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Biometrical analysis of pathogenicity in the Ustilago hordei--Hordeum vulgare host-parasite system Pope, David D. 1982

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BIOMETRICAL ANALYSIS OF PATHOGENICITY IN THE USTILAGO HORDEI - HORDEUM VULGARE HOST-PARASITE SYSTEM by DAVID D. POPE B . S c . , U n i v e r s i t y of N o r t h C a r o l i n a , R a l e i g h , 1 9 7 5 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n _ THE FACULTY OF GRADUATE STUDIES (Department o f B o t a n y ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r 1982 0 D a v i d U. Pope, 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 fo r 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 f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Genetics (Botany) The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date .'October 29, 1982 E-6 (3/81) i i ABSTRACT This study involves a measure of the v a r i a b i l i t y of descendants from a cross between Ustilago hordei race 7 and race 11, on two v a r i e t i e s of barley, Trebi and Odessa. Components of v a r i a b i l i t y were defined, s t a t i s t i c a l l y described and compared. Biometrical analyses uncovered the action of s i g n i f i c a n t additive and non-additive genetic e f f e c t s . D i f f e r e n t i a l interactions between treatments and v a r i e t i e s revealed the the existence of at least one virulence gene. Specific polygenes and the virulence gene were found to produce s i g n i f i c a n t interactions with d i f f e r e n t environmental conditions. Homogeneity of variance of the genetic components of the F2 from three randomly chosen F1 dikaryotic l i n e s demonstrated the highly homozygous condition of the parental teliospores. Covariance - variance regression analysis was used to study the dominance and e p i s t a t i c differences between treatment dikaryons. There i s evidence for ambidirectional dominance. The number of e f f e c t i v e factors operating against the v a r i e t i e s , Trebi and Odessa, were estimated to be between 4-6 and 1-2 respectively. TABLE OF CONTENTS ABSTRACT i i L I S T OF TABLES v i L I S T OF FIGURES v i i i ACKNOWLEDGEMENTS i x I . INTRODUCTION 1 I I . RESISTANCE 2 S p e c i f i c R e s i s t a n c e 2 N o n s p e c i f i c R e s i s t a n c e 4 I I I . PATHOGENICITY 10 S p e c i f i c P a t h o g e n i c i t r y 10 N o n s p e c i f i c P a t h o g e n i c i t y 13 S p e c i f i c P o l y g e n i c P a t h o g e n i c i t y 16 IV. S T A B I L I T Y OF POLYGENIC SYSTEMS 19 V. HISTORY OF THE STUDY OF VARIABILITY 24 V I . BIOMETRICAL ANALYSIS 27 V I I . E F F E C T I V E FACTORS 32 V I I I . CONSTANT RANKING 36 IX. QUANTITATIVE STUDIES OF FUNGI 37 S t u d i e s o f U s t i l a g o h o r d e i 40 X. PURPOSE OF THIS STUDY 49 X I . MATERIAL AND METHODS 50 E x p e r i m e n t a l D e s i g n 50 S p o r i d i a I s o l a t i o n 53 L o n g t e r m S p o r i d i a S t o r a g e 54 i v Seed P r e p a r a t i o n , 54 I n o c u l u m P r e p a r a t i o n 54 I n o c u l a t i o n 55 P l a n t i n g 55 H a r v e s t 55 S t a t i s t i c a l A n a l y s i s 56 X I I . RESULTS 58 V a r i a n c e A n a l y s i s 58 R e g r e s s i o n A n a l y s i s 103 Homogeneity of V a r i a n c e o f Sample P o p u l a t i o n s 115 E f f e c t i v e F a c t o r s 116 C o n s t a n t R a n k i n g 116 X I I I . DISCUSSION 122 V a r i a n c e A n a l y s i s 122 R e g r e s s i o n A n a l y s i s 125 Homogeneity of V a r i a n c e o f Sample P o p u l a t i o n s 126 E f f e c t i v e F a c t o r s 128 C o n s t a n t R a n k i n g 130 XIV. REFERENCES 133 XV. APPENDICES 150 A p p e n d i x I 150 1 M i n i m a l Medium 150 Comp l e t e Medium 150 Bauch M a t i n g Type T e s t P l a t e s 150 V o g e l ' s S o l u t i o n 1 50 T r a c e E l e m e n t S o l u t i o n 150 V i t a m i n S o l u t i o n 151 V A p p e n d i x II 152 E q u a t i o n f o r C a l c u l a t i n g " t " V a l u e s 152 A p p e n d i x I I I 153 E q u a t i o n s f o r C a l c u l a t i n g "k" V a l u e s 153 A p p e n d i x IV 155 Spearman Rank C o r r e l a t i o n C o e f f i c i e n t C a l c u l a t i o n ...155 LIST OF TABLES Table 1. Compilation of variance components and estimations of h e r i t a b i l i t i e s from experiments on pathogenicity in the smut-barley system 47 Table 2. Ebba's and Tapke's disease readings from s e l f i n g T1 and T4, expressed as a percentage of smutted plants . 59 Table 3. Eight dikaryotic l i n e (DL) disease readings from the cross between T1 and T4 61 Table 4. Six grids representing transformed treatment and array means for the disease readings of the three DL's on Trebi (T) and Odessa (0) 63 Table 5. Fundamental s t a t i s t i c s compiled for the six grids 72 Table 6. ANOVA components for pathogenicity readings of the three DL's on the two v a r i e t i e s 74 Table 7. Components of variance for pathogenicity readings given in Table 6 78 Table 8. ANOVA components for pathogenicity readings of the three DL's on each variety 81 Table 9. Components of variance for pathogenicity readings given in Table 8 83 Table 10. ANOVA components for pathogenicity readings of each DL on the two v a r i e t i e s 86 Table 11. Components of variance for pathogenicity readings given in Table 10 91 Table 12. ANOVA components for pathogenicity readings of each DL on each variety 96 Table 13. Components of variance for pathogenicity readings given in Table 12 .-. 99 Table 14. Actual and r e l a t i v e contributions of the additive and the genetic components for each DL on each variety .101 Table 15. Results of tests of significance for the deviation of the regression slopes from 0.0 and 0.5 ....111 Table 16. Type and presence of dominance and e p i s t a s i s , respectively, for the regression plots in Figure 5 113 v i i i L I S T OF FIGURES F i g u r e 1. The l i f e c y c l e o f U s t i l a g o h o r d e i . 42 F i g u r e 2. E x p e r i m e n t a l d e s i g n 51 F i g u r e 3a. F r e q u e n c y d i s t r i b u t i o n s of t h e d i s e a s e l e v e l s on T r e b i f o r t h e 36 F2 t r e a t m e n t d i k a r y o n s f r o m DL 17, 21 and 23, r e s p e c t i v e l y 67 F i g u r e 3b. F r e q u e n c y d i s t r i b u t i o n s of t h e d i s e a s e l e v e l s on Odes s a f o r t h e 36 F2 t r e a t m e n t d i k a r y o n s f r o m DL 17, 21 and 23, r e s p e c t i v e l y 68 F i g u r e 4. F r e q u e n c y d i s t r i b u t i o n o f t h e d i s e a s e l e v e l s f o r t h e 108 t r e a t m e n t d i k a r y o n s combined ( f r o m DL 17, 21 and 23) on T r e b i ( t o p ) and Ode s s a (bottom) 70 F i g u r e 5. Wr'/Vr r e g r e s s i o n s i l l u s t r a t i n g t h e r e l a t i v e m a g n i t u d e s o f dominant and e p i s t a t i c n o n - a d d i t i v e g e n e t i c e f f e c t s of t h e t r e a t m e n t s p o r i d i a 104 ix ACKNOWLEDGEMENTS I want to express my deep appreciation to Dr. Clayton Person for the unparalleled teaching s k i l l , insight, guidance and patience he displayed throughout the evolution of t h i s work. Dr. Tony G r i f f i t h s deserves a special thank you for his continued support of thi s project. S t a t i s t i c a l advice was provided by Dr. Con Wehrhahn. Technical advice and assistance was readily available from the always effervescent Mr. Rolando Robillo. Past and present members of the Ustilaqo f r a t e r n i t y should know much I enjoyed our many 'brainstorming' sessions. 1 I . INTRODUCTION S i n c e t h e i r d i s c o v e r y , genes f o r r a c e s p e c i f i c r e s i s t a n c e have been h e a v i l y r e l i e d upon f o r p r o t e c t i o n a g a i n s t y i e l d l o s s e s c a u s e d by v a r i o u s p a t h o g e n s . The impermanence and t h e narrow r a n g e o f e f f e c t i v e n e s s o f t h e s e , genes has g e n e r a t e d i n c r e a s e d i n t e r e s t i n n o n s p e c i f i c r e s i s t a n c e . R e c e n t r e p o r t s and e x p e r i m e n t a t i o n i n v o l v i n g n o n s p e c i f i c r e s i s t a n c e has r e v e a l e d s e v e r a l a t t r a c t i v e q u a l i t i e s w h i c h i n c l u d e s t a b i l i t y and a wide s p e c t r u m o f e f f e c t i v e n e s s a g a i n s t an e n t i r e p a t h o g e n p o p u l a t i o n . Most g e n e t i c s t u d i e s of h o s t - p a r a s i t e i n t e r a c t i o n have e m p h a s i z e d t h e h o s t p o p u l a t i o n . By v i r t u e o f t h e f a c t t h a t b o t h o r g a n i s m s i n a h o s t - p a r a s i t e r e l a t i o n s h i p a f f e c t t h e d i s e a s e outcome, i t seems l o g i c a l t h a t e v e r y p e r t i n e n t a s p e c t o f b o t h p o p u l a t i o n s s h o u l d be i n v e s t i g a t e d . T h i s a p p r o a c h would u n d o u b t e d l y r e v e a l t h e v a r i a t i o n p o t e n t i a l of b o t h i n t e r a c t i n g o r g a n i s m s , and t h e i n f o r m a t i o n g a i n e d would s e r v e as a n e c e s s a r y p r e r e q u i s i t e f o r t h e d e v e l o p m e n t of e f f e c t i v e r e s i s t a n c e b r e e d i n g p r o g r a m s e m p l o y i n g n o n s p e c i f i c r e s i s t a n c e . 2 I I . RESISTANCE S p e c i f i c R e s i s t a n c e R e p o r t s t h a t r e s i s t a n c e a g a i n s t p a r a s i t e s may be i n h e r i t e d d a t e back t o 1898 ( F a r r e r , 1898), 1905 ( B i f f e n , 1905) and 1916 (Kommedahl e t a l . , 1970). S i n c e t h e n r a c e - s p e c i f i c r e s i s t a n c e has been shown t o be e f f e c t i v e a g a i n s t s p e c i f i c p a t h o g e n r a c e s . S i n c e t h e d i s c o v e r y of r a c e - s p e c i f i c r e s i s t a n c e ( a l s o known as "R" gene r e s i s t a n c e , h y p e r s e n s i t i v e r e s i s t a n c e , o l i g o g e n i c r e s i s t a n c e , v e r t i c a l r e s i s t a n c e , and major gene r e s i s t a n c e ) and t h e e l u c i d a t i o n of i t s r e l a t i o n s h i p w i t h s p e c i f i c v i r u l e n c e i n g e n e - f o r - g e n e i n t e r a c t i o n s ( F l o r , 1940, 1946, 1947, 1954, 1955, 1956; P e r s o n , 1959) i t has been u s e d e x t e n s i v e l y i n b r e e d i n g p r ograms t o combat a wide v a r i e t y of p a t h o g e n s and p e s t s . In most i n s t a n c e s , t h e p a r a s i t e p o p u l a t i o n s p o s s e s s t h e p o t e n t i a l t o q u i c k l y d e v e l o p t h e v i r u l e n c e n e c e s s a r y t o r e n d e r t h e r e s i s t a n c e u s e l e s s , l e a d i n g t o t h e "boom and b u s t " d i s e a s e c y c l e . R a ces not a f f e c t e d by t h e R gene would be t h e o n l y r a c e s t o grow u n c h e c k e d i n t h e f i e l d . T h e s e r a c e s m i g h t e x i s t i n low f r e q u e n c i e s i n t h e p o p u l a t i o n or may a r i s e v i a m u t a t i o n and d i r e c t i o n a l s e l e c t i o n . B e f o r e l o n g t h e v i r u l e n t r a c e ( s ) would become p r e v a l e n t and s e r i o u s l y t h r e a t e n t h e m o n o c u l t u r e . The onus i s t h e n p l a c e d on t h e b r e e d e r s t o s e a r c h f o r and f i n d new e f f e c t i v e R genes w e l l i n a d v ance o f t h e c o l l a p s e o f t h e p r e s e n t l y u s e d p o p u l a r R gene. The c o n t i n u o u s r e s e a r c h e f f o r t s r e q u i r e d t o s u s t a i n t h i s t y p e o f s y s t e m a r e t a x i n g w i t h 3 respect to genetic resources and to economic constraints. The search for methods of combating disease losses has led to the development of several a l t e r n a t i v e s : 1) multilines (Borlaug, 1958, 1965; Browning and Frey, 1969; 'Frey et a l . , 1973; Groth and Person, 1977) , 2) pyramiding of race-specific resistance genes (Luig and Watson, 1970) , 3) a l l e l e cycling (Person, 1966), 4) race-nonspecific resistance (Van der Plank, 1968; Main and Gallegly, 1964; Umaerus, 1969; Eide and Lauer, 1967; Simons and Murphy, 1967; Person et a l . , 1982), 5) combinations of these methods (Graham and Hodgson, 1965; Raymundo and Hooker, 1982). There are posit i v e and negative aspects associated with a l l of the above alt e r n a t i v e s . Presently, the one that promises the greatest e f f i c a c y is "race-nonspecific resistance" (also known as horizontal resistance, general resistance, nonspecific resistance, minor gene resistance, polygenic resistance and f i e l d resistance, among others). Recent studies indicate that this type of resistance w i l l be much longer l a s t i n g and more 4 stable than other alternatives (Lewellen et a l . , 1967; Caten, 1974; Van der Plank, 1975; P a r l e v l i e t and Zadoks, 1977; Fleming and Person, 1982). Investigators are not in agreement on the mechanism by which the s t a b i l i t y manifests i t s e l f but are in accord on the b e n e f i c i a l effects of i t s use in a g r i c u l t u r e . Nonspecific Resistance General resistance i s described by Van der Plank (1963) as being polygenically inherited and race-nonspecific. It is thought to be e f f e c t i v e against a l l individuals of a pathogen population, and that i t functions by reducing the rate of spread of the epidemic. F i e l d resistance in d i f f e r e n t v a r i e t i e s results from d i f f e r e n t factors (Van der Zaag, 1959; Umaerus, 1963; Lapwood, 1963; Lapwood and McKee, 1966). Examples of i l l u s t r a t i n g the existence of polygenic resistance include: 1) asparagus to Puce i n i a asparaqi D.C. (Hepler, Thompson and McCallum, 1957) 2) potatoes to late blight (Toxopeus, 1959, 1961) 3) Solanum demissum and Solanum verrucosum to late blight (Niederhauser, 1962) 5 4) m a i z e t o n o r t h e r n l e a f b l i g h t (Hughes and Hooker, 1971 ) 5) m a i z e t o r u s t ( H o o k e r , 1967) 6) wheat t o l e a f r u s t ( C a l d w e l l e t a l . , 1958) 7) wheat t o stem r u s t ( K n o t t and B r e n n a n , 1976; W i l c o x s o n , 1976) 8) wheat t o y e l l o w r u s t ( L u p t o n and J o h n s o n , 1970) 9) b a r l e y t o r u s t ( P a r l e v l i e t , 1976) 10) wheat t o s t r i p e r u s t ( S h a r p and V o l i n , 1970) 11) b a r l e y t o smut ( P e r s o n , p e r s o n a l c o m m u n i c a t i o n , 1982) S t r o n g s u p p o r t f o r i t s e x i s t e n c e was p r o v i d e d by S h a f e r e t a l . ( 1 9 6 3 ) , P e r s o n ( 1 9 6 5 ) , Pope ( 1 9 6 5 ) , S h a r p ( 1 9 6 5 ) , Van d e r P l a n k ( 1 9 6 8 ) , A b d u l l a and Hermsen ( 1 9 7 1 ) , A b d u l l a ( 1 9 7 1 ) . One p r o b l e m a s s o c i a t e d w i t h b r e e d i n g f o r g e n e r a l r e s i s t a n c e i s t h e f a c t t h a t i t can o n l y be s e l e c t e d f o r i n t h e p r e s e n c e of d e f e a t e d o r "matched" R g e n e s . O t h e r w i s e t h e e f f e c t o f t h e R gene would mask t h e e x p r e s s i o n of g e n e r a l r e s i s t a n c e . An i n t e r e s t i n g phenomenon t h a t can o c c u r f r o m t h e e x c l u s i v e 6 s e l e c t i o n o f R genes i s t h e " V e r t i f o l i a E f f e c t " (Van d e r P l a n k , 1968). I t was f i r s t o b s e r v e d i n t h e p o t a t o v a r i e t y , V e r t i f o l i a , when t h e e f f e c t o f genes f o r g e n e r a l r e s i s t a n c e were masked w h i l e R gene r e s i s t a n c e was b e i n g s e l e c t e d . The p o t e n t i a l f i t n e s s i n c r e a s e s a s s o c i a t e d w i t h t h e p o l y g e n e s c o u l d n o t be e x p r e s s e d and c o u l d n o t be s e l e c t e d f o r . As a c o n s e q u e n c e t h e y were soon r e p l a c e d by f i t n e s s n e u t r a l i s o a l l e l e s . The s e l e c t i o n f o r a majo r gene was t h e r e f o r e a c c o m p a n i e d by i n a d v e r t e n t s e l e c t i o n f o r low l e v e l s of p o l y g e n i c r e s i s t a n c e . When t h e R gene b r o k e down t h e low l e v e l s o f g e n e r a l r e s i s t a n c e became a p p a r e n t . I f h i g h l e v e l s o f g e n e r a l r e s i s t a n c e were d e s i r e d i n a v a r i e t y i t had t o be d e v e l o p e d i n t h e a b s e n c e o f e f f e c t i v e R g e n e s . The p o t a t o b l i g h t i n E u r o p e i n t h e 1840's was a t t r i b u t e d t o low l e v e l s o f h o r i z o n t a l r e s i s t a n c e (Van d e r P l a n k , 1968). The d i s e a s e was a b s e n t p r i o r t o t h e I84~0's and no s e l e c t i o n ( e i t h e r n a t u r a l o r a r t i f i c i a l ) f o r h i g h l e v e l s o f r e s i s t a n c e t o l a t e b l i g h t was t a k i n g p l a c e . T h i s r e s u l t e d i n i n a d v e r t e n t s e l e c t i o n f o r low l e v e l s of g e n e r a l r e s i s t a n c e . When a h i g h l y p a t h o g e n i c b l i g h t p o p u l a t i o n f o u n d i t s way t o E u r o p e from A m e r i c a t h e c r o p s were soon r u i n e d . S i m i l a r s u s c e p t i b i l i t y was f o u n d i n p o t a t o v a r i e t i e s f r o m t h e Andes (Simmonds and M a l c o l m s o n , 1967). T h e s e v a r i e t i e s l a c k e d R genes and needed none i n t h e a b s e n c e o f p a t h o g e n i c s t r a i n s i n t h e m o u n t a i n s . The i n t r o d u c t i o n o f a p a t h o g e n i c p o p u l a t i o n i n t o t h e a r e a soon r e s u l t e d i n w i d e s p r e a d c r o p l o s s . ' H i g h l e v e l s o f r e s i s t a n c e c o u l d be r e s t a b l i s h e d a f t e r o n l y t h r e e 7 s e x u a l g e n e r a t i o n s of mass s e l e c t i o n f o r h i g h l e v e l s , o f r e s i s t a n c e . A p a r a l l e l s i t u a t i o n t o t h e E u r o p e a n p o t a t o b l i g h t e p i d e m i c was seen i n A f r i c a (Van d e r P l a n k , 1968). A r u s t e p i d e m i c o f m a i z e c a u s e d by P u c e i n i a p o l y s o r a , i n t r o d u c e d f r o m A m e r i c a , d e s t r o y e d t h e p r e v i o u s l y f l o u r i s h i n g c r o p s . No r u s t d i s e a s e was e v i d e n t p r i o r t o t h e i n t r o d u c t i o n o f P. p o l y s o r a . T h e r e f o r e t h e r e was no p r e v i o u s s e l e c t i o n f o r r e s i s t a n c e . The V e r t i f o l i a e f f e c t was a g a i n t h o u g h t t o be t h e c a u s e of t h e sudden c r o p c o l l a p s e . As w i t h t h e p o t a t o c r o p , m a i z e r e s i s t a n c e c o u l d be r e s t o r e d r a p i d l y under p r o p e r s e l e c t i o n t e c h n i q u e s . T h e r e a r e c r i t i c s of t h e V e r t i f o l i a h y p o t h e s i s . T o x o p e u s (1956) c o n t e n d e d t h a t t h e p o t a t o e p i d e m i c o f t h e 1840's was due t o d i f f e r e n t c a u s e s . He b e l i e v e d t h a t i n i t i a l l y t h e p o t a t o v a r i e t i e s were h i g h l y r e s i s t a n t b u t t h a t t h r o u g h t h e i r c o n t i n u o u s l o n g term c u l t i v a t i o n , P h y t o p t h o r a i n f e s t a n s was a b l e t o u ndergo s m a l l c u m u l a t i v e i n c r e a s e s i n a g g r e s s i v e n e s s . The p a t h o g e n p o p u l a t i o n soon d e v e l o p e d a d a m a g i n g l y h i g h mean l e v e l of p a t h o g e n i c i t y ( G a l l e g l y , 1968). The p r e c e e d i n g h y p o t h e s e s on r e s i s t a