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The equilibrium structure and behavior of defoliating insect systems McNamee, Peter James 1987

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THE EQUILIBRIUM STRUCTURE AND BEHAVIOR OF DEFOLIATING INSECT SYSTEMS by Peter James McNamee B . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1977 A t h e s i s presented i n p a r t i a l f u l f i l l m e n t o f the requirements f o r the degree o f Doctor o f Philosophy i n The F a c u l t y o f Graduate S t u d i e s Department o f Zoology We accept t h i s t h e s i s as conforming to the r e q u i r e d standard The U n i v e r s i t y o f B r i t i s h August, 1987 © Peter James McNamee, Columbia 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) A B S T R A C T D e f o l i a t i n g i n s e c t systems, d e f i n e d f o r the purposes of t h i s t h e s i s as being composed of i n s e c t s which d e f o l i a t e f o r e s t t r e e s and the s p e c i e s with which they i n t e r a c t , such as t h e i r host t r e e s and t h e i r n a t u r a l enemy complexes, e x h i -b i t a wide v a r i e t y of p o p u l a t i o n b e h a v i o r s . S i m i l a r l y , a number of t h e o r i e s and models have been proposed to e x p l a i n these b e h a v i o r s . These t h e o r i e s emphasize the importance of d i f f e r e n t e c o l o g i c a l p r o c e s s e s , o f t e n concentrate on the d e f o l i a t o r and overlook the importance of other components. A l s o , much of the c u r r e n t understanding of the dynamics of these systems has come from f o r e s t pest r e s e a r c h and manage-ment programs, t a i l o r e d towards s p e c i f i c pest problems and o f t e n very s h o r t term i n nature. T h i s t h e s i s develops and begins to t e s t a general approach f o r the l o c a l dynamics of d e f o l i a t i n g i n s e c t sys-tems. T h i s framework o u t l i n e s the system components that are necessary to p r e d i c t the behavior of d e f o l i a t i n g i n s e c t systems. I t i n c l u d e s ways i n which the e q u i l i b r i u m s t r u c -t ure of d e f o l i a t i n g i n s e c t systems, d e f i n e d as the number of e q u i l i b r i a f o r each system component, the p o p u l a t i o n l e v e l s at which the e q u i l i b r i a occur, and the processes c r e a t i n g the e q u i l i b r i a , might be found. The framework a l s o includes methods of inducing the q u a l i t a t i v e behavior of these sys-terns, d e f i n e d as the p e r i o d i c i t y of d e f o l i a t o r outbreaks, the l e n g t h of outbreaks, and the dynamics of other important system components between, d u r i n g , and i n the d e c l i n e of d e f o l i a t o r outbreaks. The study begins with a d e t a i l e d l i t e r a t u r e review of h i s t o r i c a l t h e o r i e s of d e f o l i a t i n g i n s e c t system behavior and of the documented behavior p a t t e r n s of these systems. Major c l a s s e s of behavior are i d e n t i f i e d , as w e l l as the v a r i o u s e c o l o g i c a l processes which have been invoked to e x p l a i n these b e h a v i o r s . An a n a l y s i s and documentation of the e q u i l i b r i u m s t r u c t u r e and behavior of three d e f o l i a t i n g d e f o l i a t i n g i n s e c t systems, the e a s t e r n blackheaded budworm, the e a s t e r n spruce budworm, and the jack pine sawfly, are then used t o develop g e n e r a l r u l e s about how e q u i l i b r i u m s t r u c t u r e and behavior can be e x p l a i n e d . T h i s a n a l y s i s , coupled with the l i t e r a t u r e review, i s used to develop the framework. The framework i s then t e s t e d a g a i n s t h i s t o r i c a l d e f o l i a t o r p o p u l a t i o n data and g e n e r a l syntheses of d e f o l i -a t i n g i n s e c t system r e s e a r c h to assess i t s u t i l i t y and pred-i c t a b i l i t y . The major r e s u l t s of the t h e s i s are as f o l l o w s . F i r s t , i t appears that the s t r u c t u r e and behavior of a d e f o l i a t i n g i n s e c t system can be e x p l a i n e d with f i v e dynamic v a r i a b l e s : the abundances of the d e f o l i a t o r ; the f o l i a g e ; the f o r e s t ; the p a r a s i t o i d ; and the d i s e a s e ; and the e f f e c t s of weather a c t i n g on the d e f o l i a t o r . Second, there appear to be 4 c l a s s e s of d e f o l i a t i n g i n s e c t system behavior. T h i r d , the behavior t h a t a d e f o l i a t i n g i n s e c t system w i l l e x h i b i t seems to be determined by the magnitude of weather e f f e c t s on d e f o l i a t o r s u r v i v a l and r e c r u i t m e n t , the p a r a s i t o i d numeri-c a l response to changing d e f o l i a t o r d e n s i t i e s , the d i s e a s e numerical response to changing d e f o l i a t o r d e n s i t i e s , and the v u l n e r a b i l i t y of the f o r e s t to d e f o l i a t i o n . Fourth, there seem to be f o u r e q u i l i b r i u m s t r u c t u r e s the d e f o l i a t o r can e x h i b i t , and one each f o r the p a r a s i t o i d , the f o l i a g e , the f o r e s t , and the d i s e a s e . F i n a l l y , the framework suggests th a t d e f o l i a t i n g i n s e c t system s t r u c t u r e and behavior can be induced with a p a r t i c u l a r , w e l l - d e f i n e d s e t of i n f o r m a t i o n . The framework i s s u c c e s s f u l when a p p l i e d to p a r t i c u l a r d e f o l i a t i n g i n s e c t systems f o r e x p l a i n i n g t h e i r behavior, but l e s s s u c c e s s f u l i n e x p l a i n i n g d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e f o r other systems. O p p o r t u n i t i e s f o r more thorough t e s t i n g of the framework e x i s t i f the p a r t i c u l a r types of data o u t l i n e d above are gathered f o r d e f o l i a t i n g i n s e c t systems. T h i s lac k of data f o r t e s t i n g the framework make i t c u r r e n t l y d i f f i c u l t to c l e a r l y d e f i n e those systems i n which the framework i s u s e f u l and those systems i n which i t i s not. Experiments to t e s t the framework are d e s c r i b e d and suggestions f o r f u t u r e types of a p p l i e d r e s e a r c h on d e f o l i a t i n g i n s e c t systems are presented. V TABLE OF CONTENTS LIST OF TABLES. LIST OF FIGURES ACKNOWLEDGEMENTS 1.0 INTRODUCTION 1 1.1 Overview 1 1.2 O b j e c t i v e s 4 1.3 Bounds o f T h i s T h e s i s . . 6 1.4 Approach and O r g a n i z a t i o n o f T h i s T h e s i s . . . . 7 2.0 INSECT/FOREST SYSTEM STRUCTURE AND BEHAVIOR: METHODS OF ANALYSIS, HISTORICAL THEORIES, AND PATTERNS OF BEHAVIOR 10 2.1 I n t r o d u c t i o n 10 2.2 Methods o f A n a l y s i s 11 2.2.1 The A n a l y s i s Of E q u i l i b r i u m S t r u c t u r e . . 11 2.2.2 A n a l y s i s Of Temporal Dynamics 16 2.3 The E q u i l i b r i u m S t r u c t u r e Of I n s e c t / F o r e s t Systems, i . 17 2.4 Hypotheses For I n s e c t / F o r e s t System Behavior . . 19 2.4.1 P r e d a t i o n and P a r a s i t i s m 19 2.4.2 N u t r i e n t L i m i t a t i o n And F o l i a g e Q u a l i t y . 22 2.4.3 Q u a l i t a t i v e D i f f e r e n c e s Between I n d i v i d u a l s 26 2.4.4 Genetic Feedback 28 2.4.5" D i s p e r s a l 30 2.4.6 Density Independent Mechanisms 32 2.4.7 E x i s t i n g I n t e g r a t i v e T h e o r i e s 34 2.5 P a t t e r n s o f I n s e c t / F o r e s t System Behavior. . . . 37 2.5.1 Sources o f Information and S t r u c t u r e o f The Review 38 2.5.2 R e s u l t s 40 3.0 THE EASTERN BLACKHEADED BUDWORM SYSTEM 53 3.1 I n t r o d u c t i o n 53 3.2 The Ea s t e r n Blackheaded Budworm/Balsam F i r System . 53 3.2.1 Documented Behavior 54 3.3 System D e s c r i p t i o n 55 3.3.1 The D e f o l i a t o r . 55 3.3.2 N a t u r a l Enemies 55 3.3.3 The F o r e s t And F o l i a g e 56 3.4 Model D e s c r i p t i o n 56 3.4.1 S p a t i a l And Temporal C h a r a c t e r i s t i c s . . . 57 3.4.2 F o r e s t Dynamics 57 3.4.3 F o l i a g e Dynamics 58 3.4.4 Insect Dynamics 59 3.4.5 N a t u r a l Enemy Dynamics. . . . 65 v i TABLE OF CONTENTS continued 3.5 Model E q u i l i b r i u m S t r u c t u r e 76 3.5.1 The D e f o l i a t o r 76 3.5.2 The P a r a s i t o i d 81 3.5.3 The F o l i a g e 81 3.5.4 The F o r e s t 84 3.6 Processes Which Keep Budworm C h r o n i c a l l y Endemic 84 3.7 The Role Of Weather 86 3.8 The Role Of P a r a s i t o i d s 89 3.9 Temporal Model Behavior 93 3.9.1 Temporal Behavior With C h r o n i c a l l y Poor Weather 93 3.9.2 Temporal Behavior With Normal Weather . . 95 3.10 E f f e c t s o f A l t e r n a t e P a r a s i t o i d Attack Parameters 98 3.10.1 Good Searcher, High S u r v i v a l , Low S u p e r p a r a s i t i s m . . . . . 100 3.10.2 Poor Searcher, Low S u r v i v a l , High S u p e r p a r a s i t i s m . . . . . . 100 3.11 Summary 104 4.0 THE EASTERN SPRUCE BUDWORM SYSTEM 108 4.1 Documented Behavior 108 4.2 System D e s c r i p t i o n 109 4.2.1 The D e f o l i a t o r . . 109 4.2.2 N a t u r a l Enemies 110 4.2.3 The F o r e s t 110 4.3 Model D e s c r i p t i o n I l l 4.4 Model E q u i l i b r i u m S t r u c t u r e I l l 4.4.1 The Insect I l l 4.4.2 The P a r a s i t o i d 113 4.4.3 The F o l i a g e and The F o r e s t . 116 4.5 Review o f Previous Model Analyses 117 4.5.1 Model Behavior Under Normal C o n d i t i o n s . . 117 4.5.2 Model Behavior With Reduced F o r e s t S u s c e p t i b i l i t y 120 4.6 C h r o n i c a l l y Endemic D e f o l i a t o r P o p u l a t i o n s . . . 125 4.7 The Role o f Weather In The Budworm System. . . . 129 4.8 The Role o f P a r a s i t o i d s In The Budworm System. . 129 4.9 Summary 132 5.0 THE JACK PINE SAWFLY SYSTEM 134 5.1 Documented Behavior 134 5.2 System D e s c r i p t i o n 135 5.3.1 The D e f o l i a t o r 135 5.3.2 N a t u r a l Enemies 136 5.3.3 The F o r e s t 136 v i i TABLE OF CONTENTS continued 5.3 Model D e s c r i p t i o n 136 5.3.1 S p a t i a l and Temporal C h a r a c t e r i s t i c s o f The Model 136 5.3.2 F o r e s t Dynamics 136 5.3.3 F o l i a g e Dynamics 136 5.3.4 D e f o l i a t o r and N a t u r a l Enemy Dynamics . . 138 5.4 Model E q u i l i b r i u m S t r u c t u r e 139 5.4.1 The D e f o l i a t o r 139 5.4.2 The P a r a s i t o i d 141 5.4.3 The F o l i a g e 144 5.4.4 The F o r e s t 144 5.5 Model C o n d i t i o n s Which Keep The Sawfly C h r o n i c a l l y Endemic 148 5.6 The Role o f Weather 151 5.7 The Role o f The P a r a s i t o i d 151 5.8 Temporal Model Behavior 156 5.8.1 C h r o n i c a l l y Poor Weather C o n d i t i o n s . . . 156 5.8.2 Normal Weather C o n d i t i o n s 156 5.9 A Fourth Type o f Behavior 161 5.10 Summary 165 6.0 THE INTEGRATIVE THEORY 168 6.1 I n t r o d u c t i o n 168 6.2 Elements o f Observed Behavior Not In Model Analyses 169 6.3 System Components 170 6.4 C l a s s e s o f Behavior 171 6.4.1 C l a s s 1: Chronic Endemic 171 6.4.2 C l a s s 2: D e f o l i a t o r / P a r a s i t o i d - D i s e a s e C y c l e 171 6.4.3 C l a s s 3: D e f o l i a t o r / F o l i a g e Cycle . . . . 