POPULATION DYNAMICS OF THE CABBAGE APHID BREVICORYNE BRASSICAE (L.) (HOMOPTERA:APHIDIDAE) IN VANCOUVER BRITISH COLUMBIA: A QUANTITATIVE STUDY AND SYNTHESIS OF ECOLOGICAL RELATIONSHIPS by DAVID ARNOLD RAWORTH B.Sc,, Simon F r a s e r U n i v e r s i t y , 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE FLiQUI REMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PLANT SCIENCE and INSTITUTE OF ANIMAL RESOURCE ECOLOGY We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1982 (c) David Arnold Raworth, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e 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 h i s or her representatives. I t i s understood that copying or pu b l i c a t i o n 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 The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D F - f i (2/19) 11 ABSTRACT The population dynamics of the cabbage aphid (Brevicoryne brassicae) were studied on Maris Kestrel kale during the summer months, in Vancouver B r i t i s h Columbia, Canada. The object was to describe the temporal variation in numbers, age d i s t r i b u t i o n , and quality of B^ brassicae in terms of quantitative relationships between the aphid and i t s b i o t i c and a b i o t i c environment, using a simulation model. A technique was developed whereby aphid fecundity and developmental time could be estimated for aphids within the population. Aphid fecundity and rate of development decreased continuously through the season, probably in response to changes in plant qu a l i t y . The plant rarely posed an upper l i m i t on aphid increase, but populations consistently showed an i n i t i a l maximal rate of increase followed by a l e v e l i n g off, and eventual population decline in the autumn. Evidence presented, suggests that syrphid predation was largely responsible for the major mid-season s h i f t s in the rate of increase of the aphid. Thompson's(1924) 'random search' model did not adequately represent syrphid predation, and further detailed studies are required. Decreasing aphid developmental and reproductive rates, production of oviparae, predation, and leaf f a l l , were probably responsible for population declines in the autumn. The cabbage aphid system is compared with that described by Hughes(l963) and Hughes £• Gi lbert ( 1968) . The problems of generality, and b i o l o g i c a l control are discussed. i i i TABLE OF CONTENTS Abstract i i L i s t of tables vi L i s t of figures . v i i i Acknowledgement x i i I. Introduction 1 A. Population ecology 1 1 . Preface 1 2. Developments leading to the current work ....... 2 B. Previous studies of the cabbage aphid 5 1 . Preface 5 2. L i f e history ...6 3. Taxonomy 8 4. Morph determination 9 5 . Behavior 11 6. Host plant relationships 13 7. Predator-prey relationships 14 8. Weather 18 9. Population dynamics 19 II . The Study 22 A. Preface 22 B. Measurement of temporal va r i a t i o n in the components of the system 23 1. The study area 23 2. The plant 24 iv 3. The weather ..26 4. F i e l d sampling 27 a. The insects 27 b. The plant 36 C. Relationships 38 1 . Gains 38 a. Developmental time vs temperature 39 b. Fecundity and longevity vs aphid age and temperature 43 c. Developmental time, fecundity, and alate determination vs density, and plant quality ..48 d. Developmental time and fecundity vs plant age 60 e. Temporal variation in developmental time and f ecundi ty 61 f. Morph determination 63 2. Losses 68 a. Emigration ....69 b. Cecidomyiids ....69 c . Syrphids 77 d. Parasites 81 e. Plant growth and Development 82 D. Consolidation 95 1 . The model 95 2. Model va l i d a t i o n and predictions 95 III . Discussion 105 A. Future research 105 B. Technical considerations 109 C. Comparisons with other systems 113 D. B i o l o g i c a l and c u l t u r a l control 122 E . Summary 123 Bibliography 126 Appendix 1 . 139 Appendix 2 142 Appendix 3 . 143 VI LIST OF TABLES I . Dates for plot planting, and i n i t i a l and f i n a l aphid samples. 33 II . Developmental temperature thresholds, and developmental times for B^ brassicae. 42 III . Estimates of syrphid voracity from the l i t e r a t u r e . 78 IV. Movement of B_;_ brassicae from senescing leaves. 92 V. Coef f i c i e n t s used to predict the age d i s t r i b u t i o n in stratum 3 from that found in the whole plant. 94 VI . Relationships incorporated in the model. 96 V I 1 VII . Observed and predicted age d i s t r i b u t i o n s for the f i r s t UBC2 eld sample. VI 1 1 LIST OF FIGURES 1 . Population trends in the years 1977, 1978,1979 at Point Grey and Abbotsford. 3 4 2. Plant growth data for a l l f i e l d p l o t s . 3 7 3 . Developmental time and rate of brassicae as a function of temperature. 4 0 4 . Age-specific reproductive and survival patterns for B. brassicae. 4 5 5 . Age-specific b i r t h rates for B^ brassicae, with varying t o t a l fecundity. 4 7 6. Aphid growth as a function of physiological time. 51 ix 7. Relationships observed in the 1978 field-cage experiment (I). .. . . 56 8. Relationships observed in the 1978 field-cage experiment (II) . 57 9. Relationships observed in the 1978 field-cage experiment (III) . 59 10. Fecundity and developmental time through the 1978 f i e l d season. .62 11. Mean adult weight as a function of physiological time. 64 12. Proportion of apterous fourth-instar aphids as a function of aphid density. 66 13. Production of oviparae as a function of physiological time. X . 1 4 . Mate numbers as a function of aphid density. 70 15. Larval predator and pupal parasite numbers and as a function of aphid density. 75 16. D i s t r i b u t i o n of l a r v a l predator dry weights in f i e l d samples. 80 17. The proportion of hyperparasitized D^ rapae cocoons as a function of physiological time. 83 18. Developmental rate of Maris Kestrel kale as a function of temperature. 85 19. Leaf area per plant as a function of physiological time. 86 20. Rates of leaf production and loss as a function of physiological time. 88 xi 21 . Leaves per plant and leaves lost per plant as a function of physiological time. 8 9 22 . Numbers of senescent leaves, and proportion of the aphid population on senescent leaves as a function of physiological time. 9 0 23. Observed and predicted population trends for UBC2. 100 24. Observed and predicted population trends for UBC3. 1 02 25. Larval syrphid numbers as a function of aphid density. 1 0 3 ACKNOWLEDGEMENT I am deeply indebted to and thank Bryan Frazer and Neil Gilbert for tra i n i n g and advice prior to and throughout the work. Sincere thanks also go to Victor Runeckles, B i l l Wellington, Charles Krebs, Neil G i l b e r t , and Bryan Frazer (committee members); Marvin Weintraub and Ron Forbes (Agriculture Canada Research Station); and Peter Larkin (Graduate Studies); for help and encouragement, and for making the studies and research technically possible. Special thanks go to Sheryl McFarlane, and Bruce G i l l for devoted technical assistance. I also wish to thank: Doug Finlayson ( h o r t i c u l t u r a l advice); Don Pearce, Al Neighbor, and Henry Troelsen ( a g r i c u l t u r a l operations); Al Mosher (technical advice); Bert Pepin (Abbotsford' temperature records); Craig Sprout, Lor i Mack, and Robert Dixon (technical assistance); John Hall ( s t a t i s t i c a l advice); Dave Z i t t i n , B i l l Web, Shirley Greystone and the staff of the UBC Computing Center (computing advice and f a c i l i t i e s ) ; Tony Matsumoto and Mae Cutler ( l i b r a r y services); Wes MacDiarmid (photography); Deborah Henderson (syrphid larvae i d e n t i f i c a t i o n ) ; Manfred Mackauer(parasite i d e n t i f i c a t i o n ) ; Don MacLeod and Mary Welton (entomophagous fungus i d e n t i f i c a t i o n ) ; J.M.McAlpine and R.Gagne' (cecidomyiid larvae i d e n t i f i c a t i o n ) ; . Cho-kai Chan and R.L.Taylor (plant c l a s s i f i c a t i o n ) ; Keith Valentine ( s o i l c l a s s i f i c a t i o n ) ; and Thierry Vrain (nematode c l a s s i f i c a t i o n ) . F i n a l l y , I wish to acknowledge and thank Joan, Jeni, and Heather for holding the xi i i fort so well in my absence over a number of years. The work u t i l i z e d the a g r i c u l t u r a l land of The Department of Plant Science at UBC and Agriculture Canada at Abbotsford, the laboratory f a c i l i t i e s of Agriculture Canada Research Station in Vancouver, and the computing f a c i l i t i e s of the UBC Computing Center and the Institute of Animal Resource Ecology. 1 I. INTRODUCTION A. Population ecology 1. Preface In 1588, 200 years before Malthus, Giovanni Botero set out the f i r s t modern concepts of population regulation (Cole 1958). In his book "The Greatness of C i t i e s " , he speaks of: the potential reproduction from one man and one woman greatly exceeding that observed in the last 3000 years (the concept of geometric increase); the cessation of population growth at some lev e l (the concept of the l o g i s t i c growth curve); the factors such as famine, diseases, movement, wars, and floods, which affe c t population growth (the concept of a complex of factors a f f e c t i n g population growth); environmental resources "the f r u i t s of the earth" ultimately l i m i t i n g population growth, (the concept of carrying capacity); and the increased effects of disease and aggressive behavior with increased density (the concept of density dependence). In the intervening 400 years, the f i e l d has been expanded to include a l l plant and animal populations; more factors which affect population numbers such as population genetics, s p a t i a l and temporal heterogeneity, and predation, have been discovered; a quantitative approach to the subject, u t i l i z i n g recently developed s t a t i s t i c a l techniques has been developed; and a primitive yet substantial body of theory concerning population regulation has been formed. From 2 a broad conceptual point of view however, l i t t l e has been added to the ideas of Giovanni Botero. The major reason for the lack of conceptual development is the newness"of the f i e l d , for although Botero l a i d the ground work in 1 5 8 8 , work on populations other than human did not begin in a rigorous way u n t i l the 1 8 9 0's when Petersen undertook the sampling of marine populations (Cole 1 9 5 8 ) . Even then, work proceeded slowly u n t i l s t a t i s t i c s for sampling and experiments were developed by R.A. Fisher early in the 1 9 0 0's. In the discussion to follow I s h a l l consider the d i r e c t i o n taken by workers in the f i e l d in the last few decades, and show how i t leads to the work embodied in this thesis. 2. Developments leading to the current work The nature of the problem i s t h i s : to explain and predict in terms of b i o t i c and abiotic relationships, the abundance of organisms. This may resolve i t s e l f into questions of d i s t r i b u t i o n , of s t a t i c differences in abundance between areas, or of dynamic changes in abundance over time, but the question as Andrewartha & B i r c h ( l 9 5 4 ) have pointed out i s b a s i c a l l y the same. Following the lead of Krebs ( l 9 7 2 ) the term 'ecology' s h a l l in t h i s thesis, be r e s t r i c t e d to this problem. The question has been approached from both functional and evolutionary points of view as exemplified by Andrewartha & B i r c h ( l 9 5 4 ) and Lack ( l 9 5 4 ) respectively (Orians 1 9 6 2 ) , and from 3 the l e v e l of the individual, population, community and ecosystem (see Clark et a_l 1967, G i l b e r t et a l 1976, Rrebs 1972, and Odum 1 9 6 3 ) . What emerges, is the r e a l i z a t i o n that nature i s far more complex than o r i g i n a l l y envisioned. An i n a b i l i t y to deal with this complexity, coupled with a desire on the part of many researchers to generalize, has resulted in a tendency to take a single factor approach to ecology (eg. competition, predation, weather). A major obstacle to the understanding of the ecology of any one population, has been the i n a b i l i t y to analyze in depth, a number of complex relationships, and then consolidate the pieces into a cohesive whole, which could be tested in the f i e l d . The problem was realized in the 1950's and led to the work of M. Hafez, C S . Holling, R.D. Hughes, and R.F. Morris. H a f e z ( l 9 6 l ) , Hughes(1963), and M o r r i s ( l 9 6 3 ) provided techniques for in depth analysis of population changes in the f i e l d (predominantly temporal). M o r r i s ( 1 9 6 3 ) , and Hughes & G i l b e r t ( 1 9 6 8 ) provided mathematical and computer simulation techniques respectively, for consolidating the data. H o l l i n g ( 1 9 5 9 ) provided a technique for in depth analysis of predation processes. Several studies u t i l i z i n g a l l these techniques have since been conducted, among them: Barlow & D i x o n ( l 9 8 0 ) , Frazer & G i l b e r t ( 1 9 7 6 ) , Gilbert & Gutierrez ( 1 973 ) , Gutierrez et a j . ( l 9 7 4 ) , and Wellington et a l ( 1 9 7 5 ) . These studies s a t i s f y to some extent three desirable q u a l i t i e s suggested by H o l l i n g ( 1 9 6 6 ) namely: completeness, realism, and precision. A fourth q u a l i t y , generality, is not s a t i s f i e d , but Gilbert et §_1(1976) point out that generality 4 may be derived from comparisons among a set of r e a l i s t i c , complete, and accurate studies. Since i t i s not obvious as yet what relationships must be studied to understand the temporal and s p a t i a l abundance of any given population, how they should be described to f a c i l i t a t e comparisons, or what form generality w i l l take, a judicious approach is to start by looking at a set of organisms which d i f f e r from one another by no more than genus. Several studies have been conducted involving various genera from the family Aphididae- (Homoptera): 1 cabbage aphid Brevicoryne brassicae (L.) (Hughes & Gilbert 1968); pea aphid Acyrthosiphon pi sum (Harris) (Frazer & Gilbe r t 1976); thimbleberry aphid Masonaphis maxima (Mason) (Gilbert & Gutierrez 1973); cowpea aphid Aphis craccivora Koch (Gutierrez e_t a_l 1974); and the lime aphid' Eucallipterus t i l i a e L. (Barlow & Dixon 1980). This study is concerned with the cabbage aphid B^ brassicae. As a study organism, i t f u l f i l l e d several requirements set out by Gilbe r t et §_1(1976), and i t f a c i l i t a t e d not only i n t e r s p e c i f i c comparisons, but also i n t r a s p e c i f i c comparisons, namely the comparison of B^ brassicae in A u s t r a l i a (Hughes 1963 and Hughes & Gilbert 1968), with B_;_ brassicae in B r i t i s h Columbia, Canada. The techniques used in this study arise d i r e c t l y from Gilbe r t et al(1976) . 1. Except where noted, insect c l a s s i f i c a t i o n follows Borror et a i d 976) . 5 B. Previous studies of the cabbage aphid l . Preface B. brassicae is a cosmopolitan insect pest on cruciferous crops. Its host range includes at least 48 species from 25 genera in the family Cruciferae (Brassicaceae) (Magnoliophyta, Magnoliopsida, Capparales) 2 (Essig 1948). Among these are such major crop plants as: broccoli Brassica oleracea L. var. i t a l i c a Plenc.k, Brussels sprouts B^ oleracea L. var. gemmifera Zenker, cabbage B^ oleracea L. var. capitata L., cauliflower B. oleracea L. var. botrytis L., radish Raphanus sativus L., rape B_^ napus L. , and rutabaga B^ napobrass ica M i l l . . The aphid is as ubiquitous as the host plants on which i t feeds. Essig(l948) c i t e s 56 countries from every major region in the world. 3 It causes extensive physical damage to a g r i c u l t u r a l crops in terms of market appearance, and y i e l d (Essig 1948, Forbes & MacCarthy 1 9 5 9 , Lai 1973, Lamb & Lowe 1967, U.K. Ministry of Agriculture, Fisheries, & Food 1977), and has been implicated in the transmission of at least 16 plant viruses (Carter 1973), including bean yellow mosaic, cucumber mosaic, onion yellow dwarf, and turnip mosaic, a l l of which are of international importance (R. Stace-Smith personal 2. P l a n t c l a s s i f i c a t i o n f o l l o w s Cronquist(1971), and Bai l e y ( 1 9 5 8 ) . 3. E s s i g ( l 9 4 8 ) suggests that China i s one of the few c o u n t r i e s i n which B^ b r a s s i c a e i s not a pest. T h i s i s i n c o r r e c t ( c f . Wu et a l 1965). 6 communication). For these reasons, B. brassicae has been intensively studied. What follows is a brief summary of the voluminous l i t e r a t u r e on the aphid. 2. L i f e history The l i f e history of B_^ brassicae, p a r t i c u l a r l y i t s phenology, has been examined in many countries: Australia (Hughes 1963); China (Wu et a l 1965); Egypt (Herakly & El-Ezz 1970); France (Bonnemaison 1971); Holland (Hafez 1961); Japan (Shiga 1967); United Kingdom (U.K. Ministry of Agriculture, Fisheries & Food 1977); Slovakia (Baran 1970); and South Af r i c a (Muller & Scholl 1958), to mention only a few.' A consistent .pattern emerges. In temperate areas such as Canada, north China, and Holland, the aphid overwinters as an egg on wild and cu l t i v a t e d c r u c i f e r s . In March or A p r i l depending on temperature 4, 7-9° da i l y mean (Baran. 1970), the apterous (wingless) fundatrix (stem mother) emerges. The fundatrix, and a l l the other subsequent morphs, undergo four molts before becoming a reproductive adult, at which time, with the exception of the sexuals, they reproduce parthenogenically, and viviparously. The fundatrix produces more apterous females c a l l e d fundatrigeniae (progeny of fundatrix). These in turn grow and, by the end of May, produce both apterous and alate •4. A l l temperatures are quoted in degrees Celsius. 7 (winged) virginoparae (producer of v i r g i n s ) . Maximum production of alates coincides with the flowering and seeding of biennial c r u c i f e r s , and results in the well documented migration to newly planted crops in June or July. During the summer, virginoparae continuously give r i s e to more apterous and some alate virginoparae u n t i l vegetative growth peaks, at which time maximum alate production and f a l l migration occurs. In August or September, the virginoparae give r i s e to sexuparae (producer of sexuals). These produce alate males and apterous females, which mate and lay eggs (holocyclic l i f e cycle) on wild and cu l t i v a t e d c r u c i f e r s . The l i f e history in warm temperate, and semi-tropical areas such as Australia, C a l i f o r n i a , and France, i s similar with respect to production of alates and movement between summer and winter crops, and wild c r u c i f e r s , but the aphid forgoes the sexual and egg stages, maintaining i t s e l f as virginoparae (anholocyclic l i f e c y c l e ) . Since there is no dormant period, the aphid may go through as many as t h i r t y generations 5 in a year, as compared to fourteen in temperate countries. 5 . A generation i s taken as the time from b i r t h to reproductive age. 8 3. Taxonomy B. brassicae was o r i g i n a l l y described by C. Linne' (1 758). According to Bodenheimer & Swirski(1957), synonyms are: Aphis brassicae L., A^ raphani Shrank, A_j_ floris-rapae Curt.; Siphoicoryne brassicae Goot; Brachycolus brassicae L.. The following description is based on personal observation and Essig(l948), but Palmer(l952) provides a more technical account. B. brassicae can be separated from other aphids in the f i e l d by the very dense colonies which they form on c r u c i f e r s , the white waxy coating on their bodies, which are no greater than 2.15mm in length, and the short barrel shaped c o r n i c l e s . The alate morph is similar to that of Myzus persicae (Sulzer) (which colonizes the same host plants), but may be d i f f e r e n t i a t e d using c o r n i c l e s i z e . The oviparae are readily i d e n t i f i e d by the hind t i b i a , swollen with sex pheromone producing plaques (Eisenbach & M i t t l e r 1980), and by the scattered sensoria on the III, IV, and V antennal segments. Males are alate and have an obvious aedeagus (ph a l l i c organ). Essig(l948) provides excellent drawings of each morph. 9 4 . M o r p h d e t e r m i n a t i o n P r o d u c t i o n o f a l a t e s i s c o r r e l a t e d p o s i t i v e l y w i t h d e n s i t y a n d i n v o l v e s two f a c t o r s : p l a n t q u a l i t y , a n d i n c r e a s e d c o n t a c t d u e t o c r o w d i n g ( B o n n e m a i s o n 1951). The e f f e c t s o f p l a n t q u a l i t y a r e u n c l e a r . B a r a n ( l 9 7 0 ) s u g g e s t s t h a t a l a t e p r o d u c t i o n i s c o r r e l a t e d p o s i t i v e l y w i t h a s a p s u g a r / n i t r o g e n r a t i o e x c e e d i n g o n e , w h i l e W h i t e ( l 9 7 2 ) s u g g e s t s t h a t m o s t a p t e r a e a r e p r o d u c e d u n d e r t h e s e c o n d i t i o n s . L e e s ( l 9 6 6 ) s t a t e s t h a t t h e r e h a s b e e n no c o n c l u s i v e e v i d e n c e t h a t s a p n u t r i e n t s a f f e c t t h e p r o d u c t i o n o f a p t e r a e a n d a l a t e i n a n y a p h i d ( c f S c h a e f e r s 1972). A l t h o u g h B o n n e m a i s o n ' s c o n t a c t t h e o r y h a s become w e l l e s t a b l i s h e d , i t i s u n c l e a r when t h e m e c h a n i s m o p e r a t e s . L e e s (1966.) s u g g e s t s t h a t t h e m o t h e r d e t e r m i n e s t h e m o r p h o f h e r p r o g e n y d e p e n d i n g on c r o w d i n g by h e r own n y m p h s , b u t h i s e x p e r i m e n t s c o n f o u n d c r o w d i n g o f m o t h e r by nymphs w i t h c r o w d i n g o f nymphs by t h e m s e l v e s . K a w a d a ( l 9 6 5 ) p r e s e n t s e v i d e n c e w h i c h s u g g e s t s t h a t w i n g d e t e r m i n a t i o n o c c u r s w i t h i n 48 h o u r s a f t e r b i r t h a n d d e p e n d s on c r o w d i n g . B o n n e m a i s o n ( 1 9 7 7 ) , on t h e o t h e r h a n d , s h o w e d t h a t f e m a l e s f r o m a n h o l o c y c l i c c l o n e s w h i c h w e r e r a i s e d i n c r o w d e d c o n d i t i o n s p r o d u c e d f a r m o r e a l a t e p r o g e n y t h a n f e m a l e s f r o m h o l o c y c l i c c l o n e s r a i s e d u n d e r t h e same c o n d i t i o n s . F u r t h e r m o r e , L e e s ( l 9 6 6 ) s h o w s t h a t a f e m a l e p r o d u c e s more a l a t e s w i t h a g e . The p h e n o m e n o n i s c o m p l e x a n d n o t w e l l u n d e r s t o o d . One t h i n g i s c l e a r , a l a t e s a l m o s t e x c l u s i v e l y p r o d u c e a p t e r a e ( B o n n e m a i s o n 1951). T h i s p h e n o m e n o n i s a s s o c i a t e d w i t h 10 increased a c t i v i t y of the mother's corpus allatum after the imaginal molt. The increase in juvenile hormone i s s u f f i c i e n t to keep her progeny apteriform despite environmental conditions (White 1965). Production of sexuals i s influenced by photoperiod, temperature, parental type, and time dependent i n h i b i t o r s (Lees 1966). By varying lengths, timing, and sequences of photoperiod, for Megoura vieiae Buckton, Lees has shown that: photoperiod experienced by a virginopara a f f e c t s her grandaughter's form; night length activates the photoperiodic response, rather than day length; short nights activate the response i r r e v e r s i b l y , while the effect of long nights may be reversed by short ones; high temperatures (>20°) did not af f e c t the photoperiodic response. Presumably these results also apply to B^ brassicae except that temperatures >25° cancel the photoperiodic e f f e c t , while at 22° some males appear and <20° both males and oviparae appear (Lees 1966). C r i t i c a l day length for production of B^ brassicae sexuals i s less than 13 hours (Kawada 1967), with an optimum between 10-12 hours (Pagliai 1965). Given the proper photoperiod, production of oviparae i s p o s i t i v e l y correlated with density (Kawada 1967). B. brassicae sexuparae may be apterous or alate and can produce virginoparae as well as sexuals, (Lees 1966). 11 5. Behavior Three kinds of behavior have been intensively studied: f l i g h t , host finding, and aggregation. F l i g h t and host finding behaviors have important consequences in terms of plant virus epidemiology, (Kennedy et a l 1959). F l i g h t of newly formed alates i s generally i n i t i a t e d early in the morning (van Emden 1972), and is directed mainly by atmospheric turbulence (Taylor 1965). (Note however, that Shaw(l968) using the bean aphid Aphi s fabae Scop., distinguishes between long distant dispersers 'migrants' and lo c a l dispersers ' f l i e r s ' , varying proportions of which are produced in re l a t i o n to plant quality and population density.) Descent, given reduced atmospheric turbulence, i s i n i t i a t e d by a positive response to long wave lengths (>500mu) of li g h t radiated by both s o i l and plants (Kennedy et a l 1961, Kring 1967). The aphid does not alight p r e f e r e n t i a l l y on i t s host and only a small minority a l i g h t i n g on food-plants remain long enough to reproduce (Kennedy et a_l 1959). Petersson(1973) on the other hand found that viviparous alates were attracted through olfactory stimulation to the heads of flowering rape. V a r i e t a l differences (Dunn & Kempton 1972), and water stress (Wearing 1972), aff e c t the length of this period and hence reproduction. Those that do remain are found mainly on the plant apex and mature leaves (Wearing 1972). N a u l t d 972), and Wensler (1 962) have shown that the mustard o i l glucoside, s i n i g r i n , i s detected by an alate in the f i r s t feeding probes and acts as a stimulant for s t y l e t 1 2 penetration and hence host selection. The proportion of alates making subsequent f l i g h t s may be related to the length of the i n i t i a l f l i g h t (Woodford 1973, data for persicae). On a seasonal basis, alate f l i g h t a c t i v i t y peaks in the spring and f a l l (Robert & Rouze'-Jouan 1976, Lowe 1966, and O'Loughlin 1963). Temperature, and to some extent wind and rain, influence alate f l i g h t patterns (Fehre 1971). Aggregation behavior has important consequences for population growth at the scale of the host plant, l o c a l l y , and regionally (Way 1968). brassicae colonies are generally formed by the movement of the nymphs of an immigrant alate such that their s t y l e t s are inserted close to those of their mother's (personal observation; see Way & Cammell'1970). This gregarious behavior results in increased photosynthate production by mature leaves of older' plants, and increased translocation of nutrients, in plants of a l l ages, to aphid infested leaves, (Way & Cammell 1970). These authors show that aphid size i s at f i r s t p o s i t i v e l y , then negatively correlated with density. Gregarious behavior also affects the production of alates, both d i r e c t l y and i n d i r e c t l y as discussed in section (I.B.4). These phenomena r e s t r i c t over-exploitation of the plant and maximize production of alates which find new host plants and maintain the regional population (Hughes 1963, Way 1973). Viewing the situ a t i o n from the view point of parasitism, Rlingauf & Sengonca(1970) suggest that the lack of response by |L_ brassicae to an approaching parasite is compensated by aggregation which minimizes the number of 13 interactions between aphid and parasite. 6. Host plant relationships Several population parameters are d i r e c t l y related to host plant condition. Fecundity and survival of brassicae are affected by v a r i e t a l differences (Dunn & Rempton 1969,1971,1972, Lamb & Lowe 1967, Root & Olson 1969), and the response varies with the aphid biotype (Dunn & Kempton 1972). Fecundity i s p o s i t i v e l y correlated with t o t a l soluble nitrogen and, at f i r s t p o s i t i v e l y , then negatively correlated with potassium l e v e l s in Brussels sprout leaves (van Emden 1966). Furthermore, although fecundity does not vary with leaf age, fecundity per unit soluble nitrogen is p o s i t i v e l y correlated with leaf age (van Emden & Bashford 1969). Growth rate of the aphid i s unaffected by the age of Brussels sprout plants, but is p o s i t i v e l y correlated with p a r t i c u l a r amino acids (van Emden & Bashford 1971). Rate of nymph production i s p o s i t i v e l y correlated with intermittent water stress (van Emden & Wearing 1965), and the effects vary with leaf age (Wearing 1972(a)). Intermittent water stress reduces tugor pressure, but accelerates proteolysis in aging leaves and flushes the nitrogen r i c h phloem sap to other parts of the plant, p a r t i c u l a r l y the youngest leaves. Growth regulators and herbicides have negative e f f e c t s on B^ brassicae population growth (van Emden 1964, Honeyborne 1969). Variation in levels 14 of mineral s o i l nutrients affected population growth both p o s i t i v e l y and negatively (El-Tigani 1962). F i n a l l y , Nawrocka & Brzeski ( 1973) f i n d "that the rate of increase of brassicae is p o s i t i v e l y correlated with the density of Heterodera schacht i i Schm. (Nematodea, Tylenchida, Heteroderidae) 6 which feed on the roots of cabbage. This b r i e f review indicates that the aphid-host plant relationship i s complicated and not well understood. Certain f i e l d observations reinforce this point, notably: B^ brassicae appears to increase rapidly in both the spring and the autumn, a phenomenon which may be related to plant quality (Hafez 1961); B_^ brassicae appears to increase rapidly when the plant bolts (Paetzold & Vater 1967); resistant v a r i e t i e s lose their resistance when the plant flowers (Dunn & Kempton 1969). 