n c e and p a t h o g e n i c i t y a r e not as d i s c r e t e as one m ight i m a g i n e . T h e r e a r e e x a mples known t h a t do not f i t e i t h e r h y p o t h e s i s w e l l , and w a r r a n t f u r t h e r s t u d y . F o r example, t h e r e a r e c a s e s o f R g e n e - l i k e r e s i s t a n c e s t h a t a r e e f f e c t i v e a g a i n s t a l l r a c e s and have been shown t o be s t a b l e . T h e r e a r e a l s o examples of p o l y g e n i c a l l y i n h e r i t e d r e s i s t a n c e s b e h a v i n g r a c e - s p e c i f i c a l l y . In t h e f i r s t c a s e , f o r i n s t a n c e , one gene was f o u n d t o be e f f e c t i v e o v e r an 8 i n d e f i n i t e p e r i o d of t i m e i n c abbage a g a i n s t f u s a r i u m y e l l o w s ( W a l k e r , 1927). Sorghum v u l g a r e has d i s p l a y e d l o n g s t a n d i n g r e s i s t a n c e t o P e r i c o n i a c i r c i n a t a d e s p i t e t h e f a c t t h a t t h i s r e s i s t a n c e was i n h e r i t e d m o n o g e n i c a l l y (Van d e r P l a n k , 1968). The r e s i s t a n c e of t h e - b a r l e y v a r i e t y P r o c t o r was f o u n d t o be u n i v e r s a l l y e f f e c t i v e a g a i n s t U s t i l a g o nuda h o r d e i ( R o b i n s o n , 1973) and was c o n t r o l l e d by o n l y t h r e e genes (Maar, 1960). Q u e s t i o n s c a n be r a i s e d a b o u t t h e s e e x c e p t i o n s . Can r e s i s t a n c e t h a t i s q u a n t i t a t i v e l y i n h e r i t e d be c a l l e d g e n e r a l r e s i s t a n c e i f i t i s r a c e - s p e c i f i c ? Can r e s i s t a n c e t h a t i s q u a l i t a t i v e l y i n h e r i t e d , but w h i c h a c t s g e n e r a l l y , be c a l l e d R gene r e s i s t a n c e ? At t h i s p o i n t t e r m i n o l o g y becomes a p r o b l e m due t o t h e l a c k of c l a r i t y i n d e f i n i t i o n s of t h e s e phenomena. E x c e p t i o n s s u c h as t h e s e have l e d c r i t i c s t o c o n t e n d t h a t t h e r e i s no c l e a r c u t d i s t i n c t i o n between maj o r and m i n o r genes but t h a t t h e y e x i s t as e x t r e m e s of a c o n t i n u u m ( W o l f e , 1972); o r , t h a t a l l genes a r e of t h e m a j o r t y p e . They p a r t i c i p a t e i n g e n e - f o r - g e n e i n t e r a c t i o n s and t h e r e s i d u a l e f f e c t s of "matched" genes a c c o u n t f o r t h e so c a l l e d h o r i z o n t a l r e s i s t a n c e ( E l l i n g b o e , 1975, 1981; Nass e t a l . , 1981). N e l s o n , M a c K e n z i e and S h e i f e l e (1970) s u g g e s t e d t h a t g e n e r a l and s p e c i f i c r e s i s t a n c e i n m aize t o T r i c h o m e t o s p h a e r i a  t u r i c i c a s h a r e d g e n e t i c s i m i l a r i t i e s . C o r n i n b r e d s w i t h a l a r g e number of genes f o r h y p e r s e n s i t i v e r e s i s t a n c e r e a c t e d more u n i f o r m l y t o a range o f v i r u l e n t i s o l a t e s t h a n d i d l i n e s w i t h few e f f e c t i v e genes f o r h y p e r s e n s i t i v e r e s i s t a n c e . They a r g u e d t h a t t h e r e m o v a l o f a gene from a m u l t i - g e n e s y s t e m would have a 9 minor e f f e c t on t h e r e a c t i o n o f t h e h o s t . G r e a t e r f l u c t u a t i o n s and v a r i a t i o n would be g e n e r a t e d i n h o s t r e a c t i o n t o d i f f e r e n t r a c e s w i t h t h e r e m o v a l o f more g e n e s . I f o n l y one gene r e m a i n e d i t would t h e n s i m u l a t e a v e r t i c a l r e a c t i o n e f f e c t , i . e . , i t would d i s p l a y d i s c r e t e s e g r e g a t i o n . A b d u l l a (1971) t e s t e d t h i s h y p o t h e s i s w i t h p o t a t o e s and l a t e b l i g h t b u t d i d n o t o b t a i n s u p p o r t i n g r e s u l t s . As y e t t h e r e i s l i t t l e i n f o r m a t i o n a v a i l a b l e t o e s t a b l i s h e f f e c t i v e b r e e d i n g . p r o g r a m s i n c o r p o r a t i n g r a c e - n o n s p e c i f i c r e s i s t a n c e . T h i s i s p r i m a r i l y due t o t h e a b s e n c e of d a t a on p o p u l a t i o n v a r i a b i l i t y p a r a m e t e r s . S i n c e t h e r e a r e two p o p u l a t i o n s i n v o l v e d i n any h o s t - p a r a s i t e s y s t e m i t seems l o g i c a l t o a s c e r t a i n t h e f u l l r a n g e o f p o s s i b l e i n t e r a c t i o n s by m e a s u r i n g t h e e x t e n t o f p o t e n t i a l v a r i a b i l i t y i n b o t h ; U n t i l r e c e n t l y , v e r y few s u c h s t u d i e s have f o c u s e d on " p a r a s i t e p o p u l a t i o n s . 10 I I I . PATHOGENICITY S p e c i f i c P a t h o g e n i c i t r y Ward (1902) was one of t h e f i r s t i n v e s t i g a t o r s t o d e m o n s t r a t e t h a t v a r i a b i l i t y i n p a t h o g e n i c i t y e x i s t e d i n a p a t h o g e n p o p u l a t i o n . S h o r t l y t h e r e a f t e r , B i f f e n (1905, 1907) d i s c o v e r e d t h a t two r e c e s s i v e genes c o n t r o l l e d wheat r e s i s t a n c e t o t h e f u n g a l p a t h o g e n P u c e i n i a glumarum . T h i s d i s c o v e r y i n p l a n t s i n i t i a t e d a l a r g e number of s t u d i e s on t h e i n h e r i t a n c e o f d i s e a s e r e s i s t a n c e i n c r o p s . I n v e s t i g a t i o n s i n t o t h e i n h e r i t a n c e of p a t h o g e n i c i t y l a g g e d by many y e a r s . Much l e s s t i m e and e f f o r t were d e d i c a t e d t o i n c r e a s i n g t h e body o f knowledge a b o u t p a t h o g e n i c i t y . I n i t i a l l y , e x p e r i m e n t s i n v o l v i n g p a t h o g e n i c i t y f o c u s e d on t h e n a t u r e of t h e v i r u l e n c e d i f f e r e n c e s between p h y s i o l o g i c r a c e s (Stakman and L e v i n e , 1922). T h e s e d i f f e r e n c e s were d e t e r m i n e d t o be under s i m p l e M e n d e l i a n c o n t r o l and g e n e r a l l y i n v o l v e d one t o a few v i r u l e n c e genes (Graham, 1955; H a l i s k y , 1956; W a l l i n , 1957). The e x t e n s i v e l i t e r a t u r e on s y s t e m s o p e r a t i n g i n a g e n e - f o r - g e n e way was r e v i e w e d by S i d h u , 1980). The p r e s e n c e and e f f e c t s o f t h e s e genes were r e a d i l y i d e n t i f i a b l e b e c a u s e o f t h e i r i n t e r a c t i o n w i t h s p e c i f i c h o s t "R" g e n e s . The p r e s e n c e o f a v i r u l e n c e g e n e ( s ) c a n a l s o be u n c o v e r e d i n a s t a t i s t i c a l a n a l y s i s of p a t h o g e n i c v a r i a b i l i t y when a number of r a c e s i s t e s t e d a g a i n s t d i f f e r e n t i a l t e s t e r v a r i e t i e s . A s i g n i f i c a n t b i o m e t r i c a l r a c e x v a r i e t y i n t e r a c t i o n e f f e c t would s i g n a l t h e v e r y s p e c i a l r e l a t i o n s h i p of c e r t a i n r a c e s w i t h 11 only certain tester v a r i e t i e s . Relationships of t h i s nature are attributed to gene-for-gene interactions (Person, 1959; Fl o r , 1970) and behave such that: "A gene-for-gene relationship exists when the presence of a gene in one population i s contingent on the continued presence of a gene in the other population, and where interaction between the two genes leads to a single phenotypic expression by which the presence or absence of the gene in either organism may be recognized " (Person et a l . , 1962). The nature of thi s unique s p e c i f i c i t y allows genetic i d e n t i f i c a t i o n and manipulation of individual virulence factors via c l a s s i c a l techniques. Within each race, iso l a t e s can show a wide range of disease expression (Wallin, 1957). These differences in degree of pathogenicity, also known as aggressiveness, are controlled by polygenes (examples are discussed in d e t a i l in a l a t e r section). Polygenic systems can be i d e n t i f i e d by nondiscrete inheritance patterns and by normal d i s t r i b u t i o n s of disease readings in progeny of certain crosses. Generally, these factors show no s p e c i f i c i t y to any pa r t i c u l a r variety. In the biometrical analyses of variance the absence of a s i g n i f i c a n t race x variety interaction effect s i g n i f i e s the involvement only of polygenes. "If the t o t a l non-environmental variance in levels of resistance i s due to main effects only (differences between c u l t i v a r s and 12 differences between isolates) the resistance and pathogenicity (in the broad sense) are horizontal in nature. V e r t i c a l resistance and pathogenicity are characterized by the interaction between host and pathogen showing up as a variance component ... due to interaction between c u l t i v a r s and i s o l a t e s " ( P a r l e v l i e t and Zadoks, 1977). For any pathogen i s o l a t e , the genes for aggressiveness are believed to be e f f e c t i v e against a l l susceptible v a r i e t i e s (Van der Plank, 1968). This does not mean that i t would produce id e n t i c a l l e v e l s of disease on the several v a r i e t i e s . The variable polygenic resistance levels of the v a r i e t i e s would modulate expression of the polygenic pathogenicity to produce a variable range of disease expressions. As with virulence genes, the exact functional mechanism of pathogenicity genes i s a mystery. Tomiyama (1963) believed that physiological changes in the host and changes in the n u t r i t i o n a l balance of the host were p a r t i a l l y responsible for the a d d i t i v i t y in v a r i a b i l i t y of polygenes. Spickett and Thoday (1966) and Thompson (1973) supported the idea that genetic background was important in determining whether a l l e l i c substitutions manifested themselves by segregating into discrete phenotypic classes or by producing overlapping d i s t r i b u t i o n s . Mather and Jinks (1971) believed that major genes have a s p e c i f i c role in development, that i s , they are functionally d i s t i n c t from polygenes which play a nonspecific, less important role, in development. Pandey (1972) proposed that major genes are structural gene l o c i and minor genes have a variety of 13 regulatory functions. The p r o l i f e r a t i o n of contradictory hypotheses indicates that more precise biochemical investigations are needed. Nonspec i f ic Pathogenic i t y The importance of i n t r a r a c i a l v a r i a t i o n in pathogenic a b i l i t y has recently become of' interest because of the increasingly important role i t w i l l play in determining resistance breeding t a c t i c s . E f f o r t s are being made to measure aggressiveness (or pathogenicity) potentials of agro-economically important pathogens. Ideally, aggressiveness can be determined by the severity or degree of disease damage or y i e l d loss. Obtaining data of this kind i s not always convenient or p r a c t i c a l in most cases. One or more of the parameters of aggressiveness are measured instead. These components include: 1) inoculum concentration 2) speed of penetration 3) latent period 4) rate of spread through the host 1 4 5) degree, o f s p o r u l a t i o n , and 6) g e n e r a t i o n t i m e ( C a s t r o n o v o , T h u r s t o n and E i d e , 1954; K n u t s o n and E i d e , 1961; J e f f r e y , J i n k s and G r i n d l e , 1962). A t r u e d e t e r m i n a t i o n of a g g r e s s i v e n e s s s h o u l d i n v o l v e m e a s u r i n g p a t h o g e n r e p r o d u c t i v i t y r e l a t i v e t o t h a t of t h e h o s t . In p r a c t i c e , r e s e a r c h e r s t e n d t o c o n c e n t r a t e on o n l y one o r two of t h e components. F o r example S c h u l t z (1962) d e v e l o p e d 27 monozoospore c u l t u r e s d e r i v e d from 13 w i l d i s o l a t e s o f 5 d i f f e r e n t r a c e s of P h y t o p t h o r a i n f e s t a n s . He measured l e s i o n d e v e l o p m e n t and f i n a l l e s i o n s i z e on t h e v a r i e t y V a t a h d i n . D i f f e r e n c e s were o b s e r v e d between and w i t h i n r a c e s . O t h e r r e s e a r c h e r s who have f o u n d a g g r e s s i v e n e s s t o be i n h e r i t e d q u a n t i t a t i v e l y i n c l u d e : R e s e a r c h e r Y e a r Wellman and B a i s d e l l 1940 Paxman 1963 E y a l and P e t e r s o n 1967 K a t s u y a and G r e e n 1967 L e w e l l a n e t a l . 1967 Brown and S h a r p 1970 S e b e s t a 1972 P r i e s t l y and D o l i n g 1974 P a t h o g e n F u s a r i u m oxysporum  P h y t o p t h o r a i n f e s t a n s  Puce i n i a r e c o n d i t a  P u c e i n i a g r a m i n i s  P u c e i n i a s t r i i f o r m i s  Puce i n i a s t r i i f o r m i s  Puce i n i a c o r o n a t a a v ena P u c c i n i a s t r i i f o r m i s 15 Habgood 1976 R h y n c o s p o r i u m s e c a l i s As p r e v i o u s l y m e n t i o n e d i n t h e s e c t i o n on N o n s p e c i f i c  R e s i s t a n c e some w o r k e r s m a i n t a i n t h a t r e s i s t a n c e p o l y g e n e s do not e x i s t . By e x t r a p o l a t i o n t o t h e p a t h o g e n t h i s would mean t h a t t h e r e a r e no p o l y g e n e s f o r p a t h o g e n i c i t y . A s e r i e s o f e x p e r i m e n t s by C a t e n (1970) d i s p r o v e s t h i s i d e a . S i n g l e z o o s p o r e s f rom t h r e e w i l d i s o l a t e s o f P h y t o p t h o r a i n f e s t a n s were s t u d i e d and v i r u l e n c e and a g g r e s s i v e n e s s v a r i a t i o n s were measured. By m o n i t o r i n g g r o w t h r a t e on t u b e r s and g e n e r a t i o n t i m e on d e t a c h e d l e a v e s he was a b l e t o show t h a t v i r u l e n c e and p a t h o g e n i c i t y were two d i s t i n c t and i n d e p e n d e n t a s p e c t s o f p a t h o g e n i c i t y . S u b s e q u e n t e x p e r i m e n t s w i t h s i n g l e z o o s p o r e d e r i v a t i v e s of h y p h a l t i p s f r o m mass c u l t u r e s w h i c h were s e r i a l l y t r a n s f e r r e d on p o t a t o t u b e r s showed t h a t two i s o l a t e s of i n t e r m e d i a t e a g g r e s s i v e n e s s , w i t h t i m e , c o u l d be s e l e c t e d t o show h i g h e r l e v e l s of a g g r e s s i v e n e s s w i t h no a t t e n d a n t i n c r e a s e i n v i r u l e n c e ( C a t e n , 1971). G r o t h e t a l . ( 1 9 7 6 ) , u s i n g t h e U s t i l a q o h o r d e i - Hordeum v u l g a r e s y s t e m , a l s o f o u n d e v i d e n c e f o r two n o n - i n d e p e n d e n t r e s i s t a n c e t h r e s h o l d s . 1 6 S p e c i f i c P o l y g e n i c P a t h o g e n i c i t y T h e o r e t i c a l l y e a c h p a t h o g e n i c i t y p o l y g e n e i s e q u a l l y e f f e c t i v e a g a i n s t any r e s i s t a n c e p o l y g e n e . I s o l a t e s a r e not e x p e c t e d t o be d i f f e r e n t i a l l y a d a p t e d t o v a r i e t i e s . S t a t i s t i c a l l y t h i s s i t u a t i o n would mean t h a t no s i g n i f i c a n t d i f f e r e n c e s a r e e x p e c t e d among h o s t - i s o l a t e i n t e r a c t i o n s . D i s c r e t e s e g r e g a t i o n of p o l y g e n e s a r e n o n - e x i s t e n t . O n l y t h e c o n c e n t r a t i o n o f a l a r g e number of p o l y g e n e s i n t o a s i n g l e i s o l a t e c o u l d r e s u l t i n an e x t r e m e l y p a t h o g e n i c i s o l a t e . Paxman (1963) i n v e s t i g a t e d t h e P h y t o p t h o r a i n f e s t a n s - p o t a t o s y s t e m . By m e a s u r i n g t h e r a t e o f s p r e a d i n t u b e r s he f o u n d no e v i d e n c e o f d i f f e r e n t i a l a d a p t a t i o n o f t h e i s o l a t e s t o t h e v a r i e t i e s . A f t e r 90 g e n e r a t i o n s o f s e l e c t i o n t h e r e was no e v i d e n c e f o r d i f f e r e n t i a l i n t e r a c t i o n s on v a r i e t i e s w i t h o u t R g e n e s . During* t h e c o u r s e of h i s work he c o n c l u d e d t h a t t h e f i t n e s s of t h e p a r a s i t e was i n v e r s e l y r e l a t e d t o p a t h o g e n i c i t y . Habgood (1976) s e t out s p e c i f i c a l l y t o d e t e r m i n e i f R h y n c h o s p o r i u m s e c a l i s was d i f f e r e n t i a l l y a d a p t e d t o b a r l e y v a r i e t i e s . He worked w i t h f u n g a l i s o l a t e s f r o m b u l k s e l e c t i o n s and v a r i e t i e s w i t h no major g e n e s . A l t h o u g h t h e r e were d i f f e r e n c e s i n a g g r e s s i v e n e s s no e v i d e n c e f o r d i f f e r e n t i a l a d a p t a t i o n was d i s c o v e r e d . The t a b l e on page 4 l i s t s some of t h e o t h e r works t h a t y i e l d e d e s s e n t i a l l y t h e same r e s u l t s . T h e r e were some s t u d i e s t h a t p r o d u c e d d i f f e r e n t r e s u l t s . J e f f r e y e t a l . (1962) s t u d i e d i n t r a r a c i a l v a r i a t i o n and d i s c o v e r e d t h a t s t r a i n s of P h y t o p t h o r a i n f e s t a n s i s o l a t e d from a 1 7 p a r t i c u l a r v a r i e t y showed e n h a n c e d a g g r e s s i v e n e s s t o t h a t v a r i e t y as compared t o o t h e r v a r i e t i e s . In o t h e r words, i s o l a t e s were s p e c i f i c a l l y a d a p t e d t o t h e i r "own" v a r i e t i e s . Denward's (1967) work w i t h P. i n f e s t a n s on h o s t s w i t h t h e same "R" genes r e v e a l e d s i m i l a r a d a p t a t i o n s . In 1974, C a t e n ' s f i e l d i s o l a t e s o f P. i n f e s t a n s r a c e P4 from p o t a t o v a r i e t i e s w i t h no "R" genes showed s p e c i f i c a d a p t a t i o n . The i s o l a t e s d i f f e r e d i n a g g r e s s i v e n e s s on t h e v a r i e t i e s u s e d but were d i f f e r e n t i a l l y a d a p t e d t o t h e i r own v a r i e t y . T h e r e f o r e , t h i s t y p e of s p e c i f i c i t y c o u l d n o t have i n v o l v e d c l a s s i c a l g e n e - f o r - g e n e i n t e r a c t i o n s and would have t o have some o t h e r b a s i s f o r e x i s t e n c e . A s i g n i f i c a n t r a c e - c u l t i v a r i n t e r a c t i o n e f f e c t was a l s o r e v e a l e d i n an a n a l y s i s o f v a r i a n c e on P u c c i n i a s t r i i f o r m i s by C l i f f o r d and C l o t h i e r ( 1 9 7 4 ) . They a t t r i b u t e d t h e s e d i f f e r e n t i a l e f f e c t s t o d i f f e r e n c e s i n s p o r e g e r m i n a t i o n , a p p r e s s o r i u m f o r m a t i o n o r h o s t p h y s i o l o g y f o l l o w i n g p a t h o g e n p e n e t r a t i o n . Brennan (1975) a l s o f o u n d e v i d e n c e f o r r a c e - s p e c i f i c i t y i n wheat t o P. g r a m i n i s t r i t i c i . W h i l e t h e s e s t u d i e s i n d i c a t e t h a t t h i s t y p e o f s p e c i f i c i t y c o u l d be w i d e s p r e a d i n h o s t - p a r a s i t e s y s t e m s ( C a t e n , 1974), few t h e o r i e s have been p u t f o r w a r d t o e x p l a i n t h e r e s u l t s . Thompson and Thoday (1974) t h o u g h t t h a t t h e d e g r e e t o w h i c h a l l e l i c d i f f e r e n c e s a p p e a r t o i n v o l v e s p e c i f i c i t y may be t h e r e s u l t o f t h e i n a b i l i t y t o o b s e r v e gene e f f e c t s s u f f i c i e n t l y c l o s e l y r e l a t e d t o t h e b i o c h e m i c a l l e v e l a t w h i c h t h e y a c t r a t h e r t h a n a r e s u l t of f u n c t i o n a l d i f f e r e n c e s among l o c i . R e s u l t s s u c h as t h e s e may be i n t e r p r e t e d t o s u p p o r t t h e c o n t e n t i o n s o f E l l i n g b o e 18 (1981) and Nass e t a l . (1981) t h a t a l l r e s i s t a n c e and p a t h o g e n i c i t y genes a r e of t h e g e n e - f o r - g e n e t y p e . W i t h so l i t t l e i n f o r m a t i o n a v a i l a b l e a t p r e s e n t n o t much i s known a b o u t t h e f u n c t i o n o r i m p o r t a n c e o f t h i s s p e c i f i c i t y . More r e s e a r c h i s r e q u i r e d b e f o r e t h i s i n t e r e s t i n g and p o t e n t i a l l y u s e f u l phenomenon c a n be u n d e r s t o o d o r e x p l o i t e d . 