171 6.4.4 C l a s s 4: D e f o l i a t o r / F o r e s t Cycle 173 6.5 Processes Determining System Behavior 173 6.5.1 C l a s s 1 Behavior 173 6.5.2 C l a s s 2 Behavior 173 6.5.3 C l a s s 3 Behavior 174 6.5.4 C l a s s 4 Behavior 175 6.6 Information Required To P r e d i c t System Behavior. 175 6.6.1 Weather E f f e c t s 175 6.6.2 P a r a s i t o i d Numerical Response 175 6.6.3 The Disease . . . 177 6.6.5 The F o r e s t 178 6.7 A l t e r n a t e S t r u c t u r e s And Necessary Information . 178 6.7.1 The D e f o l i a t o r . 178 6.7.2 The Other V a r i a b l e s 185 6.8 Summary 187 v i i i TABLE OF CONTENTS continued 7.0 TESTING THE THEORY 190 7.1 I n t r o d u c t i o n 190 7.2 F i e l d Experiments . 192 7.2.1 A F i e l d Experiment For T e s t i n g E q u i l i b r i u m S t r u c t u r e . . . 192 7.2.2 A F i e l d Experiment For T e s t i n g System Behavior 196 7.3 E q u i l i b r i u m S t r u c t u r e In Long Term P o p u l a t i o n Data 198 7.4 Tes t Of System Behavior 207 7.5 T e s t s Using Information Set 210 8.0 CONCLUSIONS AND RESEARCH IMPLICATIONS 218 8.1 Con c l u s i o n s 218 8.2 R e l a t i o n s h i p To Previous T h e o r i e s 219 8.3 F a c t o r s Not Included 220 8.3.1 D i s p e r s a l 220 8.3.2 I n d i v i d u a l D i f f e r e n c e s . 222 8.3.3 F o l i a g e Q u a l i t y 223 8.4 I m p l i c a t i o n s For I n s e c t / F o r e s t System Research . 223 8.4.1 The D e f o l i a t o r 223 8.4.2 The P a r a s i t o i d And Disease Complexes. . . 224 8.4.3 The F o l i a g e 225 8.4.4 The Fo r e s t 225 9.0 LITERATURE CITED 227 A.I APPENDIX I - TIME SERIES AND SPECTRAL DENSITIES FOR DEFOLIATOR POPULATIONS. . 242 A.II APPENDIX II - ANALYSIS OF PARASITOID ISORECRUITMENT CURVES 263 i x L I S T O F T A B L E S Table I C o r r e l a t i o n s o f f e c u n d i t y and p o p u l a t i o n r e c r u i t m e n t to e a r l y i n s t a r l a r v a l s u r v i v a l f o r three f o r e s t p e s t s . . 27 Table II Sources o f i n s e c t p o p u l a t i o n data 39 Table I I I P a t t e r n s o f i n s e c t / f o r e s t system behavior . . . 41 Table IV L i t e r a t u r e sources used i n documenting p a t t e r n s o f i n s e c t / f o r e s t system behavior (Table I I I ) . . 49 Table V B a s e l i n e p o p u l a t i o n parameters f o r e a s t e r n blackheaded budworm 61 Table VI P a r a s i t o i d dynamics parameters 71 Table VII Avian p r e d a t i o n parameters f o r e a s t e r n blackheaded budworm model 77 Table V I I I Information necessary to p r e d i c t the s t r u c t u r e and behavior o f i n s e c t / f o r e s t systems 189 Table IX Number of p o p u l a t i o n groups p r e d i c t e d by the c l u s t e r a n a l y s i s • 204 Table X S i g n i f i c a n c e o f c l u s t e r a n a l y s i s r e s u l t s f o r d a t a s e t s i n which 2 o r 3 p o p u l a t i o n groups were s e l e c t e d 205 Table XI Comparison o f number o f p o p u l a t i o n groups s e l e c t e d by c l u s t e r a n a l y s i s with number p r e d i c t e d by the i n t e g r a t i v e theory 206 Table XII C l u s t e r a n a l y s i s r e s u l t s f o r each d e f o l i a t o r . . 208 Table X I I I Comparison o f p r e d i c t e d with documented behavior c l a s s . 213 Table XIV L i t e r a t u r e sources f o r the i n f o r m a t i o n contained i n Table X I I I 216 X LIST OF FIGURES Fi g u r e 1. Rep r e s e n t a t i v e r e c r u i t m e n t curves 12 Fi g u r e 2. E f f e c t o f changing environmental c o n d i t i o n s on p o p u l a t i o n r e c r u i t m e n t 15 Fi g u r e 3. A l t e r n a t e c o n f i g u r a t i o n s o f predator-prey i s o r e c r u i t m e n t curves . . . . . . . . 21 Figu r e 4. Iso r e c r u i t m e n t curve r e p r e s e n t a t i o n o f f o l i a g e q u a l i t y hypotheses 24 Figu r e 5. Is o r e c r u i t m e n t curve r e p r e s e n t a t i o n o f the hypothesis o f i n d i v i d u a l d i f f e r e n c e s . 29 Figu r e 6. Iso r e c r u i t m e n t curve r e p r e s e n t a t i o n o f the g e n e t i c feedback hypotheses 31 Fi g u r e 7. Is o r e c r u i t m e n t curve r e p r e s e n t a t i o n o f the e f f e c t s o f immigration 33 Fi g u r e 8. Iso r e c r u i t m e n t curve r e p r e s e n t a t i o n o f the e f f e c t s o f d e n s i t y independent p r o c e s s e s . . . . 35 Figu r e 9. F u n c t i o n a l response of b i r d s to e a s t e r n blackheaded budworm 75 Figu r e 10. Recruitment curves f o r e a s t e r n blackheaded budworm 78 Figu r e 11. Budworm i s o r e c r u i t m e n t curve as a f u n c t i o n o f p a r a s i t o i d d e n s i t y 80 Figu r e 12. P a r a s i t o i d r e c r u i t m e n t curve as a f u n c t i o n o f budworm d e n s i t y 82 Fi g u r e 13. F o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y 83 Fi g u r e 14. F o r e s t i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e d e n s i t y 85 Fi g u r e 15. C o n d i t i o n s p o t e n t i a l l y c r e a t i n g c h r o n i c a l l y endemic budworm p o p u l a t i o n s 87 Fi g u r e 16. Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e biomass with d i f f e r e n t l e v e l s o f weather induced l a r v a l s u r v i v a l 88 x i LIST OF FIGURES cont'd F i g u r e 17. Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f p a r a s i t o i d d e n s i t y and p a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y f o r d i f f e r e n t f o l i a g e l e v e l s 90 Figu r e 18. F o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y and budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e biomass with d i f f e r e n t p a r a s i t o i d d e n s i t i e s 92 Fi g u r e 19. Fo r e s t i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e biomass and f o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o r e s t biomass f o r d i f f e r e n t budworm d e n s i t i e s 94 Fi g u r e 20. Model behavior f o r c h r o n i c a l l y low weather induced l a r v a l s u r v i v a l . 96 Fig u r e 21. Model behavior under normal weather c o n d i t i o n s . 97 Fi g u r e 22. Model behavior f o r a 150 year s i m u l a t i o n with normal weather c o n d i t i o n s 99 Fi g u r e 23. Model e q u i l i b r i u m s t r u c t u r e f o r "super" p a r a s i t o i d 101 Fi g u r e 24. Model behavior generated with "super" p a r a s i t o i d 102 Figu r e 25. Model e q u i l i b r i u m s t r u c t u r e f o r "slow" p a r a s i t o i d 103 Figu r e 26. Model behavior generated with "slow" p a r a s i t o i d 105 Figu r e 27: Recruitment curves f o r e a s t e r n spruce budworm . 112 Fig u r e 28: Budworm i s o r e c r u i t m e n t curve as a f u n c t i o n o f f o l i a g e biomass 114 Fig u r e 29: P a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y 115 Fi g u r e 30: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e d e n s i t y and f o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y , f o r d i f f e r e n t f o r e s t biomasses 118 x i i LIST OF FIGURES cont'd F i g u r e 31: F o r e s t i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e l e v e l s and f o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o r e s t biomass, f o r d i f f e r e n t budworm l e v e l s 119 Figure 32: Model behavior f o r the unmanaged system . . . . 121 Fi g u r e 33: Budworm and f o l i a g e i s o r e c r u i t m e n t curves f o r d i f f e r e n t f o r e s t biomasses under the h i s t o r i c a l budworm spray r u l e 122 Figu r e 34: F o r e s t and f o l i a g e i s o r e c r u i t m e n t curves f o r d i f f e r e n t budworm d e n s i t i e s under the h i s t o r i c a l budworm spray r u l e 123 Fi g u r e 35: Model behavior with h i s t o r i c a l budworm spray r u l e s 124 Fi g u r e 36: Processes p o t e n t i a l l y c r e a t i n g c h r o n i c a l l y endemic budworm 126 Figu r e 37: Model behavior f o r c h r o n i c a l l y low weather induced l a r v a l s u r v i v a l 128 Fi g u r e 38: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e biomass with d i f f e r e n t normal l e v e l s o f weather-induced l a r v a l s u r v i v a l 130 Figu r e 39: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f p a r a s i t o i d d e n s i t y and p a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y , with d i f f e r e n t f o l i a g e l e v e l s . 131 Fi g u r e 40: Recruitment curves f o r jack pine sawfly . . . . 140 Fi g u r e 41: Recruitment curves f o r jack pine sawfly f o r low to high f o r e s t biomass 142 Fi g u r e 42: Sawfly i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o r e s t b a s a l area 143 Fi g u r e 43: P a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f sawfly d e n s i t y 145 Fi g u r e 44: F o l i a g e i s o r e c r u i t m e n t curve as a f u n c t i o n o f sawfly d e n s i t y 146 x i i i LIST OF FIGURES cont'd F i g u r e 45: F o r e s t i s o r e c r u i t m e n t curve as a f u n c t i o n o f f o l i a g e biomass 147 Fi g u r e 46: Sawfly i s o r e c r u i t m e n t curves as a f u n c t i o n of b a s a l area with normal to extremely poor e a r l y l a r v a l s u r v i v a l 149 Fi g u r e 47: Sawfly i s o r e c r u i t m e n t curves as a f u n c t i o n o f b a s a l area with v a r y i n g a d u l t p a r a s i t o i d d e n s i t i e s and with d i f f e r e n t f o l i a g e biomass l e v e l s . . 150 Figu r e 48: Sawfly i s o r e c r u i t m e n t curves as a f u n c t i o n o f b a s a l area with normal v a r i a t i o n i n weather-induced e a r l y l a r v a l s u r v i v a l 152 Figu r e 49: Sawfly i s o r e c r u i t m e n t curves as a f u n c t i o n o f p a r a s i t o i d d e n s i t y and p a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f sawfly d e n s i t y f o r d i f f e r e n t f o l i a g e l e v e l s 154 Figu r e 50: Model behavior with c h r o n i c a l l y poor weather-induced e a r l y l a r v a l s u r v i v a l 157 Figure 5.1: Model behavior with normal v a r i a t i o n i n weather-induced e a r l y l a r v a l s u r v i v a l . . . . 