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Growth and yield relationships in the garden pea (Pisum stivum L.) Fletcher-Paul, Lystra Mona 1985

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GROWTH AND YIELD RELATIONSHIPS IN THE GARDEN PEA (PISDM SATIVUM L.) By LYSTRA M. FLETCHER B.Sc. (Hons.), University of the West Indies, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Plant Science) We accept t h i s thesis as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA February 1985 © Lystra M. Fletcher, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of TV^R-iOT S C I E I Q C E The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date c ^ T ^ /f& DE-6 (3/81) A B S T R A C T Recently developed methods of growth and y i e l d analysis were applied to the r e s u l t s of a f i e l d experiment to determine ( i ) the e f f e c t of seed i n o c u l a t i o n on the growth and y i e l d of two cultivairs of garden pea (Pisum  sativum L.) - 'Dark Skin P e r f e c t i o n ' (DSP) and 'Early Frosty' (EF), ( i i ) the p h y s i o l o g i c a l basis for y i e l d v a r i a b i l i t y and ( i i i ) the dynamics of reproductive growth i n the pea. Seed i n o c u l a t i o n had no noticeable e f f e c t on y i e l d . There were, however, s i g n i f i c a n t c u l t i v a r d i f f e r e n c e s — D S P was l a r g e r , matured l a t e r but had lower y i e l d s than EF. Growth an a l y s i s revealed that these d i f f e r e n c e s were due to the extended vegetative growth phase, higher l e a f area r a t i o and lower harvest index of DSP. Further analysis indicated that EF had a more e f f i c i e n t growth strategy, as the maximum rate of p a r t i t i o n i n g of dry matter into the reproductive structures coincided with high l e a f a c t i v i t y . By contrast maximum sink a c t i v i t y i n DSP occured during l e a f senescence. Stem length, average l e a f area and inverse l e a f weight r a t i o were the main components of biomass v a r i a b i l i t y . Y i e l d v a r i a t i o n , however, was aff e c t e d i n d i r e c t l y by stem length, average l e a f area, reproductive e f f o r t and average seed weight, and d i r e c t l y by the number of nodes, pod set and inverse l e a f weight r a t i o . These r e s u l t s imply that the supply of photosynthetic material i s important for increased pea y i e l d s . S i g n i f i c a n t negative c o r r e l a t i o n s between vegetative components and average seed weight suggest compensation and competition between these components. Thus, y i e l d - i i i -improvement may be attainable by (1) enhancing the component which i s unaffected by this compensation or (2) reducing the competition by s h i f t i n g the equilibrium. Two c r u c i a l periods when source supply may a f f e c t y i e l d were detected during the reproductive phase. The f i r s t period (61 days a f t e r planting i n DSP and 55 days a f t e r planting in EF) was more pronounced in DSP. In the second phase (day 75 for DSP and 65 f o r EF) seed growth became important and seemed to influence leaf a c t i v i t y . This finding suggests that the rate of canopy establishment i s as important as the rate of pod f i l l i n g for improving y i e l d s . A dynamic model simulating pod y i e l d in r e l a t i o n to source supply i s o u t l i n e d . - i v -TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i i i LIST OF FIGURES x ACKNOWLEDGEMENTS x i v CHAPTER 1 - INTRODUCTION 1 1.1 Statement of the Problem 3 1.2 Objectives of the Study.. 4 CHAPTER 2 - LITERATURE REVIEW 5 2.1 General. 5 2.2 Studies of the P h y s i o l o g i c a l Changes i n the Pea.. 5 2.3 Growth and Y i e l d Analysis 14 2.3.1 Y i e l d Component Analysis 15 2.3.2 Growth Analysis 17 2.3.3 Demographic Analysis 19 2.3.4 A Combined Approach 20 CHAPTER 3 - MATERIALS AND METHODS 22 3.1 The Design 22 3.2 Primary Data C o l l e c t i o n 22 3.2.1 Destructive Harvests 23 3.2.2 Non-destructive Harvests 24 3.2.3 P r e d i c t i o n Equations 25 3.3 Data Analysis 28 - v -Page 3.3.1 Analysis of Variance 28 3.3.2 Growth Analysis 29 3.3.2.1 Growth Curves 29 3.3.2.2 Growth Indices 34 3.3.3 Y i e l d Component Analysis 36 3.3.4 Demographic Analysis 38 3.4 Temperature Correlations Al CHAPTER 4 - PRELIMINARY CONSIDERATIONS 43 4.1 Curve Sel e c t i o n 43 4.1.1 Number and P o s i t i o n of Knots 43 4.2 P r e d i c t i o n Equations 50 4.2.1 Leaf Area 50 4.2.2 Leaf Dry Weight 60 4.2.3 Total Plant Dry Weight 63 4.2.4 Pod, Seed and Pod Wall Dry Weight 63 CHAPTER 5 - RESULTS 67 5.1 The Data 67 5.2 Analysis of Variance 67 5.2.1 Overall Analysis 67 5.2.2 Subunit Analysis 71 5.3 Growth Analysis 77 5.3.1 Growth Curves ( d e s t r u c t i v e harvests) 77 5.3.1.1 Leaf Area 78 5.3.1.2, Dry Weights 78 5.3.2 Growth Indices ( d e s t r u c t i v e harvests) 85 5.3.2.1 Re l a t i v e Growth Rates 85 5.3.2.2 Unit Leaf Rate 91 5.3.2.3 Leaf Area Ratio 91 5.3.2.4 S p e c i f i c Leaf Area 93 5.3.2.5 Leaf Weight Ratio 96 5.3.3 Non Destructive Harvests 96 5.3.4 Growth Curves (non-destructive harvests).. 100 - v i -P a g e 5.3.4.1 Leaf Area 100 5.3.4.2 Dry Weights 100 5.3.5 Growth Indices (non-destructive harvests).. 104 5.3.5.1 Re l a t i v e Growth Rates 104 5.3.5.2 Unit Leaf Rate 109 5.3.5.3 Leaf Area Ratio I l l 5.3.5.4 S p e c i f i c Leaf Area I l l 5.3.5.5 Leaf Weight Ratio 115 5.4 Y i e l d Component Analysis 115 5.4.1 Model 1 119 5.4.2 Model 2 123 5.5 Demographic Analysis 128 5.5.1 Leaf Demography 128 5.5.2 Flower Demography 130 5.6 The Combined Approach 134 5.6.1 A d d i t i v e Components 135 5.6.1.1 R e l a t i v e Growth Rates 139 5.6.1.2 Unit Leaf Rates 145 5.6.2 Cohort Analysis 148 5.6.2.1 Growth Curves 148 5.6.2.2 Re l a t i v e Growth Rates 153 5.6.3 M u l t i p l i c a t i v e Components. 157 5.6.3.1 Model 1 158 5.6.3.2 Model 2 162 5.7 Temperature Co r r e l a t i o n s 167 CHAPTER 6 - DISCUSSION OF RESULTS 169 CHAPTER 7 - A MODEL SIMULATING POD GROWTH 187 7.1 The Proposed Model 187 7.2 Assumptions of the Model 189 - v i i -Page 7.3 Data Simulation 191 7.4 Results and Discussion 192 CHAPTER 8 - CONCLUSIONS AND RECOMMENDATIONS 195 8.1 Conclusions 195 8.2 Recommendations 198 CHAPTER 9 - BIBLIOGRAPHY 200 NOMENCLATURE AND SYMBOLS 208 APPENDICES 211 A. STATISTICAL APPENDICES 211 A. 1 Test of E q u a l i t y of Slopes and Intercepts 211 A.2 Weighted Least Squares 212 A. 3 C a l c u l a t i o n of I 213 B. VARIANCES OF GROWTH INDICES 214 B. l Rates 214 B.2 Ratios 215 C. NITROGEN FIXATION 216 D. COMPUTER PROGRAMS 218 D.l B-Spline Program 218 D.2 Cubic Spline Program 219 D.3 C a l c u l a t i o n of Variances of F i t t e d Values 223 D.4 C a l c u l a t i o n of Variances of Growth Indices 230 D.5 Simulation Program 235 E. RAW DATA 236 - v i i i -LIST OF TABLES Table Page 3.1 Summary of v a r i a t e s and the predictor v a r i a b l e s used in t h e i r p r e d i c t i o n 26 4.1 Summary of r e s u l t s of t e s t s to find the most s u i t a b l e number of knots for the splined regressions f i t t e d to the primary data from the d e s t r u c t i v e harvests 44 4.2 Results of tests to find the most s u i t a b l e number of knots for the splined regressions f i t t e d to the a d d i t i v e components for each c u l t i v a r 45 4.3 Summary of r e s u l t s of regression analysis to determine the p r e d i c t i o n equation f o r l e a f l e t area 54 4.4 Summary of r e s u l t s of regression analysis to determine the p r e d i c t i o n equation for s t i p u l e area 55 4.5 Summary of r e s u l t s of regression analysis to determine the p r e d i c t i o n equation for t o t a l l e a f weight 61 4.6 Summary of r e s u l t s of a l l possible subset regressions to determine the 'best' p r e d i c t i o n equation f o r t o t a l dry weight (W) at each harvest 64 4.7 Growth records of f r u i t at d i f f e r e n t stages of growth 66 5.1(a) Summary of means of primary v a r i a t e s from de s t r u c t i v e harvests 68 5.1(b) Summary of standard deviations of primary v a r i a t e s from d e s t r u c t i v e harvests...... 69 5.2 Summary of r e s u l t s of o v e r a l l ANOVA: E f f e c t of c u l t i v a r and innoculation on primary v a r i a t e s 70 5.3 Sub-unit ANOVA of e f f e c t of c u l t i v a r and in o c u l a t i o n on primary v a r i a t e s . . . . . . . . . . . . . . . . . . 73 5.4 Summary of means for primary v a r i a t e s from non-destructive harvests 98 - ix -Table Page 5.5(a) Summary of means of y i e l d components from d e s t r u c t i v e harvests 116 5.5(b) Summary of standard deviations of y i e l d components from de s t r u c t i v e harvests 117 5.6 Analysis of variance of the e f f e c t of seed i n o c u l a t i o n and c u l t i v a r on y i e l d components i n the garden pea..... 118 5.7 Model 1, Regressions of y i e l d components on independent, standardized r e s i d u a l s . Data from f i n a l harvest 121 5.8 Sequential y i e l d component an a l y s i s , Model 1 122 5.9 Model 2. Regressions of y i e l d components on independent, standardized r e s i d u a l s , ( c o e f f i c i e n t s of determination). Data from f i n a l harvest 124 5.10 Model 2. Regression of y i e l d components on independent, standardized r e s i d u a l s (regression c o e f f i c i e n t s ) . Data from f i n a l harvest 125 5.11 Sequential y i e l d component a n a l y s i s , Model 2 127 5.12 Mean l e a f b i r t h and death rates at each harvest 129 5.13 Mean flower b i r t h and death rates at each harvest 131 5.14 Percentage s u r v i v a l of cohorts of flowers at the f i n a l harvest i n garden pea 133 5.15 Summary of dry weights f o r Dark Skin P e r f e c t i o n and Early Frosty 138 5.16 C o r r e l a t i o n between temperature and unit l e a f rate 168 C.l E f f e c t of seed i n o c u l a t i o n on the C2H2~reducing a c t i v i t y in Dark Skin P e r f e c t i o n and Early Frosty 216 C.2 ANOVA of e f f e c t s of seed i n o c u l a t i o n on nitrogen f i x a t i o n a c t i v i t y i n two c u l t i v a r s of peas 217 E . l Summary of fresh and dry weights of pods, pod walls and seeds of each cohort 23 6 LIST OF FIGURES Figures Page 3.1 Flow chart of the steps involved i n s e l e c t i n g the best f i t t e d curve 33 4.1 Relat i v e l e a f area growth rate curves from data of des t r u c t i v e harvests 47 4.2 P l o t s showing f i t of splined regressions to l e a f area data 49 4.3 Scatter plot of l e a f l e t length vs l e a f l e t area 51 4.4 Scatter plot of s t i p u l e length vs s t i p u l e area 52 4.5 Residual plot of regression equation to determine s t i p u l e area 57 4.6 Residual p l o t of regression equation to determine l e a f l e t area for data at 20 days a f t e r planting (harvest 1) 58 4.7 Residual plot of regression equation to determine l e a f l e t area for pooled data of harvests 2, 9 and 12... 59 5.1 Spline regression describing time course of mean le a f area per plant (log scale) in garden pea 79 5.2 Spline regression d e s c r i b i n g time course of mean lea f weight (log scale) i n garden pea 81 5.3 Spline regression d e s c r i b i n g time course of stem dry weight per plant (log scale) in garden pea 82 5.4 Spline regression describing time course of mean vegetative dry weight per plant (log scale) i n garden pea 83 5.5 Spline regression describing time course of t o t a l plant dry weight ( l o g , scale) i n garden pea 84 5.6 Progress curves of instantaneous r e l a t i v e l e a f area growth rate 86 5.7 Progressive curves of instantaneous r e l a t i v e growth rate of leaf dry weight 87 - x i -Figures Page 5.8 Progress curves of instantaneous r e l a t i v e stem growth rate 88 5.9 Progress curves of instantaneous r e l a t i v e growth rate of vegetative dry weight 89 5.10 Progress curves of instantaneous r e l a t i v e growth rate of the whole plant 90 5.11 Progress curves of instantaneous unit l e a f rate 92 5.12 Progress curves of instantaneous l e a f area r a t i o 94 5.13 Progress curves of instantaneous s p e c i f i c l e a f area.... 95 5.14 Progress curves of instantaneous l e a f weight r a t i o 97 5.15 Cubic s p l i n e regression describing time course of mean l e a f area per plant (non-destructive harvests).... 101 5.16 Cubic s p l i n e regression describing time course of mean l e a f dry weight per plant (non-destructive harvests) 102 5.17 Cubic s p l i n e regression describing time course of mean t o t a l dry weight per plant (non-destructive harvests)...., 103 5.18 Instantaneous r e l a t i v e l e a f area growth rate curves (non-destructive harvests) 105 5.19 Instantaneous r e l a t i v e l e a f weight growth rate curves (non-destructive harvests).. 106 5.20 Instantaneous r e l a t i v e growth rate curves (non-des t r u c t i v e harvests) 108 5.21 Progress curves of instantaneous unit l e a f r a t e (non-destructive harvests) 110 5.22 Progress curves of instantaneous l e a f area r a t i o (non-destructive harvests) 112 5.23 Progress curves of instantaneous s p e c i f i c l e a f area (non-destructive harvests) 113 - x i i -Figure Page 5.24 Progress curves of instantaneous l e a f weight r a t i o (non-destructive harvests) 114 5.25 E f f e c t of seed i n o c u l a t i o n and c u l t i v a r on mean cohort y i e l d , c a l c u l a t e d as a percent of t o t a l plant y i e l d 132 5.26 Percentage dry matter d i s t r i b u t i o n in the garden pea.. 136 5.27 F i t t e d time trends for t o t a l plant biomass and i t s a d d i t i v e components 137 5.28 Progress curves of instantaneous r e l a t i v e growth rates of t o t a l plant biomass and i t s additive components 140 5.29 F i t t e d time trends f o r the absolute production rates of t o t a l plant biomass and i t s a d d i t i v e components. 142 5.30 F i t t e d time trends f o r the f r a c t i o n a l production rates of the ad d i t i v e components of t o t a l plant biomass 144 5.31 F i t t e d time trends for the components of unit l e a f rate 146 5.32 Progress curves for fresh and dry weights of the pods of the f i r s t four cohorts of Dark Skin P e r f e c t i o n and Early Frosty 150 5.33 Progress curves for fr e s h and dry weights of pod walls of the f i r s t four cohorts of Dark Skin P e r f e c t i o n and Early F r o s t y . . 151 5.34 Progress for fresh and dry weights of seeds of f i r s t four cohorts of Dark Skin P e r f e c t i o n and Ear l y Frosty 152 5.35 Mean r e l a t i v e growth rates of pods of f i r s t four cohorts of Dark Skin P e r f e c t i o n and Early Frosty 154 5.36 Mean r e l a t i v e growth rates of pod wall of f i r s t four cohorts of Dark Skin P e r f e c t i o n and E a r l y Frosty 155 - x i i i -Figure Page 5.37 Mean r e l a t i v e growth rates of seeds of f i r s t four cohorts of Dark Skin P e r f e c t i o n and E a r l y Frosty 156 5.38 F i t t e d time trends f o r t o t a l dry weight (W) per plant and m u l t i p l i c a t i v e components of dry weight 159 5.39 F i t t e d time trends for r e l a t i v e growth rates of t o t a l dry weight per plant and m u l t i p l i c a t i v e components 160 5.40 F i t t e d time trends for the f r a c t i o n a l production rates of the m u l t i p l i c a t i v e components of t o t a l dry weight per plant 161 5.41 F i t t e d time trends for y i e l d (W S e) per plant and y i e l d components 163 5.42 F i t t e d time trends for r e l a t i v e growth rates of y i e l d ( w g e ) a n a y i e l d components 165 5.43 F i t t e d time trends for f r a c t i o n a l production rates of y i e l d components 166 7.1 Simulation of pod growth at f i r s t 7 nodes of garden pea 193 - xiv -ACKNOWLEDGMENTS The success of a study such as t h i s depends on the co-operation of a number of people. I, therefore, wish to express my gratitude to a l l who have helped in some way. Special thanks to my supervisor, Dr. George W. Eaton for his confidence i n me and his h e l p f u l suggestions and guidance throughout my course of study. I also wish to thank the members of my committee: Dr. P.A. J o l l i f f e for the many stimulating discussions and invaluable advice; Dr. A. Kozak for his exc e l l e n t teachings in sampling techniques, s t a t i s t i c s and computing; Dr. N.R. Knowles and Dr. V.C. Runeckles for t h e i r i n t e r e s t and will i n g n e s s to a s s i s t me at a l l times. Acknowledgments are also due Dr. W.C. Anderson, who provided the seeds for the study, and Miss Carolyn Moore for her assistance with the s p l i n e programs. I am indebted to Miss Helen Evans for her d i l i g e n t t e c h nical a s s i s t a n c e . The cont r i b u t i o n s of the technical s t a f f and se c r e t a r i e s of the Department of Plant Science are also acknowledged with a p p r e c i a t i o n . I would also l i k e to express thanks to Dr. Norman S.W. Williams f o r his c r i t i c a l reading of my f i r s t d r a f t and for being my constant source of i n s p i r a t i o n . I am g r a t e f u l to Dr. Nazir Ahmad of the U n i v e r s i t y of West Indies, who encouraged me to pursue t h i s degree. I thank my r e l a t i v e s and fr i e n d s for their love, prayers and encouragement over the years, e s p e c i a l l y during the course of my study. F i n a l l y , the Canadian Commonwealth Scholarship Committee, the National Research Council of Canada and the government of Trinidad and Tobago are g r a t e f u l l y acknowledged for t h e i r f i n a n c i a l assistance. - XV -Dedicated to my mother, brother and s i s t e r and to my father who died before t h i s thesis was completed. - 1 -CHAPTER 1 INTRODUCTION The garden pea, Pisum sativum, i s an important source of protein for the inhabitants of many countries i n the temperate zone. In Canada, pea production accounts for approximately 40,000 he c t a r e s 1 of c u l t i v a t e d land. Of that acreage, an estimated 50% i s grown on a contract basis for processing, while the remainder i s used dried or, to a l e s s e r extent, as a fodder crop. In view of the importance of t h i s crop to the a g r i c u l t u r a l sector, i t i s not s u r p r i s i n g that the plant has been extensively studied. Despite the e f f o r t s of previous i n v e s t i g a t o r s , high crop v a r i a b i l i t y i s s t i l l an outstanding problem. V a r i a b i l i t y of the pea crop i s e s p e c i a l l y undesirable for processing (or 'vining') peas. To date, only a few researchers (Hardwick _e_t ^ 1., 1978; Hole and Scott, 1981) have examined the cause(s) of t h i s v a r i a b i l i t y . Moreover, t h e i r studies at the crop and whole plant l e v e l of organisation have concentrated mainly on the a c t i v i t y of the photosynthetic sinks ( i . e . , the pods). By comparison, very l i t t l e has been done at that l e v e l of organisation on the a c t i v i t y of the source. Hardwick and Milbourn (1967) explained that the dearth of information on the source a r i s e s from the d i f f i c u l t y i n applying t r a d i t i o n a l growth analysis techniques during the F r u i t and Vegetable production, August 1984, S t a t i s t i c s Canada Catalogue numbers 22-003 and 22-002 (June, 1984). - 2 -reproductive phase. These authors b e l i e v e that the following reasons could account for the d i f f i c u l t y : '. . . photosynthetic a c t i v i t y i s not always proportional to l e a f area. At flowering, much of the l e a f canopy i s senescent and l i k e l y to be past i t s peak a c t i v i t y . Also, during the reproductive phase of growth true l e a f area i s d i f f i c u l t to estimate, for at that time l e a f loss proceeds fa s t e r than l e a f production. Estimation of e f f e c t i v e photosynthetic area i s further complicated by the considerable area of stems and green pods present i n the crop. F i n a l l y at the time of flowering the roots almost stop growing and i t would be impossible to estimate in a f i e l d crop the extent of possible deployment of root reserves . . .' On the other hand, source a c t i v i t y has been studied at the sub-organismal l e v e l . However, the majority of these studies were conducted under c o n t r o l l e d ( i n greenhouses or growth chambers) environmental conditions. Furthermore, some of the treatments involved some form of manipulation of the major source organs (e.g., d e f o l i a t i o n or shading). Whereas information obtained from these studies i s u s e f u l , i t does not provide an explanation for the e f f e c t s of p h y s i o l o g i c a l processes at higher l e v e l s of organisation during the reproductive phase of growth. Pate and F l i n n (1977) state that: 'Although much of t h i s material i s highly relevant to our basic understanding of the process of f r u i t maturation, i t has f a i l e d to unravel the dynamic aspects of f r u i t and seed growth and to s p e c i f y which regulatory forces within the whole plant shape events during the c l o s i n g stages of the l i f e c y c l e . ' The foregoing remarks suggest the need to obtain q u a n t i t a t i v e information on the physiology of growth and y i e l d during the reproductive phase. The present e f f o r t i s directed toward t h i s end. It i s hoped that - 3 -the r e s u l t s from this study w i l l provide a basis for c o n t r o l l i n g , and thus improving, the crop performance. An a d d i t i o n a l o b j e c t i v e of t h i s study was to i n v e s t i g a t e the e f f e c t of seed i n o c u l a t i o n on growth and y i e l d i n the garden pea. European countries have obtained y i e l d increases of 20 - 30% following seed i n o c u l a t i o n with Rhizobium species (Pate, 1977). Despite these increases, i n o c u l a t i o n i s not commonly practised in North America. 1.1 S t a t e m e n t o f t h e P r o b l e m The foregoing section indicates that a c t i v i t y of the photosynthetic source as well as the sink requires further i n v e s t i g a t i o n . In a d d i t i o n , the methods of analysis a v a i l a b l e for simultaneously studying both systems, at the crop and whole plant l e v e l s of organisation have proved inadequate. Recent developments i n methods for studying plant growth and y i e l d (e.g., Hunt and Bazzaz, 1980; J o l l i f f e et _ a l . , 1982; Lovett-Doust et a l . , 1983; J o l l i f f e and Courtney, 1984) have resulted i n more powerful techniques which have provided further information on the physiology of y i e l d in a number of crops (e.g., beans, sunflower). It was, therefore, believed that these new methods could be useful in i n v e s t i g a t i n g the p h y s i o l o g i c a l basis for y i e l d v a r i a b i l i t y in the garden pea. It also appeared necessary to determine whether seed i n o c u l a t i o n i s of any s i g n i f i c a n t value under the s o i l conditions prevalent at the U n i v e r s i t y of B r i t i s h Columbia f i e l d laboratory. - 4 -1.2 Objectives of the Study The objectives of the study were: 1. to determine the main components of y i e l d v a r i a b i l i t y i n the garden pea, 2. to show the r e l a t i o n s h i p s among the y i e l d components during the reproductive growth phase, 3. to elucidate the net a c t i v i t y of the source of photosynthetic material during reproductive development, 4. to inve s t i g a t e how the y i e l d components contribute to vegetative and reproductive p r o d u c t i v i t y , and 5. to asce r t a i n the e f f e c t , i f any, of seed i n o c u l a t i o n on growth and y i e l d i n the garden pea. From the above-listed o b j e c t i v e s , the main aim was to develop a dynamic model of reproductive growth in the garden pea. It was hoped that t h i s model would be useful in p r e d i c t i n g and c o n t r o l l i n g v a r i a b i l i t y i n the pea crop. - 5 -CHAPTER 2 LITERATURE REVIEW 2.1 General Research i n t e r e s t i n the p h y s i o l o g i c a l changes which occur i n the pea dates back to the e a r l y 1900's. With the aid of sophisticated experimental techniques (e.g., r a d i o t r a c e r s and e l e c t r o p h o r e s i s ) , introduced during the l a s t two decades, a better understanding of the developmental processes and the factors which a f f e c t them has become poss i b l e . Researchers have since been able to i d e n t i f y the various compounds formed and the associated biochemical pathways involved. In an e f f o r t of improve the pea crop, a number of researchers (Milbourn and Hardwick, 1968; Eastin and G r i t t o n , 1969; Meadley and Milbourn, 1970, 1971) studied growth patterns and t h e i r influence on y i e l d . The need for r e l i a b l e data analysis which would provide valuable information to the pea producer cannot be overemphasized. The progress of research on the physiology of reproductive growth i n the garden pea, Pisum sativum i s described herein. Also, a b r i e f account of published growth and y i e l d analysis techniques i s presented in order to provide a background for the current research. 2.2 Studies of the Physiological Canages in the Pea One of the f i r s t reported i n v e s t i g a t i o n s of p h y s i o l o g i c a l changes occurring during pea f r u i t development was that of Bisson and Jones (1932). - 6 -These i n v e s t i g a t o r s observed that pod growth preceded that of the enclosed seed. Their r e s u l t s showed that t o t a l fresh weight of both pod and seeds increased to a maximum 32 days a f t e r anthesis, before d e c l i n i n g , while t o t a l dry weight increased throughout the e n t i r e period. The observed increase in dry weight a f t e r day 22 post-anthesis was a t t r i b u t a b l e only to the seeds. A s i m i l a r pattern of growth was observed by a number of other researchers (McKee et a l . , 1955; Carr and Skene, 1961; Bain and Mercer, 1966; F l i n n and Pate, 1968). Carr and Skene (1961) noticed that seed growth was d i a u x i c , having two periods of growth separated by a lag phase. They furt h e r found that t h i s lag was common among seeds of other legumes. However, they suggested that inadequate sampling procedures may have precluded i t s detection by e a r l i e r researchers. More recent l y , Hedley and Ambrose (1980) observed two lag phases i n the development of Pisum sativum seeds. The reason for the lag has not yet been determined. A number of explanations, however, have been o f f e r e d . Pate and F l i n n (1977), i n t h e i r review of the physiology of the garden pea, noticed that the lag was more pronounced when the seeds developed under coo l , slow growing condit ions. This led them to conclude that the r e s t r i c t e d growth and hence the l a g , resulted from environmental f a c t o r s which affected embryo development. The findings of Hedley and Ambrose (1980) supported Pate and Flinn's (1977) conclusions. The former authors' r e s u l t s showed no c o r r e l a t i o n between the occurrence of the lag and any p h y s i o l o g i c a l stage in the seed's development. As a r e s u l t , they suggested that other factors such as - 7 -maternal parent, i n t e r a c t i o n among seed components and genetic c o n s t i t u t i o n of the embryo were involved. Carr and Skene (1961) concluded that the l a g i s purely p h y s i c a l i n nature, r e s u l t i n g from a r e s t r i c t i o n i n the growth of the embryo. Burrows and Carr (1970) on the other hand, c i t e d a d e f i c i e n c y of nutrients and growth regulators as the cause. In a d d i t i o n to time course studies on seed dry matter accumulation, i n v e s t i g a t i o n s were a l s o conducted on nu t r i e n t supply to the seed and pod. Flintj and Pate (1968) observed that only 20% of nitrogen required by the seed was supplied by nitrogen a s s i m i l a t e d before flowering. In a l a t e r study (1970) the same authors found that two-thirds of the carbon required by the seed was supplied by the enclosing pod, l e a f l e t and corresponding s t i p u l e . F l i n n (1974) i n d i c a t e d that the l e a f l e t s were major contributors of a s s i m i l a t e during e a r l y f r u i t development ( i . e . , during pod elongation and i n f l a t i o n ) , but the r e a f t e r other sources were more important. This l a t t e r f i n d i n g i s consistent with that of Linck. and Sudia (1962) and Szynkier (1974) who observed a s i m i l a r pattern of d i s t r i b u t i o n . The l a t t e r author a l s o noticed that pods at the f i r s t and second reproductive nodes competed f o r a s s i m i l a t e s e s p e c i a l l y when the supply l e a f of the f i r s t pod was removed. Hole and Scott (1983) found that during e a r l y development, growth of f r u i t s at the f i r s t reproductive node was unaffected by the presence of a d d i t i o n a l f r u i t s regardless of t h e i r p o s i t i o n . During l a t e development (more than 20 days a f t e r a n t h e s i s ) , however, competition was observed among pods at the same node and among f r u i t s at higher nodes. - 8 -The pod i s an important source of a s s i m i l a t e to the developing seed. F l i n n and Pate (1970) showed that i n Pisum arvense the pod was t o t a l l y committed to export of carbon to the seed. Gas exchange studies by these same authors indicated that the carbon dioxide f or f i x a t i o n by the pods was supplied mainly by the r e s p i r a t i o n of the enclosed seeds. L o v e l l and L o v e l l (1970) found that the rate of importation of photosynthetic carbon from both attached and detached pods was determined by the weight of the seeds. They therefore suggested that control of CO2 f i x a t i o n and export of carbon material by the pod were independent of the rest of the plant. The above-mentioned experiments were l i m i t e d to a very short period i n the plant's development. A study which extended over the e n t i r e l i f e of the plant was performed by Pate and F l i n n (1973). This study showed that carbon assimilated during early vegetative growth was not very important in f r u i t n u t r i t i o n as the majority of i t was l o s t during growth. This l o s s was a t t r i b u t e d to r e s p i r a t i o n p r i o r to flowering and to i t s incorporation into materials which could not be r e t r i e v e d during senescence of vegetative organs. On the other hand, carbon assimilated during f r u i t i n g was found to be extremely important, accounting for over 70% of the f r u i t ' s requirement. Ai e n t i r e l y d i f f e r e n t p i c ture emerged for nitrogen. Nitrogen asim i l a t e d during e a r l y vegetative growth was e f f i c i e n t l y released to support seed development. The rate of nitrogen m o b i l i z a t i o n was observed to increase as f r u i t i n g increased. Lewis and Pate (1973) showed that the non-reproductive organs were the major source of isotopie nitrogen, 1 5N, transferred to the developing seed. - 9 -On the basis of the studies noted above, Lewis and Pate (1973) concluded that, i n s e l e c t i n g f o r improved carbon and nitrogen supply to the seeds, three p o s s i b i l i t i e s should be considered: ( i ) increased supply of carbon during f r u i t i n g by the subtending l e a f l e t s ( i i ) reduced competition by other vegetative structures during f r u i t i n g (e.g., by e a r l y senescence of the shoot apex), and ( i i i ) the accumulation of large reserves of nitrogen by the time of flowering. In breeding f o r vining.peas, the f i r s t point precludes the t h i r d as optimum maturity of the seeds i s a t t a i n e d before the maximum rate of m o b i l i z a t i o n of nitrogen i s r e a l i z e d . As a r e s u l t , breeding f o r increased vegetative s t r u c t u r e s — t o enhance nitrogen n u t r i t i o n — w o u l d increase competition among these structures for carbon a s s i m i l a t e s and therefore reduce the supply of carbon to the f r u i t . E f f o r t s need to be made, therefore, to resolve t h i s problem. Other i n v e s t i g a t i o n s on the pea have been d i r e c t e d p r i m a r i l y towards understanding the e f f e c t s of environmental f a c t o r s and management pra c t i c e s on y i e l d and i t s components. Boswell (1926) reported that high temperatures r e s u l t e d i n a reduced number of pods per plant but had no e f f e c t on average seed weight. He was unable, however, to i d e n t i f y the period of development most susc e p t i b l e to temperature. In an e f f o r t to determine the c r i t i c a l period, Lambert and Linck (1958) conducted an experiment under c o n t r o l l e d c o n d i t i o n s . In t h e i r study, the most deleterious e f f e c t of high temperature on y i e l d was seen - 10 -when plants were exposed 5 days a f t e r bloom. The number of pods decreased with increasing temperature at t h i s stage of development. Karr et a l . (1959) noted that plants were most s e n s i t i v e to the e f f e c t s of high day temperature during the period 9-11 days a f t e r f u l l bloom, while the most s e n s i t i v e period to high night temperatures was 6-9 days a f t e r f u l l bloom. Further i n v e s t i g a t i o n s on the e f f e c t of temperature were reported by F l e t c h e r et a l . (1966) and S t a n f i e l d et_ a l . (1966). The l a t t e r authors obtained r e s u l t s which agreed with those of e a r l i e r researchers (Boswell, 1926; Lambert and Linck, 1958; Karr et a l . , 1959). Their r e s u l t s also showed a negative c o r r e l a t i o n between vegetative and reproductive growth which they explained to be due to competition for photosynthetic m a t e r i a l . Fl e t c h e r _et _a l . (1966) observed an i n t e r a c t i o n between temperature and l o c a t i o n on y i e l d and i t s components which resulted in findings which are i n c o n s i s t e n t with those of e a r l i e r workers. For instance, at one l o c a t i o n mean maximum temperatures were observed to be negatively correlated with y i e l d of t o t a l dry matter, peas per pod and pea y i e l d . At a second l o c a t i o n , however, the c o r r e l a t i o n s were p o s i t i v e . The authors suggested the cause of the d i s p a r i t y was the f a c t that the temperatures at the f i r s t l o c a t i o n were above optimum while at the second l o c a t i o n they were sub-optimal. Since the temperature e f f e c t manifests i t s e l f i n r e l a t i o n to the date of p l a n t i n g , a number of researchers (Proctor, 1963; Fletcher _et _ a l . , 1966; Milbourn and Hardwick, 1968) investigated the e f f e c t of t h i s c u l t u r a l p r a c t i c e on y i e l d . Their r e s u l t s have indicated that y i e l d declined with - 11 -advancing sowing date. The reduction was apparently due to a decrease in the number of reproductive nodes and the number of pods per node. G r i t t o n and Eastin (1968) conducted experiments on the e f f e c t of planting density on y i e l d . Their experiments revealed that y i e l d increased with i n c r e a s i n g plant population. The components—plant height, t o t a l number of pods, lowest bearing node, average si z e of shelled peas and number of reproductive nodes—were unaffected by the treatment. In another paper, Eastin and G r i t t o n (1969) reported that p r o d u c t i v i t y of the pea crop was l i m i t e d by sub-optimal l e a f area index (LAI). As a r e s u l t , they suggested that an increase in LAI as well as changes i n l e a f o r i e n t a t i o n and d i s t r i b u t i o n would s i g n i f i c a n t l y improve crop performance. Mean net a s s i m i l a t i o n rate was also determined in the study but the r e s u l t s were inconclusive because of high v a r i a b i l i t y of the data. Meadley and Milbourn (1970) also worked on the e f f e c t of p l a n t i n g d e n s i t y on y i e l d and i t s components. Their r e s u l t s showed that the number of reproductive nodes increased with increasing density, however, the rate of flower a b s c i s s i o n also increased. Since the occurrence of l e a f senescence coincided with flower a b s c i s s i o n , the authors suggested that flower a b s c i s s i o n was due to a d e f i c i e n c y i n the supply of photosynthetic m a t e r i a l . Comparable r e s u l t s were obtained in a l a t e r study on the e f f e c t of shading (Meadley and Milbourn, 1971) ( i . e . , increased shading—such as that which occurs with increasing d e n s i t y — r e s u l t e d in increased a b s c i s s i o n of flowers and pods). They also found that the rate of abscission was reduced when shading was removed at the onset of flowering. Moreover, the y i e l d s - 12 -obtained thereafter were observed to be s i m i l a r to those of the unshaded p l a n t s . When shading was applied at the onset of flowering, however, the y i e l d s were s u b s t a n t i a l l y reduced. The extent of t h i s reduction was comparable to that of plants which were shaded for the e n t i r e growing season. This f i n d i n g led these authors to conclude that photosynthetic material produced af t e r flowering i s a major source of dry matter for pea y i e l d . The findings of Meadley and Milbourn (1970, 1971) as well as those of e a r l i e r researchers (Linck and Sudia, 1962; L o v e l l and L o v e l l , 1970; F l i n n and Pate, 1968, 1970; Szynkier,'1974) on the importance of the pod as a source of a s s i m i l a t e , prompted Hole and Scott (1981) to i n v e s t i g a t e the e f f e c t of f r u i t shading on y i e l d . Their r e s u l t s indicated a 12% reduction i n y i e l d due to the treatment. Compensation by the f o l i a g e was also evident as there was a greater reduction in y i e l d due to l e a f shading. I t i s i n t e r e s t i n g to note that the f i r s t reproductive node appeared to be more severely affected by the treatment. This d i f f e r e n c e i n response was suggested as a source of v a r i a b i l i t y i n y i e l d of the v i n i n g pea. A d d i t i o n a l evidence of the importance of the post-flowering period was reported by Salter (1962, 1963) and Maurer _et _al. (1968). In t h e i r studies on the e f f e c t of i r r i g a t i o n and various water regimes on y i e l d , they observed increased y i e l d s when i r r i g a t i o n was applied a f t e r bloom, despite severe water st r e s s during the vegetative phase. Experimental r e s u l t s obtained at both the crop and sub-organismal l e v e l , i n d i c a t e that the supply of a s s i m i l a t e during the reproductive phase of growth and the number of reproductive nodes and pods are the main fac t o r s which influence the y i e l d of the v i n i n g pea. This f i n d i n g l e d - 13 -plant breeders to s e l e c t and breed for plants with e a r l y senescence and more synchronous flowering habit, i n order to take f u l l advantage of the photosynthetic supply during f r u i t i n g . In a d d i t i o n , new phenotypes—the s o - c a l l e d ' l e a f l e s s ' mutants, as well as the 'semi-leafless' types, are now being considered. These mutants are homozygous for recessive genes which control f o l i a g e development and r e s u l t i n plants with: i ) t e n d r i l s rather than l e a f l e t s ( a f ) , i i ) l e a f l e t s rather than t e n d r i l s ( t l ) , and i i i ) v e s t i g e s of s t i p u l e s ( s t ) . The performance of these new plant forms has been extensively evaluated by a number of researchers (Davies, 1977; Harvey, 1972, 1973, 1978; Harvey and Goodwin, 1978; Harvey _et _ a l . , 1976; Hedley and Ambrose, 1979; Pyke and Hedley, 1982, 1983a, 1983b; Snoad, 1974, 1981; Snoad and Arthur, 1974). Results i n d i c a t e that the plants have great p o t e n t i a l f or future use because of t h e i r improved standing a b i l i t y . However, the use of improved genetic material to enhance plant performance i s l i m i t e d in i t s scope (Hobbs and Mahon, 1982). Researchers must therefore explore new avenues for crop improvement. Workers are now designing research programs aimed at gaining a better understanding of the p h y s i o l o g i c a l aspects of crop y i e l d . In t h i s regard, experimenters (Hardwick and Milbourn, 1967; Hardwick, 1969) have concentrated mainly on only one a s p e c t — t h e sink. Through y i e l d component a n a l y s i s , they have been able to i d e n t i f y a number of important components. However, as Bruinsma (1966) pointed out, y i e l d i s the product of other stages of - 14 -development which involve vegetative organs. Consequently, such an approach s u f f e r s from a fundamental l i m i t a t i o n . T r a d i t i o n a l growth a n a l y s i s i s one method which examines the a c t i v i t y of the source. However, i t s use i n pea physiology has been l i m i t e d mainly to the vegetative phase. A few workers (Brouwer, 1962; E a s t i n and G r i t t o n , 1969; Meadley and Milbourn, 1970, 1971; Milbourn and Hardwick, 1968) have app l i e d c l a s s i c a l growth a n a l y s i s methods to i n v e s t i g a t e the behaviour of growth i n d i c e s during the reproductive phase. However, the problems o u t l i n e d i n Chapter 1 concerning the a p p l i c a t i o n of these techniques have forced researchers to d i s c a r d l e a f area index and mean unit l e a f rate as s a t i s f a c t o r y i n d i c e s f o r the study of reproductive growth i n the pea crop (Pate, 1975). Although a great deal i s known about reproductive development at the sub-organismal l e v e l of o r g a n i z a t i o n , r e l a t i v e l y l i t t l e a t t e n t i o n has been paid to the physiology of the higher l e v e l s , e s p e c i a l l y the reproductive performance of the whole plant i n a crop environment. In p a r t i c u l a r , a c t i v i t y of the non-reproductive source during the reproductive phase requires more a t t e n t i o n . Improved knowledge i n t h i s area could prove h e l p f u l i n understanding and e l i m i n a t i n g the wide v a r i a b i l i t y i n pea y i e l d — a problem which continues to plague pea producers. 