19 IV. STABILITY OF POLYGENIC SYSTEMS Niederhauser (1962) found that only s l i g h t erosion of rust resistance had occurred in certain polygenic l i n e s of wheat grown in Mexico. No sudden breakdown was observed during ten years of f i e l d t e s t i n g . Other examples i l l u s t r a t i n g similar s t a b i l i t y were reported by Caldwell et. a l . (1958) who worked with cereal leaf rust and by Hooker (1967) who studied maize and maize rust. The attractiveness of the s t a b i l i t y and the longevity of polygenic systems has spawned much work to better understand them. The large number of genes involved, each of small e f f e c t , make some researchers believe that rapid evolution of high pathogenicity f a l l s outside the capacity of the pathogen population (Lewellen et a l . , 1967; Caten, 1974; Van der Plank, 1975). Van der Plank's " V e r t i f o l i a " hypothesis (1968, 1975) implies that polygenically inherited horizontal resistance could be a fitness character. Therefore, polygenically inherited pathogenicity should also be a fitness character correlated with reproductivity. This means that aggressiveness may be subject to selection pressures. Caten (1970) found evidence for d i r e c t i o n a l selection for high growth rate and rapid sporulation in nature of Phytopthora infestans . If enough resistance polygenes could be pooled in a single c u l t i v a r , i t may t h e o r e t i c a l l y remain resistant i n d e f i n i t e l y because of the large number of simultaneous mutations that would have to occur in or be recombined in a pathogen to overcome that resistance. The reason that t h i s would not occur i s because the 20 pathogen does not possess the potential to quickly amass mutations for higher pathogenicity, hence, the variety would enjoy prolonged f i e l d resistance. Some researchers think that the accumulation of large numbers of polygenes for pathogenicity by d i r e c t i o n a l selection pressures would upset the fitness balance sheet and place such isolates at a f i t n e s s (Lerner, 1954) and reproductive disadvantage. Person (1959) proposed the idea that the accumulation of genes in both interacting organisms, to optimize f i t n e s s , is a response to d i r e c t i o n a l selection pressure. Paxman (1963) thought that polygenes could be combined in pathogen isola t e s to achieve an optimum fitness after which point further increases in pathogenicity would decrease f i t n e s s , i . e . , f i t n e s s would be inversely related to pathogenicity. The result would be the i n i t i a t i o n of a s t a b i l i z i n g selection pressure diametrically opposed to d i r e c t i o n a l selection pressure (Van der Plank, 1975). Data supporting this hypothesis was provided by Watson < (1958) and by C l i f f o r d and Clothier (1974) in the wheat-stem rust system. Both studies reported reduced fitnesses associated with aggressiveness increases. However, not a l l pathogenicity genes affe c t aggressiveness so that pathogenicity increases can occur without fitness losses (Brown, 1975). An equilibrium would be established between the two selection pressures at some optimum where the mean number of pathogenicity polygenes in the population would be somewhat less than the maximum number available in the pool. At this equilibrium, the resulting disease levels would remain within an acceptable range. Super 21 races with a l l the aggressiveness polygenes would not arise (Van der Plank, 1968). Others contend that races can accumulate polygenes to maximize aggressiveness, inevitably producing super races. In accord with this view another hypothesis has been suggested by Person, Fleming and Cargeeg (1981). When a variety with a high le v e l of race-nonspecific resistance i s grown i t exerts a d i r e c t i o n a l selection pressure on the pathogen population to develop a correspondingly high l e v e l of pathogenicity in order to maximize fitness (Person, 1959; Paxman, 1963). One would expect these changes to occur over a long period of time. In order to maintain lower, acceptible disease levels the host population's resistance genetics should be controlled in such a way as to prevent an intense d i r e c t i o n a l selection pressure from occurring for a single pathogen genotype. The model presented by Person et a l . (1981) assumes that the polygenically determined c h a r a c t e r i s t i c s of aggressiveness and horizontal resistance would conform to the normal d i s t r i b u t i o n curve. The host heterogeneity would cause a s p a t i a l l y disruptive selection for pathogen isolates with optimum pathogenicity. A highly heterogeneous pathogen population would be formed producing a normal frequency d i s t r i b u t i o n of isolates for pathogenicity genes where isola t e s not having the mean, that i s , optimal number of genes, would suffer a fitness disadvantage d i r e c t l y proportional to their distance from the mean. The interaction (assumed to be either additive or m u l t i p l i c a t i v e ; Fleming and Person, 1982) of these 22 two n o r m a l l y d i s t r i b u t e d p o p u l a t i o n s w o u l d p r o d u c e a p r e d i c t a b l e , s t a b l e d i s t r i b u t i o n o f d i s e a s e l e v e l s w i t h a r e l a t i v e l y low and e c o m o m i c a l l y a c c e p t i b l e mean. The s t a b i l i t y o f t h i s s y s t e m comes from an i n t e r e g u l a t o r y r e l a t i o n s h i p between t h e p o p u l a t i o n s . A l a r g e s h i f t i n t h e mean o f one p o p u l a t i o n w ould be n o t i c e d as a r e l a t i v e l y s m a l l e r s h i f t i n t h e mean of t h e r e a l i z e d d i s e a s e l e v e l d i s t r i b u t i o n b e c a u s e o f t h e "damping e f f e c t s " of t h e o t h e r p o p u l a t i o n . Y e t a n o t h e r h y p o t h e s i s f o r t h e i n t e r p l a y of p o l y g e n i c s y s t e m s was p r o p o s e d by P a r l e v l i e t and Zadoks ( 1 9 7 7 ) . They p r o p o s e d two models, one i n v o l v e d t h e a d d i t i v e a c t i o n o f p o l y g e n e s , t h e o t h e r i n v o l v e d g e n e - s p e c i f i c i n t e r a c t i o n o f p o l y g e n e s . T h e i r models c o u l d n o t have f u n c t i o n e d i n t h e c l a s s i c a l g e n e - f o r - g e n e way ( s e n s u F l o r ) , b e c a u s e t h e y i n v o l v e d r e l a t i o n s h i p s t h a t n o r m a l l y would have e l i c i t e d " s t o p s i g n a l s " ( P e r s o n and Mayo, 1974), w h i c h i s a c o n s e q u e n c e o f g e n e - f o r - g e n e i n t e r a c t i o n s . The c h o i c e of t h e term g e n e - f o r - g e n e was u n f o r t u n a t e . A more a p p r o p r i a t e , l e s s c o n f u s i n g t e r m would have been " o n e - f o r - o n e " where a l l e l e s a t a s p e c i f i c r e s i s t a n c e l o c u s i n t h e h o s t i n t e r a c t w i t h a l l e l e s a t a s p e c i f i c l o c u s i n t h e p a t h o g e n . They s t a t e d t h a t t h e i r " i n t e r a c t i o n " model would p r o v i d e h i g h e r r e s i s t a n c e and b e t t e r s t a b i l i t y a g a i n s t t h e p a t h o g e n . A n t a g o n i s t s t o t h e c o n c e p t of l o n g e v i t y o f p o l y g e n i c s t a b i l i t y i n c l u d e Toxopeus (1956) and G a l l e g l y (1968) who i n d i c a t e d t h a t t h e l a t e b l i g h t e p i p h y t o t i c on p o t a t o e s i n E u r o p e i n 1840's was c a u s e d by t h e g r a d u a l i n c r e a s e i n a g g r e s s i v e n e s s 23 of P. infestans . The pathogen developed such a high l e v e l of aggressiveness that i t devastated the polygenic resistant potato v a r i e t i e s without ever suffering a fitness l o s s . Because polygenic resistance i s regarded by many researchers as being p o t e n t i a l l y stable, i t w i l l no doubt be studied u n t i l i t i s better understood on physiological, populational, s t a t i s t i c a l , and epidemiological l e v e l s . 24 V. HISTORY OF THE STUDY OF VARIABILITY Since Darwin directed attention to the. existence of v a r i a b i l i t y in domesticated plants and animals, investigators have searched to develop techniques by which i t could be studied and perhaps better understood. Francis Galton (1886, 1889, 1895, 1897) was among the f i r s t to apply mathematics to the problem of v a r i a b i l i t y . He used quantitative methods to study a metric character. Correlations were found between measurements of the stature of parents and their children. Although his e f f o r t s did not completely reveal a l l the underlying features of the inheritance of v a r i a b i l i t y , some important p r i n c i p l e s did a r i s e . For example, any population in harmony with i t s environment- remains s t a t i s t i c a l l y i d e n t i c a l with respect to genetic correlations in successive generations. His s t a t i s t i c a l techniques were so fundamental in studies of quantitatively inherited t r a i t s that they are the mainstay for modern day biometrical techniques. Bateson and Saunders (1902) were the f i r s t to suggest that segregation of a great number of genes could account for continuous v a r i a t i o n . Johannsen (1909) i l l u s t r a t e d that the use of pureline parents in breeding tests permitted v a r i a b i l i t y caused by inheritance to be distinguished from v a r i a b i l i t y attributable to nonheritible factors ( i . e . , environmental fac t o r s ) . Johannsen was the f i r s t to d i stinguish between the "phenotype" and the "genotype". This d i s t i n c t i o n i s p a r t i c u l a r l y important in quantitative genetic studies because of the fact that individuals of d i f f e r e n t genotypes can have i d e n t i c a l 25 phenotypes. It was later shown by Nilsson-Ehle (1909) and independently by East (1910) that continuous variation could be explained in terms of several separate Mendelian-like factors, each with a small e f f e c t on the phenotype. Segregation and recombination of these factors were shown by East (1915) and Emerson and East (1913). Proof that biometrical t r a i t s were under the control of factors inherited in a Mendelian fashion was provided by Fisher (1918). In addition, he showed evidence for the existence of dominance, linkage and gene interactions within the polygenic system. This' noteworthy work established the basis for presently used analysis of variance techniques by which phenotypic variance i s precisely partitioned according to contributing components. Genes governing continuous t r a i t s were found to be located on the chromosomes and to be inherited in a manner similar to that of other nuclear genes (Warren, 1924; Mather, 1942). Each gene for small effect was given the name "polygene" by Mather (1941). Eventually, when i t was realized that t i g h t l y linked polygenes could segregate and appear to behave as a single unit with a large effect (comprising the sum of the individual small effects) the term "eff e c t i v e factor" was coined. An e f f e c t i v e factor consists of one or more polygenes (Mather, 1949). Mather (1949) was able to associate some of the factors responsible for the genetic v a r i a b i l i t y with regions of heterochromatin. L i t t l e work has been done to follow up on this l i n e of investigation. The c l a s s i c a l Mendelian technique of genetic analysis 26 involves assigning individuals to discrete, e a s i l y distinguishable phenotypic groups. When dealing with a metrically inherited character t h i s discrete grouping i s not always possible because the number of simultaneously segregating factors and to nonheritable causes which generate s u f f i c i e n t v a r i a b i l i t y "noise" to obscure the group boundaries. 27 VI. BIOMETRICAL ANALYSIS There are three ways in which a metric character can be studied: 1) V a r i a b i l i t y generated by heritable factors can be separate from that caused by nonheritable sources i f environmental parameters during an experiment are s t r i c t l y monitored and standardized. This procedure would t h e o r e t i c a l l y eliminate most nonheritable causes of v a r i a b i l i t y . 2) Repeated inbreeding would d i l u t e the number of segregating genes to the point where individual genes could be i d e n t i f i e d for study and be eventually located on chromosomes with the aid of genetic markers; and 3) The cumulative effects of many Mendelian determinants can be biometrically studied in conjunction with associated nonheritable sources of v a r i a b i l i t y . A l l v a r i a t i o n in a truebreeding l i n e i s nonheritable ( i . e . , attributable only to the environment). A cross between two such li n e s (P1 x P2) would y i e l d a phenotypically homogeneous F1 exhibiting no heritable v a r i a t i o n . Factors segregating in the F2 28 would add a heritable component to the preexisting nonheritable one. This means that the t o t a l v a r i a b i l i t y in the F2 would be greater than that in the F1, P1 or the P2. On the average, half the polygenes in the F2 progeny would be homozygous, the rest would be heterozygous. F2 individuals would d i f f e r as to the number of genes that are homozygous, hence, F3 families would d i f f e r in their v a r i a b i l i t y . The average v a r i a b i l i t y of the families would be equal to half that of the F2. Therefore F3 families would be correlated with the founding F2 individuals. To gain an appreciation of biometrical techniques, picture the case where at any locus there exist two a l l e l e s (A and a) which can combine to create 3 genotypes (AA, Aa and aa; Mather and Jinks, 1971). (The use of c a p i t a l l e t t e r s does not denote dominance.) The A a l l e l e adds a unit to the expression of a character and the a a l l e l e subtracts a unit from the expression of the character. Let the midpoint between the readings of the two homozygous parents be represented by "m". Increments contributed to the character, as measured from the midpoint (m), can be denoted by the terms "+d", "-d" and "h" for genotypes AA, aa and Aa respectively. 29 P1 P2 aa m Aa AA < _ d > < +d > <- h -> In t h i s f i g u r e t h e "d" v a l u e s r e p r e s e n t one gene's c o n t r i b u t i o n t o t h e t o t h e a d d i t i v e component o f p h e n o t y p i c v a r i a b i l i t y . The "h" v a l u e s a r e c o n t r i b u t i o n s t o t h e dominance component of t h e t o t a l v a r i a b i l i t y . A p o l y g e n e ' s c o n t r i b u t i o n s t o t h e a d d i t i v e and t h e dominance h e r i t i b i l i t y components of v a r i a b i l i t y c an be summed o v e r a l l t h e c o n t r i b u t i n g l o c i t o g i v e t h e e q u a t i o n : 1) "Vp" i s t h e t o t a l p h e n o t y p i c v a r i a b i l i t y , 2) "Va" i s t h e a d d i t i v e g e n e t i c component o f v a r i a b i l i t y due t o t h e c u m u l a t i v e e f f e c t s o f t h e " d ' s " ; and i s a u s e f u l v a l u e f o r p r e d i c t i n g t h e e f f e c t i v e n e s s of b r e e d i n g p r o g r a m s , Vp = Va + Vd + Ve where: 30 3) "Vd" i s t h e dominance component o f v a r i a b i l i t y c a u s e d by t h e summed c o n t r i b u t i o n s o f t h e "h" e f f e c t s , and 4) "Ve" r e p r e s e n t s t h e component o f v a r i a b i l i t y g e n e r a t e d by a l l r e m a i n i n g s o u r c e s , i n c l u d i n g t h e e n v i ronment. In t h e e q u a t i o n above, t h e sum of t h e Va and t h e Vd components r e p r e s e n t t h e g e n e t i c v a r i a b i l i t y due t o g e n e t i c c a u s e s ( i . e . , V g ) . W i t h t h e u n d e r s t a n d i n g o f t h e s e b i o m e t r i c a l methods and more c l e v e r l y d e s i g n e d e x p e r i m e n t a l p r o c e d u r e s i t becomes p o s s i b l e t o f u r t h e r p a r t i t i o n p h e n o t y p i c v a r i a b i l i t y a c c o r d i n g t o a l m o s t a l l t h e c o n t r i b u t i n g v a r i a b l e s . E x a m ples of t h e s e v a r i a b l e s c an i n c l u d e : 1) r e l a t i v e c o n t r i b u t i o n s by e a c h p a r e n t and by t h e dominance and e p i s t a t i c ( n o n - a l l e l i c ) i n t e r a c t i o n s c a u s e d by d i f f e r e n t p a r e n t a l gene c o m b i n a t i o n s , 2) c o n t r o l l e d e n v i r o n m e n t a l o r t r e a t m e n t f a c t o r s s u c h as t e m p e r a t u r e , l i g h t i n t e n s i t y , s o i l pH, e t c . , 31 3) s p e c i f i c genotype-environmental interactions, 4) experiment r e p l i c a t i o n differences, and 5) technical error. Ideally, a l l sources contributing to the t o t a l phenotypic v a r i a b i l i t y of a metric t r a i t can be accounted for i f a l l the unknown error variables can be i d e n t i f i e d and controlled. 