158 Figu r e 52: Model behavior with p a r a s i t o i d progeny s u r v i v a l s et at 50% o f normal 160 Fi g u r e 53: F o r e s t e q u i l i b r i u m s t r u c t u r e with lowered v u l n e r a b i l i t y to d e f o l i a t i o n 162 Fi g u r e 54: Model behavior with p a r a s i t o i d progeny s u r v i v a l s e t at 50% o f normal and lowered f o r e s t v u l n e r a b i l i t y to d e f o l i a t i o n 164 F i g u r e 55: The 4 c l a s s e s o f i n s e c t / f o r e s t system behavior, shown i n s t y l i z e d f a s h i o n , 172 Fi g u r e 56: A r e p r e s e n t a t i v e i s o r e c r u i t m e n t curve from the European pine sawfly/red pine model 180 Fi g u r e 57: Avian p r e d a t i o n data c o l l e c t e d from v a r i o u s i n s e c t / f o r e s t systems 183 Fi g u r e 58: Small mammal p r e d a t i o n data c o l l e c t e d from v a r i o u s i n s e c t / f o r e s t systems 186 x i v LIST OF FIGURES cont'd F i g u r e 59: D e f o l i a t o r e q u i l i b r i u m s t r u c t u r e s 190 Fi g u r e 60: Experiment to t e s t f o r d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e 194 Fi g u r e 61: Experiment to t e s t whether the i n t e g r a t i v e theory can p r e d i c t c l a s s o f behavior 197 Fi g u r e 62: Gypsy moth p o p u l a t i o n d a t a s e t from a non-outbreak l o c a t i o n i n New York 200 Figu r e 63: Frequency d i s t r i b u t i o n s o f dominant p e r i o d i c i t i e s found i n long term d e f o l i a t o r p o p u l a t i o n data 211 X V A C K N O W L E D G E M E N T S Mentors are c r i t i c a l persons i n the development of s t u -dents. They provide wisdom and example. They l i g h t and maintain f i r e s of enthusiasm i n graduate s t u d e n t s . I had, and s t i l l have, three mentors, Buzz H o l l i n g , C a r l Walters, and Jack McLeod, who have i n f u s e d my academic l i f e throughout the past eleven years with e v e r y t h i n g a graduate student needs. T h i s t h e s i s has b e n e f i t e d from innumerable d i s c u s s i o n s through the years with B i l l C l a r k , R a n d a l l Peterman, B i l l N e i l l , Lee Gass, Ray H i l b o r n , John McLean, and R a l f Yorque. In p a r t i c u l a r , I was f o r t u n a t e to p r o f i t from Dr. Yorque 1s re s i d e n c e at the I n s t i t u t e of Animal Resource Ecology before h i s departure i n the e a r l y 1980s. F i n a l l y , thank you, C a r o l i n e , C o l l e e n , Benjamin, and Teresa. - 1 -1.0 INTRODUCTION 1.1 Overview D e f o l i a t i n g i n s e c t systems, d e f i n e d f o r the purposes of t h i s t h e s i s as being composed of i n s e c t s which d e f o l i a t e f o r e s t t r e e s and the s p e c i e s with which they i n t e r a c t , such as t h e i r host t r e e s and t h e i r n a t u r a l enemy complexes, e x h i -b i t a v a r i e t y of b e h a v i o r s . In terms of d e f o l i a t o r popula-t i o n dynamics, behavior v a r i e s from c h r o n i c a l l y non-outbreak to l o n g - l a s t i n g , i n f r e q u e n t i n f e s t a t i o n s ( e a s t e r n spruce budworm, C h o r i s t o n e u r a fumiferana ( L e p i d o p t e r a : T o r t r i c i d a e ) B a s k e r v i l l e 1958) to l o n g - l a s t i n g , r e g u l a r outbreaks (jack pine budworm, Ch o r i s t o n e u r a pinus ( L e p i d o p t e r a : T o r t r i c i d a e ) Canada 1939 to 1982) to r e g u l a r outbreaks of short d u r a t i o n ( D o u g l a s - f i r tussock moth, Orygia pseudotsugata (Lepidop-t e r a : Lymantriidae) Wickman 1963) to almost p e r f e c t l y regu-l a r o s c i l l a t i o n s ( l a r c h budmoth, Zeiraphera g r i s e a n a ( L e p i -doptera: T o r t r i c i d a e ) B a l t e n s w e i l e r 1968). P a r a s i t i s m r a t e s can f l u c t u a t e markedly with changing d e f o l i a t o r d e n s i t i e s ( e a s t e r n black-headed budworm, A c l e r i s v a r i a n a ( L e p i d o p t e r a : T o r t r i c i d a e ) M i l l e r 1966) or f l u c t u a t e r e l a t i v e l y l i t t l e ( e a s t e r n spruce budworm, M i l l e r 1963). S u s c e p t i b l e f o r e s t s can s u f f e r l i t t l e or no m o r t a l i t y from i n f e s t a t i o n s (spruce budmoth, Zeiraphera spp. ( L e p i d o p t e r a : T o r t r i c i d a e ) Carrow 1985) or experience extremely heavy m o r t a l i t y ( e a s t e r n spruce budworm, B a s k e r v i l l e , 1958). A d e f o l i a t i n g i n s e c t system can e x h i b i t r a d i c a l l y d i f f e r e n t behaviors i n d i f -f e r e n t p a r t s of i t s extent ( l a r c h sawfly, P r i s t i p h o r a e r i c h -- 2 -s o n i i (Hymenoptera: Tenthredinidae) (Turnock 1972) or at d i f f e r e n t p e r i o d s of time ( l a r c h sawfly, Turnock 1972, Euro-pean spruce sawfly, D i p r i o n hercyniae (Hymenoptera: D i p r i o n i d a e ) N e i l s o n and Mo r r i s 1964). S i m i l a r l y , there are a v a r i e t y of models of d e f o l i a t i n g i n s e c t systems (western t e n t c a t e r p i l l a r , Malacasoma  d i s s t r i a ( L e p i d o p t e r a : Lasiocampidae) W e l l i n g t o n et a l . 1975, D o u g l a s - f i r tussock moth, Brookes e t a l . 1979, eas t e r n spruce budworm, C l a r k and H o l l i n g 1979, l a r c h budmoth, F i s c h l i n and B a l t e n s w e i l e r 1979, e a s t e r n black-headed budworm, McNamee 1979, European pine sawfly, Neodiprion s e r - t i f e r (Hymenoptera: D i p r i o n i d a e ) Wallace and G r i f f i t h s , i n prep., gypsy moth, Lymantria d i s p a r ( L e p i d o p t e r a : Lymantri-idae) McNamee et a l . 1983). A l l these models, to a g r e a t e r or l e s s e r degree, are a r t i c u l a t i o n s of c u r r e n t understanding of the key e c o l o g i c a l processes which g i v e r i s e to the observed dynamics of the systems. S e v e r a l f e a t u r e s of these models are worth n o t i n g . F i r s t , d i f f e r e n t e c o l o g i c a l processes have been i d e n t i f i e d as important i n the v a r i o u s cases. For example, Brookes et. a l . (1979) emphasize the r o l e of a v i r a l d i s e a s e i n causing c o l l a p s e of D o u g l a s - f i r tussock moth i n f e s t a t i o n s , C l a r k and H o l l i n g (1979) d e s c r i b e f o r e s t and f o l i a g e dynamics as important determinants of e a s t e r n spruce budworm system behavior, while F i s c h l i n and B a l t e n s w e i l e r (1979) hypothesize that d i s p e r s a l and f o l i a g e q u a l i t y r e g u l a t e the dynamics of l a r c h budmoth p o p u l a t i o n s . Second, the models - 3 -tend to concentrate l a r g e l y on the i n s e c t s and t h e i r popula-t i o n behavior. Features and dynamics of other system com-ponents are o f t e n overlooked. T h i r d , many of the models were c o n s t r u c t e d under the a u s p i c e s of p a r t i c u l a r f o r e s t pest r e s e a r c h and management programs, s p e c i f i c a l l y designed to address resources a f f e c t e d by the f o r e s t p e s t . The r e s e a r c h programs which have u s u a l l y accompanied the model-l i n g e f f o r t s have been very s h o r t term i n nature, o f t e n being s h o r t e r i n d u r a t i o n than a complete d e f o l i a t o r popula-t i o n c y c l e . The end sum of these h i s t o r i c a l e f f o r t s i s a fragmented p i c t u r e of the dynamics of d e f o l i a t i n g i n s e c t systems. There i s no s i n g l e , g e n e r a l theory of d e f o l i a t i n g i n s e c t system behavior which i n t e g r a t e s a l l examples i n t o a common e c o l o g i c a l s t r u c t u r e . Of course, pest r e s e a r c h or manage-ment e f f o r t s must address s p e c i f i c needs. But, must each d e f o l i a t i n g i n s e c t system be considered a unique e n t i t y , and are we doomed to t r e a t every f o r e s t pest system as com-p l e t e l y d i f f e r e n t ? I suggest not, based on the f o l l o w i n g o b s e r v a t i o n s . Work done on the e a s t e r n spruce budworm/balsam f i r sys-tem ( B a s k e r v i l l e 1976, C l a r k and H o l l i n g 1979) i n d i c a t e d that q u a l i t a t i v e p r o p e r t i e s of i t s h i s t o r i c a l dynamics can be t r a c e d to a small s e t of i n t e r a c t i o n s among a small number of system components, or s t a t e v a r i a b l e s , each with a d i f f e r e n t temporal s c a l e , or r a t e of p o p u l a t i o n turnover, or change (Ludwig, Jones, and H o l l i n g 1978, Jones 1977a,b, - 4 -McNamee, McLeod, and H o l l i n g 1981). These i n t e r a c t i o n s i n the budworm system determine the e q u i l i b r i u m s t r u c t u r e , or the number and p o s i t i o n of p o p u l a t i o n e q u i l i b r i a (Peterman et a l . 1979) of the system. R a d i c a l l y d i f f e r e n t temporal behaviors of the model system occur when the c h a r a c t e r i s t i c s of those i n t e r a c t i o n s , and t h e r e f o r e t h e i r e f f e c t on the e q u i l i b r i u m s t r u c t u r e , are changed. Some of the d i f f e r e n t behaviors have been observed i n the r e a l world system (Clark and H o l l i n g 1979), while some behaviors have not (McLeod 1976a). But, a l l a l t e r n a t e behaviors occur r e g u l a r l y i n other d e f o l i a t i n g i n s e c t systems. A l s o , the e f f e c t of many e c o l o g i c a l processes on the e q u i l i b r i u m s t r u c t u r e of p o p u l a t i o n s i s known and p r e d i c t -able ( H o l l i n g 1959, Takahashi 1964, Southwood and Comins 1976). T h e r e f o r e , questions concerning the p r e d i c t i o n of e q u i l i b r i u m s t r u c t u r e can perhaps be reduced to questions concerning the presence or absence and c h a r a c t e r i s t i c s of a small set of e c o l o g i c a l p r o c e s s e s . These o b s e r v a t i o n s suggest that the e q u i l i b r i u m s t r u c -ture of key system v a r i a b l e s can be p r e d i c t e d by knowing whether a few processes occur i n th a t system and, i f they do, knowing t h e i r c h a r a c t e r i s t i c s and r a t e . Given the e q u i l i b r i u m s t r u c t u r e , i t may be p o s s i b l e to make some strong p r e d i c t i o n s about the temporal behavior of the sys-tem. 1.2 O b j e c t i v e s - 5 -The above o b s e r v a t i o n s l e a d to the o b j e c t i v e s of t h i s t h e s i s . S p e c i f i c a l l y , I wish to begin d e r i v i n g a g e n e r a l , i n t e g r a t i v e theory of s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems. The term " i n t e g r a t i v e theory" means, i n t h i s t h e s i s , a theory i n which a small number of e c o l o g i c a l processes are used to e x p l a i n the behavior of a l l d e f o l i a t -ing i n s e c t systems. T h i s theory w i l l : 1. d e f i n e a set of components, or s t a t e and d r i v i n g v a r i a b l e s which are necessary and s u f f i c i e n t to p r e d i c t the q u a l i t a t i v e p r o p e r t i e s of d e f o l i a t i n g i n s e c t system behavior; 2. c o l l a p s e the p l e t h o r a of d e f o l i a t i n g i n s e c t system behaviors i n t o a small s e t of c l a s s e s , each iden-t i f i e d by c h a r a c t e r i s t i c temporal p r o p e r t i e s of the components; 3. show how the c l a s s e s of behavior can be induced from a set of key i n t e r a c t i o n s among the com-ponents ; 4. show that the s t a t e components each e x h i b i t one of a small number of d i f f e r e n t e q u i l i b r i u m s t r u c -t u r e s ; and 5. show that the key i n t e r a c t i o n s among the com-ponents which determine system behavior and the e q u i l i b r i u m s t r u c t u r e s of the components i n any d e f o l i a t i n g i n s e c t system can be p r e d i c t e d with a - 6 -minimum set of i n f o r m a t i o n about the components themselves. 