s more (or less) competitive than the other. Furthermore, they demonstrated that the Competition"Ratio was, i n many instances affected by s t o t a l density, and could be useful i n i d e n t i f y i n g plant characters which are associated with competitive a b i l i t y . 2.6 Relations Between Performance i n Pure Stands and i n  Mixtures The competitiveness of species components may be accentuated by various factors such as diseases, s o i l pH, s a l i n i t y etc. The species that i s r e s i s t a n t to these factors w i l l show better performance as the competitive stress from the susceptible species i s reduced. De Wit (1960) showed that with barley and oats mixtures, the barley plants f a i l e d to e s t a b l i s h i n a c i d i c s o i l s while oat plants were unaffected. The r e l a t i v e crowding c o e f f i c i e n t of oats attained the highest value (k = 20.0) when the growth of barley was i n h i b i t e d by the low pH. The o v e r a l l experiment at low pH was therefore reduced to that of a yield-density study of oats. De Wit (1960) used equation 5a for the surviving species to develop a spacing formula for yield-density - 62 r e l a t i o n s h i p s i n pure stands. The f i n a l d e r i v a t i o n of the s p a c i n g formula i s : M s = B n / 16 B+S 2 where M = y i e l d (g/m ) i n the pure stand; ft = t h e o r e t i c a l 2 2 maximum y i e l d (g/m ), S = space per seed (1/Density, cm / seed), and B = a constant which i s n u m e r i c a l l y equal to the s p a c i n g at which y i e l d i s h a l f of the maximum, i . e . ft/2. The e x t r a p o l a t e d y i e l d of one p l a n t sown at a very wide spacing, Ms.S, equates to Bft . Equation 16 may be rearranged to the form: 1/MS = = i - ' S + - 17 s Bfi n w i t h the same n o t a t i o n s as i n Equation 16. Hence a p l o t of 1/MS versus S produces a l i n e a r r e l a t i o n s h i p from which the -B and 1/o, are the i n t e r c e p t s on the a b s c i s s a and o r d i n a t e r e s p e c t i v e l y . Y i e l d - d e n s i t y r e l a t i o n s h i p s and t h e i r b i o l o g i c a l i m p l i c a t i o n s have been e x t e n s i v e l y reviewed by W i l l e y and Heath (1969). H o l l i d a y (1960a) showed t h a t e s s e n t i a l l y two forms of y i e l d - d e n s i t y r e l a t i o n s h i p e x i s t : (1) an assymptotic r e l a t i o n s h i p i n which the y i e l d i n c r e a s e s to a maximum and reaches a p l a t e a u a t very high d e n s i t i e s . Dry matter y i e l d s n o rmally show assymptotic y i e l d - d e n s i t y r e l a t i o n s h i p ; (2) a p a r a b o l i c r e l a t i o n s h i p i n which y i e l d i n c r e a s e s to a maximum - 63 -but d e c l i n e s a t h i g h d e n s i t i e s . T h i s form i s t y p i c a l o f r e p r o d u c t i v e y i e l d s . R e c i p r o c a l e q u a t i o n s ( H o l l i d a y , 1960b; S h i z o n a k i and K i r a , 1956; de W i t , 1960) which r e l a t e t h e r e c i p r o c a l o f y i e l d p e r p l a n t t o d e n s i t y have f r e q u e n t l y been found t o p r o v i d e good models o f y i e l d - d e n s i t y r e l a t i o n s h i p s o f t h e a s y m p t o t i c t y p e ( W i l l e y and Heath, 196 9 ) . I n f a c t , the r e l a t i o n s h i p d e s c r i b e d by S h i z o n a k i and K i r a (1956) has been shown by de Wit (1960) t o r e a r r a n g e t o t h e s p a c i n g f o r m u l a ( E q u a t i o n 1 6 ) . Any i n t e r a c t i o n between s p e c i e s i n a b i n a r y r eplacement s e r i e s c o n t a i n s a component a t t r i b u t a b l e t o t h e e f f e c t s o f the i n d i v i d u a l s o f e i t h e r s p e c i e s upon t h o s e o f t h e o t h e r s p e c i e s ( i n t e r s p e c i f i c c o m p e t i t i o n ) , and a component a t t r i b u t a b l e t o the e f f e c t s o f i n d i v i d u a l s o f e i t h e r s p e c i e s on i t s own k i n d ( i n t r a s p e c i f i c c o m p e t i t i o n ) . I n t h e extreme case i n wh i c h the two s p e c i e s i n a m i x t u r e occupy e n t i r e l y d i f f e r e n t n i c h e s o r "compete f o r e n t i r e l y d i f f e r e n t space" (sensu de W i t , 1960), the r e s u l t a n t m i x t u r e y i e l d s w i l l be t h e sum o f t h e mono-c u l t u r e y i e l d s a t d i f f e r e n t s p a c i n g s . I n such a s i t u a t i o n , t h e r e l a t i v e y i e l d t o t a l s w i l l exceed u n i t y , and r e a c h a : t h e o r e t i c a l maximum o f 2, and thus t y p i f y the "non-.:... c o m p e t i t i v e i n t e r f e r e n c e " d e f i n i t i o n o f H a l l (1974a). The s p a c i n g f o r m u l a ( E q u a t i o n 16) was d e r i v e d from c o n s i d e r a t i o n s o f t h e s i t u a t i o n i n wh i c h one s p e c i e s i s "competing" f o r space w h i c h i s not o c c u p i e d by a second s p e c i e s , i . e . empty space. Where two s p e c i e s i n a m i x t u r e - 64 -occupy e n t i r e l y d i f f e r e n t n i c h e s , t h e y may a l s o be c o n s i d e r e d t o "compete" f o r such empty space. I n such a c a s e , de Wit (1960) has shown t h a t t h e c r o w d i n g f o r e i t h e r s p e c i e s a g a i n s t t h e empty space i s g i v e n by B+S k = 18 S Hence the p r o d u c t o f the c r o w d i n g c o e f f i c i e n t s o f t h e two s p e c i e s i s g i v e n by: k a e . k b e = (Ba+S) (B b - S ) 1 9 S 2 (where k a e and k^ e a r e the c r o w d i n g c o e f f i c i e n t s o f s p e c i e s a and s p e c i e s b a g a i n s t empty space as d e f i n e d i n e q u a t i o n 18) which y i e l d s a v a l u e c o n s i d e r a b l y g r e a t e r t h a n u n i t y , t h e v a l u e t o be e x p e c t e d i f c o m p e t i t i o n were e x c l u s i v e l y f o r the same space (see S e c t i o n 2.4). However, a v a l u e o f t h e p r o -d u c t o f r e l a t i v e c r o w d i n g c o e f f i c i e n t s (K) g r e a t e r t h a n one may a l s o o c c u r when one o r b o t h s p e c i e s b e n e f i t from a s s o c i a -t i o n w i t h the o t h e r (de W i t , 1960). F u r t h e r m o r e , a K-value o f u n i t y makes no statement about the r e l a t i v e magnitudes o f the i n t r a - o r i n t e r s p e c i f i c e f f e c t s e x c e p t when t h e t o t a l d e n s i t y i n t h e repl a c e m e n t s e r i e s i s so low t h a t n e i t h e r t y p e o f c r o w d i n g o c c u r s . Thus, w h i l e the predominance o f i n t r a s p e c i f i c r a t h e r t h a n i n t e r s p e c i f i c i n t e r e f e r e n c e w i l l u s u a l l y r e s u l t i n K - v a l u e s g r e a t e r t h a n one, K- v a l u e s g r e a t e r t h a n one do not n e c e s s a r i l y mean t h a t i n t r a s p e c i f i c e f f e c t s dominate t h e i n t e r a c t i o n . - 65 2.7 P r e d i c t i o n s o f Y i e l d s and Y i e l d L o s ses due t o C o m p e t i t i o n The methods o f Dew (1972), d e s c r i b e d above ( S e c t i o n 2.5), p e r m i t t h e e s t i m a t i o n o f c r o p y i e l d s under c o n d i t i o n s o f weed c o m p e t i t i o n and r e p r e s e n t an advance over p r e v i o u s methods wh i c h tended t o be concerned w i t h t h e d e t e r m i n a t i o n o f t h e " c r i t i c a l d e n s i t y " o f the weed s p e c i e s w h i c h r e s u l t e d i n a " s i g n i f i c a n t " l o s s i n c r o p y i e l d ( N i e t o e t a l " . , 1968). An o b v i o u s e x t e n s i o n o f models w h i c h p r e d i c t y i e l d s i s t h e p r e d i c t i o n o f y i e l d l o s s e s , s i n c e such p r e d i c t i o n s have immediate p r a c t i c a l a p p l i c a t i o n s i n a g r i c u l t u r a l s i t u a t i o n s i n w h i c h t h e farmer can d e t e r m i n e i f a w e e d - c o n t r o l programme i s e c o n o m i c a l l y v i a b l e a f t e r t h e emergence o f t h e c r o p and t h e weed. Dew (1972) extended h i s i n d e x o f c o m p e t i t i o n c o n c e p t ( E q u a t i o n 8) t o p r e d i c t y i e l d l o s s e s , v i a L = a b]_ \/ X 20 2 where L i s y i e l d l o s s ( i . e . L = a - p r e d i c t e d y i e l d , g/m ); a, and X are as d e f i n e d i n e q u a t i o n 9; and *b]_ = CI ( E q u a t i o n 10). E x p r e s s e d i n percentage, terms, "which may be more ' ,; convenient-, t h i s r e l a t i o n s h i p becomes: % Loss = 100 b - j v V X 21 T h i s approach i s s i m p l e t o a p p l y , once t h e i n d e x o f c o m p e t i -t i o n f o r t h e p a r t i c u l a r crop-weed i n t e r a c t i o n i s known f o r a g i v e n l o c a t i o n . - 66 -The s p a c i n g f o r m u l a ( E q u a t i o n 16) has a l s o been used by de Wit (1960) t o p r e d i c t c o m p e t i t i v e b e h a v i o u r i n b i n a r y m i x t u r e s a t c o n s t a n t t o t a l d e n s i t y . Thus de Wit (1960) has shown t h a t t h e c r o w d i n g c o e f f i c i e n t f o r one s p e c i e s on ano t h e r as d e f i n e d i n e q u a t i o n 6, i s a l s o g i v e n by: B a+S k a b = B b+S 2 2 f o r t h e s i t u a t i o n i n whi c h t h e s p a c i n g ( d e n s i t y ) o f s p e c i e s i s i d e n t i c a l , and the v a l u e s f o r B and B, are o b t a i n e d from a t ) s p a c i n g e x p e r i m e n t s on s p e c i e s a and s p e c i e s b r e s p e c t i v e l y . However, t h e use o f t h e monoculture s p a c i n g f o r m u l a i s r e s t r i c t e d t o s i t u a t i o n s i n whi c h the two s p e c i e s a f f e c t each o t h e r by "crowding f o r t h e same space", (as e q u a l l y t r u e f o r th e s i t u a t i o n d e s c r i b e d by e q u a t i o n 5) and i n whi c h t h e growth c u r v e s f o r t h e two s p e c i e s a r e s i m i l a r . When two s p e c i e s i n a rep l a c e m e n t s e r i e s do not o r o n l y p a r t l y compete f o r "the same space" (sensu de W i t , 196 0 ) , t h e r e l a t i v e y i e l d t o t a l s and t h e p r o d u c t s o f t h e cr o w d i n g c o e f f i c i e n t s (K) w i l l exceed u n i t y , as d i s c u s s e d i n S e c t i o n 2.6. I n the extreme c a s e , i n which each s p e c i e s o c c u p i e s an e n t i r e l y d i f f e r e n t n i c h e and e x e r t s no i n f l u e n c e on t h e o t h e r , t h e y i e l d o f each s p e c i e s w i l l be p r e d i c t e d by i t s s p a c i n g f o r m u l a , and K w i l l r e a c h a maximum v a l u e d e f i n e d by E q u a t i o n 9. I n any case, p r o v i d e d t h a t E q u a t i o n 5 d e s c r i b e s t h e a c t u a l form o f t h e r e l a t i v e y i e l d c u r v e f o r a s p e c i e s , i t can be used t o p r e d i c t y i e l d s , s i n c e , t h e r e l a t i o n s h i p s between y i e l d - 67 -i n m i x t u r e s and pure st a n d s a re dependent upon t h e r e l a t i v e d e n s i t i e s and t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t s , r e g a r d l e s s o f whether t h e l a t t e r r e l a t e e x c l u s i v e l y t o c o m p e t i t i o n f o r th e same space o r n o t . Baeumer and de Wit (1968) found t h a t u s i n g b a r l e y , o a t s and peas, e x t r a p o l a t i o n o f monoculture y i e l d s u s i n g t h e s p a c i n g f o r m u l a t o p r e d i c t y i e l d i n b i n a r y m i x t u r e s (as d e s c r i b e d i n S e c t i o n 2.6) h o l d s o n l y w i t h i n l i m i t s . They, t h e r e f o r e , c o n c l u d e d t h a t when such e x t r a p o l a t i o n s a re t o be made, mixed s t a n d s must be i n c o r p o r a t e d i n t o the e x p e r i -ment f o r c r o s s r e f e r e n c e p u r p o s e s . T h i s has a l s o been s t a t e d by Harper (1964): "the b e h a v i o u r o f a s p e c i e s i n i s o l a t i o n may be l a r g e l y i r r e l e v a n t t o u n d e r s t a n d i n g i t s b e h a v i o u r i n the community". - 68 -3. MATERIALS AND METHODS 3.1 General A l l experiments were conducted at the University of B r i t i s h Columbia, Vancouver, B.C. The experimental land had been under sod for seven years. In the 1980 growing season the land was ploughed and harrowed i n early May. The s o i l i s a sandy loam with pH 6.8 and according to preliminary analysis using Morgan's S o i l Test f e r t i l i z e r application was not necessary. On May 9, 1980 the s o i l was fumigated with Basamid (3,5-Dimethyltetrahydro-l, 3, 5-2H-thiadiazine-2-thione) (4 00 kg/ha), incorporated and packed on the same day. The temperatures on the date were 7.5°C (air) and 14.5°C ( s o i l at 10 cm) and the r e l a t i v e humidity was 76.5% (RH). In 1981, the barnyardgrass experiments were repeated on the same land used i n 1980, and the rapeseed experiments were repeated on d i f f e r e n t land. The land was ploughed i n late A p r i l and sub-sequently worked and harrowed i n early May. On May 7, 1981, the s o i l was limed with dolomitic lime (2241 kg/ha). The land was then fumigated with Basamid on May 12, 1981. The temperatures on the date were 11.6°C (air) and 13.0°C ( s o i l at 10 cm), and the RH was 75.0%. F e r t i l i z e r (11-55-0) was broadcast (224 kg/ha) on May 19, 1981 and on May 27, 1981 the land was t i l l e d up to allow d i f f u s i o n of the fumigant out of the s o i l . - 69 -3.2 P l a n t M a t e r i a l s The p l a n t m a t e r i a l s used i n t h e e x p e r i m e n t s were b a r n y a r d g r a s s , BYG, ( E c h i n o c h l o a . c r u s - g a l l i (L.) Beauv.), r e d r o o t pigweed, RPW (Amaranthus r e t r o f l e x u s L . ) , green f o x -t a i l , GFT ( S e t a r i a : v i r i d i s (L.) Beauv.) and b l a c k r a p e , RPS ( B r a s s i c a napus L. v a r . Annua). The c h o i c e o f t h e s e a n n u a l s p e c i e s was based on t h e i r wide o c c u r r e n c e t o g e t h e r i n v a r y -i n g c o m b i n a t i o n s and i n a wide range o f h a b i t a t s . The seeds o f b a r n y a r d g r a s s and r e d r o o t pigweed were c o l l e c t e d from a g r i c u l t u r a l f i e l d s a t A g r i c u l t u r e Canada Research S t a t i o n , A g a s s i z , B.C. i n t h e summer o f 1979. Those o f green f o x t a i l were o b t a i n e d from g r a i n s c r e e n i n g s . Commercial r a p e s e e d was purchased from B u c k e r f i e l d s L t d . , Vancouver. 3.3 P l o t s and P l a n t i n g The e x p e r i m e n t s were l a i d o u t i n E-W rows o f (3.0 x 2 1.5) m p l o t s w i t h 0.5m l a n e s between p l o t rows. The p l o t s were marked by permanent wooden s t a k e s . Seeds weighed a c c o r d i n g t o t r e a t m e n t s were b r o a d c a s t onto t h e p l o t s and g e n t l y handraked i n t o t h e s o i l . I n the m i x t u r e s , t h e seeds o f each s p e c i e s were weighed and sown s e p a r a t e l y . The d e n s i t i e s o f each s p e c i e s i n b o t h t h e pure s t a n d s and m i x t u r e s were a s s e s s e d two weeks a f t e r s e e d l i n g emergence by p l a c i n g a h a l f - m e t r e square q u a d r a t a t t h e c e n t r e o f t h e p l o t , and c o u n t i n g t h e i n d i v i d u a l s e e d l i n g s . There was n o . d i s p a r i t y i n t h e number o f s e e d l i n g s and t h e seeds sown i n a l l t r e a t -ments. W i t h i n a g i v e n s p e c i e s m i x t u r e , t h e seeds g e r m i n a t e d - 70 -a t the same time e x c e p t i n 1980 when RPW and GFT ge r m i n a t e d f o u r days l a t e r t h a n RPS. 3.4 H a r v e s t s 2 I n each e x p e r i m e n t , t h e p l a n t s w i t h i n a one m a r e a a t t h e c e n t r e o f t h e p l o t s were h a r v e s t e d by c l i p p i n g a t ground l e v e l . Shoot p a r t s were s e p a r a t e d i n t o i n d i v i d u a l s p e c i e s and d r i e d i n paper bags i n a f o r c e d a i r d r i e r a t 80°C f o r a minimum o f f o u r days. The d r i e d p l a n t m a t e r i a l s were c o o l e d i n p l a s t i c bags and weighed. The f o l l o w i n g t a b l e shows t h e sowing and h a r v e s t d a t e s f o r t h e t h r e e e x p e r i m e n t s : S p e c i e s Exp. C o m p o s i t i o n P l a n t i n g * H a r v e s t * A, BYG+RPW May 29-31, 1980 .Aug.- 25-26 , 1980 June 1, 1981 Aug. 21-22, 1981 A~ BYG+GFT June 3-5, 1980 Sept. 9-18, 1980 June 2, 1981 Aug. 23-24, 1981 A., RPS+RPW+GFT June 28, 1980 Oct. 6-9, 1980 June 3-4, 1981 . Aug. 25-28, 1981 * On o c c a s i o n s when an ex p e r i m e n t c o u l d n ot be p l a n t e d o r h a r v e s t e d w i t h i n a day, f o r example, because o f r a i n , an attempt was made t o complete a b l o c k w i t h i n the same day. 3.5 E x p e r i m e n t a l Designs and Treatments The t h r e e e x p e r i m e n t s were e s t a b l i s h e d i n t h e summer o f 1980 and were r e p e a t e d i n 1981. Experiment A^ c o m p r i s e d pure s t a n d s and b i n a r y m i x t u r e s o f BYG and RPW; exp e r i m e n t A 2 i n c l u d e d BYG and GFT; and A 3 c o m p r i s e d RPS, RPW and GFT i n b o t h b i n a r y and t e r n a r y c o m b i n a t i o n s . The t r e a t m e n t s i n v o l v e d d i f f e r e n t d e n s i t i e s o f each s p e c i e s i n pure s t a n d s ; m i x t u r e s - 7 1 -were produced by various substitutions of plants i n the pure stand by plants of another species. The experiments were designed to incorporate treatments for additive and replace-ment series for each species. Experiment A^, which included only the replacement series design i n 1 9 8 0 , was modified to incorporate additive series treatments i n the 1 9 8 1 season. There were 27 treatments for each of experiments A^ and A 2 (Table 3 . 1 ) and 28 ( 6 1 i n 1 9 8 1 ) for experiment A 3 (Table 3 . 2 ) , r e p l i c a t e d four times i n a randomized block design. The in t e r r e l a t i o n s h i p s between experiments A^, A 2 and A, can be summarized diagrammatically as follows: BYG RPS Spacing experiments for pure stand yield-density relationships Binary combinations (Additive and replacement series) Ternary combinations (replacement series) 72 -Table 3.1 Deta i l s of species combinations (Experiments A. and A„) Density (p'lants/m ) of components BYG / / RPW / or / GFT 240 480 720 960 1200 1440 0 0 0 0 0 0 0 240 240 240 480 240 720 240 960 240 1200 240 0 480 240 480 480 480 720 480-960 480 0 720 240 720 480 720 720 720 0 960 240 960 480 960 0 1200 240 1200 0 1440 Additive series run h o r i z o n t a l l y and v e r t i c a l l y . BYG mono-culture Replacement series run diagonally from lower l e f t to upper r i g h t . RPW or GFT monocultures i a D i e J . Z D e t a i l s of species combinations (Experiment A^) Treatments included i n the 1980 experiment are underlined. A l l treatments were included i n 1981, with the exception of the pure stand d e n s i t i e s of RPW and GFT since these were included i n Experi-ments A^ and A2 i n that year, i . e . only 61 out of the 73 t o t a l possible treatments were l a i d down in 1981 as part of Experiment A^. . .-. " ' Species Density Levels RPS 1 RPW2 GFT (RPS + RPW) (RPS + GFT) (RPW + GFT) (RPS + RPW + GFT) Pure stands Binary mixtures Ternary mixtures Pure stands Binary mixtures Ternary mixtures 1 2 3 4 5 6 - 1 + 1 1 + 1 1 + 1 4 + 1 + 1 — 2 + 1 2 + 1 2 + 1 3 + 2 + 1 — 3 + 1 3 + 1 3 + 1 2 + 3 + 1 — 4 + 1 4 + 1 4 + 1 1 + 4 + 1 — 5 + 1 5 + 1 5 + 1 3 + 1 + 2 — 1 + 2 1 + 2 1 + 2 2 + 2 + 2 — 2 + 2 2 + 2 2 2 1 + 3 + 2 — 3 + 2 3 + 2 3 + 2 2 + 1 + 3 — 4 + 2 4 + 2 4 + 2 1 + 2 + 3 — 1 + 3 1 + 3 1 + 3 1 + 1 + 4 (1) (2) (3) (4) (5) - 2 + 3 2 + 3 2 + 3 (6) - 3 + 3 3 + 3 3 + 3 (1) 1 + 4 1 + 4 1 + 4 (2) 2 + 4 2 + 4 2 + 4 (3) 1 + 5 1 + 5 1 + 5 (4) (5) (6) The density l e v e l s of RPS : 1, 2, 3, 4, 5 and 6 comprised 75, 150, 225, 300, 375 and 450 plants/m2 r e s p e c t i v e l y . The density l e v e l s of RPW and GFT are the same as those used i n 1980: 1 ,2,3,4,5,6 comprised 240, 480, 720, 960, 1200 and 1440 plants/m 2 r e s p e c t i v e l y . - 74 -The weed d e n s i t i e s used were based on weed c o u n t s i n v a r i o u s i n f e s t a t i o n s o f f i e l d s a t A g r i c u l t u r e Canada Research S t a t i o n , A g a s s i z , B.C. f o r BYG and RPW. I n f e s t a t i o n s o f GFT i n c r o p f i e l d s have been r e p o r t e d t o be w i t h i n s i m i l a r ranges o f d e n s i t i e s ( F r i e s e n and S h e b e s k i , 1960). The v a r i o u s p o p u l a t i o n s o f RPS i n c l u d e d d e n s i t i e s below and above t h e normal s e e d i n g r a t e s (5-6 kg / h a ) . 3.6 Approaches t o A n a l y s i s o f Data 3.6.1 I n t r a s p e c i f i c I n t e r a c t i o n s The d a t a on t h e y i e l d s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l i n t h e pure s t a n d s were a n a l y z e d by t h e s p a c i n g f o r m u l a (de W i t , 1960), M = a „ 16 s B+s (see S e c t i o n 2.6). R e g r e s s i o n s o f 1/Ms and S y i e l d e d e s t i m a t e s o f - B and 1/ ft (and hence B and ft ) as t h e i n t e r c e p t s on the a b s c i s s a and o r d i n a t e r e s p e c t i v e l y . I n t u r n , e s t i m a t e s o f y i e l d o b t a i n e d from e q u a t i o n 16 were compared w i t h the ob s e r v e d y i e l d s i n v a r i o u s e x p e r i m e n t s . 3.6.2 I n t e r s p e c i f i c I n t e r a c t i o n s 3.6.2.1 B i n a r y a d d i t i v e s e r i e s m i x t u r e s Two approaches were employed t o a n a l y z e the d a t a on the a d d i t i v e s e r i e s t r e a t m e n t s . F i r s t , the s p a c i n g f o r m u l a 75 ( E q u a t i o n 16: M B o, ) was t e s t e d f o r i t s a b i l i t y t o s B+S d e s c r i b e t h e performance o f t h e a s s o c i a t e d s p e c i e s i n the presence o f v a r i o u s c o n s t a n t d e n s i t i e s o f the i n d i c a t o r s p e c i e s . T h i s approach i s based on the assumption t h a t the e f f e c t o f t h e i n d i c a t o r s p e c i e s i s t o reduce the "space" (sensu de W i t , 1960) p o t e n t i a l l y a v a i l a b l e f o r o p t i m a l growth o f the a s s o c i a t e d s p e c i e s . Second, the y i e l d o f t h e i n d i c a t o r s p e c i e s a t d i f f e r e n t c o n s t a n t d e n s i t i e s was a n a l y z e d by t h e r e g r e s s i o n e q u a t i o n o f Dew (1972): Y = a.+ bsj x , • 9 (see S e c t i o n 2.5). The a n a l y s i s assumes t h a t t h e y i e l d o f th e i n d i c a t o r s p e c i e s d e c l i n e s a t a d i m i n i s h i n g r a t e w i t h i n c r e a s i n g d e n s i t y o f t h e a s s o c i a t e d s p e c i e s . Two v e r s i o n s o f Dew's a n a l y s i s were used. I n t h e f i r s t , o n l y t h o s e d a t a from a d d i t i v e s e r i e s e x p e r i m e n t s i n whi c h the a s s o c i a t e d s p e c i e s was p r e s e n t were used t o compute t h e c o e f f i c i e n t s and i n d i c e s o f c o m p e t i t i o n , as d e s c r i b e d by Dew (1972). I n the second, t h e a n a l y s i s was extended t o i n c l u d e t h e o b s e r v e d monoculture y i e l d s o f t h e i n d i c a t o r s p e c i e s i n E q u a t i o n 9 by i n s e r t i n g them i n t o t h e r e g r e s s i o n a g a i n s t a n e g l i g i b l y —99 s m a l l dummy v a l u e o f a s s o c i a t e d s p e c i e s d e n s i t y (X = 1x10 ). The dummy v a l u e i s needed because the r e g r e s s i o n i n v o l v e s t h e square r o o t o f the d e n s i t y o f t h e a s s o c i a t e d s p e c i e s . T h i s m o d i f i e d a p p l i c a t i o n o f E q u a t i o n 9 was t h e v e r s i o n used r o u t i n e l y i n t h e a n a l y s e s o f a d d i t i v e s e r i e s d a t a r e p o r t e d i n S e c t i o n s 4.2 and 4.3. - 76 -In addition to the estimates of y i e l d obtained by application of Equation 9, estimates of y i e l d loss were obtained by the use of Equation 20 (Section 2.7). 3.6.2.2 Binary replacement series mixtures The component yi e l d s were analyzed for r e l a t i v e yields- (r) , r e l a t i v e y i e l d - t o t a l s (RYT)", r e l a t i v e crowding c o e f f i c i e n t s (k) and th e i r products (K). Individual k values were computed from the generalized equation (de Wit, 1960; Willey, 1979), k , = a ab M -0 z a a a (Section 2.4), for each combination of r e l a t i v e d e n s i t i e s . The mean values, k , and ic, , were i n turn used to predict ' ab ba' * values of O and O^, from the general equation n ab a M O = s ; • a 5 a k , z +z, ab a b (Section 2.4). Estimated values 0 & and 0^ were subsequently used to es t a b l i s h curves i n r a t i o diagrams i n which 0 a/0j 3 i s plotted against z /z, . A rearrangement of Equation 5 permits a J3 the computation of estimated r e l a t i v e y i e l d s : r = °* = k a b z a - — 2 a — M= k ,+z, a ab b It should be pointed out that, because of the experimental designs employed, each intercomparison of two species involved a t o t a l of f i v e replacement series (at t o t a l densities of - 77 -1440, 1200, 960, 720 and 480 plants/m 2), and hence the e f f e c t s of t o t a l density on the r e l a t i v e crowding c o e f f i c i e n t s and estimated values of y i e l d s were also determined. The r e l a t i v e y i e l d data were used to determine ag g r e s s i v i t i e s by the method of McGilchrist and Trenbath (1971) (Equation 14, Section 2.5); and the Competition Ratio (CR) of Willey and Rao (1980) (Section 2.5). In addition, the experimental design permitted d i r e c t evaluation of a species 1 competitive behaviour against individuals of i t s own kind ( i n t r a s p e c i f i c ) versus those of the second species ( i n t e r s p e c i f i c ) . At several densities i t was possible to intercompare the e f f e c t s on y i e l d of adding various equal-densities of the same or of a second species. In these analyses, i t was found to be simpler to work on a y i e l d per plant rather than a t o t a l y i e l d basis. Thus, for a species 2 grown i n monoculture at a density of, say, 720 plants/m , i t was possible to determine the decrease i n y i e l d per plant caused by addition of 240, 480 or 720 plants/m of either the same or a d i f f e r e n t species. The r a t i o of the decrease i n per plant y i e l d caused by i t s e l f to that caused by a second species provides a measure of the r e l a t i v e contribution made by i n t r a - and i n t e r s p e c i f i c competitive factors, and hence a check on the v a l i d i t y of the estimates of the crowding co-e f f i c i e n t s obtained by the use of Equation 6. Although Equation 5 permits the estimation of y i e l d s , replacement series experiments alone provide no v a l i d - 78 e s t i m a t e s o f y i e l d l o s s analogous t o t h o s e a v a i l a b l e from a d d i t i v e s e r i e s e x p e r i m e n t s ( E q u a t i o n s 20 and 21, S e c t i o n 2.7), because, by d e f i n i t i o n , o n l y t o t a l d e n s i t y i s c o n s t a n t . However, e s t i m a t e s o f y i e l d l o s s were o b t a i n e d as t h e d i f f e r e n c e between e s t i m a t e s M and 0 (from E q u a t i o n 16 and a a 5 r e s p e c t i v e l y ) f o r t h e m i x t u r e and monoculture y i e l d s o f a s p e c i e s a t s p e c i f i c d e n s i t i e s . 3.6.2.3 T e r n a r y r e p l a c e m e n t s e r i e s The c r o w d i n g c o e f f i c i e n t s f o r s p e c i e s competing f o r the same r e q u i s i t e s i n b i n a r y replacement s e r i e s m i x t u r e s may be extended t o b i n a r y m i x t u r e s o f o t h e r s p e c i e s by means o f E q u a t i o n 7 ( S e c t i o n 2.4). Such e s t i m a t e s o f c r o w d i n g c o -e f f i c i e n t s , k, were c a l c u l a t e d f o r comparison w i t h o b s e r v e d v a l u e s o f k f o r d i f f e r e n t b i n a r y c o m b i n a t i o n s . I n a d d i t i o n , d a t a on b i n a r y components o f t h e t e r n a r y m i x t u r e s a t d i f f e r e n t l e v e l s o f the t h i r d s p e c i e s p e r m i t t e d c o m p u t a t i o n o f v a l u e s o f r 1 , k' and RYT' (analogous t o the v a l u e s f o r t h e s i m p l e b i n a r y m i x t u r e s ) i n o r d e r t o dete r m i n e t h e e f f e c t s o f v a r y i n g the d e n s i t y o f t h e t h i r d s p e c i e s on the i n t e r a c t i o n s between t h e r e m a i n i n g two. Thus, r e l a t i v e d e n s i t i e s o f s p e c i e s a r a n g i n g from 0 t h r o u g h 0.17, 0.33, 0.5 and 0.67 p e r m i t t e d e x a m i n a t i o n o f b i n a r y r e p l a c e m e n t s e r i e s o f s p e c i e s b and c a t d i f f e r e n t d e n s i t i e s o f a, as f o l l o w s : - 79 -when z & = 0, z^ and z c may e q u a l 0, 0.17, 0.33, 0.5, 0.67, 0.83, 1.0 when z = 0.17, z/ and z' may e q u a l 0, 0.2, 0.4, 0.6, 0.8, 3. JD C 1.0 when z^ = 0.33, z^ and z^ may e q u a l 0, 0.25, 0.5, 0.75, 1.0 when z & = 0.50, z^ and z^ may e q u a l 0, 0.33, 0.67, 1.0 when z^ = 0.67, z^ and z^ may e q u a l 0, 0.5, 1.0 (where z^ and z^ are t h e r e l a t i v e d e n s i t i e s w i t h i n each b i n a r y s e r i e s ) . These r e l a t i o n s h i p s a re i l l u s t r a t e d i n F i g u r e 3.1. S i m i l a r l y , t h e e x p e r i m e n t a l d e s i g n p e r m i t t e d the i n v e s t i g a t i o n o f " p s e u d o - b i n a r y " r e p l a c e m e n t s e r i e s i n which t h e r e l a t i v e f r e q u e n c i e s o f s p e c i e s a v a r i e d i n v e r s e l y w i t h the t o t a l s o f b and c a t a c o n s t a n t r a t i o ( i . e . t h e sum o f b and c was t r e a t e d as a s i n g l e s p e c i e s ) . Thus, f o r a 1:1 r a t i o o f s p e c i e s b and s p e c i e s c ( i . e . z^/z^ = 1 ) , t h e com-b i n e d y i e l d s o f s p e c i e s b and c when z = 0 p r o v i d e t h e a e q u i v a l e n t o f a "monoculture" y i e l d f o r t h e (b+c) c o m b i n a t i o n . A d d i t i o n a l d a t a f o r t h e 1:1 m i x t u r e o f s p e c i e s b and c a r e o b t a i n e d from t h e t e r n a r y m i x t u r e s w i t h z^ = z^ = z c = 0.333; and z & = 0.67, and z^ = z^ = 0.17, as shown i n F i g u r e 3.2. Other p s e u d o - b i n a r y r e p l a c e m e n t s e r i e s a r e a l s o shown i n F i g u r e 3.2, f o r r a t i o s o f z^/z^ e q u a l t o 0.5 and 0.2, i n whic h a c t u a l combined y i e l d s o f (b+c) are o b t a i n e d from t h e t e r n a r y m i x t u r e s a t z^ = 0.5. 