7. Predator-prey relationships Although food preference, and survival t r i a l s have indicated the u n s u i t a b i l i t y of B^ brassicae as food for many chrysopids, c o c c i n e l l i d s , and syrphids (Canard 1970, Okamoto & Sato 1973, Schmutterer 1972, Srivastava et a l 1978, Weires & Chiang 1973), a survey of f i e l d studies from 21 countries d i s t r i b u t e d throughout the world indicated the following to 6. Nematode c l a s s i f i c a t i o n follows Southey(1978). 15 u t i l i z e brassicae for food: 7 members of the family Anthocoridae (Hemiptera) (3 records); three species in the family Cecidomyiidae (Diptera), the most common8 being Aphidoletes aphidimyza (Rond.); four species in the family Chrysopidae (Neuroptera), the most common being Chrysopa carnea Steph. ; nine species in the family Coccinellidae (Coleoptera), the most common being Coccinella septempunctata L.; two species in the family Haemerobiidae (Neuroptera) (2 records); five species in the superfamily Ichneumonoidea (Hymenoptera), the most common, Diaeret i e l l a rapae (M'Intosh), being as cosmopolitan as i t s host; twenty-two species in the family Syrphidae (Diptera), the most common being Episyrphus balteatus (Deg.); one species of Trombidiid mite (Acari) (1 record); and three species of p a r a s i t i c fungus in the family Entomophthoracae (Entomophthorales) 9. The parasite D^ rapae and the syrphids are themselves parasitized by at least twelve, and nine species respectively, of Hymenoptera. Studies of the l i f e history, anatomy, i d e n t i f i c a t i o n , behavior, developmental times and temperature thresholds, voracity, reproductive rate, i n t e r s p e c i f i c interaction, and f i e l d populations, have been made for some species in the families: Cecidomyiidae (predaceous)- Adams & Prokopy(1977), Harris(1973), Havelka(1980), Linskii(1977), Markkula et al(!979), and Wood-Baker(1964); 7. The term predator includes parasites and fungal diseases. 8. Most common reference. 9. Fungi c l a s s i f i c a t i o n follows Ainsworth et a1(19 7 3 ). 16 Aphidiidae - H a f e z ( l 9 6 l ) , Pimentel(1961), Sengonca & Klingauf(1973), Takada(1976), Vater(l971) and Stary'(1970); Syrphidae (predaceous)- Chandler(1968), Glumac(1966), Pollard(1971), Schneider(1969) Sundby(1966), and Wnukd 973). Numerous claims have been made regarding the effectiveness of the various b i o t i c agents in reducing or c o n t r o l l i n g B. brassicae numbers on commercial crops (Habib 1973, Hafez 1961, Herakly & El-Ezz 1970, Tsachev 1972, Yastrebov 1979). Less numerous are claims regarding their ineffectiveness (Daiber 1971). In either case, conclusions are usually based on correlations between predator numbers, and changes in prey numbers. Rigorous quantitative assessment of the predators' effect i s rare. A subject of great concern has been the effect of the parasite EK_ rapae on numbers of B^ brassicae. Although Habi b ( l 9 7 3 ) , Herakly & El-Ezz(1970), Yastrebov(1979), and others, conclude that rapae 'controls' populations of B. brassicae, Chua(l977), H a f e z ( l 9 6 l ) , Hughes(1963), Oatman & Platner(1973), Otake(l966), and Paetzold & Vat e r ( l 9 6 7 ) come to quite the opposite conclusion. H a f e z ( l 9 6 l ) suggests that the i n e f f i c i e n t behavior of the parasite at high aphid densities, hyperparasitism, and slow development of the parasite r e l a t i v e to the host, are the factors responsible for i t s ineffectiveness. However, having modeled the aphid-parasite interaction, G i l b e r t & Hughes(l97l) suggest that the parasite, 1 7 which was recently introduced into Australia from Europe, has evolved to maximize i t s own reproduction without endangering the aphid. They suggest that although the b i o l o g i c a l d e t a i l s are d i f f e r e n t , the parasite's strategy is the same in Europe, and that, in general, a species' strategy may be, "determined more by the species on which i t feeds than by the species which feed on i t " . Frazer & Gilbert(1976) give a detailed account of a co c c i n e l l i d - a p h i d relationship, but the species involved were not those found in- the complex being studied. Similar studies using septempunctata, which at times has a major influence on brassicae numbers (Hafez 1961, Yastrebov 1979), would be inte r e s t i n g . brassicae, unlike many aphids, shows no alarm pheremone reaction (Kislow & Edwards 1972). The e f f e c t s of various c u l t u r a l practices such as the maintenance of hedgerows, or multi-species plantings, which affect the a v a i l a b i l i t y of natural enemies, are considered by van Emden(l965), Pimentel(1961 a), and E l T i t i ( l 9 7 4 ) . In general, the more complex the f l o r a , the greater the number of predators and the fewer the numbers of L brassicae. 18 8. Weather Two aspects of weather, temperature and r a i n f a l l , affect B. brassicae reproduction, developmental rate, longevity, movement, and survival, both d i r e c t l y and i n d i r e c t l y . In general, developmental rate increases l i n e a r l y with temperature above a threshold (Bonnemaison 1951, Daiber 1970, DeLoach 1974, Hafez 1961, Hughes 1963). Developmental time can be expressed in terms of day-degrees 1 0. Frazer & Gilbert(1976) provide an algorithm for calcu l a t i n g day-degrees from minimum and maximum temperatures in the f i e l d . Campbell et §_1 (1974) present evidence to suggest that the developmental temperature threshold and developmental rate of brassicae (and other aphids) are adjusted to suit l o c a l conditions, such that the threshold and developmental time are related p o s i t i v e l y to temperature. Furthermore, they suggest that parasite and hyperparasite temperature thresholds and developmental times are, in general, greater than that of their host. The rate of reproduction is also d i r e c t l y related to temperature above the developmental threshold, while longevity i s inversely related to temperature (Hughes 1963). As indicated e a r l i e r , temperature affects the production of sexual morphs. Fehre(l97l) notes that yellow water trap catches, and therefore f l i g h t a c t i v i t y of B^ brassicae, were 10. One day-degree is one degree above the temperature threshold for a period of one day. 19 d i r e c t l y r e l a t e d to temperature and l e s s so to wind and r a i n (although these v a r i a t e s must have been c o r r e l a t e d ) . Hafez(l96l) notes that a l t e r n a t i o n of warm with c o l d p e r i o d s i n the s p r i n g caused a l a r g e number of newly hatched f u n d a t r i x aphids to d i e . H u g h e s ( l 9 6 3 ) noted l a r g e decreases i n B. b r a s s i c a e p o p u l a t i o n s given heavy r a i n s a f t e r a hot dry p e r i o d . Wet weather c o n t r i b u t e s i n d i r e c t l y to B^ b r a s s i c a e m o r t a l i t y by p r o v i d i n g s u i t a b l e c o n d i t i o n s f o r e p i z o o t i c s of the entomophagous fungus (Hafez 1 9 6 1 , Hughes 1 9 6 3 ) . 9. Po p u l a t i o n dynamics Most s t u d i e s of the p o p u l a t i o n dynamics of B^ b r a s s i c a e i n v o l v e the monitoring of aphid and predator numbers through time, f o r example: Azab e_t a _ l ( V 9 6 6 ) , Bonnemai son ( 1 9 7 1 ) , D a i b e r ( 1 9 7 1 ) , Dunn & Kempton(1971 a ) , Herakly & E l - E z z ( 1 9 7 0 ) , Lamb & L o w e ( l 9 6 7 ) . These s t u d i e s were f o r the most part aimed at d eveloping proper timing of c o n t r o l measures, and determining v a r i e t a l r e s i s t a n c e . They r e v e a l l i t t l e , of the processes r e s p o n s i b l e f o r p o p u l a t i o n change. Van E m d e n ( l 9 6 3 ) , and McLaren & Pottinger(1969) attempted to b u i l d l i f e t a b l e s for Bj_ b r a s s i c a e by r e g u l a r examination of c o l o n i e s . However, o v e r l a p p i n g generations made the r e s o l u t i o n of b i r t h and death r a t e s i m p o s s i b l e . One of the most d e t a i l e d p o p u l a t i o n dynamics s t u d i e s , H a f e z ( 1 9 6 l ) , regards the a n a l y s i s of p o p u l a t i o n changes as too d i f f i c u l t f o r three reasons: o v e r l a p p i n g 20 generations; interaction of factors; complexity of f i e l d conditions. However, co r r e l a t i n g changes in various factors with population change, he concludes that population growth of B. brassicae was checked in the spring of 1959 and 1960 by predators, but was unchecked in the f a l l and could reach very high numbers unless cool wet weather (which limited alate emigration, and favored fungal disease) occurred. Hughes ( l963) attempted to circumvent the objections of Hafez ( l 9 6 l ) using an i n s t a r - d i s t r i b u t i o n analysis outlined in Hughes (1962). Hughes calculated reproductive rates in the f i e l d , and the effects of various agents on the rate of increase. He concluded that natural enemies caused aphid numbers to decline only after emigration, and a density-induced decline in the reproductive rate, reduced the rate of increase. Hughes & Gilbert ( 1 9 6 8 ) produced a computer model incorporating the major relationships (developmental time and temperature, reproduction and density, emigrant production and density, predation by syrphids and aphid density, p a r a s i t i z a t i o n and several f a c t o r s ) , which mimicked the f i e l d data very c l o s e l y . An examination of the model however, reveals some important inaccuracies, notably: the lack of age-specific reproduction (cf Hafez 1 9 6 1 ) ; and a reproductive rate of forty nymphs/instar (instead of forty nymphs/lifetime), which i s apparently corrected for by the density-induced reduction in fecundity. Further, Carter et a l ( l 9 7 8 ) show that estimates of reproductive rate based on age d i s t r i b u t i o n s are questionable at best, and that a stable age d i s t r i b u t i o n (a prerequisite for determining the reproductive 21 rate using Hughes' technique) is never achieved in Hughes' f i e l d data. Although Hughesd 963) tested for stable age d i s t r i b u t i o n , his test was less stringent than Carter et a l (1978). 2 2 II. THE STUDY A. Preface The basic approach to the study of the population dynamics of brassicae was synthetic (Barlow & Dixon 1980), and can be represented by the difference equation: N(Time(t+T))• = N(Time(t)) + Gains - Losses where: Gains = Births + Immigration Losses = Deaths + Emigration and: Time (generation time) = f(temperature, aphid density ) Births = f(aphid age, plant quality, aphid density, temperature ) Deaths= f(aphid age, predators, parasites, plant development, temperature......) Immigration = (pooled with emigration) Emigration = f (plant quality,- aphid density ) The study involved three steps: measurement of the temporal. variation in abundance, quality, and population structure of B. brassicae, as well as variation in the b i o t i c and abio t i c factors which affect these parameters (II.B.); q u a n t i f i c a t i o n of relationships between said factors and the b i r t h rates, developmental rates, survival, immigration and emigration of B. brassicae (II.C.); consolidation of the relationships to see i f they explain the-temporal variation in abundance, quality, and population structure of B^ brassicae (II.D.). For p r a c t i c a l reasons, the s p a t i a l scale was limited to a group of plants 0.1ha in area, and the temporal scale was limited to the spring and summer months when virginoparae are ac t i v e l y 23 reproducing. B. Measurement of temporal variation in the components of the system 1 . The study area Two s i t e s were chosen for climatic differences: Agriculture Canada Research Station f i e l d plots at Abbotsford (49° 01 Min. N. l a t . ; 122° 22 Min. W. long.); and University of B r i t i s h Columbia, Plant Science f i e l d station on Point Grey (49° l5Min. N. lat.,-123° 15 Min. W. long.). The former has an inland semi-arid climate; mean monthly maximum, and minimum temperatures, and r a i n f a l l from June to September inclusive over the l a s t ten years were 30.3±0.25°, 4.7±0.14°, and 2.4± 0.30cm resp e c t i v e l y . 1 The l a t t e r has a coastal marine climate, in which the same measurements were: 25.3±0.17°, 8.2±0.13°, and 2.0+0.18cm res p e c t i v e l y . 2 The Abbotsford plot was surrounded by a g r i c u l t u r a l land and the Point Grey plot was surrounded by forest and ocean on the south and west and the University of B r i t i s h Columbia and c i t y of Vancouver on the north and east. Abbotsford s o i l is 20-50cm of s i l t loam over gravelly sands, well drained, and belongs to the Abbotsford s o i l series (Luttmerding 1980). Point Grey s o i l i s about 100cm of sandy 1. A l l variation quoted is one standard error of the mean. 2. Data were obtained from Province of B r i t i s h Columbia Department of Agriculture (1967-1977). 24 loam over a generally sandy loam subsoil, moderately well drained, and belongs to the Base s o i l series (Luttmerding 1980) . 2. The plant B. oleracea L. var. acephala DC. 'Maris Kestrel', was chosen as the host plant. It is a marrow-stem kale which bears at maturity, t h i r t y to forty large (up to 2000 cm2) unwrinkled leaves on a 100-150cm high stem. These c h a r a c t e r i s t i c s f a c i l i t a t e d observation of plant growth, and sampling and observation of the insect fauna. Plants were grown in the greenhouse for four to fiv e weeks, in 10x10x10cm pots containing s t e r i l i z e d loam s o i l . The s o i l was kept moist but not wet, and was treated weekly with 20-20-20 (N,P,K) f e r t i l i z e r (0.0312ml/l). The plants were hardened off for one week before transplanting. A f i e l d plot consisted of approximately 1000 plants aligned on a 0.6x1.0m grid . The plots were f e r t i l i z e d according to normal a g r i c u l t u r a l practice (see Province of B r i t i s h Columbia Ministry of Agriculture 1977). The following was applied two weeks before planting: Sul-Po-Mag (170Kg/ha) for magnesium deficiency and whipstem, Lime (700Rg/ha) for clubroot, Boron (22Kg Borate 68(20.5%Bo)/ha) for boron deficiency and various physiological disorders, N-P-K (700Rg (10-30-10)/ha) for 2 5 optimum plant growth and development, and T r e f l a n 3 (4.251/ha) for the control of annual weeds. These chemicals were double disked and harrowed into the s o i l . Birlane* (0.6gm) was sprinkled around each plant immediately after transplanting, to protect them from the cabbage root maggot Hylemia brassicae (Bouche). The plots were weeded three and six weeks after planting. There after shade from the kale r e s t r i c t e d weed growth. In the seventh week after planting, a mid-season side dressing of nitrogen (45Kg/ha) was applied. The plots were watered using a Rainbird i r r i g a t i o n system as required. The i r r i g a t i o n system, which linked six 30b sprinkler heads with 7.5cm aluminum pipe to a water main, delivered enough water to saturate the earth in four hours. F i e l d plots were l e f t over winter to catch spring migrant aphids on the prominent, yellow flowering, reproductive s t a l k s . They were then plowed under before the seed ripened. 3. Treflan, t r i f l u r a l i n , is a d i n i t r o weedicide. 4. Birlane, chlorfenvinphos, is an organophosphate, non-systemic i n s e c t i c i d e . 26 3. The weather A l l measures of weather except temperature were obtained from the class A weather stations at the University of B r i t i s h Columbia, and Abbotsford Airport. The f i e l d plots were located within 100m, and 1km of these stations respectively. Temperature at Point Grey was measured with calib r a t e d maximum-minimum thermometers supported 20cm above the ground and shaded by aluminium shields. The thermometers were calibrated against an accurate thermometer in the laboratory, using linear regression techniques. The effects of solar radiation were checked by comparing readings of an electronic thermistor t e l e -thermometer 5 placed near the aphids, with the maximum-minimum thermometer readings. Since the l a t t e r consistently recorded lower temperatures (2.5±0.25) under sunny conditions, irrespective of plant size, a l l maximum temperatures were increased proportional to the hours of dail y bright sun (Appendix 1(a)). Missing data were estimated from regressions of f i e l d measures of maximum and minimum temperatures on weather station measures (Appendix 1(b)). Temperature at Abbotsford was measured with a calibrated thermograph located 20cm above the ground in a Stevenson screen. The dail y maximum of these measurements were adjusted for solar radiation effects as indicated above. 5. Electronic thermister - Yellow Springs Instrument Co. Inc., model.# 46TUC. 27 4. F i e l d sampling a. The insects The aphids, and a l l associated fauna were sampled using a s t r a t i f i e d random sampling scheme (Hughes 1963). A leaf was the sampling unit. In general: stratum 1 upper leaves, were young, thin, s l i g h t l y wrinkled, and l i g h t green; stratum 2 middle leaves, were older, larger, thick, f l a t , and dark green; stratum 3 lower leaves, were yellow and senescing. The size and shape of leaves included in each l e v e l varied through the season, so i t was necessary to define the stratum at each sample. Sample size varied d i r e c t l y with stratum size and available help, and inversely with aphid population size. Samples tended to be larger in the spring (40,130,30 leaves/stratum 1,2, and 3 respectively), and smaller in the f a l l (45,45,35 leaves/stratum 1,2, and 3 respectively). A computer program was written which determined, using a uniform random number generator, the co-ordinates of the plant to be sampled, and the v e r t i c a l position (a,b, and c) within each stratum, from which to take the l e a f . The technique provided an unbiased sample, because the aphids and associated fauna l i v e d exclusively on the leaves, and a l l leaves within a stratum were equally l i k e l y to be sampled. Due to the intensive labour required in processing each leaf separately, a l l leaves for each stratum were lumped together. The number of insects per plant was estimated by multiplying the mean 2 8 number per leaf (in each stratum) by the mean number of leaves per stratum, and summing over a l l st r a t a . In the laboratory, ten to twenty adult apterous - B. brassicae, and up to 200 parasite cocoons 6 were removed from a r b i t r a r i l y chosen sections of several leaves. (The former was done only in the last two sampling years.) The aphids were in d i v i d u a l l y weighed (±0.00lmg) using a micro-balance 7 and examined for parasite larvae by dissection. The cocoons were placed i n d i v i d u a l l y in gelatin capsules and the parasites or hyperparasites allowed to emerge at 21°. The leaves were then placed in a dacron R bag and heated in a forced a i r oven (60-70°) for 20-30 minutes. This treatment caused the aphids to remove their s t y l e t s from the leaf, and they and their associated fauna could be eas i l y shaken off into . the bag (Hughes 1963). The leaves were checked for remaining fauna which were not removed by the heat treatment. Insects were stored in 80% ethanol. Fauna included the aphids B^ brassicae and M^ persicae(Homoptera:Aphididae), at least three species of syrphid larvae from two genera (Syrphus, and Scaeva) (Diptera:Syrphidae), cecidomyiid larvae aphidimyza (Diptera:Cecidomyiidae), cocoons of rapae (Hymenoptera:Aphidiidae) (and associated hyperparasites from at least one genus ( A l l o x y s t a ) 8 (Hymenoptera:Cynipidae)), spiders, 6. Cocoon refers to the aphidiid pupa encased in an aphid's exoskeleton. Sometimes c a l l e d a mummy. 7. Micro-ballance - Metier, model# ME30. 8. Formerly Charips (Andrews 1978). 2 9 and the fungus Entomophthora aphidi s Hoffman (Entomophthorales:Entomophthoracae). The aphids in the sample were separated by species under a stereoscope 9 and sorted into healthy parthenogens, healthy sexuals (adult females and males), l i v e , but fungus-infected individuals (recognized by an orange-pink colouration and often granular appearance (Hughes 1963)), and cecidomyiid- and syrphid-attacked individuals (recognized by a flattened, empty exoskeleton) . A l l were counted, and except for persicae, aged to ins t a r . Reliable age-specific c h a r a c t e r i s t i c s (Appendix 2), were determined by rearing aphids i n d i v i d u a l l y , c o l l e c t i n g them after a known number of molts, and examining their morphology. In samples containing more than 2500 aphids, numbers were estimated using a subsampling technique and r a t i o estimation. The sample, was cleaned of any large debris and mixed in 80% ethanol using a magnetic s t i r r e r . Three aliquots were withdrawn from dif f e r e n t places in the vortex with a pipette (6.0mm i d , 4.0mm apperature), and placed in an Imhoff sedimentation cone. The remainder of the sample was placed in another cone. The volume of aphids and other fauna was recorded from both cones after 5 minutes. Aphids in the subsample (1.0 - 2.0ml, approximately 1300 aphids) were sorted as indicated above, and counted. These counts were multiplied by the r a t i o of the t o t a l sample to subsample volumes to 9. Stereoscope - Wild, model# M7A. 3 0 estimate t o t a l aphids. Since subsamples generally contained more than 1000 aphids, these were further subsampled to determine age d i s t r i b u t i o n s . The aphids were thoroughly mixed, a section was divided o f f , and a l l the aphids therein were aged to instar. This was repeated u n t i l a minimum of 300 aphids were examined. The accuracy of the technique rests on two assumptions: that the subsampling was unbiased with respect to age d i s t r i b u t i o n ; that packing in the subsample volume was the same as that in the main sample volume. Comparison of age d i s t r i b u t i o n s in four subsamples with that of the whole sample (3500 aphids) using Chi-square and Bonferroni Chi-square s t a t i s t i c s ( Jensen et. a l 1968) suggested that the age d i s t r i b u t i o n s were s t a t i s t i c a l l y d i f f e r e n t , but that the differences were not consistent with respect to instar. To check that packing was equivalent in both subsample and sample, samples of d i f f e r e n t sizes (3.-206.ml), were s p l i t into 'n' volumes of t y p i c a l subsample si z e . The sum of these smaller volumes was regressed on the o r i g i n a l t o t a l volume (Appendix 1(c)). This equation was used to adjust the main sample volume to a volume in which packing was equivalent to that of the subsample. Other data extracted from the samples were the numbers of syrphid larvae, cecidomyiid larvae, emerged and unemerged parasite cocoons, and spiders. Syrphid and cecidomyiid larvae and spiders were rarely numerous enough to require subsampling. However on some occasions the volume of the sample (>20ml 31 approximately 20,000 aphids) made searching for a l l the larvae impossible. In these cases the sample was thoroughly mixed and three, one-eighth portions of the sample were inspected. Ratio estimation was used to obtain the t o t a l s . One standard error was 9% of the mean. Parasite cocoons were counted d i r e c t l y , except when they became numerous (>500/sample). In this case, the f l o a t i n g cocoons were d i r e c t l y counted, and the remainder were subsampled with the aphid subsample. The precision of the estimates of mean numbers of B. brassicae per average plant was calculated on two sampling occasions (one at the beginning, and one in the middle of a f i e l d season), by processing each leaf separately. One standard error of the mean aphids/plant, was 39% and 43% for the early and later sample occasions respectively. Similar calculations made for cecidomyiid larvae, syrphid larvae, and parasite cocoons (on the later sample only) indicated that one standard error was 32%, 32%, and 27% of the mean number/average plant respectively. Variation a r i s i n g from the c a l i b r a t i o n of volumes, and subsampling was small (one standard error was 3.5% of the mean aphids/ml). The estimate for the precision of the overall sampling scheme was largely determined by leaf to leaf variation ( i e . the clumped d i s t r i b u t i o n of organisms in the f i e l d ) . In order to obtain reasonable precision (1SE = 10%), sample size in each stratum would have to be 16 times larger. This was not possible in terms of time, and would undoubtedly interfere with the fauna being studied (current sample fraction of the aphid population was 0.5-1.0%). 32 F i e l d plots were planted and sampled on several occasions over a three year period (Table I ) . Since UBC2 and UBC4 were planted a f t e r the a r r i v a l of the immigrant alates, due to unexpected greenhouse conditions, i t was necessary to transfer to plants in these plots (using random number assignment), the aged progeny (fourth instar + adult apterae) of the alates, which were reared in the laboratory. UBC3 was planted before the a r r i v a l of immigrant alates and i t was necessary to use aphids reared in the laboratory over winter. Subsequent examination of transferred aphids indicated a minimum 82% survival rate. Each plot was sampled every 7-14 days depending on weather (sample frequency increased as temperature increased), except UBC3 and UBC4 which were sampled monthly. Several patterns emerge from an examination of the population t r e n d s 1 0 (Figure 1). The i n i t i a l rate of increase was approximately the same in a l l populations irrespective of year, location, or time of planting. At densities less than that observed in a field-cage experiment (see II.C.Ic), the rate of increase dropped markedly. This suggests that the upper l i m i t in the f i e l d was not set by the host plant. Nor was i t set by emigration, since the cages were opened dai l y allowing alate f l i g h t . Major declines in the rate of increase of B^ brassicae seem to be correlated with the appearance and increase in numbers of predators, p a r t i c u l a r l y cecidomyiid 10. M^ persicae, spiders, and fungus infected B^ brassicae were not s u f f i c i e n t l y numerous to warrant consideration. 3 3 Table I. Dates for plot planting, and i n i t i a l and f i n a l aphid samples. Location Name Planting Aphid I n i t i a l F i n a l date source " sample sample Abbotsford Abb 5 May 1977 immigrants 30 Jun 6 Oct Point Grey UBC1 30 May 1 977 immigrants 28 Jun 3 Oct Point Grey UBC2 26 Jun 1 978 lab colony 17 July 19 Sep Point Grey UBC3 3 May 1979 lab colony 8 May 25 Sep Point Grey UBC4 29 Jun 1979 lab colony 24 July 24 Sep 3 4 ~i r 130 0 65 130 TIME (DRTDEGREES >6.65C) ( X 1 0 ] ) F i g u r e 1. P o p u l a t i o n trends from Abb:(a), UBC1:(b), cages (see I I . C . 1 c ) : ( c ) , UBC2:(d), UBC3:(e), and UBC4:(f). B. b r a s s i c a e : ( ), A. aphidimyza l a r v a e : (• ), D. rapae unemerged cocoons: ( - — a n d Syrphidae l a r v a e : ( T~ as a f u n c t i o n of p h y s i o l o g i c a l time. 3 5 larvae. Although unemerged parasite cocoons occurred in large numbers (due to accumulation before emergence), they apparently track aphid numbers ( i . e . changes in rates of increase of each are p o s i t i v e l y correlated). These observations suggest that cecidomyiid and perhaps syrphid predators were largely a f f e c t i n g the course of an i n f e s t a t i o n . Comparison of the plots in di f f e r e n t locations within years show similar o v e r a l l trends, but d i f f e r e n t peak abundance (one order of magnitude). This could be associated with plot surroundings. Since the Point Grey plots were bordered by forest on two sides, and surrounding plots were rarely i f ever treated with i n s e c t i c i d e , a predator fauna existed in close proximity. In contrast, the Abbotsford plots were surrounded by a g r i c u l t u r a l land on which inse c t i c i d e s were used. These differences could allow B. brassicae to increase unchecked for a longer period at Abbotsford than at Point Grey. Comparison of plots in di f f e r e n t years within location show similar o v e r a l l trends and peak abundance, except when the plot was planted early in the season, and seeded with aphids at a time which would not occur in nature. Again the difference in peak population size (greater than one order of magnitude), could be interpreted as resulting from a lack of predators and/or reduced predation due to cooler temperatures, early in the season. The v a l i d i t y of these speculations w i l l be tested when the predator-prey relationships have been quantitatively assessed and linked with the prey's capacity to increase. 36 b. The plant The size of the f i e l d plants and stratum size, was estimated at each fauna sample. Plant height was measured (from ground to uppermost leaf in stratum 1), and the number of leaves in each stratum were counted. Leaf area, wet weight, and dry weight per plant were determined using a s t r a t i f i e d random sample i d e n t i c a l to that previously discussed for the aphid samples. Five to ten leaves per stratum, cut near the main stem of the plant, were cleaned and i n d i v i d u a l l y placed in numbered, preweighed p l a s t i c bags, to prevent water loss. These were weighed in the laboratory and wet weight was calculated. Leaf areas were measured using an e l e c t r i c p lanimeter 1 1. The leaves were then dried in a forced a i r drying oven (60-70°) for 24-30 hours, and reweighed u n t i l dry weight was constant. One standard error was approximately ±15% of mean area, wet weight, and dry weight per plant. The results of the plant samples were q u a l i t a t i v e l y the same in each f i e l d plot (Figure 2). Quantitative differences occurred at the asymptote. In p a r t i c u l a r , the Abbotsford plants had a lower upper l e v e l . The reason was not known. The most s t r i k i n g feature of the data i s the fast growth rate of the plant (there were 14-18 day-degrees/day). 11. E l e c t r i c planimeter - Numonics Corporation, model# 210-117. 