1.3 Bounds of Th i s T h e s i s In g e n e r a l , the development of the i n t e g r a t i v e theory w i l l occur through a c o n s i d e r a t i o n of s p e c i f i c processes which have been w e l l - s t u d i e d i n a small number of d e f o l i a t -ing i n s e c t systems. T h e r e f o r e , by d e f a u l t , I w i l l be omit-t i n g c o n s i d e r a t i o n of other processes i n the development of the theory. I w i l l present a d e s c r i p t i o n of a l l processes which s c i e n t i s t s have f e l t are important i n the dynamics of d e f o l i a t i n g i n s e c t systems i n a review e a r l y i n the t h e s i s . In a d d i t i o n , the t h e s i s summary chapter w i l l d i s c u s s the p o s s i b l e i m p l i c a t i o n s of the r e s u l t s of t h i s theory f o r the importance f o r some of these other p r o c e s s e s . In p a r t i c u l a r , I have chosen to concentrate my e f f o r t s i n t h i s t h e s i s on the development of a gen e r a l i n t e g r a t i v e theory f o r l o c a l p o p u l a t i o n dynamics. T h i s t h e s i s w i l l not address the e f f e c t s of i n s e c t d i s p e r s a l on the behavior of d e f o l i a t i n g i n s e c t systems and the theory w i l l not p r e d i c t the s p a t i a l dynamics of these systems. A l s o , i n t h i s t h e s i s , I am onl y i n t e r e s t e d i n the q u a l -i t a t i v e behavior of d e f o l i a t i n g i n s e c t systems. I d e f i n e q u a l i t a t i v e behavior of d e f o l i a t i n g i n s e c t systems as the p e r i o d of time between i n s e c t outbreaks, the length of i n s e c t outbreaks, and the dynamics of other important s t a t e - 7 -v a r i a b l e s between, d u r i n g , and i n the d e c l i n e of i n s e c t out-breaks. T h i s i s to d i s t i n g u i s h t h i s d e s c r i p t i o n of behavior from that of d e t a i l e d d e s c r i p t i o n s of year to year changes i n abundances of the s t a t e v a r i a b l e s . 1.4 Approach and O r g a n i z a t i o n of T h i s T h e s i s The approach I have adopted to meet the o b j e c t i v e s out-l i n e d above has f i v e major components. The f i r s t component i s a d e t a i l e d l i t e r a t u r e review which d e s c r i b e s the v a r i o u s p a t t e r n s of q u a l i t a t i v e behavior found i n d e f o l i a t i n g i n s e c t systems and presents the v a r i o u s t h e o r i e s h i s t o r i c a l l y proposed to account f o r t h e i r b ehavior. T h i s review w i l l i d e n t i f y the major c l a s s e s of q u a l i t a t i v e d e f o l i a t i n g i n s e c t system behavior and l a y out the v a r i o u s e c o l o g i c a l processes which have been invoked to e x p l a i n t h i s behavior. T h i s w i l l be p a r t i c u l a r l y u s e f u l a f t e r the i n t e g r a t i v e theory has been developed to examine e x a c t l y what pr e v i o u s t h e o r i e s are i n t e g r a t e d , how they have been i n t e g r a t e d , and which p r e v i o u s t h e o r i e s remain o u t s i d e of the i n t e g r a t i v e theory. The l i t e r a t u r e review i s pro-vided i n Chapter 2. The second component of the approach i s a c a r e f u l a n a l y s i s and documentation of the e q u i l i b r i u m s t r u c t u r e and behavior of s i m u l a t i o n models of three of the d e f o l i a t i n g i n s e c t systems which have been d e s c r i b e d i n the l i t e r a t u r e review: the e a s t e r n spruce budworm, the e a s t e r n black-headed budworm, and the jack pine s a w f l y . An e x t e n s i v e s e t of - 8 -q u a n t i t a t i v e data has been c o l l e c t e d on these three systems and they are or were the s u b j e c t of r e s e a r c h and management programs. T h i s model a n a l y s i s i s provided i n Chapters 3 to 5 . The methods of model a n a l y s i s w i l l be provided i n the i n t r o d u c t i o n to Chapter 3 . These methods i n v o l v e p r i m a r i l y the use of recruitment and i s o r e c r u i t m e n t curves f o r system v a r i a b l e s and predator-prey i s o c l i n e a n a l y s i s as developed by Rosenzweig and MacArthur ( 1 9 6 3 ) . The t h i r d component of the approach i s a s y n t h e s i s of the r e s u l t s of the model analyses and the l i t e r a t u r e review i n t o an i n t e g r a t i v e theory of d e f o l i a t i n g i n s e c t system behavior. I use r e s u l t s from the p r e v i o u s chapters to d e r i v e a g e n e r a l set of r u l e s which can be used to p r e d i c t the temporal behavior of d e f o l i a t i n g i n s e c t systems with a minimum set of i n f o r m a t i o n . T h i s s y n t h e s i s and d e s c r i p t i o n of the i n t e g r a t i v e theory i s provided i n Chapter 6. The f o u r t h component of the approach i s an attempt to i n v a l i d e of the theory. I examine the p r e d i c t i v e c a p a b i l i -t i e s of the i n t e g r a t i v e theory on the other d e f o l i a t i n g i n s e c t systems presented i n the l i t e r a t u r e review. T h i s t e s t i n g i s undertaken using long term p o p u l a t i o n r e c o r d s , F o r e s t I n s e c t Survey records of Canada, and e x t e n s i v e s c i e n -t i f i c summary documents of p a r t i c u l a r case s t u d i e s where they e x i s t . I a l s o d e s c r i b e a p p r o p r i a t e f i e l d experiments which would provide d e f i n i t i v e t e s t s of the theory. T h i s i s provided i n Chapter 7. - 9 -The f i n a l component of the approach i s a c r i t i c a l exam-i n a t i o n of previous t h e o r i e s of d e f o l i a t i n g i n s e c t system s t r u c t u r e and behavior, presented i n Chapter 2, i n the l i g h t of the r e s u l t s of t h i s t h e s i s and the g e n e r a l i n t e g r a t i v e theory I have developed. I conclude by examining the i m p l i -c a t i o n s of my r e s u l t s f o r d e f o l i a t i n g i n s e c t r e s e a r c h or management programs. T h i s c r i t i c a l review and summary i s provided i n Chapter 8. - 10 -2.0 D E F O L I A T I N G I N S E C T S Y S T E M S T R U C T U R E A N D B E H A V I O R : M E T H O D S O F A N A L Y S I S , H I S T O R I C A L T H E O R I E S , A N D P A T T E R N S O F B E H A V I O R 2.1 I n t r o d u c t i o n Chapter 1 suggested the importance of both e q u i l i b r i u m s t r u c t u r e , and of e c o l o g i c a l processes a f f e c t i n g e q u i l i b r i u m s t r u c t u r e , i n determining temporal behavior of d e f o l i a t i n g i n s e c t systems. The o b j e c t i v e s presented i n Chapter 1 a l s o i n d i c a t e d that the i n t e g r a t i v e theory to be developed would u t i l i z e both e q u i l i b r i u m s t r u c t u r e and dynamic e c o l o g i c a l processes i n h e l p i n g to induce temporal behavior. I t i s t h e r e f o r e worthwhile to review the documented p a t t e r n s of d e f o l i a t i n g i n s e c t system behavior, h i s t o r i c a l e f f o r t s at e x p l a i n i n g these behavior, i n terms of e c o l o g i c a l processes hypothesized to be important and i n terms of the e q u i l i b r i u m s t r u c t u r e i m p l i e d by these p r o c e s s e s . T h i s review w i l l help to view the work that f o l l o w s i n proper context and allow comparison of the work with p r e v i o u s attempts at e x p l a i n i n g the behavior of d e f o l i a t i n g i n s e c t systems. T h i s chapter has f o u r s p e c i f i c o b j e c t i v e s : 1. present the methods of a n a l y s i s that w i l l be used i n examining h i s t o r i c a l t h e o r i e s of s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems and i n developing the i n t e g r a t i v e theory; 2. present the e v o l u t i o n of e c o l o g i c a l theory per-t a i n i n g to e q u i l i b r i u m s t r u c t u r e ; - 11 -3. present a review of the documented p a t t e r n s of d e f o l i a t i n g i n s e c t system behavior; and 4. review h i s t o r i c a l t h e o r i e s f o r the s t r u c t u r e and behavior of these systems. 2.2 Methods Of A n a l y s i s 2.2.1 A n a l y s i s Of E q u i l i b r i u m S t r u c t u r e N a t u r a l p o p u l a t i o n s are i n f l u e n c e d by many f a c t o r s . The p r o p o r t i o n a l change i n p o p u l a t i o n s i z e from one genera-t i o n to the next i s the si m p l e s t measure of the i n t e g r a t e d e f f e c t s of a l l f a c t o r s . T h i s p r o p o r t i o n a l change i s c a l l e d " r e c r u i t m e n t " (May 1977, Berryman 1978) and i s a s l i g h t l y d i f f e r e n t use of the term than i n f i s h e r i e s l i t e r a t u r e . F i s h e r i e s s c i e n t i s t s g e n e r a l l y take recruitment to mean the number of l a t e r a d u l t animals produced from a given i n i t i a l number of reproducing a d u l t s ( R i c k e r 1954). The r e l a t i o n -s h i p between recr u i t m e n t and p a r e n t a l p o p u l a t i o n d e n s i t y or s i z e can be g r a p h i c a l l y portrayed as a recru i t m e n t curve ( F i g u r e 1) and t h i s curve r e p r e s e n t s how the i n t e g r a t e d e f f e c t s of a l l f a c t o r s vary with p o p u l a t i o n s i z e . A recrui t m e n t of 1 at a p a r t i c u l a r p o p u l a t i o n l e v e l means that there w i l l , on average, be no change i n p o p u l a t i o n s i z e from one g e n e r a t i o n to the next at that p o p u l a t i o n l e v e l , pro-vided a l l other f a c t o r s a l s o remain constant over time. A recrui t m e n t g r e a t e r than 1 means an i n c r e a s i n g p o p u l a t i o n s i z e , and a recru i t m e n t l e s s than 1 means a d e c r e a s i n g popu-- 12 -f i f P O P U L A T I O N ( N ) F i g u r e 1: R e p r e s e n t a t i v e r e c r u i t m e n t c u r v e s . Curve a c o n t a i n s a s i n g l e s t a b l e e q u i l i b r i u m at f , while curve b c o n t a i n s a s t a b l e e q u i l i b r i u m at f and an unstable e q u i l i b r i u m at u. - 1 3 -l a t i o n s i z e . Consider curve a i n Fig u r e 1 and assume the f o l l o w i n g two c o n d i t i o n s (I w i l l r e l a x these c o n d i t i o n s l a t e r ) : 1. the magnitude of a l l f a c t o r s a f f e c t i n g the popula-t i o n (e.g., h a b i t a t c o n d i t i o n s , predator popula-t i o n s , c l i m a t i c v a r i a b l e s , e t c . ) remains constant; and 2. the e f f e c t of the r a t e of p o p u l a t i o n change, the leng t h of the time l a g s i n any density-dependent p o p u l a t i o n response, and the degree of non-l i n e a r i t y i n the density-dependent response can be ignored. The curve has but one p o i n t , f , at which r e c r u i t m e n t , R, i s 1. At any p o p u l a t i o n s i z e , N, g r e a t e r than f , R<1. Th i s means that any p o p u l a t i o n s i z e which begins as a p o i n t above f w i l l decrease toward f . At any N < f , R > 1. T h i s means that any p o p u l a t i o n s i z e which begins at a l e v e l below f w i l l i n c r e a s e toward f . A l l p o p u l a t i o n s i z e s i n t h i s r e cruitment curve w i l l move toward f and, t h e r e f o r e , f i s a s t a b l e e q u i l i b r i u m (Southwood 1975). Now c o n s i d e r curve b i n Fig u r e 1, and keep the magni-tude of a l l f a c t o r s a f f e c t i n g the p o p u l a t i o n constant, save one. For d i s c u s s i o n purposes, assume that t h i s f a c t o r causes reduced mating success at low p o p u l a t i o n l e v