32 VII. EFFECTIVE FACTORS Several authors have devised methods to estimate the number of genes (k) contributing to a quantitative t r a i t . "Student" (1934) determined that 20-40 and possibly 200-400 genes were involved in the control of maize seed o i l . By inbreeding selected l i n e s Falconer (1971) estimated that 80 genes determining l i t t e r size existed in his mouse population. Panse (1940) derived "k" values based on the variance of the mean variance within F3 families. He showed that t h i s variance would be equal to one quarter the sum of squares of the variances of individual factors. Yet another method depends on proportions of individuals heterozygous for at least one gene difference in the F2 or l a t e r generations (Jinks and Towey, 1976). One of the f i r s t and perhaps the most simple method to estimate "k" for a system was devised by Wright (1934, 1952) and was i n i t i a l l y used by Castle (1921). They l e t "k" represent the number of factors involved in a character where each a l l e l e had an effect "a" on the phenotype. The difference between the two parental means was: P1 - P2 = 2ka (1 ) The F2 genetic variance due to each pair of a l l e l e s was 1/2 a x a . The F2 genetic variance (Vg) produced by a l l contributing a l l e l e s was: Vg = 1/2 ka x a (2) 33 o r 2 2 Vg a = (3) k R e a r r a n g i n g e q u a t i o n 1 g i v e s : PI - P2 a = (4) 2k and s q u a r i n g b o t h s i d e s p r o d u c e s : - 2 2 (P1 - P2) a = (5) 2 4k S u b s t i t u t i n g e q u a t i o n 3 i n t o e q u a t i o n 5 g i v e s : - 2 (P1 - P2) Vg = (6) 8k 34 o r - 2 (P1 - P2) k = (7) 8Vg E q u a t i o n 7 was f o u n d t o be a c c u r a t e i n d e t e r m i n i n g t h e number of e f f e c t i v e f a c t o r s i f c e r t a i n a s s u m p t i o n s were made. The s e a s s u m p t i o n s a r e : 1) gene e f f e c t s a r e e q u a l , 2) t h e e f f e c t s of t h e l o c i a r e a d d i t i v e , 3) t h e a l l e l e f r e q u e n c i e s a r e e q u a l , and 4) t h e genes a r e u n l i n k e d . Lande (1981) r e c e n t l y e x p r e s s e d s u p p o r t f o r t h e use o f e q u a t i o n 6 as an a c c u r a t e e v a l u a t o r of k v a l u e s . As a n a l y s i s t e c h n i q u e s became more s o p h i s t i c a t e d , e f f o r t s were made t o l o c a t e , i s o l a t e and o b s e r v e t h e e f f e c t s of i n d i v i d u a l f a c t o r s . Wigan (1949) u s e d r e c o m b i n a n t chromosomes t o l o c a t e f a c t o r s i n f l u e n c i n g a b d o m i n a l c h a e t a e number i n s e v e r a l r e g i o n s of t h e X chromosome i n D r o s o p h i l a . B r e e s e and Mather (1957, 1960) u s e d a s i m i l a r but more complex t e c h n i q u e t o d i v i d e D r o s o p h i l a ' s chromosome I I I i n t o s i x segments, e a c h of wh i c h were shown t o c a r r y a t l e a s t one p o l y g e n e c o n t r o l l i n g t h e number 35 of chaetae. The most powerful technique was developed by Thoday (1961), who studied the inheritance of sternopleural chaetae and abdominal chaetae number in Drosophila . His technique involved the use of recombinant chromosomes and marker genes and provided an important method for dissection of polygenic systems. Methods have been developed for fine analysis of polygenes in other organisms (Wehrhahn and A l l a r d , 1965; Law 1966, 1967; Milkman, 1970). Unfortunately, there is a r e s t r i c t i n g factor involved in these types of precise manipulations of polygenes. It i s the degree to which the system of interest has been mapped. Naturally, an organism for which the genetics i s well known would lend i t s e l f nicely to these studies. 36 VIII. CONSTANT RANKING Because the effects of polygenes are cumulative, v a r i e t i e s that have been tested and ranked according to their levels of resistance to a single i s o l a t e should retain their ranking when tested against other i s o l a t e s , and that the ranking should be correlated with the numbers of polygenic resistance a l l e l e s that the v a r i e t i e s possess (Driver, 1962; Vanderplank, 1968). Likewise, a number of pathogen isola t e s should be s i m i l a r l y ranked when tested on a susceptible variety (Vanderplank, 1968). This ranking would also remain unchanged when the tester variety varied. Correlated rankings of susceptible v a r i e t i e s and vi r u l e n t isolates is known as "constant ranking" and is c h a r a c t e r i s t i c of a system involving only' polygenes (Vanderplank, 1968). 37 IX. QUANTITATIVE STUDIES OF FUNGI C e r t a i n f u n g i a r e w e l l s u i t e d f o r q u a n t i t a t i v e s t u d i e s b e c a u s e o f t h e i r p r o l o n g e d e x i s t e n c e i n b o t h h a p l o i d and d i p l o i d o r d i k a r y o t i c p h a s e s . D e s i r e a b l e c h a r a c r e r i s t i c s i n c l u d e , e a s e of h a n d l i n g and of e n v i r o n m e n t a l r e g u l a t i o n and t h e a b i l i t y t o be m a i n t a i n e d i n c u l t u r e f o r l o n g p e r i o d s . P r o d u c t s o f m e i o s i s can be r e a d i l y i s o l a t e d . P o l y g e n e s g o v e r n i n g s i m i l a r c h a r a c t e r s i n b o t h p l o i d i e s can be compared. C y t o p l a s m i c v a r i a t i o n c a n be s t u d i e d . R e g a r d l e s s o f t h e s e o b v i o u s a t t r i b u t e s , l i t t l e i n f o r m a t i o n i s a v a i l a b l e on q u a n t i t a t i v e l y i n h e r i t e d t r a i t s even i n t h o s e f u n g i t h a t a r e w e l l s u i t e d f o r q u a n t i t a t i v e s t u d y . One of t h e f i r s t s t u d i e s was done by Hanna ( 1 9 2 6 ) . He i n v e s t i g a t e d t h e i n h e r i t a n c e of s p o r e s i z e i n C o p r i n u s  s t e r q u i l i n u s and i n c o r p o r a t e d J o h a n n s e h i a n t e c h n i q u e s . V e r y few a d v a n c e s were made i n a n a l y t i c a l t e c h n i q u e s u n t i l M a t h e r ' s B i o m e t r i c a l G e n e t i c s ( 1 9 4 9 ) . T h i s book s p a r k e d f u r t h e r i n t e r e s t i n q u a n t i t a t i v e i n h e r i t a n c e and l a i d t h e groundwork f o r t h e d e v e l o p m e n t o f a n a l y t i c a l t e c h n i q u e s i n d i p l o i d s and h a p l o i d s . More r e c e n t e x p e r i m e n t s i n v o l v i n g M a t h e r ' s b i o m e t r i c a l p r o c e d u r e s i n c l u d e t h o s e by Pateman (1955, 1959a, 1959b), Pateman and Lee (196 0 ) , Lee and Pateman (1959, 1961) and Lee (1 9 6 2 ) . T h e s e s t u d i e s d e a l t w i t h t h e i n h e r i t a n c e o f N e u r o s p o r a a s c o s p o r e s i z e . F o r up t o s i x t e e n g e n e r a t i o n s , s e l e c t i o n s f o r l a r g e a s c o s p o r e s were made u n t i l t h e s e l a r g e a s c o s p o r e s became a s s o c i a t e d w i t h a s c i t h a t c o n t a i n e d o n l y f o u r h a p l o i d s p o r e s . S u b s e q u e n t c r o s s e s w i t h w i l d t y p e , b a c k c r o s s e s and t e t r a d a n a l y s e s r e v e a l e d t h e e x i s t e n c e o f p o l y g e n e s , p o l y g e n i c 38 i n t e r a c t i o n and t h e l o c a t i o n o f an e f f e c t i v e f a c t o r 13 cM f r o m an a l b i n o l o c u s on chromosome I . A g g r e s s i v e n e s s i n P h y t o p t h o r a i n f e s t a n s was f o u n d t o d e c r e a s e a f t e r p r o l o n g e d c u l t u r e ( J i n k s and G r i n d l e , 1963). I t was r e s t o r e d a f t e r one y e a r i n c u l t u r e by g r o w i n g t h e i s o l a t e s on l e a v e s or t u b e r s of t h e v a r i e t i e s f r o m w h i c h t h e y were o r i g i n a l l y i s o l a t e d . C y t o p l a s m i c , not p o l y g e n i c , c a u s e s were f o u n d t o be r e s p o n s i b l e . Simchen and J i n k s (1964) s t u d i e d d i k a r y o t i c c h a r a c t e r s of S c h i z o p h y l l u m commune i n p r o g e n y from c r o s s e s between w i l d i s o l a t e s . They f o u n d t h a t b i o m e t r i c a l a d d i t i v i t y and dominance were s i m i l a r t o t h a t n o r m a l l y f o u n d i n d i p l o i d s . The e x i s t e n c e of a d ominant major gene a f f e c t i n g f r u i t i n g was d i s c o v e r e d , w h i c h c o r r o b o r a t e d t h e e a r l i e r f i n d i n g s of Raper and K r o n g e l b ( 1 9 5 8 ) . A l s o a m b i d i r e c t i o n a l dominance was f o u n d f o r p o l y g e n e s a f f e c t i n g g r o w t h r a t e . Simchen and J i n k s c o n c l u d e d t h a t t h i s was e v i d e n c e f o r t h e e x i s t e n c e of s t a b i l i z i n g s e l e c t i o n . Simchen (1965) c r o s s e d m o n o k a r y o t i c d e s c e n d a n t s from s i x d i f f e r e n t C o l l y b i a v e l u t i p e s d i k a r y o n s . A f t e r c a l c u l a t i n g v a r i a n c e components f o r g r o w t h r a t e and t h r e e m e a sures of f r u i t i n g a b i l i t y , he c o u l d show e v i d e n c e f o r p l e i t r o p h y or l i n k a g e between t h e h i g h l y c o r r e l a t e d f r u i t i n g c h a r a c t e r s and c o u l d a n a l y s e g e n e t i c i n t e r a c t i o n s u s i n g v a r i a n c e / c o v a r i a n c e r e g r e s s i o n s . C y t o p l a s m i c v a r i a t i o n i n m o n o k a r y o t i c m y c e l i a l , g r o w t h r a t e of C. v e l u t i p e s was compared t o t h e g e n e t i c v a r i a t i o n i n t h a t c h a r a c t e r by C r o f t and Simchen ( 1 9 6 5 ) . S e l e c t i o n e x p e r i m e n t s by 39 Simchen (1966b) a l l o w e d v a r i a t i o n measurements i n v o l v i n g t h e g r o w t h r a t e d i f f e r e n c e s among m o n o k a r y o t i c p r o g e n y o f s i x w i l d i s o l a t e s o f S c h i z o p h y l l u m commune . H i g h and low l i n e s were s e l e c t e d f o r n i n e g e n e r a t i o n s . V a r i a b i l i t y d e c r e a s e d w i t h i n c r e a s e d s e l e c t i o n . The i m p o r t a n c e o f r e c o m b i n a t i o n i n s e l e c t i o n was i n d i c a t e d by t h e r e g e n e r a t i o n of h i g h l e v e l s of v a r i a b i l i t y when t h e s e l e c t e d l i n e s were c r o s s e d . O n l y a l l e l i c i n t e r a c t i o n s were f o u n d t o be i n v o l v e d i n t h e c o n t r o l of m o n o k a r y o t i c o r d i k a r y o t i c g r o w t h r a t e s i n S c h i z o p h y l l u m commune, b u t , dominance e f f e c t s were p r e s e n t (Simchen and J i n k s , 1964; Simchen, 1966a). Simchen (1966a) d i d d e t e r m i n e t h a t n o n a l l e l i c i n t e r a c t i o n s were i n v o l v e d i n t h e c o n t r o l o f w e i g h t and b a s i d i o c a r p m a t u r a t i o n i n S c h i z o p h y l l u m  commune . C o l l y b i a v e l u t i p e s g e n e r a t e d s i m i l a r r e s u l t s ( S i m c h e n , 1965). In a s u b s e q u e n t s t u d y Simchen (1967) f o u n d n o n a l l e l i c i n t e r a c t i o n s c o n t r i b u t i n g g r e a t l y t o g e n e t i c d i f f e r e n c e s between S. commune i s o l a t e s from d i f f e r e n t g e o g r a p h i c a l o r i g i n s . B u r n e t t (1975) t h o u g h t t h a t n o n a l l e l i c i n t e r a c t i o n s would be shown t o p l a y a g r e a t e r r o l e i n c o n t r i b u t i n g t o g e n e t i c d i f f e r e n c e s between d i s p a r a t e i s o l a t e s . 40 S t u d i e s o f U s t i l a g o h o r d e i U s t i l a q o h o r d e i ( P e r s . ) L a g e r h . i s a b i p o l a r smut f u n g u s , o b l i g a t e l y p a r a s i t i c on b a r l e y . In t h e p a s t , smuts have c a u s e d e x t e n s i v e damage t o v a r i o u s c u l t i v a t e d p l a n t s p e c i e s . U. h o r d e i i s w e l l s u i t e d f o r b i o m e t r i c a l and p o p u l a t i o n g e n e t i c s t u d i e s o f p a t h o g e n i c i t y b e c a u s e i t i s e a s y t o c u l t u r e , s t o r e and h a r v e s t . T e l i o s p o r e s of U. h o r d e i a r e g e n e r a l l y 5-11 u i n d i a m e t e r , smooth and l i g h t c o l o r e d on one s i d e ( F i s c h e r , 1953). Upon g e r m i n a t i o n , t h e d i p l o i d n u c l e u s moves out i n t o t h e l o n g s l e n d e r p r o m y c e l i u m where i t u n d e r g o e s t h e f i r s t m e i o t i c d i v i s i o n ( F i s c h e r and H o l t o n , 1957). A w a l l forms a c r o s s t h e p r o m y c e l i u m between t h e n u c l e i . The n u c l e i u n d ergo t h e s e c o n d m e i o t i c d i v i s i o n and two more d i v i d i n g w a l l s a r e f o r m e d . T h i s r e s u l t s i n f o u r l i n e a r l y a r r a n g e d , u n i n u c l e a t e c e l l s b e i n g p r o d u c e d , w i t h t h e b a s a l c e l l e x t e n d i n g i n t o t h e t e l i o s p o r e . H a p l o i d s p o r i d i a r e p r e s e n t i n g t h e p r o d u c t s o f m e i o s i s bud c o n t i n u o u s l y f r o m t h e f o u r p r o m y c e l i a l c e l l s . E a c h bud, i n t u r n , c a n d i v i d e t o p r o d u c e c l o n e s ( F i s c h e r and H o l t o n , 1957). S p o r i d i a o f o p p o s i t e m a t i n g t y p e c a n f u s e t o f o r m d i k a r y o t i c hyphae w h i c h can p e n e t r a t e and i n f e c t b a r l e y s e e d l i n g s ( F i s h e r and H o l t o n , 1957). The d i k a r y o t i c m y c e l i u m grows i n t e r c e l l u l a r l y i n a s s o c i a t i o n w i t h t h e a p i c a l t i p ( K o z a r , 1969) and forms s o r i i n t h e s p i k e l e t s r e p l a c i n g t h e s e e d s w i t h smut b a l l s c o n s i s t i n g of m i l l i o n s of s p o r e s . M e c h a n i c a l h a r v e s t i n g t e c h n i q u e s r u p t u r e t h e b a s a l p a r t of t h e glumes t h a t e n c a s e t h e smut b a l l s ( S t e v e n s , 1913) and s p r e a d t h e s p o r e s t o o t h e r s e e d s . T h e s e s e e d s can become i n f e c t e d when sown ( G r o t h 41 and P e r s o n , 1976). See F i g u r e 1 f o r t h e l i f e c y c l e o f U. h o r d e i . The b a r l e y h o s t , Hordeum v u l g a r e L. i s a p r o l i f i c , s e l f -f e r t i l i z i n g c r o p p l a n t . H i g h l y i s o g e n i c c u l t i v a r s a r e r e a d i l y a v a i l a b l e . In 1919, when K n i e p d i s c o v e r e d t h e e x i s t e n c e o f sex i n t h e smut, U. v i o l a c e a , g e n e t i c s t u d i e s o f p a t h o g e n i c i t y became more c o m p r e h e n s i v e . G o l d s c h m i d t ( 1 9 2 8 ) , s t u d i e d 6 r a c e s o f U. v i o l a c e a and d i s c o v e r e d t h a t v i r u l e n c e was c o n t r o l l e d by 1 i n c o m p l e t e l y d o m i n a n t a l l e l e i n two o f t h e r a c e s . C h r i s t e n s e n (1929) was t h e f i r s t t o r e p o r t a m u l t i f a c t o r i a l mode o f i n h e r i t a n c e i n a smut (U. m a y d i s ) . He a t t r i b u t e d t h e d i f f e r e n c e s i n t h e d e g r e e of p a t h o g e n i c i t y o f v a r i o u s s p o r i d i a l p a i r i n g s t o th e a c t i o n of many g e n e s . However h i s f i n d i n g s were r e f u t e d by Stakman e t a l . ( 1 9 3 3 ) , who c l a i m e d t h a t o n l y a few v i r u l e n c e g enes were c o n t r o l l i n g t h e l e v e l s of i n f e c t i o n . N i c h o l a i s e n (1934) showed e v i d e n c e f o r t h e e x i s t e n c e o f d o m i n a n t , i n c o m p l e t e l y d ominant and r e c e s s i v e i n h e r i t a n c e o f v i r u l e n c e i n i n t r a r a c i a l c r o s s e s of U. avena . He a l s o f o u n d t r a n s g r e s s i v e s e g r e g a t i o n i n t h e p r o g e n y o f t h e s e c r o s s e s , w h i c h c a n be i n d i c a t i v e o f p o l y g e n i c i n h e r i t a n c e . O t h e r s t u d i e s on t h e i n h e r i t a n c e of v i r u l e n c e i n c l u d e H a l i s k y (1956; U. avena ), H o l t o n (1959, 1964, 1966; U. avena ) and J o h n s o n (1960; U. avena ). E v e n t u a l l y i n v e s t i g a t o r s began t o f o c u s on t h e mode of i n h e r i t a n c e i n v o l v e d a t v a r i o u s l e v e l s or d e g r e e s o f v i r u l e n c e . Thomas and P e r s o n (1965) p e r f o r m e d e x p e r i m e n t s w i t h low l e v e l s o f p a t h o g e n i c i t y (0-5%) i n U. h o r d e i and f o u n d t h a t i t was 42 F i g u r e 1. The l i f e c y c l e of U s t i l a g o h o r d e i . k3 Figure 1 A Schematic Representation of the Life Cycle of Ustilago hordei (from Ebba, 1974) 44 controlled by two a l l e l e s at a single locus with the virulence a l l e l e being dominant. Lade (1969) obtained similar results for intermediate (5-35%) levels of pathogenicity. Sidhu and Person (1971) studied high levels of pathogenicity and i d e n t i f i e d 2 recessive a l l e l e s for two virulence genes designated Uh1 and Uh2 c o n t r o l l i n g i t s inheritance. Only in the last ten years have biometrical methods been applied to data from investigations on the inheritance of control of the degree of pathogenicity in smuts, p a r t i c u l a r l y , U. hordei . Emara (1972) was the f i r s t to determine that aggressiveness in U. hordei was quantitatively or polygenically inherited. Randomly isolated monosporidial cultures from 13 races were paired in a l l compatible combinations and tested on the barley variety, Odessa (a universal suscept). Race 1 and race 5 were the highest ' and lowest, respectively, in aggressiveness. The genetic component of v a r i a b i l i t y was calculated to be 51.23% the bulk of which was due to the additive effects of the genes. Emara and Sidhu (1974) crossed and selfed the products of meiosis from two U. hordei teliospores to produce sixteen dikaryons which were tested on c u l t i v a r Vantage. Aggressiveness was expressed as a continuous character. An analysis of variance revealed high v a r i a b i l i t y in aggressiveness between and within teliospores. Additive e f f e c t s accounted for 43.9% of the t o t a l v a r i a b i l i t y and nonadditive e f f e c t s contributed 21.3% V a r i a b i l i t y was found to be s i g n i f i c a n t l y greater between dikaryons that resulted from crossing than from s e l f i n g . This 45 phenomenon was attributed to heterosis with a l l e l e s for high aggressiveness being dominant. Caten et a l . (1981) performed biometrical analyses on the descendants of seven U. hordei dikaryons. One of these dikaryons was synthesized by mating two unrelated sporidia. A continuous l e v e l of aggressiveness was found among the progeny. Analysis of variance components indicated the presence of additive and dominance e f f e c t s . The two inbred l i n e s and the four naturally occurring dikaryons revealed low levels of v a r i a b i l i t y . These results indicated the high degree of homozygosity possessed by the four dikaryons isolated from natural populations and the higher levels of heterozygosity of the synthesized and inbred dikaryons. 46 Table 1 summarizes the v a r i a b i l i t y parameters for U. hordei known to date. 47 Table 1. Compilation of variance components and estimations of h e r i t a b i l i t i e s from experiments on pathogenicity in the smut-barley system. Bracketed numbers are the variances expressed as percentages of the t o t a l phenotypic variance. T a b l e 1 VARIABILITY COMPONENTS . HERITABILITY RESEARCHER v t Vg Va Vna Ve H 2 h 2 Emara and 301 . 69 196.76 132. 53 64. 23 104 93 0.65 0. 44 S i d h u (65.2) (43. 9) (21 . 3) (34.8) Emara 72. 1 4 36.96 30. 35 6. 61 35. 18 0.51 0. 42 (51.2) (42. 1 ) (9. 1 ) (48.8) C a t e n ( s ) 51 . 40 23.80 27.60 0.46 (46.0) (54.9) ( i ) 28. 30 1 .50 26.80 0.05 (5.0) (95.0) ( i ) 31 . 60 5.90 25.70 0.19 (19.9) (81.0) (n) 35. 00 3.20 31 .80 0.09 (9.0) (91.0) (n) 40. 40 4.10 36.30 0.10 (10.0) (90.0) (n) 45. 50 1 .60 43.90 0.04 (4.0) (96.0) (n)- 40. 10 0.00 40. 1 0 0.00 (0.0) (100.0) V t = t o t a l v a r i a n c e ; Vg = g e n e t i c v a r i a n c e ; Va = a d d i t i v e g e n e t i c v a r i a n c e ; Vna = n o n - a d d i t i v e g e n e t i c v a r i a n c e ; Ve = e n v i r o n m e n t a l v a r i a n c e ; H 2 = b r o a d s e n s e h e r i t a b i l i t y ; h 2 = narrow s e n s e h e r i t a b i l i t y ; s = s e l f e d t e l i o s p o r e ; i = i n b r e d t e l i o s p o r e ; n = n a t u r a l i s o l a t e . X. PURPOSE OF THIS STUDY The purpose of this study i s to: 1) e n l i s t analysis of variance techniques for characterizing pathogenicity as an alte r n a t i v e to using c l a s s i c a l tetrad analysis; 2) study covariance/variance regressions of the treatment sporidia to more c l e a r l y determine the role of non-additive genetic e f f e c t s on pathogenicity; 3) determine the genetic background of race 7 and race 11 of Ustilago hordei; 4) estimate the number of e f f e c t i v e factors c o n t r o l l i n g pathogenicity; 5) determine i f constant ranking can be detected. 