37 (DRYDEGREES > 0 . 0 I <19.4C) F i g u r e 2. Leaf a r e a : ( a ) , wet w e i g h t : ( b ) , d r y w e i g h t : ( c ) , and l e a f number:(d), per p l a n t , as a f u n c t i o n of p h y s i o l o g i c a l t i m e . (Abb:A, UBC1:B, UBC2:C, UBC3:D, UBC4:E) 3 8 C. Relationships 1. Gains Reproductive potential, generation time, and physiological longevity are basic to the representation of the population dynamics of any organism. This section i s concerned with the prediction of these variables for brassicae. The general techniques are described below. Developmental time, and age-specific fecundity, and longevity of brassicae were determined by caging and continuously monitoring single aphids of a pa r t i c u l a r morph, or instar, under given environmental conditions. Laboratory studies were conducted on Maris Kestrel kale six to eight weeks old, grown and maintained as indicated in section (II.B.2). F i e l d studies were conducted either on f i e l d plants, or a group of plants, grown and maintained in a similar way. C l i p cages (two plexiglass cylinders 3.2cm in diameter x 0.8cm high), one with a gauze cover and both with a f e l t pad base, held together on either side of a leaf by a hair c l i p (melted into the pl e x i g l a s s ) , were used to contain individual aphids. Aphids were caged on the lower side of stratum 1 or stratum 2 leaves, their preferred feeding s i t e (Wearing 1972). A #000 camel hair brush was used to move them. Developmental time was measured by monitoring the development of individual aphids from b i r t h to adult.. Two adult aphids were caged separately on each of ten plants, for 39 eight to sixteen hours at 20°. The adults, and a l l but one of the nymphs produced per adult were then removed. The nymphs were checked for a molt (cast off exoskeleton) at regular i n t e r v a l s . The time of any given molt was taken as the mid-point of the interval between the time of observation of a molt, and the time last checked. Age-specific fecundity schedules were constructed from the number of nymphs counted and removed from caged adults each day. When only t o t a l fecundity was required, adults were allowed to reproduce u n t i l the oldest nymph molted to fourth instar. The nymphs were then counted and removed. Longevity was measured by checking d a i l y , aphids which had been reared from b i r t h , for time of death. An age-specific survival schedule was then derived. a. Developmental time vs temperature Developmental time was determined for approximately f i f t y aphids divided between four constant temperatures (8,13,18, and 23°). The frequency with which nymphs were checked depended upon temperature: three times a day at 23°, twice a day at 13 and 18°, and once a day at 8°. The experiment was performed for aphids c o l l e c t e d from both Abbotsford and Point Grey. Time from b i r t h to .birth of f i r s t nymph was greatly influenced by temperature (Figure 3(a)). The relationship was lin e a r i z e d and the developmental threshold determined by 4 0 0 8 16 24 TEMPERATURE (C) Figure 3. Developmental time of brassicae from b i r t h to f i r s t b i r t h : ( a ) , and i t s reciprocal:(b), as a function of temperature. Abbotsford and Point Grey aphid data combined. 41 regressing the reciprocal of developmental time (rate) against temperature (Figure 3(b)). The 'x' intercept is the theoreti c a l temperature at which no development occurs. Figure 3 lumps data from Abbotsford and Point Grey aphids since neither the slopes nor the intercepts were s i g n i f i c a n t l y d i f f e r e n t . The obvious, and s i g n i f i c a n t curvature in the data, p a r t i c u l a r l y at cool temperatures, i s real and expected (Campbell et a_l 1974). The linear model is an approximation, which works because temperatures which are normally experienced by the aphids in the f i e l d consistently l i e in the linear portion of the curve. Thresholds for each instar were also calculated (Table T l ) . The threshold from b i r t h to b i r t h of f i r s t nymph was adopted for the cal c u l a t i o n of physiological time since no obvious age-specific trends existed. Developmental time in day-degrees i s the reciprocal of the slope of the l i n e (Figure 3(b)). The developmental time of each instar (based on the same temperature threshold) was calculated (Table I I ) . The length of the fourth alate instar was determined by comparing i t to the length of the fourth apterous instar, measured simultaneously. The respective lengths 49.±1.2 and 35.±1.8 day-degrees(>6.7°) d i f f e r e d by a factor of 1.4. Developmental time was measured in the f i e l d with techniques similar to those used in the laboratory, except that temperatures were not constant, and the host plants were large (leaf area 25,000. cm 2). Developmental time in day-degrees was derived by integrating between a sine wave, f i t to maximum 42 Table II. Developmental temperature thresholds and developmental times for brassicae. Abbotsford and Point Grey aphid data combined. Threshold Standard Developmental Standard Instar (°C) error time error (day-degrees>6.7°) I 6.4 0.63 31.7 0.24 II 5.7 1 .39 32.9 0.45 III 7.1 1.18 27.8 0.52 IV 6.3 0.63 33.9 0.50 b i r t h to adult 6.5 0.29 126. 0.37 b i r t h to f i r s t b i r t h 6.7 0.29 1 42. 0.35 43 and minimum temperatures, and the developmental temperature threshold obtained in the laboratory (Morris & Bennett 1967, Frazer & Gilber t 1976), over the periods between successive molts. Developmental time from b i r t h to adult was 166.±4.2 day-degrees(>6.7°). This was spread evenly over each instar as in the laboratory, but was 1.31 times the laboratory value. Since laboratory and f i e l d measurements were made simultaneously with aphids from the same source, and possible errors in the measurement of temperature were i n s u f f i c i e n t to account for the difference, host plant qual i t y , or differences in aphid density (discussed later) were thought to be responsible for the reduced developmental rate in the f i e l d . b. Fecundity and longevity vs aphid age and temperature Age-specific fecundity was measured for Abbotsford and Point Grey B^ brassicae at the three highest temperatures (13,18, and 23°) of the previous laboratory experiment. Analysis of v a r i a n c e 1 2 indicated that t o t a l nymphs per female did not vary s i g n i f i c a n t l y with location, temperature, or frequency of removal of nymphs. Mean nymphs/female for the t o t a l reproductive period was 40.7±1.18. Regression of the rate of nymph production for the f i r s t 50% of the reproductive period against temperature, indicated a linear relationship 12. A l l significance tests were at p<0.05. 44 with a threshold of 5.6±2.31°. Age-specific fecundity tables were therefore constructed for each aphid based on physiological time above the developmental threshold of 6.7°, beginning at the molt to adult. The data were consolidated into a single age-specific fecundity curve (Figure 4(a)) since no trends in height of peak production, time of that peak, or end of reproductive period were obvious when comparing locations or temperatures. Alate fecundity was measured re l a t i v e to apterous fecundity. The t o t a l number of nymphs born to the former was 0.469±0.0830 times that born to the l a t t e r . The reproductive pattern for alates was assumed to be the same as for apterae, but reduced by the given factor. Longevity was measured for Point Grey brassicae at 13, 18, and 23°. The reciprocal of the reproductive time was related l i n e a r l y to temperature with a threshold of 4.8±5.05°. The reciprocal of the post-reproductive time was not related to temperature. However, since more than 80% of an aphid's l i f e was related to temperature around the developmental threshold, a survival curve based on physiological time above the developmental threshold was constructed (Figure 4(b)). Relationships between t o t a l nymphs produced and the time and height of peak reproduction, length of the reproductive period, and longevity were determined using the data c i t e d above. A l l variables were corrected for temperature above the 45 Figure 4. Age-specific fecundity:(a) and survival:(b) of laboratory reared brassicae as a function of physiological time from b i r t h . 46 developmental threshold. Mean time of peak reproduction 1 3 75.± 4.8 day-degrees after the molt to adult, was not related to t o t a l nymphs produced. The rate of reproduction at t h i s time, averaging 0 . 247±0.0063 nymphs/day-degree, was related l i n e a r l y to t o t a l nymphs produced (Appendix 1(d)). Length of the reproductive period, 249.110.9, was also related l i n e a r l y to t o t a l nymphs produced (Appendix 1(e)), but longevity was not. These analyses suggest that age-specific fecundity increases in both rate and duration as t o t a l fecundity increases. Attempts to represent the consistent changes in age-specific b i r t h rate as a simple gamma function (in which the c o e f f i c i e n t s were dependent upon t o t a l nymphs produced), f a i l e d . A polynomial (Appendix 1(f ) ) , represented the data adequately (Figure 5). Fecundity and longevity were measured in the f i e l d at the same time, using aphids from the same source as the laboratory experiments. Age-specific fecundity q u a l i t a t i v e l y followed the pattern obtained in the laboratory, but t o t a l nymphs produced per female was 27.0±2.40, 0.663 times the laboratory value. Although survival to reproductive age was 1.0 as in the laboratory, mean longevity was 1.2±0.01 times the laboratory value. As with the f i e l d measures of developmental time, i t was thought that differences in plant quality or aphid density were responsible. The discrepancies between laboratory and f i e l d estimates led to the following series of f i e l d 13. Peak reproduction was taken as the mid-point in time, at which the most nymphs were produced over a period of 60. day-degrees above the developmental threshold. 47 i 1 1 r 10 20 30 40 TIME (DRYDEGREES > 6 . 6 5 C ) (X10] ) F i g u r e 5. A g e - s p e c i f i c f e c u n d i t y of l a b o r a t o r y reared B. b r a s s i c a e as a f u n c t i o n of p h y s i o l o g i c a l time "(beginning at the molt to a d u l t ) and t o t a l f e c u n d i t y , (nymphs/female - 25:A, 35:B, 45:C, 55:D) 4 8 experiments and measurements (II.C.Ic - I l . C . l e ) . c. Developmental time, fecundity, and alate determination vs density, and plant quality The effects of aphid density, and plant quality on developmental time, fecundity, and alate determination were examined in a f a c t o r i a l field-cage experiment. Three levels of aphid density were obtained by allowing brassicae to reproduce for varying lengths of time before st a r t i n g the experiment. Two levels of plant quality were obtained by adjusting the watering regime (see I.B.6). These factors at the given le v e l s , produced six possible treatments, which were blocked, and replicated eight times. For each r e p l i c a t e , eight 25x30cm p l a s t i c greenhouse pots f i l l e d with f i e l d s o i l , were sunk into the earth around a c i r c l e 2m in diameter. Cages were b u i l t over six of the pots. Cheese clo t h 90cm wide, was wrapped around and stapled to wooden stakes such that a cage was formed when the bottom edge was buried, and the top edge was gathered together with an e l a s t i c band. Each pot recieved a kale plant, a 2cm diameter water pipe, and three sheets of p l a s t i c : one with holes, placed under the water pipe, to d i s t r i b u t e the water evenly, and two placed over the water pipe and held up by wood blocks, to shed rain. A l l eight water pipes led to the base of one of two central buckets, which were nailed to plywood placed on l e v e l 49 ground. These buckets had l i d s to shed rain and were used to supply water equally at the required rate. Treatments were assigned at random to the six caged plants in each r e p l i c a t e . The two uncaged plants were used to compare plant growth inside and outside the cage under the treatment conditions of high and low water and medium aphid numbers. Eight irrometers 1", one per r e p l i c a t e , divided equally between wet and dry treatments, were used to assess s o i l moisture. Two maximum-minimum thermometers were used to record temperatures in the cages. Response variates were leaf water/dry weight, leaf length and width, adult aphid weight, aphid fecundity, aphid developmental time, and f i n a l aphid numbers by instar. Leaf water/dry weight (an index of plant quality) was measured by weighing, drying, and reweighing, a 26mm diameter leaf bore from the middle of the second leaf from the top of stratum' 2. F i e l d plant samples were used to determine that subsample water/dry weight was l i n e a r l y related to whole leaf water/dry weight, (Appendix 1(g)). A relationship between leaf water/dry weight of the chosen le a f , and the whole plant was developed from the 1977 and 1978 f i e l d plant samples, (Appendix 1(h)). . Leaf length and width was measured for a l l leaves on a plant. The relationship between the length and width of a leaf and i t s area was determined using f i e l d plant samples (Appendix l ( i ) ) . Adult aphid weight (an index of aphid quality) was measured 14. Irrometer - moisture indicator, T.W. Prosser Co. Riverside C a l i f . 5 0 shortly after i n i t i a l reproduction. Weight before this time is affected by aphid growth, whereas weight after i s constant (Figure 6). 1 5 Data were obtained by weighing and discarding, at intervals of one instar period, three nymphs from a cohort produced over a 24 hour period. Aphid fecundity and developmental time were measured as indicated in section (II.C.1). F i n a l aphid numbers were obtained by applying the aphid removal, and subsampling techniques of section (II.B.4a) to whole plants. The experiment began June 9, 1978 after the cages were set up,, by introducing a large kale plant into each pot, to dry out the s o i l . On June 19 the s o i l in a l l pots was dry, and the watering regimes were established by adding d i f f e r e n t amounts of water to the two central buckets each day. Current a g r i c u l t u r a l practice is to i r r i g a t e when the irrometer reads 40 (0 is saturated). However, laboratory tests showed that s o i l watered to f i e l d capacity, lost 0.32±0.007 and 0.78±0.052 of i t s water between the readings 0. to 10. and 0. to 60. respectively. Therefore, the wet treatment was to hold the irrometer reading below 10., and the dry treatment was to allow i t to fluctuate between 0. and 60.. Even at readings over 75. however, the plants did not w i l t . Considerable variation in moisture of pots receiving the same treatment was noticed shortly after the experiment began. An electronic moisture 15. Linear and non-linear least-squares regression techniques were used to obtain this and other relationships. 51 n i i 1 r— 0 - 10 20 30 40 TIME (DRTDEGREES >6.65C) ( X 1 0 ] ) F i g u r e 6 . A p h i d g r o w t h a s a f u n c t i o n o f p h y s i o l o g i c a l t i m e . 52 meter 1 6 was used thereafter to assess moisture in each pot every two to five days. Water was regulated by corking or uncorking the appropriate pipe within the central bucket. Regression techniques were used to translate the watering rules from irrometer to electronic moisture meter. On June 26 the large plants were replaced by the experimental plants (six weeks old), and on June 30 (day-degree 0 ) , the high aphid density treatment was set up by adding three new adult apterous aphids to each of the appropriate plants. Using the maximum-minimum temperature data, and the relationships between time and temperature examined e a r l i e r , physiological time was determined (see I l . C . l a ) . The medium and low aphid densities were set up by adding fiv e new adult apterous aphids and six f i r s t instar aphids, to each of the appropriate plants at day-degrees 126 and 134 respectively. Each caged plant was checked to insure survival of the o r i g i n a l adults, and aphids of known age were added where required. On July 7, climbing cutworms became a problem on plants inside the cages, and birds, apparently trying to eat the larvae, poked large holes in the cheesecloth walls. Thereafter, the cages were checked d a i l y for bird holes and lepidopterous larvae. Approximately 240 day-degrees after the f i r s t aphids were introduced, second generation nymphs in the high density treatment, and f i r s t generation nymphs in the medium and low density treatments were in their fourth instar. Two of these aphids per plant were 16. Moisture meter - Wilson Laboratories, Dundas Ontario. 53 caged separately to measure fecundity. Once a l l females were reproducing, they were weighed. Developmental time was measured on a l l nymphs (1-7/clip cage) produced by one of the caged females in the 24 hour period following the weighing. The weight of these aphids was measured when they became adults and had produced some nymphs. Leaf subsamples were taken three times during the experiment: July 17, 29, and August 15-21. Both the wet and dry water regimes were maintained at their respective le v e l s , except the dry regime experienced three flushes of water (2. 1/plant), on July 11, 27 and August 3, with 15, 16, 6, and 16 intermediate days of dry conditions. The experiment was terminated August 15-21 by processing approximately one block per day. For each caged plant: 9-26 a r b i t r a r i l y s e l e c t e d 1 7 adult aphids were weighed; a l l aphids were removed'and stored in ethanol for subsequent subsampling, aging to instar, and counting; the length and width of a l l leaves was measured. For each uncaged plant, leaf length and width was measured. Analysis of variance was used to examine the effect of the treatments and blocking on each response v a r i a t e . 1 8 The watering regime had a s i g n i f i c a n t e f f e c t on s o i l moisture but no detectable effect on any of the other response variates. 17. Five a r b i t r a r i l y selected leaves were divided v i s u a l l y into 4 sections. A l l the adult aphids from one section of each leaf were removed. If a dense colony was encountered, a l l adults were removed from a part of i t . 18. Duncan's New Multiple Range Test was used to compare means of the aphid density treatment. 54 The aphid density treatment s i g n i f i c a n t l y affected f i n a l aphid numbers (low<medium=high density), leaf area (high<low=medium density), mean adult weight measured at the end of the experiment (high<low<medium density), and weight of the adults in the developmental time t r i a l (high<low=medium density). It had no detectable effect on any of the other response variates. Covariance analysis was used to correct developmental time, and adult weight of the aphids in the developmental time t r i a l for the effects of aphid density within a c l i p cage (Appendix 1 ( j ) ) . There were no s i g n i f i c a n t block e f f e c t s , or f i r s t order interactions. Despite the important lead time of the high density aphids, f i n a l aphid numbers between high and medium densities were not s i g n i f i c a n t l y d i f f e r e n t . Low leaf area and low adult weight at high aphid density suggests a possible density-dependent feed-back mechanism between plant and aphid. One might have expected adult weight of the aphids in the fecundity t r i a l , fecundity, and developmental time estimates to have followed a similar pattern. The anomaly can be explained in terms of the time at which these measurements were made re l a t i v e to actual aphid numbers. Where the high, medium, and low densities were i n i t i a t e d at day-degree 0, 126, and 134 respectively, weight of the adults in the fecundity t r i a l was taken at day-degree 386, peak fecundity occurred about day-degree 402, aphids in the developmental time t r i a l were i n i t i a t e d at day-degree 402, their adult weight was taken at day-degree 586, and f i n a l adult weight was measured about day-55 degree 663. Hence i t appears that the ef f e c t s of density on B. brassicae were s i g n i f i c a n t only near the end of the experiment when aphid numbers per plant (due to exponential increase), were high (188,117. on one plant). Regression analysis was used to elucidate relationships. Fecundity, and developmental time were related to adult weight, (Figure 7). Figure 7(a) contains data obtained in the f i e l d (see I l . C . l e ) , since the regressions using cage and f i e l d data were not s t a t i s t i c a l l y d i f f e r e n t . Adult weight could be a function of maternal effects as well as plant q u a l i t y . Maternal effects were examined by regressing the mean weight of the adults in the developmental time t r i a l , adjusted for numbers of aphids/clip cage and blocked by treatment, on the weight of their mother (adult weight in the fecundity t r i a l ) . No relationship was detected. Average adult weight measured at the end of the experiment was related to the index of plant quality (Figure 8(a)), but the re l a t i o n s h i p explained l i t t l e of the variation in adult weight. The range of leaf water/dry weight observed in the cages (8.3-14.1 on a per plant basis), exceeded that measured for f i e l d plants (6.0-8.0). Furthermore, f i n a l mean adult weight in the low density treatments (0.611±0.0412mg), equaled that measured in the f i e l d at the same time (day-degree 652, see Figure 11(a)), despite the fact that water/dry weight measures were d i f f e r e n t . The value of the measure, leaf water/dry weight, as a tool for predicting the plant's effect on aphid weight and hence fecundity and developmental time in 56 F i g u r e 7. R e l a t i o n s h i p s o b s e r v e d i n the 1978 f i e l d -cage experiment ( I ) . F e c u n d i t y : ( a ) and d e v e l o p m e n t a l t i m e : ( b ) as a f u n c t i o n of a d u l t w e i g h t . CD cn o X a CL a a t 57 o Y=0.110+0.0417*X r=0 .382 ( 3 4 d f ) 1 1 r L E A F 3WATER/DRY WEIGHT 16 32 48 DENSITY (flPHJDS/CMXCM) Figure 8. Relationships observed in the 1978 f i e l d -cage experiment ( I I ) . Adult aphid weight:(a) and leaf area/plant:(b) as a function of water/dry weight and aphid density respectively. 58 the f i e l d , i s therefore dubious. Aphid density has a major impact on plant growth (Figure 8(b)), and hence undoubtedly affects plant q u a l i t y , perhaps in a way not detected by leaf bore water/dry. weight. Average adult weight was related to f i n a l density (Figure 9(a)), in a way which suggests that there is a density at which plant quality is optimal for the production of large aphids. To check that the relationship was not an a r t i f a c t of the sampling procedure, twenty adults (in 2 groups of 10), were taken from the subsamples used to estimate t o t a l aphid numbers on each plant at the end of the experiment. These were dried and weighed. The results were q u a l i t a t i v e l y similar to those obtained above. The positive part of the relat i o n s h i p cannot be explained by. aphid density at the l o c a l l e v e l (Appendix l ( j ) ) , since most of the aphids, even at low densities existed in colonies of more than seven individuals. The concept of whole plant conditioning (Way & Cammel 1970), was tested by comparing adult dry weight on medium and heavily infested leaves (8. and 34. aphids/ cm2 respectively), from a medium density plant (13. aphids/ cm 2), with adult dry weight on the remainder of the plant (11. aphids/ cm 2). Since no differences in adult dry weight were detected, the concept was supported. The negative part of the relationship was probably a result of competition for food. Use of the relationship for prediction of f i e l d events was not possible as i t required data on the d i s t r i b u t i o n of aphids between plants. Casual observation while sampling, indicated that for Abb and UBC3, most plants Figure 9. Relationships observed in the 1978 f i e l d -cage experiment ( I I I ) . Adult aphid weight:(a) and apterous f o u r t h - i n s t a r / t o t a l fourth-instar aphids:(b) as a function of aphid density. 60 were sparsely infested but approximately 0.5% of the plants appeared to have aphid densities as high as the plants in the high-density treatment of the experiment. The phenomenon of high densities therefore occurs in the f i e l d , but only obviously when aphid densities reach that for Abb, and UBC3. d. Developmental time and fecundity vs plant age The effect of plant age on developmental time and fecundity was examined by measuring these variables on plants of two di f f e r e n t ages. The experiment was replicated four times in each of two blocks. The physical arrangement was id e n t i c a l to that of the previous experiment, except that s o i l moisture was maintained at f i e l d capacity. The response variates, developmental time, fecundity, and adult weight of the aphids in the fecundity t r i a l , were measured as in the previous experiment. Old plants were obtained by transplanting six week oid plants to the f i e l d on June 27, 1978 and allowing them to grow u n t i l July 27. At this time, another set of six week old plants was transplanted (young plants). On August 2, second instar aphids were used to i n i t i a t e the fecundity measurement. The aphids were mature and reproducing by August 11, at which time they were weighed. The progeny, produced in the 24 hr. period after weighing, .ini t i a t e d the developmental time measurement. The experiment ended September 14. The aphids in the fecundity t r i a l were v i r t u a l l y a l l 61 preyed upon by cecidomyiids during the l a t t e r part of the experiment, making the measure of fecundity unreliable. Analysis of variance was used to examine the effect of plant age and blocks on the two remaining response variates. Developmental times were adjusted for aphids/clip cage (Appendix l ( j ) ) . No plant age or block effects were observed. This suggests that plant age differences in the order of 500 day-degrees(>0.0 & <19.4°) during the growth phase of the plant, have l i t t l e effect on the variables measured. e. Temporal variation in developmental time and fecundity Aphid developmental time and fecundity were measured three times during the 1978 season in the UBC2 f i e l d p l o t . The i n i t i a l fecundity t r i a l began with ten fourth apterous, and ten fourth alate brassicae, raised in the laboratory (see II.B.4a), and transferred to ten randomly selected f i e l d plants on June 29. The i n i t i a l developmental t r i a l began with second instar nymphs obtained July 7, from the adults of the fecundity t r i a l . Each succeeding t r i a l was generated from the progeny of the previous t r i a l . Adult weights were measured during the second fecundity t r i a l and contributed to the relationship between fecundity and adult weight discussed previously. Fecundity and developmental time were the same for the two i n i t i a l measures, but changed s i g n i f i c a n t l y in the t h i r d (Figure 10). This change was probably associated with 62 0 TIME (DAYDEGREES 120 (X103 Figure 10. Fecundity: (a) and developmental time:(b)» as a function of physiological time in the 1978 f i e l d season. (average times for - molt to adult.:(*), birth:(B), death:(D)) 63 variation in plant quality unconfounded with aphid density because densities in UBC2 were low (Figure 1(d)). Adult aphid weights measured for UBC2 and UBC3 f i e l d samples (Figure 11) give a more continuous picture of changes in developmental time and fecundity. Although the data confound the effects of overlapping generations, aphid density, and plant qual i t y , they suggest a continuous decrease in developmental rate, and fecundity through the season. f. Morph determination Aphid population dynamics are complicated by the production of several morphs which have d i f f e r e n t developmental times and reproductive potentials. This section i s concerned with predicting the proportions of two morphs: alate as opposed to apterae; and oviparae as opposed to virginoparae. Kawada(l965) found that the alate condition in B. brassicae was determined (at 25°) within 24-48 hours after b i r t h . Assuming a threshold of 6.7°, this i s approximately 28 day-degrees after b i r t h . Using the laboratory estimates of developmental time, alate determination was calculated to have occurred approximately 85 day-degrees prior to the mid-point of the average of the fourth alate and apterous instars. Aphid numbers 85 day-degrees prior to each sample were calculated, using linear interpolation, for Abb, UBC1, and UBC2 f i e l d samples. Leaf areas 85 day-degrees prior to each sample were 64 0 50 100 150 TIME (DRTDEGREES >6.65C) ( X 1 0 3 ) Figure 11. Mean adult weight in,the UBC2:(a) and UBC3:(b) f i e l d samples as a function of physiological time. 65 obtained using non-linear least-squares curve f i t s to the plant data in each plot. The proportion (fourth apterae/total fourths per plant) in each f i e l d sample, was regressed against estimated aphid density 85 day-degrees e a r l i e r (Figure 12). The transform used was unusual (an arcsine square root, or l n ( l - p) would be more t y p i c a l ) , but the relationship is b i o l o g i c a l l y reasonable in that a threshold density greater than 0.0 i s required for the production of fourth alates. Although there i s l i t t l e data at high densities, the relationship is very similar to that obtained in the f i e l d cage experiment(11.C.1c), where densities per plant were 40 times higher (Figure 9(b)). No relationship was observed between the plant q u a l i t y index and fourth alate production in that experiment. Oviparae were found in the two f i n a l UBC1 samples. The proportion (oviparous a d u l t s / t o t a l adult apterae) was calculated in each case and used, assuming a linear model, to derive an equation which predicted the proportion as a function of physiological time, (Figure 13). The equation places the occurrence of f i r s t oviparous adults at approximately day-degree 1160 or September 9-10. Developmental time of virginoparae measured at this time in the f i e l d was 166 day-degrees(>6.7 0). Assuming that oviparae develop in the same time as virginoparae, the f i r s t oviparae were born around day-degree 994 or August 23. It would be preferable to back track oviparae production to the grandmothers (photoperiod experienced by the grandmother determines production of sexuals 66 Figure 12. The proportion (apterous fourth-i n s t a r / t o t a l fourth-instar aphids) as a function of aphid density 85 day-degrees e a r l i e r . 