e l s . The same arguments f o r p o p u l a t i o n l e v e l s near f* hold as f o r - 14 -p o i n t f i n curve a. However, at p o p u l a t i o n l e v e l u, R = 1 as w e l l but when N < u, R < 1 and the p o p u l a t i o n l e v e l decreases toward 0. When N > u, R > 1 and the p o p u l a t i o n l e v e l i n c r e a s e s to f 1 . P o p u l a t i o n l e v e l u, then, i s an unstable e q u i l i b r i u m (Southwood 1975). But F i g u r e 1 presents a s t a t i c and u n r e a l i s t i c view of f a c t o r s that a f f e c t p o p u l a t i o n change. The p o s i t i o n of the curve w i l l change when the magnitude of any one process a c t -ing on the p o p u l a t i o n changes. T h i s i s demonstrated i n F i g -ure 2, where the e f f e c t of a changing environment on a popu-l a t i o n i s shown. For the sake of d i s c u s s i o n , i t i s assumed that the e f f e c t i s the same at any l e v e l of p o p u l a t i o n ; that i s , the e f f e c t i s d e n s i t y independent. As the environment becomes l e s s f a v o r a b l e the unstable e q u i l i b r i u m moves to u l from u4 ( F i g u r e 2a). The upper e q u i l i b r i u m s h i f t s to f l from f 4 . Given a s u f f i c i e n t l y severe environment, only p o i n t e w i l l g i v e a p o p u l a t i o n r e c r u i t m e n t of 1 or more. An even more severe environment w i l l lower the r e c r u i t m e n t curve even f u r t h e r , so that a l l r e c r u i t m e n t s are l e s s than 1. The range of i n i t i a l p o p u l a t i o n s i z e s that ensure popu-l a t i o n p e r s i s t e n c e g r a d u a l l y narrows, while the range of i n i t i a l p o p u l a t i o n s i z e s that r e s u l t s i n e x t i n c t i o n gradu-a l l y widens. A s u f f i c i e n t l y severe environment w i l l make any i n i t i a l p o p u l a t i o n l e v e l go to e x t i n c t i o n . Changing processes a c t i n g on a p o p u l a t i o n t h e r e f o r e change the e q u i l i b r i u m s t r u c t u r e of that p o p u l a t i o n by changing the number and p o s i t i o n of p o p u l a t i o n e q u i l i b r i a . - 1 5 -F i g u r e 2: E f f e c t of changing environmental c o n d i t i o n s on p o p u l a t i o n r e c r u i t m e n t . Curves 1 to 5 i n F i g u r e a r e f l e c t the e f f e c t s of an i n c r e a s i n g l y unfavorable environment. The curve i n F i g u r e b i s an i s o r e c r u i t -ment curve and c o n t a i n s a l l p o p u l a t i o n e q u i l i b r i a f o r the range of environmental c o n d i t i o n s . - 1 6 -A summary of the p o s i t i o n of the e q u i l i b r i a as a func-t i o n of the p a r t i c u l a r environmental f a c t o r of concern, shown i n F i g u r e 2b, w i l l be termed an " i s o r e c r u i t m e n t curve" or " i s o c l i n e " f o r the purposes of t h i s t h e s i s . The e q u i l i -brium s t r u c t u r e of a p o p u l a t i o n can be s u c c i n c t l y captured using i s o r e c r u i t m e n t curves. 2 . 2 . 2 A n a l y s i s Of Temporal Dynamics The a n a l y s i s above was conducted i g n o r i n g the r a t e and nature of p o p u l a t i o n change and response. E q u i l i b r i u m s t r u c t u r e cannot by i t s e l f be used to i n d i c a t e what the tem-p o r a l dynamics of a p o p u l a t i o n w i l l be. Knowledge of the r a t e of p o p u l a t i o n change, the l e n g t h of time l a g s i n any density-dependent response, and the degree of n o n - l i n e a r i t y i n the density-dependent response are c r i t i c a l l y important as w e l l (May 1976, May and Oster 1976). In g e n e r a l , popula-t i o n behavior w i l l move from monotonic damping to damped o s c i l l a t i o n s to s u s t a i n e d s t a b l e c y c l e s as the r a t i o of r a t i o of l e n g t h of the time delay i n the e f f e c t of the regu-l a t o r y mechanism to the p o p u l a t i o n r e t u r n time i n c r e a s e s f o r both d i f f e r e n t i a l and d i f f e r e n c e models. In d i f f e r e n c e models, a s u f f i c i e n t l y l a r g e r a t i o w i l l c r e a t e c h a o t i c b ehavior, l a r g e l y i n d i s t i n g u i s h a b l e from random process models (May and Oster 1976), although techniques f o r d i s t i n -g u i s h i n g d e t e r m i n i s t i c behavior i n a p p a r e n t l y c h a o t i c behavior have been developed (e.g., S c h a f f e r and Kot i n p r e s s ) . S h i f t s i n behavior occur a b r u p t l y with s m a l l l - 1 7 -changes i n model parameters, and these s h i f t s are c a l l e d b i f u r c a t i o n s . B i f u r c a t i o n s e x i s t i n the three models analyzed i n Chapters 3 to 5, and these b i f u r c a t i o n s represent the d i f f e r e n t c l a s s e s of d e f o l i a t i n g i n s e c t system behavior. The p o i n t s made above are e s p e c i a l l y r e l e v a n t f o r the analyses of the d i f f e r e n c e models made i n Chapters 3 to 5 of t h i s t h e s i s . Temporal behavior cannot e a s i l y be deduced from by a n a l y z i n g e q u i l i b r i u m s t r u c t u r e , and I w i l l have to use model s i m u l a t i o n s to e x p l a i n model b e h a v i o r s . 2 . 3 The E q u i l i b r i u m S t r u c t u r e Of I n s e c t / F o r e s t Systems A c e n t r a l f e a t u r e of most t h e o r i e s of d e f o l i a t i n g i n s e c t system behavior i s that of s t a b i l i t y of numbers. S t a b l e , low i n s e c t p o p u l a t i o n s are a primary aim of b i o l o g i -c a l c o n t r o l programs (Huffaker et a_l. 1971), and e a r l y popu-l a t i o n models were very much concerned with t h i s concept. Thus, i t i s p o s s i b l e to speak of the " n e u t r a l s t a b i l i t y " of the L o t k a - V o l t e r a model (Lotka 1926, V o l t e r r a 1928), the " g l o b a l i n s t a b i l i t y " of the N i c h o l s o n - B a i l e y model ( N i c h o l -son and B a i l e y 1935) and so on. Voute (1947) f i r s t i ntroduced the concept of " m u l t i p l e s t a b i l i t y " , t h a t i n s e c t s p e c i e s could have s t a b l e numbers at more than one l e v e l by proposing the n o t i o n of an "escape p o i n t " between endemic and epidemic p o p u l a t i o n l e v e l s . Once a p o p u l a t i o n had in c r e a s e d past t h i s escape p o i n t , he argued, i t would be very d i f f i c u l t to prevent i t from reach-- 1 8 -ing epidemic l e v e l s . M o r r i s (1963) proposed that e a s t e r n spruce budworm had a s t a b l e e q u i l i b r i u m at a low p o p u l a t i o n l e v e l and suggested that b i r d p r e d a t i o n may be the m o r t a l i t y agent which c r e a t e s t h i s e q u i l i b r i u m . Takahashi (1964) a p p l i e d M o r r i s ' concepts and suggested v e r t e b r a t e p r e d a t i o n could c r e a t e a s t a b l e e q u i l i b r i u m at a low i n s e c t d e n s i t y . C l a r k (1964), working on C a r d i a s p i n a a l b i t e x t u r a , and Readshaw (1965), working on sap-sucking i n s e c t s , recognized 2 p o p u l a t i o n "modes": one endemic and the other epidemic. H o l l i n g ( 1,965) found that p r e d a t o r s e x h i b i t i n g a sigmoid f u n c t i o n a l response could p o t e n t i a l l y c r e a t e a s t a b l e e q u i l i b r i u m i n the prey popula-t i o n . The concept of the occurrence and r o l e of m u l t i p l e e q u i l i b r i a was f o r m a l i z e d by H o l l i n g (1973) who d e f i n e d " s t a b i l i t y domains" as regions of l o c a l s t a b i l i t y separated by unstable e q u i l i b r i a . Southwood (1975, 1977) and South-wood and Comins (1976) developed an i n s e c t p o p u l a t i o n model with 2 s t a b l e e q u i l i b r i a caused by the e f f e c t s of pre d a t o r s and by i n t r a - s p e c i f i c c o m p e t i t i o n . They maintained that p o p u l a t i o n s of K - s e l e c t e d animals l i v i n g i n r e l a t i v e l y s t a b l e h a b i t a t s should o f t e n be at the upper e q u i l i b r i u m s e t by i n t r a - s p e c i f i c c o m p e t i t i o n , while p o p u l a t i o n s of r -s e l e c t e d animals l i v i n g i n ephemeral environments should s h i f t from e q u i l i b r i u m to e q u i l i b r i u m . They d e s c r i b e d the dynamics of p s y l l i d s ( C l a r k 1964) and European spruce sawfly ( N e i l s o n and Mo r r i s 1964) using t h e i r model. - 1 9 -The concept that m u l t i p l e e q u i l i b r i a e x i s t i n i n s e c t p o p u l a t i o n s has been developed on l a r g e l y t h e o r e t i c a l grounds ( H o l l i n g 1973, May 1977, Berryman 1978, May 1979). E m p i r i c a l evidence i s based l a r g e l y on o b s e r v a t i o n s of pre-d a t i o n e f f e c t s on endemic i n s e c t p o p u l a t i o n d e n s i t i e s (e.g., H o l l i n g 1956, Mason and Torgerson 1977, Campbell and Sloan 1978, Rose and Harmsen 1978). But, the concept i s not unan-imously accepted and v a r i o u s workers argue f o r a l t e r n a t e e x p l a n a t i o n s f o r the same o b s e r v a t i o n s (e.g., Royama 1984). C r i t i c a l f i e l d experiments which would t e s t the m u l t i p l e s t a b i l i t y concept have not been undertaken. I w i l l come back to t h i s p o i n t i n the i n v a l i d a t i o n and summary chapters of the t h e s i s . 2.4 Hypotheses For I n s e c t / F o r e s t System Behavior T h i s s e c t i o n reviews e x i s t i n g t h e o r i e s f o r d e f o l i a t i n g i n s e c t system behavior. I w i l l r e t u r n to the ideas presented here and i n Chapter 3 to examine how t h i s t h e s i s compares with h i s t o r i c a l attempts to understand and e x p l a i n the behavior of these systems. Throughout the f o l l o w i n g d i s c u s s i o n , I w i l l make e x t e n s i v e use of i s o r e c r u i t m e n t curves to present the t h e o r i e s i n a c o n s i s t e n t framework th a t allows f o r easy comparison among them. I w i l l assume, i n u s i n g these curves, that parameter c o n d i t i o n s g i v e r i s e to damped o s c i l l a t i o n s . The techniques of Rosenzweig and MacArthur (1963) w i l l be used i n the a n a l y s i s . 2.4.1 P r e d a t i o n And P a r a s i t i s m - 20 -P r e d a t i o n and p a r a s i t i s m have been c i t e d as important r e g u l a t i n g f a c t o r s of i n s e c t p o p u l a t i o n s ( M i l l e r 1966, B a l -t e n s w e i l e r 1968, Bigger 1973, Holmes et a l . 