2.3 G r o w t h and Yield Analysis Both y i e l d component and c l a s s i c a l growth a n a l y s i s have been used to study the reproductive growth of the pea. Y i e l d component models have - 15 -concentrated mainly on reproductive structures and as a result, a comprehensive understanding of the activity of the source is lacking. Classical growth analysis has focused on the activity of the source (Milbourn and Hardwick, 1968). However, high data variability has resulted in inconclusive findings. Hence, this technique has not been widely used. It is necessary, therefore, to apply improved techniques of growth and yield analysis in an effort to gain a better understanding of both sink and source activity under field conditions. Since the early 1960's, great strides have been made in the methodology of these techniques (Vernon and Allison, 1963; Hughes and Freeman, 1967; Hunt and Parsons, 1974, 1977; Hunt, 1982a,b; Venus and Causton, 1979). It is therefore important to understand these developments, as they pertain to the limitations of the previous approaches, so that their application may be justified. 2.3.1 Yield Component Analysis This is by far the most widely used approach for studying the reproductive phase of peas. In this method, yield is subdivided into various morphological components which contribute to its variability. These components may be expressed as ratios of plant parts, the product of which is yield. Statistical methods used to quantify the contribution of yield components have been reviewed by Fraser and Eaton (1983). These methods range from simple regression and analysis of variance (Angus and Sage, - 16 -1980; Karami, 1980; Mason and Rath, 1980) to more complicated techniques such as m u l t i v a r i a t e analysis (Dale and Topham, 1980; Dougherty et a l . 1978; Walton, 1971). A major shortcoming of the aforementioned techniques i s that they do not take into account the sequential nature of plant development. This d e f i c i e n c y was f i r s t alluded to by Eaton and Kyte (1978) in the analysis of y i e l d components of cranberry, then by Huxley _et _a l . (1979) in the study of white clover; by Shawa et a l . (1981) i n cranberries and more re c e n t l y by Neilson and Eaton (1983) in strawberry. The improved t e c h n i q u e — s e q u e n t i a l y i e l d component analysis ( S Y C A ) — i n v o l v e s the stepwise i n s e r t i o n of y i e l d components into the mu l t i p l e regression equation in the order in which they occur during plant development. The c o n t r i b u t i o n of each new independent v a r i a b l e included in the equation i s measured by the increment in the c o e f f i c i e n t of determination, R . Recently, a new method "Backward Y i e l d Component Analysis" (BYCA), (Bowen and Eaton, 1983) has been developed. In BYCA, the sequence in which y i e l d components are entered i s reversed ( i . e . the l a s t to appear c h r o n o l o g i c a l l y must be entered f i r s t ) . When used in combination with SYCA, an estimate of the " d i r e c t e f f e c t " of a p a r t i c u l a r component on y i e l d i s obtained. For example, i f a component acts independently of the e a r l i e r o components in the sequence, i t s c o e f f i c i e n t of determination (R ) in SYCA would be 0. On the other hand, i f that same component, when taken as the independent v a r i a b l e in BYCA, has an R value greater than 0, then i t s e f f e c t on y i e l d i s d i r e c t . The e f f e c t i s d i r e c t because the influence of - 17 -c h r o n o l o g i c a l l y l a t e r y i e l d components has been removed and that of e a r l i e r components i s 0. 2.3.2 Growth Analysis T r a d i t i o n a l plant growth analysis has been used i n the study of pea physiology to a les s e r extent than y i e l d component a n a l y s i s . It was f i r s t developed i n the early part of th i s century, through the work of Gregory (1918), Blackman (1919), Briggs, Kidd and West (1920) with l a t e r improvements by Williams (1946) and Watson (1952). In t h i s method dry matter production i s subdivided into i n d i c e s of e f f i c i e n c y and extent of the a s s i m i l a t o r y system, rate and duration of production and the p a r t i t i o n i n g of the product (dry matter) into economic y i e l d . Evans (1972), Kvet et a l . (1971), Causton and Venus (1981) and Hunt (1978b, 1982b) reviewed the methodology of growth an a l y s i s and i t s • a p p l i c a t i o n to the study of a wide range of crops. Present day t r a d i t i o n a l growth a n a l y s i s has s h i f t e d from the c l a s s i c a l approach to the so-called f u n c t i o n a l approach. With t h i s improved technique, growth indices are derived from f i t t e d curves of the time course of the primary values. Thus, instead of mean values of the t r a d i t i o n a l i n d i c e s , instantaneous values are derived from simple mathematical expressions. In add i t i o n , the problems (e.g., p a i r i n g , unequal sample s i z e s , large harvests and harvest i n t e r v a l s and the c a l c u l a t i o n of mean values of indices such as unit l e a f rate) associated with the a p p l i c a t i o n of the c l a s s i c a l approach (Hunt, 1979) were circumvented. - 18 -According to Hunt, " . . . the main concern of the functional approach i s to describe r e a l i t y i n a convenient way." To t h i s end, two methods of curve f i t t i n g have been adopted i n which curves are f i t t e d by ( i ) non-linear regression and ( i i ) l e ast squares estimation. Several advocates of the non-linear approach (Richards, 1959; Venus and Causton, 1979; Causton, 1969) c i t e the b i o l o g i c a l s i g n i f i c a n c e of the parameters as the f o r t g of t h i s method. The a p p l i c a b i l i t y of non-linear regression i s l i m i t e d , however, to data sets with asymptotic growth patterns. Least squares estimation Is more widely used. The a p p l i c a t i o n of polynomials to growth data i s described in papers by Vernon and A l l i s o n (1963), Hughes and Freeman (1967), N i c h o l l s and Calder (1973), E l i a s and Causton (1976), Hunt and Parsons (1974) and in a recent review by Hunt (1982b). These polynomials were found, however, to be too r i g i d and u n r e a l i s t i c for d e s c r i b i n g lengthy data sets. As a r e s u l t , Hunt and Parsons (1977) f i t t e d segmented polynomials to such data s e t s . This method proved superior to the previously used stepwise polynomials as the f i t was improved and r e s i d u a l error was reduced. However, the s t a t i s t i c a l v a l i d i t y of the subjective method of segmentation of the data caused the authors some concern. This problem was eventually overcome through the use of splined regressions. In p a r t i c u l a r , Hunt and Evans (1980) applied the B-splines formerly described by Wold (1974). These s p l i n e s are polynomial ( u s u a l l y cubic) pieces joined at points c a l l e d knots. The knots have - 19 -special properties of continuity in both first and second derivatives which make them well suited for growth studies. Another type of cubic spline, which has been used by Jolliffe and Courtney (1984) in growth studies, is that of Reinsch (1971). The spline includes a smoothing factor and is therefore appropriate for the study of highly variable data. Some degree of smoothing is done automatically by the program through a weighting process which involves the use of standard deviations of means of variates at each harvest. In addition, a smoothing factor is included which can be set by the programmer. Recently Hunt (1982a) has used the second derivatives from the B-spline regressions to derive new growth indices. These indices are: the relative growth rate-rate (R'y), the relative acceleration rate (Vy) and the unit acceleration rate (W). Although these indices have provided additional information for growth analysis, more research is needed on their behavior under varying environmental conditions. 2.3.3 Demographic Analysis This third method of growth analysis has not been used in pea physiology. The plant and its organs (e.g., leaves and flowers) are likened to a population of modules which is well suited to cohort analysis. "Birth" and "death" rates of the modules are recorded throughout the growth period. Bazzaz and Harper (1977), Clark (1980) and Lovett Doust (1981) have applied this technique in the study of leaf demography, while Lovett Doust et al. (1983) studied flower demography. - 20 -Hunt (1978a) showed that demography and t r a d i t i o n a l growth analysis were complementary, the former dealing with changes in the number of a s s i m i l i a t o r y organs while the l a t t e r examined the size and a c t i v i t y of these organs. Hunt and Bazzaz (1980) were able to obtain a d d i t i o n a l information on the growth of Ambrosia t r i f i d a at sub-organismal l e v e l s by combining the two methods. 2.3.4 A Combined Approach The a d d i t i o n a l information possible through the use of a combined approach has prompted researchers to l i n k a l l of the three afore-mentioned methods of growth and y i e l d a n a l y s i s . Hunt and Bazzaz (1980) for example, have combined t r a d i t i o n a l growth analysis with demography. Lovett Doust et a l . (1983) have joined SYCA and demography of flowers i n inve s t i g a t e y i e l d i n beans Phaseolus v u l g a r i s . J o l l i f f e et _al. (1982) used the p r i n c i p l e s of growth analyses and SYCA to produce sequential plant growth analysis (SPGA) i n the study of beans. By using t h i s method, t r a d i t i o n a l growth indices such as l e a f area index and l e a f area r a t i o are expressed as component r a t i o s in the p r e d i c t i o n of y i e l d , where y i e l d i s t o t a l plant dry matter. Problems associated with the large number of r e p l i c a t e s required for estimation of unit leaf rate, E, resulted in a new approach. Thus, in a subsequent paper, J o l l i f f e and Courtney (1984) were able to use a l l three methods—SYCA, demography and growth a n a l y s i s — t o determine contributions made to t o t a l plant performance by both a d d i t i v e and m u l t i p l i c a t i v e components. - 21 -The a p p l i c a t i o n of these new techniques of growth and y i e l d analysis would ( i ) help to overcome some of the problems which have stymied progress i n the study of the a c t i v i t y of the source during the reproductive phase of growth and ( i i ) promote an understanding of the dynamics of reproductive growth—an area which has heretofore been neglected. - 22 -CHAPTER 3 MATERIALS AND METHODS This chapter describes the experimental procedure as well as the methods of ana l y s i s which were used i n the present study. 3.1 The Design A 2 x 2 f a c t o r i a l experiment was used. Two c u l t i v a r s — ' D a r k Skin P e r f e c t i o n ' and 'Early Frosty'—were chosen f o r th i s experiment. The seeds, i n each case, were eit h e r untreated or inoculated with a Rhizobium  1eguminosarium-Rhizobium phaseoli-peat mixture. 1 Planting was done on May 11, 1983 at the Totem F i e l d of the U n i v e r s i t y of B r i t i s h Columbia Plant Science F i e l d Laboratory. The plot was arranged in a randomized block design with eight blocks (7m x lm) and four treatments. Within each block there were four rows of plants (1 row/treatment) with 104 plants per row. These plants were thinned to 52/row (spacing approximately 10cm x 20cm) at 13 days a f t e r planting and standard c u l t u r a l p r a c t i c e s , such as weeding and i r r i g a t i o n were applied as needed. No f e r t i l i z e r was applied throughout the experiment. 3.2 Primary Data C o l l e c t i o n Both d e s t r u c t i v e and non-destructive harvesting were done. The mixture was supplied by Buckerfield's Limited, 3311 Kingsway, Vancouver, B r i t i s h Columbia. 3.2.1 Destructive Harvests Two harvests were taken during the vegetative phase. One at e a r l y growth (20 days a f t e r planting) and the other at l a t e growth (50 days a f t e r p l a n t i n g ) . On each occasion 96 plants (three plants/treatment/block) were randomly sampled. Since the reproductive phase i s of primary i n t e r e s t in th i s study, i t was necessary to harvest more frequently i n the l a t e r stages of growth. Thus, from the onset of flowering (53 days a f t e r planting) 16 plants per treatment were sampled once every three days u n t i l the f i n a l harvest at 80 days a f t e r p l a n t i n g . The following q u a n t i t i e s were obtained from each harvested plant: Plant height (S) cm Number of leaves (Lfl) Tot a l l e a f area ( L ^ ) * cm2 T o t a l l e a f dry weight (W L)** g Stem dry weight (Wg)** g Number of flowers (FJJ) Number of pods (P) Pod length (P L) cm Pod fresh weight (Wp) g Number of seeds per pod (Se) *Leaf area was measured by using a L i Cor, model LI-3100, l e a f area meter. **For dry weight determination, the sample was oven dried (at 105°C) for 3 days before weighing i t . - 24 -Seed fresh weight (Wge) g Pod wall fresh weight (W(]) g 3.2.2 Non-Destructive Harvests At thinning ( i . e . 13 days a f t e r planting) two plants from each row of treatments were randomly selected and l a b e l l e d . Measurements were repeated on these plants at three-day i n t e r v a l s , throughout the growing period (21 days a f t e r planting to 81 days a f t e r p l a n t i n g ) . The q u a n t i t i e s determined on a per plant basis were: Plant height (S) cm Pod length ( P L ) cm Sti p u l e length (s) cm L e a f l e t length (1) cm Number of flowers (F^) Number of pods (P) Number of leaves (Ljj) A l l l a b e l l e d plants were d e s t r u c t i v e l y harvested at 81 days a f t e r planting and a d d i t i o n a l information was obtained as follows: Total l e a f area ( L ^ ) * cm2 T o t a l l e a f dry weight (WL)** g Stem dry weight (Wg)** g Seed fresh weight (Wge) g Pod f r e s h weight (Wp) g Pod wall fresh weight (Wrj) g Number of seeds per pod (Se) - 2 5 -3.2.2.1 Prediction Equations I t was not po s s i b l e to measure the weights and l e a f areas from the non-destructively harvested p l a n t s . As a r e s u l t , these q u a n t i t i e s (Table 3.1) were estimated from p r e d i c t i o n equations derived by regressions on the measured v a r i a b l e s . At each d e s t r u c t i v e harvest, two leaves were se l e c t e d from each harvested p l a n t . Measurements were made of the s t i p u l e lengths, l e a f l e t lengths and t h e i r respective areas. (In an e f f o r t to obtain a representative sample of the e n t i r e range of l e a f s i z e s , leaves were non-randomly s e l e c t e d ) . A l l p r e d i c t i o n equations were derived by using the BMDPIR s t a t i s t i c a l package (Dixon, 1983). Separate regressions were done f o r each treatment and f o r each harvest. Then the data were pooled and equations were c a l c u l a t e d f o r the pooled data. These regressions were then tested using the method described by Weisberg (1980), to determine whether a generalized equation could be used i n a l l instances (Appendix A . l ) . The areas and weights of i n d i v i d u a l leaves were c a l c u l a t e d using the fol l o w i n g equation: * [1] * and W A, " 2(V + V i i i ) [2] *The values were m u l t i p l i e d by two because each l e a f of Pisum sativum i s u s u a l l y comprised of p a i r s of l e a f l e t s and s t i p u l e s . - 26 -Table 3.1 - Summary of v a r i a t e s and independent v a r i a b l e s used in t h e i r p r e d i c t i o n equations P r e d i c t o r (Independent Variable) S t i p u l e length L e a f l e t length Sti p u l e length, l e a f l e t length T o t a l l e a f area Stem length, t o t a l l e a f area, number of leaves, t o t a l l e a f dry weight Pod fresh weight Seed fresh weight Variate (Dependent Variable) S t i p u l e area L e a f l e t area T o t a l l e a f area Total l e a f dry weight Total plant dry weight Pod dry weight Seed dry weight - 27 -where L. = area of l e a f i A i = dry weight of l e a f i 1 A = estimated l e a f l e t area of l e a f i A i s^ = estimated s t i p u l e area of l e a f i i l w = estimated l e a f l e t dry weight of l e a f i i Sy = estimated s t i p u l e dry weight of l e a f i To t a l l e a f area per plant, L^ ., i s obtained from: V X i=l " i L A = Z , L A . t3] Total l e a f dry weight was calculated from regressions on l e a f area, whereas t o t a l plant dry weight was estimated from multiple regressions with stem length, number of leaves and leaf areas. Using the BMDP9R program, a l l possible sub-set regressions were done at each harvest to determine the 'best' p r e d i c t i o n equation for p r e d i c t i n g t o t a l plant dry weight on each occasion. Stem dry weight was determined by subtracting t o t a l l e a f dry weight from t o t a l plant dry weight. In t h i s study pod and seed, dry weights were not measured because of time and labour c o n s t r a i n t s . However, these dry weights were estimated by using equations derived from the data of e a r l i e r researchers (Bisson and Jones, 1932). These equations are s p e c i f i e d on pages 63 and 64. - 28 -Bain and Mercer (1966) compared the data on fresh and dry weight of seeds and pods of a number of v a r i e t i e s , over the period 15-38 days a f t e r a n thesis. They found that the data sets were s i m i l a r over the period of study. They therefore suggested that p a r a l l e l i s m holds over the period 0-54 days a f t e r anthesis. In another study Hedley and Ambrose (1980) investigated seed development in six genotypes of Pisum sativum over the period 0-45 days post-anthesis. Their r e s u l t s also indicate s i m i l a r r e l a t i o n s h i p s between fresh and dry weights of the genotypes. Since the present study was conducted over the period 0-30 days post-anthesis, the use of equations derived from another data source over the same period was considered acceptable. 3.3 Data Analysis 3.3.1 Analysis of Variance Univariate analysis of variance (ANOVA) was used to test f o r s i g n i f i c a n t treatment e f f e c t s on the primary v a r i a t e s measured at each destructuve harvest. The analysis was done in two parts: ( i ) O v e r a l l analysis using a l l the data ( i i ) Sub-unit analysis for each harvest separately. O v e r a l l a n a l y s i s serves to show the manner in which the treatment e f f e c t s changed with time. Sub-unit a n a l y s i s , on the other hand, ind i c a t e s the time that a p a r t i c u l a r e f f e c t became apparent. In the sub-unit a n a l y s i s , each test was assumed to be independent because d i f f e r e n t plants were sampled on each occasion. - 29 -3 . 3 . 2 G r o w t h A n a l y s i s 3 . 3 . 2 . 1 G r o w t h C u r v e s F i t t e d curves were used to describe the time course of the primary growth v a r i a t e s as w e l l as to derive the t r a d i t i o n a l growth i n d i c e s . It was important, therefore, that the most appropriate curve be selected f o r t h i s part of the study. In order to make such a s e l e c t i o n , three stages of d e c i s i o n making were required: a. to determine the c h a r a c t e r i s t i c s of the 'best' curve and hence the c r i t e r i a f o r s e l e c t i o n , b. to a s c e r t a i n the most appropriate method of curve f i t t i n g , and c to s e l e c t the best curve from amongst the p o s s i b i l i t i e s . Stage 1: Defining the 'best' curve. The best curve i s defined as the one which describes the trend of the data i n a b i o l o g i c a l l y r e a l i s t i c and s t a t i s t i c a l l y p r e c i s e manner. S t a t i s t i c a l p r e c i s i o n , i n t h i s context, r e f e r s to how w e l l the data f i t the curve. The index of f i t used i s the r e s i d u a l mean square (RMS). This quantity i s a measure of the spread of the treatment means about the f i t t e d l i n e (a small RMS denotes a good f i t and v i c e v e r s a ) . B i o l o g i c a l realism, on the other hand, deals with the a b i l i t y of the f i t t e d curve to describe and quantify the plant's true and n a t u r a l response. That i s , the trend of the curve must be b i o l o g i c a l l y - 30 -v e r i f i a b l e . It i s important to note that b i o l o g i c a l realism was considered a more important s e l e c t i o n c r i t e r i o n than s t a t i s t i c a l p r e c i s i o n i n a l l cases. Stage 2: The method of curve f i t t i n g . Hunt (1982b), i n his review of the f u n c t i o n a l approach to plant growth analysis states that: ". . . i f the f i t t i n g of a function i s handled clumsily, then the experimenter's perception of r e a l i t y w i l l flow f u r t h e r along i t s corrupted course." With t h i s in mind, i t i s important that the method of curve f i t t i n g used r e f l e c t s the true trends of the data. Four methods of curve f i t t i n g are a v a i l a b l e . They are: i . Stepwise polynomial regression i i . Non-linear estimation i i i . Cubic s p l i n e regression i v . B-spline regression Stepwise polynomial regression was used only where the number of observations, N, was l e s s than 7 ( i . e . the time period l e s s t h a n 24 days). Over a longer period, i t was u n l i k e l y that a s i n g l e low-order polynomial could amply describe the trend of the v a r i a t e s . On the other hand, higher order polynomials could cause o v e r f i t t i n g . Thus for N greater than 7 t h i s method was r e j e c t e d . Non-linear estimation methods assume an asymptotic shape of the growth curve. To describe the trend of the t o t a l l e a f area and dry weight of the pea, t h i s assumption would be i n v a l i d since a l o s s of leaves occurs during the reproductive phase. Hence, a d e c l i n i n g trend rather than a l e v e l l i n g o f f would be expected. - 31 -The smoothing-factor feature renders cubic s p l i n e f i t t i n g well suited to the h i g h l y v a r i a b l e data of the pea crop. In order to make v a l i d comparisons of the treatment e f f e c t s , the same smoothing factor was required for each treatment. Using t h i s method, however, 'oversmoothing' of the curves of some treatments and 'undersmoothing' of others resulted in the case of the d e s t r u c t i v e harvest data. One way of overcoming t h i s problem was to scale the data and/or make further transformations. With t h i s approach, however, there e x i s t s the r i s k of v i o l a t i n g some of the assumptions of l e a s t squares regression (e.g. normality and independence of the errors) which could lead to erroneous inferences on the confidence i n t e r v a l s and the e f f e c t s of treatments. Furthermore, the re s i d u a l s obtained by t h i s method of curve f i t t i n g are co r r e l a t e d (Wold, 1974). As a r e s u l t , confidence i n t e r v a l s must be c a l c u l a t e d by non-parametric methods [such as Tukey's j a c k n i f e (1959)] which are not as precise as those obtained by l e a s t squares. In view of the foregoing concepts, the cubic s p l i n e method of curve f i t t i n g was selected f o r use on the non-destructively harvested data and the B-spline method was used for the d e s t r u c t i v e l y harvested data. With t h i s l a t t e r method ( B - s p l i n e s ) , smoothing i s done automatically by the program. Moreover, the errors are independent, thereby r e s u l t i n g i n more precise confidence i n t e r v a l s and hence more powerful tests of treatment e f f e c t s . Stage I I I : The 'best' curve. A computer program (see Appendix D) s i m i l a r to that developed by Hunt and Parsons (1981), was used to f i t the B-splines. As explained in Chapter 2, the splines are polynomial pieces - 32 -joined at points c a l l e d knots. These knots have s p e c i a l properties of co n t i n u i t y i n both the f i r s t and second d e r i v a t i v e s . During the execution of the program, the number and p o s i t i o n of the knots may be s p e c i f i e d e i t h e r a r b i t r a r i l y or s u b j e c t i v e l y by the i n v e s t i g a t o r . Then, by invoking c e r t a i n subroutines,* the curve was f i t t e d by l e a s t squares regression. From t h i s f i t t e d curve, in t e r p o l a t e d values, f i r s t and second d e r i v a t i v e s , t h e i r respective confidence i n t e r v a l s and a covariance matrix are generated. The form of the growth curve i s di c t a t e d by the number and p o s i t i o n of the knots. Therefore, a number of simulations were necessary to determine i t e r a t i v e l y the optimum values of these two parameters. Figure 3.1 i s a diagramatic representation of the simulation process. F i r s t the maximum number of knots was determined. In the present study, t h i s maximum was three in accordance with the recommendation of Wold (1974), who suggested a maximum of N/4 (where N i s the number of observations). The p o s i t i o n of the knot(s) was determined at Step 2 i n the diagram. Two a l t e r n a t i v e s were av a i l a b l e for the s p e c i f i c a t i o n of the p o s i t i o n s — subjective s e t t i n g by the programmer or objective s e t t i n g by the computer. Using the l a t t e r option i n i t i a l positions were f i r s t s p e c i f i e d . Then, the optimum p o s i t i o n s were obtained i t e r a t i v e l y by migrating the knots along the abscissa u n t i l the sum of squares r e s i d u a l was minimized. The i n i t i a l p o s i t i o n s were set to equidistant points along the absciss a . *The subroutines-DBSPLP and DL2APP are a v a i l a b l e at the U n i v e r s i t y of B r i t i s h Columbia Computing Centre. Figure 3.1. Flow chart of the steps involved i n s e l e c t i n g the 'best' f i t t e d curve. STEP 1 STEP 2 STEP 3 Set T| No k Computer setting of Yes SAVE Sublective s e t t i n g of NO LEGEND I Number of knots M Maximum number of knots N Number of observations R Instantaneous RQR R Mean RQR Tj I n i t i a l knot p o s l t l o n ( s ) T p F i n a l knot p o s l t l o n ( s ) T Q Optimum knot po s i t i o n ! a ) Good f i t Use for G r o w t h Ano y t i t - 34 -In the present study, a combination of the two a l t e r n a t i v e s was employed. F i r s t , the optimum po s i t i o n was determined o b j e c t i v e l y . The r e l a t i v e growth rates were then examined to determine i f the f i t was b i o l o g i c a l l y r e a l i s t i c . If i t was, then the curve was selected for the next step. If not, the knot p o s i t i o n was s p e c i f i e d s u b j e c t i v e l y u n t i l a more r e a l i s t i c trend was obtained. For each v a r i a t e , there were three possible curves (one f o r each of 1, 2 and 3 knots); from which the most appropriate was s e l e c t e d . The f i n a l choice (Step 3) was obtained by comparing the instantaneous r e l a t i v e growth rate curve, derived from the f i t t e d curves, with the mean r e l a t i v e growth r a t e , derived from the o r i g i n a l data. Rel a t i v e growth rates rather than the actual values of the variates were compared because the instantaneous r e l a t i v e growth rate curves were more s e n s i t i v e to changes i n the number and p o s i t i o n of the knots. The 'best' curve was therefore the one whose instantaneous growth rate curve followed the trend of the mean r e l a t i v e growth rate most c l o s e l y . • 3.3.2.2 Growth Indices The i n t e r p o l a t e d values of the f i t t e d curves for mean l e a f area per p l a n t , mean l e a f dry weight per plant, W-^; mean t o t a l plant dry weight, W and mean stem dry weight, Wg were used to derive the following growth i n d i c e s as described by Hunt (1978b): Instantaneous Relative Growth Rate, RGR ( d a y - 1 ) R' = 1/W • dW/dt [4(a)] or R' = d(log W)/dt [4(b)] - 35 -Leaf Area Ratio, f o r LAR (dm 2 g - 1 ) F = LA/W [5(a)] because log transformed data were used i n the present study, the following formula was used to c a l c u l a t e F: F = a n t i l o g ( l o g L - log W) [5(b)] S p e c i f i c Leaf Area, SLA (cm 2 g - 1 ) SLA = LA/WL [6(a)] l o g transformed: SLA = a n t i l o g ( l o g L - log W ) [6(b)] e A e Li Leaf Weight Ratio, LWR (g g - 1 ) LWR - WT/W [7(a)] Li l o g transformed: LWR = a n t i l o g ( l o g W - log W) [7(b)] Unit Leaf Rate, E (g m~2 d a y - 1 ) E =,1/L^ . dW/dt [8(a)] Using f i t t e d curves: E = R'/F [8(b)] N.B. This r e l a t i o n s h i p holds only i n the instantaneous case. Instantaneous Relative Leaf Area Growth Rate, RLGR ( d a y - 1 ) R£ = 1/L A • dL A / d t [9(a)] or = d ( l o g e L A ) / d t [9(b)] Instantaneous Relative Stem Growth Rate, RSGR ( d a y - 1 ) Ri = 1/Wg • dWg/dt [10(a)] or R ' s = d ( l o g e W s)/dt [10(b)] 2 1 Unit Non-Leaf Rate (g m- day - ) - 1/L A • dWs/dt [11(a)] = R s/(L A/w s) [11(b)] 3.3.3 Yield Component Analysis Two models were studied. In the f i r s t , the y i e l d v a r i a t e (Y) i s the t o t a l plant dry weight. Seed f r e s h weight was the dependent v a r i a b l e in the second model. Mathematically, the models are as follows: Y = W = S x LJJ/S x L A / L N x W^/LA x W/w"L [12] Y = WSe = S x LJJ/S x L A / L N x W^/LA x WV/WL x FN/WV x P/F N x Se/P x WSe/Se [13] Each component r a t i o has a p h y s i o l o g i c a l meaning. Thus L^/S - 37 -represents the number of nodes; L^/L^ = mean l e a f area; Wi/L^ = the r e c i p r o c a l of s p e c i f i c l e a f area (1/SLA); W/WL = inverse l e a f weight r a t i o (1/LWR); FN/Wy = reproductive e f f o r t ; P/F N = pod set and Se/P and Wge/Se are i n d i c a i v e of pod f i l l i n g . Applying the methodology described by Eaton and Kyte (1978), n a t u r a l logarithms were taken of both sides of Equations 12 and 13 to y i e l d the fol l o w i n g a d d i t i v e models: log e(W) = l o g e ( S ) + l o g e ( L N / S ) + l o g e ( L A / L N ) + log e(W L/L A) + lo § e(W/W L)[14] log (W ) = lo g (S) + log (L /S) + + log (W /Se) [15] e Se e e N e be The components were i n s e r t e d s e q u e n t i a l l y i n t o the y i e l d equation, i n the order i n which they appear during ontogeny ( i . e . , as stated i n Equations 14 and 15). The c o n t r i b u t i o n of each component to y i e l d was determined as the increment i n the c o e f f i c i e n t of determination, R^, due to the i n s e r t i o n . This a n a l y s i s was done on the pooled treatment data f o r each harvest separately. By so doing, both the important y i e l d components and c r u c i a l stages of development were i d e n t i f i e d . F i n a l l y , the growth rates of the components were derived from f i t t e d curves of t h e i r time course.' The fo l l o w i n g equations summarize the d e r i v a t i o n : N c I f : l o g o Y = £ log C [16] e i = l - 38 -where Y = y i e l d v a r i a t e = component r a t i o i ( i . e . the r a t i o of morphological features, the product of which i s y i e l d ) N c = number of components i n the m u l t i p l i c a t i v e y i e l d equation Then, according to J o l l i f f e and Courtney (1984): N c d(log Y)/dt = Z d(log C )/dt [17(a)] e 1=1 N or RA = T R' [17(b)] T i = l C i where R' = instantaneous r e l a t i v e growth r a t e . Assuming R'Y i s s i g n i f i c a n t l y d i f f e r e n t from zero, Equation (17b) becomes, N c 1 = Z Rl /Rl [18] i = l °i * The f r a c t i o n a l c o n t r i b u t i o n to the o v e r a l l r e l a t i v e growth rate was c a l c u l a t e d using Equation (18). 3.3.4 Demographic Analysis The plants which were sampled non-destructively were used i n t h i s part of the study. At each non-destructive harvest, the number of new leaves - 39 -and flowers were recorded. Cohorts were i d e n t i f i e d by tagging each new l e a f and flower on the day they appeared with colour-coded wire. A d i f f e r e n t colour was used at each date. Leaf b i r t h was denoted as the time at which the l e a f f i r s t became v i s i b l e , while the b i r t h date of the flower was the day i t had f u l l y emerged. Leaf and flower deaths were a l s o noted at each harvest. A l e a f was considered dead when i t began to turn yellow i n colour. In a d d i t i o n to the flowers on the non-destructively harvested p l a n t s , the flower cohorts on a l l the other plants i n the study were l a b e l l e d . By so doing, the age of the pods of the d e s t r u c t i v e l y harvested plants was determined. I t was p o s s i b l e , therefore, to compare the weights by age of the pods i n the present study with those of others (McKee e_t a l . 