67 w-I L5™ cc CD. CO ZD O zc b i r t h of grandparents V Y=-2.85+0.00245*X r=1.0 (Odf) 1 ^ 1 — - — r — 40 80 120 160 TIME (DAYDEGREES >6.65C) (X10] ) CO 0 0 ID CO ID O CC coLU •(— ° Q _ CE CE I— *£ CO Q CE rsi ID O cr: CE Q_ I—1 •o Figure 13. The proportion (oviparous a d u l t s / t o t a l adults):( ) and hours of daylight: ( ) as a function of physiological time. Data from UBC1 and Spector(1956). 6 8 (Lees 1966)), but no estimate was available for developmental time of previous generations. Using August 23 as the start of oviparae production, physiological time for '1978, and the equation c i t e d above, oviparae were predicted for the f i n a l and only UBC2 sample which contained that morph. Predicted and observed were 0.249 and 0.356 (adult oviparae/total apterous adults) respectively. Alate males appeared in such low numbers that a similar analysis was not possible for this morph. Use of the model to predict oviparae at Abbotsford in 1977 would be misleading since, for reasons unknown, sexuals were not observed in Abb samples. Assuming a minimum of 120 day-degrees (>6 . 7° ) for development of each generation, day length experienced by the grandmothers of the oviparae was >13 hours (Figure 13). 2. Losses To t h i s point, only the 'gains' portion of the difference equation (II.A.) has been considered. Results of a simulation model and the field-cage experiment (II.B.4a, II.C.Ic), suggest that the 'losses' side of the equation must be examined to explain observed population trends. This section is concerned with the development of relationships for the estimation of aphid losses due to emigration, cecidomyiids, syrphids, p a r a s i t i e s , and plant development. 6 9 a. Emigration A considerable proportion of fourth-instar aphids found in f i e l d samples were alate, even at low aphid densities (Figure 12). After molting tb adult they remain on the plant for a period of time before f l i g h t . Van Emden(l972) suggested that alates f l y from their host plant the morning aft e r they have molted, i f weather is suitable. A non-reproductive p r e f l i g h t time of 10 day-degrees, approximately 3/4 of an average summer's day, was adopted for modeling purposes. Alates found in the f i e l d samples consisted of resting, young alates as well as immigrants and alates which nad moved to a new plant within the p l o t . Lumped together, these were expressed as a function of aphid density (Figure 14) using Abb, UBC1, and UBC2 f i e l d samples. Losses to the population due to emigration were estimated as the difference between alates produced (Figure 12), and alates observed at a given aphid density. b. Cec idomyi ids Numerous reports of the effectiveness of cecidomyiids in eliminating B_^ brassicae (Adams & Prokopy 1980, Markkula e_t a l 1979, Pollard 1969), and the apparent c o r r e l a t i o n between increases in A^ aphidimyza and decreases in B^ brassicae (Figure 1), led to a detailed study of the predator. Thompson's(1924) predation model (Appendix 1(1)) was used to 7 0 O «—i X ' '< ( r — ~Z. cr _ i CL \ CO o m .O .CM ZD Q (X d o . I"" cr Y=e**(-3.03+0.857*(ln(X))) r=0.909 (23df) T ~ ~ l I 1 8 0 160 2 4 0 3 2 0 RPHIDS/PLANT ( X 1 0 2 ) Figure 14. Alate numbers as a function of aphid density. 71 estimate the survival of brassicae given predation by A. aphidimyza. The following work describes the measurement of parameters necessary for modeling the predator from egg to pupa: l a r v a l voracity, developmental temperature threshold and developmental times, and the numerical response. The assumptions of the predation model were also examined. A. aphidimyza was reared in the laboratory at 23°, 50% RH, and 16/8 hours light/dark. F i e l d - c o l l e c t e d leaves with A. aphidimyza larvae were placed on 3cm of sand in a 60x50x60cm cage. The cage had clear p l a s t i c roof and sides, a screen front and back, and forced a i r v e n t i l a t i o n . After fiv e days most of the larvae had pupated in the sand and the leaves were removed. Adults emerged approximately eight days l a t e r , and kale plants infested with brassicae were placed in the cage. The adults l a i d eggs on these plants and within one week, f i n a l - i n s t a r larvae appeared. The cycle, was repeated approximately every 21 days. A. aphidimyza l a r v a l voracity was measured at d i f f e r e n t aphid densities in the laboratory. Thirty-one plants in 15cm diameter pots, were infested with d i f f e r e n t numbers of B. brassicae, and introduced into a cage containing A. aphidimyza adults for one day. They were then removed, and a p l a s t i c cone was taped around the stem of the plant, such that larvae f a l l i n g from the plant to pupate would be caught. The cone was checked twice a day for larvae, which were counted and removed. It was also checked for aphids that had been preyed upon, but none was found. According to Harris(1973), 72 aphids eaten by cecidomyiids do not f a l l off the plant because cecidomyiid larvae paralyze them before they can remove their s t y l e t s . Once a l l aphidimyza larvae had f a l l e n from a plant to pupate, each leaf was inspected for dead aphids which were removed and stored in ethanol. The dead aphids were found in patches, and were recognized by their black color and flattened (sucked out) appearance. Surrounding healthy-looking aphids were checked to see i f they were a l i v e . No paralyzed, uneaten aphids were found. Eight to twelve l i v e adult aphids were weighed, the remainder of the l i v e aphids -were removed and stored in ethanol, and the area of the leaves was measured. Both l i v e and dead aphids were counted and aged to instar. The average number of aphids consumed per larva was 19.1±2.11. Age d i s t r i b u t i o n was taken into account by converting numbers dead to weight dead in each ins t a r . The relationship between aphid weight gain and physiological time (see II.C.I.c) was used to estimate aphid weight at the mid-point of each instar. This was then expressed as a proportion of adult weight. Weight of the alate morphs was determined as a function of the weight of their apterous counterparts. The proportions for the f i r s t , second, t h i r d , fourth, and fourth alate instars, and apterae and alate adults were 0.084, 0.109, 0.404, 0.764, 0.838, 1.0, 0.988 respectively. Using the numbers dead in each instar, the estimate of adult weight, and the d i s t r i b u t i o n of aphid weight, A. aphidimyza voracity was determined to be 2.05±0.187mg per larva. The voracity estimate was checked in the f i e l d in nine 7 3 (60x60x60cm) cages. Each was framed from two inverted 'U's' of masonry wire, pushed into the ground at right angles to each other and t i e d in the center. A cheesecloth cylinder 180cm high and 70cm in diameter, t i e d at the bottom, and gathered together at the top of the frame with an e l a s t i c band, formed the walls. One kale plant was planted in each cage. A Dacron R ground sheet, which was sewn in such a way that i t formed 5cm high walls and could be cinched t i g h t l y around the stem of the plant in the center, was used to catch aphidimyza larvae f a l l i n g to pupate in the s o i l . The ground sheet, allowed rain through, but not larvae. Except that A^ aphidimyza eggs were transferred by hand from laboratory plants to the f i e l d plants, the f i e l d and laboratory experiments were i d e n t i c a l . The number of B. brassicae eaten per larva was 11.2±1.60, s i g n i f i c a n t l y less than in the laboratory t r i a l . This result was attributed to the greater weight of f i e l d aphids compared with laboratory aphids (mean adult weight 0.904±0.0383 vs 0.294±0.0148mg respectively). The weight of aphids eaten per larva in the f i e l d was 2.35±0.252mg, close to the laboratory estimate. The weighted average of the f i e l d and laboratory estimates was 2.14±0.152mg. Developmental temperature threshold was determined for A. aphidimyza pupae. Mature larvae which had dropped from the plant in the f i e l d voracity t r i a l were placed in cheese cloth covered v i a l s (5cm high x 3cm diameter) containing 3cm of moist sand. These were placed in environmental chambers at 17., 22., and 25.° and were checked twice da i l y for emergence of adults. 74 Adults were sexed using the length and shape of the antennae (females have short semicircular antennae while males have long, f u l l y - c u r l e d , feathery antennae). Calculations were i d e n t i c a l to those for brassicae ( I l . C . l a ) . The developmental temperature threshold and developmental time for pupae of both sexes (they were not s t a t i s t i c a l l y different) were 9.2±0.31° and 171.±4.1 day-degrees, respectively. The developmental temperature threshold for other stages in the l i f e history was assumed to be the same as the threshold for the pupal stage. Developmental times for the egg, larva, and complete l i f e cycle, determined independently in the laboratory at 22.° were 32.±7.7, 66.±12.1, and 283.±13.2 day-degrees ( >9 . 2° ) , respectively. The numerical response of A^ aphidimyza (Figure 15(a)) was determined by regressing the number of larvae observed in each sample (Abb, UBC1, UBC2) against aphid density at the time of egg production. Aphid density was estimated by linear interpolation assuming egg production occurred 65 day-degrees(> 9.2°) before the sample. This i s the number of day-degrees from egg lay to the mid-point of the l a r v a l period. There was no s t a t i s t i c a l difference between p l o t s . The predation model assumes that each aphid i s equally l i k e l y be eaten (random search). Comparison of the age d i s t r i b u t i o n s of l i v e and dead aphids with Chi-square contingency tables and Bonferroni Chi-square s t a t i s t i c s (Jensen et a l 1968) suggested that the age d i s t r i b u t i o n s were the same, except for the second and fourth alate instars. The proportion Figure 15. Larval predator and pupal parasite numbers as a function of aphid density at the time of egg production. (A. aphidimyza:(a), syrphids:(b), D. rapae:(c)) 76 dead for the f i r s t , second, t h i r d , fourth, and fourth alate instars, and apterae and alate adults was 0.24, 0.30, 0.26, 0.23, 0.17, 0.21, and 0.23 respectively. The fourth alates were probably d i f f e r e n t because their numbers increased as the experiment progressed. A_;_ aphidimyza larvae were therefore exposed to fewer fourth alates during the experiment than the f i n a l age d i s t r i b u t i o n indicated. There was no obvious explanation for the greater proportion of dead second-instar aphids. The Chi-square tests were not conclusive evidence for random search (the age d i s t r i b u t i o n of the l i v e aphids was one of a s p e c i f i c moment, namely the end of the experiment, while that of the dead aphids was one which had accumulated over time), but they did support the assumption. The predation model only works well at high prey-to-predator ra t i o s (Gilbert et a_l 1976). These ratios were calculated using the two 1979 f i e l d samples in which kale leaves were examined i n d i v i d u a l l y . Of 92 aphidimyza larvae found on 21 leaves, 50% existed on leaves in which numbers of prey per predator were 30-105 (about l0.4-36.5mg brassicae per larva) and the remaining 50% existed on leaves with 105-1522 aphids per predator (about 36.5-529.7mg brassicae per larv a ) . In terms of aphid weight required for l a r v a l development, there was at least five times more food available than necessary. Given the c o l o n i a l habit of B_j_ brassicae, the fact that aphidimyza eggs are l a i d in or near aphid colonies (Harris 1973), and the high prey-to-predator r a t i o , the assumption that food was s u f f i c i e n t and required l i t t l e or no 7 7 search time to obtain seems v a l i d . Regression of numbers, and weight of prey eaten per larva against f i n a l aphid density (4-22 "aphids/ cm 2), suggested that l a r v a l demand for prey was constant with prey density. A. aphidimyza demand for prey with respect to l a r v a l age (3 instars (Harris 1973), was assumed to be the same as that observed for corollae. The l a t t e r has three instars with proportional lengths 1:1:2, and v o r a c i t i e s 2.5%, 12.5%, and 85.0% of t o t a l voracity, respectively (Benestad 1970). c. Syrphids Thompson's(1924) predation model was also used for . estimating the survival of B^ brassicae given syrphid predation. Time did not permit a detailed study, so most of the necessary information was extracted from the l i t e r a t u r e . Estimates of syrphid voracity are varied (Table I I I ) . The average of the estimates for Syrphus spp. (this genus occurred in the f i e l d samples (H.B.4a)) was 399 aphids. This value was converted to weight eaten by a technique which involved numerous assumptions. An aphid simulation model was written for UBC2 which had no mortality factors other than longevity, but which included f i e l d adult weight changes ( I l . C . l e ) . The ratio ( t o t a l aphid weight/aphid numbers) decreased exponentially and leveled after 350 day-degrees. The average ra t i o a f t e r that time, calculated every 50 day-degrees to the 7 8 Table I I I . Estimates of syrphid voracity (for complete l a r v a l development) from the l i t e r a t u r e . Author Syrphid Aphid Aphid size Number eaten Benestad(1970) SL corollae M. persicae 307-385 George(l957) S_^ balteatus B. brassicae f i e l d aphids 230-600 Schneider(1969 ) Lasiopticus pyrastri A. fabae fourth instar 162 S. r i b e s i i A. fabae fourth instar 234 S. v i t r i p e n n i s A. fabae fourth instar 134 Simpson & Alloqrapta Therioaphis Burkhardt(1960) obliqua maculata adult 182-375 79 end of the season, was 0.184±0.0180. This r a t i o was used to estimate l a r v a l voracity at 73.5mg. The estimate was checked using~Abb, UBC1, and UBC2 f i e l d samples. From samples in which at least five A^ aphidimyza and five syrphid larvae were recorded, the three largest individuals of each type were removed, dried to completion, and weighed. The t o t a l weight range for each predator was then divided into ten equal sections to obtain a d i s t r i b u t i o n of weights, and the individuals in the two highest weight categories were averaged. The r a t i o (mean syrphid dry weight/mean A^ aphidimyza dry weight), multiplied by A. aphidimyza voracity produced an estimate of syrphid voracity, 70.9±5.50mg, that was close to the former estimate, but was derived from . individuals that were feeding on B. brassicae in the f i e l d . Although mature A^ aphidimyza larvae were consistently observed in f i e l d samples, mature syrphid larvae were not, a difference that was supported by the weight frequency data (Figure 16). The data suggest that although syrphid larvae have the capacity to eat far more aphids than A_j_ aphidimyza, they have trouble finding enough to eat (see van Emden 1965). Larval developmental time for Syrphus corollae was 7.5 days at 23° (males and females combined), and 9 days for S. luniger at 22° (Schneider 1969). Assuming a threshold of 6.7° (the l i t e r a t u r e did not provide an estimate of the threshold), the average of the two estimates was 132 day-degrees. Time for egg hatch i s not dealt with in the l i t e r a t u r e , so i t was 80 Figure 16. D i s t r i b u t i o n of the dry weights of A. aphidimyza larvae: (/////) , and syrphid larvae: See text for d e t a i l s . 81 assumed to be the same as for A. aphidimyza (2.4 days at 22.4°). Time from egg production to pupation was therefore estimated as 170 day-degrees(>6.7°) . The numerical response of the syrphids was determined as for A^ aphidimyza (Figure 15(b)). The relationship was not accurate. The average age of the syrphid larvae was assumed to be the mid-point of the length of the l a r v a l period, but most of the larvae found in the f i e l d were small (Figure 16). The problem was considered minor, however, since a submodel incorporating the numerical response, syrphid developmental times, and observed ( f i e l d ) aphid densities, predicted the numbers of syrphid larvae found in the f i e l d samples reasonably well. That i s , the residuals (observed - predicted) were scattered evenly about y = 0.0 when plotted against aphid density. d. Parasites Aphid dissections were not performed to obtain the rate of p a r a s i t i z a t i o n . The effect of the parasites was therefore modeled in terms of cocoon formation. Development of D^ rapae from egg to cocoon was 116.±9.4 day-degrees above a threshold of 4.9±0.94° (Campbell et a l 1974). The length of the cocoon stage was assumed to be equal to the l a r v a l stage (Hughes & Gil b e r t 1968). The numerical response of D^ rapae was determined as for aphidimyza (Figure 15(c)). The 8 2 r e l a t i o n s h i p was not accurate because increasing proportions of hyperparasitized.cocoons over the season (Figure 17) (data from Abb, UBC1, UBC2, and UBC3 f i e l d samples), would tend to lengthen the average l i f e of an unemerged cocoon. The submodel used to assess the effects of a similar problem for the syrphids, was adapted to the parasite data. No obvious bias was observed when the predicted numbers of cocoons were compared to the f i e l d data. Aphid death due to rapae cocoon formation was assumed to occur at any time in the adult l i f e of B. brassicae. Whereas some parasite species prefer immature hosts, a l l ages of IK_ rapae larvae were found in dissections of adult B^ brassicae. e. Plant growth and Development Kale plants continually produce new leaves which enlarge, age and drop. B^ brassicae t y p i c a l l y colonizes the young to f u l l y developed leaves, but by the time these leaves senesce the colonies may be very large. Mortality may therefore be considerable when the leaf f a l l s off the plant. This section is concerned with estimating the effects of plant development on aphid s u r v i v a l , and begins by defining a time scale on which relationships were based. The time scale on which Maris Kestrel kale operates was determined in a way similar to that described for B^ brassicae. Eighty kale seeds were planted two per pot, at a depth of 1cm * * * * * * * * * * ~i i r 40 80 120 160 TIME (DRYDEGREES >6.65C) ( X 1 0 3 ) Figure 17. The proportion of hyperparasitized rapae cocoons as a function of physiological time. 84 in sieved (10 mesh) s o i l . The forty pots were divided evenly between four environmental chambers set at 7.9, 13.3, 19.4, and 22.9°. S o i l was kept moist throughout the experiment. The number of leaves were counted every other day. The experiment was terminated after 6 leaves were produced. Developmental rate of leaf production was not l i n e a r l y related to temperature, (Figure 18). It was l i n e a r l y related to the three lower temperatures, which were used to calculate temperature thresholds as the plant grew. Thresholds based on data to the second, t h i r d , fourth, f i f t h , and sixth leaves were 4.5±0.81°, 4.0±0.71°, 2.3±0.75°, -0.1±0.94°, and 0.0±0.90° respectively. Assuming that the threshold s t a b i l i z e s at 0.0° for the remainder of the plant's growth, 0.0° was adopted for calc u l a t i o n of physiological time. An upper temperature threshold of 19.4° was associated with plant development by determining the temperature at which the developmental rate at 22.9° intersected with the linear model based on the three lower temperatures. Calculation of physiological time was si m p l i f i e d by setting such an arbi t r a r y upper l i m i t on plant development, since developmental rate undoubtedly slows before becoming zero. The double threshold for ca l c u l a t i n g plant time s u f f i c i e n t l y reduced variation in the plant growth data to allow a single curve to be used for the d i f f e r e n t f i e l d plots (Figure 19). Plant development was examined in the f i e l d . Estimates of the number of leaves lost were obtained for each plot at the end of the season by counting the number of leaf scars on ten 8 5 co-de: ZD Q X O a LU I— c n _J° c r i— zz. UJ 21 Q-m O •. _ l a UJ > UJ a o a " 1 12 18 2 4 TEMPERRTURE (C) Fi g u r e kale as 1 8 . Rate of l e a f p r o d u c t i o n a f u n c t i o n of temperature. i n Maris K e s t r e l a a, CE CM — I O \ x ° CE — LU on — CE 21 CJ Lu X CE 51 a LU O S ' 1 50 i 100 I 150 TIME (DRYDEGREES >6.65C) ( X 1 0 ] ) B o B B B B B R R fc Y=(1000./C0. 0412+361.E6 * ( X - 1 . ) * * ( - 3 . 5 ) ) ) + 1 8 0 . 0 T 70 T 210 140 TIME (DRYDEGREES >0.0 I <19.4C) ( X 1 0 ] ~ ) Figure 19. Leaf area per plant as a function of physiological time based on the aphid threshold:(a), and the plant thresholds:(b). (Abb:A, UBC1:B, UBC2:C) 8 7 randomly selected plants. These estimates were biased since leaf scars become obscured by growth and expansion of the stalk. Therefore, at approximately weekly in t e r v a l s , the number of leaves and leaf scars were counted on six randomly selected plants in the UBC3 f i e l d p l o t . A marking system was used that prevented old leaf scars from being re-counted in subsequent weeks. The rate of leaf addition and leaf f a l l was estimated (Figure 20). The estimates apply to a l l f i e l d plots because a discrete time-step model constructed from these data predicted with acceptable accuracy, both the number of leaves and leaf losses per average plant in the d i f f e r e n t f i e l d plots (Figure 21 ) . The estimate of the number of aphids on a f a l l e n leaf was derived as the r a t i o of the number of leaves l o s t since the last time step to the number of leaves in stratum 3 at the l a s t time step, multiplied by the proportion of aphids in stratum 3, and by the number of aphids per plant. The number of leaves and the proportion of aphids in stratum 3 were obtained from f i e l d sample data (Abb, UBC1, UBC2) (Figure 22). In both cases there was no s t a t i s t i c a l difference between p l o t s . A preliminary simulation model of the Abb population required a non-zero survival rate for aphids on f a l l e n leaves in order to keep the population from becoming extinct half way through the f i e l d season. Accordingly, the movement of aphids on senescing leaves was observed in the f i e l d . One mature leaf on each of three plants was infested with B^ brassicae and a 88 Figure 20. Rate of addition:(a) and loss:(b) of leaves per plant in the UBC3 f i e l d p l o t . 8 9 230 T 70 140 TIME (DAYDEGREES >0.0 I <19.4C) ( X 1 0 3 ) Figure 21. Leaves per plant:(a) and leaves lost per plant:(b) as a function of physiological time. (Abb:A, UBC1:B, and UBC2:C, model prediction:( )) Y=0 .626+0 .279* (X/100 . ) r=0 .764 ( 2 6 d f ) 0 7 0 1-40 23 0 T I M E ( D R Y D E G R E E S >0.0 I < 1 9 . 4 C ) ( X 1 0 ] ) Figure 22. Numbers of stratum 3 (senescent) leaves:(a), and the proportion of the aphid population on stratum 3 leaves:(b) as a function of physiological time. 91 p l a s t i c sheet (40x40cm) with a Stikem S p e c i a l 1 9 ring on i t s periphery was taped around the stem. When the leaf began senescing, a l l aphids on the rest of the plant were removed. The plant was checked d a i l y , and the aphids on the senescing leaves were counted, while the aphids on the rest of the plant were counted and removed. The l a t t e r counts ignored f i r s t -instar aphids which were in close proximity to an adult, and alates and their young. Aphids on the p l a s t i c sheet were also counted. A proportion of aphids did move off senescing leaves, some onto the ground, but most moved elsewhere on the plant (Table IV). One f a l l e n leaf was c o l l e c t e d from the base of plant number three on September 11. Approximately 2232 aphids remained on the leaf, which was s t i l l succulent. In contrast (Table IV), the great proportion moving off the senescent leaf of plant number two, which dried noticeably in the hot July weather before f a l l i n g , suggests that the movement of aphids from senescing leaves may vary through the season as a function of the loss of water in the senescing leaf as well as the rate of leaf f a l l . The e f f e c t of cooler f a l l temperatures on the rate of aphid movement is probably not important since adult and fourth-instar aphids moved at a rate of 0.76±0.070 cm/min/0 above a threshold of 7.2±0.98°, and second-instar aphids at 23° moved at a rate of 2.5±0.37 cm/min. The survival rate of aphids on f a l l e n leaves was measured 19. Stikem Special - (polymerized 1-Butene, 2-Methylpropene, 1-Butane) Michel & Pelton Co. 5743 Landregan, Emeryville, C a l i f . • 92 Table IV. Movement senescing leaves. of B. brassicae from Plant Total aphids # on senescing leaf Proport ion moving off leaf Proport ion found on plant Proport ion found on ground 67 69 93 4 0 610 820 3060 2720 2640 0.15 0.50 0.28 0.79 Terminated due to cecidomyiid predation 0.71 0.75 Terminated due 0.005 0.041 0.017 0.059 0.092 to 0.86 1 .00 leaf f a l l 0.0 1 .00 0.93 0.97 0.88 0.50 0.21 0 0 1 4 0 00 1 0. 0.07 0.03 0.12 Terminated due to alate contamination on plant 9 3 once under hot (maximum 21.8 - 31.6°; mininum 11.9 - 15.7°) dry f i e l d conditions in 1979. Twenty-five aphid-free kale plants approximately 40cm t a l l were planted in a 5x5 grid with 60x100cm spacings. A senescing leaf from UBC3 was cleaned of aphids, and 25 apterous f i e l d - c o l l e c t e d brassicae from each of the second, t h i r d , and fourth instars, and the adult stage, were added to i t s lower side. Once they had settled, the leaf was placed lower side down on the s o i l , with i t s stem touching the center plant in the g r i d . After one instar period (3 days) the dead leaf and each plant were examined for aphids, which were sorted to instar and counted, ignoring f i r s t - i n s t a r and alate i n d i v i d u a l s . No aphids l i v e or dead remained on the excised l e a f . Of 100 aphids, 57 moved successfully from the drying, leaf to a new host plant; 43 were found on the center plant, 9 on two adjacent plants, and 1 two plants from the center. These data suggest that even i f B_^ brassicae does not walk off a leaf before i t f a l l s , i t can s t i l l f i nd i t s way to a host plant. The age d i s t r i b u t i o n on senescent leaves (stratum 3) from Abb and UBC1 was s i g n i f i c a n t l y d i f f e r e n t from that on the remainder of the plant. Bonferroni Chi-square s t a t i s t i c s indicated a s h i f t toward older ages, reduced reproductive rate, and greater numbers of fourth alates in stratum 3. The age d i s t r i b u t i o n in stratum 3 was determined as a function of the age d i s t r i b u t i o n on the whole plant (Table V). 9 4 Table V. Coeff i c i e n t s for the equation y = (sin(a + b * x)) ** 2., used to predict the proportion of each instar in stratum 3:(y), from that found in the whole plant:(x). Coefficients are expressed in radians. Instar a b r df I 0.247 0.923 0.565 20 II 0.287 0.695 0.691 21 III 0.429 0.0 0.384 21 Apterous IV 0.139 1.87 0.696 21 Apterous adult 0.196 1.57 0.815 20 Alate IV 0.178 2.63 0.764 16 Alate adult 0.100 0.0 0.099 21 9 5 D. Consolidation 1. The model The data were consolidated in a deterministic, discrete, computer simulation model (Appendix 3) written in FORTRAN. The model predicts aphid numbers and age d i s t r i b u t i o n , incorporating the effects of: temperature; morph determination (apterae:alate, and virginoparae:oviparae); plant quality ( i n d i r e c t l y assessed with mean adult weight measured in the f i e l d ) ; predators and parasites; and leaf f a l l (Table VI). Events are simulated for an average plant, on a physiological time scale. To f a c i l i t a t e examination of the effects of various factors, the model was b u i l t so that the value of several input variables could be set at run time. 2. Model validation and predictions UBC2 f i e l d data were used to adjust the model. The i n i t i a l observed and predicted rates of increase of the aphid, before predators and parasites appeared (approximately 1.6 aphid generations), were 0.0248 and 0.0247 (In(aphids/day-degree(>6.7°))) respectively, which suggests that the values for fecundity and developmental time used in the model were correct. Both of these values were dependent on the f i e l d measures of adult weight. The rate of increase given a 9 6 Table VI. Relationships incorporated into the model. Rate Factors Source of informat ion Reference developmental -reproductive i n t r i n s i c survival alate product ion oviparae production A. aphidimyza 'successful' egg product ion developmental -predation temperature instar morph new adult aphid weight temperature morph age tot a l fecundity new adult aphid weight temperature age laboratory+field fig.3 laboratory+field table II f i e l d IIC1a estimated in model figs.7(b),11 from mean f i e l d adult weight laboratory f i e l d laboratory+field laboratory estimated in model from mean f i e l d adult weight laboratory + f i e l d laboratory aphid density f i e l d at (t-85) physiological time after a set date (day length) f i e l d developmental t ime aphid density temperature sex stage of l i f e cycle age aphid density vorac i t y laboratory f i e l d laboratory laboratory laboratory l i t e r a t u r e l i t e r a t u r e laboratory+field IIC1b IIC1b f igs.4(a),5 IIC1b f igs.7(a) , 1 1 IIC1b fig.4(b) f i g . 