1979, Hanski and Otronon 1985, Smith 1985). The f i r s t p o p u l a t i o n models (Lotka 1926, V o l t e r a 1928) suggested t h a t p r e d a t o r s and p a r a s i t o i d s could t h e o r e t i c a l l y r e g u l a t e i n s e c t numbers. Ni c h o l s o n and B a i l e y (1935) developed a p o p u l a t i o n model i n which the predator could d r i v e the prey to e x t i n c t i o n and so i t s e l f become e x t i n c t . H a i r s t o n e_t al.. (1961) argued f o r the r o l e of p r e d a t i o n because of the g e n e r a l absence of food d e p l e t i o n by h e r b i v o r e s . I t has been shown that the f u n c t i o n a l response of a predator can be one of 4 types ( H o l l i n g and Buckingham 1976) each of which c o n f e r s d i f f e r e n t e q u i l i b r i u m s t r u c t u r e s to the prey, given no predator numerical response. The t o t a l p redator or p a r a s i t e response ( f u n c t i o n a l p l u s numerical) has very d i f f e r e n t i m p l i c a t i o n s f o r predator dynamics. Three examples ( F i g u r e 3) r e f l e c t d i f f e r e n t s i t u a t i o n s which w i l l be encountered i n the a n a l y s i s of the three s i m u l a t i o n models i n l a t e r c h a p t e r s . The f i r s t ( F i gure 3a) i s f o r a prey p o p u l a t i o n with a s i n g l e s t a b l e s u r f a c e . T h i s s i t u a t i o n c r e a t e s a predator i s o c l i n e which i s always to the r i g h t of the peak of the prey i s o c l i n e and t h e r e f o r e temporal behavior c h a r a c t e r i z e d by dampening o s c i l l a t i o n s . The second ( F i g u r e 3b) i s f o r a prey p o p u l a t i o n which has depensatory m o r t a l i t y caused, say, by a Type II f u n c t i o n a l response. In t h i s s i t u a t i o n , the - 2 1 -o EH < Q pa PREY F i g u r e 3: A l t e r n a t e c o n f i g u r a t i o n s of predatory-prey i s o -r e c r u i t m e n t c u r v e s . Each c r e a t e s d i f f e r e n t s t a b i l i t y p r o p e r t i e s of the system, a - prey has a s i n g l e s t a b l e s u r f a c e . T h i s means that predator and prey p o p u l a t i o n s o s c i l l a t e around the j o i n t e q u i l i b r i u m , b - the prey has a s t a b l e s u r f a c e at high d e n s i t i e s and an unstable s u r f a c e at lower d e n s i t i e s . The prey, followed by the pre d a t o r , can go e x t i n c t i f the j o i n t e q u i l i b r i u m remains on the unstable s u r f a c e , c - the prey has two s t a b l e s u r f a c e s separated by an unstable s u r f a c e . - 22 -p o t e n t i a l e x i s t s f o r the predatory i s o c l i n e to be to the l e f t of the peak of the prey i s o c l i n e . T h i s s i t u a t i o n causes i n c r e a s i n g o s c i l l a t i o n s r e s u l t i n g i n eventual e x t i n c -t i o n of both the prey and the p r e d a t o r . The t h i r d ( F i gure 3c) i s f o r a prey p o p u l a t i o n which has a p o p u l a t i o n i s o c l i n e with two s t a b l e s u r f a c e s separated by an unstable s u r f a c e . T h i s can be caused by, say, a p r e y - s w i t c h i n g predator e x h i b i t i n g a Type I I I f u n c t i o n a l response. The system p e r s i s t s i n t h i s case even though the common e q u i l i b r i u m may be to the l e f t of the peak of the prey i s o c l i n e . The s w i t c h i n g predator c r e a t e s a prey "refuge" at low prey d e n s i t i e s which prevent prey, and t h e r e f o r e , p r e d a t o r , e x t i n c t i o n . 2 . 4.2 N u t r i e n t L i m i t a t i o n And F o l i a g e Q u a l i t y The n u t r i t i o n a l q u a l i t y of p l a n t p a r t s favored by i n s e c t s f o r f e e d i n g has been c i t e d as a mechanism evolved by the p l a n t f o r c o n t r o l l i n g numbers of i t s i n s e c t enemies (Wallner and Walton 1979, Haukioja 1980, Rhoades 1983, 1985). White (1969, 1974, 1976, 1978) maintains that the food resource f o r i n s e c t s i s u s u a l l y n i t r o g e n d e f i c i e n t and t h e r e f o r e n u t r i t i o n a l l y inadequate f o r proper h e r b i v o r e s u r -v i v a l and f e c u n d i t y . White hypothesizes t h a t , when the host p l a n t i s s t r e s s e d through l a c k of water, i t produces r e l a -t i v e l y n i t r o g e n - r i c h f o l i a g e ; consumption of higher q u a l i t y food g i v e s b e t t e r s u r v i v a l of the very young i n s e c t s , usu-a l l y the f i r s t i n s t a r s which i n i t i a t e f e e d i n g . T h i s , i n - 23 -t u r n , leads to higher f e c u n d i t y and in c r e a s e i n numbers. The pas s i n g of drought c o n d i t i o n s leads the p l a n t to be able to produce n i t r o g e n poor food which once again c r e a t e s poor s u r v i v a l f o r e a r l y i n s t a r s and lowered f e c u n d i t y . Haukioja and Hakala (1975) and Rhoades (1985) hypothesize t h a t p l a n t s , r a t h e r than r e g u l a t i n g necessary chemicals f o r i n s e c t growth, r e g u l a t e chemicals i n t h e i r t i s s u e s which are d e t r i m e n t a l to i n s e c t p o p u l a t i o n s . Rhodes d i s t i n g u i s h e s two types of compounds i n the host p l a n t : " q u a l i t a t i v e " com-pounds — compounds of l i m i t e d use a d e f e n s i v e agents but e n e r g e t i c a l l y cheap to manufacture — and " q u a n t i t a t i v e " compounds — e f f e c t i v e d e f e n s i v e compounds which are ener-g e t i c a l l y expensive to make — and argues that changes i n the r e l a t i v e p r o d u c t i o n of each, caused by environmental s t r e s s on the p l a n t , determine i n s e c t s u r v i v a l and t h e r e f o r e p o p u l a t i o n change. The e f f e c t s of changing food q u a l i t y on the e q u i l i b r i u m s t r u c t u r e of an i n s e c t p o p u l a t i o n can be p i c t u r e d as a change i n f o l i a g e abundance and q u a l i t y (Figure 4 ) . In t h i s case, the f o l i a g e i s the prey and the d e f o l i a t o r becomes the pr e d a t o r . U s u a l l y the f o l i a g e q u a l i t y i s too poor f o r good s u r v i v a l and f e c u n d i t y and can onl y support a low p o p u l a t i o n ( F i g u r e 4, curve a ) . The common e q u i l i b r i u m i s at a high f o l i a g e biomass and low d e f o l i a t o r d e n s i t y . When the host p l a n t i s s t r e s s e d by some event or process and i s fo r c e d to produce b e t t e r q u a l i t y food, the resource base can support a higher d e f o l i a t o r d e n s i t y . The predator i s o c l i n e s h i f t s to - 24 -FOLIAGE Fi g u r e 4 : I s o r e c r u i t m e n t curve r e p r e s e n t a t i o n of f o l i a g e q u a l i t y hypotheses. The predator ( i . e . , d e f o l i a t o r ) curve s h i f t s from a to b (endemic to epidemic) as f o l i a g e q u a l i t y improves because a given amount of good q u a l i t y f o l i a g e i s able to support a g r e a t e r number of d e f o l i a t o r s than the same amount of poor q u a l i t y f o l i a g e . P o p u l a t i o n s c y c l e around the e q u i l i b r i a . - 25 -the l e f t i n Fig u r e 4 , to curve b. T h i s causes the common e q u i l i b r i u m to move to a c o n d i t i o n of high d e f o l i a t o r den-s i t y and decreased f o l i a g e biomass. Removal of the s t r e s s on the p l a n t r e - c r e a t e s the c o n d i t i o n s f o r curve a and the p o p u l a t i o n c o l l a p s e s . M c N e i l l and Lawton (1979) pr o v i d e a gene r a l review of the r o l e s of p r e d a t i o n , p a r a s i t i s m , n u t r i e n t a v a i l a b i l i t y , and chemical defense on i n s e c t popu-l a t i o n s . A drawback of the n u t r i e n t / c h e m i c a l r e g u l a t i o n hypotheses i s that the i n s e c t i s regarded as a non-evolving a c t o r i n the dynamics of d e f o l i a t i n g i n s e c t systems. Chang-ing s u s c e p t i b i l i t i e s of i n s e c t s p e c i e s to p l a n t compounds are not c o n s i d e r e d . The s p e c i f i c t h e o r i e s d e s c r i b e d above can t h e r e f o r e not e x p l a i n phenomena such as d i f f e r e n t out-break f r e q u e n c i e s f o r d e f o l i a t o r s with s i m i l a r l i f e h i s -t o r i e s f e e d i n g on the same resource (e.g., e a s t e r n b l a c k -headed budworm and e a s t e r n spruce budworm (McNamee 1977)). A l s o , r e c a l l t h a t the key l i f e h i s t o r y stage i n the food q u a l i t y t h e o r i e s d e s c r i b e d above i s the stage i n which feed i n g i s i n i t i a t e d . Changes i n n u t r i e n t q u a l i t y a f f e c t s u r v i v a l of t h i s stage which then a f f e c t s p o p u l a t i o n l e v e l s . I f t h i s hypothesis i s v a l i d , measures of p o p u l a t i o n change such as p o p u l a t i o n recruitment and f e c u n d i t y should be p o s i -t i v e l y c o r r e l a t e d with the s u r v i v a l r a t e of l a r v a e which i n i t i a t e f e e d i n g . U n f o r t u n a t e l y , very few r e s e a r c h programs have estimated e a r l y l a r v a l s u r v i v a l r a t e s , probably because those stages cause so l i t t l e of the t o t a l d e f o l i a t i o n . - 26 -However, the proper types of data f o r t e s t i n g the food q u a l -i t y hypothesis have been c o l l e c t e d f o r the pine looper (Klomp 1966), European pine sawfly (Lyons et a_l. 1972), and jack pine sawfly (McLeod 1977a). C o r r e l a t i o n s between s u r v i v a l of the f i r s t l a r v a l f e ed-ing stage and f e c u n d i t y , then p o p u l a t i o n recruitment (Table I) are i n c o n c l u s i v e . 3 out of 6 c o r r e l a t i o n s are s i g n i f i -cant at the l e v e l of .05. T h i s i s a crude t e s t but i t does i n d i c a t e that e x i s t i n g data do not support the n u t r i e n t q u a l i t y h y p o t h e s i s . 2.4.3 Q u a l i t a t i v e D i f f e r e n c e s Between I n d i v i d u a l s D i f f e r e n c e s between i n d i v i d u a l s of a p o p u l a t i o n may be important i n causing temporal change i n the d e n s i t y of that p o p u l a t i o n . The h y p o t h e s i s , f i r s t proposed by C h i t t y (1960), i s that s p e c i e s are capable of r e g u l a t i n g t h e i r p o p u l a t i o n l e v e l s with g e n e t i c a l l y and i n t r i n s i c a l l y induced changes i n the v i a b i l i t y of i n d i v i d u a l s i n the p o p u l a t i o n . W e l l i n g t o n (1957, 1960, 1964), working on western tent c a t e r p i l l a r , m o d i f i e d C h i t t y ' s theory f o r western tent c a t e r p i l l a r to be p r i m a r i l y p h y s i o l o g i c a l , r a t h e r than g e n e t i c a l l y based. W e l l i n g t o n found western te n t c a t e r p i l l a r i n d i v i d u a l s could be c l a s s i f i e d i n t o e s s e n t i a l l y two types: a c t i v e and s l u g g i s h . A c t i v e i n d i v i d u a l s have a high f e e d i n g r a t e , are good d i s p e r s e r s and can s u r v i v e w e l l under poor environmen-t a l c o n d i t i o n s . S l u g g i s h i n d i v i d u a l s are the o p p o s i t e . - 27 -Table I: C o r r e l a t i o n s o f f e c u n d i t y and p o p u l a t i o n r e c r u i t m e n t to e a r l y i n s t a r l a r v a l s u r v i v a l f o r three f o r e s t p e s t s . F E C U N D I T Y R E C R U I T M E N T V E R S U S E A R L Y V E R S U S E A R L Y L A R V A L S U R V I V A L L A R V A L S U R V I V A L INSECT DATA SPECIES SOURCE n r p n r p j a c k pine McLeod 3 .148 .027 31 .215 .001 Sawfly (1977a) Pine Klomp 9 .002 >.l 8 .556 .034 Looper (1966) European Lyons 8 " .012 >.l 43 .013 .1 Pine e_t a l . Sawfly (1972) - 28 -Popu l a t i o n s j u s t beginning to i n c r e a s e are composed l a r g e l y of a c t i v e i n d i v i d u a l s which can emigrate and c o l o n i z e other s i t e s and have high recruitment ( F i g u r e 5 ) . Western te n t c a t e r p i l l a r p o p u l a t i o n s i n c r e a s e u n t i l the food resource becomes l i m i t i n g . The p a r t i t i o n i n g of maternal food r e s e r v e s i s unequal so that some of the eggs l a i d i n a popu-l a t i o n which i s f o o d - l i m i t e d c o n t a i n l e s s than o p t i m al food r e s e r v e s . These hatch to become s l u g g i s h i n d i v i d u a l s . The feedback i s perpetuated, with the s l u g g i s h i n d i v i d u a l s hav-ing lower and lower food consumption and producing a higher and higher p r o p o r t i o n of s l u g g i s h i n d i v i d u a l s i n the succeeding g e n e r a t i o n s . The d e t e r i o r a t i o n i n h e a l t h of the p o p u l a t i o n i s exacerbated by a high i n c i d e n c e of disease which develops i n s l u g g i s h i n d i v i d u a l s and spreads to both s l u g g i s h and a c t i v e i n d i v i d u a l s . L o c a l p o p u l a t i o n s eventu-a l l y d e c l i n e to e x t i n c t i o n . The p e r s i s t e n c e of the s p e c i e s over l a r g e areas i s ensured by the f a c t that not a l l s i t e s are i n the same p o i n t i n the p o p u l a t i o n c y c l e . T h i s means that a c t i v e i n d i v i d u a l s always e x i s t to c o l o n i z e l o c a t i o n s which have gone e x t i n c t . A s i m i l a r hypothesis was proposed f o r e x p l a i n i n g the dynam-i c s of the l a r c h budmoth/Alpine l a r c h system ( B a l t e n s w e i l e r 1964). 