1955; Bisson and Jones 1932; F l i n n and Pate, 1968; Carr and Skene, 1961). The most analogous data set was then used to derive the p r e d i c t i o n equations f o r pod, seed and pod w a l l dry weight. The contributions of the leaves, pod, pod w a l l and seeds to the o v e r a l l plant performance were determined by the methods described by J o l l i f f e and Courtney (1984). F i t t e d curves were calculated, f o r the growth of each component and from these curves the component i n d i c e s were derived. A summary of the r e l a t i o n s h i p s i s given below: W=W L +W s+W c+W S e [19] w p dW W dW W dW W 1 dW 1 L , L. , 1 S / S. , , 1 Se / Ses n n / v, w dT = w T d T ^ + wc IT ( w - } + ' ' * ' + w - I T ( w - } [ 2 0 ( a ) 1 Li b b6 - 40 -or W L W S WSe R* " K <VT> + RS ^ + * ' ' ' + RSe ^ 120(b)] I f R' i s s i g n i f i c a n t l y d i f f e r e n t from zero, the f r a c t i o n a l contributions of the a d d i t i v e components to the r e l a t i v e growth rate i s : R^ Wj Ri W„ R i . Wr 1 - r <sr> + i r <ir> + + « " i Using the same p r i n c i p l e s , the u n i t component rates are derived by the foll o w i n g s e r i e s of equations: 1 d W _ l d V l d V l d W S e L A dt" ~ ~dt L A-dT + ' ' ' ' [ 2 2 ( a ) ] or E = E L + E g + . . . . E g e [22(b)] If E i s s i g n i f i c a n t l y d i f f e r e n t from zero, the f r a c t i o n a l production rates are: *E E E 1 = E i l + E i + -T-*A11 symbols defined i n t h i s chapter and summarized i n the Nomenclature and Symbols on page 208. - 41 -3.4 Temperature Correlations Under f i e l d conditions, i t i s d i f f i c u l t to make d e f i n i t e statements about the e f f e c t s of temperature since these e f f e c t s are u s u a l l y confounded with other environmental f a c t o r s . It i s u s e f u l , however, to determine whether any r e l a t i o n s h i p s e x i s t between temperature and the growth i n d i c e s . This information i s important i n understanding the physiology of growth and u l t i m a t e l y y i e l d under uncontrolled environmental conditions. Simple c o r r e l a t i o n s were c a r r i e d out between unit l e a f rate (E) and temperature. Unit l e a f rate was the growth index studied because, compared to the other i n d i c e s , i t best r e f l e c t s the photosynthetic a c t i v i t y of the plant organs. The dependent v a r i a b l e was the d i f f e r e n c e between mean unit l e a f rate (E) and the instantaneous unit l e a f rate (E') at the mid-point of the harvest i n t e r v a l . E was calculated from the o r i g i n a l data set, using the" formula derived by Williams (1946). The d i f f e r e n c e denotes the short-term f l u c t u a t i o n s of the unit l e a f rate from the ontogenetic trend and i s therefore a good index of i t s v a r i a t i o n . Temperature, the independent v a r i a b l e , was expressed i n degree days because t h i s was more s i g n i f i c a n t p h y s i o l o g i c a l l y (Edey, 1977), than the d a i l y mean temperature. Thus mean degree-day of the harvest i n t e r v a l was used i n the computations. The temperature data were obtained from the d a i l y records at the Un i v e r s i t y of B r i t i s h Columbia F i e l d Laboratory. The transformation into degree days was accomplished by using the following formula: - 42 -, rTMAX + TMIN, Degree days = [ ^ J ~ T L where,- = maximum d a i l y temperature (°C) ^MIN = m ^ n : u l i u m d a i l y temperature (°C) T T = minimum temperature below which pea growth f a i l s to occur L (5.5° C). - 43 -CHAPTER 4 PRELIMINARY CONSIDERATIONS Before proceeding with the r e s u l t s of the study, preliminary analyses were needed to ( i ) s e l e c t the best curve for growth a n a l y s i s and ( i i ) derive the p r e d i c t i o n equations. The r e s u l t s of this preliminary a n a l y s i s are presented in t h i s chapter. 4.1 Curve Selection Since the same method of s e l e c t i o n was applied for each v a r i a t e , only the d e t a i l s for one v a r i a t e , l e a f area, w i l l be presented. Results for the other v a r i a t e s are summarized in Tables 4.1 and 4.2. 4.2 Number and Position of Knots Figures 4.1(a) to (c) show the degree of f i t of the instantaneous r e l a t i v e growth rate curve, R' , to the mean r e l a t i v e growth rate, R, f o r one, two and three knots r e s p e c t i v e l y i n uninoculated Dark Skin P e r f e c t i o n (DSP). The r e l a t i v e l e a f growth rates were ca l c u l a t e d from the data of the d e s t r u c t i v e harvests. Splined regressions using one [Figure 4.1(a)], two [Figure 4.1(b)] and three [Figure 4.1(c)] knots were f i t t e d to the primary data. The f i t t e d values of R' were superimposed on the histograms of R. Optimum knot p o s i t i o n s are indicated by an arrow on the respective graph. F i g u r e 4 . 1 . R e l a t i v e l e a f a r e a g r o w t h r a t e c u r v e s f r o m d a t a o f d e s t r u c t i v e h a r v e s t s , ( a ) t o ( c ) a r e t h e i n s t a n t a n e o u s r e l a t i v e g r o w t h r a t e s o f u n i n o c u l a t e d D a r k S k i n P e r f e c t i o n , w i t h 1 t o 3 k n o t s r e s p e c t i v e l y . T h e k n o t p o s i t i o n s a r e r e p r e s e n t e d b y a r r o w s , ( d ) t o ( f ) a r e t h e c o r r e s p o n d i n g c u r v e s f o r i n o c u l a t e d D a r k S k i n P e r f e c t i o n ! ( g ) t o ( i ) f o r u n i n o c u l a t e d E a r l y F r o s t y a n d ( j ) t o ( 1 ) a r e f o r i n o c u l a t e d E a r l y F r o s t y . T h e c u r v e s a r e s u p e r i m p o s e d o n t h e h i s t o g r a m s o f t h e m e a n r e l a t i v e g r o w t h r a t e , R . CD 4> n) U .C +-> o u w> cd <D u cd <m ci CD > cd 0) - •2 t t • SO 66 80 Days after planting Figure '».]. (Continued) 9 h 50 65 60 50 65 80 50 65 80 Day3 after planting - 46 -Using one knot [Figure 4.1(a)] resulted in a h e a v i l y smoothed curve. The r i s e i n the curve toward the end of the growth phase (74 to 80 days a f t e r planting) i s b i o l o g i c a l l y i n c o n s i s t e n t since i t i s u n l i k e l y that the r e l a t i v e growth rate of a monocarpic plant would increase during senescence. However, the confidence l i m i t s i n d i c a t e that the R' values at that time are not s i g n i f i c a n t l y d i f f e r e n t from zero. Thus the curve i s acceptable. The f i t was improved with two knots [Figure 4.1(b)] [ r e s i d u a l sum of squares (RSS) of 0.047 [Table 4.1]. There was no increase i n R' during the l a t e r stages of development and maximum R' coincided more c l o s e l y with maximum R. Also, the value of R' at day 50 was a better estimate of R, than the corresponding R' for the curve with 1 knot. Figure 4.1(c) shows the f i t with three knots. This curve was the l e a s t smoothed of the three and had the best f i t (RSS = 0.045). However, the increase in the number of knots resulted in a decrease in the number of degrees of freedom f o r e r r o r . Consequently, the confidence i n t e r v a l s were wider than those of the previously mentioned curves. Thus te s t i n g f or treatment d i f f e r e n c e s with t h i s curve would not be as p r e c i s e . The best curve for untreated Dark Skin P e r f e c t i o n (DSP) i s , therefore, the one with two knots although the curve with one knot i s also acceptable. For v a l i d comparisons among the treatments, the same amount of smoothing i s required. Since the number of knots determines the degree of smoothing, the same number of knots was used for the l e a f area curve of each treatment. Owing to the d i f f e r e n c e s among data sets, however, the p o s i t i o n of the knots v a r i e d . Figures 4.1(d) to (1) show curves of the degree of f i t of R' to R for l e a f area of the other treatments. - 47 -Table 4.1 - Summary of the r e s u l t s of the tests to find the most s u i t a b l e number of knots for the splined regressions f i t t e d to the primary data ( l o g transformed) from the destructuve harvests. For each treatment, and number of knots, r e s i d u a l sums of squares are given f o r t o t a l dry weight, W; l e a f area, L^; l e a f dry weight WL; and stem dry weight, Wg. Residual Sum of Squares Number of V a r i a t e : Knots DSP* IDSP EF IEF 1 L A 0.061 0.139 0.165 0.077 W L 0.081 0.196 0.083 0.062 W S 0.027 0.205 0.072 0.085 W 0.038 0.141 0.071 0.056 2 LA 0.047 0.133 0.094 0.069 W L 0.059 0.133 0.070 0.062 W S 0.017 0.197 0.068 0.034 W 0.018 0.139 0.067 0.045 3 LA 0.045 0.134 0.093 0.053 W L 0.046 0.133 0.060 0.060 w s 0.015 0.180 0.046 0.034 W 0.011 0.117 0.059 0.037 *Treatments -DSP: Uninoculated Dark Skin P e r f e c t i o n , EF: Uninoculated E a r l y Frosty IDSP: Inoculated Dark Skin P e r f e c t i o n , IEF: Inoculated Early Frosty. r- 48 -Table 4.2 - Results of t e s t s to f i n d the most s u i t a b l e number of knots f o r the s p l i n e d regressions f i t t e d to the a d d i t i v e components f o r each c u l t i v a r . Residual Sum of Squares (Optimum Knot Position(s),DAP) Number of V a r i a t e — Knots DSP* EF L ** A 0.055 (65) 0.115 (65) W L 0.075 (65) 0.054 (62) w s 0.066 (65) 0.056 (65) W P 0.431 (65) 0.290 (65) w c 0.425 (65) 0.259 (65) WSe 0.182 (65) 0.145 (65) WNL 0.051 (65) 0.077 (65) W 0.048 (65) 0.059 (65) L A 0.055 (65, 65) 0.086 (60, 70) W L 0.072 (60, 70) 0.051 (60, 65) w s 0.063 (60, 65) 0.039 (60, 65) W P 0.059 (60, 65) 0.156 (57.1, 65.4) w c 0.084 (60.5, 69.1) 0.123 (55.5, 62.1) WSe 0.236 (62.0, 68.8) 0.138 (61.5, 68.1) WNL 0.046 (60, 70) 0.067 (59.6, 69.6) W 0.044 (60, 70) 0.052 (60, 70) *Treatments -DSP: Dark Skin P e r f e c t i o n , EF: E a r l y Frosty, DAP: Days a f t e r p l a n t i n g . * * L ^ = l e a f area/plant, WL = l e a f dry weight/plant, Wg = stem dry weight/plant, Wp = t o t a l pod dry weight/plant, = t o t a l pod w a l l dry weight/plant, W S e = t o t a l seed dry weight/plant, W N L = t o t a l non-leaf dry weight per plant and W = t o t a l plant dry weight. - 49 -For inoculated DSP and Ea r l y Frosty (EF) the curves with e i t h e r one or two knots [Figures 4.1(d), ( e ) , ( j ) and (k)] provided a good f i t . The most r e a l i s t i c curve for uninoculated EF i s the one with one knot [Figure 4.1(g)]. Therefore, the 'best' curves selected to describe the time course of l e a f area of a l l treatments were those with one knot. Figure 4.2 shows the f i t of these curves to the actual data. 4.2 Prediction Equations P r e d i c t i o n equations were required to estimate ( i ) the primary growth v a r i a t e s from the non-destructive data and ( i i ) the pod, pod wall and seed dry weights. 4.2.1 Leaf Area As explained in Chapter 3, t o t a l l e a f area was derived from the sum of the i n d i v i d u a l l e a f areas and the i n d i v i d u a l l e a f areas were ca l c u l a t e d from the following equation: \ = 2 ( 1A. + SA.> t 1 ] i l l Both 1 ^ and s ^ were estimated from regressions on t h e i r respective lengths. Figures 4.3 and 4.4 are sc a t t e r plots of l e a f l e t area vs. l e a f l e t length and s t i p u l e area vs. s t i p u l e length r e s p e c t i v e l y . The - 5 0 -Figure 4.2. Plots showing the f i t of splined regressions to leaf area data (log scale), (a) Uninoculated Dark Skin Perfection, Co) Inoculated Dark Skin Perfection, (c) Uninoculated Early Frosty and (d) Inoculated Early Frosty. 8 . 0 -i CM e at < 7.0 -6 .0 5 .0 S . O - i E u < et < < (d) 1 r 1 50 60 70 80 50 60 70 SO DAYS AFTER P L A N T I N G DAYS AFTER P L A N T I N G - 51 -Figure 4.3. Scatter plot of l e a f l e t area vs l e a f l e t length. 2 0 . 7 B O 1 8 . 4 8 1 1 6 . 1 8 2 1 3 . 8 8 3 CM E U 11.S84 ca <u u < ; 9 . 3 8 9 6 -H <D iH C_, CC 8' 9 8 6 7 CD 4 . 6 8 7 8 2 . 3 8 8 9 . 9 0 0 0 0 - ! } • . 4 O 0 O 0 2 2 " 2 • 2 2 * • 2 3 2 « 2 * 3 3 . 2 4 4 4 4 6 6 6 7 6 0 8 8 9 L I N 2 5 3 3 3 3 . 9 5 5 6 5 3 7 7 8 6 8 0 0 0 L e a f l e t Length (cm) - 52 -Figure 4.4. Scatter plot of s t i p u l e area vs s t i p u l e length. 3 9 . 0 0 0 CM £ o 3 0 . 3 5 8 2 6 . 0 3 7 2 1 . 7 1 6 cd U < i-l a, •H -H CO 1 7 . 3 9 4 1 3 . 0 7 3 S . 7 5 2 2 2 ' . . > 2 • 3 4 3 2 • 2 4 -2 " 2 * 2 • • 2 . 5 0 O O 0 2 . 6 5 5 6 4 . 8 1 1 1 6 . 9 6 6 7 9 . 1 2 2 2 STL ' • 5 7 7 8 3 . 7 3 3 3 5 . 8 8 8 9 8 . 0 4 4 4 1 0 . 2 0 0 Stipule Length (cm) - 53 -plo t s reveal a s l i g h t c u r v i l i n e a r trend for both v a r i a t e s which suggests that a transformation was necessary. Consequently, the independent v a r i a b l e s - l e a f l e t length (1) and s t i p u l e length (s) were transformed to 2 2 1 and s . Tables 4.3 and 4.4 summarize the r e s u l t s of the regression a n a l y s i s for each treatment separately ( f u l l model) and pooled (reduced model) at the following p h y s i o l o g i c a l stages of growth - (1) e a r l y vegetative growth [20 days a f t e r planting (DAP)], ( i i ) l a t e vegetative growth (50 DAP), pod f i l l i n g (71 DAP) and f i n a l harvest (80 DAP). The r e s u l t s reveal that the regression c o e f f i c i e n t s for each v a r i a t e of the f u l l and reduced models are quite s i m i l a r . For example, the slope, b i at 50 DAP for l e a f l e t area i s 0.3775, 0.4214, 0.4171 and 0.4608 for uninoculated DSP, inoculated DSP, uninoculated EF and inoculated EF r e s p e c t i v e l y and 0.4219 for the pooled data (see Table 4.3). Tests of e q u a l i t y of the two models ( f u l l and reduced) yielded F-values of 1.48, 0.93, 0.46 and 0.23 for the l e a f l e t data at 20, 50, 71 and 80 DAP, r e s p e c t i v e l y . The corresponding values f o r s t i p u l e area are 0.52, 1.45, 0.56 and 0.97. Thus, the n u l l hypothesis that the two models are equal i s a c c e p t e d — i . e . the p r e d i c t i o n equations for s t i p u l e and l e a f l e t area of each treatment i n d i v i d u a l l y are not s i g n i f i c a n t l y d i f f e r e n t from the pooled equations. Moreover, a better estimate of the regression c o e f f i c i e n t s i s obtained by pooling the data. A second test was conducted to determine whether the regression c o e f f i c i e n t s of the p r e d i c t i o n equations at each harvest were s i g n i f i c a n t l y d i f f e r e n t . The F-values for l e a f l e t and s t i p u l e areas were 5.11 and 0.97 Table 4.3 - Summary of r e s u l t s of regression analysis to determine the p r e d i c t i o n equation f o r l e a f l e t area. Harvest Number (days a f t e r planting) 1 (20) 2 (50) 9 (71) 12 (80) F u l l * Reduced F u l l Reduced F u l l Reduced F u l l Reduced Intercept (b o) - 0.2424 - 0.7932 - 0.3316 - 0.0307 slope ( b i ) - 0.6262 - 0.4219 - 0.4362 - 0.4316 Zl 0.0714 - 1.2899 - 0.2292 - -0.5824 -z 2 o.oo56 ; - 1.0333 - 0.1077 - 0.4128 -z 3 -0.0011 - 1.0018 - 0.4098 - 0.3238 -z 4 0.3793 - 0.0529 - 0.2266 - 0.3811 -Wi 0.8017 - 0.3775 - 0.4509 - 0.4578 -w2 0.7108 - 0.4214 - 0.4605 - 0.4127 w3 0.6644 - 0.4171 - 0.4231 - 0.4210 -0.5649 - 0.4608 -• 0.4249 - 0.4088 -* The form of the equation i s 1 A - z l + Wl 1^ + 2 Z 2 + W2l 2 + ... Z 4 + W^lJ for the f u l l model and 1^ = bg + b j l for the reduced model. zl i z2, Z3 and Zi+ are the Intercepts for uninoculated Dark Skin P e r f e c t i o n , inoculated Dark Skin P e r f e c t i o n , uninoculated Early Frosty and inoculated Early Frosty r e s p e c t i v e l y . wl » w2 > w3 a n a w>t a r e t n e slopes for uninoculated Dark Skin P e r f e c t i o n , inoculated Dark Skin P e r f e c t i o n , uninoculated Early Frosty and inoculated Early Frosty r e s p e c t i v e l y . Table 4.4 - Summary of r e s u l t s of regression analysis to determine the p r e d i c t i o n equation for s t i p u l e area. Harvest Number (days a f t e r planting) 1 (20) 2 (50) 9 (71) 12 (80) F u l l * Reduced F u l l Reduced F u l l Reduced F u l l Reduced Intercept (b 0) - 0.0562 - -0.2835 -1.1004 - 0.4217 Slope ( b i ) - 0.4031 - 0.3760 0.3877 - 0.3569 0.0752 - -1.2667 - -2.0783 0.6947 -z 2 -0.0048 ~ - -0.0120 - 0.1987 -1.0524 -z 3 0.2185 - 0.8292 - -1.1592 1.0489 --0.0001 - -1.1327 - -1.2936 -0.8324 -Wl 0.3871 0.3940 - 0.4031 0.3406 -w2 0.4282 - 0.3764 - 0.3740 0.3750 -w3 • 0.3757 - 0.3509 - 0.3906 0.3443 -0.3990 - 0.3877 - 0.3793 - . 0.4004 -* The form of the equation i s s A = 2 Zi + Wisi + 2 Z2 + W2S2 + ... 2 Zi» + Wi+sit f o r the f u l l model and SA = Do + D l s ^ o r t n e reduced model. Z l , Z2, Z3 and Zi* are the intercepts for uninoculated Dark Skin P e r f e c t i o n , inoculated Dark Skin P e r f e c t i o n , uninoculated Early Frosty and inoculated Early Frosty r e s p e c t i v e l y . Wl, W2, W3 and Wit are the slopes for uninoculated Dark Skin P e r f e c t i o n , inoculated Dark Skin P e r f e c t i o n , uninoculated Early Frosty and inoculated Early Frosty r e s p e c t i v e l y . - 56 -r e s p e c t i v e l y . This r e s u l t implies that a general equation was f e a s i b l e f o r the p r e d i c t i o n of s t i p u l e area but not l e a f l e t area. Further t e s t s revealed that the equations f o r p r e d i c t i o n of l e a f l e t area at days 50, 71 and 80 were not s i g n i f i c a n t l y d i f f e r e n t . However, they d i f f e r e d from the equation at 20 DAP. This l a t t e r equation was therefore used to pr e d i c t l e a f l e t area during e a r l y vegetative growth. On the other hand, l e a f l e t area f o r a l l subsequent days was derived from the equation obtained by pooling the data at days 50, 71 and 80. The r e s i d u a l p l o t s [Figures 4.5 to 4.7] of these equations i n d i c a t e no serious v i o l a t i o n s f o r the l e a f l e t data, but the s t i p u l e data were heteroscedastic ( i . e . non-constant v a r i a n c e ) . Weighted l e a s t squares a n a l y s i s was used, therefore, to s t a b i l i z e the variance. Having decided on the appropriate p r e d i c t i o n equations, the respective areas were c a l c u l a t e d . To avoid the negative values obtained f o r the areas of the smaller leaves, the regressions were forced through the o r i g i n . Tests of s i g n i f i c a n c e of the i n t e r c e p t were not s i g n i f i c a n t , thus the conditioned regression was v a l i d . Therefore, the fo l l o w i n g equations were used: 0.38546 * s 2 [24] 0.67535 * 1? growth duration = 20 days [25(a)] or 0.44547 * l 2 otherwise [25(b)] - 57 -Figure 4.5. Residual plo t f o r stipule area p r e d i c t i o n . 3 . 7 4 2 9 2 . 8 6 0 7 1.0962 CM E U .21399 cd #Q - . 6 6 8 2 4 «-4 CO CO t x - 1 . S 5 0 S - 2 . 4 3 2 7 - 3 . 3 1 4 9 3 2 " 3 2 2 3 45 - 4 . 1 9 7 1 1 4 0 0 5 2 . , „ „ 8 . 5 9 6 7 , , 7 0 5 3 2 5 . 5 1 0 3 3 9 6 7 POES 4 3 6 8 4 1 2 . 8 2 5 2 1 . 2 8 2 2 9 . 7 3 8 ne 1 9 Predicted Stipule Area (cm ) - 58 -Figure 4.6. Residual p l o t f o r l e a f l e t area p r e d i c t i o n at Harvest 1 (20 Days a f t e r planting). .69278 E c CO 3 T3 to CD cr . 1S498 -.24821 -1 - . 2 0 4 2 2 . S 6 3 0 2 - . 7 4 2 4 2 - .92182 .34 261 1 . 4 1 1 3 2 4 8 0 O 3 5 4 8 8 4 6 1 7 5 »BES . 8 7 6 9 7 1 . 9 4 5 7 3 0 1 4 4 4 0 8 3 1 5 1 5 1 8 Predicted L e a f l e t Area (cm ) - 5.9 -Figure 4.7. Residual plot f o r l e a f l e t area p r e d i c t ! (Pooled data from Harvests 2,9 and 12). 2 . 2 9 3 9 I . 7 7 0 6 CM E c 1.2473 . 7 2 4 0 T .20079 03 3 to <D or - 8 4 9 7 8 - 1 . 3 6 9 0 2 • 2 • 1.8923 -2.4 156 1.4596 3.5324 5 6 0 5 1 7 6 7 7 9 9 . 7 5 0 7 13.896 18 0 4 2 POES Predicted L e a f l e t Area (cm ) - 60 -4.2.2 Leaf Dry Weight Four regression models were applied to the data f o r each harvest i n order to determine the most s u i t a b l e p r e d i c t i o n equation. The models were: (a) l i n e a r , (b) l i n e a r through the o r i g i n (c) l o g - l i n e a r and (d) l o g - l o g l i n e a r . The regression c o e f f i c i e n t s and summary s t a t i s t i c s f o r each of these models, at each harvest i n d i v i d u a l l y and pooled are presented i n Table 4.5. The u n i t s of the dependent v a r i a b l e i n models (c) and (d) ( l o g e g) are d i f f e r e n t from those of models (a) and (b) ( g ) . This d i f f e r e n c e i s due to the negative bias introduced i n the transformation from an arithmetic scale (g) to a geometric scale ( l o g e ) . Thus i t i s necessary to express the c o e f f i c i e n t of determination ( r ^ ) and the r e s i d u a l (RMS) i n s i m i l a r u n i t s f o r v a l i d model comparisons. To t h i s end, I values and adjusted r e s i d u a l s were computed (Appendix A.3 describes the computation). In a d d i t i o n , i t i s possible to retransform the logarithmic values from the geometric scale to an unbiased arithmetic scale by using a c o r r e c t i o n f a c t o r such as that described by B a s k e r v i l l e (1972). S i m i l a r l y , i n model (b) the r ^ values were computed from the uncorrected sum of squares and sum of products (Draper and Smith, 1981) and therefore, cannot be compared with the r ^ or I^'s of the other models. Consequently, only the r e s i d u a l s for model (b) were compared with that of. the other models. The models provided a f a i r l y good f i t i n most cases, r ^ or I2 values ranged from 24.4 % to 97.8 %. In a l l cases model (c) e x h i b i t e d the poorest f i t . Model (d) showed the best f i t at harvests 2, 4, 5 and 9. F-tests f o r e q u a l i t y of the regression c o e f f i c i e n t s of i n d i v i d u a l harvests revealed that f o r each model the equations were s i g n i f i c a n t l y r 61 r Table 4.5 - Summary of r e s u l t s of regression a n a l y s i s to determine the p r e d i c t i o n equation f o r t o t a l l e a f dry weight. The four models are (a) l i n e a r , (b) l i n e a r through the o r i g i n , (c) l o g - l i n e a r and (d) l o g - l o g l i n e a r . Harvest Regression Intercept Slope r 2 or I 2 RMS No (DAP) Model b0 b l 1 (20) a 0.0024 0.0054 76.8 0.0007 b 0 0.0054 76.8 0.0007 c -3.0235 0.0382 74.8 0.0008 d -4.9047 0.9044 75.3 0.0008 2 (50) a 0.7343 0.0046 72.6 0.1468 b 0 0.0064 72.6 0.2191 c 0.0231 0.0022 57.3 0.2284 d -3.7912 0.7923 72.8 0.1455 3 (53) a 0.5374 0.0047 89.9 0.1876 b 0 0.0056 89.9 0.2487 c 0.0921 0.0017 80.0 0.3701 d -4.1049 0.8333 89.9 0.1877 4 (56) a 0.7163 0.0048 87.9 0.1489 b 0 0.0060 87.9 0.2305 c 0.2518 0.0016 76.4 0.2900 d -3.8208 0.7993 88.3 0.1437 5 (59) a 1.2238 0.0041 67.2 1.0318 b 0 0.0055 67.2 1.3610 c 0.5311 0.0011 62.9 1.1675 d -3.2732 0.1743 70.2 1.0314 6 (62) a 0.1815 0.0060 88.4 0.5769 b 0 0.0062 88.4 0.5751 c 0.3676 0.0014 79.7 1.0104 d -4.1430 0.8573 86.2 0.6866 7 (65) a 1.0492 0.0039 82.0 0.4848 b 0 0.0053 82.0 0.7079 c 0.4292 0.0011 74.7 0.6799 d -3.8105 0.7860 81.8 0.4892 8 (68) a 1.0517 0.0043 89.8 0.5661 b 0 0.0054 89.8 0.9727 c 0.5703 0.0010 24.4 4.2044 d -3.0758 0.6886 86.9 0.7290 9 (71) a 0.9422 0.0049 86.2 1.1039 b 0 0.0057 86.2 1.3576 c 0.6556 0.0010 47.9 4.1778 d -3.9651 0.8311 86.4 1.0894 Continued . . . - 62 -Table 4.5 continued Harvest Regression Intercept No (DAP) Model b 0 Slope RMS 10 (74) a b c d 0.5695 0 0.3225 -4.2475 0.0051 0.0057 0.0013 0.8678 93.4 93.4 45.5 93.7 0.3227 0.4186 2.6648 0.3086 11 (77) a b c d 0.0175 0 0.2966 •4.8808 0.0067 0.0067 0.0014 0.9783 92.1 92.1 25.2 91.8 0.8632 0.8497 8.1294 0.8959 12 (80) a b c d 0.1410 0 0.3657 -4.2977 0.0059 0.0060 0.0013 0.8749 85.0 85.0 82.3 82.3 1.0695 1.0581 1.7033 1.2632 Pooled a b c d 0.4105 0 -0.2999 -4.9996 0.0053 0.0058 0.0020 0.9864 88.2 88.2 56.9 86.4 0.6560 0.7184 1.7203 0.7565 - 63 -different. Thus, a generalized equation was inappropriate for this variate. Model (b) was selected because i t is unlikely that leaf dry weight is significantly different from zero when the leaf area is zero. Tests to determine whether the intercept (b Q) was significantly different from zero, were insignificant for a l l harvests. Thus, the null hypothesis ( n U =» 0) is not rejected. 4.2.3 Total Plant Dry Weight Stem length, leaf area, leaf dry weight and number of leaves were a l l included in the prediction equation for total plant dry weight. Then, using the BMDP9R program (Dixon, 1983), the 'best' subset was selected from a l l possible combinations of the independent variables. The 'best' equations for each harvest are presented in Table 4.6. At harvests 3 to 7 the regression coefficients were fairly similar so tests were conducted to determine whether the data at these times could be pooled. The F-values for the test of equality of the regressions were, however, highly significant. Thus, no pooling was done. 4.2.3 Pod, Seed and Pod-wall Dry weight Table 4.7 was taken from the paper by Bisson and Jones (1932). The values of the pod lengths, pod fresh weights and seed fresh weights were found to be similar to the data for the present study up to 32 days after anthesis. These data were therefore used to determine the prediction equations for pod, seed and pod wall dry weights. r 64 r Table 4.6 - Summary of results of a l l possible subset regression to determine the 'best' prediction equation for total dry weight (W) at each harvest. *Adj. R2 RMS 95.7 0.014 2.16 95.6 0.035 3.29 97.6 0.115 5.00 Harvest Selection Criterion Number (days) Prediction Equation 1 (20) 0.035 + 1.184 WT Li 2 (50) -1.001 + 0.021 S + 0.055 L + 0.336 WT N Li 3 (53) 0.962 + 0.019 S - 0.001 L. - 0.134 L.T + A N 1.787 WT 4 (56) 1.387 + 0.038 S - 0.002 L - 0.211 L + 95.1 0.162 5.00 A IN 1.893 WT Li 5 (59) -1.520 + 0.050 S - 0.003 L. + 0.449 WT 95.2 0.399 3.93 A Li 6 (62) -1.057 + 0.052 S - 0.003 L + 1.877 WT 93.3 0.993 4.20 A Li 7 (65) 2.392 + 0.079 S - 0.004 - 0.385 1^ + 86.3 1.769 5.00 2.667 W. 8 (68) 1.067 + 0.105 S - 0.374 L + N 1.918 WL 87.6 3.846 4.60 9 (71) 3.973 + 0.144 S - 0.638 L + N 2.007 91.8 3.976 3.07 10 (74) 2.375 + 2.917 WT 93.2 2.99 3.23 11 (77) -2.409 + 0.082 S + 2.805 WL 93.8 6.27 3.79 12 (80) 2.003 + 0.059 S + 0.073 L 4 + A 0.002 96.0 4.33 5.00 0.007 WT Li *Adj. R2 = 1 - (—)(1-R 2) n-pyv p y where: n = number of observations p = number of parameters in the model R = coefficient of determination. P The adjustment facilitates the comparison of equations with different numbers of independent variables. C = (RSS/s2) + 2p - n P where RSS = residual sum of squares for subset s 2 = residual mean square for f u l l model Cp is a measure of the precision of estimation (small Cp implies a good f i t ) . * T a b l e 4.7. G r o w t h r e c o r d s o f f r u i t a t d i f f e r e n t s t a g e s o f g r o w t h . . 1 2 3 4 5 1 6 7 1 8 9 10 I I DATE HARVESTED (1925) AOE IN DAYS N o . o r FRUIT A v . WEIGHT o r FRUIT AVEOAOE WEIflllT OF PODS AVERAOE WEIOIIT OF PEAS PER POD A v : DRY WEIGHT OF FRUIT FKF.HII WEIGHT RATIO PODS/PEAS DRY WEIGHT RATIO PODB/PKAS FRESH WEIOIIT DRY WEIOIIT FRESH WEIGHT DRY WEIUIIT gm. pm. gm. gm. gm. gm. 4/21 12 150 3.33 3.02 0.37 0.31 0.05 0.42 0.7 7.0 4/27 18 110 4.90 4.04 0.50 0.86 0.14 0.73 4.7 4.3 4/29 ~ 20 113 5.11 3.06 0.57 1.45 0.20 0.83 2.52 2.2 5/1 22 no (1.13 4 22 0.61 1.01 0.35 0.00 2.22 1.8 5/3 24 122 6.31 3.98 0.59 2.33 0.47 1.00 1.71 1.3 5/5 26 108 6.05 4.00 0.57 2.59 0.55 1.12 1.67 1.1 . 6/7 28 101 6.60 3.82 0.54 2.78 0.60 1.20 . 1.87 0.81 5/9 30 5/11 32 86 7.22 4.00 0.52 3.22 0.82 1.34 1.24 0.64 6/13 34 . 117 6.21 3.18 0.41 3.03 0.93 1.34 l.Ofi 0.44 5/15 311 118 5.31 2.44 0.30 2.87 0.93 1.29 0.85 0.39 5/19 40 105 5.59 2.42 0.36 3.17 1.09 1.45 0.76 0.33 5/23 44 •106 4.80 1 .lift 0.37 3.14 1.22 1.59 0.53 0.31 5/27 ' 48 139 2.15 0.45 0.36 1.70 1.17 1.53 0.20 0.30 * T a k e n f r o m B i s s o n a n d J o n e s ( 1 9 3 2 ) . 66 Pod dry weight was estimated by using the following equation: W p ( D ) = 0.168 *Wp(p) (R 2 = 96.8) [26] Where Wp^^ = pod dry weight W P(F) = pod f r e s h weight Seed dry weights were c a l c u l a t e d from: WSe(D) = ° * 2 6 2 * WSe(F) ( R ' " 8 2 ' ° > ^27] and pod wall dry dry weight. weight was derived by subtracting seed dry weight from pod - 67 -CHAPTER 5 RESULTS 5.1 The Data Calculated means and standard deviations of the v a r i a t e s measured at each d e s t r u c t i v e harvest are l i s t e d i n Tables 5.1 (a) and ( b ) . The increase in standard deviation at each successive harvest i s evident. This increase in v a r i a t i o n , implies that a variance s t a b i l i z i n g transformation i s required for the regression analysis (Weisberg, 1980). 5.2 Analysis of Variance 5.2.1 Overall Analysis Table 5.2 summarizes the r e s u l t s of the o v e r a l l analysis for each primary v a r i a t e . There were four main r e s u l t s . 1. There were no s i g n i f i c a n t e f f e c t s due to seed i n o c u l a t i o n , e i t h e r as a main e f f e c t or as an i n t e r a c t i o n with the other f a c t o r s . 2. The i n t e r a c t i o n between harvest dates and c u l t i v a r s and the date main e f f e c t were highly s i g n i f i c a n t for each v a r i a t e (e.g. for the v a r i a t e , stem length, the F values for the date x c u l t i v a r i n t e r a c t i o n and the date main e f f e c t were 4.1 and 249.3 r e s p e c t i v e l y ) . 3. C u l t i v a r main e f f e c t s were s i g n i f i c a n t in a l l v a r i a t e s except the number of pods (P) and the number of seeds per plant (Se). These two v a r i a t e s had F values of 0.9 and 0.3 r e s p e c t i v e l y . - 68 -Table 5.1(a) - Summary of means vi p r i m a r y v a r i a t e s from d e s t r u c t i v e h a r v e s t s . Harvest Treatment* (DAP) S**(cn) V \ < « > u s (*° " v <*> Se WSe («> I 1 (20 9.050 4.292 30.362 0.168 0.039 0.207 - _ -1 2 (50 49.542 12.417 388.994 2.418 1.276 3.694 1.208 - - -1 3 (53 51.731 13.188 456.463 2.561) 1.506 4.066 1.250 - - -1 4 (56 56.725 14.125 582.636 3.424 1.979 5.403 1.688- 0.063 0.500 0.003 1 5 (59 64.756 15.250 869.662 4.769 2.90b 7.675 3.313 0.81 3 5.875 0.047 1 6 (62 73.319 16.313 844.4 76 4.889 3.416 8.304 2.81 3 1.250 9.188 0.175 I 7 (65 69.744 15.688 842.046 4.221 3.254 7.474 4. IHM 2.438 17.175 0.496 1 a (68 73.312 16.250 925.812 5.119 3.927 9.047 S.50U 3.5UO 24.4)8 1.2 52 1 9 (71 73.250 16.938 850.435 4.855 " 4.024 8.879 i.81 3 5. )l 1 16.750 3.686 I 10 (74 77.887 17.063 861.943 4.743 4.172 8.915 1.875 6.56) 45.31) 7.872 1 11 (77 79.450 17.500 804.024 5.254 4.522 9.777 0.81 1 7.81 3 52.875 13.299 I 12 (80 79.981 17.750 846.490 5.173 4.705 9.878 O.bSri 1 1.875 90.438 • 25.410 2 1 (20) 9.054 4.583 29.212 0.174 0.035 0.209 - - - -2 2 (50) 46.783 12.458 350.003 2.263 1.124 3.387 1.208 - - -2 3 (53 55.087 13.125 576 . 622 3.109 1.781 4.889 1 .60) - - -2 4 (56) 56.275 14.250 489.034 2.919 1.636 4.555 1.313 - - -2 5 (59) 65.331 15.375 690.621 3.710 2. 374 6.084 2.250 0.938 b.625 0.046 2 6 (62) 68.037 15.750 658.864 4.258 3.023 7.282 2.875 1.500 10.56) U.315 2 7 (65) 72.212 16.687 815.860 4.163 3.088 7.251 4.500 2.438 17.188 0.384 2 8 (68) 73.375 16.563 709.571 4.127 3.239 7.366 4.500 3. US 22.875 1.373 2 9 (71) 78.019 16.875 1105.510 6.856 5.398 12.254 5. 688 5.563 39.125 4.157 2 10 (74) 76.937 17.063 694.673 4.262 3.466 7.729 1.375 b.l 88 43.688 8.164 2 11 (77) 76.100 17.188 866.078 5.892 4.454 10.346 t . 125 8.500 55.250 1 1.348 2 12 (80) 85.212 18.250 780.234 4.777 4.276 9.053 0.125 13.125 83.125 26.377 3 1 (20) 8.375 4.042 27.917 0.142 0.027 0.168 - - - -3 2 (50) 47.558 11.500 309.807 2.224 1.192 3.416 1.792 - - -3 3 (53) 55.000 12.750 496.226 3.078 1.878 4.956 1.500 - - -3 4 (56) 60.662 13.375 449.878 2.984 1.938 4.921 2.125 1 . )7S 10.250 0.142 3 5 (59) 67.912 14.813 594 . 94 5 3.661 2.559 6.220 4.063 1. 56 1 18.875 0.437 3 t> (62) 67.025 14.813 604.840 4.041 2.959 7.001 2.62 5 >. n \ 1b.6H8 1 .04 5 3 7 (65) 71.412 14.938 721.054 3.930 3.133 7.062 1 .750 5.250 18.375 1.648 3 8 (68) 66.962 14.875 508.622 3.363 2.562 5.926 0.938 4.81 3 32.81 3 3.674 3 9 (71) 71.819 14.875 650.747 3.967 3.177 7.084 0.625 6.75U 46 . 500 8.668 3 10 (74) 68.006 14.375 454.278 2.899 2.326 5.225 0.250 6.81) 42.875 13.940 3 11 (77) 67.062 14.875 456.9)5 2.983 2.539 5.522 0.06) 6.375 18.438. 15.260 3 12 (80) 71.300 14.438 588.538 3.836 2.967 6.802 O.OUO 8.918 5 3.313 27.684 4 1 (20) 8.537 3.875 29.863 0.159 0.031 0. 190 - - -4 2 (50) 49.204 11.750 343.784 2.374 1.173 3.546 1.625 - - -4 3 (53) 56.250 12.500 507.566 3.010 1.953 4.963 I . 56.1 - - -4 4 (56) 60.637 13.625 423.366 2.866 1.913 4.779 1.81 3 1.438 10. 500 0.101 4 5 (59) 65.775 14.625 446.058 3.326 2.403 5.729 2.438 2.500 19.438 0.941 4 6 (62) 63.744 14.313 493.222 3.219 2.249 5.468 1 .688 2.625 18.b25 1 .459 4 7 (65) 68.369 15.000 562.040 3.349 2.515 5.864 1 .875 4.125 28.688 3.067 4 8 (68) 69.950 14.688 497.327 3.083 3.043 6.126 1.125 5.000 34.250 4.474 4 9 (71 ) 69.262 15.438 600.212 3.872 2.993 6.866 0. 125 7.56 1 51.06) 10.405 4 10 (74) 68.181 14.938 4 70.868 3.044 2.384 5.429 0.1100 6. 175 42.250 1 3.354 4 U (77) 67.587 15.188 423.611 2.946 2.151 5.075 U.000 0.4)8 38.063 15.376 4 12 (80) 67.506 14.688 421.592 2.433 1.969 4.402 0.000 h. 750 40.063 22.533 * 1 • unlnoculaced DSP, 2 - lnocul.aced DSP, 3'- unlnoculaced KF and 4 • Inoculaceu KF **S • seen lengch, » nuaber of leaves/plane, " leaf area/plane, • leaf dry weight/pianc, W$ = stem dry weight/plane, Wy - vegecaclve dry weight/plane, F N - nuaber of flower s/ plane, P - number of pods/plant, Se -nuaber of seeds/plane and Wse " tota l seed fresh weight. DAP - days afcer planting. - 69 -Table 5.1(b) - Scandard deviation of prlaary variates froa destructive harvests. Harvest (DAP) S"(ca) s LA Cc-2) wL (g) ws (g) Se HSe (*» 1 (20) 1.710 0.690 10.287 0.057 0.023 0.065 - - - -2 (50) 5.665 0.654 158.026 0.774 0.338 1.059 0.415 3 (53) 9.965 0.750 222.710 0.992 0.641 1.624 0.577 4 ( 5 6 ) 9.909 1.147 279.467 1.425 0.977 2.392 0.793 0.250 2.000 0.013 5 (59) 7.706 0.683 447.065 2.030 1.257 3.2b5 2.152 0. 544 4.272 0.053 6 ( 6 2 ) 9.632 0.946 375.337 2.500 1.424 3.883 1.167 U.683 5.612 0.136 7 (65) 12.034 2.204 421.789 1.594 1.321 2.884 2.401 I. 143 10.813 0.444 8 ( 6 8 ) 17.276 1.483 756.761 3.537 2.690 6.205 4.242 1.265 10.178 0.646 9 (71) 14.311 2.351 582 . 866 2.991 2.648 5.614 3.449 3.092 20.895 2.084 10 (74) 16.956 1.731 539.613 2.773 2.806 5.567 2.062 •3.385 2 5.2 3.800 U ( 7 7 ) 15.489 2 . 0 0 0 449.446 2.899 2.648 5.489 1.424 4.651 31.983 7.520 12 ( 8 b ) 12.472 1.844 540.483 3.710 3.175 6.801 2.272 8.641 58.586 12.776 I (20) 1.543 0.776 10.298 0.062 0.014 0.U74 2 (50) S.465 0.658 115.924 0.560 0.293 0.786 0.41 5 3 (53) 8.543 0.885 268.556 1.323 0.732 2.034 0.443 4 (56) 8.670 0.775 168.644 0.805 0.402 1.742 0.602 5 (59) 9.763 0.806 325.451 1.465 0.883 2.335 1.571 0.574 4.319 0.029 6 (62) 12.045 1.732 252.672 1.793 1.277 3.055 2.062 0.966 6.957 0.414 7 (65) 12.610 1.250 365.683 1.563 1.068 2.590 2.280 0.727 5.822 0.207 a (68) 17.561 1.750 429.859 1.838 1.612 3.435 2.582 1.328 9.229 1.019 9 (71) 18.940 1.821 672 . 523 3.272 2.758 5.960 3.092 3.054 22.256 2.313 10 (74) 13.830 2.081 435.907 2.367 2.018 4.363 1.360 3.692 2 5.968 5.244 a ( 7 7 ) 16.756 2.198 665.577 4.823 4.004 8.558 1.893 5.241 41.093 11.582 12 (80) 8.030 1.125 34 9 . 7 70 2.118 2.215 4.307 0.500 6.561 39.893 11.552 i (20) 1.404 0.550 7.799 0.048 0.016 0.061 2 (50) 7.175 0.659 128.833 0.758 0.487 1.216 0.779 3 (53) 10.540 0.856 263.914 1.358 0.820 2. 170 0.81 7 4 (56) 6.442 0.619 192.519 1.105 0.669 1 . 730 1.408 0.806 6.202 0.1 3U 5 (59) 9.783 0.750 269.754 1.340 0.932 2.2b3 2.542 0.727 6. 228 0.189 6 (62) 11.864 1.328 384.846 2.695 1.809 4.473 2.277 1.195 8.623 0.921 7 (65) 14.136 1.843 381.926 1.719 1.352 3.057 1 .693 1.693 13.084 1.887 a (68) 10.098 1.586 307.592 1.543 1.276 2.791 0.998 2.373 16.183 2.002 9 (71) 17.295 1.9% 357.467 1.837 1.528 3.351 I. 147 2.887 20.080 3.745 10 (74) 17.277 2.125 256.895 1.469 1.219 2. 666 I. 000 2.786 20.353 4.689 11 (77) 16.577 2.335" 272.101 1.787 1.471 3.211 0.250 3.096 21 . 74 7 8.577 12 (80) 12.920 1.750 389.123 2.404 1.944 4.200 0.000 5.627 36.666 15.341 I (20) 1 .'336 0.537 8.563 0.057 0.015 0.069 2 (50) 9.375 0.608 134.794 0.821 0.351 1 .345 0.576 3 (53) 11.177 1.265 331.990 1.696 1.145 2.819 0.727 4 (56) 9.863 1.025 186.580 0.984 0.681 1.659 1.109 0. 72 7 5.441 0.052 5 (59) 13.451 1.310 225.104 1.925 1.473 3.393 2. 128 1 .033 7. 164 1.952 6 (62) 14.569 1.778 282.078 1.532 1.149 2.671 2.056 1.784 13.822 1.077 7 (65) 12.283 1.633 301.391 1.635 1.058 2.628 2.754 I .857 13.622 2.267 8 (68) 13.251 1.702 330.626 1.439 2.700 3.563 2.363 1.932 15.776 I .996 9 (71) 16.360 1.896 302.495 1.993 1.439 3.416 0. 342 2.804 22.368 4.216 10 (74) 19.057 1.877 235.863 1.459 1.194 2.640 o.ooo" 2.029 15.537 5.624 II (77) 11.969 1.559 207.015 1.615 1.155 2.622 0.000 2.828 18.617 7.620 12 (80) 15.479 1.957 107.016 0.885 0.796 1.652 0.000 2.671 t 5.948 8.626 •1 • uninoculated DSP. 2 - Inoculated DSP, 3 - uninoculated EF and 4 - Inoculated EF * * S • atea length, lg - nuaber of leaves/plant, LK - leaf area/plant, WL - leaf dry weight/plane, Us - sten dry milghc/plant, Hy " vegetative dry wight/plant, PJJ - rubber of flowers/plane , P - number of pod a/ plant, Se • nuaber of seeds/plant and - total seed fresh wight. DAP » days after planting. Table 5.2 - Summary of results of overall ANOVA: Effect of cultivar and inoculation on primary variates Source of Variation df S1 LN LA W L WS WV FN P Se Se F-values Block 7 21.1*** 3.6*** 19.5*** 7.4*** 8.3*** 7.8*** 3.8*** 6.0*** A.6*** 4.2*** Cultivar (C) 1 9.6** 141.9*** 37.6*** 16.2*** 15.1*** 15.9*** 34.3*** 0.9 0.3 15.4*** Inoc (I) 1 0.03 0.7 2.0 0.6 0.9 0.7 1.2 0.3 0.3 0.01 C x i 1 0.1 0.04 0.01 0.1 0.1 0.1 0.3 0.2 0.1 0.2 Error 1 21 4.1*** 1.2 2.1* 3.0*** 2.6*** 5.1*** 1.7 1.1 1.3 1.2 Date (D) 11 249.3*** 441.5*** 36.0*** 37.9*** 41.5*** 40.8*** 28.0*** 114.7*** 98.0*** 171.2*** D x C 11 4.1*** 6.3*** 3.5*** 4.1*** 5.2*** 4.7*** 15.4*** 10.1*** 11.0*** 3.3*** D x I 11 0.4 0.5 1.2 1.3 0.8 1.1 1.2 0.6 0.6 0.4 D x C x I 11 0.7 0.4 0.9 0.8 0.8 0.8 1.0 0.2 0.1 0.6 Error 2 308 1.5*** 1.3*** 1.8*** 1.6*** 1.8*** 1.7*** 1.9*** 1.6*** 1.5*** 1.8*** •S = stem length, Lfj = number of leaves/plant, •» leaf area/plant, = leaf dry weight/plant, Wg = stem dry weight/plant, Wy = vegetative dry weight/plant, F N = number of flowers/plant, Se = number of seeds/plant and Wge = total seed fresh weight/plant. * significant at 5% level ** significant at 1% level *** significant at 0.5% level - 71 -4. The block effects and the main and sub-plot errors were all significant. 