80 -" i i n II to to ro 10 3.1 Binary-series components of ternary replacement at d i f f e r e n t levels of species a Fig.3.2 Pseudo-binary replacement series combinations -82-3.6.3 S t a t i s t i c a l Analyses and Curve F i t t i n g The s i g n i f i c a n t e f f e c t s of treatments on y i e l d were i d e n t i f i e d by Student-Newman-Keuls procedure for multiple range tests (Bancroft, 1968). Estimates of the yiel d s of the components across the density treatments and within replacement series (obtained from appropriate equations) were compared with observed values by computing regression and c o r r e l a t i o n c o e f f i c i e n t s . -83-4. RESULTS AND DISCUSSION 4.1 Y i e l d - d e n s i t y R e l a t i o n s h i p s o f B a r n y a r d g r a s s , Redroot  Pigweed, Green F o x t a i l and Rapeseed The y i e l d s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l a c r o s s t h e d e n s i t y t r e a t m e n t s i n b o t h 1980 and 1981 are p r e s e n t e d i n T a b l e 4.1 t o g e t h e r w i t h the y i e l d s f o r r a p e s e e d i n 1981. As e x p e c t e d , f o r each s p e c i e s , t h e y i e l d i n c r e a s e d w i t h i n c r e a s i n g d e n s i t y but t h e s p e c i e s tended t o r e a c h p l a t e a u y i e l d s a t d i f f e r e n t d e n s i t y l e v e l s . The d a t a were a n a l y z e d f o r each s p e c i e s i n d i v i d u a l l y by t h e s p a c i n g f o r m u l a ( E q u a t i o n 16, S e c t i o n 2.6). The c o n s t a n t s B and °. were o b t a i n e d from the i n t e r c e p t s o f the r e g r e s s i o n s o f t h e double r e c i p r o c a l p l o t s o f 1/Mg v e r s u s S ( i . e . 1 / D e n s i t y ) , ( a c c o r d i n g t o E q u a t i o n 17, S e c t i o n 2.6) such as t h a t shown f o r BYG i n the 1981 season i n F i g u r e 4.1. The i n c r e a s i n g d i v e r g e n c e e x h i b i t e d by the d a t a f o r 1/Mg a t low s p a c i n g ( h i g h d e n s i t y ) i n F i g u r e 4.1 i s the r e s u l t o f t h e f a c t t h a t y i e l d o f BYG c o n t i n u e d t o i n c r e a s e w i t h d e n s i t y t h r o u g h o u t t h e range o f d e n s i t i e s employed. T h i s i s an analogous s i t u a t i o n t o t h a t r e p o r t e d by de Wit (1960) f o r c r o p s grown a t o p t i m a l c o n d i t i o n s . The s p e c i e s d i f f e r markedly i n t h e i r p r o d u c t i v e b e h a v i o u r . At each d e n s i t y , t h e y i e l d s f o r each s p e c i e s were c o n s i s t e n t l y i n the d e s c e n d i n g o r d e r : r a p e s e e d , b a r n y a r d g r a s s , Table 4.1 Yields (g/m ) of barnyardgrass (BYG), redroot pigweed (RPW) green f o x t a i l (GFT) and rapeseed (RPS) in varying densities of the monocultures during 1980 and 1981 seasons DENSITY YIELDS (g/m2) ("RPS-units") 1 2 (plants/m ) BYG RPW GFT RPS RPS 1980 1981 1980 1981 1980 1981 1981 240 75 653.2 684.5 342.4 334.3 290.9 354.0 574.5 480 150 988.2 863.2 558.2 509.2 481.5 494.6 596.8 720 225 1167.1 987.4 782.2 618.1 655.7 622.6 728.0 960 300 1276.0 1097.1 830.0 720.4 696.8 667.5 839.6 1200 375 1295.0 1161.5 895.9 785.9 737.9 749.0 892.6 1440 450 1327.6 1265.0 916.2 846.4 783.6 804.6 964.9 L.S.D. (0.05) 54.84 92.10 43.19 49.26 50.56 71.33 51.76 B(cm 2/plant) 2 24.51 38.64 11.89 16.55 12.30 22.00 15.89 1/ 0(cm 2/g) 2 5.61 7.18 6.45 8.56 7.76 9.89 7.27 0. (g/m2) 1782.5 1392.8 1150.4 1168.2 1288.7 1011.1 1376.1 sM (g/plant) 4.37 5.39 1.84 1.93 1.58 2.22 2.19 4 r 0.997 0.985 0.996 0.999 0.996 0.995 0.999 (50.73T (7.27) (1376.1) (7.00) One plant of RPS i s equivalent to 3.2 plants of BYG, RPW or GFT. Derived from reciprocal plots such as Figure 4.1 and Equation 16. 2 Computed from actual densities (plant/m ) of RPS. Correlation c o e f f i c i e n t between observed y i e l d and calculated y i e l d . Omitting the lowest density of RPS. r -85-1/M S 1 2 0 -10 T 38.6M=-B - 2 0 - 1 0 0 10 20 30 1/DENSITY 40 -S ( c m 2 / p l a n t ) F i g u r e 4.1. The y i e l d - d e n s i t y r e l a t i o n s h i p i n a spac i n g experiment w i t h BYG i n 1981. Regression i s given by 1/MS = 7.18+0.186S (Equation 17). -86-r e d r o o t pigweed and green f o x t a i l . The y i e l d c h a r a c t e r i s t i c s o f r a p e s e e d were c o n s i d e r a b l y g r e a t e r t h a n f o r t h e o t h e r s p e c i e s ; hence RPS d e n s i t i e s were t r a n s f o r m e d t o "rapeseed u n i t s " where 1 r a p e s e e d p l a n t = 3.2 RPS u n i t s , i . e . an "RPS u n i t " p l a n t o c c u p i e s 0.3125 o f the space o f an a c t u a l p l a n t a t p l a t e a u y i e l d , and weighs 0.3125 o f t h e w e i g h t o f an a c t u a l p l a n t a t p l a t e a u y i e l d . The impact o f i n t r a s p e c i f i c c o m p e t i t i o n on y i e l d appeared t o o c c u r a t lower d e n s i t i e s i n t h e case o f GFT t h a n w i t h the o t h e r s p e c i e s , as suggested by the g r a p h i c a l p r e s e n t a t i o n o f t h e y i e l d d a t a i n F i g u r e 4.2. However, i t s h o u l d be n o t e d t h a t t h e t r a n s i t i o n s t o t h e p l a t e a u x were r e l a t i v e l y g r a d u a l and i n no case was the maximum y i e l d r e a c h e d (Table 4.1). The de Wit (1961) s p a c i n g f o r m u l a r e v e a l s u s e f u l i n f o r m a t i o n on the y i e l d - d e n s i t y r e l a t i o n s h i p s . . The p r o d u c t o f t h e c o n s t a n t s (B ti ), f o r example, i s the p o t e n t i a l y i e l d p e r p l a n t grown i n i s o l a t i o n . F o r BYG, RPW and GFT, the B ti v a l u e s a r e r a n k e d i n a s i m i l a r manner t o t h e i r o b s e r v e d y i e l d i n 1980. However, w h i l e BYG s t i l l m a i n t a i n e d a h i g h v a l u e , RPW had a lower B ti v a l u e t h a n GFT i n the 1981 season even though i t produced a g r e a t e r y i e l d a t the h i g h e r d e n s i t i e s s t u d i e d (Table 4.1). Green f o x t a i l and ra p e s e e d (based on " u n i t s " ) gave s i m i l a r Bti v a l u e s a l t h o u g h t h e a c t u a l y i e l d s o f RPS were c o n s i s t e n t l y h i g h e r over the range o f d e n s i t i e s i n v e s t i g a t e d . A l t h o u g h t h e y i e l d s o f BYG, RPW, GFT were g e n e r a l l y h i g h e r i n 1980 th a n i n 1981, t h e v a l u e s f o r B show £7 F i g u r e 4.2. Mean y i e l d s (g/m ) o f b a r n y a r d g r a s s (•, BYG), r e d r o o t pigweed (0, RPW), green f o x t a i l (A, GFT) and r a p e s e e d (•, RPS) i n m o n o c u l t u r e s d u r i n g 1980 (a) and 1981 (b) seasons r e s p e c t i v e l y . -88--89-that i n both seasons BYG required most space per plant to produce half i t s maximum y i e l d and that RPW required the least. In 1981, RPS required most space when actual densities are compared, but least space after conversion to "RPS units". The curves derived from the spacing formula f i t the observed y i e l d s well, with c o r r e l a t i o n c o e f f i c i e n t s greater than 0.97 i n a l l cases except for rapeseed (Table 4.1). Omission of the apparently high value for rapeseed y i e l d at the lowest density provided a better f i t over the remaining densities (Table 4.1). The development of estimates of competitive behaviour of these species when grown together i n various combinations based upon t h e i r performance i n monoculture density experi-ments according to de Wit (1960) i s presented i n Sections 4.4.4 and 4.5.4 i n connection with the results of binary replacement series experiments. 4.2 Yields of Barnyardgrass, Redroot Pigweed and Green  F o x t a i l i n Binary Additive Series Mixtures Binary combinations of BYG, RPW and GFT were included in Experiments A^ and A 2, each of which was conducted i n both 1980 and 1981. In each experiment, treatments were included which permited either of the species i n any binary combination to be evaluated as the indicator species. The results for each binary combination are presented separately i n the following sections. -90-4.2.1 Y i e l d s o f B a r n y a r d g r a s s and Redroot Pigweed i n A d d i t i v e M i x t u r e s 4.2.1.1 B a r n y a r d g r a s s as i n d i c a t o r s p e c i e s The y i e l d d a t a f o r BYG and RPW i n t h e m i x t u r e s w i t h BYG as t h e i n d i c a t o r s p e c i e s a r e p r e s e n t e d i n F i g u r e 4.3 f o r t h e 1980 and 1981 seasons. The c u r v e s f o r b a r n y a r d g r a s s were g e n e r a t e d from E q u a t i o n 9 ( S e c t i o n 2.5). The a c t u a l h a r v e s t e d y i e l d s o f b a r n y a r d g r a s s i n t h e presence o f t h e c o m p e t i t o r were compared t o t h e y i e l d s e s t i m a t e d from E q u a t i o n 9. At a l l d e n s i t i e s o f BYG t h e r e was a c l o s e agreement between th e a c t u a l and t h e e s t i m a t e d y i e l d s (P < 0.01). The c l o s e f i t t o t h e d a t a and t h e h i g h r - v a l u e s show t h a t the y i e l d o f BYG was r e l a t e d t o t h e square r o o t o f t h e d e n s i t y o f RPW. I n b o t h seasons, i n c r e a s i n g the d e n s i t i e s o f RPW caused s i g n i f i c a n t (P < 0.05) and p r o g r e s s i v e l y g r e a t e r d e p r e s s i o n s o f t h e y i e l d o f BYG a t t h r e e BYG d e n s i t i e s (240, 480 and 720 p l a n t s / m 2 ) w i t h t h e e x c e p t i o n o f t h e h i g h e s t BYG d e n s i t y i n 1981 (see Appendix 2 ) . The r e g r e s s i o n s o f b a r n y a r d g r a s s y i e l d s tended t o be a s s y m p t o t i c as t h e RPW d e n s i t y i n c r e a s e d ; d e n s i t i e s o f RPW g r e a t e r t h a n 960 p l a n t s / m 2 (1980) o r 720 p l a n t s / m 2 (1981) caused no f u r t h e r s i g n i f i c a n t d e c r e a s e s i n BYG y i e l d a t low o (24 0 p l a n t s / m ) BYG d e n s i t y ; a t h i g h e r BYG d e n s i t i e s the 2 e f f e c t o f RPW d e n s i t y was r e a c h e d a t 480 p l a n t s / m (1980) o r 2 even 240 p l a n t s / m (1981). I n g e n e r a l , t h e r e f o r e , t h e c o m p e t i t i v e e f f e c t s o f RPW on t h e y i e l d o f BYG were more F i g u r e 4.3. Mean y i e l d s (g/m z o f r e d r o o t pigweed (P) i n m o noculture (M Sp, • , • ) and i n t h e p r e s e n c e o f t h r e e d e n s i t i e s (240, 480, 720 p l a n t s / m 2 ) o f b a r n y a r d g r a s s ( Y p , •, ) , and o f b a r n y a r d g r a s s ( B ) , ( Y B , o, ) a t t h e s e d e n s i t i e s . The c u r v e s were f i t t e d by E q u a t i o n s 9 (Yg) and 16 ( M s p , Y p ) . 1980 and 1981 d a t a . severe i n low than i n medium - and high-density BYG, with the y i e l d curves for the d i f f e r e n t densities of BYG (Figure 4.3) p a r a l l e l l i n g each other (1980) or even tending to diverge (1981) as the density of RPW increased. The y i e l d curves for redroot pigweed i n Figure 4.3 were generated from the spacing formula (Equation 16 Section 2.6) for each density of BYG. At any given density of the indicator, there was a close one-to-one relationship (P c 0.05) between the actual and the estimated y i e l d s of RPW. The generally good f i t s of the curves to the data i l l u s t r a t e the v a l i d i t y of t h i s approach. The y i e l d of RPW was generally higher i n 1980 than i n 1981 (Figure 4.3 and Appendix 2 ) . At any given density of BYG the y i e l d of RPW increased with density and tended towards a maximum. The tr a n s i t i o n s to plateau y i e l d s tended to occur at lower RPW densities i n the presence of high densities of BYG. The application of the spacing formula to generate the curves for RPW yi e l d s i n Figure 4.3, permits the c a l c u l a -t i o n of estimated per plant y i e l d s , as B ft . The estimated y i e l d per RPW plant was markedly lower i n the mixtures than in the pure stand as shown i n Table 4.2. The e f f e c t of BYG on the estimated y i e l d per RPW plant was greater i n 1981 than i n 1980. While Bft values were comparable i n the monocultures for the two seasons, the 1981 values for the mixtures were con-siderably less than those obtained in 1980. The markedly lower values of B a i n the mixture than i n the monoculture suggests - 94 -that competitive interaction was occurring to the detriment of RPW. The seasonal difference i n the Bfi values also shows that competition from BYG was more severe in 1981. Similar observations were revealed by the data on the competitive interactions between BYG and RPW i n replacement series mix-tures (Section 4.4.1). The enhanced competitiveness of BYG in 1981 may be attributable to the higher p r e c i p i t a t i o n i n that season than i n 1980, which established conditions more favourable for i t s growth than for that of RPW. However the actual monoculture y i e l d s of BYG at the densities investigated were somewhat less i n 1981 than i n 1980 (Table 4.1), and RPW also demonstrated a greater competitive e f f e c t on BYG i n 1981, as shown l a t e r i n Table 4.3. Table 4.2 Estimated y i e l d (g per plant) of redroot pigweed (BQ ) i n the presence of barnyardgrass (BYG) as indicator species based upon Equation 16 DENSITY OF BYG AS INDICATOR SPECIES (Plants/m 2) 0* 240 480 720 1980 1.844 1.997 1.778 1.190 1981 1.927 1.226 0.855 0.801 * From monoculture yield/density data (Table 4.1). 4.2.1.2 Redroot pigweed as indicator species The y i e l d s of barnyardgrass and redroot pigweed i n the mixtures i n which RPW was the indicator species are presented i n Figure 4.4. The general patterns of y i e l d response were similar to those observed for BYG as the indica tor species (compare Figures 4.3 and 4.4) but with some important differences. F i r s t , i n both years, BYG depressed the y i e l d of RPW at any density l e v e l more than RPW depressed the y i e l d of BYG. Second, while increasing densities of BYG depressed y i e l d s of RPW s i g n i f i c a n t l y at a l l densities of the l a t t e r (Appendix 3), i n both years the magnitude of the depressions were greatest at the highest RPW densities, as revealed by the tendency of the RPW curves in.Figure 4.4 to -converge: This i s i n contrast to the response of high-density BYG to.'.increasing densities of RPW (Figure 4.3). The curves for redroot pigweed (Figure 4.4) show that as the indicator species, i t s y i e l d i s related to the square root of the density of BYG. The application of the spacing formula to generate the yield-density curves for BYG at d i f f e r e n t densities of RPW also provides a reasonable f i t i n both 1980 and 1981. The BYG data also show that, whereas in 1980, increased competition from RPW progressively lowered the BYG yield-density curves, there was r e l a t i v e l y l i t t l e e f f e c t i n 1981. However, i n neither year was the magnitude of the e f f e c t of the indicator species (RPW) on the competing species (BYG) as great as with the roles reversed (compare 9U 2 Figure 4.4. Mean y i e l d s (g/m ) of barnyardgrass (B) i n monoculture (M S B, • , ) and i n the presence of three densities (240, 480, 720 plants/m 2) of redroot pigweed (Y B, •, ), and of redroot pigweed (P), (Yp, o, ) at these d e n s i t i e s . The curves were f i t t e d by Equations 9 (Y p) and 16 (M s B, Y B ) , 1980 and 1981 data. -97-DENSITY OF BYG (Plants/m 2) - 98 -Figures 4.3 and 4.4). The e f f e c t of RPW on BYG i s also demonstrated by the computed BJX values, (Table 4.3) which show that the e f f e c t i s considerably less than that of BYG on RPW (Table 4.2). Table 4.3 Estimated y i e l d (g per plant) of barnyardgrass (Bn. ) in 'the presence of redroot pigweed (RPW) as indicator species based upon Equation 8 DENSITY OF RPW AS INDICATOR SPECIES (Plants/m 240 480 720 4.20 4.14 3.60 3.84 2.79 2.05 * From monoculture yield/density (Table 4.1). 4.2.2 Yields of Barnyardgrass and Green F o x t a i l i n Additive Mixtures 4.2.2.1 Barnyardgrass as indicator species The component yi e l d s from the mixtures i n which barnyardgrass was the indicator species in varying densities of green f o x t a i l are presented in Figure 4.5. The two 0* 1980 4.37 1981 5.39 99 F i g u r e 4.5. Mean y i e l d s (g/m^) o f green f o x t a i l (G) i n monoculture (M s , • , ) and i n t h e pr e s e n c e o f thrcie d e n s i t i e s (240, 480, 720 p l a n t s / m 2 ) o f b a r n y a r d g r a s s ( Y Q , •, ) , and o f b a r n y a r d g r a s s ( B ) , ( Y B , o, ) a t t h e s e d e n s i t i e s . The c u r v e s were f i t t e d by E q u a t i o n s 9 ( Y B ) and 16 ( M s G , Y G ) . 1980 and 1981 d a t a . - 100 -BYG AS INDICATOR IN GFT B. 1981. / DENSITY OF GFT (piants/m 2) - 101 -s p e c i e s e x h i b i t e d a s i m i l a r y i e l d response p a t t e r n t o t h a t shown by BYG and RPW b i n a r y m i x t u r e s ( F i g u r e 4.3). Both GFT and RPW e x p e r i e n c e d y i e l d d e p r e s s i o n s from comparable monoculture d e n s i t i e s (see F i g u r e s 4.3 and 4.5). A g a i n , the c u r v e s g e n e r a t e d by E q u a t i o n 9 f o r the performance o f BYG, and by E q u a t i o n 16 f o r .GET ^provided r e a s o n a b l y good f i t s t o t h e d a t a . • • . , C o n s i d e r i n g t h e performance o f the i n d i c a t o r s p e c i e s (BYG) f i r s t , i t s y i e l d d e c l i n e d p r o g r e s s i v e l y w i t h i n c r e a s i n g d e n s i t i e s o f GFT i n b o t h 1980 and 1981. G e n e r a l l y , BYG y i e l d e d more i n 1981 t h a n i n 1980 ( F i g u r e 4.5). In b o t h seasons, t h e e f f e c t o f v a r y i n g d e n s i t i e s o f GFT was more 2 pronounced on t h e low (240 p l a n t s / m ) d e n s i t y BYG th a n on t h e medium - and h i g h - d e n s i t i e s . However, w i t h t h e e x c e p t i o n o f the l o w e s t BYG d e n s i t y , i n c r e a s i n g d e n s i t i e s o f GFT d i d not s i g n i f i c a n t l y d e p r e s s t h e y i e l d o f BYG a t any g i v e n d e n s i t y of t h e l a t t e r i n 1981, a l t h o u g h t h e y d i d so i n 1980 (Appendix 4) . The performance o f v a r y i n g d e n s i t i e s o f GFT a g a i n s t t h e background p o p u l a t i o n s o f t h e i n d i c a t o r s p e c i e s showed t h a t i t , t o o , was g e n e r a l l y more p r o d u c t i v e i n 1980 t h a n i n 1981 ( F i g u r e 4.5 and Appendix 4 ) . The c u r v e s g e n e r a t e d f o r GFT by t h e s p a c i n g f o r m u l a a t d i f f e r e n t d e n s i t i e s o f BYG te n d towards maxima, as was t r u e o f RPW a t d i f f e r e n t BYG d e n s i t i e s . ( F i g u r e 4.3). The r e l a t i v e d e p r e s s i o n o f t h e s e y i e l d c u r v e s by even t h e l o w e s t d e n s i t i e s o f BYG i n d i c a t e -102-t h a t t h e growth o f GFT was s e r i o u s l y i m p a i r e d by t h e presence o f BYG. The e s t i m a t e d y i e l d p e r GFT p l a n t (B Q) was lower i n t h e m i x t u r e t h a n i n t h e mo n o c u l t u r e s b o t h i n 1980 and i n 1981 (Table 4.4). In 1981 the B Q v a l u e s i n t h e monoculture 2 and i n t h e l o w - d e n s i t y (24 0 p l a n t s / m ) o f t h e i n d i c a t o r were h i g h e r t h a n i n 1980 but t h e r e v e r s e was t r u e f o r t h e medium-and h i g h - d e n s i t i e s o f t h e i n d i c a t o r s p e c i e s . The d e p r e s s i v e e f f e c t o f t h e i n d i c a t o r s p e c i e s (BYG) on t h e y i e l d o f GFT i s r e v e a l e d by t h e lower v a l u e s o f B fl i n the m i x t u r e t h a n i n the pure s t a n d s . T a b l e 4.4 E s t i m a t e d y i e l d (g per p l a n t ) o f green f o x t a i l (B^ ) i n t h e p r e s e n c e o f b a r n y a r d g r a s s (BYG) as i n d i c a t o r s p e c i e s based upon E q u a t i o n 16 DENSITY OF BYG AS INDICATOR SPECIES (P l a n t s / m ) 0* 240 480 720 1980 1.58 1.23 1.11 0 .58 B Q 1981 2.22 1.46 0 .83 0.61 From monoculture y i e l d / d e n s i t y (Table 4.1). -103-„ 4.2.2.2 Green f o x t a i l as i n d i c a t o r s p e c i e s The d a t a f o r t h e y i e l d s o f b a r n y a r d g r a s s and green f o x t a i l w i t h t h e l a t t e r as t h e i n d i c a t o r s p e c i e s a re p r e s e n t e d i n F i g u r e 4.6, and Appendix 5. The re s p o n s e s are g e n e r a l l y s i m i l a r t o t h o s e shown by BYG w i t h RPW as i n d i c a t o r s p e c i e s ( F i g u r e 4.4). I n b o t h y e a r s , y i e l d s o f GFT were s i g n i f i c a n t l y r e duced by i n c r e a s e d BYG d e n s i t i e s , w i t h t h e g r e a t e s t r e l a t i v e e f f e c t s o c c u r r i n g on the y i e l d s o f GFT a t t h e h i g h e s t d e n s i t y , r e s u l t i n g i n a convergence o f the GFT y i e l d c u r v e s . The y i e l d d e n s i t y c u r v e s f o r BYG ( F i g u r e 4.6) show l i t t l e e f f e c t o f i n c r e a s i n g d e n s i t y o f t h e i n d i c a t o r GFT, i n e i t h e r t h e 1980 o r 1981 d a t a . Only i n 1980 were t h e y i e l d s o f BYG s i g n i f i c a n t l y r educed from t h o s e o b t a i n e d i n monocul- . t u r e s . I n 1981, t h e y i e l d d e n s i t y r e l a t i o n s h i p s o f BYG appear t o be l a r g e l y d i c t a t e d by i n t r a s p e c i f i c i n t e r a c t i o n s . The per p l a n t y i e l d s ( e s t i m a t e d as B ft-values) a re p r e s e n t e d i n T a b l e 4.5 and are c o n s i s t e n t w i t h t h e c o n t e n t i o n t h a t i n n e i t h e r y e a r was any a p p r e c i a b l e i n t e r s p e c i f i c c o m p e t i t i v e e f f e c t o c c u r r i n g . 4.2.3 Y i e l d s o f Redroot Pigweed and Green F o x t a i l i n A d d i t i v e M i x t u r e s 4.2.3.1 Redroot pigweed as i n d i c a t o r s p e c i e s The y i e l d d a t a f o r green f o x t a i l and r e d r o o t pigweed i n a d d i t i v e s e r i e s m i x t u r e s a r e p r e s e n t e d i n F i g u r e 4.7a f o r 1981, t h e o n l y y e a r i n w h i c h t h e s e m i x t u r e s were s t u d i e d . The to4 F i g u r e 4.6 Mean y i e l d s (g/m ) o f b a r n y a r d g r a s s (B) i n monoculture ( M s B , M , ) and i n t h e p r e s e n c e o f t h r e e d e n s i t i e s (240, 480, 720 p l a n t s / m 2 ) of green f o x t a i l ( Y B , •, ) , and o f green f o x t a i l (G), ( Y Q , O, ) a t t h e s e d e n s i t i e s . The c u r v e s were f i t t e d by E q u a t i o n s 9 ( Y „ ) and 16 ( M s B , Y B ) . 1980 and 1981 d a t a . -105-• 1 1 r -240 480 720 960 1200 DENSITY OF BYG ( p l a n t s / m 2 ) DENSITY OF.BYG ( p i a n t s / m 2 ) -106-T a b l e 4.5 -Estimated y i e l d (g per p l a n t ) o f b a r n y a r d g r a s s (Bft ; ) i n t h e p r e s e n c e o f green f o x t a i l (GFT) as i n d i c a t o r s p e c i e s based upon E q u a t i o n 16 DENSITY OF GFT AS INDICATOR SPECIES (Plants/rrT) 0* 240 480 720 1980 4.37 4.37 3.25 2.30 B ft 1981 5.39 4.65 4.13 3.64 * From monoculture y i e l d / d e n s i t y d a t a (Table 4.1). y i e l d s o f t h e two s p e c i e s when RPW was t h e i n d i c a t o r s p e c i e s showed t h a t , a t any g i v e n d e n s i t y l e v e l , i t d i d not respond s i g n i f i c a n t l y t o v a r y i n g d e n s i t i e s o f GFT (Appendix 6 ) . However, i n c r e a s i n g i t s d e n s i t y d e p r e s s e d the y i e l d o f GFT below t h e monoculture y i e l d ( F i g u r e 4.7a). The y i e l d o f GFT i n c r e a s e d p r o g r e s s i v e l y as i t s d e n s i t y i n t h e m i x t u r e was r a i s e d but w i t h l i t t l e i n d i c a t i o n o f i t s y i e l d r e a c h i n g a p l a t e a u a t any d e n s i t y l e v e l o f RPW ( F i g u r e 4.7a, and Appendix 6 ) . The e s t i m a t e d y i e l d p e r GFT p l a n t (Bft ), computed from E q u a t i o n 16, was p r o g r e s s i v e l y reduced by RPW as shown i n T a b l e 4.6. 101 F i g u r e 4.7a. Mean y i e l d s (q/xxv) o f green f o x t a i l (G) i n m o n o c u l t u r e ( M s G , • , ) and i n t h e pre s e n c e o f t h r e e d e n s i t i e s (240, 480, 720 p l a n t s / m 2 ) o f r e d r o o t pigweed ( Y G , •, ), and o f r e d r o o t pigweed ( P ) , (Yp, o, ) a t t h e s e d e n s i t i e s . The c u r v e s were f i t t e d by E q u a t i o n s 9 (Yp) and 16 (M SGf Y G ) . 1981 d a t a . 2 F i g u r e 4.7b. Mean y i e l d s (g/m ) o f r e d r o o t pigweed (P) i n m o n o c u l t u r e (M sp, • , ) and i n t h e pr e s e n c e o f t h r e e d e n s i t i e s (240, 480, 720 p l a n t s / m 2 ) o f green f o x t a i l (Yp, •, ) , and o f green f o x t a i l (G), ( Y G , o, ) a t t h e s e d e n s i t i e s . The c u r v e s were f i t t e d by E q u a t i o n s 9 (Y G) and 16 (M sp, Y p ) . 1980 and 1981 d a t a . -108-A, RPW AS INDICATOR IN GFT -109-T a b l e 4.6 E s t i m a t e d y i e l d (g per p l a n t ) o f green f o x t a i l ( 3 f t ) i n t h e presence o f r e d r o o t pigweed (RPW) as i n d i c a t o r s p e c i e s , based upon E q u a t i o n 16 (1981 data) DENSITY OF RPW AS INDICATOR SPECIES ( P l a n t s / m ) 0* 240 480 720 B ft 2.22 1.51 1.303 1.259 * From monoculture y i e l d / d e n s i t y d a t a (Table 4.1). 4.2.3.2 Green f o x t a i l as i n d i c a t o r s p e c i e s The y i e l d s o f green f o x t a i l as i n d i c a t o r s p e c i e s were s i g n i f i c a n t l y (P < 0.05) d e p r e s s e d by r e d r o o t pigweed from t h o s e i n t h e monoculture a t a l l GFT d e n s i t i e s ( F i g u r e 4.7b). The response was s i m i l a r t o t h a t o b s e r v e d f o r GFT as an i n d i c a t o r s p e c i e s i n t h e pr e s e n c e o f GYG (compare F i g u r e s 4.6 2 and 4.7b). I n l o w - d e n s i t y GFT (240 p l a n t s / m ), i t s y i e l d was d e p r e s s e d s i g n i f i c a n t l y (P < 0.05) by i n c r e a s i n g d e n s i t i e s 2 o f RPW up t o 480 p l a n t s / m , but not t h e r e a f t e r (Appendix 7 ) . 2 However, i n medium- and h i g h - d e n s i t i e s (480 and 720 p l a n t s / m r e s p e c t i v e l y ) i t s y i e l d d e c l i n e d s i g n i f i c a n t l y w i t h each i n c r e m e n t s o f RPW d e n s i t y i n t h e m i x t u r e . Redroot pigweed on t h e o t h e r hand responded more t o i t s own i n c r e a s i n g d e n s i t i e s t h a n t o t h e presence o f GFT, as shown by i t s y i e l d - d e n s i t y c u r v e s i n F i g u r e 4.7b, wh i c h are -110-a l m o s t s u p e r i m p o s a b l e . The per p l a n t y i e l d s (Table 4.7) were o n l y m a r g i n a l l y lower i n the presence t h a n i n t h e absence of green f o x t a i l . T a b l e 4.7 E s t i m a t e d y i e l d (g per p l a n t ) o f r e d r o o t pigweed (B ) i n t h e p r e s e n c e o f green f o x t a i l (GFT) as i n d i c a t o r s p e c i e s , based upon E q u a t i o n 16. (1981 data) DENSITY OF GFT AS INDICATOR SPECIES (P l a n t s / m ) 0* 240 480 720 B a 1.93 1.81 1.66 1.63 From monoculture y i e l d / d e n s i t y d a t a (Table 4.1). 