2 .4.4 Genetic Feedback Pimentel (1961) and Pimentel and Stone (1968) proposed a g e n e t i c feedback mechanism to e x p l a i n f l u c t u a t i o n s i n - 29 -F i g u r e 5:- I s o r e c r u i t m e n t curve r e p r e s e n t a t i o n of the hypothesis of i n d i v i d u a l d i f f e r e n c e s . The i n c r e a s i n g p r o p o r t i o n of s l u g g i s h i n d i v i d u a l s i n the d e f o l i a t o r p o p u l a t i o n s h i f t s the predator curve s h i f t s to the r i g h t , e v e n t u a l l y past f o l i a g e c urve. T h i s causes a c o l -l a pse of the d e f o l i a t o r p o p u l a t i o n . D i s p e r s a l serves to r e c o l o n i z e s i t e s where the d e f o l i a t o r has gone e x t i n c t . - 30 -i n s e c t d e n s i t y . T h i s mechanism operates as a negative feed-back between p a r a s i t o i d - h o s t and/or h e r b i v o r e p l a n t l e v e l s through the e f f e c t s of d e n s i t y on i n t e n s i t y of s e l e c t i o n f o r l e s s t i g h t l y coupled ( i . e . , l e s s e f f i c i e n t p r e d a t i o n ) i n t e r a c t i o n s . T h i s type of mechanism i s thought to be most important when a s p e c i e s i s introduced to a new environment; i n i t i a l v i o l e n t f l u c t u a t i o n s i n p o p u l a t i o n s of the s p e c i e s at both t r o p h i c l e v e l s decrease over time as g e n e t i c feed-back a c t s to weaken the i n t e r a c t i o n between the s p e c i e s (Figure 6 ) . 2.4.5 D i s p e r s a l The processes of d i s p e r s a l have been shown to be impor-tant i n the p o p u l a t i o n dynamics of many f o r e s t d e f o l i a t o r s (Greenbank 1957, Leonard 1970a, 1970b, C l a r k 1979). Huf-f a k e r (1958) using l a b o r a t o r y experiments, and G i l p i n (1975) and H i l b o r n (1976, 1978), using s i m u l a t i o n models, have shown that s p a t i a l h e t e r o g e n e i t y and d i s p e r s a l can s t a b i l -i z e , or at l e a s t allow p e r s i s t e n c e o f , predator and prey p o p u l a t i o n s that are unstable i n l o c a l , s p a t i a l l y homogene-ous areas. The theory of i n d i v i d u a l d i f f e r e n c e s proposed by W e l l i n g t o n (1957, 1960, 1964) r e q u i r e s d i s p e r s a l between s i t e s as a mechanism f o r r e d i s t r i b u t i n g a c t i v e , vigorous i n s e c t s . Ormond (1977) suggests that i n s e c t s whose h a b i t a t d i s t r i b u t i o n i s patchy may have evolved the c a p a c i t y to pro-duce outbreaks to provide a source of i n s e c t s f o r r e d i s t r i -b u t i o n and t h e r e f o r e avoid the consequences of l o c a l e x t i n c -t i o n by p r e d a t o r s . - 3 1 -F i g u r e 6: I s o r e c r u i t m e n t curve r e p r e s e n t a t i o n of the g e n e t i c feedback hypotheses. The s t r e n g t h of the negative feedback between predator and prey p o p u l a t i o n s changes v i a changes i n s e l e c t i o n p r essure through time. T h i s causes dampening o s c i l l a t i o n s to a j o i n t s t a b l e e q u i l i b r i u m from the time of i n t r o d u c t i o n . - 32 -S u f f i c i e n t immigration to a s i t e can swamp any e q u i l i -brium s t r u c t u r e c r e a t e d by l o c a l processes such as p r e d a t i o n (Figure 7 ) . The e f f e c t of a g i v e n l e v e l of immigration w i l l be more pronounced at lower p o p u l a t i o n s i z e s than at high because the e f f e c t i s p r o p o r t i o n a t e l y much g r e a t e r at lower p o p u l a t i o n l e v e l s . The e f f e c t of emigration on l o c a l e q u i l i b r i u m s t r u c t u r e i s more complicated and depends very much on the c h a r a c t e r i s t i c s of the exodus response ( C l a r k 1979). 2.4.5 Density Independent Mechanisms Weather and c l i m a t e have long been thought to determine the p a t t e r n of i n s e c t numbers (Larsson and Tenow 1984, Thom-son et a_l. 1984). The c l a s s i c examples were g i v e n by Andrewartha and B i r c h (1954) who argued that i n s e c t abun-dance was l i m i t e d by the l e n g t h of time c o n d i t i o n s f o r feed-ing and r e p r o d u c t i o n were f a v o r a b l e ; c l i m a t i c f a c t o r s were c i t e d as primary agents a f f e c t i n g the l e n g t h of time a v a i l -able f o r these p r o c e s s e s . White (1969, 1974, 1976, 1978) maintained that the a v a i l a b l e n i t r o g e n i n the food supply, which determines the v i g o r of the p o p u l a t i o n , i s determined l a r g e l y by c l i m a t i c c o n d i t i o n s . Outbreaks of many f o r e s t d e f o l i a t o r s are sometimes preceded by a few g e n e r a t i o n s of weather f a v o r a b l e to the i n s e c t (Greenbank 1956, Stark 1959, Lessard 1974) and c o l l a p s e of i n f e s t a t i o n s o f t e n c o i n c i d e s with unfavorable weather c o n d i t i o n s ( S i l v e r 1960, 1963, Campbell 1979). The e f f e c t of d e n s i t y independent processes on the e q u i l i b r i u m s t r u c t u r e of a p o p u l a t i o n i s simple ( F i g -- 33 -PREY F i g u r e 7: i s o r e c r u i t m e n t curve r e p r e s e n t a t i o n of the e f f e c t s of immigration. The e f f e c t of constant immigration i s most pronounced at low d e n s i t i e s . Immigration t r a n s -forms an unstable j o i n t e q u i l i b r i u m between predator and prey (prey curve a) to a s t a b l e j o i n t e q u i l i b r i u m (prey curve b ) . - 34 -ure 8 ) . Density independent mechanisms a c t e q u a l l y at a l l p o p u l a t i o n l e v e l s and t h e r e f o r e s h i f t the i s o r e c r u i t m e n t curve e q u a l l y at a l l p o p u l a t i o n l e v e l s . These mechanisms cannot be i n v o l v e d i n " c o n t r o l " , " r e g u l a t i o n " , or " l i m i t a -t i o n " i n so f a r as these concepts are d e f i n e d i n terms of feedback mechanisms that act d i f f e r e n t l y at d i f f e r e n t popu-l a t i o n s i z e s . 2 . 4 . 6 E x i s t i n g I n t e g r a t i v e T h e o r i e s - The above s e c t i o n s d e s c r i b e the consequences f o r numer-i c a l behavior of p o p u l a t i o n s a r i s i n g from the e f f e c t s of s i n g l e p r o c e s s e s . But, a number of i n t e g r a t i v e t h e o r i e s e x i s t f o r e x p l a i n i n g the dynamics of p a r t i c u l a r d e f o l i a t i n g i n s e c t systems. For example, the s t u d i e s of W e l l i n g t o n ( 1957, 1960, 1964) and W e l l i n g t o n et. a l . 1975) f o r western ten t c a t e r p i l l a r and of B a l t e n s w e i l e r (1964) and B a l -t e n s w e i l e r et a_l (1977), f o r example, i n t e g r a t e the dynamics of n a t u r a l enemy complexes, p a r t i c u l a r l y d i s e a s e e p i z o o t i c s , e f f e c t s of i n d i v i d u a l d i f f e r e n c e s i n a p o p u l a t i o n , and d i s p e r s a l among s i t e s to e x p l a i n the behavior of these s y s -tems . There are a l s o i n t e g r a t i v e t h e o r i e s which attempt to e x p l a i n the behavior of many d e f o l i a t i n g i n s e c t systems. For example, the s y n o p t i c model of Southwood and Comins (1977) uses p r e d a t i o n ( c r e a t i n g a p o t e n t i a l endemic s t a b l e e q u i l i b r i u m ) , i n t r a - s p e c i f i c c o m p e t i t i o n and h a b i t a t s t a b i l -i t y to e x p l a i n the dynamics of f i v e i n s e c t pest systems. - 35 -F i g u r e 8: I s o r e c r u i t m e n t curve r e p r e s e n t a t i o n of the e f f e c t s of d e n s i t y independent p r o c e s s e s . Density independent processes a c t i n g on the prey s h i f t the prey curve e q u a l l y at a l l p o p u l a t i o n l e v e l s and t h e r e f o r e do not change the e q u i l i b r i u m s t r u c t u r e of the system. - 36 -There are two i n t e g r a t i v e t h e o r i e s f o r the behavior of the e a s t e r n spruce budworm system. C l a r k and H o l l i n g (1979) and C l a r k (1979), using d e t a i l e d analyses of the Green R i v e r , New Brunswick data (Morris 1963), i n t e g r a t e e f f e c t s of i n t r a - s p e c i f i c c o m p e t i t i o n , v e r t e b r a t e p r e d a t i o n , d i s p e r -s a l and d i s p e r s a l e f f e c t s on s u r v i v a l , weather e f f e c t s on s u r v i v a l , and f o l i a g e and f o r e s t dynamics i n t h e i r theory f o r the behavior of- the ea s t e r n spruce budworm system. They maintain that the budworm system i s m u l t i p l y s t a b l e : a low d e n s i t y s t a b i l i t y r e g i o n caused l a r g e l y by avian p r e d a t i o n on l a r g e l a r v a e , and a high d e n s i t y s t a b i l i t y r e g i o n caused by f o l i a g e l i m i t a t i o n . They a l s o m a i ntain that outbreaks are i n i t i a t e d and terminated through the inc r e a s e d d i s p e r s a l s u r v i v a l of f i r s t and second i n s t a r l a r v a e , which i s r e l a t e d to f o r e s t m a t u r i t y and branch s u r f a c e area ( C l a r k 1979). On the other hand, Royama (1984), i n h i s a n a l y s i s of the Green River data, hypothesizes that there i s no low d e n s i t y s t a -b i l i t y r e g i o n , l a r g e l y because the p o p u l a t i o n d e n s i t i e s appear to be more c y c l i c a l than bimodal (Royama 1984, Fig u r e 1). He a l s o hypothesizes that outbreak i n i t i a t i o n and t e r -m ination i s caused by changes i n l a r g