50 XI. MATERIAL AND METHODS Experimental Design Representative teliospores from Race 11 and Race 7 of Ustilaqo hordei (Tapke 1937, 1945) were obtained by Ebba (1974) from N. Dakota and renamed T1 and T4 respectively. Sporidia from single parent teliospores of each race were isolated by Ebba (1974) during the course of his Ph.D. thesis work. Eight F1 dikaryotic l i n e s , numbered 17 through 24 were formed by crossing products of meiosis from T1 with those of T4 in compatible combinations (Figure 2). Dikaryotic lines (subsequently referred to as DL) 17,' 21, and 23 were randomly chosen and 12 sporidia, 6 of each mating type, were isolated at random from each of the three DL's. A 6x6 North Carolina Mating Design II mating g r i d (Comstock and Robinson, 1952) was set up to produce 36 F2 progeny for each DL (Figure 2). (Included in the design was an uninfected control.) A l l 108 F2's were tested on two c u l t i v a r s of barley, Trebi and Odessa (hereafter designated T and 0, respectively), in three r e p l i c a t e t r i a l s . The res u l t i n g disease readings were subjected to s t a t i s t i c a l analysis on a computer. 51 F i g u r e 2. E x p e r i m e n t a l d e s i g n . S p o r i d i a from s i n g l e p a r e n t t e l i o s p o r e s (T1 and T4) were c r o s s e d i n c o m p a t i b l e c o m b i n a t i o n s t o p r o d u c e 8 F1 d i k a r y o t i c l i n e s . The d i k a r y o t i c l i n e s were numbered DL 17 t o DL 24. S i x s p o r i d i a o f b o t h m a t i n g t y p e s were i s o l a t e d from 3 ra n d o m l y c h o s e n d i k a r y o t i c l i n e s ( i e . DL's 17, 21 and 2 3 ) . The "-" s p o r i d i a were l a b e l e d "a t o f " and t h e "+" s p o r i d i a were l a b e l e d "g t o 1". The 12 s p o r i d i a from e a c h DL were c r o s s e d t o p r o d u c e 3 g r i d s , e a c h c o n s i s t i n g o f 36 F2 t r e a t m e n t d i k a r y o n s . C o n t r o l s c o n s i s t e d o f i d e n t i c a l l y h a n d l e d t r e a t m e n t s b ut w i t h t h e e x c l u s i o n of t h e p a t h o g e n from t h e i n o c u l u m . Figure 2 P [ *T1 T4 FI D L 17 -18 19 20 21 -22 23-24 F2 grid 1 g h i j k I 1 2 3 4 5 6 7 36 grid 2 g h i j k I 36 grid 3 g h i j k I a bl c I d e f 36 53 Sporidia Isolation The work was performed under aseptic conditions whenever possible. Teliospores were wetted in s t e r i l e d i s t i l l e d H20 for 30 minutes before a small quantity of the spore suspension was spotted onto the center of a 20 mm x 20 mm x 3 mm agar block that contained minimal medium (Appendix I ) . These blocks, mounted on 25 sq mm cover-slips, were incubated for 18h at 22°C to permit teliospore germination and s p o r i d i a l production. The inverted blocks were placed onto a moveable stage microscope and the spores were viewed at 150 magnifications. The needle fine point of a glass probe mounted on a de Fonbrune micromanipulator (CH. Beaudouin, Paris) was used to coax a single sporidium to the edge of the block. Within 4 days at 22°C, v i s i b l e colonies produced by isolated sporidia could be picked and cultured on complete medium agar plates (Appendix I ) . A modified Bauch test (Bauch, 1932) was used to id e n t i f y the mating types of the isolated clones. C e l l s of each iso l a t e were mixed with standards of known mating type on water agar plates. The production of protruding dikaryotic hyphae ("Suchfaden"), v i s i b l e under a dissecting microscope, indicated the compatibility of the mixed c e l l s and revealed the mating type of the i s o l a t e as being the opposite of that of the known standard. 54 L o h g t e r m S p o r i d i a S t o r a g e Screw c a p p e d t u b e s were h a l f f i l l e d w i t h d r y s i l i c a g e l . The t u b e s w i t h l o o s e l y f i t t e d c a p s were s t e r i l i z e d a t 180°C f o r 90 m i n u t e s . Upon r e m o v a l f r o m t h e oven t h e c a p s were t i g h t e n e d and t h e t u b e s were a l l o w e d t o a i r c o o l t o room t e m p e r a t u r e . F o u r t o f i v e day s p o r i d i a l g r o w t h s were e m u l s i f i e d i n 1 ml o f s t e r i l e d i s t i l l e d H20 and 1 ml o f d o u b l e s t r e n g t h s k i m m i l k . One ml o f t h i s m i x t u r e was p l a c e d i n t o t h e s t e r i l e , c o o l t u b e s and shaken u n t i l a l l t r a c e s of m o i s t u r e d i s a p p e a r e d . The t u b e s were i m m e d i a t e l y c o o l e d i n an i c e b a t h f o r 15 m i n u t e s and t h e n s t o r e d a t 4°C. Seed P r e p a r a t i o n Seeds were s o a k e d i n 0.12% f o r m a l i n f o r 30 m i n u t e s and t h e n washed t h o r o u g h l y i n t a p H20 f o r 1 h o u r . Wet s e e d s were s p r e a d t h i n l y on newspaper and a l l o w e d t o a i r d r y f o r 48 h o u r s b e f o r e d i s p e n s i n g 100-125 s e e d s i n t o 25 ml p l a s t i c v i a l s . I n o c u l u m P r e p a r a t i o n I s o l a t e s were t r a n s f e r r e d t o t e s t t u b e s c o n t a i n i n g 5 ml o f c o m p l e t e medium and 0.075 t e t r a c y c l i n e H C l mg/ml and p l a c e d i n a s h a k e r i n c u b a t o r a t 22° C . A f t e r 24 h o u r s , 1 ml o f e a c h s u s p e n s i o n was t r a n s f e r r e d t o a s e p a r a t e 250 m l f l a s k c o n t a i n i n g 60 ml of c o m p l e t e l i q u i d medium and 0.075 t e t r a c y c l i n e H C l mg/ml; t h e s e f l a s k s were s h a k e n a t 22°C f o r 48 h o u r s . 55 Inoculation Seed f i l l e d , labeled v i a l s were inoculated with 2.5 ml of each s p o r i d i a l suspension of the appropriate mating type. The v i a l s were then placed in a b e l l jar and subjected to a p a r t i a l vacuum for 30 minutes. The excess l i q u i d was poured off and seeds were transferred to labeled 2 coin envelopes to permit a i r drying for 48 hours. Planting The seeds were planted in completely randomized blocks organized in banks of 111 rows with three feet separating each bank. Rows were 10 feet long separated from adjacent rows by 1 foot. The seeds were planted approximately 3/4 of an inch deep with the aid of a simple belt-driven single-row planter. The rows were weeded regularly and watered as necessary. Harvest Approximately 3-4 months after planting the f i r s t 50 plants in each row were uprooted, examined and c l a s s i f i e d according to whether they were healthy or diseased ( c r i t e r i o n being one or more diseased t i l l e r s ) . Sample diseased heads from each row were stored in coin envelopes. 56 S t a t i s t i c a l Analysis Disease readings were calculated for each row. These readings, usually expressed in percentages, were subjected to the angular transformation prior to analysis. A l l F2 disease readings l i s t e d for th i s experiment are transformed readings and should not be confused with disease percentages. Various s t a t i s t i c a l packages available on the MTS and the pdpl1(UNIX) computer systems were used to analyse the data. Analyses of variance were employed to p a r t i t i o n the t o t a l phenotypic v a r i a b i l i t y of disease readings into source components. For th i s p a r t i c u l a r experiment, there were several i d e n t i f i a b l e sources of v a r i a b i l i t y . These included: 1) v a r i e t a l differences.(var) 2) DL differences (DL) 3) treatment differences (treat) a. "+" sporidia (+) b. "-" sporidia (-) c. "+" x "-" sporidia (+ x -) 4) replicate environment differences (rep) 57 5) interactions between these sources, i d e n t i f i e d by the presence of an "x" placed between source abbreviations 6) residual error (error) This breakdown permitted comparisons of individual component v a r i a b i l i t i e s between the F2's of each DL in the absence of the confounding e f f e c t s of other factors. 58 X I I . RESULTS V a r i a n c e A n a l y s i s T r a n s f o r m e d d i s e a s e l e v e l v a l u e s a r e u s e d t h r o u g h o u t t h i s t h e s i s . T h e s e v a l u e s r e p r e s e n t t h e means from t h r e e r e p l i c a t e d t r i a l s . R e s u l t s from T1 and T4, when s e l f e d , a r e l i s t e d i n T a b l e 2. The v a l u e s t h a t Tapke (1937, 1945) o b t a i n e d f o r t h e same r a c e s on T were 43% and 5%. He a l s o o b t a i n e d r e a d i n g s of 34% f o r T4 and 39% f o r T1 on 0. No F1 r e a d i n g s were a v a i l a b l e f o r 0. When t e s t e d on T, Ebba f o u n d t h a t t h e mean d i s e a s e r e a d i n g was 44.0% f o r T1 and 2.5% f o r T4. E a c h of t h e f o u r r e a d i n g s from b o t h s e l f s were s u b j e c t e d t o a C h i - s q u a r e t e s t t o examine t h e h y p o t h e s i s t h a t t h e y were not s i g n i f i c a n t l y d i f f e r e n t f r o m t h e r e s p e c t i v e means of t h e s e l f s . The C h i s q u a r e v a l u e of 0.6818 (DF=3) f o r T and 0.040 (DF=3) f o r 0 ( T a b l e 2 ) , i n d i c a t e t h a t t h e f o u r s p o r i d i a f r o m e a c h p a r e n t a l t e l i o s p o r e behaved s i m i l a r l y . When t h e s p o r i d i a from t h e two p a r e n t a l t e l i o s p o r e s were c r o s s e d i n a l l p o s s i b l e c o m b i n a t i o n s t h e F1 r e a d i n g s v a r i e d f r o m 37.0% t o 49.0% w i t h a mean of 45.0% ( T a b l e 3 ) . The C h i s q u a r e v a l u e o f 2.6222 (DF=7) c a l c u l a t e d f r o m t h e F1 r e a d i n g s ( T a b l e 3) i n d i c a t e s no s i g n i f i c a n t d i f f e r e n c e s between c o n t r i b u t i o n s o f s p o r i d i a i n c a u s i n g d i s e a s e l e v e l s i n t h e F 1 . T a b l e 4 shows t h e t r a n s f o r m e d means o f e a c h of t h e 3 DL g r i d s on T and 0. The 6 t r e a t m e n t g r i d s from T a b l e 4 d i s p l a y n o r m a l d i s t r i b u t i o n s ( F i g u r e 3a, 3b and 4 ) . T h i s i s t o be e x p e c t e d f o r a c o n t i n u o u s l y i n h e r i t e d c h a r a c t e r and a g r e e s w i t h t h e c l a i m 59 Table 2. Ebba's and Tapke's disease readings from s e l f i n g T1 and T4, expressed as a percentage of smutted plants. Table 2 TREBI ODESSA TELIOSPORE RACE SELF EBBA % TAPKE % TAPKE % T1 11 T1-1 X T1-2 42 - -- 1 x -4 49 - --3 x -2 44 - --3 X -4 43 - -ave = 44 43 39 T4 7 T4-1 x T4-3 2 -1 x -4 3 -2 x -3 2 -2 x -4 3 ave = 2.5 5 34 61 Table 3. Eight dikaryotic l i n e (DL) disease readings from the cross between T1 and T4. T a b l e 3 CROSS DL -1 X T4-3 17 37 -1 X -4 18 49 -2 X -1 1 9 44 -2 X -2 20 48 -3 X -3 21 49 -3 X -4 22 47 -4 X -1 23 43 -4 X -2 24 43 ave = 45 DL = dikaryotic l i n e number 63 Table 4. Six grids representing transformed treatment and array means for the disease readings of the three DL's on Trebi (T) and Odessa ( 0 ) . Six isolates of each mating type (a-f and g-1) were combined in a l l possible ways. Each treatment value represents the mean of three r e p l i c a t e s . 6<f VARIETY DL T 1 7 ( g r i d 1) T 21 ( g r i d 2) T 23 ( g r i d 3) T a b l e 4 m a t i n g t y p e n _ »t g h i j k 1 mean a 23.9 24.2 22.5 24.2 32.8 23. 1 25. 1 b 17.7 26.6 24.9 28.3 27.0 25.7 25.0 c 8.7 11.5 22.3 15.6 25.8 22. 1 17.7 d 18.8 14.3 14.2 26.0 31.0 25.7 21.7 e 13.4 8.0 14.1 24.5 23.9 20.6 17.4 f 27.3 26.4 23.5 25.0 22. 1 25.5 25.0 mean 18.3 18.5 20.2 23.9 27. 1 23.8 22.0 9 h i j k 1 mean a 13.0 18.3 17.4 26.4 24.3 26.0 • 20.9 b 21.6 15.0 14.5 16.7 25.2 23.3 19.4 c 17.3 31.0. 30. 1 24.0 26.2 34.8 27.3 d 16.2 5.7 8.1 21.6 28.0 28.5 18.0 e 18.4 17.0 15.4 22.8 26.6 32.4 22. 1 f 20.3 36.0 30. 1 27.7 31.4 .31.8 29.6 mean 17.8 20.5 19.3 23.2 26.9 29.5 22.9 g h i j k 1 mean a 30.4 15.8 14.8 22.0 6.1 27.9 19.5 b 24.4 21 .5 16.3 31.1 25.7 29.9 24.8 c 24.4 21.1 14.0 26.4 15.8 18.9 20. 1 d 29. 1 13.6 7.5 23.2 11.8 31 .0 19.3 e 16.6 27.4 25.0 23.5 22.4 26.9 23.6 f 20.0 9.0 12.2 18.7 7.8 18.4 14.3 mean 24. 1 18.1 15.0 24. 1 14.9 25.5 20.3 T a b l e 4 ( c o n t i n u e d ) m a t i n g t y p e VARIETY DL O 17 ( g r i d 4) 0 21 ( g r i d 5) 0 23 ( g r i d 6) g h i j k 1 mean a 37.2 25.3 35.3 37.2 32.9 23.0 31.8 b 26.5 34.2 43.0 32.9 35.2 32.2 34.0 c 34. 1 29.9 26.3 26.5 33.2 33.9 30.6 d 43.0 33.6 27.6 39.2 37. 1 31.1 35.3 e 28.8 34.2 12.7 29.7 30.0 29.9 27.6 f 45.0 31.1 31.1 22.5 34.2 16.7 30. 1 mean 35.8 31.4 29.3 31.3 33.7 27.8 31.6 g h i j k 1 mean a 21 .0 29.6 30.7 29.6 32.5 23. 1 27.8 b 17.3 31.0 28. 1 30.8 32.2 25.6 27.5 c 20.8 27.0 36.5 24.5 29.6 28.4 27.8 d 27.8 44.4 28.0 28.8 28.2 32.3 31.6 e 18.4 34.5 19.4 20.5 35.7 26.2 25.8 f 20.4 40.7 30.2 35.8 26.0 38.5 31.9 mean 21.0 34.5 28.8 28.3 30.7 29.0 28.7 g h i j k 1 mean a 40. 1 34.2 36.4 42.0 39.2 37.7 38.3 b 32.3 38.2 25. 1 31 .0 25.6 21 .3 28.9 c 31.1 34.2 31.7 35.6 31 .7 40.5 34. 1 d 22.5 32.6 40.8 38.4 37.3 31.7 33.9 e 28.8 34.5 28. 1 25.3 30. 1 29.9 29.4 f 28.8 36.5 32. 1 32.4 29.9 39. 1 33. 1 mean - 30.6 35.0 32.4 34. 1 32.3 33.3 33.0 66 that pathogenicity, in the case of the descendants of a cross between Tapke's race 7 and 11, i s controlled by a number of factors (Person, personal communication). Table 5 l i s t s the ov e r a l l means, variances and other s t a t i s t i c s of the DL's on the two v a r i e t i e s . The average disease reading on Odessa was almost 50% higher than that on Trebi, but at the same time, the average phenotypic v a r i a b i l i t y was 25% higher on T than on 0. Table 6 displays the ANOVA diagnostics for the data compiled in the six grids representing the treatments of the three DL's on both v a r i e t i e s . A l l possible combinations and permutations of factors gave 19 possible sources of v a r i a b i l i t y , where, the highest order interaction source was redefined as the error source. The low error mean square indicates that the magnitude of the technical (experimental) error was not unusual. In addition the v a r i e t i e s were s i g n i f i c a n t l y d i f f e r e n t . This i s not a surprising result because of the vastly d i f f e r e n t readings of the parental teliospores on the two v a r i e t i e s . This s-uggests that the v a r i e t i e s d i f f e r e d s i g n i f i c a n t l y in their resistance genotypes. The genotypic difference probably r e f l e c t s the presence in T of at least one race-specific resistance gene. Within the treatments both the "+" and "-" sporidia showed s i g n i f i c a n t differences r e f l e c t i n g the segregation of pathogenicity polygenes in the F2 to both mating types. The s i g n i f i c a n t interaction of v a r i e t i e s with treatments also indicates the existence of a gene(s) for s p e c i f i c e f f e c t . 67 Figure 3a. Frequency d i s t r i b u t i o n s of the disease levels on Trebi for the 36 F2 treatment dikaryons from DL 17, 21 and 23, respectively. Figure 3b. Frequency d i s t r i b u t i o n s of the disease levels on Odessa for the 36 F2 treatment dikaryons from DL 17, 21 and 23, respectively. DL 17 15 Figure 3a i(H cr 5H 10 20 30 40 — i 50 DL 21 15T cr 10 20 30 40 — l 50 DL 23 15T 10H cr 0) 5H 10 20 30 Transformed disease readings 40 50 DL 17 15n Figure 3b 10H cr CD 5H DL 21 15 n 10-CD 5H P L 23 15n 10H or 9) 5H 4=1 10 20 30 40 50 10 20 30 40 50 10 20 30 40 Transformed disease readings -1 50 70 Figure 4. Frequency d i s t r i b u t i o n of the disease lev e l s for the 108 treatment dikaryons combined (from DL 17, 21 and 23) on Trebi (top) and Odessa (bottom). Trebi 40n cr 9 20H ion Figure 4 10 20 30 40 50 Odessa 40n 30H cr CD 20H 10 20 30 40 50 Transformed disease readings 72 Table 5. Fundamental s t a t i s t i c s compiled for the six grids ( i . e . , 3 treatment grids on 2 v a r i e t i e s ) . 73 Table 5 VARIETY DL N MEAN VARIANCE ST. DEV. SE MIN MAX T 1 7 36 22.0 35.89 5.99 1 .00 8.0 32.8 T 21 36 22.9 54.09 7.35 1 .23 5.7 36.0 T 23 36 20.3 51 .20 7.16 1.19 6.1 31.1 0 1 7 36 31.6 44.29 6.65 1.11 12.7 45.0 0 21 36 28.7 39.92 6.32 1 .05 17.3 44.4 0 23 36 33.0 28.02 5.29 0.88 21.3 42.0 N = sample size; ST. DEV. = standard deviation; SE = standard error; MIN = minimum disease reading; MAX = maximum disease reading 74 Table 6. ANOVA components for pathogenicity readings of the three DL's on the two v a r i e t i e s . 7fT Table 6 SOURCE DF MS VR p 1. var 1 14244. 22 22 .775(3) 0. 01 -0.05 2. DL 2 59. 06 0 .346(9) > 0. 05 3. var x DL 2 625. 44 3 .664(9) > 0. 05 4. treat 1 05 87. 94 1 .722(11 ) < 0. 01 a . + sporidia 1 5 1 94. 23 3 .434(4c) < 0. 001 b . - sporidia 1 5 1 38. 53 2 .440(4c) < 0. 01 c . + x - 75 56. 56 1 .140(12) > 0. 05 5. var x treat 1 05 64. 76 1 . 268(11) 0. 01 -0.05 a . var x + 1 5 66. 19 0 .994(5c) > 0. 05 b . var x - 1 5 54. 30 0 .816(5C) > 0. 05 c . var x + x - 75 66. 56 1 .341(12) > 0. 05 6. rep 2 366. 80 7 .187(11) < 0. 001 7. var x rep 2 383. 92 7 .522(11) < 0. 001 8. DL x rep 4 171. 68 1 .001(9) > 0. 05 9. var x DL x rep 4 1 70. 70 3 .344(11) 0. 01 -0.05 10. treat x rep 210 51 . 1 7 1 .003(11) > 0. 05 a . + x rep 1 5 110. 04 2 . 1 88(10c) 0. 01 -0.05 b . - x rep 1 5 59. 40 1 . 181(10c) > 0. 05 c . + x - x rep 75 50. 30 1 .014(12) > 0. 05 1 1 . var x treat x rep 210 51 . 04 a . var x + x rep 75 1 22. 90 2 .477(12) < 0. 001 b . var x - x rep 75 52. 30 1 •054(12) > 0. 05 12. error 60 49. 62 647 DF = degrees of freedom; MS = mean square; VR = variance r a t i o ; P = probability of s i g n i f i c a n t differences; var = v a r i e t i e s ; DL = dikaryotic l i n e s ; treat = treatments; + = + sporidia; - = - sporidia; rep = re p l i c a t e s ; error = residual error; x = denotes interaction. For t h i s and subsequent tables, source abbreviations are as follows: var = v a r i e t i e s rep = replicates DL = dikaryotic lines + = "+" mating type - = "-" mating type treat = treatments error = residual error 76 B a s e d on t h e s i g n i f i c a n t v a r i e t a l d i f f e r e n c e s , t h i s g e n e ( s ) o f s p e c i f i c e f f e c t c an be c o n s i d e r e d t o be a v i r u l e n c e g e n e ( s ) . P e r s o n ( p e r s o n a l c o m m u n i c a t i o n ) f o u n d e v i d e n c e f o r t h e s e g r e g a t i o n o f a s i n g l e v i r u l e n c e gene i n t h i s s y s t e m . S i n c e t h e r e i s no e v i d e n c e f o r t h e e x i s t e n c e of more t h a n one f a c t o r , s u b s e q u e n t d i s c u s s i o n of t h i s v i r u l e n c e f a c t o r w i l l be i n t h e s i n g u l a r f o r m . The r e p l i c a t e e n v i r o n m e n t s were s i g n i f i c a n t l y d i f f e r e n t a s were t h e i n t e r a c t i o n s of t h e v a r i e t i e s w i t h t h e r e p l i c a t e e n v i r o n m e n t s and t h e v a r i e t i e s w i t h t h e DL's o v e r t h e r e p l i c a t e e n v i r o n m e n t s . W i t h i n t h e t r e a t m e n t x r e p l i c a t e s o u r c e t h e i n t e r a c t i o n s of t h e "+" s p o r i d i a w i t h t h e r e p l i c a t e e n v i r o n m e n t s were s i g n i f i c a n t l y d i f f e r e n t . T h i s same s o u r c e f a c t o r , i n t e r a c t i n g w i t h t h e v a r i e t i e s , showed s i g n i f i c a n t d i f f e r e n c e s . To g e t an i d e a of t h e c o n t r i b u t i o n of e a c h o f t h e s e f a c t o r s , most i m p o r t a n t l y t h e s i g n i f i c a n t o n e s , t o t h e t o t a l p a t h o g e n i c v a r i a b i l i t y , t h e a c t u a l v a r i a n c e v a l u e s were c a l c u l a t e d . From t h e s e numbers r e l a t i v e v a r i a n c e v a l u e s were d e r i v e d and were e x p r e s s e d as p e r c e n t a g e s of t h e t o t a l p h e n o t y p i c v a r i a n c e . These a r e shown i n T a b l e 7. Of t h e s o u r c e s d i s p l a y i n g s i g n i f i c a n t d i f f e r e n c e s , t h e l a r g e s t r e l a t i v e v a r i a n c e , 34%, was c a u s e d by t h e v a r i e t i e s , w h i l e t h e summed r e l a t i v e v a r i a n c e s of t h e o t h e r s i s j u s t under 15% w i t h t h e h i g h e r o r d e r r e p l i c a t e i n t e r a c t i o n s a c c o u n t i n g f o r n e a r l y h a l f t h i s f i g u r e . The r e l a t i v e v a r i a b i l i t y g e n e r a t e d by t h e p o l y g e n i c d i f f e r e n c e s (5.69%) was g r e a t e r t h a n t h a t g e n e r a t e d by t h e v i r u l e n c e gene ( 4 . 