1 2 fig.13 IIC2b f i g . 15(a) IIC2b IIC2b IIC2b IIC2b IIC2b IIC2b 9 7 Syrphidae 'successful' egg production developmental -predat ion D. rapae 'successful' cocoon product ion developmental t ime aphid density temperature stage of l i f e cycle - age - aphid density - voracity - developmental t ime - aphid density developmental - temperature - stage of l i f e cycle Maris Kestrel kale developmental - temperature threshold growth (leaf area) development (leaf f a l l ) - physiological t ime - physiological t ime l i t e r a t u r e f i e l d assumpt ion literature+ laboratory l i t e r a t u r e 1i terature literature+ f ield+model l i t e r a t u r e f i e l d l i t e r a t u r e l i t e r a t u r e aphid survival given leaf f a l l - rate of leaf f a l l - age d i s t r i b u t i o n laboratory f i e l d f i e l d f i e l d f i e l d IIC2c figs.15(b), 25 IIC2c IIC2c IIC2c IIC2c IIC2c IIC2d fig.15(c) IIC2d IIC2d IIC2e fig.19(b) fig.20(b) fig.20(b) table V 9 8 constant average f i e l d value for adult weight (0.716mg) was 0.0229, considerably less than observed. Using laboratory estimates of fecundity and developmental time produced greater discrepancies. Observed and predicted age d i s t r i b u t i o n s (Table VII) were not s t a t i s t i c a l l y d i f f e r e n t , but the model generated alate adults within the population, whereas alates observed in the f i e l d during t h i s period were probably immigrants. After the f i r s t sample, the model consistently predicted aphid numbers less than observed and the population became extinct half way through the season (Figure 23(a)). Changing various parameters which affected aphid survival showed that population trends were sensitive to changes in syrphid l a r v a l voracity. Assuming that syrphid larvae could not find enough to eat at low prey densities, the amount eaten was modified as a function of aphid density, using the relationship ( l . 0 - e * * ( -k*aphid density)). A value for 'k' was derived by running the model for d i f f e r e n t values of that parameter, u n t i l predicted and observed numbers of aphids remained reasonably close for approximately half the season. Survival of aphids on f a l l e n leaves was then varied in proportion to the rate of leaf f a l l u n t i l observed and predicted aphid numbers also remained close through the f i n a l half of the season (Figure 23(b)). To i l l u s t r a t e that the survival of aphids on f a l l e n leaves was greater than zero (as suggested by f i e l d observations), zero survival was assumed, which destroyed the aphid population 70 day-degrees(>6.7°) before the f i n a l sample. Table VII. Observed and predicted age di s t r i b u t i o n s for the f i r s t UBC2 sample. Instar Proportion of each instar Model F i e l d I 0.539 0.448 II 0.187 0.269 III 0.068 0.137 Apterous IV 0.058 0.033 Apterous adult 0.119 0.108 Alate IV 0.013 0.0 Alate adult 0.016 0.005 100 F i g u r e 23. Observed:( ) and p r e d i c t e d : (- ) p o p u l a t i o n trends f o r UBC2 f i e l d p l o t . I n i t i a l model:(a) and f i n a l model:(b). 101 Although the model mimicked UBC2, i t was unstable. A small change in any of the parameters caused monotonic increase or decrease of the simulated population. Changing the p r e f l i g h t time of alates by one day-degree, i n i t i a l aphid numbers by 0.0007 aphids/plant, syrphid developmental time by one day-degree, or the f i r s t measure of adult weight by 0.0l2mg, a l l produced these extremes. This s e n s i t i v i t y suggests that the density-dependent responses of the predators as modeled were inadequate, and that other feed-back mechanisms may be missing. The model was tested against independent UBC3 f i e l d data. Predicted and observed population trends were very d i f f e r e n t , (Figure 24(a)). The numerical response of rapae, and A. aphidimyza in UBC3 was consistent with that found in the other plots, but the syrphids' numerical response was low. In p a r t i c u l a r , the depauperate syrphid fauna of the Abb plot was responsible for the depressed production of syrphid larvae in the regression equation used in the model. A new regression, derived from UBC1, UBC2, UBC3, and UBC4 data (Figure 25), was substituted, with the result that predicted aphid numbers s t i l l increased continuously, but at a lower rate (Figure 24(b)). Low i n i t i a l predicted aphid numbers suggest that predation by syrphids was i n i t i a l l y overestimated. Although the search parameter 'k' could be adjusted to solve the problem, so also could a number of other parameters. For example, lengthening the developmental time of the syrphid larvae by 30 day-degrees (162 day-degrees(>6.7°) is a reasonable estimate for l a r v a l 102 00 _ ,* (N _ / / / / i o X f * t / CO ~ +• \ * * IT t / t / t / / / (LNn i / / / t/ 'PLANT 18 o O [DS/ i X t—* s * • 1 /X / f ,A CD ~ / / / f * Q - r 1 1 r -0 50 100 150 TIME (DATDEGREES >6.65C) (X10 ] ) F i g u r e 24. Observed: ( ) and p r e d i c t e d : ( ) p o p u l a t i o n t r e n d s f o r UBC3 f i e l d p l o t . I n i t i a l model:(a) and f i n a l m o d e l : ( b ) . 1 03 P R E Y / P L A N T ( X 1 0 2 ) Figure 25. Larval syrphid numbers as a function of aphid density at the time of egg production. 1 0 4 . developmental time), corrected the discrepancy. No further manipulations of this sort were performed, however, because the numerous parameters must be measured, to obtain the more r e a l i s t i c values required to correct the model. 105 I I I . DISCUSSION A. Future research The objectives of the research have been met: temporal variation was measured for brassicae and major components of the system; relationships between the components and aphid development, reproduction and survival were quantified; the relationships were* consolidated such that predicted and observed temporal variation could be compared. Quantitative understanding of the system i s not complete, but the direction of future research is c l e a r . Although previous quantitative studies (Hughes & Gilbert 1968, and G i l b e r t et a_l 1976) • found that Thompson's random search model adequately represented syrphid predation, this was not the case in the present study. Syrphid predation must be analyzed in d e t a i l . The functional response of at least one species and the numerical response of a l l species should be examined, as well as the d e t a i l s of the biology of each species, such as developmental temperature thresholds, developmental times, number and timing of generations, and oviposition behavior. Despite the fact that syrphid predation has been found to contribute s i g n i f i c a n t l y to the population dynamics of many aphids (van Emden 1965, Hughes 1963, Pollard 1971, Schneider 1969), a quantitative study in which the dynamics of the prey have been accounted for in terms of the numerical and functional response of syrphid predators has, to the author's knowledge, never been attempted. A 106 substantial body of knowledge on syrphid ecology exists (see Schneider 1969), but from the viewpoint of quantitatively assessing predation by a given species, i t is fragmented. The importance of syrphid predation to the dynamics of the present system w i l l be clear only when the b i o l o g i c a l d e t a i l s have been added to the simulation model. The aphid-plant relationship is basic to the system. Average l i v e adult weight was used to assess i n d i r e c t l y the effe c t of the plant on the aphid. Assuming that adult weight is a r e l i a b l e predictor of fecundity and developmental time under a l l conditions, i t combines the effects of spa t i a l and temporal variation in plant quality in one simple measure which relates d i r e c t l y to the aphid's capacity to increase. As a cor o l l a r y , using adult weight dispenses with the objection that the c l i p cage may have an effect on fecundity and developmental time. If i t does, i t is irrelevant, so long as the range of adult weights span those found in the f i e l d . Furthermore, developmental time and fecundity can be estimated in a colony, whereas most workers have r e s t r i c t e d measurement of these variables to isolated aphids. The f i e l d measure of adult weight was based on adults from a random sample of leaves since i t was technically impossible to take a random sample of l i v e adults. It therefore reflected to some degree the effect of changes in plant quality independent of aphid density (aphids were not evenly d i s t r i b u t e d between plants). This 'density-independent' variation constitutes a major problem with the technique since aphid density also a f f e c t s plant quality (both 107 p o s i t i v e l y and negatively) and hence adult weight. The present technique could be modified to include the density e f f e c t , by removing a l l the aphids from sample leaves using heat treatment, subsampling them as indicated in the text, and obtaining adult dry weight. This dry weight could be converted to l i v e weight using regression techniques, or fecundity and developmental time could be expressed in terms of dry weight. A problem of equal importance i s the eff e c t of density on plant development. The production of senescent leaves, and leaf f a l l were modeled as functions of physiological time. For an average plant in the f i e l d , this i s an adequate representation. Some plants, however, have very high aphid densities. Leaves on such plants tend to senesce faster, thereby subjecting a larger portion of the population to mortality than would be expected on the basis of an average plant. The problems of assessing aphid d i s t r i b u t i o n between plants, and defining rates of leaf senescence and leaf f a l l as a function of aphid density, are not insurmountable. They lead however to the question of aphid survival on senescent leaves, made d i f f i c u l t because i t involves aphid movement. Although the interaction between aphid density and plant development becomes important as the season progresses, i t is not p a r t i c u l a r l y tractable, and may have limited generality. The model either circumvented or ignored a number of bi o l o g i c a l interactions: the aphid-plant interaction was handled empirically; parasite (larval)-predator and aphid-parasite interactions were avoided by considering only parasite 1 08 cocoons; parasite-hyperparasite interaction was ignored; syrphid-cecidomyiid interaction was ignored, and predation was assumed to be additive; predator-prey interaction in the case of syrphid larvae was oversimplified. Furthermore, plant-to-plant v a r i a t i o n in aphid density and i t s effects on these b i o l o g i c a l interactions were ignored. The phenomena are however of b i o l o g i c a l interest, and undoubtedly bestow certain properties, such as ' r e s i l i e n c e ' (Holling 1973), on the system which were not observed in the model. Future work should consider the aphid-syrphid and aphid-plant interactions in p a r t i c u l a r . •Plant-to-plant variation in aphid density may be of considerable importance in r e l a t i o n to these interactions. Given the high food requirements of syrphid larvae, a per plant as opposed to per average plant treatment of the aphid-syrphid interaction could produce very d i f f e r e n t population trends. This i s simply i l l u s t r a t e d by considering three plants each with 10 aphids and 1 syrphid larva, a fourth plant with 10 aphids, and a f i f t h plant with 110 aphids and 2 syrphid larvae. If 40 aphids are required per syrphid larva, then a model based on average numbers of predators and prey per plant (1 and 30 respectively), would predict extinction of the aphids. In fact, extinction would occur on three plants but not on the other two. Further differences in population trends predicted by the two kinds of models, could be produced by.the aphid-plant interaction, since adult weight (Figure 9(a)) and fourth alate production (Figure 12) are non-linear functions of aphid 109 density. For example, estimates of adult weight given average aphid density per plant, w i l l in general be higher than the average of the estimates for individual plants. This would affe c t both b i r t h and developmental rates. An i n i t i a l question of some importance i s : how does the searching behavior of predators (syrphids s p e c i f i c a l l y ) lead to a p a r t i c u l a r aphid d i s t r i b u t i o n , and what are the ramifications^ in terms of subsequent searching and egg laying, and aphid and syrphid survival? It is interesting to note that a model of the populati-on dynamics of the thimbleberry aphid (M^ maxima) required allowance for plant-to-plant v a r i a t i o n in aphid numbers and plant quality (Gilbert 1980(a)). B. Technical considerations Details of the biology of B^ brassicae observed in the laboratory in the present study were similar to those found by other workers. Developmental temperature threshold and developmental times of B^ brassicae were close to the estimates of Hughes(1963). The reproductive pattern resembled that c i t e d by H a f e z ( l 9 6 l ) . Although t o t a l fecundity was greater (1.4X) than that found by H a f e z ( l 9 6 l ) , i t was similar to the estimates of . Bonnemaison(1951) and Hughes(1963). In the f i e l d , however, developmental rate and fecundity vary markedly through the season, being higher in the spring when the aphids f i r s t colonized young plants, and lower in the autumn. A. similar discrepancy between laboratory and f i e l d observations occurred n o in the study of A_;_ aphidimyza voracity. Laboratory estimates of the number of aphids eaten were considerably higher than f i e l d estimates because of weight differences in the prey. Estimates of l a r v a l voracity of predaceous Diptera in the l i t e r a t u r e , are based on numbers of aphids eaten. If the authors used laboratory-reared aphids, the estimates (as in this study) would probably be too high. But even i f the authors used f i e l d aphids, their estimates would not be correct at a l l times of the year unless aphid weight was constant. F i n a l l y , .Kawada's(1967) and Pagliai's(1965) laboratory estimates of the daylength required for the production of sexuals c o n f l i c t with the findings in this study. The aphids may have been i n t r i n s i c a l l y d i f f e r e n t since the former studies, performed in Japan and Italy respectively, u t i l i z e d individuals from populations existing at 40-45° N. l a t . . Al t e r n a t i v e l y , the discrepancy may r e f l e c t differences between laboratory and f i e l d conditions (e.g. temporal variation in plant and l i g h t q u a l i t y ) . These cases emphasize the importance of f i e l d measurements of b i o l o g i c a l phenomena. The current work could not avoid laboratory estimates. Although the estimates of A. aphidimyza developmental time agree with those of Harr is ( 1 973 ) , Uygun(l97l), and Markkula et a l d 979), they were not obtained in the f i e l d where prey quality could aff e c t the res u l t s . Problems of scale were evident in several relationships. The relationship observed for the production of fourth alates was similar to that c i t e d in Hughes & Gilbert(1968). It was 111 not b i o l o g i c a l l y correct, however, because the mechanism ('contact') operates at the l e v e l of the colony rather than the plant. This probably explains why an unusual transform was required to f i t a reasonable l i n e to the data ( i l . C . l f ) . Given the regular gregariousness of the aphid, i t was assumed that the r e lationship defined at either scale would produce similar answers despite the di f f e r e n t c o e f f i c i e n t s . Adams & Prokopy's(1980) observation that A^ aphidimyza voracity increased with increasing prey densities contradicts the findings of this study. Events at scales less than a whole plant may be involved. The sp a t i a l d i s t r i b u t i o n of the prey ( M. persicae and Aphis pomi DeGeer) that Adams and Prokopy used, d i f f e r s from that of brassicae. In a IK brassicae colony an A. aphidimyza larva would spend l i t t l e i f any' time searching for food whereas, with a less c o l o n i a l aphid, search time would vary inversely with density. In the model, the time scales of the predators and parasite were assumed to be a constant proportion of aphid time. The assumption was v a l i d for the syrphids, since their developmental temperature threshold was 6.7°, but was not v a l i d for A^ aphidimyza and rapae. The r a t i o of time based on one threshold to time based on another varied through the season in a dir e c t i o n which was dependent on the r e l a t i v e position of one threshold to the other. Hence, when aphid time was the denominator, the ra t i o for A^ aphidimyza was greater in the summer (0.80±0.006) and less in the f a l l (0.69±0.012), while for L\_ rapae i t was less in the summer (1.14±0.006) , and 1 1 2 greater in the f a l l (1.22±0.012) . By using an average value, A. aphidimyza predation was overestimated during cool weather and underestimated when i t was hot, and the opposite was true for rapae. If syrphid predation proves to be as important as t h i s study suggests, and their developmental thresholds d i f f e r from B^ brassicae's, then syrphid time scales should be modeled separately from the aphid's. Simulation models were used throughout th i s study to consolidate information and perform mathematical calculations which would otherwise have been d i f f i c u l t ; e.g., the c a l c u l a t i o n of i n i t i a l rates of increase of the aphid, given variable age-specific fecundity and developmental time. The models provided a tool whereby b i o l o g i c a l understanding could be assessed in a quantitative manner (e.g., in plant development), and assumptions could be examined (e.g., the e f f e c t s of leaf f a l l and syrphid predation on aphid s u r v i v a l ) . Much as in experimental component analysis (Rolling 1963), the experiments dictated the form of the models and the models in turn suggested further research. Models cannot replace good b i o l o g i c a l studies, but they can aid in synthesizing and d i r e c t i n g those studies. 1 1 3 C. Comparisons with other systems The basic components and many of the relationships in the present system were the same as those described by Hughes(1963), but differences in growth rate and f i n a l size of the host plant affected the r e l a t i v e importance of pa r t i c u l a r components and relationships. In t h i s study, plants infested with 120,000 aphids (medium-density treatments, see II.C.Ic) were the same size and apparently as healthy as plants infested with 12,000 (low-density treatments) or 600 aphids (UBC2 f i e l d p l o t ) . Furthermore, the aphids on the plants in the medium-density treatment had the highest mean adult weight. In contrast, fecundity and recruitment to the reproductive cohort on the plants u t i l i z e d by Hughes was maximal u n t i l densities reached 60 aphids per plant (maximum value for the threshold), and then declined exponentially. Whereas reduced recruitment with increasing density was the main factor a f f e c t i n g the rate of increase of the population in Hughes' study (Hughes & Gilbert 1968), there was no evidence that - the phenomenon occurred in the present study. Plants, and even leaves, were so large that there was always space for new adults to r e s e t t l e . Hughes(l963) suggested that natural enemies of B. brassicae could not normally prevent the aphid from increasing to levels set by the food supply, and that they reduced aphid numbers only after emigration and density-induced decline in the reproductive rate had lowered the rate of 1 1 4 increase. In this study: food was not l i m i t i n g (except on occasional plants and in cages when young plants were infested - with aphids); alate emigration was i n s u f f i c i e n t to prevent population growth; aphid fecundity and developmental time were related more to seasonal changes in plant quality than to the deleterious effects of density; and predators were probably responsible for holding brassicae to the levels observed in the f i e l d . Hughes(l963) found that the delayed build-up of alate emigrants permitted populations to increase to lev e l s at which the l i f e of the host plant was threatened, and that the effect of density on the reproductive rate and recruitment prevented premature death. In this study, alate production reached high levels well before plant l i f e was threatened, and at densities at which aphid fecundity and developmental rate were either maximal or being affected p o s i t i v e l y through plant conditioning. Is there any generality? Using the approach of G i l b e r t e_t §_1(1976), the population parameters in the present study could be compared to those in other studies. However, adding a column for brassicae in Vancouver to Table 8.1 of G i l b e r t ej: §_1 (1976), completely a l t e r s the patterns derived from the four species already represented. According to Gilbert et al(1976) B. brassicae , a s e s s i l e species, has a long season on one host plant, strong density-dependent control of fecundity, low maximum fecundity, and long maturation time as compared to Macrosiphum rosae (L.), Aphis craccivora Koch, and Masonaphis maxima,which were termed ephemeral. Given that c l a s s i f i c a t i o n , 1 15 B. brassicae in the present study has q u a l i t i e s of both se s s i l e and ephemeral species, namely a long season on one plant, weak density-dependent control of fecundity, and intermediate maximum fecundity and maturation time. The differences in population parameters of B_^ brassicae as measured in Australia and Canada, could be ascribed to i n t r i n s i c differences between the aphids in the two areas, but probably result from differences in the host plant (see I.B.6). This suggests that some parameter besides 'ephemeral', describing the nature of the host plant (e.g. size, nitrogen content, growth rate, or a combination of these), must be added to Table 8.1 of Gilbert et §_1(1976) i f we are to make any sense of the aphid data. It would be interesting to measure the population parameters of B. brassicae on a small non-cultivated plant such as shepherd's-purse Capsella bursa-pastoris (L.) Medic. and add that information the table. At the moment not enough cases exist to generalize from this comparative approach. Generality may arise from comparisons of relationships between and within aphid species, but w i l l require that the relationships are expressed in similar units. Gilbert & Gutierrez(1973), and Gilbert(1980(a)) express the fecundity per individual of M^ maxima as "a negative exponential function of the t o t a l number of adults currently on the terminal". They use the current number of adults because generations are discrete and previous generations do not a f f e c t host plant quality for the current generation. Also, adults being the largest morph and being reproductive, exert the greatest 1 1 6 competitive effect on the plant. But generations of B. brassicae are not discrete. Previous generations affect the food source of current and subsequent generations, in that they produce sa l i v a r y secretions and leave feeding tubes which, at high densities, cause c h l o r o s i s . Hughes(l963) showed that aphid fecundity on ch l o r o t i c leaves was greatly reduced r e l a t i v e to controls. Furthermore, competition actually can be advantageous to IK brassicae at low densities (plant conditioning effect) and can be mediated by nymphs. These b i o l o g i c a l factors explain why adult weight expressed as a function of adult density (Appendix 1(k)), tends to obscure the plant-conditioning effect (II.C.Ic), and is less predictive than when t o t a l aphid density i s used as the independent variable. G i l b e r t ' s suggestion (personal communication) that t o t a l aphid biomass is the most appropriate 'x' variate does not solve the problem. The reduction of body weight at high density w i l l ameliorate the effect of numbers but, as Hughes(l963) points out, the physical damage to leaf tissues remains constant. In the absence of data which would allow the separation of the effects of competition and physical damage, the best variate for the prediction of adult weight is one which provides the greatest p r e d i c t a b i l i t y and is b i o l o g i c a l l y reasonable. In this study, current aphid density f u l f i l l e d both r e q u i s i t e s . This i s an unfortunate result, since i t suggests that the b i o l o g i c a l d e t a i l s of t h i s relationship preclude comparisons and hence generality. A review of the l i t e r a t u r e suggests that the problem is 1 17 general. There are numerous ways of expressing common relationships. Physiological time (day-degrees), a unit which is basic to the approach of Gilber t et § _ 1 ( 1 9 7 6 ) was not used by Barlow & D i x o n ( l 9 8 0 ) . The l a t t e r authors were concerned with the curvature in developmental rate at high and low temperatures, since they simulated events from year to year. They therefore modeled events in calendar time and accounted for the effects of temperature each day. This makes addition of their data to Table 8 . 1 of Gilber t et a l ( l 9 7 6 ) d i f f i c u l t . It also affects comparisons of relationships based on time, such as age-specific fecundity. Density-dependent reduction in fecundity is basic to most studies, but has been expressed as a function of: aphid weight, which was i t s e l f a function of aphid density and cumulative aphid density (Barlow & Dixon 1 9 8 0 ) ; adult density (Gilbert 1 9 8 0 ( a ) ) ; cornicle length, which was i t s e l f a function of aphid density (Gutierrez et a l 1 9 7 4 ) ; aphid density (Hughes & Gilbert 1 9 6 8 ) . Production of alates is expressed in most studies as a function of*aphid density, but for maxima, Gilber t e_t § _ 1 ( 1 9 7 6 ) expressed i t as a function of time. There is no perfect way of representing a relationship, and workers tend to use the way which they consider most convenient, or which best f i t s the biology of the organism in question. This makes comparisons extremely d i f f i c u l t and suggests that variable research techniques and/or differences in the biology of the organisms preclude comparisons at th i s l e v e l . Generality i s apparent at a higher l e v e l . . If the 118 comparisons between the present and Hughes'(1963) system are v a l i d , .the o v e r a l l differences are an important re s u l t , since they suggest that a major change in one component of the system (the plant), can be compensated by other components of the system to produce similar r e s u l t s . Charnov et §_1(1976) reached a similar conclusion by applying various rates of predation to a set of pea aphid (A^ pisum) populations and observing that a l l population trends were the same. Barlow & Dixon(l980) were able to examine compensation more cl'osely in their detailed model of lime aphid (E^ ti1iae) population dynamics. They concluded that: there was no key regulating factor; the effects of the control processes were not additive; h i e r a r c h i c a l regulation existed in which each process was capable of substituting for another; the d i f f e r e n t processes interacted and d i f f e r e n t ones were involved at d i f f e r e n t i n i t i a l d e n s i t i e s . Gilbert(1980(b)) did not address the problem of compensation, but l i s t e d six factors which were essential to the population dynamics of maxima. There was no single key factor. The extent to which the dynamics of an organism are based on a complex of interacting factors that can compensate for one another, w i l l be evident given more case h i s t o r i e s . It i s worth considering the ramifications of the nature of the complexity of a system to the approach one takes in examining the population dynamics of an organism. The c l a s s i c a l experimental approach in which the importance or effect of a factor i s assessed by changing that factor and observing the response, may lead to misleading results when 1 19 applied to a system in which one factor may compensate for the loss of another, or other parts of the system may respond to counteract a change in the response variate. The key to such experiments, the assumption ' a l l other things being equal', may be exceedingly d i f f i c u l t to assess, yet interpretation of the results hinges on that assumption. Another approach, which consists of breaking the system down into component processes, each of which is described mathematically and consolidated in some form of model, may also produce misleading re s u l t s . The usual procedure i s to build the model piece by piece u n t i l i t predicts observed population trends. Given compensation, such a model may be grossly incomplete yet give reasonable re s u l t s . Furthermore, mere comparison of observed with predicted data gives no assurance that the model is giving the right answer for the right reason. Neither i s the fitness test (Gilbert et al 1976) a sati s f a c t o r y check on the v a l i d i t y of the model, for although t h i s check was s a t i s f i e d for maxima (Gilbert & Gutierrez 1973), the model was not correct (cf Gilber t 1980(b)). The obvious solution is a combination of techniques in which a mathematical model i s f i r s t b u i l t and at some point used to supply hypotheses which are then checked in f i e l d experiments. This technique was used by Frazer & Gilbert(1976), and Jones et alO980) to validate models of par t i c u l a r relationships, and by Gilbert(1980(b)) to validate a complete population dynamics study. The models of Barlow & Dixon(l980) and Gutierrez et al0974) could be p r o f i t a b l y tested in t h i s way. 1 2 0 The nature of the complexity of ecological systems has a further ramification with respect to generalizations. How can a set of complex, non-linear, interacting, and compensating factors be summarized, such that between- and within-species comparisons may be made for di f f e r e n t systems? Generalization requires comparison of a set of accurately described phenomena at a pa r t i c u l a r l e v e l , but in the case of ecological systems, descriptions involving even a modest degree of complexity cannot be adequately grasped by the human mind. Indeed, mathematical models are used to consolidate our understanding of a pa r t i c u l a r system for that very reason. The approach of Gilbert et al(l976) (Table 8.1) is worth a try, but i t includes a r e s t r i c t e d number of variables, and the le v e l of d e t a i l may be less than adequate (strong vs weak density-dependent control of fecundity). A possible solution i s to use the models themselves. Given a set of population models b u i l t at the same general l e v e l (in terms of factors a f f e c t i n g b i r t h , death, immigration and emigration rates), and tested adequately in the f i e l d , one could compare the responses of each model to sp e c i f i c variable changes. Generality might then be possible in terms of re l a t i n g the nature of the response to the nature of the change. For example, one could add a predator to each model and vary the developmental temperature threshold and developmental rate, and/or the numerical and functional response of that predator. Given d i f f e r e n t i a l responses of the models, one could then attempt to c l a s s i f y the properties of the systems which give r i s e to the di f f e r e n t behaviors. 