4.2.4 C o m p e t i t i o n Among B a r n y a r d g r a s s , Redroot Pigweed and Green F o x t a i l R e v e a l e d by A d d i t i v e S e r i e s E x p e r i m e n t s . The i n t e r s p e c i f i c c o m p e t i t i o n among b i n a r y combina-. t i o n s o f b a r n y a r d g r a s s , r e d r o o t pigweed and green f o x t a i l was i n v e s t i g a t e d by means o f t h e Index o f C o m p e t i t i o n (Dew, 1972) ( S e c t i o n 3.6.2). I n g e n e r a l , i n each b i n a r y combina-t i o n , t h e y i e l d s o f t h e i n d i c a t o r s p e c i e s were r e l a t e d t o t h e square r o o t o f t h e d e n s i t y o f the accompanying s p e c i e s , as p r e v i o u s l y shown i n F i g u r e s 4.3 t o 4.7. For d i f f e r e n t d e n s i t i e s o f each i n d i c a t o r s p e c i e s , t h e r e g r e s s i o n o f i t s y i e l d a g a i n s t t h e square r o o t o f t h e d e n s i t y o f t h e accompanying s p e c i e s p e r m i t t e d t h e d e t e r m i n a -t i o n o f t h e c o e f f i c i e n t s a (the e s t i m a t e d pure s t a n d y i e l d ) and b (the s l o p e o f t h e r e g r e s s i o n ) . The v a l u e s f o r t h e s e c o e f f i c i e n t s f o r t h e d i f f e r e n t c o m b i n a t i o n s o f s p e c i e s and d e n s i t i e s are p r e s e n t e d i n T a b l e s 4.8 and 4.9 t o g e t h e r w i t h the d e r i v e d Index o f C o m p e t i t i o n . The d a t a i n T a b l e 4.8 were o b t a i n e d w i t h o u t the i n c l u s i o n o f the monoculture y i e l d d a t a , w h i l e t h o s e i n T a b l e 4.9 i n c l u d e d t h e monoculture y i e l d s as d e s c r i b e d i n S e c t i o n 3.6.2. There i s good agreement between th e v a l u e s f o r the i n d i v i d u a l i n d i c e s o f c o m p e t i t i o n f o r t h e f o u r c o m b i n a t i o n s s t u d i e d i n b o t h 1980 and 1981. The r a n k i n g o f the i n d i c e s from g r e a t e s t t o l e a s t i s : b a r n y a r d g r a s s on green f o x t a i l ) ) a p p r o x i m a t e l y b a r n y a r d g r a s s on r e d r o o t pigweed ) e q u a l ) r e d r o o t pigweed on green f o x t a i l ) r e d r o o t pigweed on b a r n y a r d g r a s s green f o x t a i l on b a r n y a r d g r a s s green f o x t a i l on r e d r o o t pigweed i n b o t h seasons and u s i n g b o t h approaches t o t h e d e r i v a t i o n o f t h e i n d i c e s . Hence, GFT c l e a r l y emerges as the l e a s t a g g r e s s i v e c o m p e t i t o r and BYG as t h e most a g g r e s s i v e . BYG and RPW i n 1981 appear t o be anomalous i n t h a t the v a l u e s o f b d e c r e a s e w i t h i n c r e a s i n g d e n s i t y as shown i n T a b l e s 4.8 and 4.9. T h i s makes the d e r i v a t i o n o f CI o f q u e s t i o n a b l e v a l u e s i n c e t h e method r e q u i r e s t h a t t h e r e g r e s s i o n o f a and b, upon w h i c h i t i s based, pass t h r o u g h t h e o r i g i n . T h i s Table 4.8 Regression c o e f f i c i e n t s , c o r r e l a t i o n values and Indices of competition (CI) for barnyardgrass (BYG), redroot pigweed (RPW) and green f o x t a i l (GFT), based upon the method by Dew (1972) (Equations 9 and 20) without monoculture data Mixtures Indicator Density a b r CI a b r CI BYG+RPW BYG 240 480 720 RPW 240 480 720 BYG+GFT BYG 240 480 720 GFT 240 480 720 RPW+GFT RPW 240 480 720 GFT 240 480 720 1980 763.3 9.68 0.994 911.3 8.31 0.968 0.01035 1176.0 11.48 0.986 473.4 9.52 0.968 604.5 11.10 0.999 0.02130 951.6 21.44 0.999 774.9 11.77 0.976 1084.5 11.50 0.985 0.01139 1164.2 11.01 0.999 314.1 6.10 0.983 587.8 14.21 0.933 0.02240 686.0 14.74 0.984 _ -- - -1981 719.3 10.45 0.966 -877.4 7.57 0.994 0 .01127 980.9 0.67 0.976 336.9 7.15 0.973 555.5 12.07 0.972 0 .02215 744.1 16.78 0.970 754.6 8.24 0.995 919.5 6.46 0.976 0 .00790 986.2 2.64 0.999 363.6 8.54 0.983 486.0 10.69 0.993 0 .02200 693.6 14.92 0.976 351.0 2.06 0.988 535.6 2.82 0.997 0 .00051 615.5 0.30 0.999 404.8 8.81 0.966 508.6 10.47 0.968 0 .02187 741.3 11.65 0.999 Table 4.9 Regression c o e f f i c i e n t s , c o r r e l a t i o n values and Indices of competition (CI) for barnyardgrass (BYG), redroot pigweed (RPW) and green f o x t a i l (GFT), based upon the method by Dew (1972) (Equations 9 and 20) using X = l x l 0 - 9 9 f o r monoculture Mixtures Indicator Density CI CI BYG+RPW BYG+GFT RPW+GFT 1980 1981 BYG 240 658.3 6.34 0.987 692.9 9.50 0.986 480 974.2 10.81 0.988 0.01033 865.8 7.11 0.998 720 1168.2 11.12 0.998 986.6 0.93 0.991 RPW 240 373.8 5.92 0.913 334.9 7.08 0.992 480 566.6 9.60 0.996 0.01772 517.6 10.57 0.989 720 802.3 14.78 0.981 633.1 11.83 0.975 BYG 240 682.4 8.44 0.957 701.3 6.32 0.979 480 1005.7 8.38 0.974 0.00976 873.4 4.63 0.968 720 1166.8 11.13 0.999 987.3 2.68 0.999 GFT 240 296.5 5.46 0.991 356.3 8.29 0.994 480 500.8 10.76 0.958 0.02065 492.7 11.03 0.998 720 659.3 13.55 0.996 631.0 12.13 0.989 RPW 240 - ' - - 338.3 1.60 0.978 480 - - - - 514.0 1.96 0.972 720 - - - 617.8 0.40 0.994 GFT 240 - - - 366.2 7.41 0.979 480 - - - - 497.1 10.01 0.991 720 - - - 636.7 11.98 0.986 0.01038 0.01968 0.00616 0.02103 0.00365 0.01950 s i t u a t i o n occurred in other additive series and i s discussed below i n Section 5. 4.2.5 Predictions of Yields and Y i e l d Losses Among Barnyard-grass, Redroot Pigweed and Green F o x t a i l based upon Additive Series Experiments. The y i e l d density relationships established for the indicator species (using the approach by Dew, 1972) and for the accompanying species (using the spacing formula of de Wit, 1960), presented i n Figures 4.3 to 4.7, and Appendices 2 to 7; a l l had s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t s , i n d i c a t i n g the generally good f i t of the t h e o r e t i c a l curves to the observed data. The use of the spacing formula of de Wit (1960) (Equation 16) to estimate y i e l d s of the competing species in additive series appears to be j u s t i f i e d by the good agreements between observed and estimated y i e l d s , as revealed i n Figures 4.3 to 4.7 and the c o r r e l a t i o n c o e f f i c i e n t s which i n a l l cases exceeded 0.93 as shown i n Table 4.10, together with the c o e f f i c i e n t s for the regressions of observed and estimated y i e l d . Y i e l d losses of indicator species were calculated by means of Equation 20, with and without the incl u s i o n of the monoculture data as described i n Section 3.6.2.1. The data for several mixtures with a t o t a l density of 1440 plants/ 2 m are presented i n Table 4.11, together with the losses -115-Table 4.10 C o r r e l a t i o n and r e g r e s s i o n c o e f f i c i e n t s between observed and estimated y i e l d s of competing species i n a d d i t i v e s e r i e s experiments i n v o l v i n g barnyardgrass (BYG), redroot pigweed (RPW) and green f o x t a i l (GFT) Competing I n d i c a t o r I n d i c a t o r r b pecies species de n s i t y 1980 1981 1980 1981 BYG RPW 240 0.987 0.991 0.991 0.992 480 0.981 0.990 0.992 0.991 720 0.977 0.994 0.990 0.987 RPW BYG 240 0.979 0.998 1.008 0.996 480 0.977 0.996 0.988 0.999 720 0.999 0.963 1.000 1.000 BYG GFT 240 0.990 0.985 1.002 0.993 480 0.978 0.989 0.951 0.993 720 0.984 0.993 1.006 0.996 GFT BYG 240 0.965 0.976 0.988 0.976 480 0.988 0.990 1.006 0.988 720 0.997 0.987 0.996 0.980 RPW GFT 240 - 0.997 - 0.958 480 - 0.995 - 0.993 720 - 0.934 - 0.978 GFT RPW 240 - 0.997 - 0.993 480 - 0.999 - 0.995 720 - 0.996 - 0.993 Table 4.11 Ac t u a l and estimated losses of y i e l d (g/m ) of BYG, RPW and GFT as i n d i c a t o r s p e c i e s , based on Equation 20, f o r den s i t y r a t i o s 1:1, 1:2 and 1:5 Ac t u a l Excluding I n c l u d i n g Mixtures I n d i c a t o r l o s s monoculture* monoculture* 1980 1981 1980 1981 1980 1981 1:1 r a t i o (720+720) BYG + RPW BYG 292 25 326 297 318 275 RPW 407 340 543 442 381 334 BYG + GFT BYG 296 72 356 214 306 209 GFT 375 342 412 409 365 356 RPW + GFT RPW - 14 - 84 - 61 GFT - 327 - 435 - 333 1:2 r a t i o (480+960) BYG + RPW BYG 321 217 292 306 306 278 RPW 300 347 399 381 311 316 BYG + GFT BYG 321 134 383 225 304 167 GFT 364 344 408 331 320 321 RPW + GFT RPW - 59 - 84 - 58 GFT - 311 - 345 - 300 1:5 r a t i o (240+1200) BYG + RPW BYG 229 301 274 281 231 249 RPW 213 258 349 259 229 228 BYG + GFT BYG 229 209 306 206 231 150 GFT 188 274 244 277 212 260 RPW + GFT RPW - 52 - 62 - 43 GFT - 277 - 307 - 247 Excluding monoculture y i e l d s from Equation 20. ** . I n c l u d i n g monoculture y i e l d s i n Equation 20. o b s e r v e d . W h i l e t h e r e i s g e n e r a l l y good r e l a t i v e agreement between t h e r e s u l t s o b t a i n e d w i t h t h e two approaches t h e method i n w h i c h monoculture d a t a were i n c l u d e d c o n s i s t e n t l y p r o v i d e s e s t i m a t e s w h i c h a r e i n c l o s e r agreement w i t h t h e a c t u a l l o s s e s . The approach w i t h o u t t h e monoculture d a t a tends t o o v e r e s t i m a t e t h e l o s s e s , whereas t h e method which i n c l u d e s t h e monoculture d a t a o v e r e s t i m a t e s i n f o u r t e e n c a s e s and u n d e r e s t i m a t e s i n s i x t e e n . The most s e r i o u s o v e r -e s t i m a t e s a r e f o r BYG i n t h e 1981 season based upon th e 1:1 r a t i o . T h i s i s u n d o u b t e d l y due t o t h e a p p a r e n t l y anomalous s i t u a t i o n mentioned i n S e c t i o n 4.2.4, i n which t h e r e g r e s s i o n c o e f f i c i e n t s d e c r e a s e d w i t h i n c r e a s i n g d e n s i t y o f BYG as t h e i n d i c a t o r s p e c i e s . 4.3 Y i e l d s o f Rapeseed, Redroot Pigweed and Green F o x t a i l i n  B i n a r y A d d i t i v e S e r i e s E xperiments B i n a r y c o m b i n a t i o n s o f r a p e s e e d , r e d r o o t pigweed and green f o x t a i l i n a d d i t i v e s e r i e s were i n c l u d e d i n t h e 1981 d e s i g n o f Experiment A3. Treatments were i n c l u d e d w h i c h p e r m i t t e d e i t h e r o f t h e s p e c i e s i n any b i n a r y c o m b i n a t i o n t o be e v a l u a t e d as t h e i n d i c a t o r s p e c i e s . The r e s u l t s f o r each b i n a r y c o m b i n a t i o n are p r e s e n t e d s e p a r a t e l y i n t h e f o l l o w i n g s e c t i o n s , e x c e p t f o r t h o s e i n v o l v i n g r e d r o o t pigweed and green f o x t a i l , w h i c h have been p r e s e n t e d above i n S e c t i o n s 4.2.3.1 and 4.2.3.2. -118-4.3.1 Y i e l d s o f Rapeseed and Redroot Pigweed i n A d d i t i v e M i x t u r e s 4.3.1.1 Rapeseed as i n d i c a t o r s p e c i e s The d a t a on t h e y i e l d s o f r a p e s e e d and r e d r o o t pigweed i n a d d i t i v e s e r i e s b i n a r y m i x t u r e s were a n a l y z e d i n t h e same way as t h o s e f o r b a r n y a r d g r a s s and r e d r o o t pigweed i n a d d i t i v e s e r i e s m i x t u r e s ( S e c t i o n 4.2). When RPW was t h e i n d i c a t o r s p e c i e s , i n c r e a s i n g d e n s i t i e s o f RPW caused s i g n i f i c a n t (P < 0.05) and p r o g r e s s i v e l y g r e a t e r d e p r e s s i o n s o f t h e RPS y i e l d from t h e m onoculture o n l y i n t h e l o w - d e n s i t y (75 p l a n t s / 2 m ) RPS ( F i g u r e 4.8a; Appendix 8 ) . However, r a i s i n g t h e d e n s i t y 2 o f RPW beyond 720 p l a n t s / m had no s i g n i f i c a n t added e f f e c t on t h e y i e l d o f l o w - d e n s i t y RPS ( F i g u r e 4.8a). The e f f e c t o f t h e i n d i c a t o r s p e c i e s was t o d e p r e s s t h e y i e l d o f RPW below t h e monoculture y i e l d s a t comparable d e n s i t i e s ( F i g u r e 4.8a). A t any g i v e n d e n s i t y o f RPS, t h e y i e l d o f RPW i n c r e a s e d as i t s d e n s i t y was r a i s e d and approached p l a t e a u x a t t h e h i g h e r d e n s i t i e s . The t r a n s i t i o n s t o p l a t e a u y i e l d s o f RPW tended t o o c c u r a t lower d e n s i t i e s as t h e 2 d e n s i t y o f RPS i n c r e a s e d . I n t h e low d e n s i t y (75 p l a n t s / m ) 2 RPS t h e y i e l d o f RPW approached a p l a t e a u a t 96 0 p l a n t s / m 2 w h i l e i n t h e medium RPS d e n s i t y (150 p l a n t s / m ) i t was a t 2 2 720 p l a n t s / m . However, i n t h e h i g h d e n s i t y (225 p l a n t s / m ) t h e r e was a s i g n i f i c a n t (P < 0.05) y i e l d i n c r e a s e w h i c h was independent o f t h e RPW d e n s i t y (Appendix 8 ) . Figure 4.8a. Mean y i e l d s (g/m^) of redroot pigweed (P) i n monoculture (M s P, • , ) and in the presence of three densities (240, 480, 720 plants/m 2) of rapeseed (Yp, •, ), and of rapeseed (R), (Y R, O, ) at these d e n s i t i e s . The curves were f i t t e d by Equations 9 (Y R) and 16 (M s P, Y p ) . 1980 and 1981 data. Figure 4.8b. Mean y i e l d s (g/m'') of rapeseed (R) i n monoculture (M s R, • , ) and i n the presence of three densities (240, 480, 720 plants/m2) of redroot pigweed (Yp, •, ), and of redroot pigweed (PJ, (Yp, o, ) at these d e n s i t i e s . The curves were f i t t e d by Equations 9 (Y P) and 16 (M s R, Yp). 1980 and 1981 data. -120-DENSITY OF RPS (' RPS-units 1 ) . The estimated y i e l d s per RPW plant (Bft ) were lower in the mixtures with RPS than i n the monoculture (Table 4.12). The Bft values declined with increasing RPS den s i t i e s . Hence, the y i e l d of RPW was considerably depressed by increas-ing densities of RPW. Table 4.12 Estimated y i e l d (g per plant) of redroot pigweed (B'd ) i n the presence of rapeseed (RPS) as an indicator species based upon Equation 16. (1981 data DENSITY OFRPS AS INDICATOR SPECIES (Plants/m ) 0* 75 150 225 B tt 1.933 1.11 0.78 0.67 * From monoculture 'yield/density data (Table 4.1). 4.3.1.2 Redroot pigweed as indicator species The y i e l d s of rapeseed and redroot pigweed i n the mixtures i n which RPS was the indicator species are presented in Figure 4.8b. A similar y i e l d response pattern to that of RPS as the indicator species with RPW was exhibited with RPW as indicator. However, RPS depressed the RPW y i e l d at any density l e v e l more than RPW depressed the RPS y i e l d . Low-2 density (240 plants/m ) RPW suffered more y i e l d depressions 2 from.RPS than either medium (480 plants/m ) or high (720 plants/ IP/) d e n s i t i e s ( F i g u r e 4.8b). W i t h i n a g i v e n d e n s i t y o f RPW, t h e r e was no s i g n i f i c a n t i n c r e a s e i n t h e d e p r e s s i v e e f f e c t o f i n c r e a s i n g RPS d e n s i t y on y i e l d o v e r t h a t caused by 150 RPS 2 p l a n t s / m (Appendix 9 ) . T h i s i s i n c o n t r a s t t o the response o f RPS t o i n c r e a s i n g d e n s i t i e s o f RPW i n w h i c h h i g h - d e n s i t y RPS d i d not respond t o t h e p r e s e n c e o f RPW ( F i g u r e 4.8a). The e f f e c t o f r e d r o o t pigweed on the v a r y i n g d e n s i t i e s o f r a p e s e e d was t o d e p r e s s y i e l d below t h a t a t comparable d e n s i t i e s i n t h e monoculture ( F i g u r e 4.8b). Hence, the e s t i m a t e d y i e l d per RPS p l a n t (B ft) was lower i n t h e m i x t u r e s t h a n i n the monoculture (Table 4.13). The d e p r e s s i v e e f f e c t o f RPW tended t o i n c r e a s e as t h e d e n s i t y o f RPS i n t h e m i x t u r e was r e d u c e d . T a b l e 4.13 E s t i m a t e d y i e l d (g per p l a n t ) o f r a p e s e e d (BQ ) i n the p resence o f r e d r o o t pigweed (RPW) as an i n d i c a t o r s p e c i e s based upon E q u a t i o n 16 (1981 data) DENSITY OF RPW AS INDICATOR SPECIES ( p l a n t s / m 2 ) 0* 240 480 720 B ft 2 . 1 8 6 1 ' 3 1.739 1.493 1.290 ( 6 . 9 9 5 ) 2 ' 3 (5.566) (4.778) (4.129) * From m o n o c u l t u r e / d e n s i t y d a t a (Table 4.1) 1 O b t a i n e d from "RPS u n i t s " 2 O b t a i n e d from a c t u a l d e n s i t i e s o f r a p e s e e d 3 2 The y i e l d d a t a f o r t h e l o w e s t d e n s i t y (75 p l a n t s / m ) o f r a p e s e e d were o b t a i n e d from t h e f i t t e d c u r v e f o r r a p e s e e d i n F i g u r e 4.8b. 4.3.2 Yields of Rapeseed and Green F o x t a i l i n Additive Mixtures 4.3.2.1 Rapeseed as indicator species Y i e l d data for rapeseed and green f o x t a i l i n additive series binary mixtures were subjected to the same analysis as that used for the y i e l d of BYG and RPW additive series binary mixtures ', (Section 4.2.1). The yi e l d s of RPS and GFT i n the mixtures i n which RPS was the indicator species are presented in Figure 4.9a). Increasing GFT densities caused s i g n i f i c a n t (P <0.05) increased depression of the y i e l d of RPS only at low-o density (75 plants/m ) (Appendix 10). Green f o x t a i l densities 2 greater than 720 plants/m did not cause any further y i e l d depression i n the y i e l d of low-density RPS. The y i e l d of GFT at any density l e v e l of the i n d i c a -tor, increased as i t s density was raised and approached plateaux at the higher densities only i n the medium- (150 2 2 plants/m ) and high- (225 plants/m ) RPS densities (Figure 4.9a). The tr a n s i t i o n s to plateau y i e l d s of GFT tended to 2 occur at the same density (480 plants/m ) i n both medium- and high-density RPS (Appendix 10). The y i e l d per GFT plant (B ft ) was higher i n the pure stand than i n the mixtures (Table 4.14). Increasing densi-t i e s of RPS resulted i n increasing decline on the y i e l d per GFT plant. Hence, the GFT y i e l d i n the mixture with RPS i s lower 'than that i n the monoculture and i t declined as the density of RPS i n the mixture was raised. Fig. 4.9a Mean yiel d s (g/m^) of green f o x t a i l (G) in monoculture (MgG, • , — ) and i n the presence of three densities (240, 480, 720 "RPS-units") of rapeseed (YQ, • , ), and of rapeseed (R), ( Y R , 0, ) at these densities. The curves were f i l l e d by Equations 9 (YR) and 16 (MSG, YQ). 1981 data. Fig. 4.9b Mean uields (g/m2) of rapeseed (R) i n monoculture (MSG, • , ) and i n the presence of three densities (240, 480, 720 "RPS-units") of green f o x t a i l ( Y R , • , ) , and of green f o x t a i l (G), ( Y Q , 0, ) at these densities. The curves were f i t t e d by Equations 9 (YQ) and 16 (MSR, Y R ) . 1981 data. -125-T a b l e 4.14 E s t i m a t e d y i e l d (g per p l a n t ) o f green f o x t a i l (B Q ) i n t h e p r e s e n c e of' r a p e s e e d (RPS) as an i n d i c a t o r s p e c i e s based upon E q u a t i o n 16. (1981 data) DENSITY OF RPS AS INDICATOR SPECIES ( P l a n t s / m 2 ) 0* 75 150 225 B a 2 .223 1.350 1.070 0.849 * From monoculture yield/density data (Table 4.1). 4.3.2.2 Green f o x t a i l as i n d i c a t o r s p e c i e s The y i e l d s o f r a p e s e e d and green f o x t a i l i n the mix-t u r e s i n which GFT was the i n d i c a t o r s p e c i e s a re p r e s e n t e d i n F i g u r e 4.9b. The y i e l d r e s p onse p a t t e r n was s i m i l a r t o t h a t shown by RPS and RPW i n wh i c h the l a t t e r was the i n d i c a t o r s p e c i e s ( F i g u r e 4.8). I n c r e a s i n g RPS d e n s i t i e s caused s i g n i f i c a n t (P< 0.05) i n c r e a s e d d e p r e s s i o n i n the y i e l d o f a l l t h e t h r e e GFT d e n s i t i e s (240, 480 and 720 p l a n t s / m 2 ) . (Appendix 1 1 ) . The y i e l d o f RPS i n the presence o f GFT i n c r e a s e d as i t s d e n s i t y i n t h e m i x t u r e was r a i s e d . A t any g i v e n GFT d e n s i t y , a s i g n i f i c a n t (P ;,< 0.05) RPS y i e l d i n c r e a s e was r e a l i z e d f o r each increment i n RPS d e n s i t y (Appendix 11). However, the y i e l d tended t o s a t u r a t e a t h i g h e r d e n s i t i e s o f RPS. The d e p r e s s i v e e f f e c t o f GFT on the y i e l d o f RPS i s -127-i l l u s t r a t e d by the e s t i m a t e d y i e l d p e r p l a n t o f r a p e s e e d (Bft ) i n t h e m i x t u r e compared t o t h a t i n the monoculture (Table 4.15). The B ft v a l u e was h i g h e s t i n t h e monoculture and i t d e c l i n e d as t h e d e n s i t y o f GFT i n the m i x t u r e was r a i s e d . T a b l e 4.15 E s t i m a t e d y i e l d (g p er p l a n t ) o f rapeseed• (B 'ft") i n the presence o f green f o x t a i l (GFT) as i n d i c a t o r s p e c i e s based upon E q u a t i o n 16. [ (1981 data) DENSITY OF GFT AS INDICATOR SPECIES ( P l a n t s / m 2 ) 0* 240 480 720 Bft "RPS u n i t s " 2.19 1.95 1.72 1.62 A c t u a l RPS d e n s i t y (7.00) (6.25) (5.50) (5.18) * From mon o c u l t u r e y i e l d / d e n s i t y d a t a (Table 4.1). 4.3.3 Y i e l d s o f A d d i t i v e Redroot Pigweed and Green F o x t a i l M i x t u r e s 4.3.3.1 Redroot pigweed as i n d i c a t o r s p e c i e s (see S e c t i o n 4.2.3.1 4.3.3.2 Green f o x t a i l as i n d i c a t o r s p e c i e s (see S e c t i o n 4.2.3.2) -128-4.3.4 Competition Among Rapeseed, Redroot Pigweed and Green F o x t a i l Revealed by Additive Series Experiments The i n t e r s p e c i f i c competition among binary combinations of rapeseed, redroot pigweed and green f o x t a i l was investigated by means of Dew's Index of Competition. As i n the case of additive series involving barnyardgrass (described i n Section 4.2.4) i n each binary combination the y i e l d s of the indicator species were related to the square root of the density of the indicator species, as shown i n Figures 4.7 and 4.8. The regression c o e f f i c i e n t s a (the estimated pure stand yield) and b (the slope) were used to estimate the Index of Competition, with and without the incl u s i o n of the monoculture data, as described i n Section 3.6.2. Table 4.16 presents the estimates obtained without the incl u s i o n of the monoculture y i e l d s , and Table 4.17 presents the estimates obtained when the monoculture y i e l d s were included. Both approaches y i e l d the same rank order of indices: rapeseed on redroot pigweed (greatest) rapeseed on Green f o x t a i l redroot pigweed on green f o x t a i l redroot pigweed on rapeseed green f o x t a i l on rapeseed green f o x t a i l on redroot pigweed (least). from which rapeseed c l e a r l y emerges as the most aggressive competitor and green f o x t a i l as the least. -129-Table 4.16 Regression c o e f f i c i e n t s , c o r r e l a t i o n values and Indices of Competition (CI) for rapeseed (RPS) redroot pigweed (RPW) and green f o x t a i l (GFT), based upon the method of Dew (1972) (Equations 9 and 20) without monoculture data (1981 data) Density Mixtures Indicator "RPS u n i t s " a b r CI RPS + RPW RPS 240 640.1 11.91 0.995 480 582.4 3.89 0.967 0.01450 720 677.3 1.65 0.986 RPW 240 304.8 10.76 0.975 480 501.7 18.33 0.986 0.03959 720 777.0 32.07 0.999 RPS + GFT RPS 240 603.2 10.20 0.991 480 606.9 3.62 0.990 0.01211 720 707.6 2.75 0.984 GFT 240 433.1 16.84 0.984 480 625.3 23.45 0.982 0.03670 720 756.1 26.71 0.978 RPW + GFT (see Table 4.8) -130-Table 4.17 Regression c o e f f i c i e n t s , c o r r e l a t i o n values and Indices of Competition (CI) of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT), based upon the method of Dew (1972) (Equations 9 and 20) using X = l x l O - 9 9 for monoculture Density Mixtures Indicator "RPS-units" a CI RPS + RPW RPS 240 480 720 590.2 594.2 722.0 10.11 4.36 3.65 0.992* 0.992 0.973* 0.01202 RPW 240 480 720 327.2 507.8 637.0 12.21 18.76 20.90 0.992 0.997 0.974* 0.03500 RPS + GFT RPS 240 480 720 581.4 598.6 728.6 9.41 3.30 3.55 0.989 0.996 0.994 0.01117 GFT 240 480 720 373.0 518.4 638.5 12.96 15.86 17.33 0.975* 0.960* 0.966* 0.02984 RPW + GFT (see Table 4.9) r-values less than when monoculture data was omitted. -131-The incl u s i o n of the monoculture data consistently r e s u l t s i n lower estimates of the indices of competition, as was also observed i n the barnyardgrass series (Section 4.2.4). As i s shown i n Tables 4.16 and 4.17, the values of b decrease while those of a increase with increasing density of rapeseed as indicator species i n both RPW and GFT se r i e s . This i s similar to the si t u a t i o n i n the BYG serie s . (Tables 4.8 and 4.9). 4.3.5 Predictions of Yields and Y i e l d Losses among Rapeseed, Redroot Pigweed and Green F o x t a i l based upon Additive Series Experiments The application of the Dew's (1972) procedure for the analysis of the behaviour of the indicator species, and of the de Wit (1960) spacing formula for the accompanying species provided acceptable estimates of y i e l d , as indicated by s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t s of the curve i n Figure 4.7 and 4.8. Use of the spacing formula (Equation 16) again provided excellent estimates of y i e l d s of the competing species i n additive series experiments involving rapeseed, as revealed by the curves i n Figures 4.7 and 4.8, and the co r r e l a t i o n co-e f f i c i e n t s presented i n Table 4.18. Estimates of y i e l d losses for three density r a t i o s , based upon Equation 20 (Section 3.6.2) are presented i n Table 4.19, together with the actual losses observed. As was Table 4.18 Correlation and regression c o e f f i c i e n t s between observed and estimated y i e l d s of competing species i n additive series experiments involving rapeseed (RPS) redroot pigweed (RPW) and green f o x t a i l (GFT). 1981 data. Competing Indicator Indicator • species species density r b plants/m 2 RPS-units * ** * ** RPS RPS 240 0.925 0.997 0.974 0.997 480 0.978 0.999 0.983 1.000 720 0.955 0.999 1.117 0.999 RPW RPS 75 240 0.993 - 0.977 150 480 0.997 - 1.009 225 720 0.999 - 1.000 RPS GFT 240 0.959 0.999 0.982 0.998 480 0.981 0.997 0.986 0.998 720 0.999 0.999 1.001 1.001 GFT RPS 75 240 0.998 - 1.006 150 480 0.998 - 0.997 225 720 0.999 - 1.002 RPW GFT 240 480 720 As for Table 4.10 GFT RPW 240 480 720 * . . . , 9 From curves including rapeseed density 75 plants/m z. From curves excluding rapeseed density 75 plants/m , observed with the series involving BYG, the treatments of y i e l d losses based upon the Dew approach excluding monoculture data were greater than those obtained when monoculture data were included. Indeed, the estimates obtained by the former approach for the losses of RPW and GFT i n the presence of RPS i n 1:1 mixtures exceed the observed yie l d s of these species i n the monoculture (cf. Tables 4.1 and 4.19). However, at the 1:1 and 1:2 r a t i o s the inclusion of the monoculture data f a i l e d to provide good agreement with the observed losses except i n the cases of RPW or GFT as indicator species in the presence of GFT or RPW. With regard to the remaining estimates they are i n the same rank order as the observed losses, but are i n many cases at least a factor of two greater in magnitude. The lack of agreement between estimated and observed y i e l d losses i s attributable to the anomalous fa-values for RPS referred to i n Section 4.3.4, which decreased as RPS density increased. 4.4 Yields of Barnyardgrass (BYG), Redroot Pigweed (RPW) and  Green F o x t a i l (GFT) i n Binary Replacement Series  Experiments Binary combinations of barnyardgrass, redroot pigweed and green f o x t a i l i n replacement series were included i n Experiments A^, A 2 and A^ each of which was conducted in both 1980 and 1981. Table 4.19 Ac t u a l and estimated losses of y i e l d (g/m ) of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) as i n d i c a t o r s p e c i e s , based on Equation 20, f o r de n s i t y r a t i o s 1:1, 1:2 and 1:5. 1981 data. Mixtures I n d i c a t o r A c t u a l l o s s Excluding monoculture* I n c l u d i n g monoculture** 1:1 r a t i o (720+720) RPS + PRW RPS RPW RPS + GFT RPS GFT RPW + GFT RPW GFT 94 323 92 279 . 14 327 264 825 230 744 84 435 233 597 218 511 61 333 1:2 r a t i o (480+960) RPS + RPW RPS + GFT RPW + GFT RPS RPW RPS GFT RPW GFT 128 333 99 293 59 311 262 615 228 711 84 345 221 550 207 479 58 300 1:5 r a t i o (240+1200) RPS + RPW RPS RPW RPS + GFT RPS GFT RPW + GFT RPW GFT 338 230 302 264 52 277 322 418 253 551 62 307 246 392 225 386 43 247 Excluding monoculture y i e l d s from Equation 20. I n c l u d i n g monoculture y i e l d s from Equation 20. The experimental design permitted the examination of binary replacement series at f i v e t o t a l densities. The number of d i f f e r e n t density r a t i o s decreased as the t o t a l density decreased, with only the simple d i a l l e l system occurring at the lowest t o t a l density. The re s u l t s for the f i v e replacement series for each combination of species are presented separately i n the following sections. 