5.2.2 Sub-unit A n a l y s i s The interaction between cultivars and inoculum was insignificant throughout the experimental period (Table 5.3). For example, the F value for leaf number (Ljj) ranged from 0.01 at the sixth harvest [62 days after planting (DAP)] to 2.39 at the first harvest (20 DAP). Inoculum main effects were significant for: (a) leaf area at 59 DAP (F value, 10.78) and 61 DAP (F value, 6.12). (b) stem dry weight at 61 DAP (F value, 4.93) and (c) number of flowers at 59 DAP (F value, 9.48). In the case of cultivar main effects, for all variates, this source of variation was significant at different times. Stem length differences were apparent at 56 DAP (early reproductive growth), 61 DAP and from 74 DAP onwards. During the early reproductive phase Early Frosty (EF) was taller than Dark Skin Perfection (DSP) [60.7 cm for EF vs. 56.5 cm for DSP (Table 5.1a)], but from day 61 onwards, DSP was taller (Table 5.1a). DSP had significantly more leaves than EF throughout the growing period. For example, inoculated and uninoculated DSP had 4.5 and 4.3 leaves respectively at 20 DAP and 18.3 and 17.8 leaves at 80 DAP (Table 5.1a). The corresponding number of leaves for inoculated and uninoculated EF were 3.9 and 4.0 at 20 DAP and 14.7 and 14.4 at 80 DAP. Significant leaf area differences were not apparent until the late vegetative phase (50 Table 5.3 - Subunlt ANOVA of the effect of cultivar and Inoculation on primary values. Source of Variation Harvest Number (Days After Planting) Blocks Variate 1(20) ^  2(50) 3(53) 4(56) 5(59) 6(62) 7(65) 8(68) 9(71) 10(74) 11(77) 12(80) S1  LN 0.70 0.98 7.85*** 2.35* 4.91*** 1.63 19.13*** 3.18* 7.27*** 1.95 F-values 4.83*** 2.31 6.96*** 3.21* 5.71*** 1.82 3.77** 2.59* 7.13*** 0.93 5.36*** 0.90 4.66*** 1.68 LA 1.14 10.18*** 17.26*** 6.20*** 13.26*** 5.54*** 12.56*** 10.54*** 7.76*** 5.81*** 5.86*** 4.78*** W L 1.31 6.16*** 7.77*** 4.41** 3.30** 3.66** 4.55** 6.33** 3.63** 4.08*** 4.45*** 2.56* ws 2.63* 3.97** 6.14*** 8.27*** 2.59* 5.18*** 4.84*** 4.70*** 5.72*** 4.90*** 4.70*** 3.82*** w v 1.67 5.92*** 7.16*** 5.82*** 3.02** 4.26** 4.87*** 6.35*** 4.57** 4.48** 4.94** 3.21* . FN - 3.48** 0.74 1.08 4.04*** 2.55* 1.06 3.57** 3.99*** 3.35* 0.97 i.33 ' P - - - 0.91 1.38 3.29* 1.09 5.86*** 5.29*** 1.00 1.82 3.84*** Se - - - 0.92 1.06 2.81* 1.90 6.81*** 4.57** 1.02 1.43 3.38** - - - 0.88 1.13 1.84 0.28 2.39* 1.27 2.84* 0.90 5.42*** Table 5.3 continued Harvest Number (Days After Planting) Source of V a r i a t i o n C u l t i v a r V a r i a t e P Se U 1(20) 1.19 14.30*** 0.21 2.91 6.29* 4.09 2(50) 0.03 43.46*** 4.23* 0.12 0.07 0.11 25.04*** 3(53) 1.01 5.67* 0.14 0.70 2.68 1.36 4.80* Se 4(56) 14.44*** 16.13** 5.92* 1.20 0.99 0.15 3.17 88.00*** 84.25*** 41.47*** 5(59) 0.87 6.12* 27.03*** 4.00 0.36 2.05 1.15 85.12*** 86.80*** 7.81* 6 ( 6 2 ) P-values 4.84* 20.27*** 11.37* 5.41* 6.15* 5.83* 2.75 16.33*** 13.62*** 30.97*** 7(65) 0.22 11.61 *** 11.98** 3.54 2.54 3.26 22.09*** 37.57*** 39.81*** 44.58*** 8(68) 2.88 17.11*** 16.16*** 13.19*** 0.06 8.95*** 60.41*** 22.32*** 18.79*** 59.67*** 9(71) 1.82 14.26*** 14.66** 12.64** 16.08*** 14.40*** 87.5*** 8.24** 5.94* 41.88*** 10(74) 11(77) 8.85** 22.37*** 17.86*** 12.32*** 14.98*** 13.67*** 38.4*** 0.07 0.11 27.17*** 12.35*** 19.56*** 21.31*** 18.15*** 20.03*** 20.86*** 10.00*** 3.33 5.48* 0.90 12(80) 29.82*** 91.67*** 14.70*** 1Q.98*** 18.11*** 14.70*** 1.90 17.23*** 19.63*** 0.11 Table 5.3 continued Source of Variation Harvest Number (Days After Planting) Variate 1(20) ~ 2(50) 3(53) 4(56) 5(59) 6(62) 7(65) 8(68) 9(71) 10(74) 11(77) 12(80) F-values Inoc Sl 0.52 0.20 1.09 0.04 0.16 3.17 0.01 0.28 0.09 0.01 0.23 0.09 LN 0.24 1.40 0.49 1.20 0.02 2.65 2.21 0.03 0.29 0.31 0.00 1.09 LA 0.04 0.01 2.75 2.17 10.78*** 6.12* 2.93 2.11 1.23 1.02 0.03 2.10 WL 1.01 0.000 0.93 1.91 3.50 3.21 1.18 2.72 3.07 0.15 0.24 2.62 WS 0.004 1.70 1.10 2.41 1.71 4.93* 3.23 3.49 2.29 0.73 0.23 2.25 wv 0.74 0.26 1.02 2.17 2.17 3.92 2.03 1.03 2.78 0.37 0.00 2.56 FN - 0.70 0.13 1.70 9.48*** 1.11 0.16 0.63 2.16 2.40 0.18 0.91 P - - - 0.00 0.03 1.08 2.35 0.04 0.79 0.25 0.15 1.16 Se - - - 0.01 0.22 0.62. 3.68 0.00 0.61 0.04 0.02 1.29 WSe - - - 1.38 1.20 2.71 0.63 1.65 1.62 0.02 0.00 0.75 Table 5.3 continued Source of V a r l a t i o n V a r i a t e 1(20) 2(50) Harvest Number (Days A f t e r P l a n t i n g ) 3(53) 4(56) 5(59) 6(62) F-values 7(65) 8(68) 9(71) 10(74) 11(77) 12(80) Cvs X Inoc P Se W 0.13 2.39 0.96 0.36 1.46 0.79 2.20 0.61 2.35 0.98 0.66 0.94 0.42 0.38 0.14 1.47 1.24 0.32 0.82 0.62 Se 0.01 0.05 0J56 0.57 0.83 0.69 0.02 0.24 0.14 1.40 0.41 0.93 0.05 0.82 0.46 0.67 0.30 0.25 0.00 0.90 0.12 0.01 0.19 0.02 0.15 0.06 0.95 0.01 0.01 0.28 0.91 1.15 0.57 0.32 0.46 0.39 0.02 2.26 2.70 0.61 0.19 0.42 0.87 0.35 1.15 0.72 0.51 0.33 0.19 0.92 1.25 0.44 2.26 2.78 2.12 2.51 3.55 0.20 0.06 1.04 0.03 0.37 1.11 0.41 0.69 0.55 0.10 0.00 0.01 1.39 0.30 0.39 0.26 0.21 0.05 0.13 0.39 0.10 0.03 0.00 2.03 0.06 0.40 0.63 0.35 0.53 1.12 0.29 0.11 1.22 • S i g n i f i c a n t at 5% l e v e l * * S i g n i f l e a n t at IX l e v e l * * * S l g n i f i c a n t at 0.5Z l e v e l lS = stem len g t h , -number of leaves/plant, L A - leaf area/plant, WL - leaf dry weight/plant, Wg - stem dry weight/plant, Wy dry weight/plant, F(j = number of flow e r s / p l a n t , P = number of pods/plant, Se - number of seeds/plaint and Wge vegetative t o t a l seed f r e s h weight. - 76 -DAP) and from 56 DAP onwards. By the f i n a l harvest, l e a f area of 2 uninoculated and inoculated DSP were 846.5 and 780.2 cm compared with 588.5 and 421.6 cm2 for uninoculated and inoculated EF (Table 5.1a). Because much of the t o t a l vegetative dry weight was accounted f o r by leaves, s i g n i f i c a n t d i f f e r e n c e s i n t h i s v a r i a t e ( t o t a l vegetative dry weight) were evident at the same time as l e a f dry weight (61 DAP and from 65 DAP onwards). Uninoculated and inoculated DSP had t o t a l vegetative dry weights of 9.88 and 9.05 g at the f i n a l harvest, whereas uninoculated and inoculated EF were 6.80 and 4.40 g r e s p e c t i v e l y (Table 5.1a). Early Frosty had s i g n i f i c a n t l y more flowers per plant during the e a r l y reproductive phase (50 to 63 DAP). (DSP had on the average 1.2 flowers/plant at 50 DAP while EF had 1.7). However, between 62 and 74 DAP, DSP was more p r o l i f i c (Table 5.1a). For example, uninoculated DSP and inoculated DSP bore 5.5 flowers/plant and 4.5 flowers/plant r e s p e c t i v e l y at 68 DAP. At that time uninoculated and inoculated EF had 0.94 and 1.13 flowers per plant. As a r e s u l t of the e a r l i e r flowering, there was a s i g n i f i c a n t d i f f e r e n c e in number of pods per plant during 56 to 71 DAP (Table 5.3). EF had more pods at that time (Table 5.1a) (e.g. at 68 DAP, uninoculated and inoculated EF had 4.8 and 5.0 pods/plant while uninoculated and inoculated DSP had 3.5 and 3.2 pods/plant). Nonetheless, by the f i n a l harvest date (80 DAP), DSP exceeded EF (13.9 f o r uninoculated DSP, compared with 8.9 for uninoculated EF). T h i s d i f f e r e n c e i n the number of pods was also manifested in the number of seeds per plant and the t o t a l fresh weight of the seeds (Table - 77 -5.3). Thus, during 56 to 71 DAP, EF had significantly more seeds and higher total seed fresh weight than DSP. At 59 DAP uninoculated and inoculated DSP had 5.9 and 6.6 seeds per plant while uninoculated and inoculated EF had 18.9 and 19.4 seeds/plant. The corresponding seed fresh weights at that time were 0.047, 0.315, 0.435 and 0.941 g. From 77 DAP onwards, DSP had more seeds (52.9 and 55.3 seeds/plant for uninoculated and inoculated DSP, compared with 38.4 and 38.1 seeds/plant for uninoculated and inoculated EF respectively). Total seed fresh weight in DSP, however, was always less than in EF. 5.3 Growth Analysis Growth analysis was used to determine the net activity, extent and efficiency of the photosynthetic source. Values of the growth indices analysed in this section were derived from the selected curves as outlined in Chapter 4. Only confidence limits for uninoculated DSP are included in the graphs. Those for the other treatments are depicted by symbols which represent mean multiples of the limits of the standard—uninoculated DSP. That i s , for each treatment, the mean harvest standard error of each variate was calculated. This mean was then expressed as a multiple of' the mean for uninoculated DSP. Assignment of uninoculated DSP as the standard is important to this study. This cultivar has been used by a number of pea producers in North America and the United Kingdom (Milbourn and Hardwick, 1968) for many years. Consequently, i t is considered a standard for the comparison of other cultivars and treatments. - 78 -5.3.1 Growth Curves • As stated i n Section 5.1, the data were subjected to a n a t u r a l -logarithmic transformation, before f i t t i n g the respective curves, i n order to s t a b i l i z e the variance. 5.3.1.1 Leaf Area Figure 5.1 shows the time course of mean l e a f area per plant of a l l treatments during the reproductive phase. Marked d i f f e r e n c e s i n l e a f area became apparent from 56 DAP onwards. A f t e r day 56, DSP had a higher l e a f area than d i d EF regardless of whether the plants were inoculated or not. This f i n d i n g was a l s o e x h i b i t e d i n the sub-unit a n a l y s i s , already described i n Section 5.2. Within each c u l t i v a r , the uninoculated plants tended to achieve maximum l e a f area e a r l i e r than t h e i r i noculated counterparts. For example, uninoculated plants of DSP and EF a t t a i n e d maximum l e a f area [925.8 cm2 and 721.1 cm 2 r e s p e c t i v e l y (Table 5.1a) at 68 and 65 DAP, while the inoculated plants reached t h e i r maxima (1105.5 cm 2 and 600.2 cm 2 f o r DSP and EF r e s p e c t i v e l y ) l a t e r at 71 DAP. 5.3.1.2 Dry Weights The growth curves f o r mean l e a f dry weight, stem dry weight and t o t a l vegetative dry weight per plant (Figures 5.2 to 5.4) were very s i m i l a r to that of l e a f area. Among the four treatments the dry weights were almost i d e n t i c a l at l a t e vegetative and e a r l y reproductive growth (50 to 53 DAP). During the next 16 days (54 DAP to 70 DAP) l e a f , stem and hence vegetative - 79 -Figure 5.1. Spline regression describing the time course of mean.leaf area per plant (log scale) i n garden pea. o LEGEND -7- Uninoculated DSP with 955* confidence limits (CL) a Inoculated DSP (2.83 x CL) o uninoculated E7 ( 2 . ^ 7 x CL) A Inoculated E? (1.9^ x CL) 50 60 DAYS AFTER r 70 P L A N T I N G 80 •r 80 r Figure 5 . 2 . Spline regression describing the time course of mean l e a f dry weight per plant (log scale) i n garden pea. q m 0 w> I A a 0 x o U l 5 u. < 50 — Uninoculated DSP with 95?* confidence limits (CL) • Inoculated DSP (2.28 x CL) c Uninoculated EF (1.77 x CL) A Inoculated EF (1.3^ x CL) T 60 70 DAYS AFTER P L A N T I N G 80 - 81- -Figure 5.3. Spline regression describing the time course of mean stem dry weight per plant ( l o g scale) i n garden pea. SO.O 60.0 70.0 DAYS AFTER P L A N T I N G 80.0 - 82 -Figure 5.4. Spline regression describing the time course of mean vegetative dry weight per plant ( log scale) i n garden pea, o m _ ci "3 w I * a o X O >» oc a Ul > Ul O o ci -f- Uninoculated DSP with 957* confidence limits (CL) • Inoculated DSP (2.58 x CL) o Uninoculated EF (I.90 x CL) A Inoculated EF (1.^2 x CL) 50 60 70 80 DAYS AFTER P L A N T I N G - 83 r dry weights of the uninoculated plants exceeded those of their inoculated counterparts. For example, at 50 DAP the untransformed means of vegetative dry weights of uninoculated DSP, inoculated DSP, uninoculated EF and inoculated EF were 3.7, 3.4, 3.4 and 3.5 g respectively (Table 5.1a). However, at 62 DAP, their respective weights were 8.3, 7.3, 7.0 and 5.5 g. From day 62 onwards, both inoculated and uninoculated DSP had higher dry weights than inoculated and uninoculated EF. The inoculated plants of each cultivar attained maximum dry weights 3-9 days after the uninoculated plants. Maximum leaf, stem and total vegetative dry weights were 6.9, 5.4 and 12.3 g respectively for inoculated DSP at 71 DAP (Table 5.1a) and 3.9, 3.0 and 6.9 g for inoculated EF at 71, 68, 71 DAP, respectively. Uninoculated plants attained maxima of 5.1, 3.9 and 9.0 g for DSP at 68 DAP and 4.0, 3.2 and 7.1 g at 71 DAP for EF. Total plant dry weight (W) was calculated by adding the total vegetative dry weight to the pod dry weight estimated in section 4.2.3. Figure 5.5 shows the growth curve of W. The confidence limits indicate that there was no significant difference among the treatments. However, by the final harvest (80 DAP), both inoculated and uninoculated DSP had higher total dry weight per plant than EF (compare 20.8 and 20.3 g uninoculated and inoculated DSP compared with 16.3 and 11.3 g for uninoculated and inoculated EF). In addition, the dry weights of the untreated plants continued to increase during the late reproductive phase (from 74 DAP onwards) while those of the inoculated plants either f e l l (EF from 74 DAP) or levelled off (DSP, 78 DAP). - 84 -Figure 5.5. Spline regression d e s c r i b i n g the time course of mean t o t a l plant dry weight ( l o g scale) i n garden pea. o 6 LEGEND —— Uninoculated DSP with 95?S confidence limits (CL) • Inoculated DSP (1.9** x CL) o Uninoculated EF (1.38 x CL) A Inoculated EP (1.22 x CL) 50 60 70 80 DAYS AFTER P L A N T I N G - 85 -5.3.2 Growth Indices 5.3.2.1 Relative Growth Rates Figures 5.6 to 5.10 are the r e l a t i v e growth rate curves for l e a f area, l e a f dry weight, stem dry weight, t o t a l vegetative dry weight and t o t a l dry weight per plant, r e s p e c t i v e l y . Marked d i f f e r e n c e s in the time course of the r e l a t i v e growth rates are apparent during the period 50 to 56 DAP. Re l a t i v e l e a f area growth rate (RL^^» r e l a t i v e stem growth rate (R^g) and the r e l a t i v e growth rate of the whole plant (Ry) of uninoculated DSP increased to maxima of 0.11, 0.09 and 0.08 d a y - 1 , r e s p e c t i v e l y , a t 54, 55 and 56 DAP. By contrast, RT^, RWs and % of the other treatments showed no such increase. Instead, they decreased s t e a d i l y during that e a r l y period. The values of RL^> W^g a n& % at 50 DAP were 0.095, 0.086 and 0.075 d a y - 1 , r e s p e c t i v e l y for inoculated DSP; 0.14, 0.11 and 0.095 d a y - 1 for uninoculated EF and 0.04, 0.12 and 0.10 d a y - 1 for inoculated EF (Figures 5.6, 5.8 and 5.10). Both uninoculated DSP and EF showed increasing r e l a t i v e l e a f growth rate (Ry^) during 50 to 56 DAP. In the former, the maximum R r ^ (0.08 d a y - 1 ) was reached at 56 DAP, while the l a t t e r attained i t s maximum (0.07 d a y - 1 ) at 53 DAP. Ry i n inoculated DSP and EF f e l l s t e a d i l y from 0.077 and 0.067 day - 1 v r e s p e c t i v e l y at 50 DAP. There was only a s l i g h t increase i n r e l a t i v e growth rate of the vegetative dry weight ( R t ^ ) of uninoculated EF during 50 to 53 DAP (Figure 5.9). Maximum was 0.09 d a y - 1 at that time. In the case of - 86 -Figure 5*6. Progress curves of instantaneous r e l a t i v e l e a f area growth rate. ci DAYS AFTER P L A N T I N G - 87 -Figure 5.7. Progress curves of instantaneous r e l a t i v e growth rate of l e a f dry weight. C O 6 0 a O 1 6 1 50 -7- Uninoculated DSP wi-th 95% confidence l i m i t s (CL) • Inoculated DSP (2.15 x CL) o Uninocula-te'd EF (1.77 x CL) A Inoculated EF (1.26 x CL) 60 70 80 DAYS AFTER P L A N T I N G - 88 -Figure 5.8. Progress curves of instantaneous stem growth rate. o o i i 1 50 60 70 80 DAYS AFTER P L A N T I N G - 89 -F i g u r e 5.9. P r o g r e s s c u r v e s o f r e l a t i v e g r o w t h r a t e o f v e g e t a t i v e d r y w e i g h t . to Ci 6 1 0 o a •o 1 0 T"" o I - j - Uninocula-ted DSP with 95# confidence limits (CL) • Inoculated DSP (2.12 x CL) o Uninoculated EF (1.86 x CL) A Inoculated EF (1.1? x CL) 50 60 7 0 80 DAYS AFTER P L A N T I N G - 90 -Figure 5.10. Progress curves of instantaneous relative growth rate of whole shoot. o • _ o i DAYS AFTER PLANTING - 91 -the other treatments R^ declined from 0.09 day- for uninoculated DSP, 0.08 day - 1 for inoculated DSP and 0.08 day - 1 for inoculated EF. The confidence intervals indicate no significant difference among the relative growth rates due to treatment. However, between 55 and 74 DAP, the relative growth rates of DSP were higher than those of EF. 5.3.2.2 Unit Leaf Rate There was no significant difference in unit leaf rate (E) among the treatments during the period 50 to 65 DAP. At that time, E ranged between 5 and 10 g m~2 day - 1, EF having somewhat higher rates than DSP. After day 65, the unit leaf rate of the uninoculated cultivars f e l l slightly at 68 DAP, then increased sharply for the rest of the growth period. On the other hand, E of the inoculated cultivars rose slightly then declined. The decrease in E of inoculated EF was greater than that of inoculated DSP (between 74 and 80 DAP, E for DSP f e l l from 9.9 g m-2 day - 1 — 2 — 1 to 5.6 g m- day- ) while the decline for EF over the same time period was from 3.1 g m-2 day - 1 to -17.2 g m-2 day - 1. 5.3.2.3 Leaf Area Rat i o No significant difference was discernable among the treatments during early reproductive growth (50 to 56 DAP). However, the trends in leaf area ratio (F) were different (Figure 5.12). In inoculated DSP and uninoculated - 92 -Figure 5*11• Progress curves of instantaneous unit l e a f rate, o b • o 6 I i 1 1 50 60 70 80 DAYS AFTER PLANTING - 93. -- 9 4 -EF, l e a f area r a t i o increased to 110 and 94 cm g » r e s p e c t i v e l y , at 56 DAP then declined s t e a d i l y t h e r e a f t e r . Leaf area r a t i o decreased during days 50 to 53 a f t e r p l a n t i n g , rose to 111 cm g over the next three days, then f e l l i n uninoculated DSP (Figure 5.12). However, in inoculated EF, there was no increase, as F declined over the e n t i r e period from a high of 95.9 cm2 g _ 1. The confidence l i m i t s suggest that there was no s i g n i f i c a n t d i f f e r e n c e i n l e a f area r a t i o between inoculated and uninoculated plants within each c u l t i v a r . Between c u l t i v a r s , DSP had s i g n i f i c a n t l y higher l e a f area r a t i o compared to EF during the period 53 to 74 DAP. 5.3.2.4 Specific Leaf Area There was no s i g n i f i c a n t d i f f e r e n c e in s p e c i f i c l e a f area (SLA) among the treatments (Figure 5.13). However, both inoculated and uninoculated DSP had higher s p e c i f i c l e a f area than inoculated and uninoculated EF up to 71 DAP. For example, at 62 DAP, SLA of uninoculated and inoculated DSP was 2 — 1 172.7 and 154.7 cm g~ r e s p e c t i v e l y while the corresponding values for uninoculated and inoculated EF were 149.7 and 153.2 cm g • In both uninoculated and inoculated DSP, SLA rose to maxima of 182 and 179.1 cm2 g - 1 at 59 and 62 DAP, r e s p e c t i v e l y . The former maintained that SLA over the next 11 days before d e c l i n i n g . On the other hand, SLA of inoculated DSP f e l l soon a f t e r the maximum was a t t a i n e d . By contrast, SLA of both uninoculated and inoculated EF was more 2 _ 1 v a r i a b l e than DSP. In uninoculated EF, SLA rose sharply to 159.8 cm g - 95 -at 53 DAP, levelled off somewhat over the following 20 days, then f e l l from 73 DAP onwards. The trend of SLA for inoculated EF was the opposite of its uninoculated counterpart. SLA declined to 147.5 cm2 g~l at 53 DAP, then increased to a high of 158.9 cm2 g - 1 at 65 DAP. After that time the index f e l l again before rising from 75 DAP onwards. 5.3.2.5 Leaf Weight Ratio The curves for leaf weight ratio (Figure 5.14) were similar to those of leaf area ratio (Figure 5.12). As with the latter growth index, the confidence intervals indicated no significant difference between inoculated and uninoculated plants within a cultivar. However, DSP had significantly higher leaf weight ratio than EF during the period 56 to 77 DAP. AT 65 DAP, the leaf weight ratios of uninoculated DSP and inoculated DSP were 0.47 and 0.46 respectively, whereas the leaf weight ratios for inoculated and uninoculated EF were 0.37 and 0.38. 5.3.3 Non-destructive Harvests This part of the analysis was done primarily to determine the activity of the plants during the vegetative phase of growth. The data used for the study were derived from the prediction equations defined in Chapter 3 and are summarized in Table 5.4. -96 -Figure 5.13- Progress curves of instantaneous s p e c i f i c l e a f area. - j - Uninoculated DSP with 95# confidence limits (CL) • Inoculated DSP (0.55 x CL) O Uninoculated EF (0.53 * CL) A Inoculated EF (0.99 x CL) 50 60 70 DAYS AFTER PLANTING —1 80 - 97 -Figure 5.14. Progress curves of instantaneous l e a f weight r a t i o . 50 60 70 80 DAYS AFTER PLANTING - 98 -Table 5.4 - Summary of means for primary v a r i a t e s from non-destructive harvests Days Primary Variate itraent* A l t e r Planting S (cm)** L N L, (cm2) A w L ( g ) W (g) I 21 3.75 1 8.38 0.05 0.06 1 24 5.06 1 7.90 0.05 0.06 1 27 6.57 2 13.93 0.09 0.11 1 30 7.44 3 21.76 0.14 0.16 1 33 8.91 4 28.73 0.18 0.22 1 36 12.44 5 44.77 0.29 0.34 1 39 17.14 6 69.63 0.45 0.53 1 42 18.23 7 90.61 0.58 0.69 1 45 21.61 9 134.81 0.86 1.03 1 48 24.94 10 169.08 1.08 1.29 1 51 28.79 12 228.69 1.46 2.06 1 54 31.73 14 286.51 1.60 2.20 1 57 39.07 17 382.49 2.29 2.68 1 60 43.75 17 440.40 2.42 4.09 1 63 46.84 18 501.11 2.70 4.46 1 66 49.92 19 561.80 2.98 4.83 1 69 56.93 19 553.68 2.99 5.67 1 72 54.92 19 490.94 2.80 5.39 1 75 57.28 18 466.93 2.66 10.13 1 78 58.32 18 496.47 3.32 11.82 1 81 58.60 18 461.67 2.77 11.62 2 21 4.69 1 9.56 0.06 0.07 2 24 5.94 2 9.00 0.06 0.07 2 27 7.10 3 15.83 0.10 0.12 2 30 8.97 4 23.73 0.15 0.18 2 33 10.62 4 29.02 0.19 0.22 2 36 13.91 5 45.56 0.29 0.35 2 39 16.66 6 66.01 0.42 0.51 2 42 20.19 7 98.28 0.63 0.75 2 45 24.08 9 133.91 0.85 1.02 2 48 27.45 11 186.92 1.20 1.43 2 51 31.35 12 244.39 1.56 2.23 2 54 36.63 15 319.44 1.79 2.45 2 57 45.01 17 443.61 2.66 3.45 2 60 50.58 17 535.54 2.95 5.17 2 63 54.00 18 600.9 3.24 5.46 2 66 57.42 19 666.26 3.53 5.74 2 69 61.11 19 659.43 3.56 7.20 2 72 65.12 19 580.28 3.31 7.89 2 75 68.80 19 588.80 3.36 12.16 2 78 70.48 19 585.35 3.92 14.24 2 81 70.65 19 551.61 3.31 14.13 Continued. Table 5.4 continued - 99 -Days Primary Variate A f t e r Treatment* Planting S (cm)** L N L A (cm ) W L (g) W (g) 3 21 4.10 1 7.81 0.05 0.06 3 24 5.75 2 10.53 0.07 0.08 3 27 7.49 2 17.12 0.11 0.13 3 30 8.61 3 23.44 0.15 0.18 3 33 10.68 4 32.90 0.21 0.25 3 36 14.39 4 50.88 0.33 0.39 3 39 16.59 5 69.31 0.44 0.53 3 42 22.31 6 109.14 0.70 0.83 3 45 25.55 8 152.88 0.98 1.17 3 48 30.23 9 205.27 1.31 1.57 3 51 35.64 11 268.11 1.72 2.45 3 54 40.66 12 321.54 1.80 2.94 3 57 47.06 14 409.97 2.46 3.86 3 60 55.71 14 473.15 2.60 4.95 3 63 57.14 15 514.06 2.77 5.59 3 66 58.56 17 554.96 2.94 6.22 3 69 62.95 16 510.88 2.76 6.98 3 72 63.49 16 493.85 2.81 8.58 3 75 63.83 15 486.16 2.77 10.46 3 78 64.91 15 510.80 3.42 12.46 3 81 65.75 14 493.04 2.96 12.87 4 21 4.37 1 7.50 0.05 0.06 4 24 5.83 1 10.82 0.07 0.08 4 27 7.74 2 17.17 0.11 0.13 4 30 8.99 3 22.89 0.15 0.18 4 33 11.53 4 32.16 0.21 0.25 4 36 14.47 5 48.10 0.31 0.37 4 39 17.89 5 69.67 0.45 0.53 4 42 21.95 7 98.82 0.63 0.76 4 45 25.71 8 147.19 0.94 1.13 4 48 30.03 9 193.28 1.24 1.48 4 51 35.82 11 256.05 1.64 2.36 4 54 41.52 12 303.60 1.70 2.80 4 57 47.62 14 " 383.78 2.30 3.65 4 60 52.41 15 457.48 2.52 4.66 4 63 55.33 16 484.90 2.62 5.21 4 66 58.24 17 512.32 2.72 5.75 4 69 59.14 17 479.01 2.59 6.25 4 72 59.37 17 468.07 2.69 7.69 4 75 59.73 ' 17 482.30 2.75 10.39 4 78 60.31 17 505.55 3.39 12.11 4 81 60.65 16 502.80 3.02 12.76 *1 = Uninoculated Dark Skin P e r f e c t i o n 2 = Inoculated Dark Skin P e r f e c t i o n 3 = Uninoculated Early Frosty 4 = Inoculated Early Frosty. **S = stem length/plant; = number of leaves/plant; = le a f area/ plant; WL = leaf dry weight/ plant and W = t o t a l dry weight/plant. - 100 -5.3.4 Growth Curves 5.3.4.1 Leaf Area Figure 5.15 shows the growth curves of the,mean t o t a l l e a f area per plant (logarithmic scale) of the four treatments. During the vegetative phase (21 to 53 DAP), mean l e a f area did not d i f f e r with treatment. For example, at 30 DAP the l e a f areas of inoculated and uninoculated EF were 2 22.9 and 23.4 cm r e s p e c t i v e l y , while those of inoculated and uninoculated DSP were 23.7 and 21.8 cm2 (Table 5.4). Treatment d i f f e r e n c e s became apparent from the time of flowering (53 DAP) onward. A f t e r that time, inoculated DSP had the highest l e a f area (666.3 cm ) and by the f i n a l harvest (81 DAP) uninoculated DSP had the lowest (561.8 cm 2). 5.3.4.2 Dry Weights The growth trends for leaf weight were s i m i l a r to those f o r l e a f area (Figure 5.16). Noticeable l e a f weight d i f f e r e n c e s were not evident u n t i l the time of flowering, with inoculated DSP having the highest value (3.33 g at 81 DAP). Whereas the l e a f area curves (Figure 5.15) for inoculated and uninoculated DSP showed a tendency to de c l i n e o f t e r 65 DAP, this was not the case with l e a f weight. Instead, these l a t t e r curves l e v e l l e d o f f af t e r that time. At the f i n a l harvest, uninoculated DSP had the lowest l e a f weight while that of inoculated and uninoculated EF was 3.01 and - 101 -Figure 5.15. Cubic spline regression describing time course of mean l e a f area per plant (non-destructive harvests). N DAYS AFTER P L A N T I N G - 102 -Figure 5.16. Cubic spline regression describing time course of mean l e a f dry weight per plant (non-destructive harvests). m ? H 1 1 1 1 1 1 1. 20 30 40 50 60 70 80 90 DAYS AFTER P L A N T I N G - 103 -2.95 g, r e s p e c t i v e l y . Total plant weight increased throughout the growth period. During the vegetative phase weights were very s i m i l a r , with values ranging between 0.17 g for uninoculated DSP and 0.18 g for inoculated DSP (Figure 5.17). In the reproductive phase inoculated EF, uninoculated EF and inoculated DSP had almost i d e n t i c a l weights (12.9, 12.8 and 14.1 g, r e s p e c t i v e l y ) while that of uninoculated DSP was somewhat lower (11.6 g). 5.3.5 Growth Indices 5.3.5.1 R e l a t i v e Growth Rates The r e l a t i v e growth rate curves for l e a f area and leaf weight (Figures 5.18 and 5.19) r e f l e c t the s i m i l a r i t y of the two sets of growth curves. However, unlike t h e i r growth curves, c u l t i v a r d i f f e r e n c e s were apparent during early vegetative growth. In the case of DSP, the r e l a t i v e growth rate of l e a f area (Rj.) ci. increased from 0.1 d a y - 1 at 21 DAP to 0.12 d a y - 1 ( i n inoculated DSP) and 0.13 d a y - 1 ( i n uninoculated DSP) at 40 DAP and 37 DAP r e s p e c t i v e l y . The corresponding values for l e a f weight (Ry^) were 0.11 d a y - 1 at 21 DAP and 0.13 d a y - 1 over the same time periods for inoculated and uninoculated DSP (see Figure 5.19). By contrast, Rj. and R^ f o r inoculated and uninoculated EF started off at 0.12 d a y - 1 and remained constant over the period 21 to 30 DAP. - 104 -Figure 5-17- Cubic spline regression describing time course of mean t o t a l dry weight per plant (non-destructive harvests) m -o •• v I A 0 o at a < O I n ' 20 Uninoculated DSP Inoculated DSP Uninoculated EF Inoculated 2 F 30 40 —r~ 50 —r— 60 — i — 70 — I 8 0 — I 90 DAYS AFTER PLANTING - 105 -Figure 5.18. Instantaneous r e l a t i v e l e a f area growth rate curves (non-destructive harvests). - 106 -Figure 5-19- Instantaneous r e l a t i v e l e a f weight growth rate curves (non-destructive harvests). in * o o o 1 > o < o 5 O oe O < - J o 111 OE O J O o d i Uninoculated DSP Inoculated DSP Uninoculated EF Inoculated EF 2D 3 0 4 0 5 0 jSO 7 0 DAYS AFTER P L A N T I N G 8 0 90 - 107 -For both c u l t i v a r s , t h i s i n i t i a l p eriod was followed by a phase of r a p i d d e c l i n e i n R L a and R W l. This phase l a s t e d u n t i l 70 DAP and for most of that time DSP had the higher r a t e s . For example, at 50 DAP, R ^ f o r inoculated and uninoculated DSP was 0.10 and 0.08 day--*- while that f o r both inoculated and uninoculated EF was 0.075 day" 1. From 70 DAP onward, R L a and R w^ l e v e l l e d o f f i n a l l four treatments. At the f i n a l harvest R L a f o r inoculated and uninoculated DSP was approximately -0.01 day--'- and f o r inoculated and uninoculated EF, the. values were 0.02 and 0.01 day -* - r e s p e c t i v e l y . ^  The f i n a l values of R™ were somewhat higher—0.0 d a y - 1 f o r both inoculated and Li uninoculated DSP and 0.023 and 0.02 d a y - 1 f o r inoculated and uninoculated EF. Noticeable d i f f e r e n c e s between inoculated and uninoculated plants were not detected f o r EF, but f o r DSP, maximum R L a and R ^ of the uninoculated plants preceded that of the inoculated (Figures 5.18 and 5.19). In the inoculated plants the maximum occurred 3 days l a t e r . Also, i n the case of EL a» t n e uninoculated plants had higher rates (0.13 vs. 0.12 d a y - 1 ) . Unlike the l e a f and l e a f weight r e l a t i v e growth rate curves, the curves f o r whole plant r e l a t i v e growth rate (Ry) (Figure 5.20) exhibited no trend d i f f e r e n c e s among the treatments. In a l l cases Ry maintained a high, constant l e v e l over the period 21 to 35 DAP, followed by a period of rapid d e c l i n e (36-70 DAP) and a t h i r d phase i n which the rates l e v e l l e d o f f . - 108 -Figure 5.20. Instantaneous r e l a t i v e growth rate curves (non-destructive harvests). DAYS AFTER PLANTING - 109 -During the f i r s t phase, uninoculated DSP and EF had the highest rates (0ol2 and 0.117 d a y - 1 r e s p e c t i v e l y ) , while in th e i r inoculated counterparts the rates were 0.114 and 0.115 d a y - 1 . In the second phase inoculated and uninoculated EF had i d e n t i c a l rates (e.g. at 50 DAP both had rates of 0.094 d a y - 1 ) . On the other hand, the rates of inoculated DSP were somewhat higher than EF and the uninoculated somewhat lower (0.097 and 0.092 d a y - 1 r e s p e c t i v e l y at 50 DAP). By the f i n a l harvest the rates were 0.063, 0.069, 0.064 and 0.065 d a y - 1 for uninoculated DSP, inoculated DSP, inoculated EF and inoculated EF r e s p e c t i v e l y . 5.3.5.2 Dnit Leaf Rate Figure 5.21 depicts the un i t l e a f rate curves of the four treatments. During the vegetative phase (21-53 DAP), the curves of EF d i f f e r e d from DSP. In the former, the unit l e a f rate declined l i n e a r l y from values of 10 g m - 2 d a y - 1 for both uninoculated and inoculated plants at 21 DAP to 6.9 g — 2 — 1 m day at 55 DAP. By contrast, the unit l e a f rate of inoculated and uninoculated DSP increased to maxima of 9 and 10 g m - 2 d a y - 1 at 28 DAP, — 2 1 before d e c l i n i n g to 6.1 and 5.5 g m day at 60 DAP, r e s p e c t i v e l y . During the reproductive phase, the unit l e a f rates of a l l four treatments rose sharply. At the f i n a l harvest t h e i r values were 18, 21.8, 19.8 and 19.2 g m - 2 d a y - 1 for uninoculated DSP, inoculated DSP, uninoculated EF and inoculated EF, r e s p e c t i v e l y . - 110 -Figure 5«21. Progress curves of instantaneous unit l e a f rate (non-destructive harvests). a 'E < ae Z 3 O -20 — r ~ 30 Uninoculated DSP Inoculated DSP Uninoculated EF Inoculated EF 40 —r— 50 —r-60 70 - r -80 90 DAYS AFT^R P L A N T I N G r- 111 -5 . 3 . 5 . 3 L e a f A r e a R a t i o The curves for leaf area ratio of the four treatments indicate no marked differences between inoculated and uninoculated plants of EF (Figure 5.22). On the other hand, some differences were apparent in the case of DSP. During the period 25 to 50 DAP uninoculated DSP appeared to have a higher leaf area ratio than its inoculated counterpart (123.3 as opposed to 120.4 cm2 g - 1 at 32 DAP). However, after that time (50 to 60 DAP) the inoculated plants had higher ratios (141.3 as opposed to 144.2 cm2 g-^" at 53 DAP). Cultivar differences were also evident. In EF, leaf area ratio increased linearly from 113.7 at 21 DAP to 139.0 cm2 g" 1 at 45 DAP. This was not the case for DSP. In this cultivar, leaf area ratio first f e l l from 124.9 at 21 DAP to 117.9 cm2 g - 1 at 27 DAP, before increasing to a maximum of 142.1 cm2 g _ 1 at 50 DAP. During the reproductive phase the leaf area ratios of both cultivars declined sharply, with DSP having higher values than EF (e.g., 181.9 for inoculated DSP and 175.3 cm2 g -* for EF). At the final harvest, however, the ratios were not significantly different. 5 . 3 . 5 . 4 S p e c i f i c L e a f A r e a The progress curves for specific leaf area (SLA) (Figure 5.23) reveal noticeable cultivar differences. In EF, SLA increased gradually from 154.2 at 21 DAP to 165.8 cm2 g - 1 at 50 DAP. In DSP, however, SLA declined from 159.6 at 21 DAP to 155.0 (uninoculated) at 26 DAP and 153.8 cm2 g - 1 - 112 -DAYS AFTER P L A N T I N G - 113 -Figure 5.23 Progress curves of instantaneous s p e c i f i c l e a f area (non-destructuve harvests). o _ o Uninoculated DSP Inoculated DSP Uninoculated EF Inoculated EF © DAYS AFTER PLANTING - 114-(inoculated) at 32 DAP, before rising. SLA in both cultivars increased to a maximum at 65 DAP. The respective maxima were 185.6 for DSP and 176.7 cm2 g~ 1 for EF. There were no differences between inoculated and uninoculated plants. 5.3.5.5 Leaf Weight Ratio The trends for leaf weight ratio (Figure 5.24) were.similar to those of leaf area ratio (Figure 5.22). The main difference between the two sets of curves was seen during the period 32 to 55 DAP. During that time, the leaf weight ratio of uninoculated DSP exceeded that of its inoculated counterpart (e.g., at 46 DAP, 0.90 for uninoculated DSP and 0.88 for inoculated). In the leaf area ratio curves, however, inoculated DSP had higher values toward the end of the period (50 - 55 DAP). DSP reached higher maximum leaf weight ratio (0.90) 3 days later than EF (0.87) at 46 DAP. From that time onward the leaf weight ratio of both cultivars f e l l steadily until the final harvest date. 5.4 Yield Component Analysis Sequential yield component analysis subdivides yield into its morphological components and identifies the significant components of yield variability, their interrelationships and the important stages of growth. The means and variances of the untransformed component ratios are given in Tables 5.5(a) and (b). By using the overall ANOVA, the components were analysed—the results are presented in Table 5.6. - 115 -Figure 5-24. Progress curves of instantaneous l e a f weight r a t i o (non-destructive harvests). o i S I I 1 I I i 20 30 40 50 60 70 80 90 DAYS AFTER P L A N T I N G - 116 -Table 5.5(a) - Cuamary of means of y i e l d components from the destructive harvests. Harvest Treatment* (DAP) s * * V s V L N V L A V W L P / F N Se/P WSe/Se WSe 1 20 9.050 0.483 6.995 0.0056 1.262 - - - - -1 50 49.542 0.254 31.338 0.0065 1.560 0.365 • - - - - -1 53 51.731 0.264 34.33*8 0.0059 1.588 0.358 - - - -1 56 56.725 0.257 41.583 0.0061 1.561 0.350 0.021 0.500 0.000 0.003 1 59 64.756 0.238 56.614 0.0058 1.611 0.555 0.240 5.375 0.006 0.047 1 62 73.319 0.225 51.903 0.0059 1.718 0.551 0.321 6.281 0.018 0.176 1 65 69.744 0.231 56.914 0.0056 1.789 0.921 0.385 6.245 0.026 0.496 1 68 73.312 0.230 55.754 0.0065 1.722 1.105 0.455 6.869 0.052 1.252 1 71 73.250 0.235 50.065 0.0061 1.826 1.034 0.649 6.969 0.108 3.686 1 74 77.887 0.226 50.278 0.0058 1.850 1.071 0.783 6.354 0.176 7.872 1 77 79.450 0.225 44.925 0.0066 1.851 1.039 0.902 6.746 0.268 13.299 1 80 79.981 0.224 45.941 0.0061 1.939 1.505 0.977 6.448 0.315 25.410 2 20 9.054 0.521 6.426 0.0063 1.204 - - - - -2 50 46.783 0.274 28.066 0.0068 1.507 0.377 - - - -2 53 55.087 0.243 43.438 0.0056 1.585 0.256 - - - -2 56 56.275 0.2S8 33.979 0.0061 1.572 0.307 - - - -2 59 65.331 0.241 44.422 0.0056 1.650 0.635 0.322 5.688 0.006 0.046 2 62 68.037 0.235 41.808 0.0064 1.712 0.609 0.338 5.688 0.022 0.315 ' 2 65 72.212 0.237 48.845 0.0054 1.755 0.971 0.370 7.047 0.022 0.384 2 68 73.375 0.237 41.258 0.0065 1.774 1.114 0.455 7.205 0.060 1.373 2 71 78.019 0.224 63.480 0.0070 1.780 0.949 0.501 6.965 0.118 4.156 2 74 76.937 0.228 40.196 0.0063 1.825 0.982 0.783 6.642 0.178 8.164 2 77 76.100 0.233 50.673 0.0069 1.784 1.139 0.915 6.103 0.237 13.348 2 80 85.212 0.215 42.894 0.0062 1.880 1.469 0.994 6.391 0.327 26.377 3 20 8.375 0.496 7.013 0.0051 1.182 - - - - -3 50 47.558 0.246 26.673 0.0074 1.531 0.537 - - - -3 53 55.000 0.240 38.371 0.0066 1.608 0.361 - - -3 56 60.662 0.222 33.328 0.0068 1.665 0.766 0.366 6.000 0.011 0.142 3 59 67.912 0.222 39.956 0.0064 1.698 1.103 0.425 7.323 0.023 0.436 3 62 67.025 0.226 39.519 0.0068 1.744 0.807 0.509 6.789 0.055 1.045 3 65 71.412 0.215 47.165 0.0058 1.801 1.071 0.792 7.277 0.099 3.648 3 68 66.962 0.225 33.663 0.0078 1.755 1.023 0.815 6.397 0.107 3.674 3 71 71.819 0.213 43.230 0.0068 1.781 1.067 0.931 6.832 0.191 8.668 3 74 68.006 0.221 30.167 0.0069 1.796 1.522 0.983 6.139 0.347 13.940 3 77 67.062 0.230 30.756 0.0067 1.853 1.263 0.984 5.881 0.400 15.260 3 80 71.300 0.205 42.379 0.0075 1.792 1.344 1.000 5.847 0.552 27*684 4 20 8.537 0.459 7.672 0.0053 1.198 - - - - -4 50 49.204 0.250 29.042 0.0071 1.511 0.543 - - - -4 53 S6.250 0.228 39.324 0.0064 1.653 0.417 - - - -4 56 60.637 0.232 31.613 0.0072 1.666 0.756 0.471 6.865 0.009 0.101 4 59 65.775 0.230 30.157 0.0092 1.716 0.943 0.552 8.688 0.039 0.941 4 62 63.744 0.234 33.524 0.0070 1.682 0.843 0.619 5.651 0.068 1.459 4 65 68.369 0.225 36.554 0.0062 ' 1.777 1.129 0.770 6.883 0.100 . 