121 G e n e r a l i t y o f t h e f o r m ' g i v e n t h e s y s t e m p a r a m e t e r s x 1 , x 2 , x 3 . . . , a n d p r e d a t o r p a r a m e t e r s y l , y 2 , y 3 . . . , t h e p o p u l a t i o n b e c o m e s e x t i n c t ' , c o u l d be f i e l d t e s t e d . The a p p r o a c h h a s t h r e e a d v a n t a g e s : i t i s n o t n e c e s s a r y t h a t r e l a t i o n s h i p s ( e . g . a p h i d f e c u n d i t y v s a p h i d d e n s i t y ) be e x p r e s s e d i n s i m i l a r u n i t s ; t h e s y s t e m i s t r e a t e d a s a c o m p l e t e e n t i t y ; ' e x p e r i m e n t s ' c a n be d o n e i n s e c o n d s w i t h a l l v a r i a b l e s o b s e r v e d . C l a r k e t a _ l ( 1 9 6 7 ) a t t e m p t e d t o g e n e r a l i z e a b o u t i n s e c t p o p u l a t i o n d y n a m i c s . The r e s u l t w a s : a r e d e f i n i t i o n o f t h e o b j e c t o f s t u d y ; a l i s t o f f a c t o r s w h i c h a f f e c t p o p u l a t i o n g r o w t h ; a n a m a l g a m a t i o n o f s e v e r a l o f t h e o l d e r t h e o r i e s o f p o p u l a t i o n r e g u l a t i o n , n o t a b l y N i c h o l s o n , a n d A n d r e w a r t h a & B i r c h ; a n d a s e t o f c a s e h i s t o r i e s w h i c h s u p p o r t t h e i r ' n e w ' t h e o r y . I t h i n k , h o w e v e r , i t i s n o t u n f a i r t o s a y , t h a t g i v e n t h e i r g e n e r a l i z a t i o n s , we s t i l l c a n n o t p r e d i c t t h e e f f e c t o f a n y g i v e n e l e m e n t i n a ' l i f e s y s t e m ' o r t h e . p r o p e r t i e s ( b e h a v i o r u n d e r a s e t o f c h a n g e s i n o n e o r more c o m p o n e n t s ) o f a n y g i v e n ' l i f e s y s t e m ' . A t h e o r y m u s t n o t o n l y e x p l a i n , b u t a l s o p r e d i c t , s u c h t h a t i t c a n be e x p e r i m e n t a l l y t e s t e d . G i l b e r t e t a _ l ( l 9 7 6 ) p r o v i d e s a n a p p r o a c h w h i c h may l e a d t o t e s t a b l e q u a n t i t a t i v e t h e o r i e s o f d i s t r i b u t i o n a n d a b u n d a n c e . T h e r e i s o f c o u r s e no g u a r a n t e e , a n d i t w i l l be many more y e a r s b e f o r e we a r e a b l e t o a s s e s s i t s v a l u e i n t h i s r e s p e c t . 1 22 D. B i o l o g i c a l and c u l t u r a l control The work suggests that B_j_ brassicae does not aff e c t the growth (leaf area) of Maris Kestrel kale, given the normal complement of predators and the growing conditions found at Point Grey. Unless the crop serves as a source of alate emigrants l i k e l y to infest other less tolerant and economically superior crops, chemical control of B^ brassicae i s probably not necessary. The results of the field-cage experiment (II.C.Ic), contradict Wearing's(1972a) suggestion that continuous i r r i g a t i o n would reduce the rate of aphid increase in f i e l d crops. In the present study aphid developmental time, fecundity, and adult aphid' weight were the same under both fluctuating and continuous watering regimes. It is possible, however, since no plants showed signs of wil t i n g , that the fluctuating water regime was not severe enough to produce enriched sap (see I.B.6). A. aphidimyza i s a good candidate for further work as a b i o l o g i c a l control agent. Large numbers of pupae can be e a s i l y obtained in the laboratory. Diapause is f a c u l t a t i v e , so colonies can be maintained through the winter. The adult female apparently has excellent host-finding a b i l i t i e s , since single caged B^ brassicae females on f i e l d plants with no other aphids were attacked by A^ aphidimyza larvae. The small food requirement for l a r v a l development of A_^ aphidimyza makes i t less suitable for control at high aphid densities, unless large 123 numbers are introduced, but ideal at low densities. A high developmental temperature threshold r e l a t i v e to i t s prey (cf Campbell et a_l 1974), and competitive interactions with syrphid larvae are two potential problems. F i e l d t r i a l s , p a r t i c u l a r l y early in the season, are necessary to establish the usefulness of A^ aphidimyza as a control agent. The current work supports the findings of van Emden(l965) in that the syrphids' numerical response was reduced in plots surrounded by a g r i c u l t u r a l land. His observation that syrphid egg numbers were related to the close proximity of flowers (pollen i s a requirement for egg production (Schneider 1969)), suggests that syrphid predation could be substantially increased in a g r i c u l t u r a l crops by growing flowering plants within a crop. E. Summary B. brassicae develops and reproduces very quickly. Plant conditioning, a density-dependent phenomenon, increases both the developmental and reproductive rate of the aphid. Unchecked, B_;_ brassicae can destroy i t s host plant i f the plant is young at the time of i n i t i a l i n f e s t a t i o n . The production of alates, which increases exponentially at low densities, ameliorates the problem. It i s probable, however, that alate production i s not designed to reduce the aphid's impact on the plant, since the rate of alate production slows sharply at the time when the aphid is making maximum use of the plant for 124 reproduction (Figure 9 ) . Alate production probably r e f l e c t s the 'strategy' of the species to disseminate over a wide geographic area. If the aphid threatens the existence of i t s host plant, density-dependent reduction in fecundity and developmental rate slow the rate of increase of the aphid, and extend the length of time over which the aphid may produce alate emigrants. It is possible that d i f f e r e n t i a l dispersal (with respect to distance moved) occurs, since the weight of alates varies with density. From the aphid's point of view, l i f e appears to be mainly concerned with using the host plant to produce the the maximum number of alate emigrants. These emigrants, in turn, would enable the aphid to keep one step ahead of predators, as well as d i s t r i b u t e overwintering eggs in a variety of environments. Aphid densities s u f f i c i e n t to e l i c i t severe density-dependent effects were only occasionally observed in the f i e l d on scattered single plants. The enormous growth rate of Maris Kestrel kale i s undoubtedly partly responsible. In most cases the plant simply outgrows the aphid population. Results of cage and modeling experiments suggest that predators (syrphids in p a r t i c u l a r ) are also responsible. Further work i s necessary to e s t a b l i s h the exact effect of syrphid predation on both the temporal and s p a t i a l abundance of brassicae. Aphid weight decreases through the season, probably in response to changes in plant q u a l i t y . This change not only reduces the rate of increase of the aphid, but also increases the predation rate in terms of numbers eaten, since l a r v a l 1 25 predator voracity i s a function of aphid biomass. It is possible that the interaction between changing aphid weight and predation, in conjunction with the predators' numerical response and decreasing aphid fecundity and developmental rate through the season, greatly af f e c t the ultimate rate of increase of the aphids. The end of the season is marked by the production of oviparae, and an increase in the rate of loss of leaves from the plant. An increasing proportion of the population is found on these leaves, and movement off them appears to decrease as the season progresses. Population decline in the autumn therefore seems to be due to the combined effects of decreasing aphid fecundity and developmental rate, the production of fewer virginoparae, predation, and leaf f a l l . 1 26 BIBLIOGRAPHY Adams, R.G., & R.J. Prokopy. 1977. 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L i . 1965. A preliminary study on the l i f e history of cabbage aphid in Urumchi, Sinkiang. Acta Phytophylacica Sin. 4(1): 77-82. Abstracted from Rev. Appl. Entomol. A 55: No. 487. Yastrebov, I.O. 1979. [Enemies of cabbage pests.] Zashchita Rastenii 1:34. Abstracted from Rev. Appl. Entomol. A 67: No. 3886. 1 39 APPENDIX 1 Equations Appendix 1(a) (2.46 * (HBS / MaxHBS) where HBS = hours of daily bright sun MaxHBS = maximum hours of d a i l y bright sun. during the season Appendix 1(b) For example: y = -0.0361 + 0.780 * x r=0.894 (62df) where y = max-min thermometer minimum (2.5 to 12.8) x = weather-station minimum temperature (5.5 to 18.0) Appendix 1(c) y = -0.443 + 1.28 * x r=1.000 (5df) where y = sum of the subsample sized volumes (3.0 to 266.) x = o r i g i n a l volume (3.0 to 206.) Appendix 1(d) y = 0.0985 + 0.00357 * x r= 0.7l2 (35df) where y = nymphs produced/day-degree at peak production (0.165 to 0.330) x = t o t a l nymphs produced during the reproductive period (28. to 56.) Appendix 1(e) y = 142. + 2.69 * x r=0.328 (36df) where y = reproductive period in day-degrees above 6.7° (89.3 to 412.0) x = t o t a l nymphs produced during the reproductive period (28. to 56.) 1 40 Appendix 1(f) where y = -0.00255+0.00400*x-0.112*X-0.0112*x**2-0.0033 6*x**3+0.0812*x**4-0.0171*x**5-0.0284*X**6+0.0142*X**7-0.00187*X**8-0.00146*x*x1**2+0.000328*x*x1**3 R = 0.649 (971df) y = age-specific b i r t h rates (0.0 to 1.31) x = t o t a l fecundity (12. to 56.) x1 = physiological time (1 to 488) Appendix 1(g) y = 1.96 + 0.641 * x r=0.884 (73df) where y = leaf water/dry weight (4.48 to 11.4) x = leaf bore water/dry weight (3.52 to 15.7) Appendix 1(h) y = -1.89 + 1.33 r=0.748 (25df) where y = plant water/dry weight (3.06 to 7.97) x = the second, stratum 2 leaf water/dry weight (4.79 to 7.35) Appendix 1(i) y = 0.786 r=0.992 (74df) where y = leaf area ( cm2) (14.0 to 1610.) x = leaf length * width (15.8 to 2320.0) (This i s exactly the equation of an elipse.) Appendix 1(j) Aphids/clip cage were not correlated with treatment. adult weight (0.342 to 1.22) vs number aphids/clip cage (1. to 7.) slope = 0.0618±0.0129 r=0.613 (42df) developmental time (106. to 152.) vs number aphids/clip cage (1. to 7.) slope = -2.217±0.845 r=-0.384 (44df) 141 Appendix 1(k) y = e**(-0.388 - 0.176 * x) r=0.445 (45df) where y = average adult weight/female (0.299 to 0.968) x = number of adult IK brassicae/ cm2 (0.048 to 2.69) Appendix 1(1) s = e**(-k * b / a) where s = prey survival rate k = the number of prey required/predator/time period (voracity) b = number of predators a = number of prey 1 42 APPENDIX 2 Age-spec i f ic Morphological Characteristics of B. brassicae The f i r s t instar has only fiv e antennal segments (length of #1+2 equal to or greater than the length of #3), and short (as wide at the base as long) c o r n i c l e s . The second instar has five antennal segments (length of #1+2 s l i g h t l y greater than half the length of #3), and the cornicles are longer than they are wide at the base. The t h i r d apterous instar has six antennal segments (length of #1+2 s l i g h t l y less than the length of #3). The fourth apterous instar has six antennal segments (length of #1+2 equal to or s l i g h t l y greater than half the length of #3) . The adult was quickly recognized by the presence of a d i s t i n c t anal pad and cauda. The fourth instar and adult alates were recognized by their wing buds and wings respectively. This description d i f f e r s from that of Dodd(l976), who used di f f e r e n t characters, one of which was the number of caudal hairs. Although both keys should produce similar results, the one just described worked well at a magnification which f a c i l i t a t e d both counting and aging simultaneously. 143 APPENDIX 3 Appendix 3(a) Simulation Model 1 C**********BREVICORYNE BRASSICAE POPULATION SIMULATION********** 2 C 3 C MAIN CONTROLS PROGRAM FLOW 4 C 5 C N(TIME T+1)=N(TIME T) + GAINS - LOSSES 6 C WHERE GAINS ARE IN BRTHAG, TMSHFT, ALATE 7 C LOSSES ARE IN PPSURV, LNGVTY, FLIGHT 8 C GAINS AND LOSSES MAY BE SWITCHED IN POSITION, BY SETTING IORDER 9 C TO 1 OR 0 (0 = PREDATION FIRST) THIS GIVES DIFFERENT RESULTS 10 C DEPENDING ON STEP LENGTH (WHICH CAN NOT BE VARIED) AND MAGNITUDE 11 C OF GAINS AND LOSSES 12 C 13 C STEP LENGTH IS 1 DAYDEGREE > 6.65C 14 C PLANT TIME IS CALCULATED SEPARATELY FROM APHID TIME 15 C PREDATOR TIME IS ASSUMED TO BE A CONSTANT PROPORTION OF APHID TIME 16 C 17 C LOSSES DUE TO LEAF FALL = 0 IF CNSTNT = 0.0 18 C =MAXIMUM ( I E . NO SURVIVAL) IF CNSTNT='-' 19 C =PROPORTIONAL TO RATE OF LEAF FALL 20 C IF CNSTNT = 1.0 21 C (THIS EFFECT OF LEAF FALL IS REDUCE BY SETTING CNSTNT 22 C TO A VALUE BETWEEN 0.0 AND 1.0, 23 C OR INCREASED BY SETTING CNSTNT >1.0 24 C 25 C LOSSES DUE TO CECIDOMYIID, SYRPHID, OR PARASITE ATTACK = O 26 C IF VORAC(I) IS SET TO 0.0 RESPECTIVELY 27 C VORACITY/LARVAL DEVELOPMENTAL TIME IS SET BY VORAC(I) IN MG EATEN 28 C IN THE CASE OF NO PREDATION FROM ANY PREDATOR, IPREND(I) 29 C CAN BE SET TO 1 TO SAVE COMPUTER RUN TIME 30 C LENGTH OF CECIDOMYIID AND SYRPHID EGG STAGES IS SET IN THAT ORDER 31 C IN IEGGND(I) 32 C LENGTH OF CECIDOMYIID, SYRPHID AND PARASITE LARVAL STAGES, 33 C AND PARASITE PUPAL STAGE IS SET IN THAT ORDER IN IPREND(I) 34 C 35 C LOSSES DUE TO APHID FLIGHT = O IF IFLYTM = 524 36 C TIME OF APHID FLIGHT IN DAYDEGREES >6.65C IS SET.BY IFLYTM 37 C 38 C FECUNDITY AND DEVELOPMENTAL TIME CHANGES WITH MEAN FIELD ADULT 39 C WEIGHT MEASURES AND CAN BE MADE CONSTANT BY SETTING 40 C FLDVWT(I) CONSTANT 41 C THERE MUST BE AT LEAST 2 FLDVWTS 42 C 43 C LENGTH OF ADULT APTERAE AND ALATE LIFE IS SET IN IAPEND(5) AND 44 C IAPEND(7) 45 C 46 C IV ALATES ARE PRODUCED IF ALMRPH IS SET TO 1.0 47 C 48- C OVIPARAE PRODUCTION STARTS ON*DAY 234 (AUGUST 23) 49 C WHEN IDAY IS SET TO THE PLANTING DAY AND TEMPERATURES ARE 50 C READ AS MIN - MAX FROM THAT DAY, SEXUAL PRODUCTION STARTS 51 C AT THE APPROPRIATE TIME 52 C IF IDAY IS SET TO (-234) NO SEXUALS WILL BE PRODUCED 53 C 54 C 55 REAL*8 TIMREM(3) 56 COMMON /TIME/ I END, IPRINT, ISMP(20), IDAY 57 COMMON /DDTIME/ IDD 58 COMMON /TMPSUM/ TIMREM, TEMP(300), TIMRTO, CECTM, PARSTM, ITMINC, 59 1 IHFDAY 60 COMMON /APHTOT/ SUM(7), TOT, DENSE, APHDWT 1.44 61 COMMON /IVALMD/ ALMRPH, IORDER 62 C 63 C READ INITIAL DATA 64 CALL INFORM 65 C INITIALIZE TIME, AND PLANT CONSTANTS AND VARIABLES 66 CALL SETPLT 67 C INITIALIZE APHID CONSTANTS AND VARIABLES 68 CALL SETAPH 69 C INITIALIZE PREDATOR CONSTANTS AND VARIABLES *70 CALL SETPRD 71 C SUM APHID ARRAYS FOR INITIAL CONDITIONS 72 CALL TOTAPH 73 C SUM PREDATOR ARRAYS FOR INITIAL CONDITIONS 74 CALL TOTPRD 75 C PRINT INITIAL CONDITIONS 76 CALL RESULT 77 C INITIALIZE TIME CONSTANTS FOR DAYDEGREES /(1/2)DAY 78 ITIME = 2 79 IF (ITMINC .LE . 0) GO TO 70 80 10 IDDST = IDD + 1 81 IDDEND = IDD + ITMINC 82 C CALCULATE AND APPLY GAINS AND LOSSES FOR 1/2 DAY 83 DO 60 I = IDDST, IDDEND 84 IDD = I 85 C INCREMENT PLANT VARIABLES 86 CALL PLANT 87 C CALC. BIRTHS AND AGE APHIDS 88 IF (IORDER . EO. 0) GO TO 30 89 20 CALL BRTHAG 90 C CALC. NEW ADULT WEIGHT, REPRODUCTIVE RATE 91 C AND DEVELOPMENTAL TIME 92 C SHIFT LENGTH OF IMMATURE ARRAYS ACCORDINGLY 93 CALL TMSHFT CALC. # IV ALATES GIVEN DENSITIES AT (TIME-85) 94 C 95 C SHIFT THE APPROPRIATE NUMBER OF NEW IV APTERAE 96 C TO NEW IV ALATES 97 IF (ALMRPH . EO. 1.0) CALL ALATE 98 C IF DAY TIME SHORT ENOUGH (AUGUST 23) INITIATE 99 C SEXUALS 100 IF ((IHFDAY/2) + IDAY .GE. 234) CALL SEXUAL 101 IF (I ORDER . EO. O) GO TO 40 102 C AGE PREDATORS AND CALC. H OF NEW (EGGS) 103 C CALC. AND APPLY LOSSES DUE TO PREDATORS 104 C AND LEAF FALL 105 30 CALL PPSURV 106 C APPLY AGE SPECIFIC SURVIVAL 'LONGEVITY' 107 CALL LNGVTY 108 C CALC. /PALATES REQUIRED / PLANT AND REMOVE 109 C THE EXCESS BUT ONLY AFTER FULL WING DEVELOPMENT 1 10 CALL FLIGHT 1 1 1 IF (IORDER . EO. 0) GO TO 20 112 c SUM APHIDS AND PREDATORS 113 40 CALL TOTAPH 1 14 CALL TOTPRD "1 15 • ITMINC = ITMINC - 1 1 16 C AT FIXED INTERVALS OR SAMPLE TIMES PRINT RESULT 117 IF ((IDD - (IDD/IPRINT)*IPRINT) .EQ. 0) CALL RESULT 1 18 IF (IDD .NE. ISMP(ITIME)) GO TO 50 1 19 CALL RESULT 120 ITIME = ITIME + 1 1 4 5 121 C STOP AT LAST SAMPLE 122 IF (IDD . G E . I END) GO TO 80 123 C STOP IF THE POPULATION GOES EXTINCT 124 50 IF (TOT .GT . 0 . 0 ) GO TO 60 125 WRITE ( 6 , 9 0 ) 126 GO TO 80 127 60 CONTINUE 128 C GO ON TO THE NEXT 1/2 DAY 129 70 IHFDAY = IHFDAY + 1 130 C CALC. DAYDEGREES FOR THE NEXT 1/2 DAY 131 CALL TEMPDD 132 C START AGAIN 133 GO TO 10 134 C 135 80 STOP 136 90 FORMAT ( ' ' , 'POPULATION EXT INCT ' ) 137 END 138 C 139 C * * * * * » * * * * R E & D & L L INPUT DATA********** 140 C WRITE INPUT DATA BY SETTING LIST TO >0 141 C 142 SUBROUTINE INFORM 143 DIMENSION GARB(126) , FMT( 1 ) 144 REAL*8 TIMREM(3 ) 145 ' COMMON /TIME/ I END, IPRINT, ISMP(20) , IDAY 146 COMMON /PRDATR/ P R E D ( 3 5 0 , 3 ) , DDVORA(350,2) , V0RAC(3 ) , SUMPRD(3), 147 1 SUMV0R(2), SRVPRD, SRVPAR, IPREND(3) , IPRED(3 ) , IEGGND(3), 148 2 CBS, EAT. SMLFAL 149 COMMON /APHIDS/ A P ( 5 2 4 , 7 ) , IAPEND(7) , IAP(7) 150 COMMON /START/ S T ( 7 ) , FLDVWT(20) , ITVWT(20) , ITMAX, NVWT 151 COMMON / L E F A L L / AGESRV(7) , CNSTNT 152 COMMON /FCNDTY/ RATAP(524) 153 COMMON /FLYING/ VALSTA, WING, IFLYTM 154 COMMON /AGSURV/ SURV(524) 155 COMMON /TMPSUM/ TIMREM, TEMP(300) , TIMRTO, CECTM, PARSTM, ITMINC, 156 1 IHFDAY 157 COMMON /AGEDTN/ Y C E P T ( 7 ) , SL0PE(7 ) 158 COMMON /IVALMD/ ALMRPH, IORDER 159 COMMON /BOUND/ DELTA 160 COMMON /COHORT/ ICOHRT 161 COMMON/SYRDEX/SAFIND,PRPVOR(2) 162 COMMON /SYRPAR/T, A , B 163 DATA FMT / ' * ' / 164 READ ( 2 , F M T ) GARB, SURV 165 READ ( 5 , F M T ) IORDER, ICOHRT, SAFIND 166 READ ( 5 , F M T ) T , A , B 167 READ (5 .FMT) IDAY 168 READ (5 .FMT) YCEPT, SLOPE 169 READ (5 ,FMT) IAPEND 170 READ (5 .FMT) ST 171 READ (5 ,FMT) ITMAX, NVWT, DELTA 172 READ ( 5 . F M T ) ( ISMP(I ) ,I = 1 , ITMAX) 173 READ ( 5 , F M T ) (FLOVWT(I ) , I=1,NVWT) 174 READ ( 5 , F M T ) (ITVWT(I ) ,I = 1,NVWT) " 1 7 5 ' READ ( 5 . F M T ) VORAC, IPREND, IEGGND, CNSTNT, ALMRPH, IFLYTM, CBS, 176 1 IPRINT 177 READ ( 5 , F M T ) LIST 178 READ (5 ,FMT,END=10) ( T E M P ( I ) , I = 1 , 3 0 0 ) 179 10 LAST = 1 - 1 180 IF (L IST . L E . 0) GO TO 20 146 181 WRITE (6,30) IORDER, ICOHRT, SAFIND 182 WRITE (6,35) T, A, B 183 WRITE (6,40) IDAY, YCEPT, SLOPE 184 WRITE (6,50) ST, IAPEND, ITMAX, NVWT, DELTA 185 WRITE (6,60) (ISMP(I),1=1,ITMAX) 186 WRITE (6,70) (FLDVWT(I),I=1,NVWT) 187 WRITE (6,80) (ITVWT(I ) ,I = 1,NVWT ) 188 WRITE (6,90) VORAC, IPREND, IEGGND, CNSTNT, ALMRPH, IFLYTM, CBS, 189 1IPRINT 190 WRITE (6,100) (TEMP(I),1=1.LAST) 191 WRITE (6,110) SURV 192 20 WRITE (6,120) 193 RETURN 194 30 FORMAT ('1', 'MORTALITY FIRST IF I0RDER=O, IORDER=', 15, /' ', 195 1 'NO COHORT ADULT WEIGHT IF ICOHRT=0, ICOHRT=', 15,/' ', 196 2 'REDUCE ABILITY OF SYRPHID SEARCH WITH SAFIND (1-E', 197 3 '**(-SAFIND*DENSE) SAFIND=',F10.4) 198 35 FORMAT (' ','SYRPHID EGG PRODUCTION THRESHOLD'',F10.3, 199 1 ' APHIDS',/' ', 'SYRPHID EGG PRODUCTION CONSTANTS ARE', 200 2 'A=',F10.4,' B=',F10.4) 201 40 FORMAT (' ', 'PLANTING DAY=' , 15, /' ', 'CONSTANTS (RADIANS)', 202 1 'FOR PREDICTING AGE', ' DISTRIBUTION IN STRATUM 3 FROM THAT 203 2 IN THE WHOLE PLANT ARE', /' ', 'Y INTERCEPT', 7F10.4, /' ', 204 3 'SLOPES ', 7F10.4) 205 50 FORMAT (' ', 'APHID POPULATION SIMULATION STARTED WITH', /' ', 206 1 7F10.5, /'APHIDS IN INSTARS I,11,111,IV,V,IVALATE,VALATE' , 207 2 ' RESPECTIVELY', /' ', 'LENGTH OF EACH OF THE ABOVE INSTARS 208 3 IS', 715, /' ', '*(LENGTH OF THE IMMATURES IS SET IN THE PROGRAM 209 4USING', ' DEVELOPMENTAL TIME)*', /' ', 'NUMBER OF SAMPLES ARE', 210 5 15, /' ', 'NUMBER OF MEASURES OF ADULT WEIGHT ARE', 15, / 21 1 6 ' ', 'CHANGE IN NEW ADULT WEIGHT LIMITED TO', F10.5, 'MG') 212 60 FORMAT (' ', 'SAMPLE TIMES IN DAYDEGREES >6.65C ARE', 213 1 5 ( / ' ',2015)) 214 70 FORMAT (' ', 'MEASURES OF MEAN ADULT WEIGHT IN THE FIELD ARE', 5 ( / 215 1 ' '.10F8.3)) 216 80 FORMAT (' ', 'TIME (DAYDEGREES) MEASURES WERE MADE', 5 ( / ' ',1018)) 217 90 FORMAT (' ', 'CECIDOMYIID V0RACITY=', F10.3, ' SYRPHID VORACITY=', 218 1 F10.3, /' ', 'PARASITES IN MODEL? 0.0=NO; 1.0=YES;', F5.1, 219 2 /' ', 'LENGTH OF CECIDOMYIID, SYRPHID, AND PARASITE ', 220 3 ' AGE RESPECTIVELY', 315, /' ', 'LENGTH OF CECIDOMYIID AND, 221 4SYRPHID EGG AND', ' PARASITE LARVAL STAGES', ' RESPECTIVELY=', 222 5 315, /' ', 'MORTALITY DUE TO LEAF FALL', 223 6 ' IN MODEL? 0.0=NO 1.0=YES', F10.3, /' ', 224 7 'PRODUCE IV ALATES? O.O=N0 1.0=YES', F10.3, /' ', 225 8 'DAYDEGREE AFTER', ' MOLTING AT WHICH ALATES MAY FLY=', 15, 226 9 /' ', 'BLACK BOX', ' BACKGROUND MORTALITY APPLIED ACROSS TH 227 *E B0ARD=', F10.5, /' ', 'PRINT INTERVAL=', 15, ' DAYDEGREES') 228 100 FORMAT (' ', 'TEMPERATURES SINCE PLANTING ARE', .15(/' '.20F5.1)) 229 1 10 FORMAT ('1', 'AGE SPECIFIC SURVIVAL VALUES/DAYDEG>6.65C ARE', 50(/ 230 1 ' '.10F10.7)) 231 120 FORMAT ('1' ) 232 END 233 C 234 C **********INITIALIZE TIME AND PLANT CONSTANTS AND VARIABLES****** 235 ' C 236 SUBROUTINE SETPLT 237 REAL*8 TIMREM(3) 238 COMMON /TIME/ I END, IPRINT, ISMP(20), IDAY 239 COMMON /DDTIME/ IDD 240 COMMON /START/ S T ( 7 ) , FLDVWT(20), ITVWT(20), ITMAX, NVWT 1 4 7 241 COMMON /LEFALL/ AGESRV(7), CNSTNT 242 COMMON /PLANTP/ PLNTM, FALL, SUMFAL, PLEAF, PLS3, PRATIO, AREA, 243 1 PRPOS3, FALLSV, FALMAX 244 COMMON /TMPSUM/ TIMREM, TEMP(300), TIMRTO, CECTM. PARSTM, ITMINC, 245 1 IHFDAY 246 IHFDAY = 1 247 PLNTM = 0.0 248 FALLSV = 0.0 249 C INITIALIZE AGE SPECIFIC SURVIVAL DUE TO LEAF DROP 250 DO 10 I = 1, 7 251 AGESRV(I) = 1.0 252 10 CONTINUE 253 C INITIALIZE REMAINDER DAYDEGREES AFTER TRUNCATION 254 DO 20 I = 1 , 3 255 TIMREM(I) = DBLE(O.O) 256 20 CONTINUE 257 C INITIALIZE TIME TO TIME OF PLANTING KALE 258 IDD = O 259 ISTART = ISMP(1) 260 I END = ISMP(ITMAX) 261 C INCREMENT PLANT GROWTH FROM PLANTING TIME TO 262 C TIME OF FIRST SAMPLE 263 C CALC. #DAYDEGREES FOR NEXT 1/2 DAY 264 30 CALL TEMPDD 265 -IDDST = IDD + 1 266 IDDEND = IDD + ITMINC 267 C INCREMENT PLANT GROWTH FOR THIS 1/2 DAY 268 DO 40 I = IDDST, IDDEND 269 IDD = I 270 CALL PLANT 271 C IF IT IS FIRST SAMPLE RETURN WITH ANY REMAINING 272 ' C DAYDEGREES 273 IF (IDD .GE. I START) GO TO 50 274 40 CONTINUE 275 C GO ON TO THE NEXT 1/2 DAY 276 IHFDAY = IHFDAY + 1 277 GO TO 30 278 50 ITMINC = IDDEND - IDD 279 RETURN 280 END 281 C 282 C **********INITIALIZE APHID CONSTANTS AND VARIABLES********** 283 C 284 SUBROUTINE SETAPH 285 COMMON /DDTIME/ IDD 286 COMMON /APHIDS/ AP(524,7), IAPEND(7), IAP(7) 287 ' COMMON /START/ S T ( 7 ) . FLDVWT(20), ITVWT(20). ITMAX, NVWT 288 COMMON /FCNDTY/ RATAP(524) 289 COMMON /IVALDL/ DENLAG(85), PRPCLC, CONVRT, PRPMOD 290 COMMON /DEVTME/ INSTR, IDT, IDT1 291 COMMON /FLYING/ VALSTA, WING, IFLYTM 292 COMMON /APHWT/ VWT(524), DDVWT(1600), VWTOT, VWTA, VWTMN 293 COMMON /OVIPAR/ SEXRT0(524), CLCSEX, PRPSEX, SUMSEX, MRKSEX, 294 1 ISEXTM '295 • VALSTA = 0.0 296 WING = 0.0 297 PRPCLC = 1.0 298 CONVRT = 0.0 299 PRPMOD = 1.0 300 VWTMN = 0.0 1 48 301 ISEXTM = 0 302 MRKSEX = 0 303 PRPSEX = 0.0 304 CLCSEX = 0.0 305 SUMSEX = 0.0 30S C INITIALIZE APHID WEIGHT AND REPRODUCTIVE RATIO 307 DO 10 I = 1, 524 308 VWT(I ) = 0. 0 309 RATAP(I) = C O 310 SEXRTO(I) = 1.0 311 10 CONTINUE 312 C FOR EACH INSTAR 313 DO 30 I = 1, 7 314 C INITIALIZE APHID NUMBERS 315 DO 20 J = 1 , 524 316 A P ( J . I ) = 0. 317 20 CONTINUE 318 30 CONTINUE 319 C TIME - FIRST MEASURE OF MEAN FIELD ADULT WEIGHT 320 L = ITVWT(1) 321 C SET ADULT WEIGHT IN EACH DAYDEGREE PREVIOUS TO 322 C FIRST MEASURE EQUAL TO FIRST MEASURE 323 DO 40 I = IDD, L 324 DDVWT(I) = FLDVWT(1 ) 325 40 CONTINUE 326 C INTERPOLATE BETWEEN MEASURES OF FIELD ADULT 327 C WEIGHT TO OBTAIN MEAN ADULT WEIGHT IN EACH 328 C DAYDEGREE 329 L = NVWT - 1 330 DO 60 I = 1. L 331 0 = 1 + 1 332 IS = ITVWT(I) 333 IE = ITVWT(U) 334 X = FLDVWT(I) 335 B = (X - FLDVWT(J)) / (IS - IE) 336 IS = IS + 1 337 DD 50 K = IS, IE 338 X = X + B 339 DDVWT(K) = X 340 50 CONTINUE 341 60 CONTINUE 342 C NEW ADULT WEIGHT = MEAN FIELD ADULT WEIGHT 343 i VWTA = DDVWT(IDD) 344 VWT(1) = VWTA 345 C DEVELOPMENTAL TIME 346 CALL DEVTIM 347 IDT = IDT1 348 INDT = IDT / 4 349 .IREM = IDT - INDT * 4 350 C SET INSTAR LENGTHS 351 C EXCEPT FOR REMAINDER ALL LENGTHS ARE EQUAL 352 DO 70 I = 1. 4 353 IAP(I) = INDT 354 70 CONTINUE 355 • C ADD 1 DAYDEGREE TO EACH LENGTH FROM INSTAR 356 C IV TO I I I TO II TO I UNTIL REMAINDER = 0 357 INSTR = 4 358 80 IF (IREM .EO. 0) GO TO 90 359 IAP(INSTR) = IAP(INSTR) + 1 360 INSTR = INSTR - 1 1 49 361 IREM = IREM - 1 362 GO TO 80 363 C SET LENGTH OF IV ALATE AS A PROPORTION OF IV 364 C APTERAE 365 90 IAP(6) = (IAP(4)*7) / 5 366 C SET OLDEST ADULTS AGE AT 39 DAYDEGREES 367 IAP(5) = 39 368 IAP(7) = 39 369 C DISTRIBUTE APHIDS EVENLY IN EACH INSTAR 370 DO 110 I = 1, 7 371 APIDS = ST(I) / IAP(I) 372 K = IAP(I) 373 DO 100 J = 1 , K 374 AP(J , I ) = APIDS 375 100 CONTINUE 376 1 10 CONTINUE 377 C CALC. FECUNDITY AND REPRODUCTIVE RATIO 378 CALL FECUND 379 C GIVE ALL ADULT AGES (TO 39) THE SAME 380 C ADULT WEIGHT AND REPRODUCTIVE RATIO 381 C AS TH NEW ADULTS 382 VWTOT = 0 . 0 383 d = IAP(5) 384 XRATAP = RATAP(1 ) 385 DO 120 I = 2, J 386 VWT(I) = VWTA 387 RATAP(I ) = XRATAP 388 120 CONTINUE 389 C TOTAL ADULT WEIGHT 390 VWTOT = VWTA * ST(5) 391 C INITIALIZE DENSITY (TIME-85) 392 DO 130 I = 1. 85 393 DENLAG(I) = 0 .0 394 130 CONTINUE 395 RETURN 396 END 397 C 398 C **********INITIALIZE PREDATOR CONSTANTS AND VARIABLES********** 399 C 400 SUBROUTINE SETPRD 401 DIMENSION V0RAGE(3) 402 COMMON /PRDATR/ PRED(350,3), DDVORA(350,2) , V0RAC(3), SUMPRD(3), 403 1 SUMV0R(2), SRVPRD, SRVPAR, IPREND(3), IPRED(3), I EGGND(3) 404 2 CBS, EAT, SMLFAL 405 COMMON/SYRDEX/SAFIND,PRPVOR( 2) 406 DATA VORAGE /0.025, 0.125. 0.85/ 407 PRPVOR( 1 ) = 1 .0 408 PRPV0R(2) = 1 .0 409 SMLFAL = 0 .0 410 SRVPRD = 1.0 4 1 1 SRVPAR = 1.0 412 EAT = 0 .0 413 SUMVOR(1 ) = 0 .0 414 SUMV0R(2) = 0 .0 -415 - C IF CECIDOMYIIDS AND OR SYRPHIDS ARE IN MODEL 416 M = 1 417 N =" 2 418 IF (V0RAC(1) .EO. 0 .0 .AND. V0RAC(2) .EO. 0.0) GO TO 50 419 IF (VORACO) .EO. 0.0) M = 2 420 IF (V0RAC(2) .EO. 0 .0) N = 1 150 421 C CALCULATE VORACITY/DAYDEGREE OF 422 C LARVAL LIFE USING A SIGMOID CURVE 423 10 DO 40 I = M, N 424 C 2.5% TOTAL VORACITY IN FIRST INSTAR(>25% TIME) 425 C 12.5% TOTAL VORACITY IN SECOND INSTAR(-i25% TIME) 426 C 85.% TOTAL VORACITY IN THIRD INSTAR(->50% TIME) 427 IXEGND = IEGGND(I) 428 INCREM = (IPREND(I) - IXEGND) / 4 429 - K = IXEGND + INCREM 430 L = IXEGND + 1 431 V = VORAC(I) 432 DO 30 d = 1, 3 433 XVORAC = V * VORAGE(J) / (K - L + 1) 434 DO 20 ITIME = L, K 435 DDVORA(ITIME,I) = XVORAC 436 SUMVOR(I) = SUMVOR(I) + XVORAC 437 • 20 CONTINUE 438 L = K + 1 439 K = IXEGND + INCREM * d * 2 440 30 CONTINUE 441 40 CONTINUE 442 50 DO 60 I = 1 , 3 443 C INITIALIZE LENGTH OF LARVAL PREDATORS 444 C AND PUPAL PARASITE 445 IPRED(I) = 1 446 C INITIALIZE TOTAL PREDATORS 447 SUMPRD(I) = 0.0 448 C AND AGE SPECIFIC PREDATOR NUMBERS 449 PRED(1,1) = 0.0 450 PRED(IEGGND(I) + 1,1) = 0.0 451 60 CONTINUE 452 RETURN 453 END 454 C ; 455 C **********CALCULATE APHID AND PLANT TIME********** 456 C * * *ALGORITHM FROM FRAZER & GILBERT( 1967)*** 457 C 458 SUBROUTINE TEMPDD 459 REAL*8 THRESH(3), DAYDEG(3), TIMREM(3), XMAX, XMIN, Y, T 460 COMMON /TMPSUM/ TIMREM, TEMP(300), TIMRTO, CECTM, PARSTM, ITMINC, 461 1 IHFDAY 462 DATA THRESH /O.O, 19.4, 6.65/ 463 10 IHD1 = IHFDAY + 1 464 C PUT MAXIMUM=XMAX AND MINIMUM=XMIN 465 IF (TEMP(IHFDAY) .LE. TEMP(IHDI)) GO TO 20 466 XMAX = DBLE(TEMP(IHFDAY)) 467 XMIN = DBLE(TEMP(IHD1)) 468 GO TO 30 469 20 XMAX = DBLE(TEMP(IHD1)) 470 XMIN = DBLE(TEMP(IHFDAY)) 471 C FOR EACH THRESHOLD CALC. DAYDEGREES 472 30 DO 60 I = 1 , 3 473 Y = XMAX + XMIN - 2.0 * THRESH(I) 474 C IF THE MINIMUM IS LESS THAN THE THRESHOLD '475 • IF (XMIN .LT. THRESH(I)) GO TO 40 476 DAYDEG(I) f (0.25*Y) + TIMREM(I) 477 GO TO 60 478 C AND THE MAXIMUM IS GREATER THAN THE THRESHOLD 479 40 IF (XMAX .GT. THRESH(I)) GO TO 50 480 DAYDEG(I) = 0.0 + TIMREM(I) 151 481 GO TO 60 482 C DAYDEGREES - FROM THE POINT AT WHICH 483 C SINE CURVE CUTS THE THRESHOLD TO XMAX 484 50 T = DARSIN(Y/(XMIN - XMAX)) 485 DAYDEG(I) = (0.125*Y*(1.0 - 0.63661977*T) + 0.079577472*(XMAX -486 1 XMIN)*DCOS(T)) + TIMREM(I) 487 60 CONTINUE 488 C IF LESS THAN 1 DAYDEGREE >6.65C (APHID TIME) 489 C HAS ACCUMULATED, GO ON 490 70 IF (DAYDEG(3) .GT. 1.0) GO TO 90 491 C TIME LEFT OVER = ACCUMULATED TIME 492 DO 80 I = 1, 3 493 TIMREM(I) = DAYDEG(I) 494 80 CONTINUE 495 C GO ON TO THE NEXT HALF DAY 496 IHFDAY = IHFDAY + 1 497 GO TO 10 498 C GET INTEGER NUMBER OF DAYDEGREES >6.65C 499 90 XDAYDG = SNGL(DAYDEG(3)) 500 ITMINC = IFIX(XDAYDG) 501 C RATIO OF PLANT TO APHID TIME 502 TIMRTO = SNGL((DAYDEG(1) - DAYDEG(2))/DAYDEG(3)) 503 C NUMBER OF REMAINING DAYDEGREES AFTER 504 C TRUNCATION 505 TIMREM(3) = DAYDEG(3) - ITMINC 506 C REMAINDER DAYDEGREES FOR THE OTHER 507 C TWO THRESHOLDS 508 DO 100 1 = 1 , 2 509 TIMREM(I) = (DAYDEG(I)/DAYDEG(3 ) ) * TIMREM(3) 510 100 CONTINUE 511 RETURN 512 END 513 C 514 C ***********INCREMENT PLANT VARIABLES********** 515 SUBROUTINE PLANT 516 REAL*8 TIMREM(3) 517 COMMON /DDTIME/ IDD 518 COMMON /PLANTP/ PLNTM, FALL, SUMFAL, PLEAF, PLS3, PRATIO, AREA, 519 1 PRP0S3, FALLSV, FALMAX 520 COMMON /TMPSUM/ TIMREM, TEMP(SOO), TIMRTO, CECTM, PARSTM, ITMINC, 521 1 IHFDAY 522 C PLANT TIME 523 PLNTM = PLNTM + TIMRTO 524 C tOTAL LEAVES FALLEN SINCE PLANTING 525 SUMFAL = 0.0000019616 * (PLNTM**2.1) 526 C NUMBER LEAVES FALLING/DAYGREE (APHID) 527 FALL = SUMFAL - FALLSV 528 FALLSV = SUMFAL 529 FALMAX = 0.02091002 * TIMRTO 530 C NUMBER OF LEAVES IN STRATUM 3 531 PLS3 = 0.5004 + 0.2698 * PLNTM / 100. 