4.4.1 Yields of Barnyardgrass and Redroot Pigweed Mixtures The r e l a t i v e performance of barnyardgrass and redroot pigweed in the mixtures d i f f e r e d markedly from each other (Table 4.20). In general, the y i e l d s of BYG did not d i f f e r to any s i g n i f i c a n t extent between the two seasons. However, the y i e l d of RPW was lower i n 1981 than i n 1980. In both seasons, increasing the proportions of BYG i n the mixture resulted i n depression of the yie l d s of RPW below those expected from i t s monoculture at comparable RPW densities (Table 4.21). The y i e l d s of RPW were also consistently lower than those of BYG at comparable dens i t i e s . In contrast, RPW caused r e l a t i v e l y less y i e l d depression of the y i e l d of BYG below those expected from the pure BYG stands, e s p e c i a l l y at high BYG d e n s i t i e s . At no proportions of BYG/RPW was there any in d i c a t i o n that mixture productivity exceeded the y i e l d of BYG i n the pure stand nor did any mixture y i e l d less than that of RPW i n the pure stand (Table 4.20). These data, Table 4.20 2 Mean y i e l d s (g/m ) of barnyardgrass (BYG) and redroot pigweed (RPW) i n binary replacement series mixtures and the i r mixture y i e l d s including r e l a t i v e y i e l d t o t a l s (RYT) during 1980 and 1981 seasons 1 . . . . 1980 . | . 0 240 480 720 900 1200 1440 Z 0 - 653 - 988 - 1167 1276 1295 - 1328 - 1.0 - 1.0 - 1.0 1 .0 1.0 1.0 240 _ 342 605 930 794 1004 1004 1204 1065 1273 1192 1321 - 1.0 325 1.194 210 0.891 200 1.028 208 1 .054 129 1.039 480 - 558 561 995 714 1070 912 1222 968 1228 - 1.0 434 0.995 356 0.989 310 1.050 260 1 .010 720 - 782 512 1130 679 1163 875 1250 - 1.0 618 1.146 484 1.101 375 1.068 960 — 830 458 ' 1107 667 1171 - 1.0 649 1.081 504 1.053 1200 — 895 424 1102 KEY - 1.0 678 1.060 Y i e l d of species a 1440 - 916 1.0 (horizontal) Y i e l d of x: >CX xxx Total 'RPW species b y i e l d ( v e r t i c a l ) xxx xxx RYT Table 4.20 Continued. 1981 240 480 720 960 1200 1440 RPW 334 1.0 509 1.0 618 1.0 720 1.0 786 1.0 846 1.0 240 685 1.0 574 228 485 362 413 472 384 528 348 608 802 1,113 847 1.077 885 1.032 912 1.002 992 1.023 480 803 1.0 765 172 704 291 674 403 646 451 937 1.053 995 1.046 1077 1.093 1097 1.044 720 987 1.0 970 145 967 258 962 278 1115 1.085 1225 1.160 1240 1.089 960 1097 1.0 1047 136 1041 162 1183 1.074 1203 1.014 1200 1162 1.0 1153 76 1229 1.001 KEY 1 4 4 0 Z«vn 1265 1.0 Y i e l d of species a (horizontal) Y i e l d of species b ( v e r t i c a l ) 04 :xxx -xxx X X X -xxx •Total y i e l d RYT See Appendix 2 for levels of si g n i f i c a n c e between treatments -138-Table 4.21 Relative performances of barnyardgrass (BYG) and redroot pigweed (RPW) expressed as r a t i o s of y i e l d of species i n mixture to i t s monoculture at comparable densities Density .(Plants/m ) Y i e l d r a t i o s of barnyardgrass and redroot pigweed 1980 1981 BYG or RPW Competitor^" BYG RPW BYG RPW 240 1200 0.649 0.377 0.560 0.226 480 960 0.675 0.462 0.749 0.318 720 720 0.750 0.479 0.975 0.450 960 480 0.759 0.607 0.949 0.626 1200 240 0.920 0.757 0.993 0.774 Density of competing species i n the mixtures. -139-therefore, conform to the frequently observed s i t u a t i o n in which mixture yie l d s f a l l between the pure stand y i e l d s of the higher and the lower y i e l d i n g monocultures. However, i n terms of r e l a t i v e y i e l d t o t a l s (RYT), in both years values greater than unity were observed (Figure 4.10), i n d i c a t i n g that the species were not competing exclusively for the same space or resources (sensu de Wit, 1960). In both seasons, decreasing t o t a l densities below 1440 plants/m resulted i n an increase i n RYT (Figure 4.10), which was p a r t i c u l a r l y 2 marked i n the 1980 season at the lowest density (480 plants/m ). The r e l a t i v e competitiveness of barnyardgrass over redroot pigweed during the two seasons was also indicated by the r e l a t i v e crowding c o e f f i c i e n t s . The c o e f f i c i e n t s for BYG were greater than unity while those of RPW were consider-ably less than one i n both seasons (Figure 4.10). In general, the crowding c o e f f i c i e n t s for BYG declined as the t o t a l density of the mixture was reduced but the converse was true for those of RPW. The products of the crowding c o e f f i c i e n t s (K) were greater than unity i n a l l f i v e t o t a l densities during the 1980 and 1981 growing seasons, which also suggests that the two species were not competing exclusively for the same space or resources. This i s also shown i n the r a t i o diagrams depicted i n Figure 4.11 i n which any deviation from a straight l i n e with a 45° slope i s interpreted as ind i c a t i n g the occurrence of noncompetitive i n t e r a c t i o n . Barnyardgrass per-forms better under cooler and more humid conditions than /VO F i g u r e 4.10. Replacement s e r i e s diagram f o r barnyard-grass (BYG) and r e d r o o t pigweed (RPW) based upon r e l a t i v e y i e l d s (r) d u r i n g 1980 and 1981. The k-values r e p r e s e n t the r e -l a t i v e crowding c o e f f i c i e n t s f o r BYG and RPW a t d i f f e r e n t t o t a l d e n s i t i e s ( Z a+Z b) • A.1980. B Y G / R P W : R P W / B Y G ^ P W : 0 Z B Y G + Z R P W : 1 W 0 3.1 1.0 Z B Y G / Z G F T I 10 F i g u r e 4.11. R a t i o d i a g r a m f o r BYG and RPW a t 1440 p l a n t s / m 2 t o t a l d e n s i t y f o r 1980 (o) and 1981 (•) seasons based upon t h e d a t a i n F i g u r e 4.10. -143-r e d r o o t pigweed (Holm e t a l _ . , 1977). The b e t t e r BYG p e r f o r m -ance and hence i t s g r e a t e r c o m p e t i t i v e n e s s over RPW (as i n d i c a t e d by t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t s ) i n 1981 season as compared t o 1980 can be a t t r i b u t e d t o the g r e a t e r p r e c i p i t a t i o n e x p e r i e n c e d i n 1981 (Appendix 1 ) . 4.4.2 Y i e l d s o f B a r n y a r d g r a s s (BYG) and Green F o x t a i l (GFT) i n B i n a r y Replacement S e r i e s The y i e l d d a t a f o r b a r n y a r d g r a s s and green f o x t a i l were a n a l y s e d i n the same manner as f o r b a r n y a r d g r a s s and r e d -r o o t pigweed ( S e c t i o n 4.4.1). I n b o t h s e a s o n s , t h e y i e l d o f BYG was markedly h i g h e r t h a n t h a t o f GFT (Table 4.22). G e n e r a l l y , the y i e l d s o f e i t h e r s p e c i e s i n t h e m i x t u r e were lower t h a n t h o s e from comparable d e n s i t i e s i n t h e m o n o c u l t u r e s (Table 4.23). However, f o r a g i v e n m i x t u r e p r o p o r t i o n , GFT s u f f e r e d much g r e a t e r y i e l d d e p r e s s i o n s t h a n BYG. I n t h e 1:1 m i x t u r e p r o p o r t i o n s , the GFT y i e l d was d e p r e s s e d t o 43% and 45% o f the monoculture y i e l d d u r i n g 1980 and 1981 r e s p e c t i v e l y . The d e p r e s s i v e e f f e c t o f GFT on the y i e l d o f BYG was g r e a t e r i n 1980 t h a n i n 1981 (Table 4.23). The y i e l d s o f BYG i n e q u i p r o p o r t i o n a l m i x t u r e s (1:1) w i t h GFT were 75% and 93% o f t h e monoculture, y i e l d s a t comparable d e n s i t i e s i n 1980 and 1981 r e s p e c t i v e l y . B a r n y a r d g r a s s was s i m i l i a r l y a f f e c t e d more i n 1980 t h a n i n 1981 by RPW ( S e c t i o n 4.4.1). The c o m p e t i t i v e n e s s o f BYG i n t h e m i x t u r e s w i t h GFT i s d e p i c t e d i n t h e r e l a t i v e y i e l d diagrams ( F i g u r e 4.12). The Table 4.22 Mean y i e l d s (g/m ) of barnyardgrass (BYG) and green f o x t a i l (GFT) in binary replacement series mixtures and t h e i r mixture y i e l d s including r e l a t i v e y i e l d t o t a l s (RYT) during 1980 and 1981 seasons 1 240 653 1 -0 480 988 1.0 1980 720 1167 1.0 960 1276 1.0 1200 1295 1.0 1440 -J3YG 1328 1.0 GFT 291 1.0 482 1.0 656 1.0 697 1.0 738 1.0 784 1.0 606 212 516 338 431 450 402 466 390 469 818 1.053 854 0.957 881 0.984 868 0.969 859 0.893 915 195 825 321 761 381 742 402 1110 1.081 1146 1.108 1142 1.104 1144 1.072 995 148 919 221 871 281 1143 0.992 1140 1.008 1152 1.014 1058 121 1021 118 1179 0.981 1139 0.919 1151 103 1254 0.998 KEY Y i e l d of species a (horizontal) xxx Y i e l d of species b , (v e r t i c a l ) • xxx xxx-xxx Total y i e l d RYT Table 4.22 Continued. 1981 0 i 240 480 720 960 1200 1440 0 _ 685 _ 863 _ 987 _ 1097 1162 1265 - 1.0 - 1.0 - 1.0 - 1.0 1.0 1.0 240 - 354 626 870 827 992 945 1066 1063 1161 1172 1252 1.0 244 1.21? 165 1.102 121 1.042 98 1.046 80 1.025 480 495 579 891 769 1031 929 1122 1055 1206 1.0 312 1.088 262 1.093 193 1.057 151 1.022 720 623 533 986 738 1127 915 1196 1.0 453 1.125 389 1.154 281 1.072 960 668 490 977 729 1155 1.0 487 1.072 426 1.105 1200 749 476 1031 1.0 555 1.065 1440 805 1.0 KEY BTG GFT Y i e l d of species a (horizontal) See Appendix 3 for levels of s i g n i f i c a n c e between treatments Y i e l d of — species b ( v e r t i c a l ) xxx xxx-• xxx xxx •Total y i e l d RYT -146-Table 4.23 Relative performance of barnyardgrass (BYG) and green f o x t a i l (GFT) expressed as the r a t i o s of y i e l d of species i n mixture to i t s monoculture y i e l d at comparable densities . Density 2 (Plants/m ) Y i e l d r a t i o s of barnyardgrass and green f o x t a i l 1980 1981 BYG or GFT Competitor 1 BYG GFT BYG GFT 240 1200 0.598 0.354 - 0.695 0.226 480 960 0.751 0.245 0.844 0.305 720 720 0.746 0.428 0.927 0.451 960 480 0.800 0.577 0.962 0.639 1200 240 0.889 .0.636.. 1.009 0.741 Density of competing species i n the mixture. J F i g u r e 4.12. Replacement s e r i e s diagram f o r BYG and GFT based upon r e l a t i v e y i e l d s (r) d u r i n g 1980 and 1981 seasons. The k-value r e p r e s e n t the r e l a t i v e crowding c o e f f i c i e n t s f o r BYG and GFT a t d i f f e r e n t t o t a l d e n s i t i e s ( z a + z b ) . A. 1980. • ZBYG + Z, G F T -149-BYG k - v a l u e s were h i g h e r t h a n t h o s e o f green f o x t a i l i n b o t h 1980 and 1981 seasons. I n 1981, the BYG c o e f f i c i e n t s were g r e a t e r than t h o s e i n 1980. However, t h e c o n v e r s e was t r u e f o r GFT e x c e p t i n t h e low d e n s i t y (480 p l a n t s / m 2 ) m i x t u r e s i n w h i c h t h e c r o w d i n g c o e f f i c i e n t f o r green f o x t a i l i n 1981 exceeded t h a t i n 1980. The c r o w d i n g c o e f f i c i e n t s f o r BYG were r e l a t i v e l y s t a b l e i n a l l t h e f i v e l e v e l s o f d e n s i t y w h i l e t h o s e f o r GFT tended t o d e c l i n e w i t h i n c r e a s i n g t o t a l d e n s i t y ( F i g u r e 4.12). However, t h e p r o d u c t s o f t h e c r o w d i n g c o -e f f i c i e n t s (K) were c l o s e t o u n i t y a t t h e h i g h (1440 and 1200 2 p l a n t s / m ) t o t a l d e n s i t y i n 1980 and g r e a t e r t h a n u n i t y a t lower t o t a l d e n s i t i e s i n 1980 and a t a l l d e n s i t i e s i n 1981. T h i s s u g g e s t s t h a t BYG and GFT were competing f o r the same r e s o u r c e s o n l y i n t h e h i g h t o t a l d e n s i t y d u r i n g 1980 season. However, i n 1981 and i n the low t o t a l d e n s i t i e s o f t h e m i x t u r e s d u r i n g 1980, t h e two s p e c i e s e x h i b i t e d a d d i t i o n a l noncompeti-t i v e i n t e r a c t i o n s (de W i t , 1960; H a l l , 1974a). T h i s i s a l s o shown by t h e r e l a t i v e y i e l d t o t a l s i n T a b l e 4.22; i n 1980, t h e s e f l u c t u a t e d above and below u n i t y i n t h e h i g h d e n s i t y o f the m i x t u r e s , whereas i n t h e low d e n s i t i e s and i n a l l the p l a n t i n g d e n s i t i e s d u r i n g 1981 t h e y were c o n s i s t e n t l y g r e a t e r t h a n one. I n no c o m b i n a t i o n d i d t h e m i x t u r e y i e l d exceed t h e monoculture y i e l d o f BYG o r f a l l below t h a t o f GFT i n t h e h i g h d e n s i t y m i x t u r e s d u r i n g 1981 and i n a l l d e n s i t y l e v e l s i n 1980 (Table 4.22). The r a t i o diagrams i n F i g u r e 4.13 a l s o i n d i c a t e t h a t i n 1981 t h e s l o p e o f t h e y i e l d - r a t i o c u r v e -150-F i g u r e 4.13. R a t i o diagrams f o r BYG and GFT a t 1440 p l a n t s / m 2 t o t a l d e n s i t y f o r 1980 (o) and 1981 (•) seasons based upon t h e d a t a i n F i g u r e 4.12. - 151 -d i f f e r e d from 45° indicating competition for d i f f e r e n t space (sensu de Wit, 1960). Although BYG i s ranked among the three most serious weeds in a number of crops on a world-wide basis (Holm et al_. , 1977), i t was not able to suppress the growth of GFT completely in the present experiments, even at the highest r e l a t i v e 2 densities i n the high (1440 plants/m ) t o t a l density mixture (Figure 4.12a and f ) . The two species occur together i n a g r i c u l t u r a l f i e l d s , but i n i r r i g a t e d f i e l d s BYG i s reported to be more abundant and more competitive (Dawson and Bruns, 1975) . . The less pronounced response of BYG to GFT observed in 1981 i s in agreement with t h i s suggestion even though the yi e l d s of GFT tended to be s l i g h t l y higher than in 1980 (Table 4 .22) . 4.4.3 Yields of Binary Redroot Pigweed and Green F o x t a i l Mixtures Redroot pigweed was more productive than green fox-t a i l both i n the monocultures and at comparable r e l a t i v e densities i n the mixtures (Table 4.24). The y i e l d of RPW was generally higher during 1981 than during 1980. Green f o x t a i l tended to y i e l d more i n 1981 than i n 1980 i n the treatments with low RPW densi t i e s . The response of RPW to the presence of GFT was more pronounced i n 1980 than i n 1981 (Table 4.25). Within a given season, the r a t i o of mixture to monoculture y i e l d s of RPW at comparable densities showed l i t t l e decline even at the highest Table 4.24 Mean y i e l d s (g/m ) of redroot pigweed (RPW) and green f o x t a i l (GFT) i n binary replacement series mixtures and t h e i r t o t a l mixture y i e l d s including r e l a t i v e y i e l d t o t a l s (RYT) during 1980 and 1981 seasons 1 240 480 1980 720 960 1200 1440 797 1.0 240 480 720 960 1200 1440 GFT 722 91 813 1.039 633 156 789 1.024 542 310 852 1.036 680 1.0 391 390 781 1.063 253 537 790 1.108 KEY Y i e l d of species a (horizontal) xxx xxx-Y i e l d of species b — ( v e r t i c a l ) -Total y i e l d -xxx xxx RYT Table 4.24 Continued. 240 334 1.0 480 509 1.0 1981 720 618 1.0 960 720 1.0 1200 786 1.0 1440 846 1.0 RPW 354 1.0 495 1.0 623 1.0 668 1.0 749 1.0 805 1.0 322 263 302 335 296 484 286 561 282 618 585 1.164 637 1.027 780 1.136 847 1.113 900 1.101 493 211 473 305 459 375 449 436 704 1.137 778 1.44 834 1.085 885 1.073 611 172 609 214 608 296 783 1.106 823 1.061 904 1.087 734 158 711 184 GFT See Appendix 7 for levels of s i g n i f i c a n c e between treatments, 892 1.145 895 1.069 793 77 870 1.033 KEY Y i e l d of species a (horizontal) Y i e l d of —-species b ( v e r t i c a l ) xxx -xxx xxx Total y i e l d xxx RYT GFT densities (Table 4.25). At low GFT density (240 plants/ m ), RPW showed no response to the presence of GFT i n the 1981 experiment. Hence, RPW responded more to i t s own density than to the density of GFT i n the mixture. The y i e l d of GFT on the other hand was considerably depressed below comparable densities i n the monoculture by a l l proportions of RPW i n the mixture (Table 4.25). The depressive e f f e c t of RPW on the y i e l d of GFT tended to be greater i n 1980 than i n 1981. Table 4.25 Relative performances of redroot pigweed (RPW) and green f o x t a i l (GFT) expressed as r a t i o s of y i e l d of species i n mixture to i t s monoculture y i e l d at comparable densities Densities Y i e l d r a t i o s of redroot pigweed (Plants/m 2) and green f o x t a i l RPW or GFT Competitor RPW 1980 GFT 1981 RPW GFT 240 .. . 1200 0 .739 0.314 0.842 0 .217 480 960 0.700 0.325 0.883 0 .372. 720 720 0.693 0 .472 0.983 0 .475 960 480 0.763 0.559 - 0.986 0 .652 1200 240 0.803 0 .728 1.009 0.825 In both seasons, the mixture y i e l d was greater than that of the lower y i e l d i n g monoculture species (GFT) i n a l l r a t i o s and i n 1981 the mixture y i e l d was consistently greater than the y i e l d of RPW (Table 4.24). However, RPW contributed proportionately more to the mixture y i e l d than did GFT. In both seasons the r e l a t i v e y i e l d t o t a l s consistently exceeded unity at a l l r a t i o s (Table 4.24). At the highest t o t a l density (1440 plants/m 2) the mean RYT for 1980 was 1.054, and i n 1981 i t was 1.072. The RYT tended to increase as the t o t a l density was reduced as shown i n Figure 4.14 for 1981. Hence, RPW and GFT i n the mixed stands exhibited noncompeti-t i v e interactions (de Wit and van den Bergh, 1965). However, since both species experienced y i e l d depressions below t h e i r monoculture y i e l d s at comparable densities (Table 4.25) competitive interactions between them were also occurring. The r e l a t i v e crowding c o e f f i c i e n t s for RPW were greater than 1.0 while those for GFT were consistently less than unity i n both seasons. In 1981, the RPW c o e f f i c i e n t s declined as the t o t a l mixture density was reduced (Figure 4.14) while the reverse was true for GFT. The crowding c o e f f i c i e n t s for both 2 species at 480 plants/m were greater than unity i n both species. This suggests that RPW had a competitive advantage over GFT i n both seasons; but i t s competitiveness declined as the t o t a l density was reduced as shown i n Figure 4.14 for the 1981 season. The products of the crowding c o e f f i c i e n t s were greater than 1.0 i n both 1980 and 1981. They tend to be greater i n low rather than i n high t o t a l density mixtures (Figure 4.14). This indicates that although competitive interaction was occurring, noncompetitive int e r a c t i o n was also present. In Figure 4.14. Replacement series diagram for redroot pigweed (RPW) and green f o x t a i l (GFT) based upon r e l a t i v e y i e l d s (r) during 1980 and 1981 seasons. The k-values represent the r e l a t i v e crowding co-e f f i c i e n t s for GFT and RPW at the d i f f e r e n t t o t a l densities (Z a+Zk). A. 1980. k R P W / G F T : -158-turn, the substantial noncompetitive interactive component leads to r a t i o diagram slopes being less than 45° at the 2 highest density (1440 plants/m ) of the mixtures i n both seasons, as shown i n Figure 4.15). Hence, the noncompetitive int e r a c t i v e component i n the interactions between RPW and GFT i n the present experiments was consistently revealed i n the actual y i e l d s (Table 4.24), i n r e l a t i v e y i e l d t o t a l s (RYT >• 1.0, Table 4.24), i n the products of the crowding c o e f f i c i e n t s (K > 1.0, Figure 4.14) and i n the r a t i o diagrams (Figure 4.15). Redroot pigweed i s inherently t a l l e r than green f o x t a i l . Hence, when the two are grown together i n mixed stands, competition for l i g h t to the detriment of GFT may occur. However, the two species d i f f e r considerably in th e i r root morphology; RPW has a tap root system while that of GFT i s fibrous and occupies the top s o i l horizons. In mixed stands therefore, the two species exploit d i f f e r e n t s o i l layers. The noncompetitive component of the int e r a c t i o n of these two species may therefore r e f l e c t these differences i n t h e i r root systems. 4.4.4 Competition among Barnyardgrass, Redroot Pigweed and Green F o x t a i l based upon Replacement Series Experiments The r e l a t i v e crowding c o e f f i c i e n t , k, may within l i m i t s be used as a measure of the competitiveness of a species in a binary replacement seri e s . While a k-value greater than unity implies greater competitive a b i l i t y , t h i s -159-F i g u r e 4.15. R a t i o diagrams f o r RPW and GFT a t 1440 p l a n t s / m 2 t o t a l d e n s i t y f o r 1980 (o) and 1981 (•) seasons based upon t h e d a t a i n F i g u r e 4.14. -160-may only be true when the product of the r e l a t i v e crowding c o e f f i c i e n t s (K) and the r e l a t i v e y i e l d t o t a l (RYT) are both equal to unity, and the two species are competing for the same resources (de Wit, 1960). When the values for K and RYT are greater than one, an i n d i v i d u a l k-value greater than one may indicate: (1) greater competitiveness, (2) that the species in question i s exp l o i t i n g resources not available to the second species, or (3) some combination of both. The k-values for the binary combinations of BYG, RPW and GFT are presented i n Table 4.26. The mean values suggest that i n both seasons, at a l l t o t a l densities except the lowest 2 (480 plants/m ), BYG was strongly competitive against both of the other species, and RPW was also strongly competitive against GFT. However, i n a l l combinations, except BYG and GFT i n 1980, the products of the r e l a t i v e crowding c o e f f i c i e n t s exceeded unity, and hence some part of the better performance of these species i s probably due to th e i r a b i l i t y to exploit resources not available to the competing species. As described previously i n Sections 4.4.1, 4.4.2 and 4.4.3, the k-values for the more aggressive species tended to decline with decreasing t o t a l density, while those for the less aggressive species tended to increase. S i m i l a r l y , the products of the crowding c o e f f i c i e n t s (K) and the r e l a t i v e y i e l d t o t a l s (RYTs) tended to increase with decreasing t o t a l density, which i s to be expected as less crowding for "space" or resources occurs. This i s shown i n another way i n Figures Table 4.26 Relative crowding c o e f f i c i e n t s (k) for binary combinations of BYG, RPW and GFT for 1980 and 1981 BYG (horizontal) and RPW ( v e r t i c a l ) 0 1980 1981 k 240-1980 1981 480 1980 1981 1.57 1.99 - 720 : 1980' 1981 1.46 1.83 - 960 1980 "1981 1.50 2.05 1200 : 1980 1981 1.64 2.41 1440 1980 ""1981 1.89 2.36 BYG 1.39 0.81 0.84 0.74 0.89 0.69 0.86 0.70 0.70 0.51 RPW 1.57 1.99 1.39 0.81 1.85 1.93 0.62 0.71 2.01 1.81 0.97 0.63 2.19 1.97 0.66 0.51 2.35 2.17 0.57 0.51 1.06 1.05 1.27 0.75 1.65 0.79 2.02 0.61 1.72 0.77 1.79 0.68 2.07 0.70 2.09 0.57 1.23 0.95 1.59 0.79 1.94 0.69 2.55 0.76 3.31 0.73 3.18 0.49 16 21 1.35 0.79 2.28 0.84 2.32 0.47 KEY 1980 data 1.76 0.82 2.06 0.49 1981 data xxx xxx xxx xxx i—^BYG (Parts A and B) CRPW (Part C) R^PW (Part A) o r *GFT (Parts B and C) Table 4.26 Continued. B. BYG (horizontal) and GFT ( v e r t i c a l ) 0 1980 1981 k 240 1980 1981 480 1980 1981 1.59 2.64 720 1980 1981 1.71 2.71 960 1980 1981 1.51 2.42 1200 1980 1981 1.67 2.72 1440 1980 1981 1.89 2.68 GFT 0.79 1.03 0.69 0.56 0.76 0.62 0.64 0.59 0.50 0.54 1.59 2.64 0.79 1.03 1.59 2.84 0.53 0.45 1.53 2.84 0.61 0.62 1.80 2.92 0.43 0.49 2.08 3.02 0.30 0.48 1.82 0.85 1.83 0.89 2.14 0.71 2.53 0.53 2.58 0.67 2.34 0.60 2.61 0.74 2.72 0.59 1.18 0.81 1.63 0.64 1.91 0.56 2.07 0.63 2.67 0.53 2.62 0.56 1.12 0.78 1.66 0.35 KEY 1980 data 2.68 0.61 2.51 0.48 1.30 0.76 2.52 0.57 1981 data xxx xxx xxx xxx. BYG (Parts A and B) o r CRPW (Part C) "RPW (Part A) o r GFT (Parts B and C) Table 4.26 Continued. C. RPW (horizontal) and GFT (v e r t i c a l ) 0 1980 1981 k 240 1980 1981 480 1980 1981 1.72 720 1980 1981 1.94 960 1980 1981 1.96 1200 1980 1981 2.56 1440 1980 1981 2.05 2.59 240 480 720 960 1200 1440 GFT 1.13 0.80 0.92 0.77 0.73 0.59 1.72 1.13 1.91 0.58 2.09 0.88 2.29 0.75 2.33 2.50 0.75 0.66 1.93 0.67 1.97 1.02 1.91 0.84 2.11 0.67 2.26 0.59 0 2.13 0.84 1.87 1.04 2.29 0.60 2.55 0.58 KEY 1.93 0.60 3.53 1.07 2.63 0.59 1980 1981 data data xxx xxx xxx xxx BYG (Parts A and B) or CRPW (Part C) CRPW (Part A) or GFT (Parts B and C) 4.10, 4.12 and 4.14 which indicate that, as t o t a l density decreased, there was a progressive tendency, for the r e l a t i v e y i e l d curves, whether concave or convex, to become straight l i n e s , or i n the case of the less aggressive species, to change from concave to convex, and thus begin to approach the yield-density curve for the species i n monoculture. Computations of aggressivity, A (McGilchrist and Trenbath, 1971) (based on the d i a l l e l mixture with 720 plants/ 2 m of each species)are presented i n Table 4.27, together with the mean Competitive Ratios, CR (Willey and Rao, 1980), mean Interference Ratios, (IR, the r a t i o of the suppression of the y i e l d per plant of species a caused by increased density of species a to the suppression caused by species b; see Section 3.6.2.2) and mean r e l a t i v e crowding c o e f f i c i e n t s (k) for the replacement series at maximum t o t a l density (1440 plants/m 2) . From Table 4.27 i t can be c l e a r l y seen that regardless of the s p e c i f i c attributes of the d i f f e r e n t measures of competitiveness, there i s consistency with regard to the general behaviour of the d i f f e r e n t species i n binary combina-tio n s . In 1980, the rankings based upon aggressivity from greatest to the least are: barnyardgrass vs green f o x t a i l barnyardgrass vs redroot pigweed redroot pigweed vs green f o x t a i l . Table 4.27 Aggressivity (A), Competition Ratio (CR), Interference Ratio (IR) and Relative Crowding Coefficients (k) among barnyardgrass (BYG), redroot pigweed (RPW) and green f o x t a i l (GFT) A* CR** IR** k** 1980 1981 1980 1981 1980 1981 1980 1981 BYG vs RPW 0.125 0.216 1.63 2.10 2.13 1.75 1.89 2.36 RPW vs BYG -0.125 -0.216 0.64 0.48 0.92 0.56 0.70 0.51 BYG vs GFT 0.149 0.188 2.07 2.22 2.18 1.97 1.89 2.68 GFT vs BYG -0.149 -0.188 0.51 0.46 0.69 0.55 0.50 0.54 RPW vs GFT 0.112 0.175 1.66 1.97 5.44 5.89 2.04 2.58 GFT vs RPW -0.112 -0.175 0.61 0.51 0.90 0.60 0.73 0.59 * A g g r e s s i v i t i e s based upon 1:1 density r a t i o 2 at 1440 plants/m t o t a l density. ** Mean Competition Ratios, Mean Interference Ratios and mean k-values based upon replacement series at 1440 plants/m 2 t o t a l density. - 1 6 6 -Based upon c o m p e t i t i v e r a t i o , r e d r o o t pigweed v s green f o x t a i l moves s l i g h t l y ahead o f b a r n y a r d g r a s s vs r e d r o o t pigweed. However, based upon i n t e r f e r e n c e r a t i o and k - v a l u e i t moves f u r t h e r ahead so t h a t t h e r a n k i n g becomes: r e d r o o t pigweed vs green f o x t a i l b a r n y a r d g r a s s vs r e d r o o t pigweed b a r n y a r d g r a s s vs green f o x t a i l . I n 1981, t h e r a t i n g s based upon a g g r e s s i v i t y a r e : b a r n y a r d g r a s s vs r e d r o o t pigweed b a r n y a r d g r a s s vs green f o x t a i l r e d r o o t pigweed vs green f o x t a i l , i . e . , a r e v e r s a l i n the r e l a t i v e b e h a v i o u r o f BYG t o GFT and RPW, which i n c r e a s e d t h e c o m p e t i t i v e n e s s o f BYG t o RPW. On t h e o t h e r hand, i n 1981 t h e r a t i n g s based upon IR a r e t h e same as i n 1980, a l t h o u g h t h e a b s o l u t e v a l u e s f o r IR a r e l o w e r . Of p a r t i c u l a r , i n t e r e s t i s the d i v e r g e n c e between IR and k v a l u e s f o r 1981. Thus i n terms o f IR, the g r e a t e s t c o m p e t i t i v e n e s s was shown by RPW a g a i n s t GFT, whereas a c c o r d -i n g t o k - v a l u e s , t h e c o m p e t i t i v e n e s s o f RPW a g a i n s t GFT was l i t t l e d i f f e r e n t from e i t h e r o f t h e s i t u a t i o n s i n w h i c h BYG was t h e a g g r e s s o r . S i n c e t h e IR v a l u e s a r e d i r e c t measures o f t h e e f f e c t i v e n e s s o f a g i v e n d e n s i t y o f a s p e c i e s i n r e d u c i n g the y i e l d p e r p l a n t o f a second s p e c i e s r e l a t i v e t o t h e e f f e c t i v e n e s s o f an e q u a l i n c r e a s e i n d e n s i t y o f the second s p e c i e s , t h e y s h o u l d p r o v i d e e x p e r i m e n t a l c o n f i r m a t i o n o f t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t s . From the d a t a i n Table 4.27, i t i s apparent that t h i s i s not always the case. 4.4.5 Predictions of Y i e l d and Yi e l d Losses i n Binary Replacement Series among Barnyardgrass, Redroot Pigweed and Green F o x t a i l Equation 5 permits the estimation of yiel d s i n binary mixtures, once mean values for r e l a t i v e crowding c o e f f i c i e n t s have been determined. The observed and estimated y i e l d s for the various binary mixtures among BYG, RPW and GFT are presented i n Table 4.28, together with the co r r e l a t i o n co-e f f i c i e n t s for each set of observed and estimated y i e l d s . The high r-values indicate the general v a l i d i t y of Equation 5 i n providing reasonable estimates of y i e l d i n binary replacement series mixtures. The d i f f i c u l t i e s inherent i n determining meaningful y i e l d losses i n replacement series have been discussed i n Section 3.6.2. Estimated r e l a t i v e losses, RL (relative to the monoculture y i e l d s at equivalent densities to those i n the binary mixtures), together with actual r e l a t i v e losses, RL, are presented i n Table 4.29 for binary combinations with the density r a t i o s , 1:1, 1:2 and 1:5 at t o t a l density of 2 1440 plants/m . Only these density r a t i o s are presented since they provide data which may be compared with losses estimated from additive series studies (Section 4.2.5). Such intercomparisons are discussed below (Section 5. 