3.067 4 68 69.950 0.215 33.544- 0.0075 1.986 1.092 0.878 6.731 0.140 4.474 4 71 69.262 0.232 37.960 0.0065 1.793 1.297 0.988 6.626 0.209 10.405 4 74 68.181 0.230 30.892 0.0066 1.776 1.341 1.000 6.529 0.325 13.354 4 77 67.587 0.228 27.235 0.0071 1.764 1.427 1.000 5.853 0.420 15.376 4 80 67.506 0.225 28.501 0.0060 1.802 1.578 1.000 5.925 0.577 22.533 *1 - Uninoculated Darlc Skin Parfecclon, 2 - Inoculated Dark Skin Perfection, 3 - Uninoculated Early Frosty and 4 -Inoculated Early Frosty. **S " Stem length, L J J / S • nmber of leaves/stem length, L A / L N " leaf area/leaf, W ^ / L ^ " l e a * d r v «*ighc/leaf area, Hv / , WL " t o c a l vegetative dry weight/leaf dry weight, FN/WV - number of flowers/vegetative dry weight, P/F N - number of pods/flower, Se/P - number of seeds/pod, WSe/Se - seed fresh weight/seed and WSe - t o t a l seed fresh weight. ' - 117 -Table 5.5(b) - Summary of standard deviation of yield components from the destructive harvescs. Treatment* Harvest S** LN/S L^/L^ W /^L^ Wy/WL FN/WV P/FN Se/P w S e / S e ' 1 20 1.710 0.075 1.958 0.0011 0.191 - - - - -1 50 5.665 0.032 12.665 0.0012 0.207 0.194 - - - -1 ' 53 9.965 0.051 16.043 0.0010 0.050 0.202 - - - -1 56 9.909 0.049 21.384 0.0008 0.073 0.152 0.083 2.000 0.002 0.013 1 59 7.706 0.024 28.314 0.0009 0.077 0.162 0.194 3.386 0.005 0.053 I 62 9.632 0.024 24.134 0.0013 0.104 0.229 0.187 2.664 0.015 0.136 1 65 12.034 0.051 34.047 0.0014 0.097 0.269 0.208 2.632 0.022 0.444 1 68 17.276 0.045 42.962 0.0027 0.125 0.279 0.197 0.777 0.022 0.646 1 71 14.311 0.031 34.777 0.0017 0.132 0.242 0.203 0.427 0.043 2.084 1 74 16.956 0.043 29.629 0.0011 0.090 0.463 0.264 1.781 0.075 3.800 1 77 15.489 0.034 23.873 0.0007 0.142 0.448 0.153 0.864 0.114 7.520 1 80 12.472 0.024 26.417 0.0012 0.194 0.224 0.066 0.682 0.091 12.776 2 20 1.543 0.126 2.230 0.0030 0.044 - - - - -50 8.465 0.047 9.118 0.0013 0.L16 0.161 - - - -2 53 8.543 0.037 18.771 0.0013 0.075 0.157 - - - -2 56 8.670 0.038 10.640 0.0007 0.079 0.156 - - - -2 59 .9.763 0.044 20.110 0.0008 0.069 0.529 0.198 0.044 0.003 0.029 2 62 12.045 0.029 15.460 0.0007 0.065 0.276 0.233 0.029 0.025 0.414 2 65 12.610 0.042 21.059 0.0011 0.096 0.205 0.090 0.042 0.007 0.207 2 68 17.561 0.057 23.016 0.0017 0.075 0.329 0.183 0.057 0.046 1.019 2 71 18.940 0.039 33.789 0.0017 0.116 0.199 0.130 0.039 0.071 2.313 2 74 13.830 0.045 25.284 0.0011 0.153 0.415 0.264 0.045 0.088 5.244 2 77 16.757 0.042 40.966 0.0013 0.232 0.425 0.123 0.042 0.084 11.582 2 80 8.030 0.024 19.414 0.0012 0.093 0.197 0.023 0.024 0.052 11.552 3 20 1.404 0.107 2.095 0.0015 0.071 - - - - -3 50 7.175 0.029 10.307 0.0010 0.101 0.168 - - - -3 53 10.540 0.046 19.600 0.0013 0.049 0.221 - - - -3 56 6.442 0.021 13.426 0.0007 0.098 0.438 0.222 3.055 0.008 0.130 3 59 9.783 0.031 17.686 0.0008 0.060 0.274 0.163 0.753 0.008 0.189 3 62 11.864 0.036 22.913 0.0010 • 0.094 0.341 0.281 1.930 0.042 0.921 3 65 14.136 0.034 23.631 0.0013 0.067 0.310 0.183 0.796 0.047 1.887 3 68 10.098 0.025 19.141 0.0038 0.101 0.260 0.265 1.785 0.046 2.002 3 71 17.295 0.031 22.567 0.0023 0.079 3.234 0.114 0.655 0.069 3.745 3 74 17.277 0.042 15.020 0.0017 0.100 0.590 0.067 0.811 0.086 4.689 3 77 16.577 0.044 19.178 0.0013 0.180 0.353 0.063 0.829 0.073 8.577 3 80 12.920 0.019 36.178 0.0046 0.191 0.314 . 0.0 0.846 0.091 15.341 4 20 1.336 0.063 1.786 0.0010 0.070 - - - - -4 50 9.375 0.063 11.054 0.0012 0.091 0.390 - - - -4 53 11.177 0.037 23.583 0.0012 0.129 0.329 - - - -4 56 9.863 0.054 15.295 0.0017 0.035 0.471 0.225 2.026 0.004 0.052 4 59 13.451 0.042 14.130 0.0108 0.056 0.295 0.204 5.707 0.063 1.952 4 62 14.569 0.055 18.353 0.0012 0.077 0.360 0.367 2.853 0.053 1.077 4 65 12.283 0.035 18.676 0.0013 0.107 0.467 0.296 0.942 0.043 2.267 4 •68 13.2S1 0.033 21.727 0.0027 0.797 0.423 0.196 0.857 0.082 1.996 4 71 16.360 0.043 17.291 0.0012 0.118 0.575 0.035 0.833 0.051 4.216 4 74 19.057 0.046 14.100 0.0008 0.085 0.451 0.0 0.799 0.088 5.624 4 77 11.969 0.025 13.400 0.0028 0.144 0.575 0.0 0.983 0.119 7.620 4 80 15.479 0.044 10.438 0.0011 0.119 0.333 0.0 0.734 0.119 8.626 *1 - Uninoculated Dark Skin Perfection, 2 - Inoculated Dark Skin Perfection, 3 • Uninoculated Early Frosty and 4 - Inoculated Early Frosty. **S - Stem length, I*i/S " number of leaves/stem length, L^/L^ " leaf area/leaf, ^/t-A - leaf dry weight/leaf area, Uy/W^ - total vegetative dry weight/leaf dry weight, F^ /Wy - number of flowers/vegetative dry weight, P/F)4 • number of pods/flower, Se/P - nuaber of seeds/pod, W /^Se - seed fresh weight/seed and WSe - total seed fresh weight. ' - 118 " Seed i n o c u l a t i o n had no e f f e c t on any y i e l d component except leaves per stem length (L^f/S). For t h i s component, i t i s seen that the second order i n t e r a c t i o n among inoculum, c u l t i v a r and date, was s i g n i f i c a n t at the 5% l e v e l . The date and c u l t i v a r i n t e r a c t i o n was s i g n i f i c a n t for a l l components except L]yj/S and the c u l t i v a r main e f f e c t was s i g n i f i c a n t among a l l components except inverse l e a f weight r a t i o (W/WL) (F value < 1 ) . The main e f f e c t of date was s i g n i f i c a n t for a l l components. Block e f f e c t s proved to be s i g n i f i c a n t for a l l components except seeds per pod (Se/P) and average seed fresh weight (Wg e/Se). Main and sub-plot e r r o r s were also s i g n i f i c a n t for a l l the v a r i a t e s . Two y i e l d component models were studied. In the f i r s t model (Model 1), the y i e l d v a r i a t e was t o t a l plant biomass. The y i e l d v a r i a t e in the second model (Model 2) was seed fresh weight per plant. 5.4.1 Model 1 The r e s u l t s of the regression a n a l y s i s of the f i n a l harvest (80 DAP) are presented i n Table 5.7. Stem length (S) and average l e a f area ( L ^ / L N ) were the major contributors to t o t a l biomass v a r i a t i o n , accounting for approximately 49% and 45% of the t o t a l , r e s p e c t i v e l y . When backward y i e l d component a n a l y s i s was applied to the data, L^/LJJ and inverse l e a f weight r a t i o (W/W^) were shown to be the s i g n i f i c a n t c o n t r i b u t o r s . They accounted for 87% and 6%, r e s p e c t i v e l y , of the t o t a l v a r i a t i o n . Table 5.6 - Analysis of variance of the e f f e c t of seed i n o c u l a t i o n and c u l t i v a r on y i e l d components in the garden pea Source of V a r i a t i o n df V s V LN V LA V WL V wv P/F ' N Se/P W S e/Se Block 7 0.059*** 17424.48*** 0.77 X Mean Squares 10" ***** 0.084* 0.863*** 0.101* 3.226 0.010 C u l t i v a r (C) 1 0.035** 16976.00*** 0.68 X i o - 1 * * * * 0.013 5.549*** 6.713*** 66.637*** 0.924*** Inoc (I) 1 0.003 2368.1 0.59 X 10 - 5 0.024 0.053 0.054 0.447 0.003 C x I 1 0.002- 1.0242 0.12 X 10~ 5 0.081 0.050 0.085 0.540 0.003 Error 1 21 0.004** 709.71*** 0.42 X 10~5 0.024 0.174*** 0.034*** 2.868 0.005*** Date (D) 11 0.515*** 10270.00*** 0.16 X \Q~ ***** 2.751*** 20.448*** 10.261*** 668.14*** 1.505*** D x C 11 0.002 833.48*** 0.86 X 10~ 5 0.067* 0.615*** 0.522*** 60.107*** 0.104*** D x i 11 0.001 490.37 0.39 X 10~5 0.045 0.068 0.025 2.691 0.002 D x C x I 11 0.004** 385.86 0.56 X 10" 5 0.021 0.092 0.019 1.820 0.001 Error 2 308 0.002 353.31*** 0.53 X 0.029 0.098* 0.029 2.986*** 0.003*** Samp. Error 448 0.002 214.05 0.35 X 10~5 0.027 0.078 0.161 2.044 0.002 * S i g n i f i c a n t at 5% l e v e l * * S i g n i f i c a n t at 1% l e v e l * * * S i g n i f i c a n t at 0.5% l e v e l ^N/S = number of leaves/stem length, L A/L^ = lea f area/leaf, W^/L^ = l e a f dry weight/leaf area, Wy/W^  = vegetative dry weight/leaf dry weight, F^Wy = number of flowers/vegetative dry weight, P/ F N = number of pods/flower, Se/P = number of seeds/pod, Wge/Se = seed fresh weight/seed and Wge = t o t a l seed fresh weight. - 120 -The r e s u l t s of the forward and backward analyses imply that stem length acted i n d i r e c t l y i n a f f e c t i n g t o t a l dry matter v a r i a b i l i t y . The r o l e of average l e a f area was both d i r e c t and i n d i r e c t , the former c o n t r i b u t i o n being much higher than the l a t t e r . It was shown, however, that inverse l e a f weight r a t i o made a d i r e c t c o n t r i b u t i o n . In a d d i t i o n to the r e l a t i o n s h i p between each y i e l d component and the y i e l d v a r i a t e , the i n t e r r e l a t i o n among the components was a l s o i n v e s t i g a t e d . The r e s u l t s of t h i s part of the study provide further information on the nature of the c o n t r i b u t i o n s of the components. The r e s u l t s l i s t e d i n Table 5.7(b) i n d i c a t e that stem length i s p o s i t i v e l y c o r r e l a t e d with average l e a f area and inverse l e a f weight r a t i o . A l l adjacent components i n the y i e l d equation (Equation 12 i n Chapter 3) were negatively c o r r e l a t e d . The data at each harvest were analysed v i a sequential y i e l d component a n a l y s i s to determine the stage of growth when i n d i v i d u a l components became important (Table 5.8). Stem length was important throughout the growth period. I t s c o n t r i b u t i o n to t o t a l v a r i a b i l i t y ranged from 29% to 72%. Leaves per stem length was not important at any time. Average l e a f area became a major contri b u t o r from the l a t e vegetative phase (50 DAP) onward. The c o n t r i b u t i o n of average l e a / area v a r i e d between 10% at 53 DAP and 45% at the f i n a l harvest. Inverse s p e c i f i c l e a f area accounted f o r between 7 and 38% of the t o t a l at a l l harvests except the f i n a l two. Inverse l e a f weight r a t i o was important at 62, 65, 68 and 71 DAP, c o n t r i b u t i n g between 6 and 10% of the t o t a l v a r i a t i o n at these times. Table 5.7 - Model 1. Regressions of yield components on independent, standardized residuals. Data from the f i n a l harvest (a) Independent Variable L / C p C I 1 U C I 1 V Variable S 1 Vs LA / LN V LA w/wL Total Forward Coefficient of Determination (%) Vs 38.5** 38.5 V L N 32.7** 5.0 37.7 V LA 3.7 0.4 5.5 9.6 w/wL 0.2 2.0 0.0 68.8** 71.0 W 49,1** 0.4 45.1** 1.5 3.9 100.0 Backward W 0.1 5.9 87.2** 0.3 6.4* 100.0 (b) Regression Coefficients (sign) V s V LN W/W, _** +** + +** -** +** *Slgnlflcant at 5% level; **Signifleant at 1% l e v e l . *S = stem length, L^/S = number of leaves/stem length, L A / L N = leaf area/leaf, WL/LA = leaf dry weight/leaf area, W/WL = total plant dry weight/leaf dry weight, W = total plant dry weight. 2 ' Negative signs of the regression coefficients indicate compensation of one component by another. The c o e f f i c i e n t s of determination measure Increments in v a r i a b i l i t y of a single yield component, taken as a dependent variable accounted for after including each preceding yield component sequentially in a stepwise multiple regression. Table 5 . 8 - S e q u e n t i a l y i e l d component a n a l y s i s , Model 1 . Increments I n c o e f f i c i e n t s o f d e t e r m i n a t i o n f o r each y i e l d component taken i n s u c c e s s i o n as an independent v a r i a b l e w i t h t o t a l d r y weight ( W ) as t h e dependent v a r i a b l e . Harvest Number (days a f t e r p l a n t i n g ) V a r i a b l e 1 ( 2 0 ) 2 ( 5 0 ) 3 ( 5 3 ) 4 ( 5 6 ) 5 ( 5 9 ) 6 ( 6 2 ) 7 ( 6 5 ) 8 ( 6 8 ) 9 ( 7 1 ) 1 0 ( 7 4 ) 1 1 ( 7 7 ) 1 2 ( 8 0 ) S 1 7 2 . 0 * * 6 8 . 6 * * 7 8 . 1 * * 5 5 . 0 * * 2 9 . 7 * * 5 7 . 8 * * 4 5 . 3 * * 6 7 . 9 * * 6 2 . 5 * * 4 8 . 5 * * 6 5 . 7 * * 4 9 . 1 * * V s 0 . 2 2 . 6 1 . 6 0 . 6 5 . 5 0 . 1 0 . 7 0 . 6 1 . 5 3 . 3 0 . 2 0 . 4 V L N 6 . 0 1 5 . 5 * * 9 . 5 * 2 6 . 2 * * 2 0 . 8 * * 2 5 . 0 * * 3 2 . 3 * * 1 7 . 8 * * 2 0 . 9 * * 3 2 . 5 * * 2 5 . 5 * * 4 5 . 1 * * V L A 1 8 . 1 * * 1 0 . 2 * 8 . 2 * 1 2 . 3 * * 3 8 . 1 * * 1 1 . 0 * * 1 1 . 9 * * 4 . 2 7 . 5 * 9 . 6 * 4 . 3 1 . 5 W / W L 3 . 7 3 . 0 2 . 6 5 . 9 5 . 9 6 . 1 * 9 . 8 * 9 . 5 * 7 . 6 * 6 . 1 4 . 3 3 . 9 * 1 / F 2 1 . 8 * * 1 3 . 2 * * 1 0 . 8 * * 1 8 . 2 * * 4 4 . 0 * * 1 7 . 1 * * 2 1 . 6 * * 1 3 . 7 * * 1 5 . 1 * * 1 5 . 7 * * a . 6 * 7 . 9 * • S i g n i f i c a n t a t 5% l e v e l ; ** s i g n i f i c a n t a t 1 % l e v e l . *S = stem l e n g t h , Lj]/S = number of l e a v e s / s t e m l e n g t h , L ^ / I N » l e a f a r e a / l e a f , WL /L^ « l e a f d r y w e i g h t / l e a f a r e a , W/WL «• t o t a l p l a n t d r y w e i g h t / l e a f dry weight and F = l e a f area r a t i o . - 123 -5.4.2 Model 2 On the l a s t harvest date (Table 5.9) stem length, average l e a f area, reproductive e f f o r t (F^/Wy) and average seed weight (Wge/Se) were the main contributors to y i e l d v a r i a b i l i t y . These components accounted for approximately 29, 36, 8 and 21% of the t o t a l v a r i a t i o n , r e s p e c t i v e l y (Table 5.9). Backward y i e l d component analysis r e s u l t s indicate that the r o l e of these major components was i n d i r e c t . In a d d i t i o n , pod set (P/Fjj), leaves per stem length and inverse l e a f weight r a t i o (Wy/W^) made d i r e c t c o n t r i b u t i o n s of approximately 73, 8 and 8%, r e s p e c t i v e l y , to y i e l d . A l l vegetative components (S, Lfl/S, L A / LN, W L / L a and WV/WL) were negatively c o r r e l a t e d with average seed fresh weight (Table 5.10). This f i n d i n g , therefore, suggests some compensation between the vegetative components and y i e l d . S i g n i f i c a n t compensatory r e l a t i o n s h i p s were also .evident between: ( i ) stem length and leaves per stem length ( i i ) reproductive e f f o r t and inverse s p e c i f i c l e a f area ( i i i ) inverse s p e c i f i c l e a f area and inverse l e a f weight r a t i o and ( i v ) average l e a f area and pod set. Stem length showed a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n with average l e a f area and inverse l e a f weight r a t i o while leaves per stem length exhibited a p o s i t i v e c o r r e l a t i o n with reproductive e f f o r t . Average l e a f area and seeds per pod also indicated a p o s i t i v e c o r r e l a t i o n with each other. Table 5.9 - Model 2. Regressions of yield components on independent, standardized residuals. Data from the f i n a l harvest Independent Variable uepenaenc Variable s1 Vs V LA V W L V WV P/F N Se/P Wge/Se Total Forward Coefficient of Determination (%) L N/S 38.5** 38.5 L A / L N 32.7** 5.0 37.7 W L / L A 3.7 0.4 5.5 9.6 V W L 17.0** 0.3 0.5 34.9** 52.7 V WV 0.5 7.4* 0.0 29.3** 4.9 42.1 P/F N 4.4 5.0 8.1* 3.3 0.1 0.0 20.9 Se/P 4.1 6.1 8.4* 0.0 0.3 4.8 0.3 24.0 WSe/Se 21.7** 17.9** 11.3** 5.5 3.9 0.0 0.2 1.0 61.5 Y 28.5** 2.9 35.8** 0.1 / 0.4 7.7* 0.8 2.5 21.3** 100.0 Backward 1.2 8.3* 0.8 3.9 7.5* 0.1 72.5** 0.0 5.7 100.0 *Significant at 5% level **Significant at 1% level \s = stem length, L^j/S = number of leaves/stem length, I-A/LN = leaf area/leaf, WT^ /L^  = leaf dry weight/leaf area, Wy/W^  = vegetative dry weight/leaf dry weight, F^ /Wy = number of flowers/vegetative dry weight, P/FN =• number of pods/flower, Se/P = number of seeds/pod, Wge/Se = seed fresh weight/seed and Y = yield = total seed fresh weight. Table 5.10 - Model 2. Regressions of yield components on independent, standardized residuals. Data from the f i n a l harvest Independent Variable Dependent Variable S 1 L^/S L A / L N W L / L A * V W L FN / WV P / F N S e / P W S e / S e Total Regression Coefficients (sign) Vs -** LA / LN -W L / L A - + -W V / W L - + -** V wv - +** - -** + P/FN - - _* - - + Se/P + + +* - - -W S e / S e _** -** - - + Y +** - +** - + +* + Backward - +* - + . +* - +** + + •Significant at 5% level **Signifleant at 1% level Negative signs of the regression coefficients indicate compensation of one component by another. *S = stem length, %/S = number of leaves/stem length, LA/L n = leaf area/leaf, W L/L A = leaf dry weight/leaf area, Wy/wL = vegetative dry weight/leaf dry weight, FN/Wy = number of flowers/vegetative dry weight, P/FN = number of pods/flower, Se/P = number of seeds/pod, Wge/Se = seed fresh weight/seed and Y = yield = total seed fresh weight. - 126 -The components representing reproductive structures (with the exception of seeds per pod) were s i g n i f i c a n t contributors to y i e l d v a r i a b i l i t y at most of the harvests according to Table 5.11. Average seed weight proved to be s i g n i f i c a n t throughout the e n t i r e period. Its c o n t r i b u t i o n ranged from 11% at 59 DAP to 37% at 74 DAP. Pod set appeared important u n t i l the penultimate harvest, accounting for between 8 and 43% of the t o t a l (Table 5.11). The highest contributions occurred between 9 and 18 days a f t e r f i r s t flowering. Reproductive e f f o r t showed s i g n i f i c a n c e at a l l dates a f t e r flowering except 68 DAP. The c o n t r i b u t i o n of t h i s component was gene r a l l y lower than that of the other reproductive components (6% - 25%). Among the non-reproductive source components, stem length became important from 15 days post flowering (68 DAP) onward. It accounted f o r 10-29% of the t o t a l v a r i a t i o n . S i m i l a r l y , the co n t r i b u t i o n of number of leaves per stem length showed no s i g n i f i c a n c e u n t i l 62 DAP. (At that time i t s c o n t r i b u t i o n was 18%, but declined at subsequent harv e s t s ) . By contrast, average l e a f area showed a s i g n i f i c a n t c o n t r i b u t i o n during early reproductive growth (approximately 13% at 56 to 59 DAP). Thereafter, i t exhibited s i g n i f i c a n t contributions only at 71 DAP (6%) and at the f i n a l harvest (36%). Inverse l e a f weight r a t i o showed s i g n i f i c a n c e at 59 DAP only (9%) , whereas inverse s p e c i f i c l e a f area seemed to make s i g n i f i c a n t contributions to y i e l d during pod f i l l i n g (59 to 65 DAP) and at l a t e reproductive growth (77 DAP). Table 5.11 - Sequential yield component analysis of Model 2. Increments in co e f f i c i e n t s of determination for each yi e l d component taken in succession as an independent variable with total seed fresh weight (W S e) as the dependent variable. Harvest Number (Days After Planting) uepenaenc Variable 4 (56) 5 (59) 6 (62) 7 (65) 8 (68) 9 (71) 10 (74) 11 (77) 12 (80) S 1.7 0.1 0.0 0.2 16.2** 11.0* 10.2* 26.3** 28.5** Vs 2.2 4.6 17.9** 7.7* 7.0* 5.8 8.0* 9.2* 2.9 L A / L N 13.4** 12.8** 2.0 1.0 2.0 6.4* 0.0 1.2 35.8** V L A 6.2 29.9** 12.4** 14.4* 1.1 0.2 4.4 8.1* 0.1 V W L 3.9 9.1* 2.1 1.3 0.3 0.0 1.8 1.1 ' 0.4 V WV 10.0* 19.0** 9.0* 6.4* 2.8 14.8** 12.0** 24.9** 7.7* P / F N 29.5** 13.0** 33.7** 43.2** 41.6** 31.7** 26.6** 8.2* 0.8 Se/P 2.0 0.9 0.0 2.3 2.0 0.3 0.0 4.5 2.5 WSe/Se 31.1** 10.6* 22.9** 23.5** 27.0** . 29.8** 37.0** 16.5** 21.3** 1/P 10.1* 39.0** 14.5** 15.7** 1.4 0.2 6.2* 9.2* 0.5 *Signifleant at 5% le v e l **Significant at 1% level S = stem length, L^/S = number'of leaves/stem length, L A / L N = leaf area/leaf, W^ /L^  = leaf dry weight/leaf area, WV/WL = vegetative dry weight/leaf dry weight, FN/WV = number of flowers/vegetative dry weight, P/F N = .number of pods/flower, Se/P = number of seeds/pod, Wge/Se = seed fresh weight/seed and F = leaf area r a t i o . - 128 -5.5 Demographic Analysis This method of analysis was used to study the dynamics of l e a f and flower populations on the plants. 5.5.1 Leaf Demography The b i r t h rates of leaves from inoculated and uninoculated plants within each c u l t i v a r were not s i g n i f i c a n t l y d i f f e r e n t (Table 5.12). Between c u l t i v a r s , DSP produced more leaves per day than EF from 36 DAP onward. In a l l treatments the general trend of l e a f production was the same. During e a r l y vegetative growth (21-36 DAP) the rates tended to f l u c t u a t e . There was a rapid increase i n rates over the period 36-45 DAP. This phase was followed by a " l a g " phase of reduced production which la s t e d 6 days, followed by a second phase of rapid l e a f b i r t h . At the end of the second period (60 DAP f o r DSP and 57 DAP f o r EF), inoculated and uninoculated DSP attained maximum production rates of 0.90 and 0.92 leaves per plant per day r e s p e c t i v e l y . The corresponding values for inoculated and uninoculated EF were 0.71 and 0.65 leaves per plant per day. After that time, l e a f production declined s t e a d i l y i n EF, but was more e r r a t i c in DSP. Leaf death proceeded a c r o p e t a l l y ( i . e . , from the base up) in the p l a n t s , with l e a f a b s c i s s i o n i n DSP beginning 6 days e a r l i e r than in EF (Table 5.12). There was no noticeable d i f f e r e n c e in death rates among the treatments. The highest rate (0.41 leaves per plant per day) was attained by inoculated DSP and i t coincided with the time of maximum l e a f production Table 5.12 - Mean l e a f b i r t h and death rates at each harvest In (1) Uninoculated Dark Skin P e r f e c t i o n , (2) Inoculated Dark Skin Perfection (3) Uninoculated Early Frosty and (4) Inoculated Early Frosty. Treatment Days After P l a n t i n g 1 2 3 4 1 2 3 4 Leaf B i r t h Rates (Leaves/Plant/Day) Leaf Death Rates (Leaves/Plant/Day) 21 0.17 0.29 0.10 0.10 - - - -24 0.15 0.06 0.25 0.23 - - - -27 0.31 0.33 0.25 0.29 - - - -30 0.21 0.31 0.23 0.21 - - - -33 0.31 0.19 0.25 0.25 - - - -36 0.33 0.31 0.29 0.27 - - - -39 0.33 0.31 0.33 0.31 - - - -42 0.58 0.42 0.31 0.40 - - - -45 0.53 0.56 0.52 0.42 - - - -• 48 0.60 0.60 0.50 0.50 0.02 0.02 - -51 0.60 0.67 0.50 0.50 0.00 0.02 - -54 0.67 0.78 0.51 0.56 0.04 0.00 0.07 0.06 57 0.81 0.83 0.71 0.65 0.12 0.10 0.11 0.15 60 0.92 0.90 0.62 0.64 0.26 0.41 0.27 0.33 63 0.77 0.87 0.56 0.60 0.00 0.15 0.04 0.07 66 0.85 0.77 0.53 0.52 0.10 0.15 0.02 0.06 69 0.72 0.69 0.42 0.35 0.31 0.19 0.16 0.25 72 0.72 0.77 0.18 0.35 0.05 0.28. 0.22 0.10 75 0.46 0.64 0.24 0.08 0.31 0.10 0.36 0.06 78 0.26 0.62 0.09 0.02 0.03 0.31 0.22 0.29 81 0.21 0.41 0.02 0.00 0.28 0.31 0.22 0.23 - 130 -(60 DAP). Inoculated EF also showed high l e a f death rate (0.33 leaves/ plant/day) at that time. By the end of the experimental period l e a f death rates i n a l l treatments except inoculated DSP exceeded leaf b i r t h r a t e . 5.5.2 F l o w e r D e m o g r a p h y Flower production i n EF preceded DSP by 3 to 6 days (Table 5.13). There was no s i g n i f i c a n t d i f f e r e n c e between inoculated and uninoculated plants within a p a r t i c u l a r c u l t i v a r . However, the inoculated plants had higher maximum, production rates at an e a r l i e r date than the uninoculated " plants. For example, inoculated DSP and EF attained maxima of 1.06 flowers/plant/day and 0.69 flowers/plant/day at 69 and 63 DAP, r e s p e c t i v e l y . The corresponding values for uninoculated DSP and EF were 0.95 and 0.62 flowers/plant/day at 72 and 69 DAP. From 63 DAP onward, DSP produced more flowers than EF and by the end of the experiment DSP was s t i l l flowering while EF had ceased. In inoculated and uninoculated DSP, cohorts 7 to 11 made the greatest c o n t r i b u t i o n to the t o t a l number of flowers and pods produced (Figure 5.25). These cohorts accounted for 13, 14, 16, 18 and 11% of the t o t a l number of flowers and 15, 17, 18, 12 and 10% of the t o t a l number of pods r e s p e c t i v e l y . By contrast, cohorts 5-9 in uninoculated EF and 4-8 in inoculated EF contributed the highest to the t o t a l number of flowers and pods r e s p e c t i v e l y . For inoculated EF, the percentages for cohorts 5-9 were 11, 13, 18, 17 and 17% for flowers and 14, 9, 19, 18 and 15% for pods. The corresponding values for cohorts 4-8 of inoculated EF were: 10, 10, 13, 23 and 19% for flowers and 14, 11, 14, 20 and 20% for pods (Figure 5.25). Table 5.13 - Mean flower b i r t h and death rates at each harvest In (1) Uninoculated Dark. Skin P e r f e c t i o n , (2) Inoculated Dark Skin Perfection (3) Uninoculated Early Frosty and (4) Inoculated E i r l y Frosty. Treatment Days After Planting 1 2 3 * 4 I 2 3 4 Flower Birt h Rates (Flower9/Plant/Day) Flower Death Rates (Flowers/Plant/Day) 45 - - — 0.02 - - - -48 - - - 0.02 - - . - -51 - - 0.23 0.25 - - - -54 0.13 0.13 0.29 0.33 - - - -57 0.31 0.24 0.42 0.31 - - -60 0.44 0.39 0.47 0.44 - - - -63 0.54 0.56 0.49 0.69 - - - -66 0.72 0.72 0.62 0.65 0.05 0.05 0.11 0.08 69 0.94 1.06 0.62 0.29 - 0.03 0.04 0.15 72 0.95 0.87 0.13 0.21 - 0.03 0.19 0.08 75 0.56 0.77 0.16 0.04 0.13 0.10 0.04 0.15 78 0.44 0.82 0.09 - 0.18 0.10 0.11 0.08 81 0.10 0.21 - - 0.03 0.10 0.07 0.02 1 0 0 i c o 75 > o JZ o o i 13 11 10 i i 13 i a i i 10 i i i 10 i v ztt= 10 - I l -i a i i 10 i i 13 12 11 10 i i i 11 J9_ i v 351 c o 3 50 tz o o 25 c CD O i— 0) a 4 3 A Flowers B Pod set Figure 5 . 2 5 . Effect of seed inoculation and cultivar on mean cohort y i e l d , calculated as a percent of total plant yield (yield i n each case as indicated on the figure). (1) uninoculated Dark Skin Perfection! (11) inoculated Dark Skin Perfectioni ( i l l ) uninoculated Early Frosty and (iv) inoculated Early Frosty. * Inoculated Early Frosty (lv) produoed flowers e a r l i e r than the other treatments, as a result Its f i r s t cohort i s 1. Uninoculated Early Frosty ( i l l ) flowered 6 days later, thua i t s f i r s t cohort Is 3 and Inoculated and uninoculated Dark Skin Perfection (11 and 1) flowered 9 days later than (lv) so their f i r s t cohort i s k. - 13J -Flower a b s c i s s i o n rate was e r r a t i c in a l l treatments. Uninoculated DSP had the highest rate (0.18 flowers/plant/day) at 78 DAP (Table 5.13). With the exception of inoculated DSP, the flowers produced i n the e a r l i e r cohorts tended to have a higher percentage s u r v i v a l than those i n the l a t e r cohorts ( i . e . , those at the l a t e r nodes) (Table 5.14). For example, i n uninoculated DSP, the percentage s u r v i v a l of flowers i n cohort 4 was approximately 83% at the f i n a l harvest (80 DAP), while that of cohort 10 was 49% (Table 5.14). S i m i l a r l y with inoculated EF, the percentage s u r v i v a l of flowers i n cohort 3 was 83%, but that of cohort 10 was 30%. In the case of inoculated DSP, the flowers at the e a r l i e s t cohort (4) had the lowest s u r v i v a l rate at the f i n a l harvest (50%). However, the l a t e r cohorts also had low percentage s u r v i v a l s (e.g., cohorts 10 and 12 had percentage s u r v i v a l s of 56 and 66% r e s p e c t i v e l y ) . 5.6 The Combined Approach In this part of the analysis growth was subdivided into i t s a d d i t i v e and m u l t i p l i c a t i v e components. By so doing i t was possible to determine the contributions of these components to o v e r a l l plant p r o d u c t i v i t y ( i . e . , the dynamics of p a r t i t i o n i n g ) as well as to explain further the i n t e r r e l a t i o n s h i p s among the components. It was decided to combine the data of the inoculated and uninoculated plants within each c u l t i v a r . This d e c i s i o n was made because preliminary curve f i t t i n g using B-splines to describe the growth of the m u l t i p l i c a t i v e components, resulted i n poor f i t s . Furthermore, when other curve f i t t i n g methods were applied, a d d i t i o n a l problems were encountered because of - 134.-Table 5.14 - Percentage s u r v i v a l of cohorts of flowers at the f i n a l harvest (80 days a f t e r planting) i n garden pea Treatment Cohort Number Uninoculated DSP Inoculated DSP Uninoculated EF Inoculated EF 1 - - - 100.0 2 - - - 100.0 3 - - 72.7 83.3 4 83.3 50.0 84.6 100.0 5 69.2 70.0 78.9 86.7 6 70.6 80.0 47.6 80.0 7 80.8 65.4 64.5 63.9 8 85.7 67.9 67.9 74.2 9 76.5 86.8 57.1 71.4 10 48.6 55.9 50.0 30.0 11 63.6 86.7 42.9 50.0 12 58.8 65.6 50.0 -DSP = Dark Skin P e r f e c t i o n EF = Early Frosty - 135 -v a r i a b i l i t y of the data. Since the ANOVA (Section 5.2) showed no s i g n i f i c a n t d i f f e r e n c e between inoculated and uninoculated plants, the combination was considered acceptable. 5.6.1 A d d i t i v e Components During the e a r l y reproductive phase (50-53 DAP) both c u l t i v a r s had approximately the same value for the proportion of t h e i r t o t a l dry weight p a r t i t i o n e d into leaves and stems (65% and 35% r e s p e c t i v e l y ) [Figures 5.26(a) and 5.26(b)]. However, by the f i n a l harvest, a greater proportion of the t o t a l was a l l o c a t e d to the reproductive structures in EF (47%) compared to DSP (32%). Total plant biomass increased throughout the reproductive phase [Figures 5.27(a) and ( b ) ] . The increase was due mainly to the growth of the pods rather than the leaves and stems; the curves for leaves and stems remained f a i r l y constant from about 60 DAP onward while that of pod dry weight increased. Total pod dry weight, which consisted of pod wall and seed dry weight, exhibited a biphasic growth pattern i n both c u l t i v a r s [Figures 5.27(a) and ( b ) ] . Pod growth commenced 3 days e a r l i e r in EF at 50 DAP but by the f i n a l harvest DSP had the higher pod weight (Table 5.15). Thus at 80 DAP, t o t a l pod dry weight of DSP was 11.1 while that of EF was 8.2 g. During the f i r s t 6-9 days post anthesis, pod growth was due p r i m a r i l y to that of the pod wall [Figures 5.27(a) and ( b ) ] . However, pod wall dry weight declined from 24 days post anthesis in DSP (21 days in EF) onward. After that time the increment i n pod weight was due mainly to the seeds. For example, - 136 -Figure 5.26. Percentage dry matter d i s t r i b u t i o n i n the garden pea. (a) Dark Skin Perfection (b) E a r l y Frosty. a Days after p lant ing F i g u r e 5.27. F i t t e d t i m e t r e n d s f o r t o t a l p l a n t b i o m a s s ( W ) a n d i t s a d d i t i v e c o m p o n e n t s — l e a f d r y w e i g h t ( W L ) , s t e m d r y w e i g h t ( W g ) , p o d d r y w e i g h t ( W p ) , p o d w a l l d r y w e i g h t C O a n d s e e d d r y w e i g h t ( W q ) . ( a ) D a r k S k i n P e r f e c t i o n a n d ( b ) E a r l y F r o s t y . , , , ( - , , 1 1 50.0 60.0 70.0 B0.0 50.0 60 0 70.3 80.0 OAYS FiTTER PLANTING DftfS AFTER PLANTING Table 5.IS - Summary of dry weights for Dark Skin Perfection and Early Frosty Days After > Planting 20 50 53 56 59 62 65 68 71 74 77 . 80 Dark Skin Perfection (g) Leaf 0.17 2.34 2.83 3.17 4.24 4.57 4.19 4.62 5.86 4.50 5.57 4.98 Stem 0.04 1.20 1.64 1.81 2.64 3.22 3.17 3.58 4.71 3.82 4.49 4.49 Pod Wall _ - f 0.44 1.06 1.74 2.39 3.51 4.29 5.38 6.76 0.05 0.08 i Seeds - - *- 0.01 0.07 0.12 0.27 1.01 2.09 3.47 4.32 Total 0.21 3.54 4.52 5.06 7.33 8.92 9.22 10.86 15.09 14.70 18.91 20.55 Early Frosty Leaf 0.15 2.30 3.04 2.92 3.49 3.63 3.64 3.22 3.92 2.97 2.96 3.13 Stem 0.03 1.18 1.92 1.92 2.48 2.60 2.82 2.80 3.06 2.36 2.34 2.47 Pod Wall - r 0.60 1.36 1.67 2.68 2.44 3.62 2.93 2.62 1.60 0.03 0.34 Seeds - »- 0.02 0.12 0.33 0.88 1.06 2.50 3.58 3.99 6.60 Total 0.18 3.51 5.30 5.46 7.45 8.23 10.02 9.52 13.10 11.84 11.91 13.80 - 139 -between the ultimate and penultimate harvests, pod wall dry weight i n DSP declined from 5.4 to 4.3 g, whereas seed and t o t a l pod dry weights increased from 3.4 to 6.7 g and from 8.5 to 11.1 g, r e s p e c t i v e l y (Table 5.15). S i m i l a r l y i n EF, the corresponding changes were from 2.6 to 1.6 g f o r pod wall dry weight, from 4.0 to 6.6 g for seed dry weight and from 6.7 to 8.2 g for t o t a l pod weight. 5.6.1.1 R e l a t i v e Growth Rates In both c u l t i v a r s , l e a f , stem and t o t a l plant r e l a t i v e growth rates declined s l i g h t l y during the reproductive phase [Figures 5.28(a) and ( b ) ] . In DSP, for example, t o t a l plant r e l a t i v e growth rate f e l l from 0.084 d a y - 1 a t 50 DAP to 0.043 d a y - 1 at 80 DAP. S i m i l a r l y , i n EF, the corresponding drop was from 0.098 to 0.015 d a y - 1 over the same time period. By contrast, the pod, pod wall and seed r e l a t i v e growth rates changed s u b s t a n t i a l l y during the growth period. Also, the growth rate patterns, d i f f e r e d between the two c u l t i v a r s . In the case of DSP, pod and pod wall r e l a t i v e growth rates increased exponentially over the f i r s t 5 days a f t e r flowering. At the end of t h i s time (58 DAP), the maximum r e l a t i v e growth rates of the pod and pod wall were 0.52 and 0.49 d a y - 1 , r e s p e c t i v e l y . On the other hand, t h i s exponential phase was not observed in EF. Instead, i t s pod and pod wall r e l a t i v e growth rates declined from values of 1.02 and 1.15 d a y - 1 , r e s p e c t i v e l y , to 0.17 and 0.16 d a y - 1 , r e s p e c t i v e l y , over the same time period [Figure 5.28(a) and ( b ) ] . A f t e r a t t a i n i n g the maximum growth rate at 58 DAP, pod and pod wall r e l a t i v e growth rate in DSP f e l l r a p i d l y to 0.095 and 0.066 d a y - 1 at 65 DAP F i g u r e 5^28. P r o g r e s s c u r v e s o f i n s t a n t a n e o u s r e l a t i v e g r o w t h r a t e s o f t o t a l p l a n t b i o m a s s ( W ) a n d i t s a d d i t i v e c o m p o n e n t s . — l e a f d r y w e i g h t ( W L ) , s t e m d r y w e i g h t ( W g ) , p o d d r y w e i g h t ( W p ) , p o d w a l l d r y w e i g h t ( W c ) a n d s e e d d r y w e i g h t ( W S e ) . ( a ) D a r k S k i n P e r f e c t i o n a n d ( b ) E a r l y F r o s t y . 50.0 60.0 7 0 0 DAYS AFTER PLANTING eo. o so.o 60.0 70.0 DAYS AFTER PLANTING BO. 0 - 141 -and 67 DAP r e s p e c t i v e l y . There was a s l i g h t increase over the next 5 days, then both rates declined to 0.01 and -0.18 d a y - 1 by the f i n a l harvest. In EF, the r e l a t i v e growth rates of the pod and pod wall continued to f a l l a f t e r the i n i t i a l phase. However, the rate of decline was slower than the i n i t i a l phase [Figure 5.28(b)]. By the f i n a l harvest the respective rates were 0.04 and -0.16 d a y - 1 . The r e l a t i v e growth rate of t o t a l seed dry weight, Rg e, was biphasic i n both c u l t i v a r s . Phase 1 (56-64 DAP f o r DSP and 56-67 DAP f o r EF) was characterized by a rapid decline i n r e l a t i v e growth rates of both c u l t i v a r s . R g e f e l l from 1.13 to 0.30 d a y - 1 in DSP and 0.82 to 0.19 d a y - 1 i n EF during that period. In the second phase, the rate increased s l i g h t l y between 65 and 70 DAP then f e l l in DSP. For EF, the rate continued to f a l l during t h i s phase but the descent was not as steep as i n Phase I [Figure 5.28(b)]. I n i t i a l seed r e l a t i v e growth rate in DSP (1.13 d a y - 1 ) coincided with the attainment of maximum pod and pod wall r e l a t i v e growth ra t e s . In co n t r a s t , i n i t i a l seed r e l a t i v e growth rate i n EF occurred at the end of the f i r s t phase of pod and pod wall growth. The rates and patterns of p a r t i t i o n i n g of dry matter in the a d d i t i v e components were important i n determining the i n t e r r e l a t i o n s h i p s of these components as well as t h e i r r o l e in a f f e c t i n g t o t a l plant p r o d u c t i v i t y . In DSP, during the period 50 to 55 DAP, the leaves contributed more than the non-leaf components to the r e l a t i v e growth rate of the whole plant [Figure 5.29(a)]. For example, at 50 DAP, the absolute and f r a c t i o n a l production rate of the leaves were 0.04 d a y - 1 and 0.5 r e s p e c t i v e l y while those of the non-leaf components were 0.03 d a y - 1 and 0.4 [Figures 5.29(a) and 5.30(a)]. Figure 5.29. F i t t e d time trends f o r the absolute production rates of t o t a l plant biomass (W) and the additive components — l e a f (W L). stem (Ws) , pod (Wp) , pod wall (W c), seed (W S e) and non-leaf (W N L) dry weights, (a) Dark Skin Perfection and (b) Ea r l y Frosty. o o 5 0 . 0 NL Gfl.O 70.3 DAYS AFTER PLANTING 8 0 . 0 ? 5 0 . 3 6 0 . 0 7 0 . 0 DAYS AFTER PLANTING 8 0 . 0 Figure 5-30. Fitted time trends for the fractional production rates of the additive components of total plant biomaas — leaf (WL), stem (Wg), pod (Wp), pod wall (Wc), seed (WSe) and non-leaf (WNL) dry weights, (a) Dark Skin Perfection and (b) Early Frosty. a 1 , 60. o ? a . o DAYS AFTER PLANTING BO. 0 .0 73.Q DAYS AFTER PLANTING en - 144 -By contrast, at 50 DAP i n EF both l e a f and non-leaf components made equal contributions (50%) to t o t a l plant p r o d u c t i v i t y [Figure 5.30(b)], with absolute production rates of 0.06 d a y - 1 [Figure 5.29(b)]. From day 55 onward in DSP the rate of accumulation of dry matter i n the non-leaf components exceeded that of the leaves. By the f i n a l harvest, the production rate of the non-leaf components was 0.05 d a y - 1 while that of the leaves was -0.01 d a y - 1 [Figure 5.29(a)]. These rates were 1.1 and -0.1 times the r e l a t i v e growth rate of the whole plant [Figure 5.30(a)]. In EF, the production rate of the non-leaf components also surpassed that of the leaves. However, the rates became higher at an e a r l i e r date (from 51 DAP onwards). Furthermore, whereas the absolute production rate of the non-leaf components increased then l e v e l l e d o f f in DSP [Figure 5.29(a)], i t declined s t e a d i l y i n the case of EF to 0.01 d a y - 1 at 80 DAP (Figure 5.29(b)]. On the other hand, the f r a c t i o n a l production rate of the non-leaf components of DSP increased from 0.3 to 1.1 over the reproductive phase while that of EF increased to 1.2 at 76 DAP, then d e c l i n e d . Further s u b d i v i s i o n of the non-leaf components reveals that during l a t e vegetative and e a r l y reproductive growth (50 to 60 DAP for DSP and 50 to 53 DAP f o r EF), dry matter accumulation in the stem accounted for most of the production rate of the non-leaf components [Figures 5.29(a), 5.29(b), 5.30(a) and 5.30(b)]. For example at 53 DAP in DSP, the f r a c t i o n a l production rate of the stem was 0.4 while that of the pod was 0.0. S i m i l a r l y , f o r EF the corresponding values were 0.3 and 0.1 at 50 DAP. A f t e r day 60 i n DSP and 53 f o r EF, the pods became stronger sinks than the stems. In both c u l t i v a r s the seeds became i n c r e a s i n g l y important, accounting f o r 0.9 times the r e l a t i v e growth rate of the whole plant i n DSP and as high as 2.9 times the rate i n EF. Moreover, the f r a c t i o n a l and absolute production rate of the seeds declined a f t e r 74 DAP (21 days a f t e r anthesis) i n DSP, while the rates continued to increase i n EF u n t i l the f i n a l harvest. 5 . 6 . 1 . 