1 8 % ) . In i n t e r a c t i o n s w i t h t h e e n v i r o n m e n t t h e 77 virulence gene produced 3.6% of the t o t a l v a r i a b i l i t y , whereas the polygenes were responsible for only 1.29%. This result indicates that the interaction of the virulence gene with the environment is of greater importance in generating variance than is the interaction of the polygenes with the environment. Of the nonsignificant sources, the largest contributor was the residual error making up 40% of the t o t a l . This i s not an unusually high t o t a l . The genetic differences between the sporidia were responsible for just under 6% of that t o t a l . These results show no relationship between the l e v e l of r e l a t i v e v a r i a b i l i t y produced by a source of v a r i a b i l i t y and the presence of s i g n i f i c a n t differences within i t . An additional analysis was performed separately on the T and 0 data (Table 8). On T the three DL's were s t a t i s t i c a l l y s i m i l a r . This indicated that these three sample populations could be considered to be samples drawn from the same large population. Within the treatment source there were large differences between the genotypes of the "+" sporidia which reveals the segregation of pathogenicity genes in the F2 progeny. The replicate environments were highly d i f f e r e n t . The interactions of the DL's with the replicate environments were s i g n i f i c a n t as were the interactions of the "+" sporidia with the r e p l i c a t e s . On 0 the DL's were s i g n i f i c a n t l y d i f f e r e n t in their action r e f l e c t i n g gross differences in the genotypes of three randomly sampled DL populations with respect to their action on 0. Neither of the s p o r i d i a l types showed s i g n i f i c a n t 78 T a b l e 7. Components o f v a r i a n c e f o r p a t h o g e n i c i t y r e a d i n g s g i v e n i n T a b l e 6. P e r c e n t a g e s o f t h e t o t a l p h e n o t y p i c v a r i a n c e a r e g i v e n as r e l a t i v e v a r i a n c e s . T a b l e 7 SOURCE ' 1 . v a r 2. DL 3. v a r x DL 4. t r e a t a. + s p o r i d i a b. - s p o r i d i a c . + x -5. v a r x t r e a t a . v a r x + b. v a r x -c. v a r x + x -6. r e p 7. v a r x r e p 8. DL x r e p 9. v a r x DL x r e p 10. t r e a t x r e p a. + x r e p b. - x r e p • c . + x - x r e p 11. v a r x t r e a t x r e p a. v a r x + x r e p b. v a r x - x r e p 12. e r r o r VARIANCE REL VARIANCE 42.04 34.25 0.00 0.00 5.29 4.30 3.82 3.10 2.28 1 .85 0.91 0.74 0.00 0.00 0.00 0.00 5.15 4.18 1 .46 1.19 1 .97 1 .60 1.19 0.97 3.34 2.71 0.98 0.80 0.25 0.20 0.36 0.29 4.43 3.60 0.00 0.00 49.62 40.32 80 differences but the interaction of the two did, i l l u s t r a t i n g the importance of dominance and/or e p i s t a s i s in t h i s system. The replicate environments were not d i f f e r e n t while the interaction of the "+" sporidia with the replicates did show s i g n i f i c a n t differences and displays the importance of the interactions of the pathogenicity genes with the environment in producing v a r i a b i l i t y . Table 9 l i s t s the actual and r e l a t i v e variances for T and O from the sources. For both the v a r i e t i e s , over 50% of the v a r i a b i l i t y was caused by residual error. The next highest contributing source was the interaction between the "+" sporidia and the environment with the value for 0 being twice that for T. The • v a r i a b i l i t i e s produced by genetic differences between sporidia amounted to roughly 15% and 19% of the t o t a l for T and 0 respectively. .The interaction between sporidia comprised approximately 44% and 61% of these values. The main ef f e c t s differences in sporidia were more important in contributing to the t o t a l genetic variation on T than on 0. The reverse was true for the differences in interactions of the two s p o r i d i a l types. Analyses of variance were run separately for the three DL's (Table 10) on T and 0 simultaneously. For DL 17 s i g n i f i c a n t differences were found between the v a r i e t i e s which i s not an unexpected r e s u l t . The "-" sporidia and the interactions of the sporidia were also s i g n i f i c a n t . This finding r e f l e c t s the r e l a t i v e s i m i l a r i t y in function of the polygenes in the "+" sporidia. The s p e c i f i c interaction of the v a r i e t i e s with the "+" sporidia and the interaction of the v a r i e t i e s with the s p o r i d i a l 81 Table 8 . ANOVA components for pathogenicity readings of the three DL's on each variety. T a b l e 8 TREBI SOURCE DF MS VR p 1. DL 2 184. 74 4 .157(6) > 0. 05 2. t r e a t 1 05 74. 61 1 .366(5) 0 .01 -0.05 a . + s p o r i d i a 1 5 1 48. 72 2 •526(2c) < 0. 01 b . - s p o r i d i a 1 5 79. 18 1 .345(2c) > 0. 05 c . + x - 75 58. 87 1 .325(6) > 0. 05 3. r e p 2 738. 42 1 3 .517(5) < 0. 01 4. DL x r e p 4 270. 68 6 .091(5) < 0. 01 5. t r e a t x r e p 214 54. 63 b . + x r e p 30 97. 1 5 2 .186(5) < 0. 01 c . - x r e p 30 34. 24 0 .771(5) > 0. 05 6. e r r o r 1 50 44. 44 323 ODESSA SOURCE DF MS VR p 1. DL 2 499 .77 1 2 .627(6) < 0. 01 2. t r e a t 1 05 78 .09 1 .500(5) 0. 01 -0.05 a . + s p o r i d i a 15 1 1 1 .69 1 .738(2c) > 0. 05 b . - s p o r i d i a 15 1 1 3 .65 1 .769(2c) > 0. 05 c . + x - 75 64 .26 1 .624(6) < 0. 01 3. r e p 2 1 2 .30 0 .236(5) > 0. 05 4. DL x r e p 4 71 .70 1 .812(6) > 0. 05 5. t r e a t x r e p 214 52 .07 b . + x r e p 30 1 34 .91 3 .409(6) < 0. 001 c . - x r e p 30 29 .07 0 .735(6) > 0. 05 6. e r r o r 1 50 39 .58 323 83 Table 9. Components of variance for pathogenicity readings given in Table 8. Percentages of the t o t a l phenotypic variance are given as r e l a t i v e variances. T a b l e 9 TREBI SOURCE VARIANCE REL VARIANCE 1 . DL 0.15 0.20 2. t r e a t a. + s p o r i d i a 4.99 6.73 b. - s p o r i d i a 1.13 1 .52 c. + x - 4.81 6.49 3. r e p 4.74 6.39 4. DL x r e p 5.10 6.88 5. t r e a t x r e p b. + x r e p 8.79 11.86 c . - x r e p 0.00 0.00 6. e r r o r 44.44 59.94 ODESSA SOURCE VARIANCE REL VARIANCE 1 . DL 3.14 4.35 2. t r e a t a. + s p o r i d i a 2.63 3.65 b. - s p o r i d i a 2.74 3.79 c. + x - 8.23 1 1 .40 3. r e p 0.00 0.00 4. DL x r e p 0.00 0.00 5. t r e a t x r e p b. + x r e p 15.89 22.01 c . - x r e p 0.00 0.00 6. e r r o r 39.58 54.81 85 i n t e r a c t i o n s were s i g n i f i c a n t l y d i f f e r e n t . T h e s e r e s u l t s i m p l y t h e e x i s t e n c e o f a s e g r e g a t i n g p a t h o g e n i c i t y gene and a t t e n d a n t dominance and e p i s t a t i c e f f e c t s t h a t s p e c i f i c a l l y i n t e r a c t w i t h one o f t h e v a r i e t i e s ( i . e . , a v i r u l e n c e g e n e ) . The r e p l i c a t e s and t h e i n t e r a c t i o n s o f t h e v a r i e t i e s w i t h t h e r e p l i c a t e e n v i r o n m e n t s were s i g n i f i c a n t . The i n t e r a c t i o n of t h e "+" s p o r i d i a w i t h t h e e n v i r o n m e n t and of t h e s p o r i d i a l i n t e r a c t i o n s w i t h t h e r e p l i c a t e s i s i n t e r p r e t e d t o mean t h a t t h e p o l y g e n e s i n t h e "+" s p o r i d i a and t h e dominance and e p i s t a t i c d i f f e r e n c e s a s s o c i a t e d w i t h t h e "+ x -" i n t e r a c t i o n s r e a c t d i f f e r e n t l y t o e n v i r o n m e n t a l p a r a m e t e r s . The i n t e r a c t i o n s of t h e v a r i e t i e s w i t h t h e "+" s p o r i d i a t y p e o v e r t h e r e p l i c a t e s and t h e i n t e r a c t i o n s o f t h e v a r i e t i e s w i t h t h e "-" s p o r i d i a o v e r t h e r e p l i c a t e s were s i g n i f i c a n t l y d i f f e r e n t . S i m i l a r l y , f o r DL 21 s i g n i f i c a n t d i f f e r e n c e s were f o u n d between t h e v a r i e t i e s , t h e "+" s p o r i d i a , t h e s p o r i d i a l i n t e r a c t i o n s , t h e i n t e r a c t i o n s of t h e v a r i e t i e s w i t h t h e s p o r i d i a l i n t e r a c t i o n s , t h e r e p l i c a t e s , t h e i n t e r a c t i o n of t h e v a r i e t i e s w i t h t h e r e p l i c a t e s , t h e i n t e r a c t i o n s of t h e "+" s p o r i d i a w i t h t h e r e p l i c a t e e n v i r o n m e n t s and t h e i n t e r a c t i o n s o f t h e v a r i e t i e s w i t h t h e "+" s p o r i d i a o v e r t h e r e p l i c a t e s . I n t e r p r e t a t i o n s o f t h e s e r e s u l t s a r e s i m i l a r t o t h o s e m e n t i o n e d above f o r DL 17. S i g n i f i c a n t d i f f e r e n c e s w i t h i n DL 23 s o u r c e s were f o u n d between t h e v a r i e t i e s , t h e "+" s p o r i d i a , t h e "-" s p o r i d i a , t h e i n t e r a c t i o n s o f t h e "+" s p o r i d i a w i t h t h e r e p l i c a t e s , and t h e i n t e r a c t i o n s o f t h e v a r i e t i e s w i t h t h e "+" s p o r i d i a o v e r t h e 86 Table 1 0 . ANOVA components for pathogenicity readings of each DL on the two v a r i e t i e s . 87 T a b l e 10 DL 17 SOURCE DF MS VR p 1 . v a r 1 491 6 .58 90 .485(3) < 0. 001 2. t r e a t 35 86 .55 2 .496(7) < 0. 01 a. + s p o r i d i a 5 1 38 .61 2 .495(2c) > 0. 05 b. - s p o r i d i a 5 189 .43 3 .410(2c) 0 .01 -0.05 c . + x - 25 55 .56 6 .561(8) < 0. 001 3. v a r x t r e a t 35 54 .83 1 .581(7) 0 .01 -0.05 a. v a r x + 5 1 07 .80 2 .651(3c) 0 .01 -0.05 b. v a r x - 5 72 .73 1 .789(3c) > 0. 05 c . v a r x + x - 25 40 .66 4 .802(8) < 0. 001 4. r e p 2 97 .96 2 .826(7) > 0. 05 5. v a r x r e p 2 461 .95 1 3 .324(7) 0 .01 -0.05 6. t r e a t x r e p 70 58 .53 1 .683(7) 0 .01 -0.05 a. " + x r e p 10 1 43 . 1 5 3 .352(6c) < 0. 01 b. - x r e p 1 0 51 .75 1 .212(6c) > 0. 05 c . + x - r e p 50 42 .71 5 .043(8) < 0. 00T 7. v a r x t r e a t x r e p 70 34 .67 a. v a r x + x r e p 1 2 141 .88 16 .755(8) < 0. 001 b. v a r x - x r e p 12 1 03 .48 1 2 .221(8) < 0. 001 . e r r o r 46 8 .47 215 T a b l e 10 ( c o n t i n u e d ) DL 21 SOURCE DF MS VR p 1. v a r 1 1863. 36 25 .575(3) < 0. 001 2. t r e a t 35 112. 85 2 .310(7) < 0. 01 a . + s p o r i d i a 5 254. 34 3 .042(2c) 0. 01 -0.05 b . - s p o r i d i a 5 117. 54 1 .406(2c) > 0. 05 c . + x - 25 83. 61 2 .386(8) < 0. 01 3. v a r x t r e a t 35 72. 86 1 .492(7) > 0. 05 a . v a r x + 5 55. 41 0 •757(3c) > 0. 05 b . v a r x - 5 88. 47 1 .208(3c) > 0. 05 c . v a r x + x - 25 73. 22 2 .089(8) 0. 01 -0.05 4. r e p 2 605. 97 1 2 .405(8) < 0. 001 5. v a r x r e p 2 245. 74 5 .030(7) < 0. 01 6. t r e a t x r e p 70 50. 65 1 .037(7) > 0. 05 a . + x r e p 1 0 96. 76 2 •048(6c) 0. 01 -0.05 b . - x r e p 1 0 21 . 60 0 .457(6c) > 0. 05 c . + x - x r e p 50 47. 24 1 .348(8) > 0. 05 7. v a r x t r e a t x r e p 70 48. 85 a . v a r x + x r e p 1 2 1 20. 89 3 .449(8) < 0. 01 b . v a r x - x r e p 1 2 64. 80 1 .849(8) > 0. 05 8. e r r o r 46 35. 05 215 T a b l e 10 ( c o n t i n u e d ) DL 23 SOURCE DF MS VR p 1. v a r 1 8670. 1 7 1 30.23(3) < 0. 001 2. t r e a t 35 64. 42 0.925(7) > 0. 05 a. + s p o r i d i a 5 189. 73 6.216(2c) < 0. 001 b. - s p o r i d i a •5 108. 63 3.559(2c) 0. 01 -0.05 c . + x - 25 30. 52 0.548(8) > 0. 05 3- v a r x t r e a t 35 66. 58 0.957(7) > 0. 05 a. v a r x + 5 35. 35 0.412(3c) > 0. 05 b. v a r x - 5 1 . 71 0.020(3c) > 0. 05 c . v a r x + x - 25 85. 79 1 .540(8) > 0. 05 4. r e p '2 6. 24 0.090(7) > 0. 05 5. v a r x r e p 2 17. 64 0.253(7) > 0. 05 6. t r e a t x r e p 70 44. 51 0.639(7) > 0. 05 a. + x r e p 10 101. 83 2.692(6c) 0. 01 -0.05 b. - x r e p 1 0 20. 56 0.544(6c) > 0. 05 c . + x - x r e p 50 37. 83 0.679(8) > 0. 05 7. v a r x t r e a t x r e p 70 69. 61 a. v a r x + x r e p 12 1 53. 48 2.754(8) < 0. 01 b. v a r x - x r e p 1 2 32. 63 0.586(8) > 0. 05 8. e r r o r 46 55. 72 215 90 r e p l i c a t e s . Interpretations of these results can be obtained from explanations of similar results for DL 17. Table 10 reveals that for a l l three DL's l i k e sources were not always s i g n i f i c a n t . The actual and r e l a t i v e variances in Table 11 derived from Table 10 shows that, in general, v a r i e t a l differences generated the largest portion of the t o t a l pathogenic v a r i a b i l i t y , followed by the residual error and the interactions of the v a r i e t i e s with one s p e c i f i c sporidia over the replicates ( i . e . , reaction of the virulence gene with the environment). The other sources l i s t e d in the table contribute to varying degrees. In two DL's, over 50% of the polygenic v a r i a b i l i t y can be attributed to non-additive (dominance and e p i s t a t i c ) e f f e c t s . Focusing attention on the polygene main-effect sources an interesting pattern emerged. S i g n i f i c a n t differences appeared in one of the s p o r i d i a l sources and/or in interaction sources exclusively involving one of the s p o r i d i a l types, p a r t i c u l a r l y in interactions involving the v a r i e t i e s . The pattern i s indicative of a s p e c i f i c factor(s) t i g h t l y linked to the mating locus that segregate in the F2. The interaction of one of the sporidia with the replicate environments also indicates the segregation of a factor(s) linked to the mating locus that i s environmentally sensitive. Within both the treatment and the variety x treatment source groups, for the 3 DL's, a l l factors involving "+ x -" interactions, with one exception, produced more r e l a t i v e v a r i a b i l i t y than the main-effect factors within each group. This 91 Table 11. Components of variance for pathogenicity readings given in Table 10. Percentages of the t o t a l phenotypic variance are given as r e l a t i v e variances. T a b l e 1 1 DL 17 SOURCE VARIANCE REL VARIANCE 1 . v a r 2. t r e a t a. + s p o r i d i a b. - s p o r i d i a c . + x -3. v a r x t r e a t a. v a r x + b. v a r x -c. v a r x + x -4. r e p 5. v a r x r e p 6. t r e a t x r e p a. + x r e p b. - x r e p c. + x - x r e p 7. v a r x t r e a t x r e p a. v a r x + x r e p b. v a r x - x r e p 8. e r r o r 44.64 27.87 2.31 1 .44 3.72 2.32 7.85 4.90 3.73 2.33 1 .78 1.11 10.73 6.70 0.00 0.00 1 2.60 7.87 8.37 5.23 0.75 0.47 17.12 1 0.69 22.24 1 3.89 1 5.84 9.89 8.47 5.29 T a b l e 11 ( c o n t i n u e d ) DL 21 SOURCE VARIANCE REL VARIANCE 1. v a r 16. 60 13. 63 2. t r e a t a. + s p o r i d i a 4. 74 3. 89 b. - s p o r i d i a 0. 94 0. 77 c . + x - 8. 09 6. 64 3. v a r x t r e a t a. v a r x + 0. 00 0. 00 b. v a r x - 0. 85 0. 70 c. v a r x + x - 12. 72 10. 45 4. r e p 7. 43 6. 10 5. v a r x r e p 5. 85 4. 80 6- t r e a t x r e p a. + x r e p 4. 13 3. 39 b. - x r e p 0. 00 0. 00 c. + x - x r e p 6. 09 5. 00 7. v a r x t r e a t x r e p a. v a r x + x r e p 14. 31 1 1 . 75 b. v a r x - x r e p 4. 96 4. 07 8. e r r o r 35. 05 28. 79 T a b l e 11 ( c o n t i n u e d ) DL 23 SOURCE VARIANCE REL VARIANCE 1. v a r 80. 73 46.22 2. t r e a t a. + s p o r i d i a 4. 42 2.53 b. - s p o r i d i a 2. 1 7 1 .23 c . + x - 0. 00 0.00 3. v a r x t r e a t a. v a r x + 0. 00 0.00 b. v a r x - 0. 00 0.00 c . v a r x + x - 10. 02 5.74 4. r e p 0. 00 0.00 5. v a r x r e p 0. 00 0.00 6. t r e a t x r e p a. + x r e p 5. 33 3.05 b. - x r e p 0. 00 . 0.00 c . + x - x r e p 0. 00 0.00 7. v a r x t r e a t x r e p a. v a r x + x r e p 16. 29 ' 9.33 b. v a r x - x r e p 0. 00 0.00 8. e r r o r 55. 72 31 .90 95 again demonstrates the presence and importance of e p i s t a s i s and/or dominance functioning on the polygene and major gene l e v e l . By comparing treatment factors (2a-b) with treatment x rep l i c a t e factors (6a-b), and s i m i l a r l y , variety x treatment factors (3a-b) with variety x treatment x r e p l i c a t e factors (7a-b), for each DL, i t can be seen that the environment can interact with the polygenes and the virulence gene to s i g n i f i c a n t l y increase or decrease the expected v a r i a b i l i t y . In a f i n a l breakdown of the data the six grids were analysed separately (Table 12). For the three T grids a l l s p o r i d i a l main effects were s i g n i f i c a n t l y d i f f e r e n t . A l l interactions and a l l , but one, of the re p l i c a t e environments were s i g n i f i c a n t l y d i f f e r e n t . For the three 0 grids only two s p o r i d i a l main effects were s i g n i f i c a n t l y d i f f e r e n t . A l l interactions and a l l , but one, replicate environments were s i g n i f i c a n t l y d i f f e r e n t . No additional information about the virulence gene or polygenes could be extracted from Table 12. Table 13 gives the actual and r e l a t i v e contributions to pathogenic variance of the six grids. Table 14 l i s t s the actual and r e l a t i v e genetic contributions to v a r i a b i l i t y taken from Table 13. The average contribution of the additive genetic variance (narrow sense h e r i t a b i l i t y ) on the three DL's to the t o t a l pathogenic v a r i a b i l i t y i s 38% on T, which i s nearly three times that on 0 (14%). The average contribution of the genetic variance (broad sense h e r i t a b i l i t y ) to the t o t a l phenotypic v a r i a b i l i t y i s 59% 96 Table 12 . ANOVA components for pathogenicity readings of each DL on each variety. T a b l e 12 VARIETY DL SOURCE DF MS VR p T 1 7 + s p o r i d i a 5 223.17 3 .878 < 0.01 - s p o r i d i a 5 242.78 4 .218 < 0.01 + x - 25 57.55 1 .737 0. 01-0. 05 r e p s 2 1 17.57 3 .548 0. 01-0. 05 e r r o r 70 33.14 1 07 T 21 + s p o r i d i a 5 376.59 4 .903 < 0.01 - s p o r i d i a 5 375.27 4 .886 < 0.01 + x - 25 76.81 2 .452 < 0.01 r e p s 2 1 6.52 0 .527 > 0.05 e r r o r 70 31.33 1 07 T 23 + s p o r i d i a 5 428.43 5 .393 < 0.01 - s p o r i d i a 5 249.42 3 . 1 39 0. 01-0. 05 + x - 25 79.45 4 .645 < 0.001 r e p s 2 99.79 5 .834 < 0.01 e r r o r 70 17.10 1 07 T a b l e 12 ( c o n t i n u e d ) VARIETY DL SOURCE DF MS VR 0 17" + s p o r i d i a 5 150.96 1 .181 - s p o r i d i a 5 139.96 1 .095 + x - 25 127.81 6 .513 r e p s 2 116.18 5 .920 e r r o r 70 1 9.62 1 07 0 21 + s p o r i d i a 5 354.62 4 .746 - s p o r i d i a 5 110.22 1 .475 + x - 25 74.71 2 .101 r e p s 2 290.57 8 . 1 72 e r r o r 70 35.56 1 07 0 23 + s p o r i d i a 5 44.06 0 .664 - s p o r i d i a 5 212.61 3 .204 + x - 25 66.36 1 .699 r e p s 2 86.36 2 .214 e r r o r 70 39.05 1 07 > 0.05 > 0.05 < 0.001 < 0.01 < 0.01 > 0.05 < 0.01 < 0.001 > 0.05 0.01-0.05 0.01-0.05 > 0.05 99 Table 13. Components of variance for pathogenicity readings given in Table 12. Percentages of the t o t a l phenotypic variance are given as r e l a t i v e variances. /oo T a b l e 13 VARIETY DL I? + II 11 _ 1! "+ X _ » REPS ERROR TOTAL T 17 9.20 (14.58) 10. (16. 