4 ), but at th i s time i t should be noted (from Table 4.29) that the Table 4.28 Observed (0) and estimated (6) y i e l d s * o f barnyardgrass (BYG), redroot pigweed (RPW) and green f o x t a i l (GFT) i n binary replacement s e r i e s mixtures during 1980 and 1981 seasons Combinations BYG+RPW BYG+GFT RPW+GFT 1980 1981 Za 0.833 0.667 0.500 0.333 0.167 0.167 0.333 0.500 0.667 0.833 r (0,6) b(0,6) BYG k=1.865 4 RPW k=0.697 o BYG k=1.897 4 GFT k=0.508 • f t 0 RPW k=2.042 GFT k=0.730 O 1191.5 967.9 875.2 667.2 423.8 1198.8 1047.5 864 .3 639.9 361.1 129 257 374 503 678 0.993 1.008 k=2.366 112.7 236 .4 376 .6 534.1 711.9 999 1.033 k=0.507 1150.8 1020.8 870.8 741.9 390.3 1200.2 1051.4 869.6 645.2 366.4 0.991 1.002 k=2.678 103.0 118.0 280.5 401.9 469.2 0. 1. 72.1 158.3 263.3 394.9 561.8 973 077 721.7 633.0 542.2 390.7 253.2 0 k=0.512 726.3 641.0 535.0 402.6 231.2 998 1.002 k=2.576 91.3 156.4 309.7 389.8 537.1 87.0 187.5 286 .9 403.9 533.7 0.994 1.002 k=0.591 0 .833 0.167 1152 .8 1166 .3 75. 7 77 .9 1172 .3 1176 .5 80 .1 74 .8 792 .9 785 .5 76 .7 85.3 0 .667 0.333 1041 .3 1044 .9 162. 1 171 .0 1055 .0 1066 .4 150 .9 164 .1 710 .6 708 .3 184 .0 183.4 0 .500 0.500 962 .4 889 .3 278. 4 284 .4 915 .4 920 .9 280 .8 272 .8 607 .5 609 .4 295 .8 298.5 0 .333 0.667 646 .2 685 .6 451. 3 426 .6 728 .8 723 .6 426 .4 407 .1 449 .8 476 .5 435 .5 436 .1 0 .167 0.833 383 .5 407 .3 608. 2 606 .9 475 .7 441 .5 555 .2 578 .5 281 .5 288 .6 618 .2 601.0 r (0,6) 0. 991 0. 998 0. 999 0 .996 0. 999 0. 999 b(0/6) 0. 996 0. 987 1. 000 1 .007 1. 004 0. 987 Y i e l d (g/m 2). Table 4.29 A c t u a l (RL) and estimated r e l a t i v e losses (RL) i n bin a r y replacement s e r i e s i n v o l v i n g BYG, RPW and GFT (g/m2) _^ RL RL 1980 1981 1980 1981 1:1 r a t i o (720:720) BYG/RPW 292 25 230 194 RPW/BYG 407 340 312 357 BYG/GFT 296 72 230 164 GFT/BYG 375 342 327 361 RPW/GFT 159 14 59 48 GFT/RPW 299 327 257 336 r=0.971 r=0.939 b=1.083 b=0.729 1:2 r a t i o (480: 960) BYG/RPW 321 217 289 266 RPW/BYG 300 347 309 350 BYG/GFT 321 134 289 229 GFT/BYG 364 344 312 363 RPW/GFT 109 59 69 61 GFT/RPW 302 311 259 344 r=0.973 r=0.956 b=1.006 b=0.917 1:5 r a t i o (240: 1200) BYG/RPW 229 301 279 291 RPW/BYG 213 258 224 256 BYG/GFT 229 209 279 258 GFT/BYG 188 274 218 278 RPW/GFT 51 52 61 58 GFT/BYG 186 277 189 268 r=0.976 r=0.971 b=1.169 b=0.927 -170-estimates and actual losses show nothing more than general agreement. The accuracy of the estimated values i s obviously limited by the degree to which the observed mixture y i e l d s follow the hyperbolic relationship required by Equation 16, and the accuracy of the estimated r e l a t i v e crowding c o e f f i -c ients. The actual r e l a t i v e losses, on the other hand, r e f l e c t the v a r i a b i l i t y of the primary data obtained from the spacing and replacement series experiments which i s magnified since the r e l a t i v e losses are differences. The c o r r e l a t i o n and regression c o e f f i c i e n t s indicate that there was closer agreement between actual and estimated losses i n 1980 than i n 1981, regardless of density r a t i o . However, the pattern of agreement between the years d i f f e r s markedly as a function of density r a t i o . In 1980, the best agreement was reached with the 1:1 and 1:2 r a t i o s , whereas i n 1981, the 1:5 r a t i o provided the best agreement. 4.5 Yields of Rapeseed (RPS) Redroot Pigweed (RPW) and Green  F o x t a i l (GFT) i n Binary Replacement Series Experiments Binary combinations of rapeseed, redroot pigweed and green f o x t a i l i n replacement series were included i n experi-ment A^ during 1980 and 1981. The experimental design i n 1980 contained only the replacement series at a t o t a l density of 2 1440 RPS units/m , whereas i n 1981, replacement series at f i v e t o t a l densities were studied. The numbers of density r a t i o s decreased as the t o t a l density decreased, with only the Table 4.30 Mean y i e l d s (g/m ) of rapeseed (RPS) and redroot pigweed (RPW) i n binary replacement series mixtures and t h e i r t o t a l mixture y i e l d s including r e l a t i v e y i e l d t o t a l s (RYT) during 1980 and 1981 seasons 1 75 150 1980 225 300 375 450 866 1.0 240 480 720 960 1200 1440 804 59 863 0.998 695 129 824 0.964 543 188 731 0.860 389 321 710 0.850 174 543 717 0.880 KEY 797 1.0 Y i e l d of species a (horizontal) xxx xxx- -Total y i e l d s RPW Yi e l d of _ species b (v e r t i c a l ) -xxx xxx RYT Table 4.30 Continued... 1981 0 75 150 225 300 375 450 0 - 575 - 597 - 728 — 840 893 965 — 1.0 - 1.0 - 1.0 - 1.0 1.0 1.0 240 334 464 687 . 527 688 653 787 744 865 864 968 1.0 223 1.215 161 0.984 - 134 0.963 121 0.987 104 1.018 480 509 369 702 493 786 639 868 751 927 1.0 333 1.046 293 0.994 229 1.007 176 0.986 720 618 321 820 471 857 634 929 1.0 499 1.075 386 1.018 295 1.006 960 720 263 855 469 910 1.0 592 1.048 441 1.007 1200 786 237 895 1.0 658 1.024 1440 846 1.0 KEY RPS IN) 13 RPW Y i e l d of species a i(horizontal) See Appendix 8 for sig n i f i c a n c e between treatments Y i e l d of species b ( v e r t i c a l ) xxx xxx Total y i e l d s xxx xxx RYT simple d i a l l e l system occurring at the lowest t o t a l density. Hence, only the data from the highest t o t a l density replace-ment series are common to both seasons. The re s u l t s for the replacement series for each combination of species are presented separately i n the following sections. 4.5.1 Yields of Binary Rapeseed and Redroot Pigweed Mixtures The r e l a t i v e performance of rapeseed and redroot pigweed d i f f e r e d considerably from each other (Table 4.30). The monoculture y i e l d s of RPS were higher than those of RPW both i n 1980 and 1981. In 1981, increasing proportions of RPS i n the mixture resulted i n depression of RPW yi e l d s below those expected from i t s monocultures at comparable densities (Table 4.31). During t h i s season, the yi e l d s of RPW were also consistently lower than those of RPS? at comparable seeding rates. In contrast, the depressive e f f e c t of RPW on RPS yield s below those expected from the pure stands of rapeseed was r e l a t i v e l y low (Table 4.31). In both seasons, there was no indicati o n of the mixture y i e l d s exceeding the monoculture y i e l d of RPS or f a l l i n g below that of RPW i n any mixture (Table 4.30). These data are similar to those obtained for barnyardgrass and redroot pigweed mixtures (Section 4.4.1) and agree with the frequently observed s i t u a t i o n i n which the mixture yie l d s f a l l between the pure stand y i e l d s of the higher and lower y i e l d i n g monocultures (Trenbath, 1974). Table 4.31 R e l a t i v e performance o f r a p e s e e d (RPS) and r e d r o o t pigweed (RPW) e x p r e s s e d as t h e r a t i o s o f y i e l d o f s p e c i e s i n m i x t u r e t o i t s m onoculture y i e l d a t comparable d e n s i t i e s d u r i n g 1981 D e n s i t y ("RPS u n i t s " ) 1 Y i e l d r a t i o s o f RPS and RPW 2 RPS o r RPW C o m p e t i t o r RPS RPW 240 1200 0 .413 0. 311 480 960 0.786 0. 346 720 720 0.871 0 . 478; 960 480 0 .894 0. 612 1200 240 0.967 0. 838 ^ One p l a n t o f ra p e s e e d r e d r o o t pigweed. 2 D e n s i t y o f competing i s e q u i v a l e n t t o 3.2 s p e c i e s . p l a n t s o f However, i n terms o f r e l a t i v e y i e l d t o t a l s , t h e 1980 season d a t a a t t h e h i g h e s t t o t a l d e n s i t y were g e n e r a l l y l e s s t h a n u n i t y (RYT = 0.912±0.067), w h i l e i n 1981 t h e v a l u e s were g e n e r a l l y v e r y s l i g h t l y g r e a t e r t h a n u n i t y a t a l l t o t a l d e n s i t i e s e x c e p t t h e l o w e s t ( F i g u r e 4.16) i n wh i c h t h e s i m p l e d i a l l e l m i x t u r e s ( F i g u r e 4.16e), t h e RYT i s c o n s i d e r a b l y g r e a t e r t h a n 1.0. Hence, i n 1980, t h e s p e c i e s appeared t o be a c t i n g i n a m u t u a l l y a n t a g o n i s t i c manner, (RYT < 1.0) w h i l e i n 1981, th e y were e s s e n t i a l l y competing f o r t h e same space 115 F i g u r e 4.16. Replacement s e r i e s diagram f o r RPS and RPW based upon r e l a t i v e y i e l d s (r) d u r i n g 1980 1981. The k - v a l u e s r e p r e s e n t t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t s f o r RPS and RPW a t d i f f e r e n t t o t a l d e n s i t i e s (Z a+Z b) i n "RPS-u n i t s " . A.1980. Z R P S : 1 0 .5 0 1 0 .5 Z R P W : 0 0 .5 0 1 0 .5 R P S + Z R P W ) : 1440 1200 -177-(sensu de Wit, 1960) except at the lowest t o t a l density (Figure 4.16) . The r e l a t i v e competitiveness of RPS over RPW at the high t o t a l density i n 1980 and at f i v e t o t a l densities i n 1981 was revealed by the r e l a t i v e y i e l d curves (Figure 4 . 1 6 ) . The r e l a t i v e crowding c o e f f i c i e n t s for RPS were greater than one while those of RPW were considerably less than one. Both species however, showed the highest crowding c o e f f i c i e n t s ( k R p s y R p w = 3.49; k R P W / R P S = 0.78) at the lowest t o t a l density of the mixtures. The r e l a t i v e crowding c o e f f i c i e n t s show that RPS outcompeted RPW i n both seasons. The difference i n the nature of interactions between the two species i s further i l l u s t r a t e d by the products of the crowding c o e f f i c i e n t s (K). In 1980, the K-value was much lower than one (K = 0.68) at the highest t o t a l density while i n 1981 i t was greater than one at a l l f i v e t o t a l densities (Table 4.30). Hence, the 1980 K-value also provides evidence for noncompetitive i n t e r -action, and, since i t i s appreciably less than unity suggests that the RPS was. i n h i b i t i n g the growth of RPW. The 1981 data, however, show that the int e r a c t i o n between the two species was predominantly competitive with RPS as the stronger competitor. The difference i n the nature of interactions between the two seasons i s c l e a r l y shown i n the r a t i o diagrams depicted i n Figure 4.17 i n which the slope of the 1980 data i s s i g n i f i -cantly greater than 1.0 while that i n 1981 for the same high t o t a l density of the mixture i s about unity. This information, -178-F i g u r e 4.17. R a t i o diagrams f o r RPS and RPW a t 1440 " R P S - u n i t s " t o t a l d e n s i t y f o r 1980 (o) and 1981 (•) seasons based upon d a t a i n F i g u r e 4.16. t o g e t h e r w i t h t h e RYT < 1.0 and K < 1.0, suggest t h a t i n 1980 RPS hampered t h e growth o f RPW by a mechanism o t h e r t h a n c r o w d i n g f o r t h e same space, p o s s i b l y a l l e l o p a t h y . I n 1980, RPS s e e d l i n g s emerged f o u r days e a r l i e r and got a head s t a r t o v e r RPW. A l l e l o p a t h i c p o t e n t i a l f o r RPS has f r e q u e n t l y been r e p o r t e d i n c e r e a l c r o p s ( H o r r i c k s , 1975; K a s t i n g e t a l . , 1973; Mason, 1979). Eussen (1979) r e p o r t e d t h a t i n Imperata  c y l i n d r i c a and maize o r sorghum i n c o n t a i n e r s RYT's as low as 0.65 were o b t a i n e d , but t h e growth o f Imperata i n t h e m i x t u r e remained r e l a t i v e l y t h e same w h i l e t h a t o f the c r o p was much lower t h a n i n t h e pure s t a n d s . De Wit (1978) c o n s i d e r e d t h i s c o n v i n c i n g e v i d e n c e f o r the e x i s t e n c e o f a l l e l o p a t h y between s p e c i e s grown i n a b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s . However, i n t h e case o f RPS and RPW, more work i s r e q u i r e d t o c o n f i r m the e x i s t e n c e o f a l l e l o p a t h y s i n c e t h e e f f e c t was o n l y o b s e r v e d i n one season. 4.5.2 Y i e l d s o f Rapeseed and Green F o x t a i l Rapeseed was more p r o d u c t i v e t h a n green f o x t a i l i n the monoculture and w i t h i n comparable d e n s i t i e s i n t h e i r b i n a r y m i x t u r e s (Table 4.32). The monoculture y i e l d s o f the two s p e c i e s were h i g h e r i n 1981 th a n i n 1980. W h i l e t h e y i e l d o f RPS i n t h e m i x t u r e d i d not d i f f e r a p p r e c i a b l y i n t h e two seasons, t h e y i e l d o f GFT was much h i g h e r i n 1981 th a n i n 1980 (Table 4.32). D u r i n g t h e 1980 growing season, t h e m i x t u r e s c o n t a i n i n g h i g h e r d e n s i t i e s o f RPS r e l a t i v e t o GFT were more Table 4.32 Mean yi e l d s (g/m ) of rapeseed (RPS) and green f o x t a i l (GFT) i n binary replacement series mixtures and the i r t o t a l mixture y i e l d s including r e l a t i v e y i e l d t o t a l s (RYT) during 1980 and 1981 seasons 1 1980 0 75 150 225 300 375 450 0 866 1.00 240 814 889 75 1.050 480 745 882 137 1.062 720 632 823 191 1.010 960 476 777 301 0.993 KEY 1200 277 679 402 0.912 Y i e l d of species a 1 (horizontal) 1440 680 1.0 xxx xxx • Y i e l d t o t a l s Y i e l d of - xxx xxx species b GFT ( v e r t i c a l ) RYT Table 4.32 Continued. 75 575 1.0 150 597 1.0 1981 225 728 1.0 300 840 1.0 375 893 1.0 450 965 1.0 JRPS 240 480 720 960 1200 1440 354 1.0 495 1.0 623 1.0 668 1.0 749 1.0 805 1.0 456 278 383 410 304 516 276 582 273 648 734 1.325 793 1.184 820 1.134 858 1.086 921 1.088 552 233 528 351 505 450 498 495 785 1.133 879 1.154 955 1.167 993 1.131 667 187 644 290 636 344 854 1.074 934 1.108 980 1.086 775 155 782 202 930 1.075 984 1.061 858 90 948 1.001 GFT KEY See Appendices 10 and 12 for signi f i c a n c e between treatments Y i e l d of _ species b ( v e r t i c a l ) Y i e l d of species a (horizontal) xxx xxx- Y i e l d t o t a l xxx xxx RYT ,1 -182-p r o d u c t i v e t h a n t h e RPS m o n o c u l t u r e s . The m i x t u r e y i e l d i n l o w e s t d e n s i t y o f rapeseed (1 RPS: 5 GFT) was e q u a l t o t h e y i e l d o f GFT i n t h e m o n o c u l t u r e . I n t h e 1981 growing season on t h e o t h e r hand, the t o t a l m i x t u r e y i e l d s were g r e a t e r than t h o s e o f RPS m o n o c u l t u r e s i n a l l m i x t u r e p r o p o r t i o n s e x c e p t i n the t r e a t m e n t s i n which e i t h e r s p e c i e s was i n the l o w e s t seed f r e q u e n c y (1 RPS: 5 GFT) and (5 RPS: 1 GFT). M i x t u r e y i e l d s were, i n a l l r a t i o s o f RPS and GFT, g r e a t e r t h a n t h a t o b t a i n e d from t h e GFT mo n o c u l t u r e s i n b o t h seasons (Table 4.32). I n terms o f t h e r e l a t i v e performance o f e i t h e r s p e c i e s i n t h e pr e s e n c e o f t h e c o m p e t i t o r r e l a t i v e t o i t s performance i n m o noculture a t comparable d e n s i t i e s , t he comparisons a r e l i m i t e d t o 1981, the o n l y season i n which a ra p e s e e d s p a c i n g experiment was co n d u c t e d . T a b l e 4.33 shows t h a t GFT su p p r e s s e d the y i e l d r a t i o o f RPS t o a much l e s s e r e x t e n t t h a n the s u p p r e s s i o n o f t h e GFT y i e l d r a t i o by RPS. The mean r e l a t i v e y i e l d t o t a l s (RYT) a t the h i g h e s t t o t a l d e n s i t y o f t h e m i x t u r e were about one i n 1980 (RYT = 1.00610.060) b u t i n 1981 t h e y were g r e a t e r t h a n u n i t y a t a l l the f i v e t o t a l d e n s i t i e s ( F i g u r e 4.18), and i n c r e a s e d as t h e t o t a l d e n s i t y d e c r e a s e d . These d a t a suggest t h a t c o m p e t i t i v e i n t e r a c t i o n s p l a y e d a major r o l e i n the i n t e r a c t i o n s d u r i n g 1980 (RYT = 1.00) w h i l e d u r i n g 1981 n o n c o m p e t i t i v e i n t e r -a c t i o n s a l s o o c c u r r e d (RYT :> 1.0) a t a l l f i v e t o t a l d e n s i t i e s (de W i t and van den Bergh, 1965). -183-Table 4.33 Relative performance of rapeseed (RPS) and green f o x t a i l (GFT) expressed as r a t i o s of y i e l d of species i n mixture to i t s monoculture y i e l d at comparable densities during 1981 Density (" RPS u n i t s " ) 1 Y i e l d r a t i o s of RPS and GFT RPS or GFT 2 Competitor RPS GFT 240 1200 0 .475 0.253 480 960 0.834 0.408 720 720 0.873 0.552 960 480 0.931 0.742 1200 240 0.961 0 .864 One plant of rapeseed i s equivalent to 3.2 plants of green f o x t a i l . Density of the competing species. The r e l a t i v e competitiveness of RPS and GFT i n binary mixtures i s r e f l e c t e d by t h e i r r e l a t i v e crowding c o e f f i c i e n t s . At the highest t o t a l density, the RPS c o e f f i c i e n t i n 1980 was greater than two ( k R ps/GFT = 2*^ 4) while that of GFT was considerably less than 1.0 ( k G F T / R p s = °-44). In 1981, while the k-value for RPS was above unity at the high t o t a l density (Figure 4.18) i t declined as the t o t a l density was reduced to 96 0 "RPS-units", and then increased at lower t o t a l densities reaching 3.23 at the lowest t o t a l density (480 "RPS-units"). This i s i n contrast with the k-values for GFT which increased -184-c o n s i s t e n t l y as t h e t o t a l d e n s i t y was reduced and a t t a i n e d v a l u e s g r e a t e r t h a n u n i t y i n m i x t u r e s i n which t h a t t o t a l d e n s i t y was l e s s t h a n 1200 " R P S - u n i t s " ( F i g u r e 4.18). However, t h e p r o d u c t s o f t h e c r o w d i n g c o e f f i c i e n t s (K) were g r e a t e r t h a n u n i t y and t h e y were h i g h e r i n 1981 t h a n i n 1980. In 1981, the K - v a l u e s i n c r e a s e d as t h e t o t a l d e n s i t y o f t h e m i x t u r e was red u c e d ^ ( F i g u r e .4.18), . i n d i c a t i n g t h a t n o n c o m p e t i t i v e i n t e r -a c t i o n s were i n c r e a s i n g as t o t a l d e n s i t y was r e d u c e d . I n s p e c -t i o n o f t h e r a t i o diagrams f o r t h e m i x t u r e s i n the h i g h e s t t o t a l d e n s i t y ( F i g u r e 4.19), c o n f i r m s t h i s i n t e r p r e t a t i o n , s i n c e the s l o p e s are l e s s t h a n 45° i n b o t h seasons. Green f o x t a i l responded t o RPS i n a s i m i l a r manner t o i t s r e s p onse t o RPW ( S e c t i o n 4.4.3). I n b o t h m i x t u r e s i t u a -t i o n s , n o n c o m p e t i t i v e i n t e r a c t i o n was e v i d e n t i n b o t h 1980 and 1981 growing season. W h i l e t h e y i e l d s o f RPW o r RPS were more dependent on t h e i r own r e l a t i v e d e n s i t i e s i n t h e m i x t u r e s , t h a n on t h o s e o f GFT, t h e y i e l d s o f GFT were g r e a t l y i n f l u e n c e d by t h e t o t a l m i x t u r e d e n s i t y . The c o m p e t i t i o n s t r e s s on GFT from e i t h e r RPS o r RPW was g r e a t l y a l l e v i a t e d by r e d u c i n g t h e t o t a l m i x t u r e d e n s i t y ( c f . F i g u r e s 4.18 and 4.13 r e s p e c - . t i v e l y ) . 4.5.3 Y i e l d s o f B i n a r y Redroot Pigweed and Green F o x t a i l M i x t u r e s These d a t a are p r e s e n t e d i n S e c t i o n 4.4.3. / 26' Figure 4.18. Replacement series diagram for RPS and GFT based upon r e l a t i v e y i e l d s (r) during 1980 and 1981. The k-values represent the r e l a -t i v e crowding c o e f f i c i e n t s for RPS and GFT at d i f f e r e n t t o t a l densities (Za+Z)3) " i n RPS- units" 1980 Z R P S : 1 0 .5 0 1 0 .5 Z G F T : 0 0 .5 0 0 0 .5 ( Z R P S + Z G F T : mW 1200 -187-F i g u r e 4.19. R a t i o diagrams f o r RPS and GFT a t 1440 " R P S - u n i t s " t o t a l d e n s i t y f o r 1980 (o) and 1981 (•) seasons based upon t h e d a t a i n F i g u r e 4.18. -188-4.5.4 Competition among Rapeseed, Redroot Pigweed and Green F o x t a i l based upon Replacement Series Experiments The r e l a t i v e crowding c o e f f i c i e n t s for the binary combinations of rapeseed, redroot pigweed and green f o x t a i l are presented i n Table 4.34. Unlike the experiments contain-ing barnyardgrass (Section 4.4), the mean values i n a l l cases, except that for RPW competing against GFT, increased as t o t a l density decreased. Thus, not only did the strong competition of RPS become more so, but the weaker competitors, RPW and GFT also tended to become more competitive as t h e i r densities increased and that of RPS decreased. As a r e s u l t , the products of the c o e f f i c i e n t s (K) increased to values greater than 3.0 at the lowest t o t a l density. In the case of RPS against RPW, t h i s increase i n K was only apparent at the lowest density, although values greater than one occurred at each t o t a l density, whereas with RPS against GFT, the increase occurred throughout the range of d e n s i t i e s . In the former case, the r e l a t i v e y i e l d t o t a l was close to unity except at the lowest density where i t rose to 1.215 (Table 4.30) whereas i n the l a t t e r , i t was greater than one through-out (Table 4.32). Hence, RPS was highly competitive against both species, and appeared to compete for the same resources as RPW. Competition against GFT, however, appeared to involve d i f f e r e n t resources. Table 4.34 Relative Crowding Coefficients (k) for binary combinations of RPS, RPW and GFT in 1981 A. RPS (horizontal) and RPW (vertical) 75 150 3.49 225 1.69 300 1.48 375 1.57 450 1.78 JRPS RPW 0.78 0.64 0.71 0.69 0.60 3.49 2.06 1.86 1.6.7 1.63 0.78 0.58 0.75 0.76 0.70 1.31 1.42 1.67 1.89 0.70 0.69 0.64 0.54 1.16 1.68 0.69 0.62 1.92 . 0.54 1.25 1.75 0.73 0.53 KEY 1.71 0.70 198,0 1981 data data . xxx .xxx xxx xxx _ KRPS (Parts A and B) k k RPW (Part G) RPW (Part A) GFT (Parts B and C) Table 4.34 Continued... B. RPS (horizontal) and GFT (vertical) 0 75 150 3.23 225 1.90 300 1.56 375 1.78 450 1.96 RPS GFT 1.28 1.08 1.14 0.97 0.73 3.23 2.22 1.70 1.79 1.97 1.28 0.96 1.13 0.87 0.83 1.57 1.69 1.95 2.13 1.19 1.11 1.00 0.80 1.29 1.72 1.93 1.17 0.95 0.75 1.64 2.13 1.04 0.67 KEY 1980 data 1.60 1981 data xxx xxx xxx xxx 0.63 'PvPS (Parts A and B) o CRPW (Part C) CRPW (Part A) or '"GFT (Parts B and C) Table 4.34 Continued. C. RPW (horizontal) and GFT ( v e r t i c a l ) GFT 1.13 0.80 0.92 0.77 0.59 240 1.72 1.91 2.09 2.29 2.50 1.13 0.58 0.88 0.75 0.66 480 1.72 1.97 1.91 2.11 2.26 1.02 0.84 0.67 0.59 720 1.94 960 1.96 1.87 2.29 2.55 1.04 0.60 0.58 3.53 2.63 KEY 1.07 0.59 1200 2.56 1980 1981 data data xxx xxx xxx xxx 2.99 0.53 1440 2.59 RPW RPS (Parts A and B) o r CRPW (Part C) RPW (Part A) o r I GFT (Parts B and C) 192-As discussed i n Section 4.4.4, RPW was a stronger competitor than GFT, although i t became less so as the t o t a l density increased. These differences i n behaviour are c l e a r l y shown by the changes i n the curves shown in Figures 4.15 and 4.17 for rapeseed mixtures and i n Figure 4.13 for RPW and GFT. The a g g r e s s i v i t i e s , A, for the d i a l l e l mixtures with o 720 plants/m of each species, and mean competitive r a t i o s , mean interference r a t i o s and mean k-values for the complete replacement series at a t o t a l of 1440 "RPS-units" are presented i n Table 4.35. These data c l e a r l y show that RPS i s consis-te n t l y a stronger competitor than either of the other species. However, the d i f f e r e n t measures of competitiveness reveal differences i n rankings. In terms of aggressivity or competitive r a t i o , the most competitive species i s RPW against GFT, followed by RPS against RPW and RPS against GFT. In terms of interference r a t i o and r e l a t i v e crowding c o e f f i -cient, RPW against GFT i s s t i l l the most competitive, but the order of the mixtures involving rapeseed i s reversed. Thus, unlike the BYG series (Section 4.4), IR and k are i n agreement with regard to the rankings of competitiveness. Further discussion of these measures of competition i s deferred u n t i l Section 5 . 4 , i n order to include intercomparison with competitive indices obtained from additive series experiments. Table 4.35 Aggressivities (A), Competitive Ratios (CR), Interference Ratios (IR) and Relative Crowding Coefficients (k) among rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) 1981 data A* CR* IR** k** RPS V S RPW 0.154 1.73 2.30 1.78 RPW vs RPS -0.154 0.58 0.62 0.60 RPS V S GFT 0.116 1.64 2.82 1.96 GFT vs RPS -0.116 0.61 0.68 0.73 RPW vs GFT 0.176 1.97 5.89 2.58 GFT vs RPW -0.176 0.51 0.60 0.59 Aggressivities and Competitive Ratios based upon 1:1 density r a t i o at 1440 "RPS-units" t o t a l density. ** Mean Interference Ratios and mean k-values based upon replacement series at 1440 "RPS-units" t o t a l density. 4.5.5 Predictions of Yields and Yi e l d Losses i n Binary Replacement Series among Rapeseed, Redroot Pigweed and Green F o x t a i l Estimates of yi e l d s i n binary mixtures can be computed using Equation 5 once the r e l a t i v e crowding c o e f f i c i e n t s have been determined. The observed and estimated y i e l d s for RPS, RPW and GFT are presented i n Table 4.36, together with the cor r e l a t i o n c o e f f i c i e n t s for each set of y i e l d s . The high Table 4.36 Observed (0) -and estimated (0) yields of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) in binary replacement series mixtures during 1980 and 1981 seasons 1980 1981 Combinations RPS+RPW RPS+GFT RPS k=1.834 RPW k=0.373 RPS k=2.738 GFT k=0.442 Za zb 0 0 0 0 0 0 -& 0 .833 0 .167 803 .9 780 .4 59 .2 55. 8 814 .2 807. 3 75 .4 55. 1 0 .667 0.333 694 .6 680 .8 129 .1 125. 2 744 .9 732. 8 137 .4 123. 1 0 .500 0 .500 543 .2 560 .4 187 .7 216. 9 632 .3 634 . 1 190 .7 208. 0 0 .333 0.667 388 .6 414 .0 321 .0 341. 2 476 .4 500. 7 301 .4 318. 9 0 .167 0.833 173 .8 233 .0 543 .5 518. 2 277 .4 306 . 6 402 .5 467 . 8 r(0,0) 0 . 912 0. 994 0 . 999 0. 998 b(0,6) 1. 130 0. 995 1. 003 1. 100 k=l .780 k=0 .601 k=l .955 k=0 .733 0 .833 0.167 863 .5 867 .4 103 .9 91. 4 858 .2 875. 2 89 .9 103. 0 0 .667 0.333 750 .9 753 .6 176 .1 195. 5 781 .6 769. 0 201 .9 215. 6 0 .500 0 .500 634 .0 617 .5 295 .2 317. 4 635 .8 638. 8 343 .6 340 . 3 0 .333 0.667 468 .9 454 .5 440 .7 462 . 1 497 .9 476 . 7 495 .2 478. 7 0 .167 0.833 237 .4 253 .8 658 .2 634 . 8 273 .1 272 . 1 647 .1 631. 6 r(0,0) 0. 998 0. 995 0. 998 0 . 999 b(0,0) 0. 996 1. 004 0 . 997 0 . 981 -195-r-values indicate the v a l i d i t y of Equation 5 i n estimating yie l d s i n binary replacement series mixtures. Estimated r e l a t i v e y i e l d losses, RE together with actual r e l a t i v e losses, RL, are presented in Table 4.37 for binary combinations with the density r a t i o s , 1:1, 1:2 and 1:5 at t o t a l density of 1440 "RPS-units", which are the only treatments that are also found i n the additive series for the purpose of intercomparison between the two experi-mental designs. Such intercomparisons are deferred to the general discussion (Section 5. 4 ). However, the estimated and actual losses presented in Table 4.37 give high r-values i n d i c a t i n g general agreement. The li m i t a t i o n s of the accuracy i n the estimated values by the hyperbolic r e l a t i o n -ships required by Equation 16 and the accuracy of the estimated k-values discussed e a r l i e r in Section 4.4.5 for barnyardgrass mixtures are further stressed. The c o r r e l a -t i o n and regression c o e f f i c i e n t s indicate that there was a closer agreement between actual and estimated losses with 1:1 and 1:2 ra t i o s than with 1:5 r a t i o , which i s the reverse of the pattern shown by barnyardgrass mixtures during 1981. 4.6 Interactions of Rapeseed, Redroot Pigweed and Green  F o x t a i l i n Ternary Replacement Series Mixtures Ternary combinations of rapeseed, redroot pigweed and green f o x t a i l in replacement series were included i n experi-ment during 1980 and 1981. The ternary series perimitted the evaluation of: -196-Table 4.37 A. A c t u a l (RL) and estimated r e l a t i v e losses (RL) i n bi n a r y replacement s e r i e s i n v o l v i n g rapeseed (RPS) redroot pigweed (RPW) and green f o x t a i l (GFT) 1981 data (g/m2) RL RL 1981 1981 1:1 r a t i o (720:720) RPS/RPW 94 117 RPW/RPW 323 318 RPS/GFT 92 95 GFT/RPS 279 279 RPW/GFT 14 48 GFT/RPW 327 336 r=0.997 b=1.014 1:2 r a t i o (480:960) RPS/RPW 128 141 RPW/RPS 280 255 RPS/GFT 99 118 GFT/RPS 172 207 RPW/GFT 59 61 GFT/RPW 311 344 r=0.976 b=1.055 1:5 r a t i o (240:1200) RPS/RPW 337 287 RPW/RPS 127 142 RPS/GFT 301 269 GFT/RPS 102 101 RPW/ GFT 52 58 GFT/RPW 277 268 r=0.992 b=0.913 1. The influence of increasing density of a t h i r d species on binary mixtures of two other species (Section 4.6.1), 2. The influence of a composite of two species in fixed r a t i o s on the t h i r d species i n pseudo-binary replace-ment series (Section 4.6.2), 3. The a p p l i c a b i l i t y of and v a l i d i t y of the "t h e o r e t i c a l " (de Wit, 1960) in t e r r e l a t i o n s h i p s among crowding c o e f f i c i e n t s (leading to estimates of the performance of the binary combinations not included i n the present experiments) (Section 4.6.3). The r e s u l t s on these ternary combinations are pre-sented separately i n the following sections. 