2 U n i t L e a f R a t e s This index i s a measure of the net rate of accumulation of dry matter i n each component per u n i t l e a f area ( J o l l i f f e and Courtney, 1984). The u n i t l e a f r a t e of the whole plant (Ey) i n DSP declined from 8 to 7 g m - 2 day~l during the period 50 to 60 DAP, then Increased f o r the r e s t of the experimental period [Figure 5.31(a)]. In EF, Ey decreased over the e n t i r e period from 10 at 50 DAP to 5.5 g m~2 d a y - 1 at 80 DAP [Figure 5.31(b)]. When the o v e r a l l u n i t l e a f r a t e was subdivided i n t o l e a f (EL) and non-leaf components (E^L)> the c u l t i v a r s d i f f e r e d i n t h e i r rates of p a r t i t i o n i n g of dry matter between these two components [Figures 5.31(a) and ( b ) ] . During the period 50 to 55 DAP, EL increased s l i g h t l y from 2.8 to 3 g m~2 day -* i n DSP while d e c l i n i n g sharply from 6 to 1.5 g m - 2 d a y - l i n EF. Over the next 13 days EL f e l l to zero at 65 DAP and then l e v e l l e d o f f f o r DSP. EF e x h i b i t e d a s i m i l a r pattern but the point of i n f l e c t i o n occurred e a r l i e r (58 DAP) and at a higher l e v e l (1.0 g m~2 day--'-). During the next phase EL increased marginally u n t i l 72 DAP i n DSP, then d e c l i n e d . However, i n EF, EL f e l l to a minimum of 1.5 g m~2 d a y - 1 at 71 DAP then increased t h e r e a f t e r . Figure 5-31. F i t t e d time trends f o r the components of unit l e a f rate i n garden pea. t o t a l plant (E) and non-leaf components (NL) j l e a f (L), stem (S) , pod wail (C) and seeds (Se) t pod (P). (a) Dark Skin Perfection and (b) Ea r l y Frosty. - 147 -ENL i° °SP decreased between 50 and 60 DAP then rose u n t i l the end of the experiment [Figure 5.31(a) and ( b ) ] . By contrast, E^L remained f a i r l y constant at about 6 g m day in EF before decreasing from 71 DAP onward. Further s u b d i v i s i o n of E^JL into unit l e a f rate of stem (Eg), pod (Ep), pod wall (Efj) and seed (Eg e) revealed that the increase in ENL w a s due mainly to the increasing rate of dry matter accumulation in the reproductive s t r u c t u r e s . Ep and EQ showed two d i s t i n c t periods of high a c t i v i t y with an intermediate lag in both c u l t i v a r s . . During the f i r s t phase, pod and pod wall unit l e a f rate in DSP rose to maxima of 5 and 4 g m - 2 d a y - 1 r e s p e c t i v e l y at 61 DAP. In the second phase the maxima were higher (10 and 5.2 g m~2 d a y - 1 at 75 DAP). At the l a g , both indic e s declined to 2 g m - 2 d a y - 1 at 63 DAP and 1.5 g n f 2 d a y - 1 at 67 DAP, r e s p e c t i v e l y , and a f t e r the second phase they decreased sharply again. In EF both phases of high pod and pod wall a c t i v i t y preceded those of DSP. Maximum Ep and E c i n Phase 1 of EF (4 and 3 g m - 2 day" 1) occurred at 55 and 53 DAP r e s p e c t i v e l y [Figure 5.31(b)]. In the second phase the 2 1 corresponding values were 7 and 4 g m~ day" at 65 DAP. The lag phase i n EF was l e s s pronounced than that of DSP, occurring between 55 and 57 DAP. A f t e r the second maximum Ep and E^ i n EF f e l l , but then increased a f t e r 75 and 79 DAP r e s p e c t i v e l y . Unit l e a f rate of the seed estimates the net rate of dry matter accumulation in the seeds per u n i t l e a f area. In DSP, Eg e remained at zero u n t i l the lag phase of the pod (63 DAP) [Figure 5.31(a)], increased - 148 -sharply to a maximum of 7.5 g m~ day" at 7 6 DAP, then f e l l r a p i d l y t h e r e a f t e r . Eg e in EF also increased during the lag phase. There was a s l i g h t reduction i n the rate at the second period of high a c t i v i t y (63 to 65 DAP), followed by a further increase u n t i l the f i n a l harvest. The net rate of accumulation of photosynthetic material i n the stem on a l e a f area basis i s qua n t i f i e d by the index Eg (the unit l e a f rate of 2 1 the stem). This index declined s t e a d i l y from highs of 2.8. g m- day - in DSP and 4.0 g m - 2 d a y - 1 in EF at 50 DAP to about zero at the f i n a l harvest [Figures 5.31(a) and ( b ) ] . 5 . 6.2 Cohort A n a l y s i s In the foregoing s e c t i o n , the rates of dry matter production and accumulation were studied i n terms of the i n d i v i d u a l plant organs. This section subdivides the sink components f u r t h e r , in an e f f o r t to understand the processes occurring in each i n d i v i d u a l cohort. Also, i n th i s s e c t i o n , the c l a s s i c a l rather than f u n c t i o n a l approach to growth analysis was used because a number of researchers (Carr and Skene, 1961; Hedley and Ambrose, 1980; Pate and F l i n n , 1977) have observed the presence of a 'lag' phase i n seed growth of the pea. It i s , therefore, p o s s i b l e that the c u r v e - f i t t i n g procedure used i n the f u n c t i o n a l approach may obscure these lags ( i f present) and hence preclude t h e i r detection. 5 . 6.2.1 Growth Curves There were no noticeable d i f f e r e n c e s among the maximum pod weights - 149 -attained by both c u l t i v a r s [Figures 5.32(a) to ( g ) ] . In EF, the pod weights declined a f t e r 71 DAP (31 days a f t e r anthesis) in the f i r s t three cohorts (2-4)* [Figures 5.32(e) to ( g ) ] , but in DSP the weights l e v e l l e d o f f in i t s e a r l y cohorts (4-6)* [Figures 5.34(a) to ( d ) ] . In a l l cohorts, the pod wall fresh and dry weights increased to a maximum, then declined a f t e r approximately 12 days [Figures 5.33(a) to ( g ) ] . This maximum weight for a p a r t i c u l a r cohort tended to be higher in DSP than in EF. For example, the maximum pod wall fresh weight of cohorts 4 and 5 of DSP were 7.3 and 5.9 g r e s p e c t i v e l y . In EF, the corresponding values were 4.6 and 4.3 g (Table E.l of Appendix). The growth curves f o r the seeds of the f i r s t four cohorts of EF [Figures 5.34(e) to (h)] e x h i b i t an asymptotic pattern. In the f i r s t two cohorts (2 and 3 ) , t h i s asymptote was attained a f t e r 9 days of exponential growth, but in the l a s t two the exponential phase was longer (15 days f o r cohorts 4 and 5 ) . Despite t h i s prolonged phase, however, there were no apparent d i f f e r e n c e s between the maximum seed weights of each cohort (e.g., maximum seed dry weights of cohorts 2-5 were 1.1, 1.04, 1.08 and 1.2 g r e s p e c t i v e l y ) . The asymptote was not c l e a r l y defined in the case of DSP [see Figures 5.34(a) to 5.34(d)], In f a c t , the seed weights in a l l cohorts seem to be increasing up to the time of the f i n a l harvest. *0nly a few plants produced flowers i n cohort 1 so complete growth records were not obtained for th i s cohort. Consequently, the f i r s t cohort for EF was cohort 2. Since DSP flowered 6 days l a t e r than EF, i t s f i r s t cohort was cohort 4. F i g u r e 5«32. P r o g r e s s c u r v e s o f f r e s h a n d d r y w e i g h t s o f t h e p o d s o f t h e f i r s t f o u r c o h o r t s o f D S P (a-d) a n d E F ( e - h ) . " T h e n u m b e r s i n e a c h f i g u r e d e n o t e t h e t i m e o f e m e r g e n c e o f e a c h c o h o r t ( e . g . 2=53 D A P , 3=56 D A P , ^=59 D A P e t c ) . ( a ) 1*) . . ( c ) ' ( d ) (e) (f) ( g ) (h) F i g u r e 5-33- P r o g r e s s c u r v e s o f f r e s h a n d d r y w e i g h t s o f t h e p o d w a l l s o f t h e f i r s t f o u r c o h o r t s o f D S P ( a - d ) a n d E F ( e - h ) . * T h e n u m b e r s i n e a c h f i g u r e d e n o t e t h e t i m e o f e m e r g e n c e o f e a c h c o h o r t ( e . g . 2=53 D A P , 3 = 56 D A P , ^=59 D A P e t c ) . < * > ( c ) ( d ) / / \ ' J i i • 1 1 1 —1—1 I 1 3 • i • • • i • i 50 65 80 / / / 1 \ ' 1 \ 1 \ 1 1 ' 4 / / —1 1 1 1—1 1 1 1 • / ' " ^ / / / • 1 1 1 1 7 I .1 1 1 .1. L.,.1—1—1-1... 50 65 D a y s a f t e r p l a n t i n g 80 Figure 5.3**« Progress curves of fresh and dry weights of the seeds of the first four cohorts of DSP (a-d) and EF (e-h). * The numbers in each figure denote the time of emergence of each cohort (e.g. 2=53 DAP, 3=> 56 DAP, *f = 59 DAP etc ). (a) . tb) , (0) , , Ldl • J / / / / / / / / / / / 1 1 II 1 1 5 —1 1 1 1 1 1 1 1 L. 1 1 1 65 80 50 65 Days after planting 50 65 BO - 153 -5.6.2.2 R e l a t i v e Growth Rates During the f i r s t few days post anthesis, pod growth was slow i n the f i r s t three cohorts of DSP (R = 0.22, -0.03 and 0.14 d a y - 1 for cohorts 4 to 6, between 50 - 53 DAP) [Figures 5.35(a) to ( d ) ] . This i n i t i a l period was followed by a period of exponential growth in which the r e l a t i v e growth rates of the cohorts reached a maximum of 0.55 d a y - 1 (between 53 to 56 DAP). After that time, the rates f e l l to zero over the rest of the growth period. In cohort 7, i n i t i a l pod growth was high (0.57 d a y - 1 ) , but i t soon declined to 0.07 d a y - 1 by the f i n a l harvest. In the case of EF, the period of e a r l y pod growth was characterized by high growth rates i n the f i r s t two cohorts (R = 0.99 and 0.54 d a y - 1 ) and low rates in the next two (0.06 d a y - 1 i n cohort 4 and 0.13 d a y - 1 i n cohort 5). Over the following three days, the growth rates declined sharply to about 0.2 d a y - 1 i n cohorts 2 and 3, whereas i t increased to 0.44 d a y - 1 i n cohorts 4 and 5. By the f i n a l harvest, the rates i n a l l cohorts f e l l to zero. Similar patterns were observed for the r e l a t i v e growth rates of pod walls of cohorts of both c u l t i v a r s [Figures 5.36(a) to ( h ) ] . The pod wall r e l a t i v e growth rate of the f i r s t three cohorts of DSP (cohorts 4-6) were low during e a r l y growth (0.2, 0.25 and 0.13 d a y - 1 r e s p e c t i v e l y ) , increased exponentially to 0.53, 0.55 and 0.6 day - over the next 3 days, then declined to about 0.25 d a y - 1 by the f i n a l harvest. In cohort 7, the rate was high (0.53 d a y - 1 ) during early growth but f e l l sharply to -0.2 d a y - 1 at 80 DAP. F i g u r e 5-35- M e a n r e l a t i v e g r o w t h r a t e s o f t h e p o d s o f t h e f i r s t f o u r c o h o r t s o f DSP ( a - d ) a n d E F ( e - h ) . * T h e n u m b e r s i n e a c h f i g u r e d e n o t e t h e t i m e o f e m e r g e n c e o f e a c h c o h o r t ( e . g . 2=53 DAP, 3=56 DAP, ^ =59 DAP e t c ) . ( a ) - (*>) r ( c ) r ( d ) — i — i k—i i i i _ I I I I • • • • • | L 1 • 1 I—I • I I | tm (e) In -J—I—I • I i I I | | » 50 65 80 3 —I 1 1—I I—I | I I I L 50 65 80 ( g ) 4 -I 1 I—I 1—I 1—I—1 1 L SO 63 80 D a y s a f t e r p l a n t i n g (h) 5 J1 — i — i — i — i — i — i i • i — i — i — 1 _ 50 65 80 F i g u r e 5-36. M e a n r e l a t i v e g r o w t h r a t e s o f t h e p o d w a l l s o f t h e f i r s t f o u r c o h o r t s o f D S P ( a - d ) a n d E F ( e - h ) . * T h e n u m b e r s i n e a c h f i g u r e d e n o t e t h e t i m e o f e m e r g e n c e o f e a c h c o h o r t ( e . g . 2=53 D A P , 3 = 56 D A P , k~ 59 D A P e t c ) . ( a ) r ( b ) r ( c ) r (d) . 1-0 0-9 I ta +» o-o -) I I—I 1—1—I l _ x: +> s - 0 5 o u wi ( e ) vor 0) > •H 4-» cd rH 0> ni o-s o-o --0-5 Ln - i i i i I I i i , 50 65 80 -I I I I I I L. 1 ( f ) 3 _ l l — I I ft_ I I I I > I I 1 I I I L ( g ) -1—1—I—I—1_ 50 65 80 SO 65 Days a f t e r planting i r t i 80 F i g u r e M e a n r e l a t i v e g r o w t h r a t e s o f t h e s e e d s o f t h e f o r s t f o u r c o h o r t s o f D S P ( a - d ) a n d E F ( e - h ) . * T h e n u m b e r s i n e a c h f i g u r e d e n o t e t h e t i m e o f e m e r g e n c e o f e a c h c o h o r t ( e . g . 2=53 D A P , 3=56 D A P , ^=59 D A P e t c ) . ( a ) _ ( b ) ( c ) ( d ) i-o • 0*8 Q.6 0-4 0-2 0-0 LT _1 I 1 I I I u i i i i i i i j i i i i i I — I i i i i - j — i — i — i — i — i — J i i » i i 10 0-8 0-6 0-4 • 0-2 • 0 0 -(e) 2 50 Ln j i i 111 r~i i 65 80 (f) 3 L 50 » ' I I I 1—L_ 65 80 ( g ) 4 50 — I — I — I — I — 63 1 80 D a y s a f t e r p l a n t i n g (h) 5 Ln i _ i — I i i i i i i i _ 65 80 - 157 -I n i t i a l pod wall growth rate was high i n the f i r s t two cohorts of EF (1.0 and 0.54 g d a y - 1 for cohorts 2 and 3) but low for the next two cohorts (0.25 d a y - 1 ) [Figures 5.36(e) to ( h ) ] . In the l a t t e r two cohorts (4 and 5), the rates increased to 0.45 d a y - 1 over the next 3 days and by the f i n a l harvest the growth rates of a l l cohorts were below zero. With the exception of cohort 5, the r e l a t i v e growth rates of the seeds of corresponding cohorts were s i m i l a r i n both c u l t i v a r s . During e a r l y seed growth (6-9 days post anthesis), the r e l a t i v e growth rate ranged between 0.5 and 0.67 d a y - 1 , with EF having s l i g h t l y higher values (e.g., i n cohort 4, ~R f o r EF was 0.65 d a y - 1 and 0.52 d a y - 1 f o r DSP) [Figures 5.37(a) to ( h ) ] . After that e a r l y phase, the rates declined to between 0.04 and 0.08 d a y - 1 at 80 DAP. During that period of d e c l i n e , two lag phases were evident. These lags occurred between 62 and 65 DAP and between 74 and 77 DAP i n cohort 5 of DSP and cohorts 2 and 3 of EF. The lag at the l a t e r date was also apparent in cohort 6 of DSP and 5 of EF. In both c u l t i v a r s , cohort 5 had exceptionally high r e l t i v e growth rates of the seeds during the i n i t i a l growth period (56-59 DAP) (1.8 d a y - 1 in DSP and 1.6 d a y - 1 i n EF). 5.6.3 M u l t i p l i c a t i v e Components This part of the study i l l u s t r a t e s g r a p h i c a l l y the r e s u l t s of the sequential y i e l d component a n a l y s i s (Section 5.4.1). - 158 -5.6 .3.1 Model 1 In both c u l t i v a r s the growth patterns of the m u l t i p l i c a t i v e components of t o t a l plant biomass during the reproductive phase are f a i r l y s i m i l a r [Figures 5.38(a) and ( b ) ] . Leaves per stem length (Lfl/S) and inverse s p e c i f i c l e a f area (Wi/L^) remained constant throughout the period i n both DSP and EF. Average l e a f area (L^/L N) and stem length (S) were almost p a r a l l e l , showing only a s l i g h t increase between 50 and 55 DAP. This increase was more noticeable in DSP than in EF. Total weight (W) i n DSP increased over the reproductive period whereas that of EF tended to l e v e l o f f a f t e r 65 DAP. A s i m i l a r trend was observed for inverse l e a f weight r a t i o (W/WL.) in both c u l t i v a r s , but i t was l e s s pronounced than W. The number of leaves per stem length was of minor importance. I t s r e l a t i v e growth rate [Figures 5.39(a) and (b)] and f r a c t i o n a l production rate [Figures 5.40(a) and (b)] were ei t h e r zero or negative in value throughout the growth phase. Inverse s p e c i f i c l e a f area also had low production rates i n EF [Figure 5.39(b)], but i t was somewhat Important in DSP [Figure 5.39(a)]. Between 60 and 70 DAP i t became i n c r e a s i n g l y s i g n i f i c a n t , accounting for about 20% of the t o t a l production r a t e . Stem length and average l e a f area were important contributors during the l a t e vegetative to e a r l y reproductive phase in both c u l t i v a r s . Maximum production rates for S and L^/L^j were 0.04 (at 50 DAP) and 0.07 d a y - 1 • (at 50 DAP) r e s p e c t i v e l y , f o r DSP and 0.052 and 0.047 d a y - 1 (at 50 DAP) f o r EF. The corresponding f r a c t i o n a l rates were 50 and 81% in DSP and 53% and 48% i n EF. Figure 5.38. F i t t e d time trends f o r t o t a l dry weight per plant (W x 2, g) and the m u l t i p l i c a t i v e components of dry weight (log scale) — stem length (S, cm)1 number of leaves per stem length (L N/S, cm" ) i l e a f area per l e a f ( L A / L N , cm ) 1 l e a f dry weight per l e a f area ( w L A A X 0.5. g cm"2) and t o t a l plant dry weight per l e a f dry weight (W/WL x 2). (a) Dark Skin Perfection and (b) E a r l y Frosty. i n o tc if o ™ CL H o 50.0 EO.O 70.0 ORrS AFTER PLANTING V1* V s wLAA eo.o 50.0 — 1 — 70.0 60.0 DflrS AFTER PLANTING V s "IAA eo.o 01 Figure 5-39« F i t t e d time trends f o r r e l a t i v e growth rates of t o t a l dry weight (W) per plant and i t s m u l t i p l i c a t i v e components stem length (S), number of leaves per stem length (LJJ/S), l e a f area per l e a f ( L ^ / L ^ ) , l e a f dry weight per l e a f area ( W L A A ) and t o t a l dry weight per l e a f dry weight (W/W ).(a) Dark Skin Perfection and (b) Early Frosty. \ 1 i 1 Y1 1 r— 50.0 60.0 70.0 80.0 50.0 60.0 70.0 DAYS RFTER PLANTING DAYS AFTER PLANTING F i g u r e 5 . 4 0 . F i t t e d t i m e t r e n d s f o r t h e f r a c t i o n a l p r o d u c t i o n r a t e s o f t h e m u l t i p l i c a t i v e c o m p o n e n t s o f t o t a l d r y w e i g h t ( S , L / S , L A / L N , W L/L a a n d W/WL). ( a ) D a r k S k i n P e r f e c t i o n a n d ( b ) E a r l y F r o s t y . - 162 -Both S and LA/Lfj decreased in Importance with advancing age. However, by 70 DAP in DSP and 74 DAP in EF, the production rate of S began to increase again. In EF, the relative growth rate of L A/LJJ (R^/L^) also rose but it continued to decline in DSP. The relative growth rate of inverse leaf weight ratio increased throughout the reproductive period in DSP. In EF it remained constant at 0.035- day - 1 until 61 DAP, increased over the next 8 days, then declined. Similar trends were observed for the fractional production rates, with W/WL contributing a maximum of 1.3 and 1.7 times the total production rate in DSP and EF respectively [Figures 5.40(a) and (b)]. 5.6.3.2 Model 2 Stem length (S), number of leaves per stem length (Lfl/S), average leaf area (L A/LN), inverse specific leaf area (WL/LA) and seeds per pod (Se/P) had fairly constant relative growth rates during the reproductive phase in both cultivars [Figures 5.41(a) and (b)]. Inverse leaf weight ratio (W V/W L), reproductive effort (F N/W V), pod set (P/Fjj) average seed weight (WSe/Se) and total seed weight (W S E) increased.during that time. In EF, WV/WL tended to level off towards the end of the period while P/FJJ levelled off in both cultivars after 68 DAP (in EF) and 77 DAP (in DSP). The relative growth rate curves [Figures 5.42(a) and (b)] and the fractional production rate curves [Figures 5.43(a) and (b)] also reflect the relatively minor role of S, Lfl/S, L A/LN, WL/La and Se/P during most of the reproductive phase (from 60 DAP onwards). In all these F i g u r e 5.41. F i t t e d time t r e n d s f o r t o t a l y i e l d per p l a n t (W S e, g) and the m u l t i p l i c a t i v e y i e l d components ( l o g s c a l e ) -- stem l e n g t h ( S , cm) j number o f l e a v e s p e r stem l e n g t h ( L N / S , 1 2 —2 cm ) i l e a f a r e a p e r l e a f (L^/h^, cm )» l e a f d r y weight p e r l e a f a r e a ( W L A A x 0.5. g cm" )i t o t a l v e g e t a t i v e d r y we i g h t p e r l e a f d r y we i g h t (Wy/WL x 10) j number o f f l o w e r s p e r t o t a l v e g e t a t i v e d r y weight (F^/W^, g - 1 ) j number o f pods p e r f l o w e r ( P / F ^ ) ; number o f seeds p e r pod (Se/P) and f r e s h weight per seed (W /3e, g ) . (a) Dark S k i n P e r f e c t i o n and (b) E a r l y F r o s t y . Q a S U . Q co u .'a a ou a S J ' J ca. o ?u. a ba.a Dm:, in"ri"R P L n y i i N i ; D A Y S n r r c R P L A N T I N G components, r e l a t i v e growth rate and f r a c t i o n a l production rates were close to zero. Wy/WL, which increased for most of the reproductive phase [Figures 5.41(a) and ( b ) ] , also had very low production rates i n both c u l t i v a r s (approximately 0.02 d a y - 1 ) . During the ea r l y part of the reproductive phase (56 to 60 DAP), S, I-A/LIN and P/F^ were somewhat important in DSP. They accounted f o r 25-40% of the t o t a l production rate at that time. This was not the case for EF ( f r a c t i o n a l production rates were l e s s than 10%). At the f i n a l harvest stem length became i n c r e a s i n g l y important i n EF (20% of t o t a l production rate) but not in DSP. The main cont r i b u t o r s to t o t a l production rate were average seed weight and reproductive e f f o r t . Average seed weight was the most important component at a l l times, i t s f r a c t i o n a l production rate averaging 75% of the t o t a l for the entire period [Fig ures 5.43(a) and ( b ) ] . In both c u l t i v a r s the r e l a t i v e growth rate of average seed weight /Se^ w a s v e r v s i m i l a r to that of the t o t a l y i e l d ( RWg g)• However, the growth patterns d i f f e r e d between the c u l t i v a r s . For DSP, &Wge and R y S e / g e increased exponentially to maxima of 0.35 and 0.21 d a y - 1 at 65 DAP. By contrast, in EF, both rates declined r a p i d l y from highs of 0.58 and 0.45 d a y - 1 to 0.16 and 0.12 d a y - 1 , r e s p e c t i v e l y , during the period 56 to 65 DAP [Figures 5.42(a) and ( b ) ] . A f t e r that time (65 DAP onward) R W g e and RWge/Se f e l l r a p i d l y i n DSP, whereas i n EF there was a s l i g h t increase over the next 6 days, then both indic e s d e c l i n e d . The f r a c t i o n a l production rate of WSe declined i n both c u l t i v a r s over the period 56 to 60 DAP ( f o r DSP) and 65 DAP ( f o r EF) [Figures 5.43(a) F i g u r e 5 . 4 2 . F i t t e d t i m e t r e n d s f o r t h e r e l a t i v e g r o w t h r a t e s o f t o t a l y i e l d p e r p l a n t (10 W S e ) a n d t h e m u l t i p l i c a t i v e c o m p o n e n t s o f y i e l d — 1= S j 2 = L N / S | 3 = L A / L N J * * - W L / L A I 5 =W V / V L J 6 = F N / W v i ? = P / F N t 8= S e / P a n d 9 = W S e / S e . ( a ) D a r k S k i n P e r f e c t i o n a n d ( b ) E a r l y F r o s t y . 60.0 70.0 DAYS AFTER PLANTING 80.0 SO. 0 60. 0 70. 0 OAKS AFTER PLANTING 80.0 F i g u r e 5.^3. F i t t e d t i m e t r e n d s f o r t h e f r a c t i o n a l p r o d u c t i o n r a t e s o f t h e m u l t i p l i c a t i v e c o m p o n e n t s o f y i e l d — • 1 = S 1 2 = L N / S j 3 = L A / L N I ^ = W L A A l 5 = W y/W L i 6 = F N/W y 1 7 = p / F N , 8 = S e / P a n d 9 = W S e / S e . ( a ) D a r k S k i n P e r f e c t i o n a n d ( b ) E a r l y F r o s t y . - 167 -and ( b ) ] . This d e c l i n e was steeper in. DSP than EF ( c f . 55% i n DSP vs 25% in EF). A f t e r that time the f r a c t i o n a l production rates increased s l i g h t l y to 75% i n DSP, then f e l l . In EF, however, the increase was gr e a t e r , with the ra t e reaching a maximum of 99% of the t o t a l at 74 DAP before i t de c l i n e d to 60% at 80 DAP. Pod set and reproductive e f f o r t seemed to a l t e r n a t e i n importance i n EF. During the period 56 to 66 DAP the r e l a t i v e growth rate of pod set (Rp/p N) increased to a high of 0.098 day" 1 at 61 DAP, then f e l l , while the r e l a t i v e growth rate of reproductive e f f o r t (Rp^/w v) declined to 0.03 day" 1 then rose. In DSP, RpN/w f e l 1 sharply from 0.15 day" 1 at 56 DAP to zero at 72 DAP, then incr e a s e d . ^P/F^ a l s o declined (minimum 0.02 day" 1 at 60 DAP) but rose to a maximum of 0.10 day" 1 at 72 DAP, before f a l l i n g o f f again [Figures 5.42(a) and ( b ) ] . Thus by 72 DAP, % / F n w a s ^ S " i n D s p w h i l e RF N/W V w a s l o w « On the other hand, i n EF, Rp/Fjj w a s l ° w while W a s The same trends were also apparent i n t h e i r r e s p e c t i v e f r a c t i o n a l production rate curves [Figures 5.43(a) and ( b ) ] . In DSP and EF, P/F N accounted for 40 and 30%, r e s p e c t i v e l y , of the t o t a l production rate at t h e i r maximum p o i n t s . The corresponding values f o r Fjj/Wy were 103 and 25% r e s p e c t i v e l y . 5.7 Temperature C o r r e l a t i o n s There were no s i g n i f i c a n t c o r r e l a t i o n s between the short-term f l u c t u a t i o n s i n unit l e a f rate and temperature (expressed as degree days) (Table 5.16) . - 168 -Table 5.16 - Correlation between temperature and unit leaf rate in the garden pea: the deviations [calculted as the difference between mean unit leaf rate, E and the instantaneous value, E', at the mid-point of the harvest interval] were correlated with (a) mean degree days for the interval and (b) mean degree days of the preceding harvest interval. Treatment Correlation Coefficient (a) (b) DSP uninoculated 0.045NS 0.006NS DSP inoculated 0.028NS -0.131NS EF uninoculated 0.157NS -0.059NS EF inoculated 0.125NS -0.212NS 169 -CHAPTER 6 DISCUSSION OF RESULTS Seed i n o c u l a t i o n had no noticeable e f f e c t on y i e l d . This r e s u l t suggests that i n o c u l a t i o n i s not necessary under the s o i l conditions at the U n i v e r s i t y of B r i t i s h Columbia f i e l d l aboratory. Whereas the present f i n d i n g i s in c o n s i s t e n t with the European studies c i t e d by Pate (1977), i t supports the b e l i e f of Pate (1977) that seed i n o c u l a t i o n i s not required under some North American s o i l c onditions. The la c k of an e f f e c t of seed i n o c u l a t i o n upon y i e l d may be explained as follows. F i r s t , the quantity of indigenous Rhizobium species in the s o i l could conceivably obscure any advantage of the treatment. Secondly, the l e v e l s of a v a i l a b l e nitrogen i n the s o i l may have suppressed the formation of nodules and thus subsequent growth and f i x a t i o n by the b a c t e r i a , in accordance with the theories of Oghoghorie and Pate (1971). Chemical tests of the nitrogen status of the s o i l were not conducted before the experiment. Consequently, i t i s not known whether nitrogen f i x a t i o n was i n h i b i t e d because of high nitrogen l e v e l s . However, the acetylene-ethylene assay performed (Appendix C) reveals that f i x a t i o n a c t i v i t y was not s i g n i f i c a n t l y d i f f e r e n t between the inoculated and uninoculated plants. This r e s u l t supports the f i r s t explanation. It i s also possible that the inter-row spacing was not wide enough to separate the roots of uninoculated plants from the inoculum. As a r e s u l t , the l e v e l s of f i x a t i o n in a l l treatments were s i m i l a r . A comparison of the c u l t i v a r s shows s i g n i f i c a n t seed y i e l d d i f f e r e n c e s . These d i f f e r e n c e s may be due to contrasting morphological - 170 -features of Dark Skin P e r f e c t i o n (DSP) and E a r l y Frosty (EF) . DSP i s a t a l l (17 - 20 nodes), l e a f y , multibranched, l a t e maturing plant whereas EF i s shorter (14 nodes), has l e s s branches and i s e a r l y maturing. It i s therefore necessary to determine whether these morphological d i f f e r e n c e s a f f e c t the physiology and hence the y i e l d of'these two c u l t i v a r s . T r a d i t i o n a l plant growth analysis was f i r s t employed to examine the a c t i v i t y of the photosynthetic source. During the vegetative phase, there was no s i g n i f i c a n t d i f f e r e n c e in the r e l a t i v e growth rates and unit l e a f rates of both c u l t i v a r s (Section 5.3.3). The r e l a t i v e l e a f growth rates of the c u l t i v a r s , however, d i f f e r e d during e a r l y growth (21 - 30 DAP). EF maintained a high constant growth rate throughout the period while DSP started o f f slowly and increased to the same l e v e l as EF by 30 DAP (Figures 5.18 and 5.19). This observation suggests that EF i s a better competitor for l i g h t during early vegetative growth because i t i s able to e s t a b l i s h i t s canopy e a r l i e r than DSP. There was no s i g n i f i c a n t d i f f e r e n c e between the t o t a l dry weights per plant of each c u l t i v a r during early reproductive growth (Figure 5.5a). However, by the f i n a l harvest DSP had s i g n i f i c a n t l y greater plant biomass than EF. The growth indic e s reveal that from 55 DAP onward, DSP had somewhat higher r e l a t i v e growth rates of leaves, stem and the whole plant than EF (Figures 5.6 to 5.10), as well as s i g n i f i c a n t l y higher l e a f area r a t i o , and leaf weight r a t i o (Figures 5.12 and 5.14). The higher rates and r a t i o s were probably due to the d i f f e r e n t flowering times of the two c u l t i v a r s . EF, the early maturing c u l t i v a r , proceeded into the reproductive phase before DSP. As a r e s u l t , vegetative growth i n EF - 171 -declined or ceased before that of DSP. Consequently, t h i s l a t t e r c u l t i v a r had higher l e a f area and dry weights by the f i n a l harvest because of a longer duration of vegetative growth. Unit l e a f rates of the two c u l t i v a r s were not s i g n i f i c a n t l y d i f f e r e n t (Figure 5.11), but there appeared to be some compensation between this index and l e a f area r a t i o . This compensation also resulted i n i n s i g n i f i c a n t d i f f e r e n c e s i n r e l a t i v e growth rates between the two c u l t i v a r s . It therefore seems that r e l a t i v e growth rate and unit leaf rate are not s u i t a b l e t r a i t s for s e l e c t i n g for high plant biomass. During the l a t e reproductive state (74 DAP onwards), the steep increase In unit l e a f rate i s thought to be an exaggeration of the same r i s e in the r e l a t i v e growth rate curves (Figure 5.10). This increase i s believed to be an a r t i f a c t of the data reduction f o r two reasons: ( i ) the demographic analysis revealed that during t h i s l a t e stage, l e a f death rate exceeded l e a f b i r t h rate i n the two treatments concerned. This f i n d i n g suggests that the plants were into the senescent phase of growth and therefore not l i k e l y to have high growth r a t e s . ( i i ) l e a f area r a t i o of the plants (Figure 5.12) declined during l a t e reproductive growth. If there were a resurgence of growth (as implied by the increasing r e l a t i v e growth rate and unit l e a f r a t e ) , t h i s index ( l e a f area r a t i o ) would have increased a l s o . Thus, the apparent further growth i s a t t r i b u t e d to inherent v a r i a b i l i t y of the data. As a r e s u l t , the aberrant points are ignored. In the case of the non-destructive data, a s i m i l a r growth pattern was observed for unit l e a f rate during the reproductive phase (Figure 5.21). - 172 -Unlike the curves for the d e s t r u c t i v e harvest, t h i s increasing trend was not due to random v a r i a t i o n or the method of curve f i t t i n g . It i s a t t r i b u t e d to an underestimation of true photosynthetic area because the area of other photosynthetic organs—the stem and pods—were not considered (Milbourn and Hardwick, 1968). Consequently, unit l e a f rate i s overestimated at this time. It should also be noted that the r e s u l t s of the d e s t r u c t i v e and non-destructive harvests d i f f e r . For example, i t was concluded from the d e s t r u c t i v e harvest data that l e a f areas of the two c u l t i v a r s were s i g n i f i c a n t l y d i f f e r e n t (Figure 5.11). On the other hand, based on the non-destructive harvest data, c u l t i v a r d i f f e r e n c e s were not apparent (Figure 5.15). This discrepancy may have resulted from frequent handling of the non-destructively measured p l a n t s . In accordance with Beardsell (1977), such handling may have increased the r e s p i r a t i o n rates of the plants and thereby affected t h e i r growth. The foregoing paragraphs discussed the a c t i v i t y of the whole plant i n terms of the extent and e f f i c i e n c y of the leaves. However, the analysis did not provide information on the r e l a t i o n between source a c t i v i t y and y i e l d . This shortcoming i s remedied v i a sequential y i e l d component a n a l y s i s . The f i r s t y i e l d component model (Model I) analyses the source a c t i v i t y of the components of t o t a l plant biomass while Model 2 examines the r e l a t i o n between both source and sink a c t i v i t y and y i e l d . This second model i s an improvement over models applied by e a r l i e r researchers (e.g., Hardwick and Milbourn, 1967; Milbourn and Hardwick, 1968 and S a l t e r , 1963) - 173 -i n which only sink a c t i v i t y was analysed. In Model 1 (Table 5.7) stem length (S) and averge l e a f area (L^/L^) were the main contributors to t o t a l dry matter v a r i a b i l i t y . Average l e a f area acted both d i r e c t l y and i n d i r e c t l y while stem length acted i n d i r e c t l y . Inverse l e a f weight r a t i o (W/WL) made a d i r e c t c o n t r i b u t i o n . The i n d i r e c t c o n t r i b u t i o n of. S seems to be through i t s c o r r e l a t i o n with the number of leaves per stem length (LJJ/S)» L^/L^ a n ^ W/W^ . For example, an increase in stem length implies more nodes per plant and hence more leaves. Since the leaves are the main photosynthetic organs, the'increase in l e a f number suggests more dry matter produced by the plant. Average l e a f area i s an index of l e a f s i z e . Thus, a large L^/L^j r e s u l t s i n an increased area for l i g h t i n t e r c e p t i o n and hence photosynthesis. The increased photosynthesis r e s u l t i n g from the l a r g e average l e a f area may therefore explain the d i r e c t c o n t r i b u t i o n of the component L^/Lfg. The compensatory r e l a t i o n s h i p between the adjacent pairs of components in the y i e l d equation (Table 5.7) implies that those components may be competing for a s s i m i l a t e s . Both W^/l^ and W/W^  are the r e c i p r o c a l s of the two components of l e a f area r a t i o ( F ) . This index (F) has already been shown to be important i n d e f i n i n g the extent of the a s s i m i l a t o r y system. Thus, the roles of both W^/L^ and W/W^  w i l l be discussed in terms of t h e i r r e l a t i o n s h i p with inverse l e a f area r a t i o , 1/F. Since the y i e l d components are expressed in logarithmic scale and they - 174 -are orthogonal (Equations 14 and 15 in Chapter 3), the sum of their increments in (coefficient of determination), yields the contribution of 1/F to total biomass variability (Table 5.7). The result is a significant 6% direct contribution by 1/F. This finding implies that less leafy plants are more efficient producers of dry matter in pea. It therefore lends support to the belief of Davies (1977), Snoad and Arthur (1974) and Snoad (1974) that the new leafless phenotypes hold great potential for future pea research programs. In the second model the major components were stem length, averge leaf area, reproductive effort (Fjj/Wv) and average seed fresh weight (Wge/Se). The findings on stem length and average seed weight concur with the results of Dahiya e£ al . (1977) and Pandey and Gritton (1975). All three components acted indirectly in affecting yield variability while pod set (P/FJJ) , LJJ/S and inverse leaf weight ratio (W/WL) acted directly. Stem length may have acted indirectly through its relationship with the number of nodes. Each pea cultivar has a characteristic node number below which flowering does not occur. Thus, an increase in stem length (and hence nodes) above that number represents an increase in the number of reproductive nodes and therefore yield. The significant direct contribution of LJJ/S is consistent with the findings of a number of researchers (Hardwick and Milbourn, 1967; Milbourn and Hardwick, 1968). In breeding for processing (or 'vining') peas, increased stem length is useless without an attendant synchronous growth of the pods at each reproductive node. This component (S) is therefore more important in - 175 -s e l e c t i n g for d r i e d peas. The roles of average l e a f area and inverse l e a f weight r a t i o have already been explained i n the f i r s t model. Their Importance from the time of flowering onward s i g n i f i e s that photosynthetic material produced during the reproductive phase i s important to high y i e l d s . This r e s u l t i s consistent with those Meadley and Milbourn (1970, 1971), Sa l t e r (1962, 1963), Hole and Scott (1981, 1983) and Falloon and White (1980). It i s , however, not in agreement with Hardwick and Milbourn (1967), who found that pea y i e l d had l i t t l e dependence of l e a f area. The s i g n i f i c a n c e of the photosynthetic source during the reproductive phase i s also indicated by the c o n t r i b u t i o n of F^j/Wv, reproductive e f f o r t . However, t h i s component also considers the p o t e n t i a l sink load, i n r e l a t i o n to the source supply. The r e s u l t that average seed weight i s a major component i s in agreement with the findings of several researchers (Boswell, 1926; Krarup and Davies, 1970 abd Stanf i e l d _et _ a l . , 1966). In v i n i n g peas, however, maximum fresh weight per seed does not imply maximum y i e l d because y i e l d i s also determined by the stage of maturity. Consequently, average seed weight i s important only up to the approximate stage. For the drie d pea indus t r y , maturity i s not c r i t i c a l . Pod set has heretofore not been found to be an important component of pea y i e l d by e a r l i e r researchers, probably because the pea i s s e l f f e r t i l e and s e l f p o l l i n a t i n g . In the present study, t h i s component was observed to have a s i g n i f i c a n t d i r e c t e f f e c t on y i e l d — t h e more pods set per flowers i n i t i a t e d — t h e higher the y i e l d . There was, however, a s i g n i f i c a n t - 176 -negative c o r r e l a t i o n between pod set and average l e a f area, thereby i n d i c a t i n g a compensatory r e l a t i o n s h i p between the two components. This compensation f u r t h e r implies that pod set i s a f f e c t e d by photosynthetic supply. Thus, pod set i s enhanced when there i s reduced competition f o r a s s i m i l a t e s by non-reproductive sinks such as young leaves. Dwarf v a r i e t i e s of peas are therefore more d e s i r a b l e than t a l l v a r i e t i e s as a p i c a l growth i n the former v a r i e t i e s ceases soon a f t e r flowering. Two important points emerge from the c o r r e l a t i o n a n a l y s i s among y i e l d components (1) y i e l d components which represent reproductive structures show no s i g n i f i c a n t c o r r e l a t i o n s with each other and ( i i ) the component— average seed f r e s h weight—had s i g n i f i c a n t negative c o r r e l a t i o n s with most of the vegetative components. The f i r s t r e s u l t implies that the reproductive components appear to be a c t i n g independently of each other. Thus, improving one of these components may not a f f e c t y i e l d . On the other hand, the second r e s u l t i n d i c a t e s that the vegetative components have a compensatory r e a c t i o n with one of the main components of y i e l d — a v e r a g e seed weight. Research e f f o r t s must therefore concentrate on the components which are not a f f e c t e d by e i t h e r of these r e l a t i o n s h i p s i n order to improve y i e l d . One such component i s reproductive e f f o r t (F j j /Wv) • It i s enhanced by i n c r e a s i n g the number of leaves per stem length and inverse l e a f weight r a t i o but reduced by an increase i n inverse s p e c i f i c l e a f area (WL/L a). However, since WL/La i s a n o n - s i g n i f i c a n t component of y i e l d , F N / W y (and hence y i e l d ) may be enhanced by reducing W L / L A . This component ( F^ /Wy ) should therefore be i n v e s t i g a t e d f u r t h e r to determine the optimum value f o r a p a r t i c u l a r c u l t i v a r . A somewhat s i m i l a r conclusion was drawn by Meadley and Milbourn (1971). These authors suggest - 177 -an optimum of 700-800 pods/m of land for DSP. However, t h e i r optimum value, unlike the component (F^/Wy) suggested herein, did not account f o r the r o l e of the source. In the present study, the values of Ffj/Wy at a p a r t i c u l a r harvest were generally higher for EF than DSP [Table 5.5(a)]. This f i n d i n g suggests that the component may d i f f e r among c u l t i v a r s and hence might be considered as a s u i t a b l e s e l e c t i o n t r a i t . Further.information i s also needed on the e f f e c t of various agronomic p r a c t i c e s (such=:as planting density and time of planting) on t h i s y i e l d component. .. u : Y i e l d compo.nent an a l y s i s f a c i l i t a t e d the i d e n t i f i c a t i o n of important y i e l d componentscin both c u l t i v a r s . However, i t does not explain the d i f f e r e n c e s between the c u l t i v a r s , nor the o v e r a l l dynamics of the growth and y i e l d process-. Furthermore, only the a c t i v i t i e s of the sinks and non-reproductive>source organs have been i n v e s t i g a t e d , with very l i t t l e a t t e n t i o n given to the reproductive source organs. Pate and F l i n n (1973), Linck and Sudia (1972), Szynkier (1974) L o v e l l and L o v e l l (1970) and F l i n n (1974) ihave a l l shown the importance of the pod wall as an a d d i t i o n a l source :of a s s i m i l a t e s to the developing seed. With t h i s i n mind, the combined approach of J o l l i f f e and Courtney (1984) was used to determine the a c t i v i t y of the a d d i t i v e and m u l t i p l i c a t i v e components of y i e l d , i n an e f f o r t .to further explain the c u l t i v a r d i f f e r e n c e s . Amdng the m u l t i p l i c a t i v e components of the f i r s t model, the main d i f f e r e n c e between DSP and EF was the production rates of inverse s p e c i f i c l e a f are-a (W L/L A) and inverse l e a f weight r a t i o W/WL) [Figure 5.39]. Since EEuwas smaller with l e s s l e a f area, shading was not a problem so the production rate of WL/LA remained f a i r l y constant at zero throughout - 178 -the reproductive phase. In DSP, however, the r e l a t i v e growth rate of W L / L A increased over the f i r s t 15 days of the reproductive period then f e l l . This pattern suggests that the e f f e c t s of shading were not apparent u n t i l about 68 DAP. The rapid decline in production rate of inverse l e a f weight r a t i o i n EF seems to be due to the time course of development as the plant entered the c l o s i n g stage of l i f e . There may also have been a reduction i n l e a f photosynthetic a c t i v i t y which resulted in a d e c l i n e i n the rate of W/WL and a compensatory increase i n production rates of stem length and average l e a f area. By contrast, production rate of W/WL "*"n i n c r e a s e d throughout the reproductve period, probably because of the l a t e maturing habit of the c u l t i v a r . Another consequence of l a t e maturity of DSP was that the r e l a t i v e growth rates of t o t a l seed fresh weight and average seed fresh weight were low during early reproductive growth [Figure 5.42 ( a ) ] . This slow rate res u l t e d in a sequential pattern flowering and pod growth which i s undesirable in the processing industry. By comparison, high growth rates in EF during the early phase suggest that a l a r g e r number of early pods would be developing almost simultaneously and this would improve harvestable y i e l d . The r e l a t i v e growth rates of reproductive e f f o r t , average l e a f area and stem length were higher i n DSP than in EF during the early reproductive phase. These higher rates r e f l e c t the larger si z e of the former c u l t i v a r . Soon a f t e r the maximum seed production rate was attained for DSP (65 DAP), the production rate of reproductive e f f o r t declined sharply. This f i n d i n g implied the occurrence of intense competition for a s s i m i l a t e s at that - 179 -time. Results of the demographic an a l y s i s (Tables 5.13 and 5.13) indicated that l e a f and flower b i r t h rates were also high at that time. Consequently, i t i s conceivable that the non-reproductive source was unable to meet these high sink demands, thus causing the decline in the rate of F N/ WV Aft e r that time, the production rate'of FN/Wy in DSP rose again, probably because t o t a l and average seed r e l a t i v e growth r a t e , l e a f b i r t h rate and flower b i r t h rate decreased. EF exhibited a more e f f i c i e n t system. The f r a c t i o n a l production rates of both FN/WV and average seed weight (Wge/Se) increased to maximum values simultaneously. This trend suggests that in t h i s c u l t i v a r , photosynthetic production by non-reproductive sources rose to meet the demands of the sink when needed. Relative growth rate of pod set was high during l a t e reproductive growth (73 DAP) in DSP, but in EF i t was high much e a r l i e r (62 DAP) [Figures 5.42 (a) and ( b ) ] . This d i f f e r e n c e i s probably a t t r i b u t e d to the contrasting maturing habits of both c u l t i v a r s . Maximum production rate of pod set in DSP coincided with minimum f r a c t i o n a l production rate of F^/Wy [Figure 5.43 (a)] which further amplified high sink demands in DSP at that time. With EF, t h i s competition was also evident, as f r a c t i o n a l production rate of Wge/Se declined at the same time that rate of pod set rose. The superior y i e l d of EF was due to early pod growth and higher r e l a t i v e growth rate of the pods [Figure 5.28(a) and ( b ) ] . The two c u l t i v a r s exhibited completely d i f f e r e n t growth s t r a t e g i e s . In the case of DSP, maximum seed growth rate coincided with maximum pod wall growth r a t e . By contrast, in EF, maximum seed r e l a t i v e growth rate proceeded during the - 180 -t r a n s i t i o n between the i n i t i a l rapid decline in pod wall growth rate and the second phase of senescence. These findings suggest that during e a r l y reproductive growth, the seeds and pod wall of DSP may be competing for a s s i m i l a t e s as they both have high growth ra t e s . As a r e s u l t , the a v a i l a b i l i t y of a l t e r n a t i v e sources of dry matter may be c r u c i a l to the maintenance of high, uniform y i e l d s at t h i s time. It also implies that the carry over of photosynthetic material from the vegetative phase as well as pod photosynthesis may be more important in DSP than EF during e a r l y reproductive growth. Further evidence of t h i s i s given by the high f r a c t i o n a l production rate of reproductive e f f o r t [Figure 5.43 (a)] i n DSP during the e a r l y reproductive phase. Growth curves for the i n d i v i d u a l cohorts of pods, pod wall and seeds (Figures 5.32 to 5.34) were s i m i l a r to those described by e a r l i e r researchers (Bisson and Jones, 1932; McKee et a l . , 1955; F l i n n and Pate, 1970; F l i n n , 1974). That i s , pod wall growth preceded seed growth for the f i r s t few days a f t e r anthesis, then pod wall fresh and dry weight declined while seed weight continued to increase. These growth patterns also revealed that the seeds of the second reproductive node in DSP, had a much higher r e l a t i v e growth rate than the other cohorts at 56 DAP [Figure 5.37 ( a ) ] . This high rate may be i n d i c a t i v e of strong sink demands at that time. Thus, seeds at the second reproductive node may well be competing with those at adjacent nodes for a s s i m i l a t e . Szynkier (1974) observed that there was competition between pods at the f i r s t and second node. Her r e s u l t s were obtained from the e a r l y v a r i e t y , 'Alaska', whereas, i n the present study, no such competition was evident among early seed cohorts i n the early v a r i e t y EF. Similar - 181 -competition was detected by Hole and Scott (1981) in the c u l t i v a r 'Feltham F i r s t ' . These authors found that the flowers at the f i r s t node were more vulnerable to the adverse e f f e c t s of competition. In a l a t e r study (1983), the same authors did not detect competition during e a r l y development between the f i r s t f r u i t and one or two a d d i t i o n a l f r u i t s regardless of t h e i r p o s i t i o n on the plant. Reduced weight of the f i r s t f r u i t was, however, observed (1) during l a t e development when, there were other f r u i t s at the same node and (2) throughout the developmental period when there was a f u l l f r u i t load on the plant. F l i n n 1 s (1974) r e s u l t s showed that the l e a f l e t s at the f i r s t reproductive node exported greater amounts of a s s i m i l a t e s to the pod two nodes above i t i n the c u l t i v a r 'Onward', thereby implying a heavy sink demand on the source at the early reproductive nodes. It therefore seems f e a s i b l e that in DSP, the i n a b i l i t y of the source organs to provide s u f f i c i e n t a s s i m i l a t e during early reproductive growth, may be the cause of y i e l d v a r i a b i l i t y . Thus, t h i s e a r l y phase of pod a c t i v i t y seems c r u c i a l i n determining the y i e l d of the p l a n t . The f i r s t phase of high pod a c t i v i t y was followed by a lag period, then a second period of high pod a c t i v i t y . During the l a g , the production rates and unit l e a f rates of the pod and pod wall decreased. [Figures 5.29, 5.30 and 5.31]. The decline was more marked in DSP than in EF and i t occurred two days l a t e r in- the former c u l t i v a r at 64 DAP. At that time, according to the demographic a n a l y s i s , l e a f and flower b i r t h rates were at or near maximum values while l e a f and flower death rates were low (Tables 5.12 and 5.13). Thus, a high proportion of the a v a i l a b l e a s s i m i l a t e s may have been used in l e a f and flower production, with a r e s u l t a n t reduced - 182 -amount a v a i l a b l e for pod growth. The reduction was probably more marked in DSP because there were more leaves and flowers than in EF. Meadley and Milbourn (1971) observed high pod and flower a b s c i s s i o n rates among plants with large vegetative structures and high pod numbers, and they a t t r i b u t e d the losses to competition among pods for a s s i m i l a t e produced by a senescent canopy. The r e s u l t s of the present study i n d i c a t e that rapid l e a f death was not apparent during the lag phase. Therefore, the competition appears to have been not only among the pods, but also between the pods and emerging leaves. These findings on high pod and flower a b s c i s s i o n rates during periods of rapid vegetative growth may also explain why inverse l e a f area r a t i o (1/F) and reproductive e f f o r t (Ffl/Wy) were s i g n i f i c a n t contributors to y i e l d v a r i a b i l i t y . Leaf area r a t i o i s an index of the extent of the a s s i m i l a t o r y system. Thus, as the siz e of the a s s i m i l a t o r y system increases ( i . e . inverse l e a f area r a t i o decreases) , there i s increased competition between the pods and leaves and so y i e l d decreases. S i m i l a r l y , reproductive e f f o r t could be considered an index of the 'carrying capacity' of the plant. That i s , Fjj/Wy i s a measure of the sink load which can be supported by the source. An increase i n Fftj/Wy implies that the number of flowers and pods which can be sustained by the source increases, and hence y i e l d i s increased. The second phase of high pod a c t i v i t y occurred immediately a f t e r the l a g . In both c u l t i v a r s t o t a l pod growth during t h i s phase was higher than in the f i r s t phase. The net rate of accumulation of dry matter in the pods increased during t h i s second phase, as a reduction in l e a f and flower b i r t h rate lessened the competition for a s s i m i l a t e s . Most of t h i s dry matter was p a r t i t i o n e d into the seeds. In EF, the unit l e a f rate of the seeds - 183 -continued to increase a f t e r maximum pod wall a c t i v i t y was attained. However, in DSP, the net rate of accumulation of dry matter in the seed ( declined 4 days a f t e r maximum pod unit l e a f rate was reached. The main reason for the di f f e r e n c e in p a r t i t i o n i n g seems to be the co n t r a s t i n g flowering habits of the two c u l t i v a r s . EF achieved maximum rate of dry matter accumulation in the pod about 15 days af t e r f i r s t flowering while DSP attained i t s maximum much l a t e r (22 days a f t e r flowering). At the same time (15 days a f t e r flowering), l e a f area of EF was also at i t s maximum (Figure 5.1), so the plant was able to sustain seed growth a f t e r that time. DSP, on the other hand, reached maximum pod and seed a c t i v i t y when i t s l e a f canopy was senescing [ i . e . , l e a f b i r t h rate was decreasing while l e a f death rate was increasing (Table 5.12)]. As a r e s u l t , DSP was unable to support further seed growth a f t e r 75 DAP. Therefore, the improvement of y i e l d i n the garden pea depends not only on the rate of accumulation of dry matter in the seeds, but also on the attainment of maximum l e a f area at the same time that the sink a c t i v i t y i s at i t s peak. Since both c u l t i v a r s investigated in th i s study d i f f e r e d i n the rates of l e a f area growth rate during the vegetative phase, as well as the pattern and rates of p a r t i t i o n i n g of dry matter in the reproductive s t r u c t u r e s , i t i s possible that s e l e c t i o n and breeding for these t r a i t s may be f e a s i b l e . Another consequence of the reduced source supply during the reproductive phase i s the increased a b s c i s s i o n rates of the pods and flowers at the l a t e r nodes (Table 5.14). These r e s u l t s have serious i m p l i c a t i o n s for the production of dried peas as the pods at a l l nodes constitute y i e l d . Thus, the second phase of high pod a c t i v i t y may be - 184 -another c r i t i c a l period in which pods are vulnerable to the l i m i t e d a s s i m i l a t e supply. It i s i n t e r e s t i n g to note that in both c u l t i v a r s , the unit l e a f rate of leaves did not decline s t e a d i l y throughout the reproductive phase. Instead, the net rate of accumulation of dry matter in the leaves increased s l i g h t l y during the second period of high pod a c t i v i t y [see Figures 5.31 (a) and ( b ) ] . This increase may be i n d i c a t i v e of an increase in the production of photosynthetic material by the leaves to meet the increasing demands of the pods (or more s p e c i f i c a l l y the seeds). Kurssanow (1934) f i r s t suggested that photosynthesis of the pea f r u i t was supressed by high a s s i m i l a t o r y a c t i v i t y of the subtending leaves. However, r e s u l t s of the present study imply that the opposite i s true. That i s , l e a f a c t i v i t y seems to be regulated by the growth pattern of the pod and seeds. For example, at f i r s t flowering (53 DAP i n DSP and 50 DAP in EF) the unit l e a f rate of the leaves were 3 and 6 gm day r e s p e c t i v e l y . However, as pod 2 1 growth proceeded, the unit l e a f rates declined to 1 gm" day - i n both c u l t i v a r s at the lag phase (64 DAP and 58 DAP, r e s p e c t i v e l y ) . These r e s u l t s are i n c o n f l i c t with the f i r s t hypothesis which suggests that a s s i m i l a t o r y a c t i v i t y of the l e a f i s high during pod growth. Thus, the second hypothesis seems more acceptable. This conclusion i s also c o n s i s t e n t with the f i n d i n g s of F l i n n (1974) and L o v e l l and L o v e l l (1970). Milbourn and Hardwick (1968) suggested that growth analysis had l i m i t e d use in the study of growth and y i e l d i n the garden pea because i t did not take into account the c o n t r i b u t i o n of the non-leaf organs to o v e r a l l pod growth. The present study shows that t h i s problem has been - 185 -overcome through the use of the r e c e n t l y developed techniques of J o l l i f f e and Courtney (1984) and J o l l i f f e et a l . (1982). As a r e s u l t of these methods, i t was possible to determine the c o n t r i b u t i o n of a l l the above-ground plant organs to o v e r a l l plant p r o d u c t i v i t y as well as to examine t h e i r i n t e r r e l a t i o n s h i p s . Moreover, the techniques are conducted under sampling conditions as opposed to the experimental manipulation of the plant organs done by L o v e l l and L o v e l l (1970), Hole and Scott (1981) and by Szynkier (1974). The present study used a l l the pods on both the main stem and branches unlike e a r l i e r studies ( F l i n n , 1974, Szynkier, 1974). The techniques have therefore proved useful i n determining the p h y s i o l o g i c a l basis for y i e l d v a r i a b i l i t y i n the pea. At the whole plant l e v e l of organization, the source a c t i v i t y was investigated and the r e l a t i o n s h i p between t h i s a c t i v i t y and o v e r a l l y i e l d and i t s components was determined. Also, at the sub-organismal l e v e l of organization, the p h y s i o l o g i c a l consequences of the morphological d i f f e r e n c e s between the two c u l t i v a r s were elucidated and the dynamics of reproductive growth were o u t l i n e d . To the author's knowledge, the present study i s the f i r s t in which a l l three methods of growth and y i e l d analysis were applied to a s i n g l e data set. T r a d i t i o n a l plant growth analysis examined the net a c t i v i t y of the a s s i m i l a t o r y system in terms of ind i c e s of the extent and e f f i c i e n c y of the system. Demographic a n a l y s i s , on the other hand, investigated changes i n the populations of source (leaves) and sink (flowers and pods) organs. In sequential y i e l d component analysis y i e l d was subdivided into i t s morphological components. The analysis then determined s i g n i f i c a n t - 186 -components of y i e l d v a r i a b i l i t y , i n t e r r e l a t i o n s h i p s among the components and important stages of growth. F i n a l l y , the combined approach of J o l l i f f e and Courtney (1984) subdivided plant p r o d u c t i v i t y into i t s addi t i v e and m u l t i p l i c a t i v e components. By so doing, the dynamics of p a r t i t i o n i n g were studied. Thus, a d d i t i o n a l information on plant performance was obtained through the use of t h i s comprehensive a n a l y t i c a l approach, than by applying only one of the above-mentioned techniques. - 187 -CHAPTER 7 A MODEL SIMULATING POD YIELD The proposed model in t h i s chapter i s a dynamic model for p r e d i c t i n g the growth of an i n d i v i d u a l pod at each reproductive node of the pea plant. This model was developed on the basis of the r e s u l t s of the present study, from the contributions of other researchers i n pea physiology and from current knowledge of the mechanism of pod growth. 7.1 The Proposed Model Hardwick and Milbourn (1967) and Hardwick (1969) developed a simple model of the sequence of events which determine the y i e l d at each node. Their model, however, did not consider the co n t r i b u t i o n of the photosynthetic source during pod development. The findings of the present study as well as those of e a r l i e r researchers (Meadley and Milbourn, 1971; Fa l l o o n and White, 1980; Hole and Scott, 1981, 1983) ind i c a t e that the source plays an important role i n the y i e l d process. Thus, the early model (Hardwick and Milbourn, 1967; Hardwick, 1969) i s inadequate. The equation which forms the basis for the present model i s s i m i l a r to that proposed by Schapendonk and Brouwer (1984) in t h e i r study of f r u i t growth i n cucumbers. This equation i s as follows: - S f ( i ) • PN [28] - 188 -where, ^ f ( i ) ^ s t n e d a i l y increment in pod dry weight. Pj^ i s the net d a i l y supply of a s s i m i l a t e to the pod and S f ( i ) i s the r e l a t i v e sink function which i s defined by S f ( i ) = a ( i ) [29] A ( t o t a l ) a( i ) i s the a c t i v i t y f u nction of an i n d i v i d u a l pod at a p a r t i c u l a r node and A ( t o t a l ) i s the a c t i v i t y function of the t o t a l sink load. Warren Wilson (1972) defined sink strength as the product of i t s size and a c t i v i t y . Thus, using t h i s d e f i n i t i o n and s u b s t i t u t i n g the r e l a t i v e growth rate as the index of a c t i v i t y and dry weight as the index of s i z e , Equation 29 becomes: S f ( i ) = w(i) 1 9 dw(i) w(i) dt [30] 1 where, w(i) i s the dry weight of an i n d i v i d u a l pod Wp i s the t o t a l pod dry weight and t i s time (days). The equation then reduces to dw(i) dt dW, S f ( i ) = [31(a)] - 189 -i n other words, the r e l a t i v e sink function of an indivdual pod i s the r a t i o of i t s absolute growth rate to the absolute growth rate of the t o t a l dry weight of pods per plant, A G Rw f i ^  i . e . , S f ( i ) = ' [31(b)] where AGR i s the absolute growth rate. By s u b s t i t u t i n g equation 31(b) into equation 28, the model for simulating pod growth i s derived F f ( i ) AGiC l J 2 ) 7.2 Assumptions of the Model There are four main assumptions of the proposed model. ( i ) the sink function of each pod i s the same regardless of the p o s i t i o n on the plant. ( i i ) each f r u i t has equal access to the pool of a s s i m i l a t e s , ( i i i ) the c o n t r i b u t i o n of the root to pod growth i s small,and ( i v ) i f competition i s apparent, the amount of a s s i m i l a t e a v a i l a b l e to the subsequent pod i s reduced by 10%. The f i r s t assumption i s reasonable since i n t h i s study, the a c t i v i t y of each pod cohort (Figure 5.35) of DSP was quite s i m i l a r . The second assumption i s p l a u s i b l e . F l i n n and Pate (1970), F l i n n (1974) and F l i n n et a l (1977) observed that the leaves subtending the pods - 190 -at each node are the main suppliers of as s i m i l a t e to the developing f r u i t . Szynkier (1974), however, found that the pods were also dependent on a s s i m i l a t e produced at d i f f e r e n t nodes when the supply was l i m i t e d . Since the proposed model simulates the growth of the pods i n the presence of the f u l l sink load, i t i s possible that pod growth may depend not only on i t s subtending leaves, but also on the general a s s i m i l a t e pool. Assumption ( i i i ) i s supported by the r e s u l t s of Pate and F l i n n (1973). These authors found that l e s s than 15% of the t o t a l amount of carbon required by the seed was translocated from the roots. The fourth assumption i s h y p o t h e t i c a l , but i s deemed necessary i n order to account for the e f f e c t of competition on the ass i m i l a t e supply. Schapendonk and Brouwer (1984) suggested that competition among the pods can be detected i f actual pod growth i s l e s s than p o t e n t i a l pod growth. P o t e n t i a l pod growth i s defined by the equation: Gp = a ( i ) x 0.35 (33) where, Gp i s p o t e n t i a l growth and 0.35g i s the maximum d a i l y increment i n pod dry weight which was observed in the present study. Thus, i f P f ( i ) < Gp, competition was evident and P^ was reduced by 10%. The value of 10% was estimated from the r e s u l t s of Hedley and Ambrose (1979). They observed that the maximum dry weight attained by plants which were 80% shaded, was 10 times lower than the unshaded p l a n t s . It i s therefore estimated that source supply i s reduced by 10% with increasing source l i m i t a t i o n . - 191 -7.3 Data Simulation The growth data of the pod with the highest maximum dry weight in t h i s study was used to derive the equation for the sink function of an depict best the growth of a pod with unlimited source supply. A l o g i s t i c curve was f i t t e d to the data. The independent v a r i a b l e , time, ranged from 0 to 30 days, with zero being the time of flowering and maximum growth a c t i v i t y occurring at t = 18. From the actual data, maximum absolute growth rate was observed at 18 days a f t e r flowering. The derived sink function which i s the f i r s t d e r i v a t i v e of the l o g i s t i c curve i s : Stepwise polynomial regression was used to determine the growth equation for t o t a l pod dry weight (Wp). The absolute growth rates of the resp e c t i v e growth functions yielded estimates of t o t a l sink a c t i v i t y and net a s s i m i l a t e supply. The equations were: where, DAP = number of days a f t e r p l a n t i n g , for t o t a l pod growth and i n d i v i d u a l pod. These data were selected because they were thought to a ( i ) = 3.2 exp (-0.4t)/[l + 4.0 exp (- 0 . 4 t ) ] 2 (34) = A ( t o t a l ) = -1.6282 x 0.034 DAP (35) 41 - P N = ° - 5 8 (36) f o r net a s s i m i l a t e supply. - 192 -7.4 Results and Discussion The simulated model [Figure 7.1(a)] indicated a stepwise reduction i n y i e l d p o t e n t i a l . For example at 80 DAP, maximum dry weight of the pods at the f i r s t node was 1.9 g [Figure 7.1 ( a ) ] , wnereas that of the fourth node was only 1.5 g. This reduction was also apparent in the actual data [Figure 7.1 (b)] (maximum pod dry weight at the second node was 2.0 g, while that of the f i f t h node was 1.1 g) and i s consistent with the findings of Milbourn and Hardwick (1968), Hardwick and Milbourn (1967) and Hedley and Ambrose (1979). There were, however, some discrepancies between the simulated data and the actual data. F i r s t , the growth patterns of the simulated pods were asymptotic while the observed growth tended to dec l i n e during the l a t e r phase of growth. For example, at the second node the observed pod dry weight declined from 2.0 g at 77 DAP to 1.8 g at 80 DAP. In contrast the dry weight of the simulated pod at that same node remained at 1.8 g. over the same period. The model also d i f f e r s i n i t s representation of the growth of the pod at the f i r s t reproductive node. The simulation r e s u l t s imply a successive decrease i n pod weight at each node. However, the r e s u l t s of t h i s study and others (Hole and Scottj 1981, 1983) indic a t e that the maximum dry weight of the pod at the f i r s t node i s l e s s than that at the second node. From the actual data, maximum pod dry weight at the f i r s t node was 1.4 g compared with 1.9 g for the second node [Figure 7.1 ( b ) ] . The d i f f e r e n c e i n size i s thought to be due to competition among the pods at the two nodes Figure 7.1. Simulation of pod growth at first 7 nodes of garden pea. (a) simulated data (b) actual data for Dark Skin Perfection. - 194 -and between the pods at t h e ' f i r s t node and the developing leaves. Since the proposed model only accounts for the e f f e c t s of competition of pods on subsequent nodes and does not adjust for the sink, strength of the newly developing leaves, growth of the pod at the f i r s t node may be overestimated. In conclusion, the model was successful in portraying the dynamics of f r u i t growth in terms of the r e l a t i o n s h i p between the sink and source. Moreover, the model can e a s i l y be modified to simulate the growth of more than one pod per node and the s p e c i f i c c o n t r i b u t i o n of the leaves at that node to the growth of these pods. For example, assuming that the leaves at a p a r t i c u l a r node are the sole suppliers of photosynthetic material to the pods at that node, then i n equation (28) can be substituted with p N L ( i ) [where p N L ( i ) ^ s t n e net assimi l a t e produced by the leaves at node ( i ) ] . S i m i l a r l y , r e l a t i v e sink function [ S f ( i ) ] may be derived from the r a t i o of the sink a c t i v i t y of an i n d i v i d u a l pod [ a ( i j ) ] and the absolute growth rate of the pods at the p a r t i c u l a r node. i . e . , S f ( i ) = a ( i j ) / d ^ ( i ) where, a ( i j ) i s the absolute growth rate of pod ( j ) at node i (derived e m p i r i c a l l y ) , and ^ P ( i ) i s t n e t o t a l dry weight of the pods at node ( i ) . This new model could prove quite useful in understanding the dynamics of pod growth at sub-organizmal l e v e l s of organization. - 195 -CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Conclusions The following conclusions are drawn, based on the r e s u l t s of the present study: 1. Since seed i n o c u l a t i o n had no noticeable e f f e c t on y i e l d t h i s agronomic p r a c t i c e i s not necessary under the s o i l conditions at the U n i v e r s i t y of B r i t i s h Columbia F i e l d Laboratory. 2. The main m u l t i p l i c a t i v e components of plant biomass i n the garden pea were: stem length and average l e a f area. Average l e a f area a f f e c t e d biomass v a r i a b i l i t y both d i r e c t l y and i n d i r e c t l y , stem length acted i n d i r e c t l y and inverse l e a f weight r a t i o acted d i r e c t l y . Thus, i n order to improve dry matter production in the pea, researchers should select for t a l l v a r i e t i e s with large leaves. 3. Since inverse l e a f weight r a t i o i s an index of the extent of the a s s i m i l a t o r y system on a dry weight b a s i s , the s i g n i f i c a n c e of t h i s component implies that l e s s l e a f y plants are better producers of dry matter i n the pea. Hence, agronomic practices which reduce the number of leaves per plant (e.g., high plant density or the - 196 -use of c u l t i v a r s such as the new mutant genotypes) should be encouraged. 4. Stem length, average l e a f area, reproductive e f f o r t and average seed f r e s h weight were the major components of y i e l d v a r i a b i l i t y . Since stem length and average l e a f area were also s i g n i f i c a n t components of plant biomass v a r i a b i l i t y , t h e i r importance i n the present y i e l d model s i g n i f i e s the value of the photosynthetic source during the reproductive phase. Increased stem length would be more desi r a b l e for the dried pea industry than for processing unless t h i s t r a i t i s accompanied by more synchronous f r u i t growth. Average seed weight, on the other hand i s important i n the processing industry only u n t i l the time of optimum maturity. 5. S i g n i f i c a n t component compensation between the vegetative components and average seed weight rendered these components unsuitable i n s e l e c t i n g for improved y i e l d as well as enhanced photosynthetic supply. Reproductive e f f o r t , however, was not adversely a f f e c t e d by the r e l a t i o n s h i p and i s therefore a favourable t r a i t for further evaluation studies. 6. The number of nodes, pod set and inverse leaf weight r a t i o made s i g n i f i c a n t , d i r e c t contributions to y i e l d v a r i a b i l i t y . Stem length acted i n d i r e c t l y through L^/S thus t h i s l a t t e r t r a i t , l i k e stem length, i s more valuable to the dried pea industry. - 197 -Since the pea i s s e l f p o l l i n a t i n g , pod set would be enhanced by ensuring adequate photosynthetic supply to the reproductive nodes as well as providing a s u i t a b l e microclimate in the crop canopy. The s i g n i f i c a n c e of inverse l e a f weight r a t i o implies that the e f f i c i e n c y of the a s s i m i l a t o r y system i s more important than i t s extent. 7. E a r l y Frosty had higher y i e l d s than Dark Skin P e r f e c t i o n . The d i f f e r e n c e in y i e l d resulted from contrasting morphology and growth patterns of the two c u l t i v a r s . The former (Early Frosty) was shorter (10 to 14 nodes), matured e a r l i e r and had a higher harvest index than Dark Skin P e r f e c t i o n (17 to 20 nodes). Thus, the e f f i c i e n c y of p a r t i t i o n i n g of dry matter in the pea i s as important as the supply of photosynthetic m a t e r i a l , and more important than the p o t e n t i a l sink load i n the determination of pea y i e l d s . 8. There were two periods during the reproductive phase when the source supply was c r u c i a l . The occurrence and extent of these periods d i f f e r e d between c u l t i v a r s . However, the f i r s t period would be expected'to be more important when growing peas for the vi n i n g industry because the f r u i t s at the lowest reproductive nodes would be at r i s k . The second phase i s thought to be more s i g n i f i c a n t for the dried pea industry because the most d i s t a l pods are vulnerable. - 198 -9. Since the net rate of accumulation of dry matter in the leaves rose i n response to increasing pod growth a c t i v i t y , i t i s concluded that pod growth (or more s p e c i f i c a l l y seed growth) controlled the photo-synthetic a c t i v i t y of the leaves. Moreover, improved y i e l d s i n the garden pea depended not only on the rate of dry matter accumulation in the reproductive s t r u c t u r e s , but also on the attainment of maximum source a c t i v i t y at the time of highest sink demands. 10. The methods of a n a l y s i s applied i n t h i s study p a r t i c u l a r l y the combined approach ( J o l l i f f e and Courtney, 1984) have proved u s e f u l in the study of y i e l d v a r i a b i l i t y and the dynamics of reproductive growth. Unlike c l a s s i c a l growth analysis methods used by e a r l i e r researchers, t h i s approach has quantified the contributions of non-leaf components to o v e r a l l pod growth. In so doing, one of the main objections to the i n a p p l i c a b i l i t y of previous techniques has been overcome. 8.2 Recommendations The following areas are recommended for further i n v e s t i g a t i o n : 1. A more d e t a i l e d study should be performed to evaluate the a c t i v i t y of the leaves at each reproductive node and a comparison should be made of t h i s a c t i v i t y with that of the leaves at the vegetative nodes. - 199 -Reproductive e f f o r t (Fjj/Wy) was the only s i g n i f i c a n t y i e l d component in which compensatory r e l a t i o n s h i p s did not a f f e c t y i e l d adversely. In a d d i t i o n , there were s i g n i f i c a n t c u l t i v a r d i f f e r e n c e s i n the value of t h i s component. Consequently, F^ /W^  should be evaluated as a s u i t a b l e t r a i t i n s e l e c t i n g for Improved y i e l d s . The r e s u l t s of the combined analysis indicated that the rate of establishment of the l e a f canopy i s as important as the rate of accumulation of dry matter in the pods. Furthermore, the two c u l t i v a r s studied d i f f e r e d in t h e i r patterns of r e l a t i v e l e a f area growth r a t e . Thus, the v a r i a b i l i t y of this p h y s i o l o g i c a l t r a i t ( r e l a t i v e l e a f growth rate) should be investigated (a) to determine i t s value for future breeding and s e l e c t i o n of programs and (b) in recommending c u l t u r a l p r a c t i c e s which enchance the r a t e . The v a r i a b l e , P^, i n the dynamic model (Chapter 7) can be predicted from equations i n v o l v i n g l i g h t i n t e n s i t y and temperature, according to Thornley (1976) and Schapendonk and Brouwer (1984). 