532 C PROPORTION OF LEAVES IN STRATUM 3 AFTER 533 C LEAF FALL 534 PRATIO = (PLS3 - FALL) / PLS3 535 C IF NO APHIDS EXIST IN STRATUM 3 GO ON 536 IF (PLNTM .GE. 54.401) GO TO 10 537 PRP0S3 = 0 .0 538 GO TO 20 539 C PROPORTION OF POPULATION IN STRATUM 3 540 C ***COEFFICIENTS HAVE BEEN CHANGED TO RADIANS 152 541 C ( IE DIVIDED BY 5 7 . 2 9 5 7 7 9 5 1 ) 542 10 PRP0S3 = ( S I N ( - 0 . 0 2 2 2 8 8 + 0 . 0 4 0 9 7 0 * ( P L N T M / 1 0 0 . ) ) ) ** 2. 543 C LEAF AREA/PLANT 544 20 AREA = ( 1 0 0 0 - / ( 0 . 0 4 1 2 + 360804934*((PLNTM - 0 . 9 9 9 ) * * ( - 3 . 5 ) ) ) ) + 545 1 1 8 0 . 0 546 RETURN 547 END 548 C 549 C **********'GAINS' RELATIONSHIPS********** 550 C 551 SUBROUTINE GNRELT 552 COMMON /FCNDTY/ RATAP(524) 553 COMMON /IVALDL/ DENLAG(85) , PRPCLC, CONVRT, PRPMOD 554 COMMON /DEVTME/ INSTR, IDT, IDT1 555 COMMON /APHWT/ VWT(524) , DDVWT(1600), VWTOT, VWTA, VWTMN 556 RETURN 557 C CALC. THE PROPORTION OF IVAPTERAE/IVALATE 558 C GIVEN DENSITIES AT T IME -85 559 ENTRY IVAL 560 XDENSE = DENLAG(85) 561 C IF DENSITY IS LESS THAN THE THRESHOLD GO ON 562 IF (XDENSE . G E . 0 . 0 0 1 6 3 2 6 ) GO TO 10 563 PRPCLC = 1 . 0 564 CONVRT = 0 . 0 565 GO TO 20 566 10 PRPCLC = ( E X P ( - 0 . 7 5 8 7 - O.1279*(ALOG(XDENSE + 0 . 0 0 1 ) ) ) ) - 0 . 0 0 1 567 20 RETURN 568 C CALC. FECUNDITY AND REPRODUCTIVE RATIO 569 C FOR THE NEW COHORT 570 ENTRY FECUND 571 RATAP( 1 ) = - 1 5 . 1 1 0 2 + 107.2162 * ( 1 . 0 - E X P ( - 1 . 5 * V W T ( 1 ) ) ) 572 RETURN 573 C CALC. DEVELOPMENTAL TIME 574 ENTRY DEVTIM 575 IDT1 = I F I X ( 1 5 0 . 9 - 30.088*VWT(1) ) 576 RETURN 577 END 578 C 579 C **********BIRTHS AND AGING********** 580 SUBROUTINE BRTHAG 581 COMMON /APHIDS/ A P ( 5 2 4 , 7 ) , IAPEND(7) , IAP(7) 582 COMMON /FCNDTY/ RATAP(524) 583 COMMON /FLYING/ VALSTA, WING, IFLYTM 584 COMMON /APHWT/ VWT(524) , DDVWT(1600), VWTOT, VWTA, VWTMN 585 COMMON /OVIPAR/ S E X R T 0 ( 5 2 4 ) , CLCSEX, PRPSEX, SUMSEX, MRKSEX, 586 1 ISEXTM 587 COMMON /COHORT/ ICOHRT 588 BIRTHS = 0 . 0 589 J = IAP(5 ) 590 IF ( J .GT . 400) d = 400 591 C NUMBER BORN 592 DO 10 I = 1 , d 593 X1 = RATAP( I ) 594 X2 = ( ( F L O A T ( I ) ) / 1 0 0 . ) - 1 .578 -595 - X3 = X2 * X2 596 X4 = X2 * X3 597 X5 = X2 * X4 598 X6 = X2 * X5 599 X7 = X2 * X6 600 X8 = X2 * X7 153 601 X9 = X2 * X8 602 X10 = X1 * X3 603 X1 1 = X1 * X4 604 BORN = -0.002551 + 0.003996 * X1 - 0.1118 * X2 - 0.01125 * X3 -605 1 0.003356 * X4 + 0.08117 * X5 - 0.01710 * X6 - 0.02840 * X7 + 0. 606 2 01423 * X8 - 0.001870 * X9 - 0.001465 * X10 + 0.0003275 * X11 607 IF (BORN .LT. 0.0) BORN = 0.0 608 BIRTHS = BIRTHS + AP(I,5) * BORN * SEXRTO(I) + AP((I + IFLYTM + 609 1 1 ) ,7) * BORN * 0.469 610 10 CONTINUE 611 C EXTEND LENGTH OF ADULT APTERAE AND ALATE 612 C UNTIL MAXIMUM LENGTH IS REACHED 613 DO 20 I = 5, 7, 2 614 IF (IAP(I) .LT. IAPEND(I)) IAP(I) = IAP(I) + 1 615 20 CONTINUE 616 C AGE APHIDS STARTING AT THE OLDEST ALATES 617 C AND MOVING TO THE YOUNGEST IV ALATES 618 C THEN STARTING AT THE OLDEST APTERAE AND 619 C MOVING TO THE YOUNGEST APTERAE 620 I = 7 621 30 d = IAP(I ) 622 40 IF (J .EO. 1) GO TO 50 623 K = J - 1 624 AP(J,I ) = AP(K,I ) 625 J = J - 1 626 GO TO 40 627 50 IF (I .EO. 6) GO TO 60 628 IF (I .EO. 1) GO TO 70 629 11 = 1 - 1 630 J = IAP(II) 631 AP( 1,1) = AP(J,II ) 632 I = II 633 GO TO 40 634 60 AP(1,6) = 0.0 635 1 = 1 - 1 636 GO TO 30 637 C NEW COHORT = BIRTHS 638 70 AP(1, 1 ) = BIRTHS 639 C AGE ADULT WEIGHTS AND REPRODUCTIVE RATIOS 640 IF (ICOHRT .EO. 0) GO TO 90 641 I = IAP(5) 642 80 d = I - 1 643 ' VWT(I) = VWT(d) 644 RATAP(I) = RATAP(d) 645 1 = 1 - 1 646 IF (I .GT. 1) GO TO 80 647 90 RETURN 648 END 649 C 650 C **********DEVELOPMENTAL TIME CHANGES********** 651 C 652 SUBROUTINE TMSHFT 653 COMMON /DDTIME/ IDD 654 COMMON /APHIDS/ AP(524,7), IAPEND(7), IAP(7) £55 COMMON /FCNDTY/ RATAP(524) 656 " COMMON /DEVTME/ INSTR, IDT, IDT1 657 COMMON /APHWT/ VWT(524), DDVWT(1600), VWTOT, VWTA, VWTMN 658 COMMON /BOUND/ DELTA 659 COMMON /COHORT/ ICOHRT 660 C MEAN FIELD ADULT WEIGHT 1 54 661 662 663 664 665 666 667 668 669 670 10 671 672 20 673 674 675 C 676 C 677 678 679 680 30 681 C 682 683 684 685 C 686 '687 688 689 690 691 692 693 694 C 695 C 696 C 697 40 698 C 699 C 700 701 702 C 703 704 705 C 706 50 707 708 C 709 C 710 C 711 712 C 713 C 714 C 715 C 716 ' C 717 718 719 720 C VWTA = DDVWT(IDD) IF (ICOHRT '.NE. O) GO TO 20 VWT( 1 ) = VWTA CALL FECUND RATAP 1 = RATAPO) J = IAP(5) DO 10 I = 2. J VWT(I) = VWTA RATAP(I) = RATAP1 CONTINUE GO TO 40 VWTOT =0.0 SUM5 = AP(1,5) J = IAP(5) SUM ADULTS SUM ADULT WEIGHT EXCEPT FOR NEW COHORT DO 30 I =2, J SUM5 = SUM5 + AP(I,5) VWTOT = VWTOT + VWT(I) * AP(I,5) CONTINUE NEW ADULT WEIGHT APVNEW = AP( 1,5) IF (APVNEW .EQ. 0.0) GO TO 150 VWT(1) = (VWTA*SUM5 - VWTOT) / APVNEW SET BOUNDS ON NEW ADULT WEIGHT VWT1 = VWT( 1 ) VWT2N = VWT(2) - DELTA VWT2P = VWT(2) + DELTA IF (VWT 1 .LT. VWT2N) VWT(1) = VWT2N IF (VWT1 .GT. VWT2P) VWT(1) = VWT2P VWT1 = VWT(1) IF (VWT1 .GT. 1.256) VWT(1) = 1.256 IF (VWT1 .LT. 0.1013) VWT(1) = 0.1013 DEVELOPMENTAL TIME IDT1 = NEW DEVELOPMENTAL TIME IDT = OLD DEVELOPMENTAL TIME CALL DEVTIM LIMIT THE CHANGE IN DEVELOPMENTAL TIME TO + OR - 4 DAYDEGREES IF ((IDT1 - IDT) .LT. - 4) IDT1 = IDT - 4 IF ((IDT1 - IDT) .GT. 4) IDT1 = IDT + 4 CHANGE IN DEVELOPMENTAL TIME IDIF = IDT1 - IDT IF (IDIF) 50, 150, 120 DEVELOPMENTAL TIME LESS THAN BEFORE IF (ICOHRT .EQ. 0) GO TO 110 ITEST = INSTR DETERMINE WHERE TO REMOVE A DAYDEGREE INSTAR MARKS THE POINT OF NEXT ADDITION OR LAST DELETION OF A DAYDEGREE ITEST 1 = 4 - ITEST IF THE DIFFERENCE IN DEVELOPMENTAL TIME IS LARGE ENOUGH THAT THE LENGTH OF INSTAR IV IS CHANGED WHEN STARTING REMOVAL AT TEST+1 AND REMOVING IN THE ORDER I-II-III-IV THEN GO ON IF (ITEST 1 .EO. 0) ITEST1 = 4 IDIF1 = -IDIF IF (IDIF1 .LT. ITEST1) GO TO 110 DERIVE LOCATION OF LAST DELETION IF ALL ARE 155 721 C DONE 722 DO 60 I = 1. IDIF1 723 IF (ITEST .EO. 4) ITEST = 0 724 ITEST = ITEST + 1 725 60 CONTINUE 726 : C NUMBER OF IV APTERAE TRANSFERRED TO ADULT 727 ' ADIT = AP(IAP(4),4) 728 C TOTAL NEW ADULTS 729 TEST2 = ADIT + APVNEW 730 C NEW, NEW ADULT WEIGHT 731 VWTST = (VWTA*(SUM5 + ADIT) - VWTOT) / TEST2 732 C SET BOUNDS ON NEW ADULT WEIGHT 733 VWT2N = VWT(2) - DELTA 734 VWT2P = VWT(2) + DELTA 735 IF (VWTST .LT. VWT2N) VWTST = VWT2N 736 IF (VWTST .GT. VWT2P) VWTST = VWT2P 737 IF (VWTST .GT. 1.256) VWTST = 1.256 738 IF (VWTST .LT. 0.1013) VWTST = 0.1013 739 C NEW DEVELOPMENTAL TIME 740 IDTST = IFIX(150.9 - 30.088*VWTST) 741 C CHANGE IN DEVELOPMENTAL TIME 742 IDIF1 = IDTST - IDT1 743 IF (IDIF1) 80, 100, 70 744 C LENGTHEN DEVELOPMENTAL TIME 745 c IF LENGTHENING IS LESS THAN ORIGINAL 746 c SHORTENING, GO ON 747 70 IF (IDIF1 .GE. - IDIF) GO TO 150 748 C SET NEW DEVELOPMENTAL TIME 749 IDT1 = IDTST 750 C RESET CHANGE IN DEVELOPMENTAL TIME 751 IDIF = IDIF + IDIF1 752 C IF IV INSTAR IS STILL TO BE SHORTENED 753 C ADD NEW ADULTS INTO ADULT ARRAY 754 ITEST 1 = ITEST + 1 755 IF (I TEST 1 .EQ. 5) ITEST 1 = 1 756 IF (IDIF1 .GE. ITEST 1 ) GO TO 110 757 GO TO 100 758 C DEVELOPMENTAL TIME SHORTER THAN FIRST 759 C REDUCTION 760 80 d = -IDIF1 761 C RESET THE DIFFERENCE IN DEVELOPMENTAL TIME 762 C LIMITING THE REDUCTION TO -4 DAYDEGREES 763 DO 90 I = 1, d 764 IF (IDIF .LE. - 4) GO TO 100 765 IDIF = IDIF - 1 766 IDT = IDT - 1 767 90 CONTINUE 768 C RESET NEW ADULT WEIGHT 769 100 VWT( 1 ) = VWTST 770 C SHORTEN ARRAYS AND CHANGE INSTAR MARKERS 771 1 10 IF (INSTR .EO. 4) INSTR = 0 772 C SET MARKER TO INSTAR TO BE SHORTENED 773 INSTR = INSTR + 1 774 C SHORTEN THE INSTAR LENGTH, MOVING THE 775 • c CONTENTS OF THE LAST CELL TO THE NEXT INSTAR 776 d = IAP(INSTR) 777 AP(1,INSTR + 1) = AP(1,INSTR + 1) + AP(J,INSTR) 778 AP(d,INSTR) = 0 . 0 779 IAP(INSTR) = IAP(INSTR) - 1 780 IDIF = IDIF + 1 156 781 IF (IDIF .EOv 0) GO TO 130 782 GO TO 110 783 C LENGTHEN ARRAYS AND CHANGE INSTAR MARKERS 784 120 IF (INSTR .EO. 0) INSTR = 4 785 IAP(INSTR) = IAP(INSTR) + 1 78G IDIF = IDIF - 1 787 INSTR = INSTR - 1 788 IF (IDIF .EQ. 0) GO TO 130 789 GO TO 120 790 C RESET NEW TO OLD DEVELOPMENTAL TIME 791 130 IDT = IDT1 792 C LENGTH OF IV ALATES 793 IAP6 = IAP(6) 794 IAP(6) = ( I A P ( 4 ) * 7 ) / 5 795 C IF NEW LENGTH IS LESS THAN THE OLD. GO ON 796 IF (IAP(6) .GE. IAP6) GO TO 150 797 M = IAP(6) + 1 798 N = IAP6 799 C MOVE THE CONTENTS OF THE LAST IV ALATE 800 C CELLS TO THE NEW ADULT ALATE 801 DO 140 I = M, N 802 AP(1,7) = AP(1,7) + AP(I,6) 803 AP(I.6) = 0.0 804 140 CONTINUE 805 C NEW ADULT FERTILIY AND REPRODUCTIVE RATIO 806 150 CALL FECUND 807 RETURN 808 END 809 C 810 C * * * * * * * * * * ( j p r , j \ T E IV ALATES********** 81 1 C 812 SUBROUTINE ALATE 813 COMMON /APHIDS/ AP(524,7), IAPEND(7), IAP(7) 814 COMMON /1VALDL/ DENLAG(85) , PRPCLC, CONVRT, PRPMOD 815 COMMON /APHTOT/ SUM(7), TOT, DENSE, APHDWT 816 c AGE DENSITIES AT TIME-85 817 U = 85 818 10 IF ( J .EO. 1) GO TO 20 819 K = J - 1 820 DENLAG(U) = DENLAG(K) 821 J = J - 1 822 GO TO 10 823 c ADD NEW DENSITY TO START OF TIME LAG ARRAY 824 20 DENLAG(1) = DENSE 825 C PROPORTION IV APTERAE/1V ALATE 826 CALL IVAL 827 C IF IV APTERAE ARE TO BE MOVED GO ON 828 IF (PRPCLC .EO. 1.0) GO TO 60 829 C TOTAL IV APTERAE AND IV ALATES 830 DO 40 I = 4 , 6, 2 831 SUM(I) = 0.0 832 U = IAP(I ) 833 DO SO K = 1, J 834 SUM(I) = SUM(I) + AP(K.I) 835 - 30 CONTINUE 836 40 CONTINUE 837 C NUMBER OF NEW IV APTERAE TO BE MOVED 838 C TO NEW IV ALATES CELL 839 SUM4 = SUM(4) 840 CONVRT = SUM4 - PRPCLC * (SUM4 + SUM(6)) 157 84 1 C IF SOME TO BE MOVED GO ON 842 • IF (CONVRT . L E . 0 . ) GO TO 6 0 843 IF (CONVRT .GE . A P ( 1 , 4 ) ) GO TO 50 844 A P ( 1 , 6 ) = A P ( 1 , 6 ) + CONVRT 845 A P ( 1 , 4 ) = A P ( 1 , 4 ) - CONVRT. 846 GO TO 6 0 847 50 A P ( 1 , 6 ) = A P ( 1 , 6 ) + A P ( 1 , 4 ) 848 CONVRT = A P ( 1 , 4 ) 849 A P ( 1 , 4 ) = 0 . 0 850 60 RETURN 851 END 852 C 853 C **********PROPORTION OVIPAROUS FEMALES********** 854 C 855 SUBROUTINE SEXUAL 856 COMMON /APHIDS/ A P ( 5 2 4 , 7 ) , IAPEND(7 ) , I A P ( 7 ) 857 COMMON /DEVTME/ INSTR, IDT, IDT1 858 COMMON /OVIPAR/ S E X R T 0 ( 5 2 4 ) , CLCSEX, PRPSEX, SUMSEX, MRKSEX, 859 1 ISEXTM MARK AGE OF OLDEST NYMPH UNTIL ADULT 8 6 0 C 861 MRKSEX = MRKSEX + 1 862 C 863 IF (MRKSEX . L E . IDT1) GO TO 40 864 C IF OVIPARAE ARE OLD ENOUGH TO BE ADULT GO ON 865 MRKSEX = 500 866 C AGE OF NEXT OLDEST COHORT OF NYMPHS PROPORTION OVIPARAE/TOTAL ADULTS 867 I F ( P R P S E X . L E . 0 . 9 9 7 5 3 8 ) P R P S E X = P R P S E X + 0 . 0 0 2 4 5 4 868 C OVIPARAE AGE (OLDEST) 869 IF ( ISEXTM .LT . 524) ISEXTM = ISEXTM + 1 870 C AGE PROPORTION VIVIPARAE/TOTAL ADULTS 871 I = ISEXTM 872 10 IF ( I .EO. 1) GO TO 20 873 J = I - 1 874 SEXRTO(I ) = SEXRTO(J) 875 1 = 1 - 1 876 GO TO 10 877 20 SE XRTO( 1 ) = 1 . 0 878 APVNEW = A P ( 1 , 5 ) 879 SUM5 = APVNEW 8 8 0 SUMSEX = 0 . 0 881 J = I A P ( 5 ) 882 C SUM ADULTS AND OVIPARAE 883 DO 30 I = 2 , d 884 XAP = A P ( I , 5 ) 885 SUM5 = SUM5 + XAP 886 SUMSEX = SUMSEX + XAP * ( 1 . 0 - SEXRTO( I ) ) 887 30 CONTINUE 888 C NUMBER OVIPARAE REQUIRED 889 CLCSEX = PRPSEX * SUM5 890 IF (APVNEW .EQ. 0 . 0 ) GO TO 40 891 C PROPORTION VIVIPARAE/TOTAL NEW ADULTS 892 S E X R T O O ) = 1 . 0 - ( (CLCSEX - SUMSEX)/APVNEW) 893 IF ( S E X R T O O ) . LT. O.O) SEXRTO(I ) = O.O 894 C NUMBER OF OVIPARAE 895 SUMSEX = SUMSEX + APVNEW * ( 1 . 0 - SEXRTOO )) 896 ' 40 RETURN 897 END 898 C 899 C **********LOSSES RELATIONSHIPS********** 9 0 0 C 158 901 SUBROUTINE LSRELT 902 COMMON /PRDATR/ P R E D ( 3 5 0 , 3 ) , DDVORA(350,2) , V 0 R A C ( 3 ) , SUMPRD(3), 9 0 3 1 SUMV0R(2) . SRVPRD, SRVPAR, IPREND(3 ) , I P R E D ( 3 ) , IEGGND(3) , 904 2 CBS, EAT, SMLFAL 905 COMMON /LEFALL/ AGESRV(7) , CNSTNT 906 COMMON /PLANTP/ PLNTM, F A L L , SUMFAL, PLEAF , P L S 3 , PRATIO. AREA, 907 1 PRP0S3 , FALLSV, FALMAX 908 COMMON /APHTOT/ SUM(7) , TOT, DENSE, APHDWT 909 COMMON /FLYING/ VALSTA, WING, IFLYTM 910 COMMON /AGEDTN/ Y C E P T ( 7 ) , S L 0 P E ( 7 ) 911 COMMON /SYRPAR/ T, A, B 912 RETURN 913 C NUMBER OF ALATES/PLANT 914 ENTRY VALFLY 915 C IF TOTAL APHIDS ARE LESS THAN THE 916 C THRESHOLD, GO ON 917 IF (TOT .GE . 0 . 0 0 9 7 8 7 7 ) GO TO 10 918 WING = 0 . 0 919 VALSTA = 0 . 0 9 2 0 GO TO 20 921 10 VALSTA = ( E X P ( - 3 . 0 2 6 1 + O.8570*(ALOG(TOT + 0 . 0 0 1 ) ) ) ) - 0 . 0 0 1 922 20 RETURN 923 C NUMBER OF PREDATORS AND PARASITES/PLANT 924 ENTRY ADPRED 925 C *CECIDOMYIIDS* 926 IF ( V O R A C O ) .EO. 0 . 0 ) GO TO 40 927 C IF TOTAL APHIDS ARE LESS THAN MINIMUM 928 C ESTIMATED VALUE FOR EGG LAYING GO ON 929 IF (TOT .GE . 5 2 . 0 ) GO TO 30 9 3 0 PRED( 1 ,1 ) = 0 . 0 931 GO TO 40 932 C /77 DATA ONLY 933 30 P R E D ( 1 , 1 ) = ( ( ( 1 . 3 6 1 5 + 1 . 7 5 5 4 * ( ( ( T O T / 1 0 0 0 . ) + O . 0 0 1 ) * * 0 . 5 ) ) * * 2 . ) 934 1 - 0 . 0 0 1 ) / ( IPREND(1) - IEGGND(1)) 935 C *SYRPHIDS* 936 4 0 • IF (V0RAC(2) .EO. 0 . 0 ) GO TO 6 0 937 C IF TOTAL APHIDS ARE LESS THAN MINUMUM 938 C ESTIMATED VALUE FOR EGG LAYING GO ON 939 IF (TOT . G E . T) GO TO 50 9 4 0 P R E D ( 1 , 2 ) = 0 . 0 94 1 GO TO 60 942 C /77 DATA ONLY - . 943 50 P R E D ( 1 , 2 ) = ( ( ( A + B* ( ( ( TOT/1000 . ) + O . 0 0 1 ) * * 0 . 5 ) ) * * 2 . ) 944 1 - 0 . 0 0 1 ) / ( IPREND(2) - IEGGND(2)) 945 C *PARASITES* 946 60 IF ( V O R A C O ) .EO. 0 . 0 ) GO. TO 80 947 C IF TOTAL APHIDS ARE LESS THAN MINIMUM 948 C ESTIMATED VALUE FOR EGG LAYING GO ON 949 IF (TOT . G E . 9 . 1 ) GO TO 70 9 5 0 PRED( 1 , 3 ) = 0 . 0 951 GO TO 80 952 C /77+/78 DATA 953 70 PRED( 1 , 3 ) = ( ( ( - 0 . 5 5 7 8 + 8 . 8 2 4 9 * ( ( ( T O T / 1 0 0 0 . ) + O . O 0 1 ) * * 0 . 5 ) ) * * 2 . ) 954 1 - O . O O D / ( IPREND(3) - I EGGND (3) ) - 9 5 5 . . 80 RETURN 956 C MORTALITY DUE TO LEAF FALL 957 ENTRY LDROP 958 C CALCULATE SURVIVAL AFTER LEAF FALL 959 SUMAGE = 0 . 0 960 C AGE DISTRIBUTION IN STRATUM 3 159 961 DO 110 I = 1 , 7 962 XI = SUM(I) / TOT 963 IF (XI .GT. 0 . 0 ) GO TO 9 0 • 964 AGESRV( I ) = 0 . 0 965 GO TO 110 966 90 AGESRV( I ) = ( S I N ( Y C E P T ( I ) + S L O P E ( I ) * X I ) ) ** 2 . 967 100 SUMAGE = SUMAGE + AGESRV( I ) 968 110 CONTINUE 969 C PROPORTION OF EACH INSTAR LOST DUE TO 9 7 0 C LEAF FALL WHERE SURVIVAL DECREASES 971 C AS A FUNCTION OF THE RATE OF LEAF FALL 972 XFP = (1.O/SUMAGE) * PRP0S3 973 IF (CNSTNT) 120, 130, 140 974 120 XPRR = PRATIO 975 GO TO 150 976 130 XPRR = 1 . 0 977 GO TO 150 978 140 XFFC = 1 . 0 - (FALL/FALMAX) * CNSTNT 979 IF (XFFC . LT . 0 . 0 ) XFFC = 0 . 0 9 8 0 XPRR = PRATIO + ( 1 . 0 - PRATIO) * XFFC 981 150 DO 160 1 = 1 , 7 982 XAGSRV = AGESRV( I ) * XFP 983 AGESRV( I ) = 1 . 0 + XAGSRV * (XPRR - 1 . 0 ) 984 160 CONTINUE 985 C 986 RETURN 987 END 988 C 989 C **********CALCULATE AND APPLY SURVIVAL********** 9 9 0 SUBROUTINE PPSURV 991 COMMON /DDTIME/ IDD 992 COMMON /PRDATR/ P R E D ( 3 5 0 , 3 ) , DDVORA(350,2) , V 0 R A C ( 3 ) , SUMPRD(3), 993 1 SUMV0R(2) , SRVPRD, SRVPAR, IPREND(3 ) , I P R E D ( 3 ) , IEGGND(3) , 994 2 CBS , EAT, SMLFAL 995 COMMON /APHIDS/ A P ( 5 2 4 , 7 ) , IAPEND(7 ) , I A P ( 7 ) 996 COMMON /LEFALL/ AGESRV(7 ) , CNSTNT 997 COMMON /PLANTP/ PLNTM, F A L L , SUMFAL, PLEAF , P L S 3 , PRATIO, AREA, 998 1 PRP0S3 , FALLSV, FALMAX 999 COMMON /APHTOT/ SUM(7) , TOT, DENSE, APHDWT 1000 C0MM0N/SYRDEX/SAFIND,PRPV0R(2) 1001 CALL TOTAPH 1002 C PRED(J ,1 )=CECIDS ,PRED(d ,2 )=SYRPHIDS ,PRED(d ,3 )=PARAS1TES ALL LARVAE 1003 C INCREASE LENGTH OF PREDATORS TO MAXIMUM 1004 DO 10 I = 1, 3 1005 IF ( I P R E D ( I ) . L T . I P R E N D ( I ) ) I P R E D ( I ) = I P R E D ( I ) + 1 1006 10 CONTINUE 1007 C AGE PREDATORS 1008 DO 30 I = 1, 3 1009 J = I P R E D ( I ) 1010 20 IF (d .EO. 1) GO TO 30 1011 K = d - 1 1012 P R E D ( d . I ) = P R E D ( K . I ) 1013 d = d - 1 1014 GO TO 20 10.15 30 CONTINUE 1016 ' C ADD NEW PREDATOR AND PARASITE EGGS 1017 CALL ADPRED 1018 C SURVIVAL DUE TO LEAF DROP 1019 CALL LDROP 1020 EAT = 0 . 0 160 1021 35 PRPV0R(2 )=1 .0 - (EXP(SAF IND*DENSE) ) 1022 C FOR CECIDOMYIIDS AND SYRPHIDS 1023 37 DO 50 1=1,2 1024 J = I P R E D ( I ) 1025 L = IEGGND(I) + 1 102G C CALC. WEIGHT OF APHIDS EATEN 1027 DO 40 K = L, <J 1028 EAT = EAT + P R E D ( K , I ) * DDVORA(K. I ) * PRPVOR(I ) 1029 40 CONTINUE 1030 50 CONTINUE 1031 C SURVIVAL DUE TO PREDATORS 1032 SRVPRD = EXP(-EAT/APHDWT) 1033 C NEW COCOONS 1034 COCOON = PRED(IEGGND(3) + 1 , 3 ) 1035 C MUMMIES ASSUMED TO FORM AFTER IV INSTAR 1036 ATRISK = SUM(5) + SUM(7) 1037 C SURVIVAL DUE TO PARASITES 1038 SRVPAR = 1 . 0 - (COCOON/ATRISK) 1039 IF (SRVPAR . L T . 0 . 0 ) SRVPAR = 0 . 0 1040 C INCLUDE BLACK BOX SURVIVAL VALUE 1041 ALLSRV = SRVPRD * CBS 1042 C IN IT IAL IZE MORTALITY DUE TO LEAF FALL 1043 SMLFAL = 0 . 0 1044 C FOR EACH INSTAR 1045 DO 70 I = 1, 7 1046 C AGE SPECIF IC MORTALITY DUE TO LEAF FALL 1047 AGSRVI = AGESRV( I ) 1048 DEDAGE = 1 . 0 - AGSRVI 1049 C INCLUDE SURVIVAL DUE TO LEAF FALL 1050 ALLSRV = ALLSRV * AGSRVI 1051 C ADD IN ADULT SURVIVAL DUE TO PARASITES 1052 IF (I .EO. 5 .OR. I .EO . 7) ALLSRV = ALLSRV * SRVPAR 1053 K = I A P ( I ) 1054 C APPLY SURVIVAL TO APHIDS 1055 C AND SUM LOSSES DUE TO LEAF FALL 1056 DO 60 J = 1, K 1057 APJ I = A P ( J . I ) 1058 A P ( d . I ) = APJ I * ALLSRV 1059 ' SMLFAL = SMLFAL + APJ I * DEDAGE 1060 60 CONTINUE 106 1 70 CONTINUE 1062 RETURN 1063 END 1064 C 1065 C **********t_ONGEVITY********** 1066 SUBROUTINE LNGVTY 1067 COMMON /APHIDS/ A P ( 5 2 4 , 7 ) , IAPEND(7 ) . I A P ( 7 ) 1068 COMMON /AGSURV/ SURV(524) 1069 C FOR ADULT APTERAE AND ALATES 1070 DO 20 I = 5 , 7 , 2 1071 J = IAP( I ) 1072 C APPLY AGE SPECIF IC SURVIVAL VALUES 1073 DO 10 K = 1, J 1074 A P ( K , I ) = A P ( K , I ) * SURV(K) 1075 . 10 CONTINUE 1076 20 CONTINUE 1077 RETURN 1078 • END 1079 C 1080 C **********ALATE EMMIGRATION********** 161 1081 C 1082 1083 1084 1085 C 1086 1087 1088 1089 C 1090 1091 1092 10 1093 c 1094 1095 c 1096 1097 1098 1099 20 1 100 1 101 1 102 C 1 103 C 1 104 1 105 1 106 1 107 1 108 1 109 30 1 1 10 1111 40 1112 C 1113 50 1114 60 1115 1 1 16 C 1 117 C 1118 C 1 1 19 1 120 1121 1 122 1 123 1 124 1 125 1 126 1 127 1 128 1129 : C 1 1 30 | 1131 1 132 1 133 C 1 134 1 155 1136 10 1 137 C 1 138 1 139 20 1 140 C WING = SUM7 SUBROUTINE FLIGHT COMMON /APHIDS/ AP(524,7), IAPEND(7), IAP(7) COMMON /FLYING/ VALSTA, WING, IFLYTM NUMBER OF ALATES REQUIRED ON PLANT CALL VALFLY SUM7 = 0.0 J = IAP(7) SUM ALATES DO 10 I = 1, J SUM7 = SUM7 + AP(I,7) CONTINUE NUMBER OF ALATES TO EMMIGRATE VALSTA IF NO EMMIGRATION, GO ON IF (WING .GT. Q.O) GO TO 20 WING = 0.0 GO TO 60 I = IFLYTM U = IAP(7) FLYOFF = WING REMOVE ALATES OF AGE >IFLYTM UNTIL ENOUGH HAVE EMMIGRATED DO 40 K = I, J IF (FLYOFF .GT. AP(K,7)) GO TO 30 AP(K,7) = AP(K,7) - FLYOFF FLYOFF = 0.0 GO TO 50 FLYOFF = FLYOFF - AP(K,7) AP(K,7) = 0.0 CONTINUE NUMBER EMMIGRATING WING = WING - FLYOFF RETURN END **********-pQj4L APHIDS********** SUBROUTINE TOTAPH COMMON /DDTIME/ IDD DIMENSION SUMWT(4), PR0PWT(4) COMMON /APHIDS/ AP(524,7), IAPEND(7), IAP(7) COMMON /PLANTP/ PLNTM, FALL, SUMFAL, PLEAF, PLS3, PRATIO, AREA, 1 PRP0S3, FALLSV, FALMAX COMMON /APHTOT/ SUM(7), TOT, DENSE, APHDWT COMMON /APHWT/ VWT(524), DDVWT(1600), VWTOT, VWTA, VWTMN DATA PROPWT /0.0835, 0.1091, 0.4045, 0.7635/ TOT = 0.0 FOR EACH INSTAR DO 20 1 = 1 , 7 SUM(I) = 0.0 K = IAP(I ) TOTAL THE APHIDS DO 10 J = 1, K SUM(I) = SUM(I) + AP(d.I) CONTINUE GRAND TOTAL TOT = TOT + SUM(I) CONTINUE DENSITY 1 6 2 1141 DENSE = TOT / AREA 1142 WTMAX = VWT(1) 1143 APHDWT = 0.0 1144 C WEIGHT OF INSTARS I II III IV 1145 DO 30 I * 1, 4 1146 WT = WTMAX * PROPWT(I) 1147 APHDWT = APHDWT + WT * SUM(I) 1148 30 CONTINUE ( 1149 C TOTAL ADULT WEIGHT 1150 VWTOT = 0.0 1151 J = IAP(5) 1152 DO 40 I • 1, J 1153 VWTOT = VWTOT + VWT(I) * AP(I,5) 1154 40 CONTINUE 1155 C WEIGHT OF ALL APHIDS 1156 APHDWT = APHDWT + VWTOT + 1.0980 * WTMAX * PR0PWT(4) * SUM(6) 1157 IF (SUM(5) .GT. 0.0) GO TO GO 1158 WRITE (6,50) IDD, TOT 1159 50 FORMAT ( ' ' . 'NO ADULT APTERAE, NO ESTIMATE OF ALATE WEIGHT', 1160 1 / ' ' , 'DAYDEGREE=', 15, ' TOTAL APHIDS"'. G16.7) 1161 GO TO 70 1162 60 APHDWT = APHDWT • 0.98826 * (VWT0T/SUM(5)) * SUM(7) 1163 70 RETURN 1164 END 1165 C 1166 C * * * * * * * * * * T 0 T A L PREDATORS********** 1167 C 1168 SUBROUTINE TOTPRD 1169 REAL*8 TIMREM(3) 1170 COMMON /DDTIME/ IDD 1171 COMMON /PRDATR/ PRED(350,3), DDVORA(350,2), V0RAC(3), SUMPRD(3), 1172 1 SUMV0R(2), SRVPRD, SRVPAR, IPREND(3), IPRED(3 ) , IEGGND(3), 1173 2 CBS, EAT, SMLFAL 1174 COMMON /TMPSUM/ TIMREM, TEMP(300). TIMRTO, CECTM, PARSTM, ITMINC, 1175 1 IHFDAY 1176 C FOR LARVAL CECIDOMYIIDS, SYRPHIDS, 1177 C PARASITES, AND PUPAL PARASITES 1178 DO 20 I - 1, 3 1179 SUMPRD(I) « 0 . 0 1180 d = IPRED(I) 1181 L = IEGGND(I ) + 1 1182 C SUM PREDATORS 1 183 DO 10 K = L. J 1184 SUMPRD(I) « SUMPRD(I) + PRED(K.I) 1185 10 CONTINUE • 1186 20 CONTINUE 1187 C CALCULATE PARASITE AND CECIDOMYIID TIME 1188 PARSTM=IDD*1.166 1189 CECTM=IDD*0.746 1190 RETURN 1191 END 1192 C 1193 C * * * * * * * * * * P R I N T R E S U L T S * * * * * * * * * * 1194 C 1t95 . SUBROUTINE RESULT 1196 REAL*8 TIMREMO) 1197 COMMON /DDTIME/ IDD 1198 COMMON /PRDATR/ PRED(350.3), DDVORA(350,2), V0RAC(3), SUMPRD(S), 1199 1 SUMV0R(2), SRVPRD, SRVPAR, IPREND(3), IPRED(3). IEGGND(3), 1200 2 CBS, EAT, SMLFAL 1 6 3 1201 COMMON /APHIDS/ AP(524,7), IAPEND(7). IAP(7) 1202 COMMON /START/ S T ( 7 ) , FLDVWT(20). ITVWT(20), ITMAX, NVWT 1203 COMMON /LEFALL/ AGESRV(7). CNSTNT 1204 COMMON /PLANTP/ PLNTM, FALL, SUMFAL, PLEAF, PLS3, PRATIO, AREA. 1205 1 PRP0S3, FALLSV, FALMAX 1206 COMMON /FCNDTY/ RATAP(524) 1207 COMMON /IVALDL/ OENLAG(85), PRPCLC, CONVRT, PRPMOD 1208 COMMON /APHTOT/ SUM(7), TOT, DENSE, APHDWT 1209 COMMON /DEVTME/ INSTR, IDT, IDT1 1210 COMMON /FLYING/ VALSTA, WING, IFLYTM 1211 COMMON /APHWT/ VWT(524), DDVWT(1600), VWTOT, VWTA, VWTMN 1212 COMMON /TMPSUM/ TIMREM. TEMP(SOO), TIMRTO, CECTM, PARSTM, ITMINC, 1213 1 IHFDAY 1214 COMMON /OVIPAR/ SEXRT0(524), CLCSEX, PRPSEX, SUMSEX, MRKSEX, 1215 1 ISEXTM 1216 IF (SUM(5) .LE. 0.0) GO TO 10 1217 VWTMN = VWTOT / SUM(5) 1218 10 TOTIV = SUM(4) + SUM(6) 1219 IF (TOTIV .LE. 0.0) GO TO 20 1220 PRPMOD = SUM(4) / TOTIV 1221 20 WRITE (6,30) IDD, TIMRTO, IHFDAY, ITMINC 1222 WRITE (6,120) PLNTM, AREA. PLS3, SUMFAL, FALL, PRATIO 1223 WRITE (6,110) PRP0S3. AGESRV 1224 . WRITE (6,100) CECTM, PARSTM, SUMVOR, SUMPRD, P R E D O . I ) . PRED(1.2). 1225 1PRED(1.3), EAT, SMLFAL, SRVPRD, SRVPAR, IPRED 1226 WRITE (6,90) SUM(7), VALSTA, WING 1227 WRITE (6,80) PRPMOD, PRPCLC, CONVRT 1228 WRITE (6,40) SUM. TOT, DENSE, DENLAG(85) 1229 WRITE (6.50) IAP 1230 WRITE (6,60) AP(1,5), VWT(1), RATAP(I), IDT 1231 WRITE (6,70) APHDWT, VWTOT, VWTMN, VWTA 1232 WRITE (6,130) MRKSEX, ISEXTM, CLCSEX, PRPSEX, SUMSEX. SEXRT0(1) 1233 RETURN 1234 30 FORMAT ('DAYDEGREE', 16, -5X, 'PLANT TIME/APHID TIME/HALF DAY = 1235 1', G13.7. 5X, ' REMAINDER APHID DAYDEGREES/HALF DAY', 15, ' »', 1236 2 13, /' ', ' ') 1237 40 FORMAT (' ', 'INSTAR', IX, ' I ' . 11X, ' I I ' , 10X. ' I l l ' , 10X, ' I V . 1238 1 4X, 'V APTERAE', 5X, 'IV ALATE', 5X, 'V ALATE', 9X, 1239 2 'TOTAL', ' DENSITY', ' DENSITY(T-85)'. /' '. 10G13.7) 1240 50 FORMAT (' ', 'INSTAR ARRAY LENGTHS'. 7110) 1241 60 FORMAT (' ', 'NEW ADULTS"', G13.7, ' NEW ADULT WEIGHT*', G13.7, 1242 1 'MG COHORT FECUNDITY-', G13.7, ' DEVELOPMENTAL TIME*'. 15) 1243 70 FORMAT (' ', 'TOTAL APHID WEIGHT"', G13.7, ' TOTAL ADULT WE1GHT=', 1244 1 G13.7. /' ', ' PREDICTED MEAN ADULT WEIGHT"', G13.7. 1245 2 ' FIELD MEAN ADULT WEIGHT"'. G13.7) 1246 • 80 FORMAT (' ', 'PROPORTION IV APTERAE/TOTAL I V , ' MODEL"', G13.7, 1247 1 ' REGRESSION REQUIREMENT GIVEN DENSITY 85 DAYDEGREES AG 1248 20=', G13.7, /' ', 'NUMBER OF IV APTERAE MOVED TO AP(1,6)', 1249 3 'TO GET REGRESSION REQUIREMENT"', G13.7) 1250 90 FORMAT (' ', ' tt V ALATES"', G13.7, ' REGRESSION REQUIREMENT (tt ON 1251 1 PLANT )=', G13.7, ' NUMBER OF V ALATES FLYING/DAYDEGREE"', G13.7) 1252 100 FORMAT (' ', 'CECIDOMYIID TIME"', F8.2, ' DAYDEGREES>9.2C', 1253 1 ' PARASITE TIME"', F8.2, ' DAYDEGREES>4.9C', /' '. 1254 2 'TOTAL CECIDOMYIID VORACITY/LARVAL DEVELOPMENT"', G13.7, 1255 3 ' TOTAL SYRPHID VORACITY/LARVAL DEVELOPMENT"', G13.7, /' ', 1256 4 'tt CECIDOMYIID LARVAE"'. G13.7. ' tt SYRPHID LARVAE-'. 1257 5 G13.7, ' tt UNEMERGED COCOONS"', G13.7. /' ', 1258 6 'tt EGGS LAID/STEP"', 3X, G13.7, 13X, G13.7. 22X, G13.7. / 1259 7 ' '. 'WEIGHT OF APHIDS EATEN/STEP"', G13.7. 'MG;'. 1260 8 ' APHID LOSSES DUE TO LEAF FALL"', G13.7. /' ', 1 6 4 1261 9 'SURVIVAL APPLIED TO ACCOUNT FOR '. 1262 * 'PREDATION AND COCOONS RESPECTIVELY"'. 2G13.7. /' ', 1263 1 'CURRENT LENGTH OF CECIDOMYIID. SYRPHID. LARVAL AND PUPAL P 1264 2ARASITE ARRAYS', ' RESPECTIVELY"', 315, /' ', ' ') 1265 110 FORMAT (' ', 'INSTAR SPECIFIC SURVIVAL DUE TO LEAF DROP"', 20X, 1266 1 '(PROPORTION OF POPULATION IN STRATUM(3)=', G13.7. ' ) ' . / 1267 . 2 ' '. 7G13.7. /' ', ' ') 126B 120 FORMAT (' ', 'PLANT TIME (DAYDEGREES)"'. G13.7, ' LEAF AREA"'. 1269 1 G13.7, 'CMXCM If LEAVES IN STRATUM 3='. G13.7, /' '. 1270 2 ' TOTAL LEAVES FALLEN SINCE PLANTING"', G13.7. 1271 3 ' CLEAVES FALLEN/APHID DAYDEGREE"', G13.7, /' ', 1272 4 ' RATIO (CLEAVES LEFT IN STRATUM 3 AFTER LEAFFALL', 1273 5 '/# LEAVES IN STRATUM 3=', G13.7) 1274 130 FORMAT (' ', 'OVIPARAE--OLDEST AGE INDEX"', 15, ' DAYDEGREES'. 1275 1 ' ADULT OLDEST AGE=', 15, ' DAYDEGREES', /' ', 1276 2 '# OVIPARAE REQUIRED"', G13.7, ' GIVEN THAT ', G13.7, 1277 3 ' OF ALL APTEROUS ADULTS SHOULD BE OVIPARAE', /' '. 1278 4 ' H OVIPARAE AFTER ADJUSTMENT OF NEW ADULTS"', G13.7, 1279 5 ' NEW VIRGINOPARAE/TOTAL NEW ADULTS)"'. G13.7, /' '. /' ') 1280 END End o f F i l e MORTALITY FIRST IF IORDER=0, IORDER= 1 NO COHORT ADULT WEIGHT IF ICOHRT=0, ICOHRT" 1 REDUCE ABILITY OF SYRPHID SEARCH WITH SAFIND ( 1-E**(-SAFIND*DENSE) SAFIND* -.130.0000 SYRPHID EGG PRODUCTION THRESHOLD" 0.640 APHIDS SYRPHID EGG PRODUCTION CONSTANTS AREA= 0.5113 B» 1.5875 PLANTING DAY= 125 CONSTANTS (RADIANS)FOR PREDICTING AGE DISTRIBUTION IN STRATUM 3 FROM THAT IN THE WHOLE PLANT Y INTERCEPT 0.2469 0.2870 0.4287 0.1393 0.1964 0.1777 0.1002 SLOPES 0.9228 0.6947 0.0 1.8675 1.5710 2.6285 0.0 APHID POPULATION SIMULATION STARTED WITH O.O 0.0 0.0 0.13228 0.13228 0.0 0.0 APHIDS IN INSTARS I.11.111,IV.V,IVALATE.VALATE RESPECTIVELY LENGTH OF EACH OF THE ABOVE INSTARS IS 0 O 0 0 524 O 433 •(LENGTH OF THE IMMATURES IS SET IN THE PROGRAM USING DEVELOPMENTAL TIME)* NUMBER OF SAMPLES ARE 4 NUMBER OF MEASURES OF ADULT WEIGHT ARE 7 CHANGE IN NEW ADULT WEIGHT LIMITED TO 0.00200MG SAMPLE TIMES IN DAYDEGREES >6.65C ARE 16 190 404 582 MEASURES OF MEAN ADULT WEIGHT IN THE FIELD ARE 1.029 1.109 1.021 0.958 0.899 0.721 TIME (DAYDEGREES) MEASURES WERE MADE 72 190 404 582 847 1189 CECIDOMYIID VORACITY" 2.140 SYRPHID VORACITY" PARASITES IN MODEL? 0.0=N0; 1.0=YES; 1.0 LENGTH OF CECIDOMYIID. SYRPHID, AND PARASITE AGE RESPECTIVELY 131 200 198 LENGTH OF CECIDOMYIID AND,SYRPHID EGG AND PARASITE LARVAL STAGES RESPECTIVELY" 43 38 99 MORTALITY DUE TO LEAF FALL IN MODEL? 0.0=N0 1.0=YES 4.500 PRODUCE IV ALATES? 0.0=NO 1.0=YES 1.000 DAYDEGREE AFTER MOLTING AT WHICH ALATES MAY FLY" 10 BLACK BOX BACKGROUND MORTALITY APPLIED ACROSS THE BOARD" 1.00000 PRINT INTERVAL' 2000 DAYDEGREES TEMPERATURES SINCE PLANTING ARE 9.8 16.8 8.9 17 11.0 19 ARE 0. 758 1550 70.960 13.0 17.6 12.1 24.6 13.4 17.8 8.5 24.4 12.6 25.7 11.9 19.5 11.9 23.8 13.5 24.9 13.5 23.0 14. 1 26.4 15.9 23.4 13.4 21.6 11.7 21.9 11.5 21.4 10.1 23 10.1 26 12.1 25 12.6 26 14.6 24 3 1 3 4 4 2 23 20 24 21 21 .9 8 . 5 17 .7 8 .2 18 .7 8 .9 18 .8 .4 1 1 .0 17 .4 8 .2 19 .8 8 .7 20 . 1 9 9 .0 18 .2 7 .3 19 .0 10 . 3 20 . 1 7 10 . 1 21 .9 8 .2 22 . 1 10 . 1 24 .0 4 1 1 2 15 7 10 .7 18 9 12 0 18 5 7 11 4 30 4 12 6 27 2 9 4 29 8 3 12 6 25 4 14 6 23 6 13 8 24 6 0 13 9 31 6 15 7 30 8 14 1 28 6 5 14 1 26 4 13 9 26 4 12 3 22 7 1 12 1 24 8 12 0 24 9 10 1 25 3 0 13 4 20 2 12 2 25 3 1 1 0 23 4 4 12 9 25. 4 13. 8 26. 4 13 8 24. 4 5 12 . 6 20. 0 12. 7 22 . 4 12. 6 21 . 9 4 12. 6 30. 1 15. 2 25. 1 12. 4 21 . 1 5 10. 8 17 . 8 10. 5 25. 3 13. 4 19. 4 8.8 16.3 9.2 22. 1 7.8 22.8 10.8 26.4 12.3 12.3 17.6 14.2 23.9 13.5 27.1 12.9 24.2 12.6 26.3 14.4 22.7 14.0 23.4 12.5 23.2 10.5 21.6 12.8 17.8 6.0 19.3 9.6 22.7 8.5 29.0 8.5 26.3 19.7 10.8 22.3 11.9 20.7 11.0 17.3 15.3 28.9 12.9 27.3 10.5 26.5 13.9 21.9 13.5 22.8 12.9 19.1 10.0 16.3 9.9 23.9 10.1 27.6 10.1 19.5 14.6 19.7 11.4 31.8 11.4 21.3 10.8 23.5 8.1 25.0 10.5 22.9 8.7 19.1 10.5 16.3 14.1 22.2 13.5 21.0 13.0 25.0 12.6 25.5 15.8 29.2 15.7 26.1 12.9 24.5 11.7 24.7 13.2 24.2 15.0. 24.7 14.1 22.8 12.5 23.3 12.0 21.4 10.9 20.3 11.9 22.0 13.7 21.8 12.8 20.3 10.0 20.2 11.7 17.8 11.7 20.9 7 1 1 13 9 14 7. 12. 13. 1 1 . 12. 16 . 14. 1 1 . 12. .7 18 .9 22 .4 25 23 26 22 21 24 25 25 24 25. 