4.6.1 Binary Replacement Series at Different Levels of a Third Species The experimental design employed involved combinations of rapeseed, redroot pigweed and green f o x t a i l which permitted examination of the eff e c t s of a t h i r d species on the perform-ance of any two species i n binary replacement seri e s . The mean r e l a t i v e crowding c o e f f i c i e n t s (k) for the various binary combinations are presented i n Table 4.38, together with t h e i r products (K). As the density of the t h i r d species increases, data available for computing k for binary mixtures decrease, so that at the highest density of the t h i r d species, only d i a l l e l systems remain .' ( i . e . 1:1 r a t i o at low density). Table 4.38 Mean r e l a t i v e crowding c o e f f i c i e n t s of binary mixtures and t h e i r products among RPS, RPW and GFT at d i f f e r e n t densities of the t h i r d species. 1980 and 1981 data. kRPS/RPW kRPW/RPS K izRPS/GFT kGFT K kRPW/GFT kGFT/RPW K Third species: GFT GFT GFT RPW RPW RPW RPW RPW RPS Density of 1980 t h i r d species: 0 1 .83 0 .37 0.68 2 .74 0. .44 1 .21 2 .04 0 .73 1 .49 240 1 .15 0 .59 0.68 1 .88 0 .50 0 .94 1 .72 0 .68 1 .17 ' 480 1 .45 0 .53 0.77 1 .68 0, .55 0 .92 2 .32 0 .66 1 .53 720 1 .38 0 .45 0.62 1 .15 0, .58 0 .67 2 .45 0 .74 1 .81 960 1 .20 0 .35 0.42 0 .81 0, .80 0 .64 1 .52 0 .79 1 .20 1981 0 1 .78 0 .60 1.07 1 .96 0. .73 1 .43 2 .58 0 .59 1 .52 240 1 .09 0 .75 0.82 1 .53 0, .76 1 .16 1 .22 0 .83 1 .01 480 1 .48 0 .52 0.77 1 .41 0. ,97 1 .37 1 .44 0 .68 0 .98 720 1 .49 0 .39 0.58 1 .12 1. .21 1 .36 1 .32 0 .72 0 .95 960 1 .10 0 .26 0.29 0 .76 1. .98 1 .50 1 .03 0 .74 0 .75 This i s analogous to the binary replacement series at d i f f e r e n t t o t a l densities discussed e a r l i e r (Sections 4.4 and 4.5) except that i n the ternary mixtures the t h i r d species makes up for the reduced densities i n the binary mixtures to maintain a constant f i n a l t o t a l density (1440 "RPS-units"). The r e l a t i v e y i e l d s together with the r e l a t i v e y i e l d t o t a l s for RPS, RPW and GFT i n various combinations at constant densities of a t h i r d species are presented i n Figures 4.20 and 4.21 for 1980 and 1981 seasons respectively. In any pairwise combination, the inte r a c t i v e behaviour i s greatly influenced by the presence and varying densities of the t h i r d species. In RPS for example, the r e l a t i v e y i e l d curves s h i f t from concave to more or less straight l i n e s i n the RPS/RPW mixture as the density of GFT i s increased (Figures 4.20 and 4.21 a-e), or even become concave i n the RPS/GFT mixtures as the density of RPW i s raised (Figures 4.20 and 4.21 f - j ) . However, while the performance of RPW i s further depressed by increasing constant densities of GFT i n the RPS/RPW mixtures, i t s ef f e c t on the performance of GFT i s to a l l e v i a t e the depres-sive e f f e c t of RPS on the r e l a t i v e y i e l d of GFT i n both seasons. These s h i f t s i n the r e l a t i v e performance as a res u l t of increasing densities of the t h i r d species are c l e a r l y shown by the trends of the k-values; those of RPS decline with increasing densities of the t h i r d species while those of RPW ( k Rp W/ Rp S)! a n d G F T *kGFT/RPs! t e n d t o i n c r e a s e (Table 4.38). These s h i f t s in the r e l a t i v e performance of Figure 4.20. Replacement series diagrams for binary combinations of two species (a and b) at constant density of the t h i r d species based upon r e l a t i v e y i e l d s (r) during 1980. The k-values represent the r e l a t i v e crowding c o - e f f i c i e n t s for the pair of species as influenced by varying densities of the t h i r d species (z c) i n ternary mixtures of RPS, RPW and GFT. A, 1980. 202. Figure 4.21. Replacement series diagrams for binary combinations of two species (a and b) at constant density of the t h i r d species based upon r e l a t i v e y i e l d s (r) during 1981. The k-values represent the r e l a t i v e crowding c o e f f i c i e n t s for the pair of species as influenced by varying densities of the t h i r d species (z c) i n ternary mixtures of RPS, RPW and GFT. -204-the component species in the RPS series resulted i n o v e r a l l depressions of the r e l a t i v e y i e l d t o t a l s below unity, except for the RPS/GFT mixtures i n 1981 (Figures 4.20 and 4.21 a - j ) . These trends are c l e a r l y depicted i n Table 4.38 i n which the products of the crowding c o e f f i c i e n t s (K) i n a l l rapeseed series were below unity except i n 1981 when RPW was the t h i r d species. Rapeseed had r e l a t i v e l y less e f f e c t on the r e l a t i v e performance of GFT than RPW (Figures 4.20 and 4.21 k-o), although the r e l a t i v e y i e l d t o t a l s tended to decline with increasing RPS density. In both seasons, the crowding co-e f f i c i e n t s for RPW ( k R p w / G p r [ J declined as the density of RPS was raised while those of GFT ^ Q p r p / R p ^ ) increased. The products of the crowding c o e f f i c i e n t s however, followed the same general trend as the r e l a t i v e y i e l d t o t a l and were greater and less than unity i n 1980 and 1981 respectively (Table 4.38). Comparisons between Figures 4.20, 4.21 and 4.16, 4.18 for the rapeseed series show that the e f f e c t of the t h i r d species was to depress the r e l a t i v e y i e l d t o t a l s and the Re-values. This was also r e f l e c t e d i n the interactive behaviour of RPW and GFT i n the presence of RPS as the t h i r d species (cf. Figure 4 . 1 4 ) . In general, there was a frequent i n d i c a -t i o n that introduction of the lowest l e v e l of the t h i r d species frequently caused dramatic s h i f t s i n the k-values of the remaining pair, which often disappeared as the density of the t h i r d species was increased ( i . e . at low density of the -205-binary mixtures), e.g. kRPS/RPW 1 " 8 3 — " 1 - S 5 — " 1 " 4 5 U 9 8 0 ) 1.78 1.09 1.48 (1981) kRPW/RPS ° ' 6 0 — - ° - 7 5 — " ° ' 5 2 U 9 8 1 ) kRPW/GFT 2 - 0 4 — " 1 ' 1 2 — " 2 ' 3 2 ( 1 9 8 0 ) kGFT/RPW ° - 5 9 — - ° ' 8 3 — ° ' 6 8 U 9 8 1 ) This seems to be a r e f l e c t i o n of the complex interactions between the pairs as the density of the t h i r d species increases. 4.6.2 Pseudo-binary Replacement Series between One Species and Constant Proportions of Two other Species The ternary replacement series experiments permitted tr e a t i n g pairs of species as single e n t i t i e s at three d i f f e r e n t r a t i o s (1:2, 1:1, 2:1) and evaluating t h e i r combined perform-ance against the t h i r d species and vice versa. The r e l a t i v e y i e l d data for the pseudo-replacement series comprising RPS, RPW and GFT presented i n Figures 4.22 and 4.23 for r a t i o s 2:1, 1:1 and 1:2 of species combination during 1980 and 1981 seasons show that RPS i s c l e a r l y dominant against RPW and GFT mixtures, while GFT i s c l e a r l y weaker than RPS and RPW together. The r e l a t i v e aggressiveness of RPS against the mix-tures i s further shown by the mean crowding c o e f f i c i e n t s depicted in Table 4.39. The products of the r e l a t i v e crowding 2olo Figure 4.22. Replacement series diagrams for pseudo-binary replacement series mixtures of RPS, RPW AND GFT i n ternary combinations during 1980. The k-values represent r e l a t i v e crowding.coefficients as i s influenced by varying r a t i o s of a pair of species. In each case, a refers to the single species (and hence z a i s i t s r e l a t i v e density), and b refers to the remaining pair of species, treated as a "composite species". The pro-portions of the species in the composite are constant for each column of diagrams. * Note re GFT vs RPS/RPW (1:1) - 2 0 7 -1980. ;RPS/(RPW + GFT): '(RPW+GFT)/RPS: 1 .0 RPS kRPW/(RPS+GFT): k(RPS+GFT)/RPW: RPW kGFT/(RPW+RPS) k(RPW+RPS)/GFT 1 .0 1 .0 (RPW + RPS) 1 .0 (RPS l + GFT ) 1 .0 (RPS + RPW) F i g . 4.22 C o n t d . * r - v a l u e s a d j u s t e d by eye GFT/ (RPW + RPS) k(RPW + RPS ) GFT GFT (RPS + RPW) F i g u r e 4.23. Replacement s e r i e s diagrams f o r pseudo-b i n a r y r e p l a c e m e n t s e r i e s m i x t u r e s o f RPS, RPW and GFT i n t e r n a r y c o m b i n a t i o n s d u r i n g 1981. The k - v a l u e s r e p r e s e n t r e l a t i v e c r o w d i n g c o e f f i c i e n t s as i s i n f l u e n c e d by v a r y i n g r a t i o s o f a p a i r o f s p e c i e s . I n each c a s e , a r e f e r s t o the s i n g l e s p e c i e s (and hence z a i s i t s r e l a t i v e d e n s i t y ) , and b r e f e r s t o t h e r e m a i n i n g p a i r o f s p e c i e s , t r e a t e d as a "composite s p e c i e s " . The p r o -p o r t i o n s o f t h e s p e c i e s i n t h e composite a r e c o n s t a n t f o r each column o f diagrams. - 2 0 9 -'RPS/(RPW+GFT): ;(RPW+GFT)/RPS: 1 .0 kRPW/(RPS+GFT): :(RPS+GFT)/RPW: 1 .0 GFT/(RPW+RPS) c (RPW + RPS)/GFT 1 .0 Table 4.39 Mean r e l a t i v e crowding c o e f f i c i e n t s (k) of pseudo-binary mixtures and t h e i r products (K) among rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) at d i f f e r e n t r a t i o s of the species c o n s t i t u t i n g combined p a i r s . 1980 and 1981 data. kRPS/(RPW k(RPW+ ••• .' K kRPW/(RPS k(RPS+ kGFT/(RPS k(RPS+ +GFT) GFT)/RPS +GFT) GFT)/RPW K +RPW) RPW)/GFT K Combination RPW+GFT RPS+GFT RPS+RPW Ratio i n 1980 combinations 1:2 2.173 0.347 0.754 0.946 0.945 0.894 0.675 3.206 2.164 1:1 1.845 0.390 0.719 0.880 1.380 1.214 0.536 4.425 2.372 (0.530) (2.578) (1.382 2:1 1.429 0.385 0.550 0.906 0.935 0.847 0.474 1.872 0.887 1981 1:2 1.783 0.536 0.956 0.887 0.949 0.842 0.745 1.623 1.209 1:1 1.569 0.518 0.813 0.928 1.006 0.934 0.687 1.547 1.063 2:1 1.331 0.594 0.791 0.891 0.925 0.824 0.587 1.775 1.042 * Adjusted by eye, see * Figure 4.22. -211-c o e f f i c i e n t (K) and the r e l a t i v e y i e l d t o t a l s (RYT) are both less than unity, suggesting that rapeseed suppresses and/or possibly i n h i b i t s the combination of RPW and GFT. Furthermore, the suppression becomes more severe as the RPW:GFT r a t i o decreases. This interaction i s analogous to that observed for the binary combinations of RPS and RPW during 1980 in which both K-values and RYTs were below unity (Section 4.5.1). Redroot pigweed against combinations of RPS and GFT yielded K-values less than one at either extreme and RYTs close to unity with the 1:1 combination. The variations i n RYTs and K-values with varying r a t i o s of RPS and GFT indicate complex interactions i n ternary mixtures that cannot be predicted from simple binary combinations. In the pseudo-binary replacement series of GFT and combined RPS and RPW, however, the combina-tion consistently dominated GFT, so that both K-values and RYTs were greater than one at low RPS:RPW ra t i o s and moved towards unity as the r a t i o increased. If we look at the r e l a t i v e crowding c o e f f i c i e n t s of the single species r e l a t i v e to either of the species i n the combination, the k-values for single species c l e a r l y f a l l into a pattern (see Table 4.40). If species b and c were independently acting as competitors against species a, z^ would be the fr a c t i o n of the r e l a t i v e crowding c o e f f i c i e n t of species a against species b, and z c the f r a c t i o n of the r e l a t i v e crowding c o e f f i c i e n t of species a against species c. The k-values i n Table 4.40, show that, while the magnitudes -21'2-Table 4.4 0 R e l a t i v e crowding c o e f f i c i e n t s (k) f o r rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) i n pseudo-binary replacement s e r i e s Species Combination Observed C a l c u l a t e d * 1980 1981 1980 1981 kRPS(RPW+GFT) RPS RPW - - (1.83) (1.78) (2 RPW + 1 GFT) 1.43 1.33 2.13 1.84 (1 RPW + 1 GFT) 1.85 1.58 2.29 1.87 (1 RPW + 2 GFT) 1.17 1.78 2.44 1.90 GFT - - (2.74) (1.96) kRPW(RPS+GFT) RPW RPS - - (0.37) (0.60) (2 RPS + 1 GFT) 0.91 0.89 0.93 1.26 (1 RPS + 1 GFT) 0.88 0.93 1.21 1.59 (1 RPS + 2 GFT) 0.95 0.89 1.48 1.92 GFT - - (2.04) (2.58) kGFT(RPS+RPW) GFT RPS - - (0.44) (0.73) (2 RPS + 1 RPW) 0.47 0.59 0.54 0.68 (1 RPS + 1 RPW) 0.54 0.69 0.59 0.66 (1 RPS + 2 RPW) 0.68 0.75 0.63 0.64 RPW — — (0.73) (0.59) Ca l c u l a t e d as k , . z, +k .z ab b ac c • -213-of the computed k-values generally agree with the observed values, the s h i f t s of the calculated values as the composi-ti o n of the combination changes do not always agree with the observed s h i f t s (e.g. both seasons for RPW, and GFT i n 1981). Hence, t h i s must indicate interactions, and the members of the combinations are not acting independently. This i s borne out by incorporating the crowding c o e f f i c i e n t s of both the single species against one member of the combination and the other member of the combination, e.g. k ^ and Since the evidence presented above indicates that i n simple binary series, the r e l a t i v e crowding coeffi-.. cients are l i t t l e affected by t o t a l density over a wide range, a simple estimate of the combined e f f e c t s of the two species upon a t h i r d i s given by the mean of the r e l a t i v e crowding c o e f f i c i e n t s , i . e . ^ a b + k b c ) / 2 represents the mean e f f e c t of species a and species b upon species c. If species b and c constitute the combination i n a pseudo-binary series, the magnitude of the e f f e c t of the mean crowding c o e f f i c i e n t s against species c on the combination w i l l be proportional to z , and w i l l z .(k +k, )/2. Si m i l a r l y , the eff e c t s on c c ac oc species b w i l l be given by z^. (k^+k^)/2 . Hence, the e f f e c t of species a on the combination w i l l be given by: z . (k +k, )/2+z, . (k ,+k , )/2 c ac be b ab cb and w i l l r e s u l t i n k-values of species a against the combina-t i o n which are dependent upon z H and z o , the composition of Table 4.41 Relati v e crowding c o e f f i c i e n t s (k) for rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) i n pseudo-binary replacement series Species Combination Observed Calculated* 1980 1981 1980 1981 RPS(RPW+GFT) RPS RPW - - (1.83) (1.78) (2 RPW + 1 GFT) 1.43 1.33 1.65 1.55 (1 RPW + 1 GFT) 1.85 1.57 1.84 1.73 (1 RPW + 2 GFT GFT) 1.17 1.78 2.02 (2.74) 1.91 (1.96) kRPW(RPS+GFT) RPW RPS - - (0.37) (0.60) (2 RPS + 1 GFT) 0.91 0.89 1.07 1.12 (1 RPS + 1 GFT) 0.88 0.93 1.40 1.47 (1 RPS + 2 GFT GFT) 0.95 0.89 1.73 (2.04) 1.74" (2.58) kGFT(RPS+RPW) GFT RPS - - (0.44) (0.73) (2 RPS + 1 RPW) 0.47 0.59 0.70 0.84 (1 RPS + 1 RPW) 0.54 0.69 0.84 0.93 (1 RPS + 2 RPW RPW) 0.68 0.75 0.99 (0.73) 1.01 (0.59) * Calculated as z . c (k +k, ac be )/2 + V ( k a b +k c b)/2 the combination (Table 4.41). This approach gives a better agreement than i n the previous case (cf. Tables 4.40 and 4.41) where the species i n the mixture were treated independently with regard to the e f f e c t of species a. The notable excep-tions, however, are the interactions between redroot pigweed and the combinations of rapeseed and green f o x t a i l , where t h i s model indicates that the r e l a t i v e crowding c o e f f i c i e n t against the combination would increase, as the composition of the combination sh i f t e d towards green f o x t a i l . This c l e a r l y sets up the l i m i t a t i o n s of using k-values where i t i s clear (from K ^ 1, RYT ^ 1) that the species i n question are not competing for the same resources. These limi t a t i o n s are discussed further i n Section 4.6.3. Alternative to investigating k-values, we can look at the actual y i e l d s of any species as influenced by changes in the composition of a competing pair of species, i n order to obtain a better understanding of the actual interactions which are occurring i n the ternary mixtures. This approach i s presented i n Section 5.5 i n discussing the general implica-tions of three-species interactions. 4.6.3 Predicted Relative Crowding Coefficients of Binary Mixtures The extension of de Wit's model to compute k-values for untested combinations i s based upon Equation 7, Since the model assumes that a l l species are competing for the same space and resources and the selective y i e l d t o t a l s are equal to one,,^then k ^ = 1/k^ . Hence i t i s possible to compute four values for k ^ : k k »k, — k • k, — k •k, — k • k, • ab ac cb ac be ca cb ca be Table 4.42 presents data for calculated k, mean k and observed k-values for the binary combinations of barnyardgrass, redroot pigweed and green f o x t a i l , and rapeseed, redroot pigweed and green f o x t a i l ; at the highest t o t a l density (1440 "RPS-units"), together with estimates for the combination of barnyardgrass and rapeseed which was not tested i n these experiments. The poor agreement between the observed and the estimated mean k-values as shown by the low regression c o e f f i c i e n t s (Table 4.42) further supports the lim i t a t i o n s of extending the de Wit's model to predict competitiveness between a pair of species when competition between the two i s not exclusively for the same resources ( i . e . when RYT # 1, K ^ 1). De Wit (1960) and l a t e r de Wit et a l . (1966) proposed the use of the spacing formula (Equation 16) to predict r e l a t i v e crowding c o e f f i c i e n t for one species on another based upon Equation 22, _ Ba+S kab ~ B^+S ~ 2 2 for the situations i n which the values for B and B, are a b Table 4.42 Computation of k-values for barnyardgrass (BYG), redroot pigweed (RPW), green f o x t a i l (GFT) and rapeseed (RPS) from the r e l a t i o n s h i p : k = k .k = k u / k = k ,/k.-. = 1/k .k ) ab ac cb ab be cb ca ca be (De Wit, 1960), based upon the mean k-values from binary replacement series at "1440 RPS-units", Mixtures ab k .k , ac cb. k /k ac be k /k cb ca 1980 1981 BYG+RPW BYG 1.87 2.37 RPW 0.70 0.51 BYG+GFT BYG 1.90 2.68 GFT 0.51 0.51 RPS+RPW RPS 1.83' 1.78 RPW 0.37 0.60 RPS+GFT RPS 2.74 1.96 GFT 0.44 0:73 RPW+GFT RPW 2.04 2.58 BYG+RPS1 GFT 0.73 0.59 BYG -A ** RPS -* 1/k. ba •kbc> 1980 1981 1980 1981 1980 1981 1980 1981 1.18 0.88 2.82 0.38 1.53 0.69 3.85 0.28 1.19 0.85 0.78 0.76 1.30 1.39 1.13 1.18 4.63 0.23 0.81 1.33 3.68 0.29 1.08 0.96 1.44 1.26 0.74 0.80 1.39 1.04 3.81 0.51 2.00 0.90 3.75 0.27 1.32 0.95 0.78 0.70 1.39 1.28 1.58 1.32 6.10 0.30 1.16 1.89 4.59 0.36 1.36 1.21 1.44 1.42 1.00 0.90 0.93 1.08 2.56 0.39 1.34 0.75 2.51 0.40 1.37 0.73 0.84 1.02 1.44 0.98 1.04 0.96 4.00 0.25 0.76 1.32 3.01 0.33 0.99 1.01 1.96 1.33 0.74 0.75 1.44 0.70 2.93 0.34 1.66 0.60 5.48 o:i8 1.02 0.98 0.69 0.54 1.16 1.87 1.15 0.87 5.08 0.20 0.81 1.24 4.29 0.23 1.13 0.88 1.37 1.19 0.70 0.84 1980 1981 0.96 0.72 1.97 0.26 1.11 0.50 3.67 0:27 1.06 0.76 0.87 0.78 1.20 1.44 0.76 1.58 3.34 0.16 0.53 0.87 2.82 0:22 0.83 0.74 1.43 1.11 0.51 0.70 Estimates of k-values for barnyardgrass on rapeseed and vice versa performance against redroot pigweed (**) or green f o x t a i l (*). are based on eith e r species' r(k, k ) Z 1980 0.836 1981 0.57 b(k, k) 1980 1.059 1981 1.021 Excluding BYG+RPS -218-obtained from spacing experiments on species a and species b respectively, provided that the two species have similar growth curves and that they compete for the same resources. Table 4.4 3 presents data on k-values for rapeseed, redroot pigweed, barnyardgrass and green f o x t a i l derived from spacing experiments (k) and from binary replacement series (k). While there was complete disagreement between observed and the calculated k-values as r e f l e c t e d by the low regression and cor r e l a t i o n c o e f f i c i e n t s , redroot pigweed and green f o x t a i l i n d i v i d u a l l y gave r e l a t i v e l y good estimates against barnyard-grass. However, given the complete disagreement between k, k and k-values (Table 4.42) for the other combinations, the agreement between estimates of kgyG/RPS a n <^ ^RPS/BYG ^ o r *"*ie untested combination, RPS and BYG, based on green f o x t a i l or redroot pigweed within a given year i s rather surprising (Table 4.44), even though there was complete reversal i n the magnitude of k-values between the two seasons. Furthermore, values of k estimated from Equations 7 and 22 for the untested combination do not bear any meaningful rela t i o n s h i p (Table 4.44). Table 4.43 Computation of k-values for barnyardgrass (BYG), redroot pigweed (RPW), green f o x t a i l (GFT) and rapeseed (RPS) based upon B and S from the spacing experiments (de Wit, 1960); k u = ab (B +S)/(B,+S) a b (Equation 22) . Mixtures Observed (k) Calculated (k) 1980 1981 1980 1981 BYG+RPW BYG 1.87 2.37 1.67 1.94 RPW 0.70 0.51 0.60 0.52 BYG+GFT BYG 1.90 2.68 1.63 1.58 GFT 0.51 0.51 0.61 0.64 RPS+RPW RPS 1.83 1.78 - 3.11 (0.97)* RPW 0.37 0.60 - 0.32 (1.03)* RPS+GFT RPS 2.74 1.96 - 2.52 (0.79)* GFT 0.44 0.73 - 0.40 (1.27)* RPW+GFT RPW 2.04 2.58 0.98 0.81 GFT 0.73 0.59 1.02 1.23 r(k,k) 0.764 0.560 (0.680)* b(k,k) 0.772 0.822 (0.671)* Computed from B values derived from S based upon "RPS-units" -220-Table 4.44 Values of k for barnyardgrass (BYG) and rapeseed (RPS) estimated from de Wit's equations Ic , = k .k , etc. and k , = (B +S)/(B,+S) ab ac cb ab a b ab ab Common species 1980 1981 1981 k , GFT 1.30 0.74 RPb/BYG 1 6 Q (0.50)* RPW 1.39 0.80 k , GFT 0.76 1.26 B Y G / K i ^ 0.63 (2.00)* RPW 0.78 1.44 K BYG 0.98 0.93 RPW 1.08 1.15 1.00 Computed from B values derived from S based upon "RPW-units" -221 -5. GENERAL DISCUSSION The present studies permit comparisons and evaluations of the d i f f e r e n t methodologies which have been used to analyze the interactions within and among species i n monocultures and in various binary and ternary mixtures. In addition, they i n -vestigate the possible use of the yield-density c h a r a c t e r i s t i c s of a species i n monoculture to provide information about i t s performance.'in mixed culture, the ways i n which t o t a l popula-t i o n density may influence the interactions between two species, and how these interactions may be influenced by a t h i r d species. These and other relationships are discussed in the following sections. 5.1 Yield-density Relationships i n Monoculture and t h e i r use  in the Prediction of Yields i n Mixed Culture The present studies have shown that the spacing formula of de Wit (1960) (Equation 16) i s capable of describ-ing the y i e l d " of barnyardgrass, redroot pigweed, green f o x t a i l and rapeseed with good precision (see Section 4.1). In the case of RPS, i t was necessary to omit the mean y i e l d 2 for the lowest density (75 plants/m ) in order to obtain a good f i t , which may indicate possible li m i t a t i o n s of the a p p l i c a b i l i t y of the spacing formula to a l l species. Never-theless i t s use i n the present studies, together with the fact that i t i s e s s e n t i a l l y i d e n t i c a l to the reciprocal formula -222-developed by Shizonaki and Kira (1956) for other species, attests to i t s general usefulness i n describing growth i n monoculture. The present studies have also shown that the spacing formula (Equation 16) can be used to describe yield-density relationships of a species growing i n the presence of a second species at constant density. Thus the additive series experiments involving BYG (Section 4.2) and RPS (Section 4.3) consistently demonstrated the o v e r a l l agreement (for a l l the combinations of BYG or RPS with RPW or GFT and of RPW and GFT, tested) between the observed yield/density data and those predicted by the spacing formula, as shown in figures 4.3 and 4.9 and Tables 4.10 and 4.18. This use of the spacing formula to describe the y i e l d curves of species growing i n the presence of a second species at fixed density must, however, be viewed with caution. Thus, while the formula can predict y i e l d values over the ranges of densities used i n i t s derivation, the t h e o r e t i c a l y i e l d per plant grown i n i s o l a t i o n (B 0, .) i s derived by extrapolation and may be subject to considerable error. While the spacing formula may provide a good f i t to the observed yi e l d s obtained in the presence of d i f f e r e n t densities of an indicator species, the shapes of the curves may d i f f e r appreciably, even though they tend to overlap each other, as for example i s shown in Figure 4.4 for barnyardgrass i n the presence of redroot pigweed. Here the f i t t e d curve for BYG in the presence of h i g h d e n s i t y RPW r e a c h e s i t s assymptote a t a much h i g h e r y i e l d t h a n i n t h e presence o f low d e n s i t y RPW. I n o t h e r words, o v e r t h e range o f d e n s i t i e s o f BYG w h i c h were used, i t s y i e l d c u r v e i n the presence o f h i g h d e n s i t y RPW has a g r e a t e r s l o p e t h a n i n t h e p r e s e n c e o f low d e n s i t y RPW. The o v e r a l l r e s u l t o f t h e s e d i f f e r e n c e s i n c u r v e shape:'.is a c o n s i d e r a b l e d e c l i n e i n B ft v a l u e s as RPW d e n s i t y i n c r e a s e s (Table 4.3). Such an e f f e c t might a t f i r s t g l a n c e appear t o suggest t h a t RPW was a g g r e s s i v e l y competing w i t h BYG i n 1981. However, t h e c l o s e n e s s o f t h e BYG c u r v e s t o each o t h e r and t o t h e monoculture c u r v e ( F i g u r e 4.4) s u g g e s t s t h a t t h i s was not so o v e r t h e d e n s i t i e s o f BYG used. A s i m i l a r s i t u a t i o n was found w i t h r a p e s e e d i n the presence o f r e d r o o t pigweed as i n d i c a t o r ( F i g u r e 4.8b; and T a b l e 4.13), and i n d i c a t e s t h a t t h e e f f e c t s o f i n c r e a s e d d e n s i t y o f the i n d i c a t o r on the Bft v a l u e s o f t h e competing s p e c i e s may g i v e a f a l s e i m p r e s s i o n of t h e c o m p e t i t i v e n e s s o f t h e second s p e c i e s . The use o f B - v a l u e s o b t a i n e d from monoculture y i e l d / d e n s i t y e x p e r i m e n t s t o p r e d i c t y i e l d s i n b i n a r y m i x t u r e s has been proposed (de W i t , 1960; de Wit e t a l . , 1966). The p r e s e n t s t u d i e s have c l e a r l y shown t h a t t h e v a l u e s f o r r e l a -t i v e c r o w d i n g c o e f f i c i e n t s (k) d e r i v e d v i a E q u a t i o n 22 f o r any o f the b i n a r y m i x t u r e s i n v e s t i g a t e d bore a t b e s t a s u p e r -f i c i a l resemblance t o the o b s e r v e d c r o w d i n g c o e f f i c i e n t s (Table 4.43). I n the m i x t u r e s o f b a r n y a r d g r a s s or rapeseed w i t h r e d r o o t pigweed o r green f o x t a i l , the e s t i m a t e d and calculated c o e f f i c i e n t s agreed with each other in indicating which species i n any pair was the stronger competitor. How-ever, for RPW and GFT, the r e l a t i v e crowding c o e f f i c i e n t s derived from Equation 22 bore no resemblance to those derived from the actual replacement series mixtures. De Wit (1960) cautioned that the use of Equation 22 should be limited to situations for which there i s evidence that the two species are competing for the same space. The evidence from the present studies shows that, for both seasons and for the d i f f e r e n t t o t a l densities studied i n 1981, t h i s was not so (Figure 4.13; RYT > 1). Hence, the lack of agreement between the d i f f e r e n t estimates of k might be expected. However, other binary mixtures for which there i s general agreement between the estimates of k (e.g. BYG and RPW i n 1980 and 1981; Table 4.43) also showed evidence for competition for d i f f e r e n t resources (RYT > 1). Hence, the usefulness of Equation 22 i s questionable. The present studies c l e a r l y support Harper's (1964) contention that the c h a r a c t e r i s t i c s which lead to competitive success i n mixed stands, can only be exposed and demonstrated when the two species are grown together. 