29 30) 8. (12. 1 4 90) 2.35 (3.72) 33. 14 (52.50) 63. 1 2 T 21 16.65 (20.89) 16. (20. 58 80) 15. (19. 1 6 02) 0.00 (0.00) 31 .33 (39.30) 79.72 T 23 19.39 (28. 10) 9. (13. 44 68) 20. (30. 78 1 1 ) 2.30 (3.33) 17.10 (24.78) 69.01 VARIETY DL II _ j _ H II _ "+ X _ II REPS ERROR TOTAL 0 17 1 .29 (2.14) 0. (1 . 68 13) 36. (59. 06 77) 2.68 (4.44) 19.62 (32.52) 60.33 0 21 1 5.55 .(21.24) 1 . (2. 97 69) 13. (17. 08 82) 7.08 (9.67) 35.56 (48.57) 73.22 0 23 0.00 8. 1 3 9. 1 0 1.31 39.05 57.59 (0.00) (14.12) (15.80) (2.27) (67.81) 1 0 1 . Table 14. Actual and r e l a t i v e contributions of the additive and the genetic components for each DL on each variety. Relative variances expressed as percentages of the t o t a l phenotypic variance are given in brackets. T a b l e 14 VARIETY DL Va Vg (Va/Vg)lOO 17 19.49 27.63 (30.88) (43.78) (70.53) 21 3.3.23 48.39 (41.69) (60.71) (68.67) 23 28.83 49.61 (41.78) (71.89) (58.12) mean 27. 18 41.88 (38.12) (58.79) (65.77) VARIETY DL Va Vg ( V a / V g ) l 0 0 0 17 0 21 0 23 mean 1 .97 ( 3.27) 17.52 (23.93) 8.13 (14.12) 9.21 (13.77) 38.03 (63.04) 30.60 (41.75) 17.23 (29.92) 28.62 (44.90) ( 5.19) (57.32) (47. 19) (36.57) Va = a d d i t i v e g e n e t i c v a r i a n c e ; Vg = t o t a l g e n e t i c v a r i a n c e ; ( V a / V g ) l 0 0 = r e l a t i v e c o n t r i b u t i o n of a d d i t i v e g e n e t i c v a r i a n c e t o t o t a l g e n e t i c v a r i a n c e . 1 03 on T and 45% on 0. T h i s i n d i c a t e s t h a t , on t h e a v e r a g e , t h e a d d i t i v e v a r i a n c e of t h e t h r e e DL's i s r e s p o n s i b l e f o r 65% o f t h e t o t a l g e n e t i c v a r i a n c e on T and a p p r o x i m a t e l y h a l f t h a t amount on 0. The n o n - a d d i t i v e g e n e t i c component i s t w i c e as i m p o r t a n t i n g e n e r a t i n g g e n e t i c v a r i a t i o n on 0 t h a n on T, a l t h o u g h t h e m a g n i t u d e of t h e a c t u a l a d d i t i v e and n o n - a d d i t i v e g e n e t i c v a r i a n c e components were l a r g e r on T. R e g r e s s i o n A n a l y s i s A m o d i f i c a t i o n of a method d e v e l o p e d by J i n k s (1954) a l l o w e d p l o t t i n g of t h e r e g r e s s i o n o f t h e v a r i a n c e ( V r ) w i t h i n e a c h ( m o n o k a r y o t i c p a r e n t ) a r r a y on t h e c o v a r i a n c e (-Wr' ) w i t h i n a r r a y s w i t h t h e means of t h e a r r a y s of t h e noncommon p a r e n t s (Simchen and J i n k s 1964). The r e g r e s s i o n o f V r on Wr' was p l o t t e d f o r e a c h a r r a y of t h e 6 g r i d s ( F i g u r e 5 ) . S l o p e s r a n g e d from 0.5052 t o 0.08906 and Wr' i n t e r c e p t s f e l l between 7.1.40 and -6.005. T a b l e 15 shows t h e p r o b a b i l i t i e s of t h e r e g r e s s i o n s l o p e s b e i n g s i g n i f i c a n t l y d i f f e r e n t f r o m 0.5 and 0.0. The f o r m u l a u s e d f o r t h e s e c a l c u l a t i o n s i s shown i n A p p e n d i x I I . O n l y g r a p h s 5B-, 5D- and 5F+ show s l o p e s s i g n i f i c a n t l y d i f f e r e n t from 0.5. T h e s e s l o p e s d e v i a t e d from 0.5 due t o t h e i n v o l v e m e n t of e p i s t a s i s . F u r t h e r a n a l y s i s of t h e r e g r e s s i o n s showed t h e i n v o l v e m e n t of dominance and e p i s t a s i s ( T a b l e 1 6 ) . T h e r e was no c o r r e l a t i o n between t h e s p o r i d i a l r a n k i n g s i n t h e s e g r a p h s and t h e r a n k i n g s d e r i v e d f r o m t h e a r r a y means i n T a b l e 4. 104 F i g u r e 5. Wr'/Vr r e g r e s s i o n s i l l u s t r a t i n g t h e r e l a t i v e m a g n i t u d e s of dominant and e p i s t a t i c n o n - a d d i t i v e g e n e t i c e f f e c t s of t h e t r e a t m e n t s p o r i d i a ( p l o t t e d p o i n t s a-1) from t h e t h r e e DL's on T r e b i and O d e s s a ( g r a p h s A-C and D-F r e s p e c t i v e l y ) . A l l g r a p h s l a b e l l e d "+" r e p r e s e n t t h e r e g r e s s i o n o f t h e "+" m a t i n g t y p e s p o r i d i a and t h o s e l a b e l l e d "-" a r e t h e "-" m a t i n g t y p e r e g r e s s i o n s . L i n e s h a v i n g a s l o p e s i g n i f i c a n t l y d i f f e r e n t f r o m 0.5 r e v e a l t h e a c t i o n of e p i s t a t i c gene e f f e c t s . A l i n e of b e s t f i t i n t e r s e c t i n g t h e Y a x i s above 0 i n d i c a t e s i n c o m p l e t e d ominance. P l o t t e d p o i n t s n e a r t h e o r i g i n r e p r e s e n t s p o r i d i a p o s s e s s i n g t h e most dominant g e n e s . Those f a r t h e s t from t h e o r i g i n a r e t h e s p o r i d i a w i t h t h e l e a s t d o m i n a n t g e n e s . S p o r i d i a l o c a t e d between t h e s e e x t r e m e s have i n t e r m e d i a t e numbers of dominant ' p a t h o g e n i c i t y g e n e s . Figure 5A Y = 1.449 + 0.4092X I i i i i i i — i i 0 40 80 120 160 Y= "1.946 + 0.5052 X I 1 1 1 1 1 1 1 • 0 40 80 120 160 Vr Figure 5B Y =4.439 + 0.3871 X r — — i 1 1 1 1 — — i 1 1 0 40 80 120 160 Y= 7.062 + 0.3273 X 1 T 1 1 1 1 1 p- - | 0 40 80 120 160 Vr Figure 5C Y = -1.823 + 0.4344X l 1 1 1 1 1 1 1 1 0 40 80 120 160 Y = 1.917 + 0.4773X 0 40 80 120 160 Vr Figure 5E Y = -6.005 + 0.4501 X Figure 5F Y= "1.883 + 0 .4524X 1 1 1 1 1 1 1 1 1 0 40 80 120 160 111 T a b l e 15. R e s u l t s o f t e s t s o f s i g n i f i c a n c e f o r t h e d e v i a t i o n o f t h e r e g r e s s i o n s l o p e s from 0.0 and 0.5 (as d e r i v e d f r o m t h e f o r m u l a i n A p p e n d i x I I ) . T a b l e 15 FIGURE # P(0.0) SEb b A / SIG(0.5) 5A- 0. 1126-02 0. 0492 0 .4092 -1 .8523 NS 5A+ 0. 3790-02 0. 8365- 01 0 .5052 0.0622 NS 5B- 0. 2906-03 0. 3267- 01 0 .3871 -3.4558 * 5B+ 0. 2692-01 0. 9585- 01 0 .3273 -1.8018 NS 5C- 0. 1 080 0. 21 06 0 . 4344 -0.3115 NS 5C + 0. 1 206 0. 1095 0 .4773 -0.2073 NS 5D- 0. 6647-01 0. 5880- 01 0 . 1 472 -6.0000 * 5D+ 0. 1112 0. 1313 0 .2677 -1.7692 NS 5E- 0. 8721-01 0. 1 996 0 .4501 -0.2500 NS 5E+ 0. 2571-01 0. 8940- 01 0 .3097 -2.1286 NS 5F- 0. 3182-01 0. 1 398 0 . 4524 -0.3401 NS 5F+ 0. 2047 0. 5884- 01 0 .8906 -6.9840 * P = p r o b a b i l i t y of r e g r e s s i o n s l o p e s d i f f e r i n g f r o m 0.0; SEb = s t a n d a r d e r r o r of r e g r e s s i o n s l o p e ; b = r e g r e s s i o n s l o p e ; / t / . = a b s o l u t e v a l u e of t c a l c ; S I G ( 0 . 5 ) = s i g n i f i c a n c e o f r e g r e s s i o n s l o p e s d i f f e r i n g f r o m 0.5 (NS = n o t s i g n i f i c a n t l y d i f f e r e n t ; * = s i g n i f i c a n t a t t h e 0.05 l e v e l ) 1 13 Table 16. Type and presence of dominance and e p i s t a s i s ' , r e s p e c t i v e l y , f o r the r e g r e s s i o n p l o t s i n F i g u r e 5. Table 16 VARIETY DL FIGURE # EPISTASIS DOMINANCE T 1 7 5A- no i T 1 7 5A+ no c T 21 5B- yes i T 21 5B+ no i T 23 5C- no c T 23 5C+ no i 0 1 7 5D- yes i 0 1 7 5D+ no c 0 21 5E- no c 0 21 5E+ no i 0 23 5F- no c 0 23 5F+ yes i EPISTASIS = presence or absence of ep i s t a s i s ; DOMINANCE = type of dominance (i = incomplete dominance; c = complete dominance). 1 15 Homogeneity of V a r i a n c e of Sample P o p u l a t i o n s T a b l e 8 shows t h a t t h e r e i s no d i f f e r e n c e between t h e t h r e e DL's on T. A B a r t l e t t t e s t m e a s u r i n g t h e h o m o s c a d a s t i c i t y of t h e t h r e e DL's gave a p ( h o m o g e n e i t y of v a r i a n c e ) of 0.444 on T and 0.387 on 0 ( S o k a l and R o h l f 1969). T h e s e h i g h p r o b a b i l i t i e s r e f l e c t t h e s i m i l a r i t y of t h e t o t a l p h e n o t y p i c v a r i a n c e s of t h e 3 DL's, t h u s p e r m i t t i n g an F m a x - t e s t t o be p e r f o r m e d between t h e a d d i t i v e g e n e t i c e f f e c t s and a l s o on t h e t o t a l g e n e t i c e f f e c t s ( f r o m d a t a i n T a b l e 12) of t h e 3 DL's on b o t h T and 0. The t -c a l c u l a t e d was t e s t e d a g a i n s t a t - t a b u l a r 0.05[3,10] o f 3.72 . In e v e r y c a s e t h e c a l c u l a t e d v a l u e n e v e r e x c e e d e d t h e t a b u l a r v a l u e . The r e s u l t s of t h e F m a x - t e s t i n d i c a t e d t h a t t h e v a r i a n c e s due o n l y t o t h e main and t h e g e n e t i c e f f e c t s of t h e t h r e e DL F2 p o p u l a t i o n s were s i m i l a r . The t h r e e DL's c o u l d be t r e a t e d as h a v i n g been randomly c h o s e n from t h e same p o p u l a t i o n . T h e r e was no s i g n i f i c a n t d i f f e r e n c e between t h e p o p u l a t i o n s w i t h r e s p e c t t o t h e i r g e n e t i c component v a r i a n c e s . T h i s f i n d i n g c o u p l e d w i t h t h e n o n - s i g n i f i c a n t X 2 v a l u e d e t e r m i n e d f o r t h e F1 r e a d i n g s , i n d i c a t e s t h a t a l l t h e F1 DL's were g e n e t i c a l l y i d e n t i c a l . F i g u r e 4 shows t h e f r e q u e n c y d i s t r i b u t i o n s of t h e p o o l e d F2 r e a d i n g s from t h e t h r e e DL's on T and 0. 1 16 t E f f e c t i v e F a c t o r s The number o f e f f e c t i v e f a c t o r s was e s t i m a t e d from d a t a d e r i v e d f r o m T r e b i and O d e s s a u s i n g m o d i f i c a t i o n s o f W r i g h t ' s f o r m u l a ( W r i g h t 1934, 1952; T a b l e 1 7 ) . F o r m u l a m o d i f i c a t i o n s i n v o l v e d o b t a i n i n g t h e n u m e r a t o r from t h r e e s e p a r a t e but e q u i v a l e n t s o u r c e s (as d e s c r i b e d i n A p p e n d i x I I I ) . The "V" v a r i a b l e i n t h e d e n o m i n a t o r came from two s e p a r a t e s o u r c e s ( e i t h e r t h e a d d i t i v e g e n e t i c v a r i a b i l i t y o r t h e t o t a l g e n e t i c v a r i a b i l i t y ) . T h i s y i e l d e d s i x e f f e c t i v e f a c t o r o r "k" e s t i m a t e s (a-d) f o r T and o n l y 4 f o r 0 ( T a b l e 1 7 ) . On T t h e means of t h e k e s t i m a t e s from e q u a t i o n s w i t h t h e same d e n o m i n a t o r s ( i . e . , a,b,c and d , e , f ) were 2 .and 4. On 0 t h e u n u s u a l l y h i g h k e s t i m a t e of 26 c a l c u l a t e d by method "d" was t h o u g h t n o t t o be t r u l y r e p r e s e n t a t i v e , arid was d i s c a r d e d . The k e s t i m a t e on 0 was d e t e r m i n e d t o be 1. C o n s t a n t R a n k i n g Spearman rank c o r r e l a t i o n c o e f f i c i e n t s , c o r r e c t e d f o r t i e s ( A p p e n d i x I V ) , were c a l c u l a t e d f o r t h e F2 t r e a t m e n t s s e p a r a t e l y by g r i d and i n c o m b i n a t i o n on T and 0 ( T a b l e 1 8 ) . The " t " v a l u e s were t h e n c a l c u l a t e d w i t h t h e o b t a i n e d " r s " v a l u e s a c c o r d i n g t o t h e e q u a t i o n below. 17. E s t i m a t i o n o f e f f e c t i v e f a c t o r (k) numbers u s i n g v a r i o u s m o d i f i c a t i o n s o f W r i g h t ' s f o r m u l a ( A p p e n d i x I I I ) . Table 17 METHOD OF "k" EVALUATION a b c d e f VAR DL 2.782 4.779 3.572 3.945 6.774 5.064 T 17 2.372 2.728 2.040 3.561 3.730 2.970 T 21 1.575 2.661 1.990 2.710 4.580 3.424 T 23 2.243 3.389 2.534 3.405 5.028 3.819 mean 2.722 4.080 a b c d e f VAR DL 3.429 - 0.030 66.199 - 0.571 0 17 3.000 - 0.037 5.240 - 0.064 ' 0 21 3.109. - 0.065 6.588 - 0.138 0 23 3.179 0.044 26.009 0.258 mean 1.612 119 T a b l e 18. T e s t f o r s i g n i f i c a n c e o f Spearman Rank C o r r e l a t i o n s C o e f f i c i e n t s . T a b l e 18 DL r s t SIGNIFICANCE 17 0.2834 1.9521 0.01-0.05 21 0.2425 1.6247 NS 23 -0.2789 0.4380 NS 17+21+23 0.0464 0.4890 NS r s = rank c o e f f i c i e n t ; NS = n o t s i g n i f i c a n t ; " t " i s d i s t r i b u t e d a s " S t u d e n t ' s " t w i t h N-2 d e g r e e s of freedom; " t " t a b u l a t e d i s 1.6892 f o r a l p h a = 0.05 and 2.423 f o r a l p h a = 0.01. 121 (Note t h a t t h i s " t " i s d i f f e r e n t f r o m t h a t f o u n d i n t h e e q u a t i o n s i n A p p e n d i x I V ) . T a b l e 18 shows t h e r e s u l t s . T h e r e was no s i g n i f i c a n t c o r r e l a t i o n i n t h e r a n k i n g of t h e d i k a r y o n s e x c e p t i n t h e c a s e of DL 17 where i t i s m a r g i n a l l y s i g n i f i c a n t a t t h e a l p h a = 0.05 l e v e l . 122 X I I I . DISCUSSION Variance Analysis The presence of pathogenicity polygenes and a virulence gene can be detected using a biometrical approach. This method requires much less time and e f f o r t to reveal the genetic nature of a host-parasite system than a c l a s s i c a l Mendelian one. Analyses of variance techniques also include the added benefits of providing detailed information on the magnitude and significance of contributions of d i f f e r e n t v a r i a b i l i t y components to the phenotype under study. Tetrad analysis and years of crossing required to develop s p e c i f i c F1,F2 and subsequent generations and l i n e s , become unnecessary. A s t a t i s t i c a l approach of t h i s type would become indispensible in cases where crossing i s not possible. The biometrical analysis of the descendants from T1 x T4 revealed several important points: 1) The existence of polygenes as well as of a virulence gene, was detected in t h i s system. The virulence gene was operative s p e c i f i c a l l y against T. Virulence gene-polygene interactions may e x i s t . 1 23 2) The e n v i r o n m e n t p l a y s an i m p o r t a n t . r o l e . i n a d d i t i v e and n o n - a d d i t i v e i n t e r a c t i o n s w i t h t h e p a t h o g e n i c i t y p o l y g e n e s and t h e v i r u l e n c e gene. 3) Of t h e p o l y g e n e g e n e t i c components, t h e a d d i t i v e e f f e c t s were more i m p o r t a n t i n g e n e r a t i n g v a r i a b i l i t y on T t h a n on 0, w h i l e t h e r e v e r s e was t r u e f o r t h e n o n - a d d i t i v e e f f e c t s . 4) An e f f e c t i v e f a c t o r , c o n t r i b u t i n g t o t h e a d d i t i v e g e n e t i c v a r i a b i l i t y , was f o u n d t o be l i n k e d w i t h t h e m a t i n g t y p e l o c u s . A n o t h e r e f f e c t i v e f a c t o r , w h i c h was i n v o l v e d i n s i g n i f i c a n t e n v i r o n m e n t a l i n t e r a c t i o n s , was a l s o f o u n d t o be l i n k e d w i t h t h e m a t i n g l o c u s . I t i s n o t known whether t h e s e a r e one and t h e s a m e " f a c t o r . Of p a r t i c u l a r i n t e r e s t i n t h i s s t u d y i s t h e p r e s e n c e of e n v i r o n m e n t a l i n f l u e n c e s w h i c h were f o u n d t o i n c r e a s e t h e p a t h o g e n i c v a r i a b i l i t y n o r m a l l y e x p e c t e d f r o m a g r o u p o f p o l y g e n e s o r an a v i r u l e n c e a l l e l e . C o n v e r s e l y , e n v i r o n m e n t a l f a c t o r s c a n a l s o d e c r e a s e t h e p a t h o g e n i c v a r i a b i l i t y n o r m a l l y e x p e c t e d from a g r o u p of p a t h o g e n i c i t y p o l y g e n e s o r a v i r u l e n c e a l l e l e . In o t h e r words, a p o l y g e n e "X" may be more p a t h o g e n i c t h a n p o l y g e n e "Y" i n one e n v i r o n m e n t and l e s s p a t h o g e n i c i n a n o t h e r . S p e c i f i c p a t h o g e n i c i t y g e n e s , t h e r e f o r e , c a n i n t e r a c t w i t h c e r t a i n e n v i r o n m e n t a l f a c t o r s . 124 E a r l i e r work by Tapke (1948) r e v e a l e d t h a t w i t h t h e s o i l a t 50% m o i s t u r e h o l d i n g c a p a c i t y , o v e r a r a n g e o f t e m p e r a t u r e s , Hannchen showed t w i c e as much s m u t t i n g a t pH 5 as a t pH 7.8. W i t h t h e s o i l a t 40% m o i s t u r e h o l d i n g c a p a c i t y , c h a n g e s i n s o i l a c i d i t y p r o d u c e d d i s e a s e r e a d i n g d i f f e r e n c e s on Hannchen a t 20° and 25°C but not a t 10° and 15°C. I t w ould be i n t e r e s t i n g t o d e t e r m i n e t h e e x t e n t t o w h i c h t h e v i r u l e n c e gene and t h e p o l y g e n e s i n t e r a c t w i t h t h e e n v i r o n m e n t . B u r n e t t (1975) b e l i e v e d t h a t b e c a u s e of t h e c o m p l e x i t i e s of t h e g e n o t y p e x e n v i r o n m e n t i n t e r a c t i o n s "... t h e r e can n e v e r be a s i m p l e r u l e o f thumb d e c i s i o n by b r e e d e r s t o s e l e c t f o r s p e c i f i c o r g e n e r a l a d a p t a t i o n , s i n c e t h e r e s p o n s e w i l l depend upon t h e k i n d o f e n v i r o n m e n t s f o r w h i c h s e l e c t i o n i s b e i n g p r a c t i s e d . " He a t t r i b u t e d t h i s t o t h e l a c k o f l i n e a r r e s p o n s e of i n t e r a c t i o n s t o e n v i r o n m e n t s . In t h e i r i n v e s t i g a t i o n of m a j o r and m i n o r genes f o r wheat r e s i s t a n c e t o Puce i n i a s t r i i f o r m i s, L e w e l l e n e t a l . ( 1 967) d e t e r m i n e d t h a t minor genes were h i g h l y s e n s i t i v e t o t e m p e r a t u r e c h a n g e s . Tomiyama (1963) s u g g e s t e d t h a t h o s t n u t r i t i o n a l b a l a n c e and p h y s i o l o g y m i g h t be r e s p o n s i b l e f o r c h a n g e s i n m i n o r gene r e s i s t a n c e . The r e s u l t s o f t h i s work s u p p o r t t h e c l a i m t h a t m i n o r genes f o r p a t h o g e n i c i t y a r e a l s o h i g h l y s e n s i t i v e t o e n v i r o n m e n t a l c h a n g e s . A n o t h e r i n t e r e s t i n g q u e s t i o n was r a i s e d a s a r e s u l t of t h i s work. Why s h o u l d t h e DL's be s t a t i s t i c a l l y , h e n c e , g e n o t y p i c a l l y s i m i l a r on T but n o t on 0? P o s s i b l e e x p l a n a t i o n s c o u l d i n c l u d e 1 25 d i f f e r e n c e s i n c e r t a i n v a r i e t y x gene i n t e r a c t i o n s , s p e c i f i c m u l t i p l e s o u r c e i n t e r a c t i o n s or p e r h a p s t h e i n v o l v e m e n t o f two d i s t i n c t v a r i e t y - s p e c i f i c o r v i r u l e n c e g e n e - s p e c i f i c s e t s of p a t h o g e n i c i t y p o l y g e n e s . The use -of s t a t i s t i c s a l s o r e v e a l e d l i n k a g e of t h e m a t i n g t y p e l o c u s t o an e f f e c t i v e f a c t o r and t o an e f f e c t i v e f a c t o r s i g n i f i c a n t l y a f f e c t e d by t h e e n v i r o n m e n t . I t would be i n t e r e s t i n g t o i n v e s t i g a t e t h i s phenomenon f u r t h e r t o d e t e r m i n e whether t h e s e p r o v e t o be 1 o r 2 d e s t i n c t f a c t o r s . The U. h o r d e i - H. v u l g a r e p o l y g e n i c s y s t e m a p p e a r s t o become i n c r e a s i n g l y more complex w i t h e v e r y s t u d y . O t h e r s y s t e m s p r o b a b l y i n v o l v e an e q u a l l y complex s e t of i n t e r a c t i o n s , t h e r e f o r e , when p e r f o r m i n g e x p e r i m e n t s w i t h o u t t h e b e n e f i t of t h e knowledge of t h e r e l a t i v e c o n t r i b u t i o n s o f t h e d i f f e r e n t components t o v a r i a b i l i t y , c a r e s h o u l d be e x e r c i s e d when i n t e r p r e t i n g - t h e r e s u l t s . Some i n t e r a c t i o n s c a n c o m p l i c a t e , mask or d i s t o r t t h e outcome o f t h e e x p e r i m e n t . T h e s e f a c t o r s s h o u l d be r e c o g n i z e d and e x c l u d e d from g e n e t i c s t u d i e s . R e g r e s s i o n A n a l y s i s R e g r e s s i o n s of Wr'/Vr were p e r f o r m e d t o more c l e a r l y v i s u a l i z e t h e n o n - a d d i t i v e e f f e c t s g i v e n i n T a b l e 13. In g e n e r a l , when t h e r e g r e s s i o n s l o p e s d i f f e r e d from 0.5 e i t h e r e p i s t a s i s o r u n e q u a l gene f r e q u e n c i e s were t h e c a u s e . As i t can be d e m o n s t r a t e d ( i n a s u b s e q u e n t s e c t i o n ) t h a t a l l e l e f r e q u e n c i e s were e q u a l , t h e n any s l o p e d e v i a t i o n s from 0.5 can be a t t r i b u t e d t o e p i s t a s i s . A Y i n t e r c e p t above t h e o r i g i n 126 i n d i c a t e s i n c o m p l e t e d o minance. The d i s p e r s i o n o f s p o r i d i a a l o n g t h e r e g r e s s i o n l i n e i s a l s o o f i m p o r t a n c e . S p o r i d i a c l o s e t o t h e o r i g i n a r e t h o s e w i t h t h e g r e a t e s t number of dominant genes and t h o s e f a r t h e s t from t h e o r i g i n have t h e l e a s t number of dominant g e n e s . F i g u r e 5 d e p i c t s t h e r e g r e s s i o n s o f t h e "+" and "-" s p o r i d i a f o r e a c h DL on T and on 0. T h e r e was no c o r r e l a t i o n between t h e s p o r i d i a l r a n k i n g s i n t h e s e g r a p h s and t h e r a n k i n g s d e r i v e d from t h e a r r a y means i n T a b l e 4. The l a c k of s u c h a r e l a t i o n s h i p p r o v i d e s e v i d e n c e f o r a m b i d i r e c t i o n a l dominance and hence t h e o p e r a t i o n o f b o t h d i r e c t i o n a l and s t a b i l i z i n g s e l e c t i o n p r e s s u r e s (Simchen and J i n k s , 1964). Homogeneity of V a r i a n c e of Sample P o p u l a t i o n s The F m a x - t e s t and t h e X 2 t e s t i n d i c a t e d t h a t t h e F1 DL's were g e n e t i c a l l y i d e n t i c a l . Thus by e x t r a p o l a t i n g back t o t h e p a r e n t a l t e l i o s p o r e s , T1 and T4, i t can be c o n c l u d e d t h a t e i t h e r : 1) t h e p a r e n t a l t e l i o s p o r e s were homozygous f o r p a t h o g e n i c i t y g e n e s , hence t h e r e would be e q u a l gene f r e q u e n c i e s o f 0.5 a t e a c h l o c u s , o r 2) t h a t t h e a l l e l e s a t some have been d i f f e r e n t but i n p o t e n t i a l v a r i a b i l i t y i d e n t i c a l . E q u a l a l l e l e t o e x i s t a t e a c h l o c u s . 