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Technoraetrics 16: 1-11. - 208 -NOMENCLATURE AND SYMBOLS a Sink function of an i n d i v i d u a l pod A Sink function of t o t a l number of pods per plant AGR Absolute Growth Rate , ANOVA Analysis of Variance DAP Days a f t e r planting DSP Dark Skin P e r f e c t i o n E' Instantaneous unit l e a f rate E Mean unit l e a f r a t e E^ Instantaneous unit l e a f rate of pod wall E^ Instantaneous unit l e a f rate of leaves E ^ Instantaneous unit l e a f rate of non-leaf components Ep Instantaneous unit l e a f rate of pods Eg Instantaneous unit l e a f rate of stem E„ Instantaneous unit l e a f rate of seeds Se EF Early Frosty F Leaf Area Ratio F^j Number of flowers Gp P o t e n t i a l growth of pod 1 L e a f l e t length 1 A L e a f l e t area L A Leaf area per plant L^j Number of leaves per plant LWR Leaf Weight Ratio P Number of pods per plant - 209 -D a i l y increment of i n pod dry weight P Pod length Li P^J Net d a i l y supply of a s s i m i l a t e to the pod P^k Net d a i l y supply of a s s i m i l a t e produced by the leaves of a p a r t i c u l a r node R' Instantaneous r e l a t i v e growth r a t e ' R Mean r e l a t i v e growth rate R C Instantaneous r e l a t i v e growth rate of pod wall % / w v Instantaneous r e l a t i v e growth rate t o t a l vegetative dry weight of the number of flowers per Instantaneous r e l a t i v e growth rate of l e a f dry weight R T L A Instantaneous r e l a t i v e l e a f area growth rate R L A / L N Instantaneous r e l a t i v e growth rate of average l e a f area R L N / S . Instantaneous stem length r e l a t i v e g rowth rate of the number of leaves per RNL Instantaneous r e l a t i v e growth rate of the non-leaf components R P Instantaneous r e l a t i v e growth rate of pods V F N Instantaneous flower r e l a t i v e growth rate of the number of pods per V Instantaneous r e l a t i v e growth rate of stem length RSe Instantaneous r e l a t i v e growth rate of the number of seeds RSe/P Instantaneous r e l a t i v e growth rate of the number of seeds per pod *W Instantaneous r e l a t i v e growth rate of whole plant Instantaneous r e l a t i v e growth rate of stem Instantaneous r e l a t i v e growth rate of seed dry weight RW Se/Se Instantaneous r e l a t i v e growth rate of average seed weight Instantaneous r e l a t i v e growth rate of vegetative organs - 210 -RGR Re l a t i v e Growth Rate s S t i p u l e length S A S t i p u l e area S Stem length Sf Relative sink f u n c t i o n SLA S p e c i f i c Leaf Area T MAX Maximum d a i l y temperature (°C) T MIN Minimum d a i l y temperature (°C) T L Minimum temperature below which pea growth does not occur (5.5°C) ULR Unit Leaf Rate w Dry weight per pod W T o t a l dry weight per plant w c T o t a l pod w a l l dry weight per plant W L T o t a l l e a f dry weight per plant WNL T o t a l dry weight per plant of non-leaf components W P To t a l pod dry weight per plant w s T o t a l stem dry weight per plant W S e T o t a l seed dry weight per plant W S e ( F ) T o t a l seed f r e s h weight per plant W V To t a l vegetative dry weight per plant Y Y i e l d - 211 -APPENDIX A STATISTICAL APPENDICES A . l Test of E q u a l i t y of Slopes and Intercepts The model: y = B Q k + 3 l k X where k = 1, 2, . . . , m and m i s the number of groups. If the regression l i n e s of a l l the groups are the same, then the n u l l hypotheses are: H 0 1 : 301 = 302 = * ' * 30m and H Q 2: S n « B 1 2 = . . . - S l m Thus, the reduced model i s : y = 3 Q + X [A.2] The test s t a t i s t i c : (RSS R - R S S p ) / ( d f R - d f p ) F RSS F/df p [ A ' 3 ] where RSS D = r e s i d u a l sum of squares of the reduced model d f R = degrees of freedom of reduced model = n-2 RSS,-, = r e s i d u a l sum of squares of the f u l l model = ERSS r m i . e . , the sum r e s i d u a l sum of squares for each group. m df„ = degrees of freedom of f u l l model Z (n, - 2) . k-1 c r i t i c a l F = F ( d f _ d f } d f R F ' F - 212 -A.2 Weighted Least Squares Since the re s i d u a l s of the mu l t i p l e regression equation for the p r e d i c t i o n of t o t a l dry weight indicated that the error was h e t e r o s c l a s t i c , i t was necessary to use a weighted least squares regression. The ANOVA for t o t a l dry weight revealed that blocking e f f e c t s were s i g n i f i c a n t . Thus, the r e s i d u a l s were grouped by block using the method outlined by Chatterjee and P r i c e (1977). The unweighted model i s : W = a + bjS + b 2 L A + b ^ + b 4W L [A.4] It i s assumed that the r e s i d u a l variance of each block i s comprised of two components: ( i ) c± an unknown weighting f a c t o r which i s unique to each 2 block and ( i i ) a the common variance. Thus, the weighted model i s : W. . L A Iv, W = 3 n — +• 6. — + 3 0 — + 3, — + 6. — + e, . [A.5] c. 0 c. 1 c. 2 c . 3 c. 4 c. i i l I i i i i J 2 where e-jj has a variance of o . Thus : c. = ( s 2 / S 2 ) 1 / 2 [A.5] l i 2 2 2 where s. = Ze./n , where n = 8 = no. of blocks and e. = r e s i d u a l mean l l ' i square for each block. - 213 -C a l c u l a t i o n of I 2 I 2 ( S STOTAL ~ S S R E S ^ S S T O T A L n - 2 S STOTAL = * ( y o b s " y ) i=l n A 2 S S R E S = * ^ o b s - ^ i=l = actual value of l e a f dry weight = predicted value of l e a f dry weight, - 214 -APPENDIX B VARIANCES OF GROWTH INDICES B. l Rates The rates are calculated as the f i r s t d e r i v a t i v e s of the f i t t e d s p l i n e regressions. These spline functions are represented by the following formula (Wold, 1974): y = P ^ x ) = a. + b.x + c.x + d,x 3 [B.l] i 1 1 1 i ***** S±-l < x < Z±> (5Q = 5m+l = - ) m d P j ( 5 i ) = P j L + i a i ) where, Pj = i s the kth d e r i v a t i v e of the j t h polynomial piece. £^ ( i = 1, 2, . . . m) are the knots * = f i t t e d value of the growth v a r i a t e x = time (days a f t e r planting) Thus the f i r s t d e r i v a t i v e , P!(x) = b. + 2c.x + 3d.,x2 ' i 1 i i var (y) = o z ( l + l/n) + E(x - x ) z V(b ) 1 3 _ _ + 2 E E (x - x.)(x - x.) cov (b., b.) i=l i<i 2 1 J i<j where V(b^) = variance of b^ cov (b^bj) = covariance between b^ and b.. [B.2] - 215 -o 2 = residual mean square B.2 Ratios Three of the derived growth i n d i c e s were simple r a t i o s of the f i t t e d primary v a r i a t e s . These r a t i o s are: l e a f area r a t i o (F = L A/W), l e a f weight r a t i o (WL/W) and s p e c i f i c l e a f area ( L A / W L ) . Let Z be the numerator and Y be the denominator of these r a t i o s . Then the variance i s calculated using the formulae of Hunt and Parson (1981) *MSEy + MSE Z - 2C0V Z V [B.3] Unit l e a f rate (E) This index was derived from the following formula from Hunt and Parsons (1981) E = R/F [B.4] The variance i s 1 [ v a r ( R ) _ 2 R cov (R,F) + R 2 var(F) [ ] J > 5 ] F F 2 * 2 MSE = mean square error of Y = E (Y obs - Y . f i t ) /5 i-1 • n 2 MSE 7 = mean square error of Z = E (Z.obs - Z . f i t ) /5 L i=l 1 1 n n C0V 7 V = covariance of Z and Y = I E (Y.obs - Y . f i t ) ( Z . o b s - Z . f i t ) / 5 L i i=j * i - 216 -APPENDIX C NITROGEN FIXATION The acetylene-ethylene assay (Hardy et a l . 1968) was used to determine the f i x a t i o n a c t i v i t y i n the root nodules at the onset of flowering (53 DAP). Table C.l below, i s a summary of the r e s u l t s of the gas chromatography readings for each plant measured. Table C.l. E f f e c t of seed i n o c u l a t i o n on C2H2~reducing* a c t i v i t y i n Dark. Skin P e r f e c t i o n and Early Frosty Block Dark Skin P e r f e c t i o n E a r l y Frosty Numb er Not Inoculated Inoculated Not Inoculated Inoculated 1 107.89 0.0 8.24 25.05 2 15.70 0.0 0.0 21.10 3 6.19 12.22 6.91 0.0 4 0.0 0.0 0.0 7.45 5 16.20 0.0 0.0 15.01 6 14.07 0.0 0.0 9.64 7 8.18 0.0 0.0 0.0 8 0.0 4370.9 82.63 4076.3 Treatment e f f e c t s were tested by a n a l y s i s of variance. The analysis (Table C.2) reveals that there was no s i g n i f i c a n t d i f f e r e n c e i n the l e v e l of f i x a t i o n among treatments. *Acetylene (C2H2) i s reduced to ethylene ( 0 2 ^ ) in a rea c t i o n s i m i l a r to the reduction of N2 to NH3 in nitrogen f i x a t i o n . Thus t h i s assay i s a good index of f i x a t i o n a c t i v i t y i n pea root nodules. - 217 -Table - C . 2 ANOVA of e f f e c t s of seed i n o c u l a t i o n on nitrogen f i x a t i o n a c t i v i t y i n two c u l t i v a r s of peas Source df SS ' ' MS F Blocks 7 C u l t i v a r s 1 Inoculum 1 Non a d d i t i v i t y 1 E r r o r 21 T o t a l 31 1 . 5 8 x 1 0 7 2 7 9 4 . 2 2 . 1 4 x 1 0 6 5512.4 1.54 x 1 0 6 3 . 3 3 x 1 0 7 2 . 2 5 x 1 0 6 3 . 0 8 * 2 7 9 4 . 2 0 . 0 0 4 2 . 1 4 x 1 0 6 2 . 9 5512.4 0 . 0 0 7 7 . 3 x 1 0 5 * S i g n i f i c a n t at 5% l e v e l ^Since there was no determine the c u l t i v a r x a d d i t i v i t y (Tukey, 1949) r e p l i c a t i o n the blocks inoculum i n t e r a c t i o n , was used. , i t was d i f f i c u l t to Thus, the test for 8 SS = [ j n o n - a d d i t i v i t y , , k=l 2 2 E E y. . i y. y . -i - 1 j = i y i « -J y • • • ( s s c + S S I + S S B L + 2 3 T ^ ) ] 2 /32 [SS C x S S 1 x SS B L] where, SSQ = sum of squares for c u l t i v a r s , SSj = sum of squares for inoculum and SSgL = sum of squares f o r blocks. - 218 -APPENDIX D COMPUTER PROGRAMS D.l P-Spllne Progr— THIS PROGRAM FINDS THE OPTIMUM NUMBER AND KNOT POSITIONS FOR FITTING B-SPLNES TO THE GROWTH DATA.THE VARIABLES ARE: X-DAYS AFTER PLANTING, Y-GROWTH VARIATE. K-ORDER OF POLYNOMIAL + 1. L-NUMBER OF KNOTS • 1. YFIT*INTERPOLATED VALUES. VFIT1-FIRST DERIVATIVE N-NUMBER OF OBSERVATIONS AND T-KNOT POSITIONS. 1 SUBROUTINE SETDAT(ICOUNT) 2 IMPLICIT REAL*8(A-H.0-Z) 3 COMMON /0ATA$/X(2OO).Y(2O0).WT(2OO),N 4 COMMON/APROX$/BREAK(100).L,K 5 COMMON/INDS/BCO.FUN,PCO.NTIMES.ADOBRK.PLOT,COV 6 LOGICAL BCO,FUN,PCO,PLOT,COV 7 IF(ICOUNT.GT.O)STOP B ICOUNT-ICOUNT-M 9 DIMENSION T(21).WORK 1(4,9),WORK2(9),BCOEF(9),VS(21), 10 1TS(21), W0RK3(4,4) ,C0EF(4,9),YL(70). 11 2YFIT(70).VFIT1(70).VFIT2(70).0IFF(70).RY(70),XX(70) 12 00 59 1-1.20 13 TS(I)-0 14 59 CONTINUE 15 C SET ORDER OF POLYNOMIAL AND NUMBER OF KNOTS AND NUMBER OF 16 C OBSERVATIONS 17 K«4 1B M*1*K 19 L-2 20 N-11 21 C READ IN DATA 22 DO 10 1-1.11 23 READ(5,1)X(I),Y(D 24 1 F0RMAT(3X,F3.0.50X,F10.5) 25 C CONVERT X TO DAYS AFTER PLANTING AND TRANSFORM TO LOGE(Y) 26 X(I) «50.0+(X(l)-2.0)*3 27 V(I )*DLOG(Y(I)) 2B 10 CONTINUE 29 C SET HEIGHTS 30 DO 5B 1*1.11 31 WT(I)*1.0 32 58 CONTINUE 33 C SET KNOT POSITIONS 34 DO 20 1*1.K 35 T(I)«X(1) 36 20 CONTINUE 37 T(5)-65.0 38 T(6)*X(11) 39 T(7)*X(11) 40 T(8)*X(11) 41 T(9)-X(11) 42 NTIMES-0 43 C FIT BSPLINE 44 CALL DL2APP(T.M,K,W0RK1.W0RK2.BC0EF.N.X.Y.WT) 45 CALL DBSPLP(T.BCOEF,M.K.WORKS.BREAK.COEF.L) 46 XX(1)«50.0 47 DO 40 1-1.30 48 XX(I+1)*XX(I)*1 49 40 CONTINUE 50 C CALCULATE INTERPLOATED VALUES AND FIRST DERIVATIVES 51 DO 140 1-1.31 52 YFIT(I)*DPVALU(BREAK.C0EF.L.K,XX(I),O) 53 YFIT1(I)-DPVALU(BREAK.C0EF.L.K.XX(I).1) 54 DIFF(I)*Y(I)-YFIT(I) 55 RY(I)*YFIT1(I) 56 140 CONTINUE 57 DO 60 1*1.31 58 WRITE(6.2)XX(I).YFIT(I),DIFF(I),RY(I) 59 2 F0RMAT(F3.0.3F13.6) 60 60 CONTINUE 61 PLOT*.FALSE. 62 BCO*.TRUE. 63 FUN*.TRUE. 64 PCO*.TRUE. 65 COV*.FALSE. 66 NTIMES*4 67 RETURN 68 END - 219 -D.2 Cubic Spline P r o g r a a 1 C SPLINE FITTING PROGRAM USING CUBIC SPLINES. 2 IMPLICIT REAL*8(A-H,0-Z) 3 DIMENSION A(60),B(60).BS(60),X(60),Y(60),DY(60),R(60) 4 DIMENSION S(2),W(300),XX(61),YY(61),YY1(61).YY2(61) 5 DIMENSION BB(61),BBS(61),XA(61),YE(61),RY(61).DDY(61) 6 1,RB(61),YB(61),SD(61) ,SDB(61),YA(61) 7 N=20 8 C READ IN DATA 9 DO 7 1=1,20 10 READ(5,1,END=11)A(I),B(I) 1 1 1 FORMAT(3X.F3.0.10X.F10.5) 12 1 1 CONTINUE 13 7 CONTINUE 14 DO 117 1=1.20 15 BS(I)=1 16 1 17 CONTINUE 17 DO 99 1=1,20 18 BB(I)=B(I) 19 BBS(I)=BS(I) 20 99 CONTINUE 21 S(1)=0.0 22 C TRANSFORMATION OF DEPENDENT VARIABLES AND ASSIGNMENT TO AXES 23 DO 2 1=1,20 24 X(1)=((A(I)-1.0)*3.0)+21.0 25 Y(I )=DLOG(BB(I)) 26 DY(I)=BBS(I) 27 2 CONTINUE 28 C TO CALCULATE PARAMETERS FOR CUBIC SPLINE 29 CALL DSPLFT(X,Y,DY,S,20,W, &1O0) 30 C TO GENERATE FITTED POINTS AND DERIVATIVES 31 XX(1)=21.0 32 DO 3 I»1,60 33 XX(I+1)»XX(I)+1.0 34 3 CONTINUE 35 CALL DSPLN(XX,YY,YY1,YY2,61,&20O) 36 C ASSIGNING NAMES TO DERIVATIVES AND TRANSFORMED DATA 37 DO 4 K=1.61 38 XA(K)=XX(K) 39 YE(K)=YY(K) 40 RY(K)=YY1(K) 41 4 CONTINUE 42 DO 67 1=1.21 43 LL = I 44 MM=1+(I-1)*3 45 IF(LL.EO.15)G0 TO 67 46 IF(LL.GE.16)LL=LL-1 47 R(LL)=RY(MM) 48 YA(LL)=YE(MM) 49 67 CONTINUE 50 CALL JKNIFE(X,Y,DY,R,N,YB,RB,SD.SDB,S(1).RS.RRS) 51 WRITE(6,89) RS.RRS 52 89 F0RMAT(2F10.5) 53 IDF=N-1 54 CALL TVAL(IDF,T1,T2,T3) 55 DO 74 1=1,20 56 CALL C0NLIM(Y(I).T1,SD(I).AL,AU) 57 WRITE(6,54)X(I),Y(I),YB(I),AL,AU,SD(I) 58 54 F0RMAT(F4.0,5F1O.4) - 220 -59 74 CONTINUE 60 DO 75 1-1,20 61 CALL C0NLIM(R(I).T1.SDB(I).AL1,AU1) 62 WRITE(6,54)X(I).RB(I).AL1.AU1.S0B(I) 63 75 CONTINUE 64 C TO FIT CUBIC SPLINES TO UNTRANSFORMED DATA 65 S1-0.0 66 DO 5 L-1.20 67 X(L)=((A(L)-1.0)*3.0)+21.0 68 Y(L)«=BB(L) 69 DY(L)*BBS(L) 70 5 CONTINUE 71 CALL DSPLFT(X,Y.DY.S1.20,W.&300) 72 CALL DSPLN(XX,YY,YY1,YY2.61.8.400) 73 DO 6 1=1,61 74 DDY(I)=YY1(I) 75 6 CONTINUE 76 C WRITE NEW FILE OF DATA FOR PLOTTING 77 DO 8 1-1.61 78 WRITE(6,22)XA(I),YE(I),RY(I),DDY(I) 79 22 F0RMAT(F4.0,3F12.5) 80 8 CONTINUE 81 STOP 82 100 STOP 1 83 200 STOP 2 84 300 STOP 3 85 400 STOP 4 86 END 87 SUBROUTINE TVAL(ID.T1,T2.T3) 88 REAL*8 E(20.3),T1.T2,T3 89 DATA E/12.706.4.303.3.182.2.776,2.571,2.447,2.356. 90 +2.306,2.262,2.228.2.201,2.179.2.160,2.145,2.131, 91 +2.12.2.11.2.101.2.093.2.086,63.657,9.925,5.841.4.604, 92 +4.032.3.707,3.499,3.355.3.25,3.169.3.106,3.055.3.012, 93 +2.997,2.947,2.921 ,2.898,2.878,2.861.2.845,636.619.31.598. 94 +12.924.8.61.6.869.5.959.5.408.5.041,4.781,4.587. 95 +4.437,4.318,4.221.4.14.4.073,4.015.3.965,3.922, 96 +3.B83.3.B5/ 97 IF(ID.LE.0)WRITE(6,9CO) 98 900 FORMAT(/'ERROR IN DEGREES OF FREEDOM FOR T-VALUES') 99 IF(10.GE.1.AND.ID.LE.20)G0 TO 720 100 IF(ID.LE.120)G0 TO 710 101 IF(ID.GT.120.AND.ID.LE.200)GO TO 700 102 T1-1.96 103 T2=2.576 104 T3-3.291 105 RETURN 106 7O0 T1»1.992-10*.O002 107 T2-2.641-ID*.0002 108 T3-3.4225-ID*.0004125 109 RETURN 110 710 T1=((((((ID*8.0520028E-15-2.8813791E-12)*ID+ 1 1 1 12.7662442E-10)*ID+1.8674944E-8)*ID-5.7885593E-6) 112 1*I0+4.7918783E-4)*ID-1.8915886E-2)*ID+2.3151075 113 T2-((((((ID*1.9464622E-14-7.3252763E-12)*1D+ 114 17.8915081E-10)MD+2.3006791E-8)*ID-1.1797539E-5) 115 1*10+1.0292022E-3)*ID-4.1164416E-2)*ID+3.3449869 116 T3=((((((ID*3.8054493E-14-1.42063E-11)*ID+ - 221 -1 17 11.5368801E-9)*ID+5.4360301E-8)*ID-2.5015934E-5) 118 1*ID+2. 186612E-3)*ID-8.7791089E-2)*ID+4.917854 1 19 RETURN 120 720 T1=E(ID,1) 121 T2=E(ID,2) 122 T3=E(ID,3) 123 RETURN 124 END 125 SUBROUTINE C0NUM( A , TV. AS, ALL .ULL) 126 REAL*8 A,TV,AS,ALL,ULL,UD 127 • ALL=A-AS*TV 128 ULL=A+AS*TV 129 IF(ULL.GE.ALL)G0 TO 920 130 UD=ULL 131 ULL=ALL 132 ALL=UD 133 920 RETURN 134 END 135 SUBROUTINE JKNIFE(X,Y,DY,RY,N,UNB,UNBR,SE,SEB.S,S1.S2) 136 IMPLICIT REAL*8(A-H,0-Z) 137 DIMENSION X(61 ) , Y(61 ) , OP 1(61 ,61 ) ,X1 (61 ) , Y1(61 ) ,DY('61 ) , 138 1UNB(61),SUM(61).Z(61),DSUM(61),ZY(61).DZY(61),W(300),ZRY(60) 139 1.RY(61),SEB(61),SE(61).QP2(61.61).UNBR(61),Y11(60),Y12(60) 140 1,SS(61).DSS(61) 141 N1=N-1 142 S1=0 143 S2=0 144 DO 67 1=1,N 145 SUM(I)=0 146 DSUM(I)=0 147 SS(I)=0 148 DSS(I)=0 149 67 CONTINUE 150 DO 2 I=1,N 151 DO 3 J-1.N1 152 IF(J.GE.I)GO TO 13 153 Z(J)=X(J) 154 ZY(J)=Y(J) 155 ZRY(J)=RY(J) 156 DZY(J)=DY(<J) 157 GO TO 3 158 13 Z(d)=X(d+1) 159 ZY(J)=Y(J+1) 160 ZRY(d) = RY(J-M ) 161 DZY(d)=DY(J+1) 162 3 CONTINUE 163 CALL DSPLFT(Z,ZY.DZY,S,N1,W,&110) 164 DO 23 JJ=1,N1 165 X1(Jd)=Z(JJ) 166 23 CONTINUE 167 CALL DSPLN(X1,Y1,Y11,Y12.N1,&120) 168 DO 5 K=1,N1 169 0P1(I,K)=(N*ZY(K))-(N1*Y1(K)) 170 QP2(I,K)=(N*ZRY(K))-(N1*Y11(K)) 171 DO 15 11=1,N 172 IF(X1(K).NE.X(II))G0 TO 15 173 SUM(II)=SUM(II)+QP1(I,K) 174 DSUM(II)=DSUM(II)+QP2(I,K) - 222 -175 SS(II)-SS(II)+0P1(I.K)**2 176 DSS(II)»DSS(II)+QP2(I.K)**2 177 15 CONTINUE 178 5 CONTINUE 179 2 CONTINUE 180 DO 6 I"1,20 181 UNB(I)»SUM(I)/N1 182 UNBR(I)»DSUM(I)/N1 183 CF=(SUM(I)*»2)/N1 184 CFR=(DSUM(I)»»2)/N1 185 SE(I)«DSORT((SS(I)-CF)/(N1-1)) 186 SEB(I)«DSORT((DSS(I)-CFR)/(N1-1)) 187 S1-S1*(UNB(I)-Y(I))**2 188 S2»S2+(UNBR(I)-RY(I))*»2 189 6 CONTINUE 190 GO TO 12 191 110 STOP 192 120 STOP 193 12 RETURN 194 END - 223--D.3 Calculation of Variances of F i t t e d Values 1 C THIS PROGRAM CALCULATES THE CONFIDENCE LIMITS OF THE INTERPOLATED 2 C VALUES AND THEIR FIRST DERIVATIVES.THE VARIABLES ARE THE SAME AS 3 C DEFINED IN BSP. 4 IMPLICIT REAL*8(A-H,0-Z) 5 C0MM0N/DATA$/X(2OO),Y(200),WT(20O) ,N e COMMON/APROX$/BREAK(100),L,K 7 COMMON/INDS/BCO,FUN,PCO,PLOT,COV 8 LOGICAL BCO,FUN,PCO,PLOT.COV 9 DIMENSION WORK 1(4,7),W0RK2(7) ,BCOEF(7 ) ,W0RK3(4,4),DL(61), 10 1C0EF(4,7),YFIT(61),DU(61 ) ,Y 1 (61 ),S(61),S2(61),S3(61),DIFF(61) 1 1 2,C(10),A(10,10),AT(10.10),AV(10,10),T(13),Y2(61),YFIT1(61) 12 1,YFIT2(61),BK(3,3,4) 13 K = 4 14 M=1+K 15 L = 2 16 N=1 1 17 TS=0 18 TS2=0 19 TS3=0 20 SS=0 21 ICOUNT=1 22 NT=(L-1) 23 DO 43 1=1,NT 24 READ(5,69)IV,IK,(BK(IV,IK,d) ,0=1,4) 25 69 F0RMAT(2I3,4F6.1 ) 26 43 CONTINUE 27 DO 1 1=1,11 28 READ(5,2)IT,X(I),Y(I) 29 2 FORMAT(I3,F3.0,10X.F10.5) 30 X(I)=50.0+(X(I)-2)*3.0 31 WT(I ) = 1 32 1 CONTINUE 33 59 DO 231 1=1,11 34 Y(I)=DLOG(Y(I ) ) 35 231 CONTINUE 36 C KNOT SEQUENCE 37 DO 32 1=1,4 38 T(I)=X(1) 39 T(I+M)=X(11) 40 32 CONTINUE 41 DO 57 J=2,L 42 d1=d-1 43 T ( K+d1)=BK(ICOUNT,d1,IT) 44 57 CONTINUE 45 NTIMES=0 46 CALL DL2APP(T,M,K,W0RK1,W0RK2,BCOEF,N,X,Y,WT) 47 CALL DBSPLP(T.BCOEF,M,K,W0RK3,BREAK,COEF,L) 48 DO 7 1 = 1, 1 1 49 YFIT(I)=DPVALU(BREAK,COEF,L,K,X(I),0) 50 YFIT1(I)=DPVALU(BREAK,COEF,L,K,X(I ) ,1 ) 51 YFIT2(I)=DPVALU(BREAK,COEF,L.K,X(I ),2) 52 DIFF(I)=YFIT(I)-Y(I) 53 SS=SS+WT(I)*DIFF(I)**2 54 7 CONTINUE 55 IDF=N-L-3 56 C THE SUBROUTINE TVAL CALCULATES THE T-VALUE FOR THE DETERMINATION 57 C OF THE CONFIDENCE LIMITS. 58 CALL TVAL(IDF,TV,TV2.TV3) - 224 -59 C THE SUBROUTINE SP3FIT CALCULATES THE COVARIANCE MATRIX FOR USE IN 60 C DETERMINING THE VARIANCES. 61 CALL SP3FIT(L.T.M,BC0EF.A.IFAIL) 62 DO 9 1=1,11 63 C THE SUBROUTINE, VAR CALCULATES THE STANDARD ERROR OF THE FITTED VALUE 64 C FOR USE IN CALCULATING THE CONFIDENCE LIMITS. 65 CALL VAR(N,K,A,T,M,L,X(I)IV,V1,V2.IFAIL) 66 S(I) =DSORT(SS/IDF*V) 67 S2(I)=DS0RT(SS/IDF *V1) 68 S3(I)=DSQRT(SS/IDF *V2) 69 C THE SUBROUTINE CONLIM CALCULATES THE CONFIDENCE LIMITS. 70 CALL CONLIM(YFIT(I),TV,S(I),DL(I),DU(I)) 71 WRITE(6.19)X(I),Y(I).YFIT(I),DL(I),DU(I),YFIT1(I),S2(I) 72 19 F0RMAT(F3.O,6F15.4) 73 9 CONTINUE 74 DO 1 19 1 = 1 , 11 75 CALL C0NLIM(YFIT1(I),TV.S2(I),AL,UL) 76 WRITE(6,219)X(I),YFIT1(I),AL,UL 77 219 F0RMAT(F3.O,3F15.4) 78 119 CONTINUE 79 ICOUNT=ICOUNT+1 80 IF(IC0UNT.EQ.2) STOP 81 IF(IC0UNT.E0.3) GO TO 330 82 GO TO 166 83 220 DO 84 1=1,11 84 Y(I)=Y1(I) 85 84 CONTINUE 86 GO TO 59 87 330 DO 331 1=1,11 88 Y(I)=Y2(I) 89 331 CONTINUE 90 GO TO 59 91 166 RETURN 92 END 93 SUBROUTINE CONLIM(YF,T,VA,AL,AU) 94 IMPLICIT REAL*8 (A-H.O-Z) 95 DO 1 1=1,11 96 AL=YF-VA*T 97 AU=YF+VA*T 98 IF(AU.GE.AL)GO TO 5 99 A=AU 100 AU=AL 101 AL=A 102 1 CONTINUE 103 5 RETURN 104 END 105 SUBROUTINE VAR(N,K,A,T,M,L,X,V,V1,V2,IFAIL) 106 INTEGER U.UM1,UP3,W,LL 107 REAL*8 A(10,10).AT(10,10),AV(30),ROW(5),T(13). 108 1T1,T2.T3,T4,T5.T6,TEMP(10.10),SOL(10),RZ(10),IPERM(10), 109 1M1,M2,N1.N2.N3.X,V,V1.V2.P.E2.E3.E4,E5,VA.D.S.DEPS 110 NCAP3=L+3 111 IERROR=0 112 IF(X.LT.T(4).0R.X.GT.T(L+4))G0 TO 510 113 GO TO 520 114 510 IERRORM 115 GO TO 690 116 520 IF(N.LE.NCAP3)G0 TO 530 - 225 -117 GO TO 540 118 530 IERR0R=2 1 19 GO TO 690 120 540 CONTINUE 121 UM1=0 122 U = L 123 550 IF((U-UM1).LE.1)G0 TO 560 124 LL=(UM1+U)/2 125 IF(X.LT.T(LL+4))U=LL 126 IF(X.GE.T(LL+4))UM1=LL 127 GO TO 550 128 5GO CONTINUE 129 T1=T(U+1) 130 T2=T(U+2) 131 T3=T(U+3) 132 T4=T(U+4) 133 T5=T(U+5) 134 T6=T(U+6) 135 P=T4-T3 136 E2=X-T2 137 E3=X-T3 138 E4=T4-X 139 E5=T5-X 140 M2=E3/((T5-T3)*P) 141 M1=E4/((T4-T2)*P) 142 N3=E3*M2/(T6-T3) 143 N2=(E2*M1+E5*M2)/(T5-T2) 144 N1=E4*M1/(T4-T1) 145 DO 680 LV=1,3 146 LEVEL=LV-1 147 IF(LEVEL.EO.O)GO TO 600 148 IF(LEVEL.EO.1)G0 TO 610 149 N3=6.0*M2/(T6-T3) 150 N2=6.0*(M1-M2)/(T5-T2) 151 N1=-6.0*M1/(T4-T1) 152 R0W(4)=N3 153 R0W(3)=N2-N3 154 R0W(2)=N1-N2 155 R0W(1)=-N1 156 GO TO 620 157 600 R0W(4)=E3*N3 158 R0W(3)=E2*N2+(T6-X)*N3 159 R0W(2)=(X-T1)*N1+E5*N2 160 R0W(1)=E4*N1 161 GO TO 620 162 610 R0W(4)=3.0*N3 163 R0W(3)=3.0*(N2-N3) 164 R0W(2)=3.0*(N1-N2) 165 R0W(1)=-3.0*N1 166 620 CONTINUE' 167 UM1=U-1 168 UP3=U+3 169 VA=0.0 170 DO 670 d=U,NCAP3 171 I F ( A ( J,1).GT.O.O)G0 TO 630 172 IERR0R=3 173 GO TO 690 174 630 IF(U.LE.UP3)G0 TO 650 - 226 -175 JM4=J-4 176 D=0.0 177 DO 640 1=1,3 178 ROW(I)=R0W(1+1) 179 IAA1=I+JM4 180 IM5=5-I 181 D=D-R0W(I)*A(IAA1, IM5) 182 640 CONTINUE 183 ROW(4)=D/A(J,1) 184 D=R0W(4) 185 GO TO 670 186 650 UMU=J-U 187 JP1=J+1 188 D=R0W(dMU+1) 189 IF(JMU.LT.1)G0 TO 665 190 DO 660 I=1,uMU 191 W=UM1+I 192 IDA1=JP1-W 193 660 D=D-R0W(I)*A(W,IDA1) 194 665 ROW(JMU+1)=D/A(J,1) 195 D=ROW(JMU+1) 196 670 VA=VA+D**2 197 IF(LEVEL.E0.O)V=VA 198 IF(LEVEL.EO.1)V1=VA 199 IF(LEVEL.E0.2)V2=VA 200 680 CONTINUE 201 690 IFAIL=IERROR 202 100 RETURN 203 END 204 SUBROUTINE SP3FIT(L,T,M,BCOEF,A,IFAIL) 205 IMPLICIT REAL*8(A-H,0-Z) 206 COMMON/DATA$/X(200),Y(200).WT(200),N 207 REAL*8 A(10,10).AT(10.10).AV(30),ROW(4),C(10),B(100) 208 REAL*8 SS.T0.T1.T2,T3.T4,T5,T6.N1,N2,N3.SIGMA,T(13), 209 +WI,XI.D4,D5,D6,D7,D8,D9,E5,E4,E3,E2,CR0W,BC0EF(7), 210 +RELMNT,D,S,SINE.COSINE,ACOL.AROW.CCOL.DABS.DSORT 211 INTEGER R 212 IERR0R=4 213 IF(L.LT.1.OR.M.LT.(L+3))G0 TO 8500 214 L3= L+3 215 LM1= L -1 216 DO 7275 1=1,4 217 T(I)=X(1) 218 11= L3+I 219 7275 T(I1)=X(N) 220 IERR0R=1 221 IF(T(5) .LE.X( 1) .OR.T( LM1+4).GE.X(N))G0 TO 8500 222 JBEG= L-2 223 DO 7300 J1=1.JBEG 224 J=JBEG+i-U1 225 IF(T(J+4).GT.T(J+5))G0 TO 8500 226 7300 CONTINUE 227 IERR0R=2 228 DO 7400 I=1,N 229 IF(WT(I).LE.O) GO TO 8500 230 7400 CONTINUE 231 IERR0R=3 232 B( 1)=X(1) - 227 -233 0=2 234 DO 7500 1=2,N 235 IF(X(I).GT.B(0-1))G0 TO 7405 236 IF(X(I).LT.B(0-1))G0 TO 8500 237 GO TO 7500 238 7405 B(0)=X(I) 239 0=0+1 240 7500 CONTINUE 241 R=0-1 242 IERR0R=4 243 IF(R.LT. L3)G0 TO 8500 244 IERR0R=5 245 DO 7600 0=1,4 246 IF(O.GE.L)GO TO 8000 247 1=1-0 248 IR=R+I 249 NI= LM1+I+4 250 IF(B(0).GE.T(0+4).0R.T(NI).GE.B(IR))G0 TO 8500 251 760O CONTINUE 252 R=R-4 253 1=4 254 IF( LM1.LT.5)G0 TO 8000 255 DO 7900 0=5, LM1 256 TO=T(0+4) 257 T4=T(0) 258 7700 1=1+1 259 IF(B(I).LE.T4)G0 TO 7700 260 IF(I.GT.R.OR.B(I),GE.TO)GO TO 8500 261 7900 CONTINUE 262 80CO IERR0R=O 263 DO 7800 1=1, L3 264 C(I)=0.0 265 DO 7800 0=1,4 266 7800 A(1,0)=0.0 267 SIGMA=0.0 268 0=0 269 0OLD=O 270 DO 8400 I=1,N 271 WI=WT(I) 272 XI=X(I) 273 8100 IF(XI.GE.T(0+4).AND.0.LE. LM1)G0 TO 8125 274 GO TO 8150 275 8125 0=0+1 276 GO TO 8100 277 8150 IF(O.NE.OOLD)GO TO 8175 278 GO TO 8200 279 8175 T1=T(0+1) 280 T2=T(0+2) 281 T3=T(0+3) 282 T4=T(0+4) 283 T5=T(0+5) 284 TG=T(0+6) 285 D4=1 ./(T4-T1 ) 286 D5=1./(T5-T2) 287 D6=1 ./(T6-T3) 288 D7=1./(T4-T2) 289 D8=1./(T5-T3) 290 D9=1 ./(T4-T3) - 228 -291 JOLD=J 292 8200 E5=T5-XI 293 E4=T4-XI 294 E3=XI-T3 295 E2=XI-T2 296 N1=WI*D9 297 N2=E3*N1*08 298 N1=E4*N1*D7 299 N3=E3*N2*D6 300 N2=(E2*N1+E5*N2)*D5 301 N1=E4*N1*D4 302 B(4)=E3*N3 303 B(3)=E2*N2+(T6-XI)*N3 304 B(2)=(XI-T1)*N1+E5*N2 305 B(1)=E4*N1 306 CR0W=WI*Y(I) 307 DO 8300 LLL=1 ,4 308 LL = LLL-1 309 RELMNT=B(LLL) 310 IF(RELMNT.E0.O.O)G0 TO 8300 311 JPLUSL=J+LL 312 L4=4-LL 313 D = A(dPLUSL. 1 ) 314 IF(D.GT.DABS(RELMNT))G0 TO 8250 315 S=D/RELMNT 316 SINE=1./DS0RT(1.0+S**2) 317 COSINE=SINE*S 318 A(JPLUSL,1)=RELMNT/SINE 319 GO TO 8275 320 8250 S=RELMNT/D 321 C0SINE=1./DSORT(1.0+S**2) 322 SINE=COSINE*S 323 A(JPLUSL.1)=D/COSINE 324 8275 CONTINUE 325 IF(L4.LT.2)GO TO 8295 326 DO 8290 IU=2.L4 327 LPLUSU-LL+IU 328 ACOL=A(JPLUSL.IU) 329 AROW=B(LPLUSU) 330 A(JPLUSL,IU)=COSINE»ACOL+SINE*AROW 331 8290 B(LPLUSU)=COSINE*AROW-SINE*ACOL 332 8295 CCOL = C(JPLUSL) 333 C(JPLUSL)=COSINE*CCOL+SINE*CROW 334 CROW=COSINE*CROW-SINE*CCOL 335 8300 CONTINUE 336 SIGMA=SIGMA+CR0W**2 337. 8400 CONTINUE 338 SS=SIGMA 339 8500 IFAIL=IERROR 340 RETURN 341 END 342 SUBROUTINE TVAL(ID,T1.T2 . T3 ) 343 REAL*8 E(20.3),T1,T2.T3 344 DATA E/12.706,4.303.3. 182 , 2 . 776 , 2.571.2.447,2.356, 345 +2.30S,2.262,2.228,2.201,2.179,2.160,2.145,2.131, 346 +2. 12.2. 1 1 ,2 . 101,2.093,2.086.63.657,9.925,5.841,4.604, 347 +4.032,3.707,3.499,3.355,3.25,3.169.3.106,3.055,3.012, 348 +2.997.2.947,2.921,2.898,2.878,2.861.2.845,636.619,31.598, - 229 -349 +12.924,8.61.6.869,5.959,5.408,5.041,4.781,4.587, 350 +4.437,4.318,4.221,4.14,4.073,4.015,3.965,3.922, 351 +3.883,3.85/ 352 IF(ID.LE.0)WRITE(6,900) 353 900 FORMAT(/'ERROR IN DEGREES OF FREEDOM FOR T-VALUES 354 IF(ID.GE.1.AND.ID.LE.20)GO TO 720 355 IF(ID.LE.120)G0 TO 710 356 IF(ID.GT.120.AND.ID.LE.200)G0 TO 700 357 T1=1.96 358 T2=2.576 359 T3=3.291 360 RETURN 361 700 T1=1.992-ID*.0002 362 T2=2.641-ID*.0002 363 T3=3.4225-ID*.0004125 364 RETURN 365 710 T1=((((((ID*8.0520028E-15-2.8813791E-12)*ID+ 366 12.7662442E-10)*ID+1.8674944E-8)*ID-5.7885593E-6) 367 1*ID+4.7918783E-4)*ID-1.8915886E-2)*ID+2.3151075 368 T2=((((((ID*1.9464622E-14-7.3252763E- 12)*ID+ 369 17.8915081E-10)*ID+2.3006791E-8)*ID-1.1797539E-5) 370 1*ID+1.0292022E-3)*ID-4.11644 16E-2 )*ID+3.3449869 371 T3=((((((ID*3.8054493E-14-1.42063E-11)*ID+ 372 11.5368801E-9)*ID+5.4360301E-8)*ID-2.5015934E-5) 373 1*ID+2.186612E-3)*ID-8.7791089E-2)*ID+4.917854 374 RETURN 375 720 T1=E(ID, 1) 376 T2=E(ID,2) 377 T3=E(ID,3) 378 RETURN 379 END - 230 -D.4 Calculation of Variances of Growth Indices 1 2 3 4 5 6 7 B 9 10 1 1 1 2 1 3 1 4 1 5 16 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 4 0 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 5 0 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) R E A L * 8 M S Y , M S Z , M S Y Z F D I M E N S I O N X ( 1 1 ) . Y 1 ( 1 1 ) , Y 2 ( 1 1 ) . Y 3 ( 1 1 ) . Y Z V A R ( 1 1 ) . S E R Y H 1 1 ) . 1 S E R Y 2 ( 1 1 ) , S E R Y 3 ( 1 1 ) , D I F Y ( 1 1 ) , D I F Z ( 1 1 ) , S E Y 1 ( 1 1 ) 1 S E Y 2 ( 1 1 ) . 2 S E Y 3 ( 1 1 ) . Y 1 F ( 1 1 ) . Y 2 F ( 1 1 ) , Y 3 F ( 1 1 ) , D Y 1 ( 1 1 ) , D Y 2 ( t 1 ) , D Y 3 ( 1 1 ) , 3 D 2 Y 1 ( 1 1 ) , D 2 Y 2 ( 1 1 ) , R Y 4 ( 1 1 ) , R Y 1 ( 1 1 ) , R Y 2 ( 1 I ) , R Y 3 ( 1 1 ) , A L 1 ( 1 1 ) , 4 S E D Y 1 ( 1 1 ) , S E D Y 2 ( 1 1 ) , S E D Y 3 ( 1 1 ) , S E D 2 Y 1 ( 1 1 ) , S E D 2 Y 2 ( 1 1 ) , Y F ( 11) . 5 D Y 4 ( 1 1 ) , Z ( 1 1 ) , Z F ( 1 1 ) , Y ( 1 1 ) , Y 4 ( 1 1 ) , Y 4 F ( 1 1 ) . S E Y 4 ( 1 1 ) , S E D Y 4 ( 1 1 ) 1 . A L 2 ( 1 1 ) , A L 3 ( 1 1 ) , U L 1 ( 1 1 ) , U L 2 ( 1 1 ) , U L 3 ( 1 1 ) . S E Y ( 1 1 ) , S E Z ( 1 1 ) 1 , D I F Y Z ( 1 1 ) , D I F Y Z F ( 1 1 ) C 0 V Y Z = O S Y Z F = 0 I C O U N T = 1 S S D Y = 0 L Y 1 = 1 L Y 2 = 1 L Y 3 = 1 L Y 4 = 2 N= 1 1 S S Y Z F = 0 S S Y = 0 S S Z = 0 S C R O S S = 0 I D F 1 = N - L Y 1 - 3 , Y 1 F , , Y 2 F , , Y 3 F , I D F 2 = N - L Y 2 - 3 I D F 3 = N - L Y 3 - 3 C I D F 4 = N - L Y 4 - 3 C C A L L T V A L ( I D F 4 C A L L T V A L ( I D F 1 C A L L T V A L ( I D F 2 C A L L T V A L ( I D F 3 C C A L L R E A D ( X , Y 4 C A L L R E A D ( X . Y 1 C A L L R E A D ( X . Y 2 C A L L R E A D ( X , Y 3 D O 1 I = 1 . N R Y 1 ( I ) = D Y 1 ( I ) S E R Y 1 ( I ) = S E D Y 1 ( 1 ) R Y 2 ( I ) = D Y 2 ( I ) S E R Y 2 ( I ) = S E D Y 2 ( I ) R Y 3 ( I ) = D Y 3 ( I ) S E R Y 3 ( I ) = S E D Y 3 ( I ) 1 C O N T I N U E DO 2 1 = 1 , N Z ( I ) = Y 1 ( I ) Z F ( I ) = Y 1 F ( I ) S E Z ( I ) = S E Y 1 ( 1 ) Y ( I ) = Y 3 ( I ) Y F ( I ) = Y 3 F ( I ) S E Y ( I ) = S E Y 3 ( I ) D I F Y ( I ) = Y F ( I ) - Y ( I ) D I F Z ( I ) = Z F ( I ) - Z ( I ) S S Y = S S Y + D I F Y ( I ) * * 2 S S Z = S S Z + D I F Z ( I 1 * * 2 2 C O N T I N U E L 1 = L Y 3 L 2 = L Y 1 1 1 1 M S Y = S S Y / ( N - L 1 - 3 ) T Y 4 1 . T Y 4 2 . T Y 4 3 ) T Y 1 1 . T Y 1 2 . T Y 1 3 ) T Y 2 1 . T Y 2 2 . T Y 2 3 ) T Y 3 1 . T Y 3 2 . T Y 3 3 ) Y 4 F , S E Y 4 , D Y 4 , S E D Y 4 ) S E Y 1 , D Y 1 , S E D Y 1 ) S E Y 2 . D Y 2 , S E D Y 2 ) S E Y 3 . D Y 3 . S E D Y 3 ) - 231* -59 MSZ=SSZ/(N-L2-3) 60 DO 3 1=I.N 61 3 COVYZ=COVYZ+(Y(I)-YF(I))*(Z(I)-ZF(I)) 62 IF(L1.GT.L2)G0 TO 20 63 IDF=N-L1-3 64 GO TO 25 65 20 IDF=N-L2-3 66 25 COVYZ=COVYZ/IDF 67 CORRYZ=COVYZ/DSQRT(MSY*MSZ) 68 SPYZ=MSY+MSZ-2*C0VYZ 69 CALL SUMS(DY3,SDY3,SSDY3) 70 DY3B=S0Y3/N 71 DO 4 1=1,N 72 SSDY=SSDY+(DY3(I)-DY3B)**2 73 4 CONTINUE 74 SSDY=DSORT(SSDY/N) 75 CALL TVAL(IDF.T1.T2.T3) 76 DO 50 1=1,N 77 SYZF = SYZF+DEXP(ZF(I )-YF(I ) ) 78 . DIFYZ(I )=DEXP(Z(I)-Y(I)) 79 OIFYZF(I )=DEXP(ZF(I)-YF(I)) 80 SEBIAS=DSQRT(DABS(SPYZ))*OIFYZF(I) 81 SRS=DSQRT(DABS(SPYZ)) 82 S7DUM=ZF(I)-YF(I) 83 CALL C0NLIM(S7DUM.T1.SRS.DL.DU) 84 DL=DEXP(DL) 85 DU=DEXP(DU) 86 RE5ID=0IFYZ(I )-01FYZF(I) 87 WRITE(6,40)X(I),DIFYZ(I).DIFYZF(I).SEBI AS.DL.DU.RESID 88 40 F0RMAT(F3.0.6F14.4) 89 YZVAR(I) = (DSORT(DABS(SPYZ))*DIFYZF(I ) ) * *2 90 50 CONTINUE 91 IF(IC0UNT.E0.2)G0 TO 150 92 IF(IC0UNT.E0.3)G0 TO 112 93 C IF(IC0UNT.E0.4)G0 TO 150 94 150 CALL SUMS(YF,SYF,SSYF) 95 CALL SUMS(ZF.SZF.SSZF) 96 YFBAR=SYF/N 97 ZFBAR=SZF/N 98 SYZFB=SYZF/N 99 DO 5 1=1,11 100 SSYZF=SSYZF+(DIFYZF(I)-SYZFB)**2 101 SCROSS=SCROSS+(OIFYZF(I)-SYZFB)*(DY3(I)-DY3B) 102 5 CONTINUE 103 MSYZF=DSQRT(SSYZF/N) 104 NEWCOR=SCROSS/(N*SSDY*MSYZF) 105 DO 70 1=1,N 106 RF=DY3(I )/DIFYZF(I ) 107 CDYZ=DSORT((SEDY3(I )**2)*YZVAR(I))*CORRYZ 108 SEF = ( 1/(SYZFB**2) )*((SEDY3(I ) **2)-(2*DY3B*CDYZ)/SYZFB+ 109 1 (•Y3B**2*YZVAR(I ) )/(SYZFB**2)) 110 SEF=DSORT(SEF ) 111 CALL C0NLIM(RF,T1,SEF,DL,UL) 112 WRITE(6,41 )X(I ) ,RF,DL,UL.SEF 113 41 F0RMAT(F3.O,4F13.7) 114 70 CONTINUE 115 112 IC0UNT=IC0UNT+1 116 IF(IC0UNT.E0.2)G0 TO 212 - 232 -1 17 IF(IC0UNT.EQ.3)G0 TO 312 118 C IF(ICOUNT.EO.4)G0 TO 412 119 GO TO 200 120 212 SSY=0 121 SSZ=0 122 DO 213 1=1,N 123 Y(I)=Y2(I) 124 YF( I ) =Y2F(I) 125 SEY(I)=SEY2(I ) 126 DIFY(I) = YF(I )-Y(I ) 127 D I F Z ( I ) = Z F ( I ) - Z ( I ) 128 SSY = SSY+DIFY(I )**2 129 SSZ = SSZ+DIFZ(I )**2 130 DY3(I )=DY2( I ) 131 SEDY3(I ) = SEDY2(I ) 132 213 CONTINUE 133 L2=LY2 134 GO TO 111 135 312 SSY=0 136 SSZ=0 137 DO 313 1 = 1 ,N 138 Z( I ) = Y2( I ) 139 ZF(I ) = Y2F( I ) 140 SEZ(I )«SEY2(I ) 141 Y(I )=Y3(I ) 142 YF(I )=Y3F(I ) 143 SE Y ( I ) = SEY3(I ) 144 DIFY(I) = YF(I )-Y(I ) 145 D I F Z ( I ) = Z F ( I ) - Z ( I ) 146 SSY = SSY+DIFY(I )**2 147 SSZ = SSZ+DIFZ(I )**2 148 '313 CONTINUE 149 L1=LY2 150 L2=LY3 151 GO TO 111 152 4 12 SSY=0 153 SSZ = 0 154 00 413 1=1,N 155 DY3(I)«DY4(I)*10**3 156 SEDY3(I)=SEDY4(I)*10**3 157 Z( I ) = Y 1 ( I ) 158 ZF( I ) = Y 1 F ( I ) 159 SEZ(I )=SEY 1(1) 160 Y(I ) = Y4(I ) 161 YF( I ) = Y4F(I ) 162 SEY(I)=SEY4(I) 163 DIFY(I ) = YF( I )-Y( I ) 164 D I F Z ( I ) = Z F ( I ) - Z ( I ) 165 SSY=SSY+DIFY(I )**2 166 SSZ = SSZ+DIFZ(I )**2 167 4 13 CONTINUE 168 L1=LY1 169 L2=LY4 170 GO TO 111 171 200 RETURN 172 END 173 SUBROUTINE WRITER(A,B,ALL,AU. S) 174 IMPLICIT REAL*8(A-H,0-Z) - 233. -175 DIMENSION A(11),B(11),ALL(1 1 ).AU(11 ) .S( 1 1 ) 176 DO 1 1=1,11 177 WRITE(6,2)A(I),B(I).ALL(I),AU(I),S(I) 178 2 F0RMAT(F3.O,4F13.4) 179 1 CONTINUE 180 RETURN 181 END 182 SUBROUTINE TVAL(ID.T1,T2,T3) 183 REAL*8 E(20.3),T1,T2,T3 184 DATA E/12.706,4.303,3. 182,2.776,2.571,2.447,2.356 185 +2.306,2.262,2.228,2.201,2.179.2.160.2.145.2.131, 186 + 2. 12.2 . 11.2.101,2.093,2.086,63.657,9.925.5.841,4. 187 +4.032.3.707,3.499,3.355,3.25.3.169,3.106.3.055,3.< 188 + 2.997.2.947.2.921,2.898,2.878.2.861 .2.845.636 . 6 19 189 +12.924,8.61.6.869,5.959,5.408.5.041.4.781.4.587. 190 +4.437,4.318,4.221.4.14.4.073,4.015.3.965.3.922. 191 +3.883.3.85/ 192 IF(ID.LE.O)WRITE(6.900) 193 900 FORMAT(/'ERROR IN DEGREES OF FREEDOM FOR T-VALUES 194 IF(ID.GE.1.AND.ID.LE,20)GO TO 720 195 IF(ID.LE.120)G0 TO 710 196 IF ( ID.GT. 120.AND.ID.LE.200)G0 TO 700 197 T1=1.96 198 T2=2.576 199 T3=3.291 200 RETURN 201 700 T1=1.992-ID*.0002 202 T2=2.641-ID*.0002 203 T3=3.4225-ID*.0004125 204 RETURN 205 710 T1=((((((ID*8.052CO28E-15-2.8B13791E-12)*ID+ 206 12.7662442E-10)*ID+1.8674944E-8 ) *ID-5.7885593E-6) 207 1*ID+4.7918783E-4)*ID-1 .8915886E-2)*ID+2.3151075 208 T2 = ((((((ID*1.9464622E-14-7.3252763E- 12 ) * ID + 209 17.8915081E-10)*ID+2.3006791E-8)* ID-1. 1797539E-5 ) 210 1*ID+1.0292022E-3)MD-4.1164416E-2 )*ID+3.3449869 21 1 T3=((((((ID*3.8054493E-14-1.42063E-11 )'ID+ 212 11.5368801E-9)*ID+5.4360301E-8)*ID-2.5015934E-5) 213 1*ID+2.186612E-3)*ID-8.7791089E-2)*ID+4.917854 214 RETURN 215 720 T1=E(ID, 1 ) 216 T2=E(ID,2) 217 T3=E(ID.3) 218 RETURN 219 END 220 SUBROUTINE CONLIM(A,TV,AS,ALL.ULL) 221 REAL*8 A,TV.AS.ALL.ULL.UD 222 ALL=A-AS*TV 223 ULL=A+AS*TV 224 IF(ULL.GE.ALL)GO TO 920 225 UD=ULL 226 ULL=ALL 227 ALL=UD 228 920 RETURN 229 END 230 SUBROUTINE READ(A,B,BF,BS,DA,DS) 231 IMPLICIT REAL*8(A-H.O-Z) 232 01MENS ION A(11),B(11),BS(1 1 ) ,DA( 1 1 ) ,DS( 1 1 ) .BF( 1 1 ) - 234 -233 DO 1 1=1,11 234 READ(5.2)A(I ) ,B(I ) , B F ( I ) .BS(I).DA(I).DS(I) 235 2 FORMAT(F4.0,5F10.5) 236 1 CONTINUE 237 RETURN 238 END 239 SUBROUTINE SUMS(C,SC,SSC) 240 IMPLICIT REAL*8(A-H,0-Z) 241 DIMENSION C(11) 242 SSC=0 243 SC=0 244 DO 1 1=1.11 245 SC = SC+C(I ) 246 SSC=SSC+C(I)**2 247 1 CONTINUE 248 RETURN 249 END - 235 -D.5 Simulation Program DIMENSION DC( 10. 5 0 ) . TC( 10, 50 ) , T P l 50 I . ' < 10. 50 ) . CWMO. 50 ) 1.DWI 1 0 . 5 0 ) , D P ( 1 0 . 5 0 ) . S ( 1 0 , 5 0 ) . C F I 5 0 I A=2.00 B=4.00 C=0.500 A1=12.0 B 1 = E X P(2 . 0 6 6 ) C 1 =0.049 DO 1 1=1.50 C F I I > = 1 TP( I )=0 1 CONTINUE DO 2 1=1.10 00 3 d=1,50 TCI I . d ) =0 DC I I , J ) =0 3 CONTINUE 2 CONTINUE DO 5 1=1.10 1 F( I .EO. 1 )L=1 I F ( I G T . 1 ) L = L + 3 DC S d= 1 .3 1 K = J - 1 T =K- 15 LL=L+K y. L = 50+ ( L L - 1 ) DW( I . J ) =0.5778 DPI I . J ) = -1 . 6 862 + ( 0 . 0 1 7 0 6 2 * X L • 2 ) DNUM=A-B*C*EXP<-CT ) DN0M=( 1 + B - E X P ( - C * T ) )-*2 DC I I . J ) =DNUM/DN0M * < ! . J ) = X L SI I . J ) =DCI I . d ) / D P ( I . J ) C W I I , J ) = S ( I . J I * DW( I , J ) * C F I I ) P = O C ( I . J ) * 0 . 3 5 I F I C W ( I , J ) .LT.P )CF( 1 + 1 )=0. 9 Ip( J . E O . 1 )TC< I . J ) = C W ( I , J ) I F 1 J . G T . 1 )TC( I , J ) = TC< I . K l + CWI I . J I 6 CONTINUE 5 CONTINUE CO 10 1=1.10 DO 1 1 J = 1 . 3 1 T P l J ) = T P ( J )*TC( I . J ) I F ( T C I I . J ) .EO.O)G0 TO 11 W R I T E ( 6 . 1 7 ) I . J . X ( I . J ) , D C ( I . J ) . ' r C I I . J I . C W I I . J l . D F ( I . J » n F O R M A T ! 2 1 3 . 5 F 1 0 . 3 I i 1 CONTINUE 1 0 CONTINUE DO 12 1=1.31 WRITE!6. 16)1 . T P l I ) 16 F O R M A T ! I 3 . F 1 0 . 3 ) 1 2 CONTINUE STOP END - 236 -APPENDIX E RAW DATA Table E . l - Summary of fresh and dry weights of pods, pod walls and seeds of each cohort. COHORT DAP DRY WEIGHTS FRESH WEIGHTS TRT" NO DAP POD SEED POD WALL POD SEED POD WALL t 3 59 0 508 0 034 0 474 3 020 0 130 2 890 1 3 68 0 858 0 286 0 572 5 100 1 090 4 010 1 3 71 0 982 0 543 0 439 5 840 2 070 3 770 1 4 53 0 057 O O O 057 0 338 O 0 0 338 1 4 56 0 109 0 004 0 105 0 647 0 014 0 633 1 4 59 0 530 0 017 0 513 3 153 0 066 3 085 1 4 62 O 834 0 090 0 744 4 962 0 345 4 616 1 4 65 0 594 0 134 O 460 3 533 0 510 3 023 1 4 68 1 241 0 0 1 241 7 380 0 0 7 380 1 4 71 0 986 0 548 0 438 5 863 2 090 3 773 1 4 74 1 351 0 780 0 572 8 036 2 974 5 063 1 4 77 1 442 0 999 0 443 8 577 3 810 4 543 1 4 80 1 421 1 185 0 236 8 450 4 519 3 931 1 5 53 0 042 0 0 0 042 0 250 0 0 0 250 1 5 56 0 046 0 000 0 045 0 272 0 001 0 271 1 5 59 0 236 0 007 0 229 1 403 0 025 1 377 1 5 62 0 652 0 044 0 608 3 878 0 169 3 708 1 5 65 0 840 0 084 0 755 4 994 0 322 4 671 1 5 68 0 861 0 172 0 689 5 119 0 656 4 453 1 5 71 1 161 0 550 0 612 6 907 2 098 4 810 1 5 74 1 430 0 790 0 640 8 503 3 012 5 491 1 5 77 1 632 0 916 0 716 9 706 3 495 5 897 1 5 80 1 658 1 377 0 281 9 858 5 252 4 511 1 6 56 0 023 0 0 0 023 0 138 0 O O 138 1 6 59 0 035 0 0 0 035 0 211 0 0 0 211 1 6 62 0 225 0 0O6 o 219 1 341 o 024 1 317 1 6 65 0 559 0 020 0 539 3 326 0 077 3 249 1 6 68 0 746 0 094 0 652 4 436 o 357 4 077 1 6 71 0 902 0 277 0 625 5 366 1 058 4 300 1 6 74 1 268 0 604 0 665 7 542 2 303 5 240 1 6 77 1 396 0 831 0 565 8 303 3 171 4 994 1 6 80 1 472 1 182 0 291 8 756 4 507 4 248 1 7 62 0 037 0 0 o 037 0 218 0 0 0 218 1 7 65 0 205 0 002 0 202 1 216 0 009 1 206 1 7 68 0 423 0 014 o 408 2 513 0 054 2 459 1 7 71 0 652 0 068 0 584 3 876 0 258 3 619 1 7 74 0 829 0 232 0 597 4 931 0 884 4.043 1 7 77 1 059 0 525 0 534 6 300 2 004 4 212 1 7 80 1 327 1 028 0 299 7 889 3 920 3 969 1 8 65 0 041 0 0 o 041 0 245 0 0 0 245 1 8 68 0 123 0 000 0 123 0 733 0 001 0 732 1 8 71 0 368 0 015 0 353 2 190 0 059 2 131 1 8 74 0 516 0 058 0 457 3 066 0 222 2 643 1 8 77 0 721 0 185 0 536 4 291 0 707 3 584 1 8 80 0 940 0 585 0 355 5 590 2 233 3 358 1 9 68 0 033 0 0 0 033 0 194 0 0 • 0 194 1 9 71 0 100 0 001 0 099 0 595 0 004 " 0 591 1 9 74 0 228 0 007 0 221 1 355 0 028 1 327 1 9 77 0 487 0 055 0 432 2 898 0 209 2 685 1 9 80 0 655 0 282 0 373 3 894 1 074 2 820 1 10 71 0 027 0 0 0 027 0 160 0 0 0 160 1 10 74 0 096 0 001 0 095 0 571 0 005 0 566 1 10 77 0 258 0 018 0 240 1 535 0 070 1 465 - 237 -Table E.1 Continued COHORT DAP DRY WEIGHTS FRESH WEIGHTS TRT NO DAP POD SEED POD WALL POD SEED POD WALL , IO 80 0 473 0 132 O 341 2 815 O 503 2 311 1 1 1 74 0 022 0 0 O 022 0 129 0 0 0 129 1 11 77 0 068 0 0 0 068 0 404 0 0 0 404 1 1 1 80 0 267 0 030 0 237 1 588 O 1 14 1 474 1 12 77 0 010 0 0 0 010 0 060 O 0 0 060 1 12 80 0 166 0 008 0 158 0 986 0 032 0 956 2 1 50 0 045 0 0 0 045 0 270 0 0 0 270 2 1 53 0 760 0 0 0 760 4 520 0 0 4 520 2 1 56 0 612 0 031 0 581 3 640 0 120 3 520 2 1 59 0 943 0 092 0 852 5 610 0 350 5 260 2 1 62 1 028 0 387 0 642 6 115 1 475 4 640 2 2 50 0 024 0 0 0 024 0 143 0 0 0 143 2 2 53 0 472 0 0 0 472 2 806 0 0 2 806 2 2 56 0 450 0 022 0 428 2 673 0 083 2 590 2 2 59 0 819 0 161 0 658 4 870 0 613 4 257 2 2 62 0 906 0 551 0 356 5 390 2 100 3 290 2 2 65 1 243 0 845 0 397 7 390 3 225 4 165 2 2 68 0 948 0 784 0 165 5 640 2 990 2 650 2 2 71 1 565 1 135 0 430 9 310 4 330 4 980 2 2 77 1 078 0 742 0 336 6 410 2 830 3 281 2 2 80 0 641 0 697 - 057 3 810 2 660 1 150 2 3 SO 0 052 0 0 0 052 0 308 0 0 0 308 2 3 53 0 264 0 0 0 264 1 568 0 0 1 568 2 3 56 0 426 0 O i l 0 416 2 536 0 041 2 494 2 *3 59 0 729 0 076 0 653 4 334 0 289 4 045 2 3 62 0 920 0 261 0 659 5 470 0 995 4 615 2 3 65 1 149 0 599 0 551 6 835 2 284 4 551 2 3 68 0 858 0 607 0 251 5 101 2 316 2 773 2 3 71 1 388 0 991 0 397 8 256 3 780 4 444 2 3 74 1 389 1 044 0 346 8 262 3 982 4 281 2 3 77 1 250 0 967 0 283 7 432 3 689 3 511 2 3 80 1 184 1 263 - 079 7 040 4 817 2 222 2 4 50 0 029 0 0 0 029 0 170 0 0 0 170 2 4 53 0 066 0 0 0 066 0 390 0 0 0 390 2 4 56 0 253 0 007 0 247 1 506 0 025 1 480 2 4 59 o 567 0 041 0 526 3 372 O 157 3 213 2 4 62 0 682 0 129 0 553 4 056 0 493 3 559 2 4 65 0 883, 0 288 0 595 5 251 1 098 4 153 2 4 68 0 951 0 49B 0 453 5 659 1 900 3 741 2 4 71 1 242 0 844 0 398 7 388 3 221 4 167 2 4 74 1 426 1 015 0 412 8 481 3 870 4 608 2 4 77 1 264 0 953 0 311 7 517 3 635 3 812 2 4 80 1 156 1 080 0 076 6 876 4 120 2 756 2 5 53 0 028 0 0 0 028 0 167 0 0 0 167 2 5 56 0 077 0 001 0 076 0 456 0 002 0 454 2 5 59 o 284 0 015 o 268 1 686 0 058 1 628 2 5 62 0 471 0 033 0 438 2 801 0 128 2 673 2 5 65 0 669 0 085 0 584 3 980 0 326 3 654 2 5 68 0 750 0 247 0 502 4 458 0 944 3 492 2 5 71 1 103 0 592 o 511 6 562 2 260 4 280 2 5 74 1 295 0 859 0 436 7 702 3 279 4 423 2 5 77 1 253 0 945 0 309 7 453 3 603 3 761 2 5 80 1 316 1 195 0 121 7 828 4 559 3 268 2 6 56 0 029 0 0 0 029 0 175 0 0 • 0 175 2 6 59 0 034 0 0 0.034 0 203 0 O 0 203 2 6 62 0 172 0 006 0 166 1 020 0 021 0 999 2 6 65 0 392 0 021 0 370 2 329 o 081 2 247 2 6 68 0 517 0 068 0 449 3 076 0 259 2 817 2 6 71 0 752 0 255 0 497 4 473 0 971 3 502 2 6 74 1 012 0 516 0 496 6 019 1 968 4 050 - 238 -Table E.1 Continued COHORT DAP DRY WEIGHTS FRESH WEIGHTS TRT NO DAP POD SEED POD WALL POD SEED POD WALL 2 6 77 1 108 0 746 0 362 6 591 2 846 3 745 2 6 80 1 280 1 033 0 247 7 614 3 941 3 674 2 7 62 0 033 0 0 0 033 0 196 0 0 0 196 2 7 65 0 147 0 O03 0 144 0 875 0 010 0 864 2 7 68 0 323 0 016 0 308 1 924 0 060 1 863 2 7 71 0 565 0 081 0 484 3 361 0 309 3 051 2 7 74 0 624 0 209 0 416 3 714 0 796 2 913 2 7 77 0 777 0 415 0 362 4 619 1 583 3 036 2 7 80 1 076 0 835 0 241 6 398 3 184 3 215 2 8 62 0 013 0 0 0 013 0 075 0 0 0 075 2 8 65 0 033 0 0 0 033 0 198 0 0 0 198 2 8 68 0 164 0 003 0 161 0 974 0 012 0 962 2 8 71 0 428 0 022 0 407 2 546 0 082 2 464 2 8 74 0 409 O 057 O 352 2 432 o 218 2 211 2 8 77 0 541 0 197 0 344 3 217 0 750 2 466 2 8 80 0 771 0 565 0 206 4 587 2 157 2 431 2 9 65 0 019 0 0 0 019 0 115 0 0 0 115 2 9 68 0 034 0 0 0 034 0 201 0 0 0 201 2 9 71 0 110 0 001 0 108 O 652 0 O05 0 647 2 9 74 0 264 0 014 0 250 1 570 0 054 1 517 2 9 77 0 320 o 050 0 269 1 903 0 192 1 710 2 9 80 0 399 0 181 0 219 2 374 0 689 1 685 2 10 71 0 023 0 O 0 023 O 134 0 0 0 134 2 io 74 0 025 0 0 0 025 0 150 0 0 0 150 2 10 77 0 168 0 0 0 168 1 OOO 0 o 1 OOO 2 10 80 0 370 0 052 0 317 2 200 0 200 2 000 1 = DSP 2 = EF 

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