5.2 Estimation of Yields and Performance i n Additive Series  Experiments The spacing formula (Equation 16) permitted estimation of yi e l d s in monocultures and i n binary additive series mixtures for the accompanying species i n the presence of a given constant density of the indicator species (Section 5.1). -225-The present studies have shown that the growth of the indicator species can adequately be described by the square root r e l a -tionship between indicator y i e l d and density of the accompany-ing species (Dew, 1972) (Equation 9), for BYG, RPW, GFT and RPS (Sections 4.2.4 and 4.3.4). Although the square root formula r e s u l t s in good agreement between the estimated and actual y i e l d s i n various combinations of species, the y i e l d curves do not always follow the same pattern at a l l density, levels of the indicator. In general, the curves for the d i f f e r e n t densities of indicators which were weaker competi-tors than the accompanying species tended to converge while those of the strong competitors tended to diverge with increasing density of the accompanying species, as shown i n Figure 4.6 and 4.3 for GFT i n BYG and BYG i n RPW (1981) respectively. Thus, in the l a t t e r case, with the strongly competitive BYG as indicator, the regression c o e f f i c i e n t (b) tends to decrease i n magnitude with increasing density of the indicator. Since t h i s c o e f f i c i e n t i s an i n d i c a t i o n of the rate at which the y i e l d of the indicator species declines with increasing density of the accompanying species, i t s lessened decline at higher densities i s a r e f l e c t i o n of reduced com-petitiveness of the accompanying species. These s h i f t s i n the curvature of the indicator y i e l d curves with density also occurred with BYG against GFT (1980) (Figure 4.5), RPS against RPW (Figure 4.8a) and GFT (Figure 4.9a) and with RPW against GFT (Figure 4.7a). Nevertheless, the square root function was found to be capable of permitting the estimation of y i e l d s with good precision as revealed by the high c o r r e l a -tions between observed and estimated yi e l d s (Tables 4.10 and 4.18). However, the inverse relationship shown between the two c o e f f i c i e n t s , a and b, required for the square root function, makes th e i r subsequent u t i l i z a t i o n i n the determina-t i o n of the competition index d i f f i c u l t , as discussed i n Section 5.4. The present studies also show that c o e f f i c i e n t s a and b from Equation 9 d i f f e r with the inclusion or exclusion of the monoculture data. However, although there was good r e l a t i v e agreement between the re s u l t s obtained with the two approaches, inclusion of the monoculture data consistently yielded better estimates of y i e l d loss (Table 4.11 and 4.19) while exclusion of the monoculture data tended to over-estimate y i e l d loss appreciably. The most serious over-estimates were generally shown to occur for the more competi-t i v e species: (BYG or RPS) i n RPW or GFT and RPW i n GFT. 5.3 Estimation of Yields and Performance i n Binary Replacement  Series Experiments The r e l a t i v e crowding c o e f f i c i e n t s (k) derived from Equation 5 permitted estimation of the yi e l d s of BYG, RPW, GFT and RPS i n binary replacement series mixtures (Tables 4.26 and 4.34). The derived y i e l d curves provided reasonably good f i t s to the observed r e l a t i v e y i e l d s as shown i n the replacement series diagrams (Figures 4.10, 4.12, 4.14 and 4.18). Conven-- 2 2 7 -t i o n a l l y , k-values greater than one have been interpreted to indicate greater competitiveness of one species against the other for which the k-value i s less than unity. But though any interaction between species in binary combinations contains components attributable to effects of both i n t r a -s p e c i f i c and i n t e r s p e c i f i c competition, the computation of the k-values does not separate the two i n absolute terms. On the other hand, the crowding c o e f f i c i e n t i s a measure of competitiveness of one species against another r e l a t i v e to a given monoculture s i t u a t i o n (see also Willey and Rao, 1980). The present studies have shown that the r e l a t i v e crowding c o e f f i c i e n t s are subject to several sources of v a r i a b i l i t y which are related to the methodology used for t h e i r determination. F i r s t , the use of Equation 6 permits the c a l c u l a t i o n of a k-value for each combination of densi-t i e s of the components of a binary replacement series, which in turn permits the computation of a mean value across the complete series. Second, the number of combinations of densities can be reduced to one, i n the simplest d i a l l e l s i t u a t i o n . Third, while the t o t a l density for any replacement series i s maintained constant, the r e l a t i v e competitive behaviour of the two components i s l i k e l y to be dependent on the t o t a l density to some extent, i f only because the y i e l d of each component i n pure stands i s density-dependent. The experimental design used i n the present studies permitted investigation of these three sources of v a r i a b i l i t y -228-with regard to the use of the complete set of independent estimates of the r e l a t i v e crowding c o e f f i c i e n t s . Thus, in the series with a t o t a l density of 1440 plants or RPS-units per square metre, the mean values may d i f f e r somewhat from that of the d i a l l e l values i n the centre of the series, as shown i n the BYG/RPW series based upon 1440 plants/m (Table 4.26) i n which the mean values for the r e l a t i v e crowding co-e f f i c i e n t of BYG on RPW are 1.59 and 2.36 for 1980 and 1981 respectively, compared with 1.94 and 3.18 for the d i a l l e l mixture. However, inspection of Tables 4.26 and 4.35 shows that i n most cases the d i a l l e l and mean values of k are i n generally good agreement for the highest t o t a l density series and the series with t o t a l densities of 720 plants or RPS-units per square metre, the only other multiple r a t i o series containing the simple d i a l l e l . Thus other than providing better estimates of the r e l a t i v e crowding c o e f f i c i e n t than the d i a l l e l , the present study provides l i t t l e evidence to support the contention of Trenbath (1978) that experimenta-ti o n involving other combinations of densities i n addition to the d i a l l e l are desirable. The values i n Tables 4.26 and 4.33 f a i l to reveal any consistent trends i n the k-values within any given replacement series, with the possible exception of those of rapeseed against RPW and GFT at t o t a l densities less than 1440 RPS-2 units/m i n which there i s a tendency for the k-values within each replacement series to decrease as the proportion of rapeseed increases i n the mixtures (Table 4.33). However, the p r e s e n t s t u d i e s have shown t h a t t h e r e i s a dependency o f t h e r e l a t i v e c r o w d i n g c o e f f i c i e n t on t o t a l d e n s i t y . W h i l e t h e changes i n k - v a l u e s w i t h t o t a l d e n s i t y a r e f a r from u n i f o r m , and t h e t r e n d s are c h a r a c t e r i s t i c o f t h e i n d i v i d u a l s p e c i e s and m i x t u r e s , t h e r e i s a p r o g r e s s i v e tendency f o r t h e k - v a l u e s f o r t h e more a g g r e s s i v e s p e c i e s t o d e c l i n e as t o t a l d e n s i t y d e c r e a s e s , and f o r t h o s e o f the l e s s a g g r e s s i v e s p e c i e s t o i n c r e a s e . I n t h e case o f RPS competing f o r w i t h SEW o r GFT, t h i s t r e n d i s u l t i m a t e l y r e v e r s e d so that a t the l o w e s t t o t a l d e n s i t y i n v e s t i g a t e d , i t s k - v a l u e s have r i s e n t o v a l u e s g r e a t e r t h a n 3.0 (Table 4.33). However, the g e n e r a l consequence i s t h a t the r e l a t i v e y i e l d c u r v e s o f t h e more a g g r e s s i v e s p e c i e s t e n d t o f l a t t e n o ut (and t h e n become convex i n t h e case o f RPS) w h i l e t h o s e o f the l e s s a g g r e s s i v e s p e c i e s t e n d t o change from concave t o convex, as d e p i c t e d i n F i g u r e s 4.10, 4.12, 4.14, 4.16 and 4.18. Hence the r e p l a c e m e n t s e r i e s methodology has a p o t e n t i a l l i m i t a t i o n i n i t s u s e f u l n e s s i n t h a t t h e r e l a t i v e c o m p e t i t i v e n e s s o f two s p e c i e s r e v e a l e d by i t s use may be i n f l u e n c e d by t h e t o t a l d e n s i t y o f t h e m i x t u r e s , p a r t i c u l a r l y i f low d e n s i t i e s are used. The s i g n i f i c a n c e o f such changes i s d i s c u s s e d f u r t h e r i n S e c t i o n 5.4 i n c o n n e c t i o n w i t h t h e use o f r e l a t i v e c r o w d i n g c o e f f i c i e n t as a measure o f c o m p e t i -t i o n . However, the good o v e r a l l agreement between th e o b s e r v e d y i e l d s and t h e r e l a t i v e y i e l d c u r v e s based upon E q u a t i o n 5 i n d i c a t e s t h e g e n e r a l v a l i d i t y o f t h e e q u a t i o n t o -230-describe the r e l a t i v e y i e l d response i n replacement ser i e s . Estimates of k-values for s p e c i f i c combinations of species derived from k-values determined for other combina-tions (Equation 7) were found to be i n complete disagreement with those obtained from actual replacement series mixtures. (Table 4.42). It has been shown i n the present studies that, i n general, BYG (or RPS) does not compete with RPW or GFT for exclusively the same resources and that RYTs are not equal to one (Tables 4.20, 4.22, 4.29 and 4.31). S i m i l a r l y , estimates of k-values derived from the spacing formula by means of Equation 22 (shown i n Table 4.42) bear no r e l a t i o n -ship with either those obtained from actual mixtures or from Equation 7, except i n the i n d i c a t i o n of which species was the stronger competitor. Differences between the k-values estimated from either Equations 7 or 22 and those calculated from Equation 6 are expected since they are based on the same assumption of competition for the same resources. However, the magnitudes of the differences observed i n the present studies suggest that, for a l l p r a c t i c a l purposes, the use of alternate methods to estimate r e l a t i v e crowding c o e f f i c i e n t s for a p a r t i c u l a r binary mixtures should be avoided, unless the s p e c i f i c r e l a -tionships defined by Equations 7 and 22 have been tested and validated. The relationship between monocultures and mixture yie l d s described by Equation 5 can be used to estimate y i e l d -2 31-losses i n addition to estimated y i e l d s . Since y i e l d loss i s equal to M -0_ (using conventional symbols), substitution a a from Equation 5 gives y i e l d loss (L) as: L = M -0 = z,/(k ,z +z, ) .M . 23a a a a b' ab a b' a where z & and z^ are the r e l a t i v e densities for species a and b, and z +z, = 1. Such losses are defined i n terms of actual a b monoculture y i e l d , Ma, at the t o t a l density employed i n the replacement series (Equation 23a) and may be converted to r e l a t i v e terms by d i v i d i n g by the monoculture y i e l d s , thus: %L a = 100(M a-O a)/M a = ( 1 0 0 z b ) / ( k a b z a ) 23b Both of these expressions are only applicable to replacement series i n which t o t a l density remains constant. Where there i s evidence that the r e l a t i v e crowding c o e f f i c i e n t i s constant over a range of t o t a l densities, they may be used to estimate y i e l d losses at other t o t a l d e n s i t i e s . However, y i e l d loss assessment i n replacement series i s of limited value because, by d e f i n i t i o n , part of such loss i s d i r e c t l y related to the decreased density of the species under investigation. Hence, where y i e l d but not s u r v i v a l i s affected by competition, the only v a l i d estimate of actual y i e l d loss in replacement series requires the a v a i l a b i l i t y of monoculture y i e l d s of a species at densities comparable to those used in i t s replace-ment serie s . The general agreement between estimated and actual r e l a t i v e y i e l d loss obtained i n t h i s manner by combining information from both monoculture and replacement series data are shown i n Tables 4.2 9 and 4.36. The accuracy of the estimated y i e l d loss i s , however, limited by the degree to which the observed monoculture yie l d s follow the hyperbolic relationship required by the spacing formula (Equation 16), and the accuracy of the estimated r e l a t i v e crowding c o e f f i -cients (Equation 6). The data presented i n Tables 4.21, 4.23, 4.25, 4.30 and 4.32 are the r a t i o s of the y i e l d of a species i n mixture to i t s y i e l d i n monoculture at an i d e n t i c a l density, and hence provide alternative measures of the r e l a t i v e y i e l d s which indicate the increasing proportionate r e l a t i v e y i e l d losses sustained as the density of the competing species i s increased. On the basis of the l i m i t a t i o n s discussed here regard-ing the use of replacement series to predict y i e l d losses i n mixed stands, Dew's (1972) method of estimating such losses based on additive series experiments (Equation 20) i s more widely applicable once the yield-density relationships and the index of competition have been determined. 5.4 Measurements of Competitiveness The present studies permitted intercomparisons and evaluations of the d i f f e r e n t methodologies employed i n measur-ing competitiveness between species i n binary mixtures, namely: the index of competition (CI; Dew, 1972), presented - 233 -i n T a b l e s 4.8, 4.9, 4.16 and 4.18, and a g g r e s s i v i t y (A; M c G i l c h r i s t and T r e n b a t h , 1971), c o m p e t i t i o n r a t i o (CR; W i l l e y and Rao, 1980), r e l a t i v e c r o w d i n g c o e f f i c i e n t (k; de W i t , 1960) and t h e i n t e r f e r e n c e r a t i o (IR) dev e l o p e d i n the p r e s e n t s t u d i e s , shown i n T a b l e s 4.27 and 4.34. The c o r r e l a -t i o n c o e f f i c i e n t s p r e s e n t e d i n T a b l e 5.1 show g r e a t v a r i a b i l i t y i n the r e l a t i o n s h i p s between t h e d i f f e r e n t measures o f c o m p e t i t i v e n e s s . Not a l l i n d i c e s c o u l d be computed f o r r a p e -seed c o m b i n a t i o n s i n 1980 and hence the r - v a l u e s f o r 1980 season were d e r i v e d o n l y from t h e BYG, RPW and GFT b i n a r y c o m b i n a t i o n s . The v a l u e s f o r 1981 were computed f o r b o t h BYG and t h e RPS s e r i e s . As was e x p e c t e d , CR i s v e r y c l o s e l y r e l a t e d t o k (r> 0.960) i n b o t h seasons, and r e l a t i v e l y l e s s so w i t h C I , IR and A i n o r d e r o f d e c r e a s i n g magnitude o f t h e i r r - v a l u e s . The r e l a t i o n s h i p between IR and k was g e n e r a l l y poor (r > 0.790, T a b l e 5.1) i n b o t h seasons, b u t i t was improved c o n s i d e r a b l y when I R - v a l u e s f o r RPW/GFT were o m i t t e d . Compe-t i t i o n i n d e x was h i g h l y c o r r e l a t e d w i t h A, CR, k and IR i n 1980, b u t l e s s so i n 1981. Indeed i t s r e l a t i o n w i t h IR ( y i e l d e d t h e l o w e s t r - v a l u e o f any comparison (Table 5.1). A g g r e s s i v i t y gave poor c o r r e l a t i o n s w i t h IR i n b o t h seasons and w i t h CR i n 1981. The problems i n v o l v e d i n t h e use o f A as a measure o f c o m p e t i t i v e n e s s have been d i s c u s s e d e a r l i e r ( S e c t i o n 2.5) and l e d W i l l e y and Rao (1980) t o d e v e l o p t h e i r CR as t h e r a t i o Table 5.1 Correlation c o e f f i c i e n t s (r) for the various measures of competitiveness 1980 1981 1980 1981 1980 1981 1980 1981 1980 1981 A 1.00 1.00 0.986 0.598 0.695 0.712 0.988 0.946 .0.995 .0.792 CR 1.00 1.00 0.654 0.703 0.961 0.990 0.980 0.741 IR 1.00 1.00 0.790 0.762 0.987 0.532 (0.999)* (0.851)* k 1.00 1.00 0.974 0.682 CI 1.00 1.00 Excluding RPW/GFT -2 35== of r e l a t i v e y i e l d s between component species i n binary mixtures, weighted by the r a t i o of the i r r e l a t i v e d e n s i t i e s . Competition r a t i o and r e l a t i v e crowding c o e f f i c i e n t were highly correlated, i n spite of the arguments of Willey and Rao (1980) that the former provides an actual measure of the degree of competitiveness, while the k-value i s l i t t l e more than a q u a l i t a t i v e measure of competition. Of p a r t i c u l a r i n t e r e s t i s the poor o v e r a l l r e l a t i o n -ship between k and IR, since these are e s s e n t i a l l y alternative statements of the performance of a species when affected by a competitor r e l a t i v e to i t s performance when influenced by more individuals of i t s own kind. Although the correlations improved when the values for the effects of RPW on GFT were omitted, the lack of correspondence for these mixtures indicates a l i m i t a t i o n i n the usefulness of the r e l a t i v e crowding c o e f f i c i e n t as a measure of competitiveness. -. The IR values were obtained as d i r e c t measures of the r e l a t i v e impacts on per plant y i e l d of adding equal densities of the same or a d i f f e r e n t species, and hence describe the r e l a t i v e a b i l i t y of the f i r s t species to withstand the second. In pa r t i c u l a r , the TR values for RPW against GFT are much higher than for other combinations, and therefore indicate that, when grown with GFT, redroot pigweed i s much better able to compete than barnyardgrass, although the r e l a t i v e crowding c o e f f i c i e n t s suggest that the two species are comparable (Table 4 . 2 7 ) . -236-Interference r a t i o s also permit a d i r e c t examination of the r e l a t i v e contributions made by i n t r a - s p e c i f i c and i n t e r - s p e c i f i c competition to the performance of mixtures. Thus, by d e f i n i t i o n , the interference r a t i o i s a measure of impact on y i e l d per plant of a species by members of i t s own kind ( i . e . i n t r a - s p e c i f i c competition) r e l a t i v e to that caused by a second species ( i . e . i n t e r - s p e c i f i c competition). Hence a value greater than unity indicates that i n t r a - s p e c i f i c competition causes a greater reduction i n per plant y i e l d than i n t e r - s p e c i f i c competition. The reverse i s true for values less than one. However, i t must be pointed out that the interference r a t i o does not provide any information about the absolute magnitude of the two types of competition. The t o t a l extent of i n t r a - s p e c i f i c competition, i n absolute terms, can only be determined i n r e l a t i o n to the projected monoculture y i e l d i f no competition of either type i s occurring, i . e . extrapolation of the i n i t i a l tangent to the yield-density monoculture curve. The interference r a t i o on the other hand provides a measure of the r e l a t i v e importance of i n t r a s p e c i f i c competi-t i o n to i n t e r s p e c i f i c competition which i s i n turn r e l a t i v e to the amount of i n t r a s p e c i f i c competition which i s already occurring at a given density. In spite of the caveat concerning the use of Bft estimates discussed i n Section 5.1, the fact that they generally decline with increasing density of the indicator species, suggests that the magnitude of the regression of B on indicator density may permit the evaluation of the compe-t i t i v e e f f e c t of the indicator on the accompanying species i n a manner somewhat similar to Dew's (1972) index of competition (Equation 20). The approach has the pot e n t i a l of complement-ing the Cl-concept by providing some measure of crop competition on a given weed in a s p e c i f i c crop-weed combination. In the present studies the great v a r i a b i l i t i e s of B discussed previously and the unequal number of treatment means for the three density levels of the indicator brought about by the constraint i n the experimental design used did not permit a c r i t i c a l evaluation of t h i s approach. For example based on t h i s method, among the various combinations of species tested, RPW was the most aggressive species i n the BYG-series and green f o x t a i l was the least i n the RPW/GFT combination. This agrees with the r e l a t i v e performances suggested by the interference r a t i o s . In contrast, the other measures of competitiveness consistently singled out barnyard-grass (or redroot pigweed against green f o x t a i l ) as the most competitive. Nevertheless the approach warrants further study with a greater range of densities of the indicator species i n order to test i t s a p p l i c a b i l i t y . 5.5 Influence of a Third Species on Behaviour of Binary  Mixtures i n Replacement Series The present studies permitted evaluation of the e f f e c t of a t h i r d species on the i n t e r a c t i v e behaviour exhibited i n -238-binary replacement series mixtures at various densities of a t h i r d species and i n pseudo-binary replacement series i n which a pair of species in the ternary combination i s treated as a single species. The dramatic s h i f t s observed i n the re l a t i v e performance of any pair of species caused by changes i n the density of the t h i r d species demonstrates the i n t e r -actions which may occur i n ternary mixtures. Green f o x t a i l has been shown i n the present studies to be the weakest competitor i n the binary combinations with either rapeseed or RPW (Section 4.4.3). In the ternary combinations, however, increasing proportions of GFT resulted i n marked progressive decline i n the r e l a t i v e performances of RPW and RPS (Figures 4.20 a-3 and 4.21 a-3) such that the RYT of the mixture dropped to 0.8 i n 1980 and 0.7 i n 1981. This c l e a r l y indicates that a three-way int e r a c t i o n was occurring, and that the presence of GFT increasingly modified the competitiveness of RPS and RPW towards each other. That t h i s was not merely an e f f e c t of t o t a l density on the RPS/RPW inter a c t i o n i s shown by the fact that, i n the absence of GFT, the RPS/RPW inter a c t i o n resulted i n RYTs as high as 1.2 as the t o t a l density decreased (Figure 4.16). In the ternary combinations, increased densities of RPW also influenced the r e l a t i v e performance of RPS and GFT, in favour of the l a t t e r (Figures 4.20 f - j and 4.21 f - j ) , while increased RPS densities tended to s h i f t the competition of RPW and GFT to a neutral position (Figures 4.20 k-o and 4.21 k-o). These responses and the various s h i f t s i n the r e l a t i v e performances of RPS, RPW and GFT were markedly d i f f e r e n t from those exhibited by the pseudo-binary replacement seri e s . However, the decline i n the r e l a t i v e performance of any species against the remaining pair of species on either side of the 1:1 r a t i o of the pair shows some s i m i l a r i t y between the two replacement series systems (compare Figures 4.20 and 4.21, with 4.22 and -4.23). Although t h i s maybe considered to be a unique phenomenon which disappears with increasing density of the t h i r d species or with increasing r a t i o within the pair of species, i t s consistent appearance within similar density ranges (see Figures 4.19 and 4.20 g-j and i-n) i s of b i o l o g i c a l i n t e r e s t . In these treatments, Equation 5 does not give a good f i t to the r e l a t i v e y i e l d curves of GFT i n either binary mixtures with RPS or RPW. But since i t has been shown that GFT does not compete exclusively for the same resources with either RPS or RPW i n d i v i d u a l l y (Sections 4.2.3 and 4.3.2), the complex inte r a c t i o n of RPS, RPW and GFT i n the ternary combi-nations may be attributable to the interactions between the competitive e f f e c t s of RPS and RPW, with the noncompetitive e f f e c t s of either species with GFT. The in t e r a c t i o n i s borne out i n Table 4.41 i n which the e f f e c t s of species a on the combination i s given by z c (k a c+kj 3 c)/2 + (k a b+k c b)/2, which c l e a r l y shows that the i n d i v i d u a l members in a given combination are not acting independently. This can be looked at i n a d i f f e r e n t way by -240-following the ef f e c t s on the actual y i e l d s of a given species as "indicator" i n the presence of a pair of species whose densities vary as a binary replacement series mixture. Table 5.2 presents the differences between the observed y i e l d s and those expected i f the ef f e c t s of each of the competing pair of species were additive and proportional to i t s r e l a t i v e density. While there were clear seasonal differences i n the yie l d s of each species, the y i e l d of rapeseed at i t s two highest r e l a t i v e densities tended to be lower i n the ternary combinations than i n the binary mixtures with either RPW or GFT during 1981. Hence, the combined ef f e c t s of RPW and GFT on the y i e l d of rapeseed were greater than the sum of the in d i v i d u a l e f f e c t s corrected for t h e i r r e l a t i v e frequency i n the combination. Similar e f f e c t s occurred i n 1980, with apparent synergistic e f f e c t s on RPS yi e l d s occurring at the highest RPS density. At the lowest RPS density i n either year, the e f f e c t s of RPW and GFT tended to be antagonistic at low proportions of RPW i n the RPW and GFT combination and syner-g i s t i c at high proportions. With RPW y i e l d s , again there were seasonal differences, but with the exception of the mixture at the highest density of RPW i n which RPS was predominant over GFT, the ef f e c t s of the combination were consistantly synergistic, with the greatest e f f e c t being caused by the combinations i n which GFT predominated. However i t should be pointed out that although the greatest suppression of RPW y i e l d occurred i n combinations r i c h i n GFT, t h i s means that Table 5.2 2 Differences between observed and expected y i e l d s (g/m ) of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) at constant r e l a t i v e d e n s i t i e s i n the presence of binary replacement series of any pa i r of species i n ternary mixtures. 1980 and 1981. Expected y i e l d s are those prorated from the indiv i d u a l y i e l d s in binary mixture assuming no i n t e r a c t i o n between the species constituting a p a i r . The actual y i e l d s and t h e i r s i g n i f i c a n c e are presented in Appendix 13 Difference* Difference Difference 1981 0 +48 -30 0 ZRPS ZRPW ZGFT 1980 1981 ZRPS ZRPW ZGFT 1980 1981 ZRPS ZRPW ZGFT 1980 0.50 0.00 0.17 0.33 0.50 0.50 0.33 0.17 0.00 0 -9 -63 0 0 -17 -84 0 0.00 0.17 0.33 0.50 0.50 0.50 0.33 0.17 0.00 0 -37 +73 0 0 -106 0 0 0.00 0.17 0.33 0.50 0.50 0.33 0.17 0.00 0.50 0 -23 -12 0 0.00 0.67 . 