1 27 p a t h o g e n i c i t y l o c i may were s u f f i c i e n t l y s i m i l a r t o be c o n s i d e r e d t o be f r e q u e n c i e s c o u l d be s a i d The c l o s e p r o x i m i t y o f s p o r i d i a f r o m a s i n g l e g e r m i n a t i n g t e l i o s p o r e a l m o s t p r e c l u d e s n a t u r a l o u t c r o s s i n g i n U. h o r d e i ( C a t e n e t a l . , 1981) e x c e p t under t h e h i g h l y u n l i k e l y i n s t a n c e o f e x t r e m e l y dense i n o c u l a t i o n s w i t h h e t e r o g e n e o u s p o p u l a t i o n s of t e l i o s p o r e s . L i t t l e i s known o f how Ta p k e ' s r a c e s a r e m a i n t a i n e d i n N. D a k o t a . Even t h e most s o p h i s t i c a t e d c r y o n i c methods have l i m i t a t i o n s , and i t i s t h e r e f o r e n e c e s s a r y f o r e a c h 'race t o be o c c a s s i o n a l l y r e c y c l e d t h r o u g h t h e h o s t t o e n s u r e i t s c o n t i n u e d e x i s t e n c e . T h e r e a r e two d i s t i n c t ways t h a t e a c h r a c e c o u l d have been p r o p a g a t e d on t h e h o s t : 1) Seeds c o u l d have been i n o c u l a t e d w i t h two •co m p a t i b l e s p o r i d i a l l i n e s from a s i n g l e t e l i o s p o r e or w i t h low d e n s i t i e s of a h e t e r o g e n e o u s m i x t u r e o f t e l i o s p o r e s . 128 2) Seeds c o u l d have been i n o c u l a t e d w i t h s p o r i d i a l l i n e s f r o m d i f f e r e n t t e l i o s p o r e s o r w i t h h i g h d e n s i t i e s of a h e t e r o g e n e o u s m i x t u r e o f t e l i o s p o r e s . In t h e c a s e of #1 a h i g h d e g r e e o f i n b r e e d i n g and hence h o m o z y g o s i t y w i t h i n t h e p o p u l a t i o n would be e x p e c t e d . I f #2 was f a v o r e d , t h e n a g r e a t d e a l of o u t c r o s s i n g and p o p u l a t i o n h e t e r o g e n e i t y would r e s u l t . The r e s u l t s of t h i s e x p e r i m e n t s u p p o r t t h e f i r s t h y p o t h e s i s f o r T a p k e ' s r a c e s 7 and 11. E f f e c t i v e F a c t o r s T a b l e 17 l i s t s t h e c a l c u l a t e d k v a l u e s u s i n g m o d i f i c a t i o n s o f W r i g h t ' s f o r m u l a . The e q u a t i o n assumes c o n c e n t r a t i o n o f a l l a l l e l e s of l i k e e f f e c t i n e a c h p a r e n t w i t h no dominance or e p i s t a s i s . I f any of t h e s e a s s u m p t i o n s i s n o t o p e r a t i v e k becomes an u n d e r e s t i m a t e o f t h e number o f e f f e c t i v e f a c t o r s . A l s o , as w i t h any e s t i m a t e , t h e o c c u r r e n c e o f u n e q u a l a l l e l e e f f e c t s and l i n k a g e would d e f l a t e t h e k v a l u e . In a d d i t i o n , i t i s i m p o s s i b l e , a t t h i s t i m e , t o e v a l u a t e t h e c o n t r i b u t i o n s o f t h e v i r u l e n c e gene t o t h e a d d i t i v e a n d / o r t h e n o n - a d d i t i v e v a r i a n c e s i f i n d e e d s u c h c o n t r i b u t i o n s e x i s t . T h i s w i l l a l s o make i t d i f f i c u l t t o d e t e r m i n e t h e e x t e n t t o w h i c h t h e k v a l u e w i l l be u n d e r e s t i m a t e d . F o r m u l a m o d i f i c a t i o n s i n v o l v e o b t a i n i n g t h e n u m e r a t o r from t h r e e s e p a r a t e but e q u i v a l e n t s o u r c e s (as d e s c r i b e d i n A p p e n d i x 1 29 I I I ) . The "V" v a r i a b l e i n t h e d e n o m i n a t o r comes from two s e p a r a t e s o u r c e s ( e i t h e r t h e a d d i t i v e g e n e t i c v a r i a b i l i t y o r t h e t o t a l g e n e t i c v a r i a b i l i t y ) . T h i s y i e l d e d s i x k e s t i m a t e s (a-d) f o r T and o n l y 4 f o r 0 ( T a b l e 1 7 ) . On T t h e means of t h e k e s t i m a t e s from e q u a t i o n s w i t h t h e w i t h t h e same d e n o m i n a t o r s ( i . e . a,b,c and d , e , f ) were 2 and 4. On 0 t h e u n u s u a l l y h i g h k e s t i m a t e o f 26 c a l c u l a t e d by method "d" was t h o u g h t not t o be t r u l y r e p r e s e n t a t i v e and was d i s c a r d e d . The k e s t i m a t e on 0 was d e t e r m i n e d t o be 1. The e s t i m a t e of t h e number of e f f e c t i v e f a c t o r s , 1 - 2 on O and 4-6 on T, a t f i r s t a p p e a r s t o be low. T h i s was a l s o t h e c a s e i n p r e v i o u s s t u d i e s w i t h o t h e r o r g a n i s m s ( J i n k s 1954). R e s e a r c h e r s s u c h as Thompson (1975) b e l i e v e d t h a t e s t i m a t e s o f l a r g e numbers of p o l y g e n e s a r e p r o b a b l y g r o s s o v e r e s t i m a t e s and t h a t i n most s y s t e m s , r e l a t i v e l y few a r e a c t u a l l y i n v o l v e d . The d a t a from t h i s s t u d y d i d n o t i n d i c a t e t h e e x t e n t t o w h i c h t h e p r e s e n c e of t h e v i r u l e n c e gene o b s c u r e d t h e a c t i o n o f t h e p o l y g e n e s . I t i s p o s s i b l e t h a t t h e r e may even be i n t e r a c t i o n s between them. A b d u l l a and Hermsen (1971) b e l i e v e t h a t m a j o r genes and p o l y g e n e s i n t e r a c t e p i s t a t i c a l l y and t h a t major genes a c t as s w i t c h genes w h i c h c a n d i r e c t p o l y g e n i c r e s i s t a n c e a g a i n s t s p e c i f i c r a c e s . The W r i g h t method of e s t i m a t i n g k ( t h e number o f e f f e c t i v e f a c t o r s ) , as w e l l as a l l o t h e r s t a t i s t i c a l methods, a r e b a s e d on a l a r g e number of a s s u m p t i o n s w h i c h may l e a d t o l a r g e u n d e r e s t i m a t e s . S t a n d a r d e r r o r a s s o c i a t e d w i t h s a m p l i n g i s an a d d i t i o n a l f a c t o r w h i c h may c a u s e t h e W r i g h t method t o 1 30 underestimate k (Mayo, 1980). A more accurate estimation of k could be obtained by retesting T with F2 and/or F3 dikaryons known to be homozygous for the virulence gene. This would also enable a study of the function of the pathogenicity polygenes without the confounding effects of a simultaneously segregating virulence gene. Experiments along these l i n e s have been completed and are presently being analyzed (Pope, unpublished). Constant Ranking There was no s i g n i f i c a n t c o r r e l a t i o n in the ranking of the dikaryons, except in the case 6f DL 1.7. F3 progeny from other T1 x T4 isol a t e s have previously been shown to exhibit ranking (Pope, unpublished). Those F3 isolates showed s t a t i s t i c a l l y s i g n i f i c a n t rankings because of the absence of a segregating virulence gene. In this study, v a r i a b i l i t y generated by the segregating virulence gene, environmental interactions and perhaps virulence gene-polygene interactions, was s u f f i c i e n t to obscure any possible ranking. Similar ranking d i s p a r i t i e s were noticed by Schwarzbach and Wolfe (1975), who found s i g n i f i c a n t ranking disruptions when v a r i e t i e s with hypersensitive and p a r t i a l resistance were used. Changes in the condition of i n f e c t i o n , incubation and in the physiological and developmental state of the host were found to a l t e r ranking. They also believed that p l e i o t r o p i c e f fects of virulence genes (as per Mather, 1973) could af f e c t ranking. 131 F i n d i n g s s u c h as t h e s e i n d i c a t e t h e i m p o r t a n c e of o b t a i n i n g g e n e t i c a l l y a p p r o p r i a t e b i o l o g i c a l m a t e r i a l p r i o r t o t e s t i n g m odels o f p o l y g e n i c s y s t e m s . Any m a t e r i a l u s e d t o t h i s end s h o u l d not i n c l u d e v i r u l e n c e gene o r R gene h e t e r o z y g o t e s . An a l t e r n a t i v e a p p r o a c h t o be a d o p t e d i n i n s t a n c e s where t h e i s o l a t i o n of a p p r o p r i a t e m a t e r i a l p r e s e n t s p r o b l e m s i s b e i n g i n v e s t i g a t e d (Pope, e x p e r i m e n t s i n p r o g r e s s ) . T h i s method i n v o l v e s a s t a t i s t i c a l a p p r o a c h , w h i c h may e v e n t u a l l y be shown t o be a more a c c u r a t e i n d i c a t o r o f C o n s t a n t R a n k i n g . D i s e a s e r e a d i n g s c a n i n v o l v e up t o s e v e r a l c o n t r i b u t i n g s o u r c e s of v a r i a b i l i t y ( i . e . , a d d i t i v e p o l y g e n e s , v i r u l e n c e g e n e s , e n v i r o n m e n t a l i n t e r a c t i o n s , e t c . ) . R a n k i n g s s h o u l d be b a s e d s o l e l y on t h e p o r t i o n of t h e p h e n o t y p e t o w h i c h t h e p o l y g e n e s c o n t r i b u t e a d d i t i v e l y ( o r m u l t i p l i c a t i v e l y ; F l e m i n g and P e r s o n , 1982). S u p e r f l u o u s v a r i a b i l i t y c o n t r i b u t i o n s t o t h e p h e n o t y p e s h o u l d be f i l t e r e d o u t . R a n k i n g s , t h e r e f o r e , would be b a s e d on th e r e l a t i v e o r d e r of s t a t i s t i c a l measurements of v a r i a b i l i t y p r o d u c e d by t h e a d d i t i v e e f f e c t s o f o n l y t h e p o l y g e n e s . A d d i t i v e p o l y g e n i c p a t h o g e n i c v a r i a b i l i t y o f p r o g e n y o f c r o s s e s o f t h e p a t h o g e n c o u l d be d e t e r m i n e d and r a n k e d on s e v e r a l v a r i e t i e s o f t h e h o s t . C o n v e r s e l y , a d d i t i v e p o l y g e n i c r e s i s t a n c e v a r i a b i l i t y o f p r o g e n y from c r o s s e s o f t h e h o s t c o u l d be d e t e r m i n e d and r a n k e d on s e v e r a l r a c e s o r i s o l a t e s o f t h e p a t h o g e n . U l t i m a t e l y , a d d i t i v e p o l y g e n i c p a t h o g e n i c and r e s i s t a n c e v a r i a b i l i t y m e asures and r a n k i n g s c o u l d s i m u l t a n e o u s l y be p e r f o r m e d on p r o g e n y from c r o s s e s of t h e p a t h o g e n w i t h p r o g e n y from c r o s s e s of t h e h o s t . T h i s t y p e of C o n s t a n t R a n k i n g o f P h e n o t y p i c 1 32 V a r i a b i l i t y Components can be p e r f o r m e d s i m u l t a n e o u s l y on any number of v a r i a b i l i t y components. F o r i n s t a n c e , a h o s t r e s i s t a n c e p o l y g e n i c s y s t e m m i g h t be i n v e s t i g a t e d by a b r e e d e r t o d e t e r m i n e t h e p r e s e n c e and m a g n i t u d e o f f a v o r a b l e i n t e r a c t i o n s w i t h l o c a l e n v i r o n m e n t a l c o n d i t i o n s . C o n s t a n t R a n k i n g of P h e n o t y p i c V a r i a b i l i t y Components c o u l d p r o v i d e i n f o r m a t i o n on w h i c h h o s t l i n e s o r v a r i e t i e s w ould b e s t be e x p l o i t e d a g a i n s t t h e p a t h o g e n p o p u l a t i o n i n t h a t e n v i r o n m e n t . P l a n t b r e e d e r s c o u l d f i n d t h i s m o d i f i c a t i o n of C o n s t a n t R a n k i n g t o be an i n d i s p e n s i b l e t o o l . 1 33 XIV. REFERENCES A b d u l l a , M.M.F. 1971. C o u l d u n i f o r m r e s i s t a n c e be ' g e n e r a t e d ' ? S t i m u l a t i v e s p e c u l a t i o n s . E u p h y t i c a 20:427-429. 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C e r e a l R u s t s C o n f . , I n t e r l a k e n , S w i t z e r l a n d pp.162-163. W o l f e , M.S. 1972. The g e n e t i c s o f b a r l e y mildew. Rev. P l a n t P a t h o l o g y 51:507-522. W r i g h t , S. 1934. The r e s u l t s of c r o s s e s between i n b r e d s t r a i n s of g u i n e a p i g s , d i f f e r i n g i n number o f d i g i t s . G e n e t i c s 19:537-551. W r i g h t , S. 1952. The g e n e t i c s o f q u a n t i t a t i v e v a r i a b i l i t y . I_n Q u a n t i t a t i v e - I n h e r i t a n c e . E d i t e d by E.C.R. Reeve and C.H. W a d d i n g t o n , HMSO, London. XV. APPENDICES Appendix I_ Minimal Medium Vogel's Solution (50x) 20 ml. D i s t i l l e d Water 1000 ml. Agar (Bacto) 20 gm. Dextrose (D-Glucose) 10 gm. S t e r i l i z e for 15 min. in autoclave at 15 lbs., 121°C. Complete Medium Vogel's Solution (50x) 20 ml. D i s t i l l e d Water 1000 ml. Tryptophan 50 mg. Casein Hydrolysate 5 mg. (vitamin and sa l t free) Yeast Extract (Difco) 5 gm. Dextrose (D-Glucose) 10 gm. Vitamin Solution 10 ml. Agar (Bacto) 20 gm. S t e r i l i z e for 15 min. in autoclave at 15 lbs., 121°C. Bauch Mating Type Test Plates Same as Minimal Medium but with only 2 gm. . Dextrose. Vogel's Solution (50x) Na2 Citrate 2H20 1 23 gm. K2HP04 250 gm. NH4N03 Anhyd. 100 gm. MgS04.7H20 1 0 gm. CaC12.2H20 5 gm. Trace Element Solution 5 ml. D i s t i l l e d Water 750 ml. Chloroform 2 ml. Heat solution and add chemicals gradually with s t i r r i n g . Store solution at room temperature in stoppered bottl e . Trace Element Solution C i t r i c Acid 1H20 5 gm. Zn S04.7H20 5 gm. Fe(NH4)2.(S04)2.6H20 1 gm. CuS04.5H20 0.25 gm. MnS04.1H20 0.05 gm. H3B03 Anhyd. 0.05 gm. Na2Mo04.2H20 0.05 gm. Chloroform 1 ml." D i s t i l l e d Water 95 ml. Store at 4°C in t i g h t l y stoppered bottle. V i t a m i n S o l u t i o n T h i a m i n 100 mg R i b o f l a v i n 50 mg P y r i d o x i n e 50 mg Ca P a n t o t h e n a t e 200 mg p - a m i n o - b e n z o i c A c i d 50 mg N i c o t i n i c A c i d 200 mg C h o l i n e C h l o r i d e 200 mg I n o s i t o l 400 mg F o l i c A c i d 50 mg D i s t i l l e d Water 1 000 ml ( B e a d l e and Tatum, 1945) D i s p e n s e i n 10 ml a l i q u o t s . S t o r e a t - 2 0 ° C . 1 52 A p p e n d i x 11 E q u a t i o n f o r C a l c u l a t i n g " t " V a l u e s Ho : B = 0.5 b - B t n - 2df = SEb / t / < t t a b . = 2.776 U d f ) Where: Ho = n u l l h y p o t h e s i s B = s l o p e of 0.5 t n = t c a l c u l a t e d (one t a i l e d ) df = d e g r e e s o f f r e e d o m b = r e g r e s s i o n s l o p e SEb = s t a n d a r d e r r o r o f b / t / = a b s o l u t e v a l u e t c a l c . T t a b = t a b l e v a l u e a t 4df ( f r o m S t e e l and T o r r i e , 1960) 1 53 A p p e n d i x I I I E q u a t i o n s f o r C a l c u l a t i n g "k" V a l u e s The b a s i c f o r m u l a f o r c a l c u l a t i n g t h e number of o p e r a t i v e e f f e c t i v e f a c t o r s i s : - 2 (P1 - P2) k = 8 Vg A l t e r n a t e c a l c u l a t i o n s f o r "k" were made by r e p l a c i n g terms i n t h e b a s i c e q u a t i o n , l i s t e d a b ove, w i t h e q u i v a l e n t v a l u e s a v a i l a b l e from t h e d a t a . The b r a c k e t e d t e r m i n t h e n u m e r a t o r was r e p l a c e d w i t h t h r e e d i f f e r e n t v a l u e s and t h e d e n o m i n a t o r was r e p l a c e d w i t h two d i f f e r e n t t e r m s . By s u b s t i t u t i n g i n t o t h e e q u a t i o n a l l p o s s i b l e c o m b i n a t i o n s of t h e s e v a l u e s 6 "k" e s t i m a t e s r e s u l t ( a - f ) . The terms u s e d t o r e p l a c e t h e b r a c k e t e d t e r m i n t h e d e n o m i n a t o r a r e : 1) t h e d i f f e r e n c e between t h e high, and low F2 r e a d i n g s (F2h - F 2 1 ) , 2) t h e d i f f e r e n c e between t h e a v e r a g e t r a n s f o r m e d d i s e a s e r e a d i n g s of Ebba's p a r e n t a l t e l i o s p o r e s (T1 - T 4 ) , and 3) t h e d i f f e r e n c e between t h e a v e r a g e t r a n s f o r m e d d i s e a s e r e a d i n g s o f T a p k e ' s r a c e s (r11 - r 7 ) . The t e r m s u s e d t o r e p l a c e t h e d e n o m i n a t o r a r e : 1) t h e a d d i t i v e component o f g e n e t i c v a r i a n c e ( V a ) , and 2) t h e t o t a l g e n e t i c v a r i a n c e ( V g ) . L i s t e d below i s a c h a r t o u t l i n i n g a l l 6 c o m b i n a t i o n s o f term r e p l a c e m e n t s t h a t were made t o g e n e r a t e 6 "k" e s t i m a t e s ( a -f ) . k e s t i m a t e n u m e r a t o r d e n o m i n a t o r a F2h -- F21 Vg b T1 -- T2 Vg c r 1 1 - r 7 Vg d F2h -- F21 Va e T1 -- T2 Va f r 1 1 - r7 Va 1 55 Appendix IV Spearman Rank Correlation C o e f f i c i e n t Calculation where and 2 2 2 Sx + Sy - Sd rs = 2 2 2 sqrt(Sx (Sy )) 3 2 N - N Sx = - STx 1 2 3 2 N - N Sy = - STy 1 2 and where: rs = Spearman Rank Correlation C o e f f i c i e n t Sx = the sum of "x's" Sy = the sum of "y's" N = the number of dikaryons 3 t - t STx = = the correction factor for "x" 2 3 t - t STy = = the correction factor for "y" 2 t h e number of o b s e r v a t i o n s t i e d a t a g i v e n rank ( f r o m S o k a l and R o h l f , 1981) 

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