22 .0 21.9 X O a O c rr TJ C rt CTl (JI AGE SPECIFIC SURVIVAL VALUES/DAYDEG>6.65C ARE 1.OOOOOOO 1.OOOOOOO 1.0000000 1.0000000 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.poooooo 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.0000000 0.9988900 0.9988900 0.9988800 0.9988800 0.9988800 0.9988800 0.9988800 0.9988700 0.9988700 0.9988600 0.9988600 0.9988600 0.9988500 0.9988500 0.9988500 0.9993600 0.9993600 0.9993600 0.9993600 0.9993600 0.9993600 0.9993600 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.999350O 0.9993500 0.9993500 0.9993400 0.9993400 0.9993400 0.9993400 0.9993400 0.9993400 0.9993400 0.9927000 0.9926500 0.9971500 0.9971400 0.9971300 0.9970800 0.9970800 0.9970700 0.9970600 0.9970500 0.9956300 0.9956100 0.9955900 0.9955800 0.9957100 0.9956000 0.9955800 0.9955600 0.9955400 0.9955200 0.9954000 0.9953800 0.9953600 O.9953300 0.9953100 0.9951800 0.9951500 0.9958700 0.9958500 0.9958300 0.9957300 0.9957100 0.9956900 0.9894200 0.9893000 0.9885700 0.9884400 0.9988000 0.9988000 0.9988000 0.9987900 0.9987900 0.9987900 0.9987900 0.99B7900 0.9987800 0.9987800 0.9987700 0.9987700 0.9987700 0.9987600 0.9987600 0.9987600 0.9987600 0.9987600 0.9987500 0.9987500 0.9987400 0.9987400 0.9987400 0.9968900 0.9968800 0.9968700 0.9968700 0.9968600 0.9967900 0.9967800 0.9967700 0.9967600 0.9967500 0.9838700 0.9836100 0.9833300 0.9830500 0.9827600 0.9875000 O.9873400 0.9890100 0.9888900 0.9887600 0.9879500 0.9878000 0.9876500 0.9875000 0.9873400 0.9642900 0.9583300 0.9565200 0.9545500 0.9523800 0.9333300 0.9285700 0.9230800 0.9166700 0.9090900 0.9892500 0.9891300 0.9890100 0.9888900 0.9887600 0.9879500 0.9878000 0.9876500 0.9875000 0.9873400 0.9863000 0.9861100 0.9859100 0.9857100 0.9855100 0.9940100 0.9939800 0.9939400 O.9939000 0.9938600 0.9936300 0.9935900 0.9935500 0.9935100 0.9934600 0.9932000 0.9931500 0.9931000 0.9930600 0.9930100 0.9927000 0.9926500 0.9925900 0.9925400 0.9924800 0.9921300 0.9920600 0.9920000 0.9919400 0.9918700 O.9914500 0.9913800 0.9913000 0.9912300 0.9911500 0.9906500 0.9905700 0.9904800 0.9903800 0.9902900 0.9896900 0.9895800 0.9894700 0.9893600 0.9892500 0.9885100 0.9883700 0.9882400 0 .0 1.0000000 1.0000000 1.0000000 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.0000000 1.0000000 1.OOOOOOO 1.OOOOOOO 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.OOOOOOO 1.0000000 1.0000000 1.0000000 1.OOOOOOO 1.0000000 0.9988900 0.9988900 0.9988800 0.9988BOO 0.9988800 0.9988700 0.9988700 0.9988700 0.9988700 0.9988700 0.9988600 0.9988600 0.9988600 0.99886OO 0.9988600 0.9993600 0.9993600 0.9993600 0.99936O0 0.9993600 0.99936OO O.9993600 0.9993600 0.9993600 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993500 0.9993400 0.9993400 0.3993400 0.9993400 0.9993400 0.9993400 0.9993400 0.9928600 0.9928100 0.9927500 0.9971300 0.9971200 0.9971100 0.9971000 0.9970900 0.9957300 0.9957100 0.9956900 0.9956700 0.9956500 0.9957000 0.9956800 0.9956600 0.9956400 0.9956200 0.9955000 0.9954800 0.995460O 0.9954400 0.9954200 0.9952900 0.9952700 0.9952500 0.9952200 0.9952000 0.9958200 0.9958000 0.9957800 0.9957600 0.9957400 0.9891900 0.9890700 0.9889500 0.9888300 0.9887000 0.9988000 0.9988000 0.9988000 0.9988000 0.9987900 0.9987800 0.9987800 0.9987800 0.9987800 0.9987800 0.9987700 0.9987700 0.9987700 0.9987700 0.9987600 0.9987500 0.9987500 0.9987500 0.9987500 0.9987500 0.9987400 0.9814800 0.9811300 0.9807700 0.9969000 0.9968500 0.9968400 0.9968300 0.9968200 0.9968100 O.99674O0 0.9967300 0.9967200 0.9843800 0.9841300 0.9824600 0.9881O0O 0.9879500 0.9878000 0.9876500 0.9886400 0.9885100 0.9883700 0.9882400 O.9881000 0.9871800 0.9545500 0.9523800 0.9666700 0.9655200 0.9500000 0.9473700 0.9444400 0.9411800 0.9375000 0.9000000 0.8888900 0.9895900 0.9894700 0.9893600 0.9886400 0.9885100 0.9883700 0.9882300 0.9880900 0.9871800 0.9870100 0.9868400 0.9866700 0.9864900 0.9852900 0.985O70O 0.9848500 0.9846100 0.9940700 0.9938300 0.9937900 O.9937500 0.9937100 0.9936700 0.9934200 0.9933800 0.9933300 0.9932900 0.9932400 0.9929600 0.9929100 0.9928600 0.9928100 0.992750O 0.9924200 0.9923700 0.9923100 0.9922500 0.9921900 0.9918000 0.9917400 0.9916700 0.9916000 0.9915300 0.9910700 0.9909900 0.9909100 0.9908300 0.9907400 0.9902000 0.9901000 O.9900000 0.9899000 0.989BOOO 0.9891300 0.9890100 0.9888900 0.9887600 0.9886400 DAYDEGRBE 16 PLANT TIME/APHID TIME/HALF DAY" 2.030556 REMAINDER APHID DAYDEGREES/HALF DAY PLANT TIME (DAYDEGREES)' 32.31577 LEAF AREA" 180.4763 CMXCM # LEAVES IN STRATUM 3»0.5875878 TOTAL LEAVES FALLEN SINCE PLANTING=0.2899880E-02 CLEAVES FALLEN/APHID DAYDEGREE=0.3694522E-03 RATIO CLEAVES LEFT IN STRATUM 3 AFTER LEAFFALL/* LEAVES IN STRATUM 3=0.9993712 INSTAR SPECIFIC SURVIVAL DUE TO LEAF DROP" (PROPORTION OF POPULATION IN STRATUM(3)=0 0 1.000000 1.OOOOOO 1.000000 1.000000 1.000000 1.000000 1.000000 70.95900 CECIDOMYIID TIME" 11.94 DAYDEGREES>9.2C PARASITE TIME" 18.66 0AYDEGREES>4.9C TOTAL CECIDOMYIID VORACITY/LARVAL DEVELOPMENT" 2.139997 TOTAL SYRPHID VORACITY/LARVAL DEVELOPMENT # CECIDOMYIID LARVAE=0.0 # SYRPHID LARVAE=0.0 * UNEMERGED COCOONS=0.0 # EGGS LAID/STEP= 0.0 0.0 0.0 WEIGHT OF APHIDS (.ATEN/STEP=0.0 MG; APHID LOSSES OUE TO LEAF FALL=0.0 SURVIVAL APPLIED TO ACCOUNT FOR PREDATION AND COCOONS-RESPECTIVELY" 1.000000 1.OOOOOO CURRENT LENGTH OF CECIDOMYIID, SYRPHID. LARVAL AND PUPAL PARASITE ARRAYS RESPECTIVELY" 1 1 1 # V ALATES=0.0 REGRESSION REQUIREMENT (<C ON PLANT)-0.0 NUMBER OF V ALATES FLYING/DAYDEGREE=0.0 PROPORTION IV APTERAE/TOTAL IV MODEL" 1.OOOOOO REGRESSION REQUIREMENT GIVEN DENSITY 85 DAYDEGREES AGO" 1.OOOOOO NUMBER OF IV APTERAE MOVED TO AP(1.6)T0 GET REGRESSION REQUIREMENT=0.0 INSTAR I II III IV V APTERAE IV ALATE O.O 0 . 0 0 . 0 0.1322796 0.1322789 0 . 0 INSTAR ARRAY LENGTHS 29 30 30 30 39 NEW ADULTS=0.3391795E-02 NEW ADULT WEIGHT" 1.029000 MG COHORT FECUNDITY' TOTAL APHID WEIGHT=0.2400403 TOTAL ADULT WEIGHT=0.1361160 PREDICTED MEAN ADULT WEIGHT" 1.029007 FIELD MEAN ADULT WEIGHT" 1.029000 OVIPARAE--OLDEST AGE INDEX" 0 DAYDEGREES ADULT OLDEST AGE" 0 DAYDEGREES K OVIPARAE REQUIRED=0.0 GIVEN THAT 0.0 OF ALL APTEROUS ADULTS SHOULD BE OVIPARAE # OVIPARAE AFTER ADJUSTMENT OF NEW ADULTS=0.0 NEW VIRGINOPARAE/TOTAL NEW ADULTS )= 1.OOOOOO V ALATE 0.0 42 69.20114 TOTAL DENSITY DENSITY(T-85) 0.2645585 39 0. 1465890E-O20.0 DEVELOPMENTAL TIME" 119 DAYDEGREE 190 PLANT TIME/APHID TIME/HALF DAY" 2.02999G REMAINDER APHID DAYDEGREES/HALF DAY 47 " 0 PLANT TIME (DAYDEGREES)" 340.2646 LEAF AREA" 2022.193 CMXCM H LEAVES IN STRATUM 3= 1.418433 TOTAL LEAVES FALLEN SINCE PLANTING»0.4068402 (CLEAVES FALLEN/APHID DAYDEGREE"0.5079031E-02 RATIO (CLEAVES LEFT IN STRATUM 3 AFTER LEAFFALL/* LEAVES IN STRATUM 3=0.9964191 INSTAR SPECIFIC SURVIVAL DUE TO LEAF DROP" (PROPORTION OF POPULATION IN STRATUM(3)=0.1365411E-01) 0.9999907 O.9999964 0.9999956 0.9999970 0.9999958 0.9999986 0.9999998 CECIDOMYIID TIME" 141.74 DAYDEGREES>9.2C PARASITE TIME- 221.54 DAYDEGREES>4.9C TOTAL CECIDOMYIID VORACITY/LARVAL DEVELOPMENT" 2.139997 TOTAL SYRPHID VORACITY/LARVAL DEVELOPMENT" 70.95900 # CECIDOMYIID LARVAE=0.0 <C SYRPHID LARVAE=0.2956635 # UNEMERGED C0C00NS=O.O » EGGS LAID/STEP" 0.0 0.2850774E-02 0.1461882E-02 WEIGHT OF APHIDS EATEN/STEP=0.4699024E-01MG: APHID LOSSES DUE TO LEAF FALL=0.6309303E-04 SURVIVAL APPLIED TO ACCOUNT FOR PREDATION AND COCOONS RESPECTIVELY=0.9889754 1.OOOOOO CURRENT LENGTH OF CECIDOMYIID, SYRPHID, LARVAL AND PUPAL PARASITE ARRAYS RESPECTIVELY" 131 175 175 (C V ALATES=0.1601517 REGRESSION REQUIREMENT (# ON PLANT)»0.3579820 NUMBER OF V ALATES FLYING/DAYDEGREE=0.0 PROPORTION IV APTERAE/TOTAL IV MODEL=0\ 8240707 REGRESSION REQUIREMENT GIVEN DENSITY 85 DAYDEGREES AGO=0.8240705 NUMBER OF IV APTERAE MOVED TO AP(1,6)T0 GET REGRESSION REQUIREMENTS.4928589E-02 INSTAR I II I I I IV V APTERAE IV ALATE V ALATE TOTAL DENSITY DENSITY(T-85) 4.485825 1.467376 1.239612 1.150253 1.471778 0.2455655 0.1601517 10.22056 0.5054194E-020.1093157E-01 INSTAR ARRAY LENGTHS 29 29 29 29 213 40 213 NEW ADULTS=0.3516587E-01 NEW ADULT WEIGHT" 1.138997 MG COHORT FECUNDITY" 72.68503 DEVELOPMENTAL TIME" 116 TOTAL APHID WEIGHT" 4.191842 TOTAL AOULT WEIGHT" 1.604448 PREDICTED MEAN ADULT WEIGHT" 1.090142 FIELD MEAN ADULT WEIGHT" 1.108899 OVIPARAE--OLDEST AGE INDEX" 0 DAYDEGREES ADULT OLDEST AGE" 0 DAYDEGREES iC OVIPARAE REQUIRED=0.0 GIVEN THAT 0.0 OF ALL APTEROUS ADULTS SHOULD BE OVIPARAE D OVIPARAE AFTER ADJUSTMENT OF NEW ADULTS=0.0 NEW VIRGINOPARAE/TOTAL NEW ADULTS)" 1.000000 CO 169 Appendix 3(b) Model Overview Input data is f i r s t read and echoed, and variables and arrays are i n i t i a l i z e d . Physiological time for both aphid and plant i s calculated for half a day (minimum to maximum temperature). For each aphid day-degree in a half day, the model calculates new values for: plant parameters according to plant time; number of aphids born, and after aging the aphids one day-degree adds new births to age one; weight of new adult aphids, developmental time of younger cohorts, and fecundity of the new adult cohort; proportion (fourth apterae/total fourths), and adjusts the age d i s t r i b u t i o n appropriately; proportion and number of oviparous females; number of cecidomyiid, syrphid, and parasite eggs l a i d , and after aging each array one time step, places the new predators and parasites in the f i r s t step; aphid survival as affected by predation by cecidomyiids and syrphids, cocoon formation by parasites, leaf f a l l , and i n t r i n s i c age-specific s u r v i v a l ; numbers of alates, and allowing an appropriate p r e f l i g h t time, removes excess alates; t o t a l aphid numbers and weight, and l a r v a l predator, and parasite cocoon numbers. For specified sampling occasions, or at fixed i n t e r v a l s , the following are printed: aphid time (day-degrees(> 6.7°), the r a t i o of plant to aphid time, the number of day-degrees l e f t in the current half day; 1 70 plant time (day-degrees(>0.0 & < 19.4°), leaf area ( cm 2), number of leaves in stratum 3, t o t a l leaves f a l l e n since planting, number of leaves fallen/aphid day-degree, the r a t i o (number of leaves l e f t in stratum 3 after leaf fall/number of leaves in stratum 3 before leaf f a l l ) , the proportion of the population in stratum 3, and age-specific survival values given leaf f a l l ; A. aphidimyza and rapae time, A_^ aphidimyza and syrphid l a r v a l voracity, the number of A^ aphidimyza and syrphid larvae, and IK_ rapae cocoons, the numbers of eggs l a i d by each predator and parasite, the weight of brassicae eaten by the predators, numbers of aphids lost due to leaf f a l l , s u rvival applied to account for predation and p a r a s i t i z a t i o n , the length of the predator and parasite arrays; the number of alates per plant, the number of alates f l y i n g , the proportion (fourth apterae/total fourths) required, the numbers of new fourth apterae moved to become fourth alates, the proportion a f t e r the adjustment, the numbers of aphids in each instar, t o t a l aphids and density, the number, weight and fecundity of the new adult cohort, new developmental time and length of each instar (daydegrees(> 6.7°), t o t a l aphid weight, t o t a l adult weight, mean adult weight in the model, f i e l d mean adult weight, age of the oviparae, proportion and number of oviparae required, number of oviparae after adjustment of virginoparae, and the r a t i o (adult virginoparae/total adults). 171 A detailed description Main Main controls the program flow, c a l l i n g each subroutine in a sp e c i f i e d order. The subroutines INFORM, SETPLT, SETAPH, SETPRD, TOTAPH, TOTPRD, and RESULT are concerned with reading and writing input data, and i n i t i a l i z i n g variables and constants. There order is fixed since the function of one depends on previous c a l c u l a t i o n s . The subroutines BRTHAG, TMSHFT, ALATE, and SEXUAL are concerned with gains to the aphid population, and morph determination, while PPSURV, LNGVTY, and FLIGHT are concerned with losses to the population. The order of these two groups of subroutines may seriously affect the results of the model depending upon step length, and the severity with which each group acts. The problem, one of representing a continuous process in a discrete fashion, i s r e c t i f i e d by choosing the appropriate step length. One day-degree was chosen as the step length to f a c i l i t a t e a smooth and simple change to the length of each instar as developmental time changed. This step length was adequately small because the order of gains and losses may be changed (IORDER) with l i t t l e e f fect on the r e s u l t s . Round off errors were not a problem because the results of simulations based on double as opposed to single precision arithmetic were v i r t u a l l y the same. Input data This subroutine reads input data free format (/'*'/), and 1 72 writes i t out again with the appropriate documentation. The following explains the meaning and source of each mneomonic as they are read into the model. GARB(126) is the immature survival values, which are a l l 1.0. SURV(524) is the age-specific physiological survival of B. brassicae(see Il.C.lb) IORDER adjusts the order of aphid gains and aphid losses subroutines. If IORDER is 0, losses are applied before gains. ICOHRT allows the age-specific adult weight array VWT to vary with mean f i e l d adult weight i f ICOHRT is set to 0. Otherwise VWT w i l l contain age-specific adult weights calculated just after the molt to adult. SAFIND is the empirical constant 'k' (see II.D.2) used to increase syrphid l a r v a l search success as a function of aphid density. T,A,B are the constants of the regression equation for syrphid numerical response. 'T' i s the threshold, 'A' the intercept and 'B' the slope (see II.C.2c and II.D.2) IDAY i s used to determine when to start oviparae production. If i t is set to the planting day then production w i l l begin August 23 (see I l . C . l f ) . By varying IDAY the date of oviparae production may be changed or production may be eliminated. YCEPT(7) and SLOPE(7) are the regression c o e f f i c i e n t s for determining the proportion of each instar in stratum 3 from the proportion in the whole plant (see II.C.2e). They are 1 7 3 expressed in terms of radians. IAPEND(7) stores the length of l i f e of the adult apterae and alate aphids (see I l . C . l b ) . For computing convenience these were stored in positions 5 and 7 , the other positions being 0 . ST ( 7 ) i s the age d i s t r i b u t i o n (instar) of the i n i t i a l aphid population. Positions one through seven are f i r s t , second, t h i r d , and fourth apterous instars, apterous adult, fourth alate, and adult alate respectively. Except for theo r e t i c a l manipulations these are obtained from f i e l d data. ITMAX and NVWT are the number of f i e l d samples, and f i e l d mean adult weight estimates respectively. DELTA is the bound placed on change in new adult weight, using the previous cohort as the standard. Its value ( 0 . 0 0 2 ) was found empirically such that rad i c a l changes in new"adult weight were smoothed, but calculated mean adult weight kept apace with f i e l d mean adult weight. ISMP ( 2 0 ) contains sample times in day-degrees(> 6 . 7 ° ) . FLDVWT(20) contains f i e l d estimates of mean adult weight (see I I . C . 1 e ) . ITVWT(20) contains the time in day-degrees(> 6 . 7 ° ) at which the elements of FLDVWT were measured. VORAC(3) i s the voracity of A_j_ aphidimyza and the syrphids (see I I . C . 2 b ) in that order. The t h i r d element of the array refers to D^ rapae. If any element is set to 0 . 0 the factor i t represents w i l l not be included in the model. IPREND(3) is the length of the egg+larval stages of 174 A. aphidimyza and the syrphids, and the egg+larval+pupal stages of rapae respectively (see II.C.2b-d). To f a c i l i t a t e computing speed these may be set to 1 i f the predator or parasite is not included in the model. IEGGND(3) is the length of the egg stage of A_^ aphidimyza and the syrphids, and the egg+larval stages of IZK_ rapae respectively (see II.C.2b-d). CNSTNT allows the eff e c t s of leaf f a l l on aphid survival (see II.C.2e) to be: ommitted i f set to 0 . 0 ; included with the assumption that no aphids survive leaf f a l l i f set to - 1 . 0 ; or included with the assumption that survival i s a function of the rate of leaf f a l l i f set to 1 . 0 . The severity of the l a t t e r i s decreased or increased by values either side of 1 . 0 . ALMRPH controls the production of fourth'alates. If set to 0 . 0 alates w i l l not be produced. IFLYTM controls the p r e f l i g h t time of adult alate aphids (see II.C.2a). CBS i s an overall survival value which may be applied. Its value i s usually set to 1 . 0 . IPRINT i s the pri n t i n g interval in day-degrees. If set to 1, output w i l l be printed every day-degree. If i t exceeds the number of day-degrees in the season, only sample times are pr inted. LIST controls the printing of the input variables. If set to 0 . 0 the input variables w i l l not be echoed. TEMP ( 3 0 0 ) contains temperature data for the f i e l d season (see I I . B. 3 ) , entered as minimum, maximum, minimum... from the 175 day of planting. Except for ISMP, FLDVWT, ITVWT, and TEMP, there must be a value for each variable or c e l l of an array. Where variables act s t r i c t l y as on off switches, zero is the off condition and one i s used for the on condition. The f i r s t l e t t e r default is taken for number type, so input data must be entered accordingly. Set up plant ^ SETPLT This subroutine i n i t i a l i z e s plant variables and arrays. Since time begins when the plants were transfered to the f i e l d , the subroutine c a l l s TEMPDD to calculate physiological time, and PLANT, to increment plant growth u n t i l such time as the f i r s t aphids were found, or introduced into the f i e l d . Set up aphid - SETAPH This subroutine i n i t i a l i z e s aphid variables and arrays. It calculates mean f i e l d adult weight on a day-degree basis by linear interpolation between data. Adult weight previous to f i e l d measurement is assumed to be the same as the f i r s t measurement, and each cohort is assumed to have the same mean weight u n t i l such time as f i e l d mean adult weight changes, in which case the youngest cohort adult weight i s adjusted (see TMSHFT). Given adult weight, developmental time is calculated, and the length of each instar is set assuming that a l l are of equal length. Any day-degrees l e f t over are added sequentially 1 76 to instars four through one. The length of the fourth alate instar is set to 7/5 times that of the fourth instar (see I l . C . l a ) , and the adult apterous and alate instars are a r b i t r a r i l y i n i t i a l i z e d to 39 day-degrees ( i . e . young adults). This estimate applies only to those cases where laboratory aphids of known age were used to start the population (UBC2, UBC3, and UBC4). The aphids in each instar which were speci f i e d as input data, are then di s t r i b u t e d evenly over the instars. Given adult weight, t o t a l fecundity i s calculated. Both adult weight, and fecundity are stored in age-specific arrays. Density 85 day-degrees prior to the f i r s t sample i s set to 0.0 for those cases in which laboratory aphids were used to start the population. For Abb, and UBC1, these densities would be calculated from plant leaf area, and estimates of aphid numbers assuming exponential increase. Set up predators and parasites ^ SETPRD This subroutine i n i t i a l i z e s predator and parasite variables and arrays. It calculates age-specific voracity for A. aphidimyza and the syrphids (see II.C.2b-c). Since there were no predators or parasites when the aphids were introduced into the f i e l d s (UBC2, UBC3, and UBC4), their age and numbers are set to zero. Calculate physiological time - TEMPDD . Several d i f f e r e n t time scales must be handled in the 1 77 model. The aphid time scale is handled d i r e c t l y since the model operates in steps based on this time scale, and each element of a l l age-specific arrays represents one day-degree above the aphid threshold. Where age-specific l i f e tables are required for the other components of the system, the modeling becomes complicated, since one aphid time step w i l l in general be equal to a non-integer number of time steps of the other components. To simplify the s i t u a t i o n , the l i f e tables were based on aphid time assuming that the time scale of the components is always a fixed proportion of aphid time. The average ratios 0.75±0.009 for A. aphidimyza, and 1.17±0.009 for parasites were determined by averaging over the t o t a l time the predator and parasite were found in the samples. Data from Abb, UBC1 and UBC2 were used. In terms of aphid time, development of A_^ aphidimyza from egg to larva and egg to pupa was 43 and 131 day-degrees and development of D^ rapae from egg to cocoon and egg to adult was 99 and 199 day-degrees respectively. The plant was not modeled using a l i f e table, but i t s time cannot be reasonably predicted from aphid time (see II.C.2e). Subroutine TEMPDD therefore calculates both aphid and plant time. For each maximum to minimum, or minimum to maximum temperature i t determines where the threshold l i e s , and integrates between the threshold, and a sine curve f i t to the pair of temperatures. In this case, the process is done for three thresholds, the aphid threshold, and the upper and lower plant thresholds,. If more than one aphid day-degree has 178 accumulated i t makes the number an integer, rounding down and saving the remainder. The r a t i o of plant to aphid time i s calculated and remainder day-degrees for the plant thresholds are saved. If less than one aphid day-degree is accumulated, the process is repeated using the next temperature (ie the next half day). A l l remainder day-degrees are added into the next half days t o t a l . Plant growth ^ PLANT Each aphid day-degree, plant time is incremented by the ra t i o of plant to aphid time calculated for the current half day. Plant parameters are calculated as a function of plant time. A l l relationships are delt with in section (see I I . C . 2 e ) . Gains relationships 2 GNRELT This i s a multiple entry subroutine which consolidates the relationships concerned with alate morph determination (see I l . C . l f ) , aphid fecundity and developmental time (see II.C.Ic). Aphid births and aging 2 BRTHAG Births are calculated as a function of aphid age and t o t a l fecundity expected (see I l . C . l b ) . Since oviparae are lumped together in the same array as virginoparae, the number born to each age of females i s reduced by the ra t i o of virginoparae to to t a l females of that age. Alates have an age-specific 1 7 9 fecundity equal to 0.469 that of the apterae (see I l . C . l b ) , and are not allowed to reproduce u n t i l p r e f l i g h t time i s over. The length of the apterous"and alate arrays i s then extended one day-degree u n t i l the maximum spe c i f i e d by IAPEND is reached. A l l aphids are aged one day-degree by s h i f t i n g the contents of an array element forward one step, sta r t i n g with the oldest element. New births are then added to the f i r s t element of the array. F i n a l l y , the age-specific adult weight, and fecundity arrays are aged one day-degree. Developmental time and fecundity - TMSHFT Fecundity and developmental time are calculated as a function of young adult weight (see II.C.Ic). The weight of young adults was not obtained from f i e l d samples, but the average weight of a l l adults was obtained (see I l . C . l e ) . The two measures are not the same. Since adult weight once set is fixed (see II.C.Ic), a change in mean adult weight suggests that new adult weight i s either greater or less than the mean depending on the dir e c t i o n of change. New adult weight is calculated, given the f i e l d estimates of mean adult weight, t o t a l known adult weight in the model, t o t a l adults, and number of new adults. The estimate is very sensitive to operations in other parts of the model such as the lengthening or shortening of developmental time, and s h i f t s of aphids from the apterous to alate morph, so new adult weight i s allowed to change from that of i t s predecessor by an amount set in DELTA. - As well, new adult weight is not allowed to exceed the bounds of the 180 data from which the fecundity and developmental time relationships were derived. The remainder of the subroutine is concerned with the problem of lengthening or shortening developmental time. The code is involved, p a r t i c u l a r l y where arrays must be shortened. The interested reader i s referred to the model. To assess the effect of determining age-specific adult weights, the model allows the condition that a l l adult weights equal the mean f i e l d adult weight. This is controlled with ICOHRT. Alate determination - ALATE This subroutine ages the elements of the array containing aphid densities by one day-degree, and places the latest calculated density into the f i r s t p osition. Since the array is 85 steps long, the 85th position contains aphid density 85 day-degrees e a r l i e r . This is used to calculate the proportion (fourth apterae/total fourths) (see II.C.2a). That proportion is then used to calculate the number of new fourth apterae which must be moved to the just vacated new fourth alate position in order to obtain the correct r a t i o . The calculated number i s then moved, or i f i t exceeds the number of new fourths, a l l the new fourths are moved. Oviparae production ^ SEXUAL Production of oviparae begins August 23, calendar day 234 (see I l . C . l f ) . Immature oviparae are assumed to develope at 181 the same rate and in the same time as virginoparae. Once the time, is reached for the f i r s t cohort to become adult, the overall r a t i o of adult oviparae to t o t a l adults is calculated each day-degree. The age-specific r a t i o (number of new adult virginoparae/total new adults), is associated with each new cohort such that the calculated o v e r a l l r a t i o of oviparae to to t a l adults i s s a t i s f i e d in the model. The age-specific r a t i o is used in BRTHAG to modify the b i r t h rate of the adult aphids which are not physically separated into virginoparae and oviparae. The elements of the age-specific r a t i o array are aged one step each day-degree after the f i r s t cohort of oviparous nymphs become adult. Losses re l a t ionships 2 LSRELT This i s a multiple entry subroutine which consolidates the relationships required to calculate aphid s u r v i v a l : alate f l i g h t (see II.C.2a); aphidimyza, syrphid, andD. rapae numerical response (see II.C.2b-d); age-specific survival given leaf f a l l (see II.C.2e). Predator and plant effects on aphid survival - PPSURV Predator and parasite arrays are lengthened to a maximum contained in IPREND and the elements therein are aged one step. Each step i s equal to a non-integer number of day-degrees in the appropriate time scale. The number of A^ aphidimyza, syrphid and rapae eggs produced, are calculated as a 182 function of current t o t a l aphids above a specified threshold (see II.C.2b-d), and l a r v a l (pupal in the parasites case) developmental time. These are placed in the f i r s t position of their respective arrays. A submodel invoking observed ( f i e l d ) aphid densities showed that this algorithm produced r e l i a b l e estimates of the numbers of each predator and parasite. The weight of aphids eaten by A^ aphidimyza and syrphids i s calculated as a function of the age-specific voracity table constructed in SETPRD, and numbers of larvae of a given age. Aphid survival is calculated as a function of weight demanded by the predators, and aphid weight available (see II.C.2b). Survival due to p a r a s i t i z a t i o n is calculated as a function of the number of newly formed cocoons, and the number of aphids at r i s k . The former is taken d i r e c t l y from the age-specific parasite array, and the l a t t e r is assumed to be the sum of a l l adults. Furthermore, p a r a s i t i z a t i o n i s assumed not to be age-s p e c i f i c . Leaf f a l l is an age-specific agent and is calculated as such. The proportion of each instar in stratum 3 i s predicted from the proportion of the given instar on the whole plant (see II.C.2e). Since these add up to s l i g h t l y more or less than one, they are standardized to one. Age-specific survival i s then calculated as a function of the proportion of the population in stratum 3 and the proportion of leaves remaining after leaf f a l l . Depending upon the state of the variable CNSTNT, the e f f e c t can be ameliorated as a function of the rate of leaf f a l l . Survival from a l l sources including longevity 183 (see Il.C.lb) are applied to the aphid array, and aphid losses due to leaf f a l l are calculated. Alate emmigration ^ FLIGHT The number of alates required per plant is calculated as a function of current t o t a l aphids" (see II.C..2a), above a specified threshold. Alates in excess of what is required are removed but only after a set p r e f l i g h t time. The number removed are summed. Sum aphid and predator arrays - TOTAPH and TOTPRD Aphid arrays are summed for each instar and grand t o t a l . Current density and t o t a l aphid weight is calculated. Weight of the nymphs is calculated as a proportion of new adult weight, and weight of the alate morphs is calculated as a proportion of their respective apterous morphs (see II.C.2b). The l a r v a l predators and parasite cocoons are summed in TOTPRD. Print results 2 RESULT Variables which need only be calculated at print time are calculated here. Totals of arrays, and the values of most variables are written with appropriate documentation. The information occupies 30 l i n e s or half a print page.
UBC Theses and Dissertations
Population dynamics of the cabbage aphid Brevicoryne Brassicae (L.) (Homoptera:Aphididae in Vancouver,… Raworth, David Arnold 1982
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