0 0 0.00 0.67 0.17 0.50 -16 -14 0.17 0.50 0.33 0.33 0.33 +14 -19 0.33 0.33 0.33 0.50 0.17 -54 -102 0.50 0.17 0.67 0.00 0 0 0.67 0.00 0 0 0.00 0.67 0 0 -69 -92 0.17 0.50 -27 +54 -28 -56 0.33 0.33 0.33 -18 +21 -6 +2 0.50 0.17 -11 +6 0 0 0.67 0.00 0 0 0.17 0.00 0.83 0 0 0.00 0.17 0.67 +16 -16 0.17 0.33 0.50 +49 +17 0.33 0.50 0.33 +17 +10 0.50 0.67 0.17 -10 -49 0.67 0.83 0.00 0 0 0.83 0.17 0.83 0 0 0.00 0.83 0.67 -93 -113 0.17 0.67 0.50 -78 -94 0.33 0.50 0.33 -43 -63 0.50 0.33 0.17 -23 -40 0.67 0.17 0.00 0 0 0.83 0.00 0.17 0 0 -7 +43 -16 +17 -17 +9 -16 +4 0 0 +: observed y i e l d > expected y i e l d ; antagonism between species i n p a i r . -: observed y i e l d < expected y i e l d ; synergism between species i n p a i r . the suppression was attributable to the low proportion of RPS present, and that as the RPS proportion increased the magni-tude of the suppression of RPW decreased. Thus, in the mixtures at the lowest density of RPW, by d e f i n i t i o n there was no r e l a t i v e suppression of i t s y i e l d i n the presence of GFT alone, but the replacement of one f i f t h of the GFT plants by RPS (units) caused the greatest suppressions (-93 and -113 g/m i n 1980 and 1981 r e s p e c t i v e l y ) . The importance of the contribution of low proportions of RPS r e l a t i v e to GFT to the synergism i s consistent at a l l RPW densities. At the highest RPW density (the mixture i n which RPW was the most abundant species of the three) although synergism occurred at the lower proportion of RPS, the higher RPS proportion resulted i n an antagonism between RPS and GFT such that RPW benefitted. In the case of GFT, i t s behaviour between the two seasons was markedly d i f f e r e n t . In 1980, RPS and RPW consist-ently caused a synergistic suppression of GFT y i e l d , while i n 1981, they reacted ant a g o n i s t i c a l l y except at the highest GFT and RPS den s i t i e s . However, i n t h i s case, unlike that of RPW at i t s highest density, the antagonism occurred i n the combination i n which RPS was less abundant. The seasonal differences for a l l combinations may be explained by the slower emergence of RPW and GFT than RPS in 1980. For example, with respect to the yi e l d s of GFT, the headstart enjoyed by RPS was such that i t tended to dominate the i n t e r a c t i o n , while i n 1981, with a l l three species develop-ing concurrently, i t s competitiveness tended to be focussed on RPW to the benefit of GFT. Hence these studies c l e a r l y demonstrate that the behaviour of the species i n ternary combinations are not predictable from t h e i r behaviour i n binary mixtures. Further-more, the e f f e c t s of combinations of any pair on the t h i r d may range from greater than additive suppressions of the y i e l d of the t h i r d species to less than additive responses indi c a t i v e of antagonism between the e f f e c t s of the components of the pair on the t h i r d species. These observations thus augment those of Haizel and Harper (1973) who observed that both antagonistic and synergistic responses could occur i n ternary mixtures of barley, wild oats and wild mustard. How-ever, t h e i r findings were based upon additive series experi-ments, i n which the combined e f f e c t s of two species on the t h i r d were caused by additions of the two species, such that the t o t a l density of the ternary mixture increased. The present studies involved replacement series i n which the t o t a l density was constant, but within which the proportions of the two i n t e r a c t i n g species were varied at three densities of the t h i r d . These studies therefore, avoid the possible confounding ef f e c t s of changes i n t o t a l density, but nevertheless demonstrate thau markedly d i f f e r e n t types of interaction can occur. It should also be noted that, i n terms of the various binary mixtures studied both i n additive and replacement series experiments, green f o x t a i l consistently emerged as the weakest competitor. However, in terms of i t s effects i n ternary combinations, i t i s revealed as having a pronounced e f f e c t on rapeseed y i e l d i n the presence of redroot pigweed. In addi-t i o n , i t was the only species which tended to benefit consistently from the presence of the other two species. It apparently gains an advantage from the strong competition between rapeseed and redroot pigweed. - 245 -6. SUMMARY AND CONCLUSIONS The o b j e c t i v e s o f the p r e s e n t s t u d i e s were t o compare and e v a l u a t e d i f f e r e n t m e t h o d o l o g i e s which have been used t o a n a l y s e the i n t e r a c t i o n s w i t h i n and mong s p e c i e s i n m o n o c u l t u r e s and i n v a r i o u s b i n a r y and t e r n a r y m i x t u r e s , and t o d e v e l o p a d d i t i o n a l a n a l y t i c a l approaches f o r d e s c r i b i n g y i e l d - d e n s i t y r e l a t i o n s h i p s i n mixed s t a n d s u s i n g b a r n y a r d g r a s s , r e d r o o t pigweed, green f o x t a i l and rap e s e e d . The e x p e r i m e n t a l d e s i g n s c o m p r i s i n g both a d d i t i v e and rep l a c e m e n t b i n a r y s e r i e s c o m b i n a t i o n t r e a t m e n t s a t d i f f e r e n t t o t a l d e n s i t i e s p e r m i t t e d i n t e r c o m p a r i s o n s between the two approaches t o p l a n t c o m p e t i t i o n . The rapeseed s e r i e s a l s o c o n t a i n e d t e r n a r y replacement s e r i e s m i x t u r e s which p e r m i t t e d e v a l u a t i o n o f t h e impact o f t h e t h i r d s p e c i e s on t h e i n t e r a c t i o n between p a i r s o f s p e c i e s i n b i n a r y m i x t u r e s . Shoot biomass was used as a measure o f y i e l d t h r o u g h o u t . V a r i a b i l i t y i n y i e l d s w i t h i n a s p e c i e s as a r e s u l t o f i n c r e a s i n g d e n s i t y o f i t s own o r o f o t h e r s p e c i e s was a t t r i b u t e d t o e f f e c t s o f i n t e r a c t i o n . V a r i o u s m a t h e m a t i c a l models were employed t o e v a l u a t e c o m p e t i t i v e n e s s i n and t o " e s t i m a t e y i e l d and y i e l d l o s s e s . The f i n d i n g s o f these i n v e s t i g a t i o n s a re p r e s e n t e d below. 1. De W i t ' s s p a c i n g f o r m u l a ( E q u a t i o n 16) d e s c r i b e s the a s y m p t o t i c y i e l d - d e n s i t y r e l a t i o n s h i p s i n monocu l t u r e s o f a l l s p e c i e s t e s t e d ( S e c t i o n 4.1). - 246 -The p r e s e n t s t u d i e s have shown t h a t the y i e l d o f the accompanying s p e c i e s i n the b i n a r y a d d i t i v e s e r i e s m i x t u r e s i n v o l v i n g b a r n y a r d g r a s s , r e d r o o t pigweed green f o x t a i l and rapeseed can a l s o be d e f i n e d by t h e s p a c i n g f o r m u l a ( S e c t i o n s 4.2 and 4.3). W h i l e the s p a c i n g f o r m u l a was a b l e t o p r o v i d e good e s t i m a t e s o f y i e l d o v e r the d e n s i t y ranges used i n i t s d e r i v a t i o n , i t s e x t r a p o l a t i o n t o p r e d i c t per p l a n t y i e l d grown i n i s o l a t i o n (Bft) and a t t e m p t s t o use B - v a l u e s t o d e t e r m i n e e f f e c t s s h o u l d be t r e a t e d w i t h c a u t i o n . A l t h o u g h , B - v a l u e s o f BYG d e c l i n e d w i t h i n c r e a s i n g d e n s i t y o f RPW i n 1981 and hence suggested t h a t RPW outcompeted BYG, the y i e l d - d e n s i t y c u r v e s showed the r e v e r s e ( S e c t i o n s 4.2 and 4.3) The use o f B - v a l u e s o b t a i n e d from s p a c i n g e x p e r i m e n t s t o p r e d i c t de W i t ' s r e l a t i v e c rowding c o e f f i c i e n t s ( E q u a t i o n 22) y i e l d e d i n c o n s i s t e n t r e s u l t s . W h i l e the e s t i m a t e d r e l a t i v e crowding c o e f f i c i e n t s f o r b a r n y a r d g r a s s ( o r rapeseed) i n r e d r o o t pigweed o r green f o x t a i l f o l l o w e d the same g e n e r a l p a t t e r n as t h o s e computed from E q u a t i o n 6, t h o s e computed f o r r e d r o o t pigweed and green f o x t a i l i n b i n a r y m i x t u r e s were d i f f e r e n t ( S e c t i o n 4.6.3). The growth o f t h e i n d i c a t o r s p e c i e s i n the b i n a r y a d d i t i v e s e r i e s m i x t u r e s was d e s c r i b e d by Dew's square - 247 -root r e l a t i o n s h i p between the indicator y i e l d and the density of the accompanying species (Equation 9). Good estimates of indicator y i e l d s were obtained with high correlations between actual and estimates y i e l d s (Sections 4.2.5 and 4.3.5). The curves for the y i e l d s of indicator species which were weaker competitors than the accompanying species in additive series tended to converge while'those of the strong competitors tended to diverge. In the l a t t e r case, the c o e f f i c i e n t s (b) of the indicator species y i e l d and the squareroot of the density of the accompanying species declined with increasing density of the indicator species. The regression c o e f f i c i e n t (b) and the estimated pure stand y i e l d (a) of the indicator species in additive series d i f f e r with the i n c l u s i o n or exclusion of the indicator monoculture y i e l d data; t h i s i n turn influences the magnitude of Dew's Index of Competition computed from Equation 9 and hence the estimated y i e l d loss based upon Equation 20 (Sections 4.2.4 and 4.3.4). Inclusion of the monoculture data for the indicator species (by means of a dummy low density for the accompanying species) consistently yielded better estimates of y i e l d losses; t h e i r exclusion tended to - 248 -overestimate y i e l d losses appreciably (Sections 4.2.5 and 4.3.4). The r e l a t i v e crowding c o e f f i c i e n t s (k) determined by Equation 6 were generally constant over a range of r e l a t i v e d e n s i t i e s , with a constant t o t a l density (Sections 4.4.4 and 4.5.4). Hence, other than i n providing better estimates of r e l a t i v e crowding c o e f f i c i e n t s , the present studies show that combinations of densities other than the d i a l l e l system may not be necessary. Relative crowding c o e f f i c i e n t s were shown to vary with changes in t o t a l density. Those of the more aggressive species tend to decline with decreasing t o t a l density while those of the less agressive species tend to increase. Estimates of the r e l a t i v e crowding c o e f f i c i e n t s for untested binary combinations based upon the i r performance in binary mixtures with a common t h i r d species (Equation 7) provide poor agreement with those obtained from actual binary mixtures by means of Equation 6 (Section 4.6.3). Alternative methods (e.g. Equations 7 and 22) for estimating k-values for a p a r t i c u l a r binary mixture should be avoided unless they have been tested experimentally. - 249 -12. The decline in estimates of B from the spacing experiment with increasing density of the indicator may o f f e r potential as a measure of competitiveness of the indicator against the accompanying species i n additive se r i e s , and thus complement the Index of Competition which relates to the accompanying species. 13. The use of k-values to predict y i e l d losses (Equation 23) in a manner comparable to Dew's Index of Competition method (Equation 20) was shown to be of limited application, p a r t l y because of the dependence of k-values on t o t a l density (Sections 4.4 and 4.5) and pa r t l y because of the change in density of any given species inherent in replacement s e r i e s . Unless the r e l a t i v e crowding c o e f f i c i e n t has been shown to remain constant over a range of t o t a l d e n sities, Equation 20 based upon additive series experiments provides the only method for estimating y i e l d losses over a wide range of density l e v e l s . 14. The present studies permitted intercomparisons between the effects on y i e l d of adding various equal densities of the same species ( i n t r a s p e c i f i c competition) or of a second species ( i n t e r s p e c i f i c competition). The r a t i o of the suppression of the y i e l d for plant of species a caused by increasing density of species a to the - 250 -suppression caused by species b, i s .termed the Interference Ratio (IR) (Section 3.6.2.2). By i t s d e f i n i t i o n , t h i s new r a t i o provides a measure of r e l a -t i v e performance analogous to the r e l a t i v e crowding c o e f f i c i e n t s derived from Equation 6. 15. The various measures of competitiveness i . e . Dew's Index of Competition (CI) obtained from the additive series experiments; de Wit's r e l a t i v e crowding c o e f f i c i e n t s , (k), Willey and Rao's Competition Ratios (CR), M c G i l c h r i s t 1 s Aggressivity (A) and the new Interference Ratio (IR) exhibited great v a r i a b i l i t y with each other (Section 5.4). Values of k were highly correlated with A and CR and i n 1980 they were also correlated with CI. However, there was only a weak cor r e l a t i o n between IR and k. 16. Among the measures of competitiveness (Section 5.4), the new IR i s the only one to dis t i n g u i s h d i r e c t l y between the r e l a t i v e contribution of i n t r a - and i n t e r -s p e c i f i c e f f e c t s i n mixed stands. The IR-values showed that the great s e n s i t i v i t y of pigweed to i n t r a -s p e c i f i c competition as compared to competition from f o x t a i l exceeded that of any other binary mixture; barnyardgrass and rapeseed also showed greater s e n s i t i v i t y to i n t r a s p e c i f i c competition than i n t e r -s p e c i f i c competition from pigweed or f o x t a i l . Experiments involving ternary mixtures of rapeseed, pigweed and f o x t a i l show that.the r e l a t i v e performance of any pair of species can be dramatically modified by changes i n the density of the t h i r d species (Section 4.6) . Green f o x t a i l (the weakest competitor r e l a t i v e to pigweed or'rapeseed i n binary mixtures) showed the greatest e f f e c t of any species in modifying the competitiveness of the other species i n any ternary mixture. Certain ternary mixtures were treated as pseudo-binary replacement series, involving one species and a pair of other species at constant r a t i o s of t h e i r r e l a t i v e d e n sities, treated as a "composite species". The ef f e c t s of changing the composition of the "composite species" on the f i r s t species showed that the in d i v i d u a l species i n given ternary combinations do not act independently (Section 4.6.2). Interaction among rapeseed, pigweed and f o x t a i l i n the ternary mixtures were both antagonistic and synergistic in nature (Section 5.5). Pigweed and f o x t a i l , for example, behaved s y n e r g i s t i c a l l y against high density rapeseed, but tended to act antagonistically at low rapeseed den s i t i e s . 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An evaluation of green f o x t a i l (Setaria  v i r i d i s (L.) Beauv.) M.Sc. Thesis, Univ. of Guelph. Snaydon, R.W. 1971. An analysis of competition between plants of Trifol i u m repens L. populations co l l e c t e d from contrasting s o i l s . J. Appl. Ecol. 8_: 687-697. Snaydon, R.W. 1979. A new technique for studying plant interactions. J . App. Ecol. J_6: 281-286. Stern, W.R. 1962. Light measurements i n pastures. Herb. Abstr. 3_2: 91-96. Stern, W.R. 1965. The e f f e c t of density on the performance of i n dividual plants i n subterranean clover swards. Austr. J. Agric. Res. J_6_: 541-555. Stern, W.R. and CM. Donald. 1962. Light relationships i n grass-clover swards. Austr. J . Agric. Res. J_3: 599-614. Sylvester, E.P. 1970. The ten worst weeds of f i e l d crops. 6. F o x t a i l s . Crop & S o i l s 23-: 11-13. Taylorson, R.B. and S.B. Hendricks. 1969. Action of phytochrome during p r e c h i l l i n g of Amaranthus retroflexus L. seeds. Plant Physiol. £4: 821-825. 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In: Mechanisms in B i o l o g i c a l Competition _1_5: 3124-329. Wit de, C.T. 1978. Summative address Iri: Plant Relations in Pastures. CSIRO (Publ.) by J.R. Wilson 1978. Pp. 405-410. Wit de, C.T. and J.P. Van den Bergh. 1965. Competition between the herbage plants. Nerth. J. Agric. Res. 13: 212-221. Wit de, C.T., P.G. Tow and G.C. Ennik. 1966. Competition between legumes and grasses. V e r s l . handbouwk, Onderz. 687 Wangeningen. Yamagishi, H. Morishima and H.I. Oka. 1978. An experiment on the interactions between cultivated r i c e and barnyardgrass at d i f f e r e n t planting d e n s i t i e s . Agro. ecosystems Ai 449-458. Appendix l Monthly mean temperatures and p r e c i p i t a t i o n at South Campus F i e l d s , U n i v e r s i t y of B r i t i s h Columbia (1979-1981) Av. Monthly A i r Av. Monthly pption. Av. Da i l y Sunshine Av. Monthly S o i l (5cm) Temp. °C mm hours per month Temp. (°C) mornings 1979 1980 1981 1979 1980 1981 1979 1980 1981 1979 1980 1981 1 tsj . ON January 0, .53 0 .99 6. . 06 .59, . 7 ]0] .] 72. . 2 3, .0 2 .8 ] , .9 0 . 3 ] .9 6, .4 February 3. . 7 5, .8 5. .3 179, .2 174, . 7 138. .0 2, .8 2. .0 3. .2 2, . 4 4, .3 5. .5 March 7. .4 5. .5 8. . 1 61, . 8 115. . 6 135. . 5 5, .9 3, .6 5. . 8 6, .4 6, .1 7. .9 A p r i l 8. . 6 10. .3 8. .6 52, .2 775. .2 151. . 8 6. .5 6, .2 5. .4 9. .2 10. .5 9. .2 May 12. , 4 12. .6 11. ,9 38. . 3 70. .7 103. , 8 7. . 8 5. .9 5. .6 14. .4 13. .9 13. .9 June 14. .7 13. . 6 13. ,5 37. .4 68. .2 126. ,4 9. .5 6. .3 4. .7 16. .3 16. .2 16. .2 Jul y 17. .1 16. .2 11. 6 25. . 8 70. . 2 41. , 9 9. .4 9. . 5 8. ,1 17. .4 18. .3 18. , 9 August 17. 1 16. .4 18. 1 20. , 0 45. .1 43. , 1 8. ,2 7. .6 9. ,8 17. .7 17. .8 18. ,7 September 15. 6 14. , 1 111. . 5 84. . 8 5. , 6 5. .1 15. .9 15. .3 October 10. 9 11. ,4 8. , 5 62. . 9 3. • 8 5. ,3 11. , 3 11. .9 Novermber 5. 8 7. ,3 79. 5 308. , 6 3. ,2 1. 3 5. .3 7. ,9 December 5. 9 5. ,2 302. 5 232. 6 1. 1 0. 5 5. 2 6. 4 MEAN 9. 98 9. 94 81. 78117. 50 5. 55 4. 66 10. ,10 10. 88 STD. DIV. 5. 5 4. 9 84. 1 80. 5 2. 8 2. 7 6. 3 5. 5 -268-Appendix 2 2 Yields (g/m ) of barnyardgrass (as indicato r species) and redroot pigweed i n binary additive series mixtures. DENSITY BARNYARDGRASS REDROOT PIGWEED (plants/m 2) (as indicator) (as competitor) BYG. RPW 1980 1981 1980 1981 240 240 604.6H1 5.73.9f 324.5ef 227.8 240 480 560.5hi 484.6g 434.4d 361.6e 240 720 512.Oij 412.8h 618.4b 472.3c 240 960 458.2jk 384.3h 649.3ab 528.4b 240 1200 423.8k 383.5h 678.3a 608.2a 480 240 793.9f 764 .7d 269.7g 172.Oh 480 480 714.4g 703.9e 365. l e f 290.6f 480 720 678.5g 674.3e 484.3c 403.8d 480 960 667.2g 646.2e 503.9c 451.3c 720 240 1003.7c 970.1c 200.3h 145. lh 720 480 6912.Ide 967.2c 310.4fg 258.4fg 720 • 720 875.2e 962.4c 374.9e 278.4f 960 240 1065.1b 1047.6b 207.6h 135.5h 960 480 967.9cd 1041.3b 259.7g 162. lh 1200 240 1191.5a 1152.8a 129.2i 75.7i Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05) . (These data are depicted i n Figure 4.3). -269-Appendix 3 2 Y i e l d s (g/m ) of redroot pigweed (as i n d i c a t o r species) and barnyardgrass i n binary a d d i t i v e s e r i e s mixtures. DENSITY2 REDROOT PIGWEED BARNYARDGRASS (plants/m ) (as i n d i c a t o r ) (as competitor) RPW BYG 1980 1981 1980 1981 240 240. 324.5ef 1 227.8g 604.6h 573.9f 240 480 269.7g 172.Oh 793.9f 764.7d 240 720 200.3h 145. l h 1003.7c 970.1c 240 960 207.6h 135.5h 1065.1b 1047.6b . 240 1200 129.2i 75.7i 1191.5a 1152.8a 480 240 434.4d 361.6e 560.5hi 484.6g 480 480 356.lef 290.6f 714.4g 703.9e 480 720 310.4fg 258.4fg 912. lde 967.2c 480 960 259.7g 162.lh 967.9cd 1041.3b 720 240 618.4b 472.3c 512.Oij 412.8h 720 480 484.3c 403.8d 678.5g 674.3e 720 720 374.9e 278.4f 875.2e 962.4c 960 240 649.3ab 528.4b 458.2jk 384.3h 960 480 503.9c 451.3c 667.2g 646.2e 1200 240 678.3a 608.2a 423.8k 383.5h ^ Values i n columns d i f f e r e n t (P > 0. followed by 05). the same l e t t e r are not s i g n i f i c a n t l y (These data are rearranged from those presented i n Appendix 2 and are depicted i n Figure 4.4). -270-Appendix 4 2 Yields (g/m ) of barnyardgrass (as indicator species) and green foxtail (GFT) in binary additive series mixtures. DENSITY BARNYARDGRASS GREEN FOXTAIL (plants/m2) (as indicator) (as competitor) BYG GFT 1980 1981 1980 1981 240 240 606.If1 625.7e 211.8f 244.3f 240 480 515.9g 579.2ef 337.5d 312.4e 240 720 431.2h 532.9ef 450.0b 452.9bc 240 960 402.2h 489.7f 466.3ab 487.3b 240 1200 390.3h 475.7f 469.2a 555.2a 480 240 914.6c 826.7d 194.8f 165.2gh 480 480 824.9d 769.3d 321.Od 262.2f 480 720 761.le 738.3d 380.8c 388.5d 480 960 741.9e 728.8d 401.9c 426.4cd 720 240 995.2b 945.3c 148.2g 121.3hi 720 480 919.0c 928.6c 221.4f 193.Ig 720 720 870.8cd 915.4c 280.5e 280.8ef 960 240 1058.0b 1062.6b 120.5gh 97.9i 960 480 1020.8b 1055.0b 118.0gh 150.9gh 1200 240 1150.8a 1172.3a 103.Oh 80.Ii Values in columns followed by the same letter are not significantly differently (P >• 0.05). (These data are depicted in Figure 4.5). Appendix 5 Yields (g/m2) of green f o x t a i l (as indicator species) and barnyardgrass (BYG) in the binary additive series mixtures. DENSITY GREEN FOXTAIL BARNYARDGRASS (plants/m 2) (as indicator) (as competitor) GFT BYG 1980 1981 1980 1981 240 240 211.8f* 244.3f 606.If 625.7e 240 480 194.8f 65.2gh 914.6c 826.7d 240 720 148.2g 21.3hi 995.2b 945.3c 240 960 120.5gh 97.9i 1058.0b 1062.6b 240 1200 103.Oh 80. I i 1150.8a 1172.3a 480 240 337.5d 312.4e 515.9g 579.2ef 480 480 321.Od 262.2f 824.9d 769.3d 480 720 221.4f 193.Ig 919.0c 928.6c 480 960 118.0gh 150.9gh 1020.8b 1055.0b 720 240 450.0b 452.9bc 431.2h 532.9ef 720 480 380.8c 388.5d 761.le 738.3d 720 720 280.5e 280.8ef 870.8cd 915.4c 960 240 466.3ab 487.3b 402.2h 487.7f 960 480 401.9c 426.4cd 741.9e 728.8d 1200 240 469.2a 555.2a 390.3h 475.7f ^ Values in columns followed by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05). (These data are rearranged from those presented i n Appendix 4, and are depicted in'Figure 4.6). -2 72-Appendix 6 2 Yields (g/m ) of redroot pigweed (as indicator species) and green f o x t a i l (GFT) i n binary additive series mixtures during 1981. DENSITY (plants/m 2) REDROOT PIGWEED (as indicator) GREEN FOXTAIL ' (as competitor) RPW GFT 1981 1981 240 240 321.6eX 262.5gh 240 480 302.3e 335.2ef 240 720 296.Oe 484.3c 240 960 286.4e 561.3b 240 1200 281.5e 618.2a 480 240 493.Od 210.8hi 480 480 472.7d 304.9fg 480 720 458.7d 374.6e 480 960 449.8d 435.5d 720 240 610.9c 172.4i 720 480 609.0c 213.6hi 720 720 607.5c 295.8fg 960 240 734.3b 158.Oi 960 480 710.6b 184.Oi 1200 240 792.9a 76.7 j Values i n column followed by the same l e t t e r are not s i g n i f i c a n t l y different (P > 0.05). (These data are depicted i n Figure 4.7a). Appendix 7 Yields (g/m ) of green f o x t a i l (as indicato r species) and redroot pigweed (RPW) i n binary additive series mixtures. DENSITY (plants/m 2) GREEN FOXTAIL (as indicator) REDROOT PIGWEED (as competitor) GFT RPW 1981 1981 240 240 262.Sgh 1 321.6e 240 480 210.8hi 493.Od 240 720 172.4i 610.9c 240 960 158.Oi 734.3b 240 1200 76.7j 792.9a 480 240 335.2g 302.3e 480 480 304.9fg 472.7d 480 720 213.6hi 609.0c 480 960 184.Oi 710.6b 720 240 484.3c 296.Oe 720 480 374.6e 458.7d 720 720 295.8fg 607.5c 960 240 561.3b 286.4e 960 480 435.5d 449.8d 1200 240 618.2a 281.5e Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05). (These data are rearranged from those presented i n Appendix 6, and are depicted i n Figure 4.7b)J - 2 7 4 -Appendix 8 2 Y i e l d s (g/m ) of rapeseed (as i n d i c a t o r spec ies ) and redroot pigweed (RPW) i n the b i n a r y a d d i t i v e s e r i e s m i x t u r e s . (1981 data) DENSITY^ RAPESEED REDROOT PIGWEED (plants/m ) (as i n d i c a t o r ) (as compet i to r ) RPS RPW 1981 1981 75 240 4 6 3 . 7 d e 2 222 .8efg 75 480 369.2ef 333.3d 75 720 3 2 1 . 2 f g 498.7b 75 960 262.9g 591.6a 75 1200 237.4g 658.2a 150 240 526.5d 161.3fgh 150 480 493.Od 292.7de 150 720 470.6de 385.5cd 150 960 468.9de 440.7bc 225 240 652.5c 133.5fgh 225 480 639.3c 229.2ef 225 720 634.0c 295.2de 300 240 744.0b 121.Ogh 300 480 750.9b 176.1fgh 375 240 863.5a 103.9h Values i n columns f o l l o w e d by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0 . 0 5 ) . (These data are d e p i c t e d i n F igure 4 . 8 a ) . -275-Appendix 9 Yields (g/m2) of redroot pigweed (as indicat o r species) and rapeseed (RPS) i n the binary additive series mixtures. (1981 data) DENSITY2 (plants/m ) REDROOT PIGWEED (as indicator) RAPESEED (as competitor) RPW RPS 1981 1981 240 75 222.8efg 1 (321.5) 463.7de 240 150 161.3fgh 526.5d 240 225 133.5fgh 652.5c 240 300 121.Ogh 744.0b 240 375 103.9h 863.5a 480 75 333.3d (292.0) 369.2ef 480 150 292.7de 493.Od 480 225 229.2ef 639.3c 480 300 176.1fgh 750.9b 720 75 498.7b (267.9) 321.2fg 720 150 385.5cd 470.7de 720 225 295.2de 634.0c 960 75 591.6a 262.9g 960 150 440.7bc 468.9de 1200 75 658.2a 237.4g ^ Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05). (These data are rearranged from those presented i n Appendix 8, and are depicted i n Figure 4.8b). Appendix 10 Yields (g/m ) of rapeseed (as indicato r species) and green f o x t a i l (GFT) i n the binary additive series mixtures. (1981 data) DENSITY (plants/m ) RAPESEED (as indicator) GREEN FOXTAIL (as competitor) RPS GFT 1981 1981 75 240 455.6e X 277.9fgh 75 480 383.Of 410.4de 75 720 304.3g 515.7c 75 960 275.9g 581.8b 75 1200 273.Ig 647.1a 150 240 551.7d 233.0ghi 150 480 528.lde 350.8ef 150 720 504.9de 449.7cd 150 960 497.9de 495.2c 225 240 666.5c 187.2i 225 480 644.2c 289.9fg 225 720 635.8c 343.6ef 300 . 240 775.3b 155.3i 300 480 781.6b 201.9hi 375 240 858.2a 89.9j Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05) . (These data are depicted i n Figure 4.9a). -277-APPENDIX 11 2 Yields (g/m ) of green foxta i l (as indicator species) and rapeseed (RPS) in the binary additive series mixtures. (1981 data) DENSITY (plants/m2) GREEN FOXTAIL (as indicator) RAPESEED (as competitor) GFT RPS : 1981 1981 240 75 277.9fgh1 (346.0) 455.6e 240 150 233.0ghi 551.7d 240 225 187.2i 666.5c 240 300 155.3i 775.3b 240 375 89.9j 858.2a 480 75 410.4de (320.0) 383.Of 480 150 350.8ef 528. Ide 480 225 289.9fg 644.2c 480 300 201.9hi 781.6b 720 75 515.7c (304.6) 304.3g 720 150 449.7cd 504.9de 720 225 343.6ef 635.8c 960 75 581.8b 275.9g 960 150 495.2c 497.9de 1200 75 647.1a 273.Ig Values in columns followed by the same letter are not s ignif icantly different (P > 0.05). (These data are rearranged from those presented in Appendix 10, and are depicted in Figure 4.9b). -278-Appendix 12 2 Mean y i e l d s (g/m ) of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) i n binary replacement series mixtures during 1980 and 1981 seasons*. JRPS RPW GFT RPS 1980 1981 RPW 1980 1981 GFT 1980 1981 0.833 0 .167 803.9a 863 .5a 59 • 2e 103 .9e - -0.667 0 .333 694.6b 750 .7b 129 .Id 167 • 7d - -0.500 0 .500 - 543.2c 634 .0c 187 .7c 295 • 2c - -0.333 0 .667 - 388.6d 468 .9d 321 .0b 440 .7b - -0.167 0 .833 - 173.8e 237 .4e 543 .5a 658 .2a - - • - 0 .167 0.833 - - 253 .2e 281 .5e 537 . l a 618 .2a - 0 .333 0.667 - - 390 .7d 449 .3d 389 .9b 435 .5b - 0 .500 0.500 - - 542 .2c 607 .5c 309 • 7c 295 .8c - 0 .667 0.333 - - 633 .0b 710 ,6b 156 .4d 184 .0d - 0 .833 0.167 - - 721 .7a 792 • 9a 91 .3e 76 .7e 0.167 0.833 277.2e 273 .le - - 402 .5a 647 .8a 0.333 - 0.667 476.4d 497 .9d - - 301 .4b 495 .2b 0.500 - 0.500 632.3c 635 .8c - - 190 .7c 343 .6c 0.667 -.333 744.9b 781 .6b - - 137 .4d 201 .9d 0.833 0.167 814.2a 858 .2a - - 75 .4e 89 .9e Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y (P > 0.05) d i f f e r e n t . -279-Appendix 13 2 Mean y i e l d s (g/m ) of rapeseed (RPS), redroot pigweed (RPW) and green f o x t a i l (GFT) i n ternary replacement series mixtures during 1980 and 1981 seasons 1. RPS RPW GFT RPS 1980 1981 RPW 1980 1981 GFT 1980 1981 0.667 0 .167 0.167 0.500 0 .333 0.167 0.333 0 .500 0.167 0.167 0 .333 0.167 0.500 0 .167 0.333 0.333 0 .333 0.333 0.167 0 .500 0.333 0.333 0 .167 0.500 0.167 0 .333 0.500 0.167 0 .167 0.667 656.8a 694.5a: 75.4e 509.6c 550.9c 189.3d 357. le 374.2e 379.0b 184.9g 195.7f 519.5a 593.2b 618.2b 93.5e 446.Od 464.2d 232.7c 232.2fg 261.8f 387.5b 434.8d 476.3d 98.le 284.8f 275.8f 256.1c 272.8f 249.9f 121.9e 99 • 2d 62 .6e 91 .5d 234 .0c 64 • 6e 93 • 2d 398 • 9b 69 .3e 98.5d 565 • 4a 80 .9e 121 .9d 112 .4d 138 .3d 196 .6c 252 .4c 142 .3d 199 .9c 397 ,8b 145 .7d 221 .7c 116 .7d 218 .5c 297 • 5b 287 .0c 247 • lb 343 • 4b 131 .Id 353 .6a 473 . l a Values i n columns followed by the same l e t t e r are not s i g n i f i c a n t l y (P > 0.05) d i f f e r e n t . - 280-Appendix 14 L i s t of Symbols A. SPACING EXPERIMENTS 1. M =Monoculture y i e l d s 2 2. S =Space per plant (cm /plant) 3. n =Yield at very high density (assymptotic yield) 4. B =Space at half the assymptotic y i e l d B. ADDITIVE SERIES EXPERIMENTS 2 1. X =Density of the accompanying species (plants/m ) 2. a =Estimated monoculture y i e l d 2 3. Y ^Mixture ^ i e l d (g/m ) 4. b1=Cl=Index of competition C. REPLACEMENT SERIES EXPERIMENTS 2 1. Z =Density (plants/m ) 2. z =Relative density 3. M =Monoculture y i e l d 4. 0 =Mixture y i e l d 5. r =Relative y i e l d 6. RYT=Relative y i e l d t o t a l 7. k =Relative crowding c o e f f i c i e n t 8. K =Products of the r e l a t i v e crowding c o e f f i c i e n t s 9. A =Aggressivity 10. CR=Competition Ratio 11. IR=Interference Ratio D. SYMBOLS USED IN BOTH TYPES OF EXPERIMENTS 1. L =Yield loss 2. r =correlation c o e f f i c i e n t 3. b =regression c o e f f i c i e n t - 281 -Appendix 15 L i s t of Equations Pages l a . ( Za ) / ( Za +V + ( Z b ) / ( Z a + V = 1 * * * 4 1 l b . z + z, = 1 . . . . . . . . 41 a b 2. r = 0 / M . . . . . . . 45 a a a 3. RYT = r + r, . . . . . . 45 a b 4. 0 a = { ( Z a ) / ( Z a + Z b) } Ma . . . . 46 5 ' °a = i ( k a b z a ) / ( k a b z a + zb> ) M a . . . 46 6- kab = ( 0 a z b ) / ( M a - ° a ) z a 4 7 V • Ic i Ic • Jc T • * • • • • • 53 ab ac cb G I _ Product of pure culture Equivalents  ~ Product of Actual Number of Plants i n Mixture 56 Y = a - b JX . . . . . . . 57 10. b i ~ b / a . . . . . . . . 57 11. A = 1/2(o a - ma) + 1/2(mb - o b) 59 12. A = (O a - l / 2 M a ) + (l/2M b - 0 b ) . . . 59 13 A = — - - a 5 9 ab 2. m m, a b 0 0, 1 4 A = — a - — R q ab M M , D y a b 15. A a b = 1/2 (r + r f a) 60 - 282 -Pages 16. Mg = B B + S 17. 1/M = 1 . S + 1 . . . . . . . 62 B ft JCL 18. k = B + S . . . . . . . 64 a — s — 19. k .k. = ( B a + S ) ( Bb - S ) . . . . 64 ae be ^ S 20. L = a.b-^  ^/X . . . . . . . 65 21. %L = lOObj^ N/X~ . . . . . . 65 B a + S 2 2 ' kab = B, + S . . . . . . 66 b 23a. L = M - 0 = z, / (k ,z + z, ) M . . . 231 a a a b ab a b a 23b. %L = 100 (M - 0-)M = (100z, )/(k ,z ) . . 231 a a a a o a.o a 

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