e l a r v a l s u r v i v a l which occurs through changes i n p a r a s i t i s m , m i c r o s p o r i d i a , and v i r a l d i s e a s e l e v e l s . A l s o , although I have bounded s p a t i a l dynamics of d e f o l i a t i n g i n s e c t systems out of t h i s t h e s i s , i t i s worth mentioning that these workers agree t h a t a d u l t d i s p e r s a l among areas i s l e s s c r i t i c a l to e x p l a i n i n g budworm p o p u l a t i o n dynamics than are l o c a l , or s i t e , p r o c e s s e s . - 37 -E s s e n t i a l l y , the d i f f e r e n c e i n hypothesized explana-t i o n s f o r l o c a l dynamics of the e a s t e r n spruce budworm sy s -tem, developed with two models u t i l i z i n g e s s e n t i a l l y the same d a t a s e t , c l e a r l y demonstrates the need to use models to develop f i e l d t e s t a b l e t h e o r i e s , and to conduct the f i e l d t e s t s i n an attempt to i n v a l i d a t e the theory (see Chapter 7 ) . The l a c k of a bimodal d i s t r i b u t i o n of budworm popula-t i o n d e n s i t i e s does not mean that a lower s t a b i l i t y r e g i o n caused by b i r d p r e d a t i o n does not e x i s t . A lower s t a b i l i t y r e g i o n (and t h e r e f o r e e q u i l i b r i u m ) may e x i s t , but i t s p o s i -t i o n very l i k e l y s h i f t s i n response to changes i n other a t t r i b u t e s of the system such as f o r e s t growth. The key qu e s t i o n r e l a t e d to the issue of whether the budworm popula-t i o n i s or i s not m u l t i p l y s t a b l e i s not whether the h i s t o r -i c a l data i n d i c a t e lower s t a b i l i t y r e g i o n s , but r a t h e r would the behavior of the budworm p o p u l a t i o n be any d i f f e r e n t i f b i r d p r e d a t i o n d i d not e x i s t . T h i s i s not known, and I out-l i n e what the necessary f i e l d experiment would be to t e s t t h i s i n Chapter 7. S i m i l a r l y , the d i f f e r e n c e s i n hypothesized causes of outbreak i n i t i a t i o n and t e r m i n a t i o n ( l a r g e l a r v a l s u r v i v a l versus s m a l l l a r v a l s u r v i v a l ) can only be c o n c l u s i v e l y t e s t e d with the proper f i e l d manipula-t i o n s . 2 . 5 P a t t e r n s Of I n s e c t / F o r e s t System Behavior I t i s important to compare the behaviors p r e d i c t e d by the i n t e g r a t i v e theory I w i l l develop with r e a l behaviors of d e f o l i a t i n g i n s e c t systems, both i n terms of temporal pat-- 38 -t e r n s and of the processes which g i v e r i s e to the behavior. I conducted a l i t e r a t u r e and data review f o r as many d e f o l i -a t i n g i n s e c t systems as p o s s i b l e to provide the b a s i s f o r comparision. I reviewed 22 d e f o l i a t i n g i n s e c t systems and gathered i n f o r m a t i o n f o r 38 d i f f e r e n t behaviors e x h i b i t e d by these systems. These systems, taken together, r e p r e s e n t examples from a wide range of g e o g r a p h i c a l l o c a t i o n , type of f o r e s t and t r e e s p e c i e s a f f e c t e d , degree of economic impor-tance, and l e v e l of understanding of f a c t o r s important i n system behavior. 2.5.1 Sources of Information and S t r u c t u r e of the Review I used three sources of i n f o r m a t i o n f o r t h i s review: the g e n e r a l f o r e s t entomological l i t e r a t u r e ; d e t a i l e d s c i e n -t i f i c reviews summarizing r e s u l t s of long term s t u d i e s ; and long term i n s e c t p o p u l a t i o n d e n s i t y data c o l l e c t e d e i t h e r as a p a r t of pest surveys or d u r i n g long term r e s e a r c h i n v e s t i -g a t i o n s . Long term p o p u l a t i o n d e n s i t y data e x i s t e d f o r twelve d e f o l i a t i n g i n s e c t systems. The data f o r these s y s -tems are summarized i n Appendix I, while t h e i r data sources are d e s c r i b e d i n Table I I . The f o l l o w i n g i n f o r m a t i o n , i f i t was a v a i l a b l e , was gathered i n order to d e s c r i b e the q u a l i t a t i v e behavior of each system: 1. the primary host t r e e s p e c i e s ; 2. the time p e r i o d of i n t e r e s t . As d e s c r i b e d i n - 39 -Table I I : Sources of i n s e c t p o p u l a t i o n d ata. BCFIDS - B r i t i s h Columbia F o r e s t Insect and Disease Survey; CFS - Canadian F o r e s t S e r v i c e ; USFS - U.S. F o r e s t S e r v i c e SAMPLING METHOD/ SPECIES AGENCY SAMPLING DESCRIPTION D o u g l a s - f i r t r e e - b e a t i n g , H a r r i s (1976) tussock moth BCFIDS H a r r i s and Brown (1976) European Pine i n t e n s i v e f i e l d Lyons e t a l . (1970) Sawfly p l o t s , CFS European Spruce t r e e - b e a t i n g , N e i l s o n and Sawfly CFS Mo r r i s (1964) Green-Striped t r e e - b e a t i n g , H a r r i s (1976) F o r e s t Looper BCFIDS H a r r i s and Brown (1976) Gypsy Moth egg mass Campbell surveys, USFS and Sloan (1978) Jack Pine i n t e n s i v e f i e l d McLeod (1972, 1975) Sawfly p l o t s , CFS Larch t r e e - b e a t i n g , H a r r i s (1976) Sawfly BCFIDS H a r r i s and Brown (1976) i n t e n s i v e f i e l d Turnock (1972) p l o t s , CFS Pine long term pupal Klomp (1966) Looper surveys Saddlebacked t r e e - b e a t i n g , H a r r i s (1976) Looper BCFIDS H a r r i s and Brown (1976) Western t r e e - b e a t i n g , H a r r i s (1976) Blackheaded BCFIDS H a r r i s and Brown (1976) Budworm Western t r e e - b e a t i n g , H a r r i s (1976) F a l s e Hemlock BCFIDS H a r r i s and Brown (1976) Looper Western Hemlock Looper t r e e - b e a t i n g , BCFIDS H a r r i s (1976) H a r r i s and Brown (1976) - 40 -Chapter 1, many d e f o l i a t i n g i n s e c t systems have e x h i b i t e d d i f f e r e n t behaviors d u r i n g d i f f e r e n t time i n t e r v a l s ; 3. the g e o g r a p h i c a l l o c a t i o n of i n t e r e s t . As d e s c r i b e d i n Chapter 1, many d e f o l i a t i n g i n s e c t systems e x h i b i t d i f f e r e n t behaviors i n d i f f e r e n t p a r t s of i t s range; 4. the len g t h of time between outbreaks; 5 . the d u r a t i o n of outbreaks; 6. f a c t o r s which have been i n f e r r e d i n the d e c l i n e of outbreaks; 7. any other f a c t o r s which have been i m p l i c a t e d i n determining the dynamics of the system; and 8. the e f f e c t of outbreaks on the host f o r e s t . The d u r a t i o n of outbreaks was determined from r e p o r t s i n the l i t e r a t u r e and from the r e s u l t s of s p e c t r a l analyses done on the d a t a s e t s f o r twelve d e f o l i a t i n g i n s e c t systems (Jenkins and Watt 1968, summarized i n Appendix I ) . The MIDAS s t a t i s t i c a l package was used to conduct these s p e c t r a l analyses (Fox and Guire 1976). 2 . 5 . 2 R e s u l t s There are four d i f f e r e n t c a t e g o r i e s of outbreak p e r i o d -i c i t i e s represented i n these systems (Table I I I ) : Table I I I : Patterns of i n s e c t / f o r e s t system behavior. References f o r i n f o r m a t i o n provided are l i s t e d i n Table IV. * - f o r a l l documented behavior; - no outbreaks; 1MMMI - c o n t i n u a l outbreaks; A - no m o r t a l i t y ; B - m o r t a l i t y p r i m a r i l y i n suppressed t r e e s ; C - m o r t a l i t y i n suppressed t r e e s and some he a l t h y t r e e s ; D - m o r t a l i t y i n healthy and suppressed t r e e s ; ?? - i n f o r m a t i o n not known; blank - information provided elsewhere i n t a b l e or not necessary. Second set of numbers under outbreak p e r i o d r e f e r s to p e r i o d i c i t y c a l c u l a t e d by s p e c t r a l a n a l y s i s (Appendix I ) . PEST LOCATION PRIMARY PERIOD HOST OF SPECIES INTEREST CAUSES OUTBREAK OF OTHER FOREST PERIOD LENGTH DECLINE FACTORS EFFECTS i D o u g l a s - f i r Tussock Moth Eastern Hemlock Looper Eastern Blackheaded Budworm Eastern Blackheaded Budworm western North America NFLD New Brunswick New Brunswick Douglas-f i r ,grand f i r , white f i r e astern hemlock balsam f i r balsam f i r 8 - 1 2 8 - 1 6 1 2 - 1 6 1 2 - 1 6 2 - 3 2 - 3 v i r u s starva-t i o n v i r u s p ara-s i t e s b i r d s and s p i d e r s ?? b i r d s ?? D B Table I I I : continued PRIMARY PERIOD CAUSES HOST OF OUTBREAK OF OTHER FOREST PEST LOCATION SPECIES INTEREST PERIOD LENGTH DECLINE FACTORS EFFECTS Eastern Spruce Budworm Eastern Spruce Budworm Eastern Spruce Budworm Eastern Spruce Budworm eastern North America ea s t e r n North America NFLD pure white spruce stands balsam f i r , white spruce balsam f i r , white spruce balsam f i r , white spruce white spruce before 1952 a f t e r 1952 20-90 5-11 8-16 3-6 10-15 4-6 s t a r v a - b i r d s t i o n , para-poor s i t e s l a r v a l d i s p e r s a l high f o l i a g e l e v e l s main-t a i n e d c o o l , wet c l i m a t e low spruce v u l n e r a -b i l i t y to d e f o l i a t i o n B B Table I I I : continued PRIMARY PERIOD CAUSES HOST OF OUTBREAK OF OTHER FOREST PEST LOCATION SPECIES INTEREST PERIOD LENGTH DECLINE FACTORS EFFECTS European Pine Sawfly European Spruce Sawfly European Spruce Sawfly On t a r i o , eastern Europe New Brunswick New Brunswick Green-Striped western F o r e s t Looper North Gypsy Moth America Mass. a l l pines white spruce white spruce Douglas-f i r white oak before 1938 a f t e r 1938 before 1923 8-12 9 1(111(11 4 4 8-10 7-16 11111(11 2-3 2-3 2-3 v i r u s i n t r o -duced v i r u s i n t r o -duced pa r a -s i t e s i n t r o -duced v i r u s small mammals small mammals small mammals b i r d s B B Table I I I : continued PEST LOCATION PRIMARY HOST SPECIES PERIOD OF INTEREST OUTBREAK PERIOD LENGTH CAUSES OF DECLINE OTHER FACTORS FOREST EFFECTS Gypsy Moth Mass. Gypsy Moth Jack Pine Budworm Jack Pine Sawfly Jack Pine Sawfly Jack Pine Sawfly eastern Europe Manitoba, Ontario Quebec Quebec Quebec white oak white oak jack pine jack pine jack pine jack pine a f t e r 1923 6-8 5- 9 6- 10 6-8 6-8 9 •?•? 2- 3 3- 4 1-3 1-3 v i r u s , p a r a -s i t e s v i r u s p a r a -s i t e s v i r u s , s t a r v a -t i o n b i r d s b i r d s , small mammals, co o l c l i m a t e B B A A D 4^ Table I I I : continued PEST LOCATION PRIMARY HOST SPECIES PERIOD OF INTEREST OUTBREAK PERIOD LENGTH CAUSES OF DECLINE OTHER FACTORS FOREST EFFECTS Larch Budmoth Larch Sawfly Larch Sawfly Larch Sawfly Larch Sawfly Swiss Alps North America c e n t r a l North America c e n t r a l North America c e n t r a l North America A l p i n e l a r c h tamarack before 1910 tamarack 1910-1932 tamarack 1932-1955 tamarack a f t e r 1955 10 15-20 6-8 6-8 6-8 1-2 7-10 2-3 2-3 2-3 f o l i a g e q u a l i t y , para-s i t e s ?? para-s i t e s p a ra-s i t e encapsu-l a t i o n new p a r a s i t e i n t r o -d u c t i o n ?? ?? b i r d s , small mammals B B A B Table I I I : continued PRIMARY PERIOD CAUSES HOST OF OUTBREAK OF OTHER FOREST PEST LOCATION SPECIES INTEREST PERIOD LENGTH DECLINE FACTORS EFFECTS Larch Sawfly Pine B u t t e r f l y Saddle-backed Looper Spruce Budmoth Western Blackheaded Budworm B r i t i s h Columbia western North America Pine Looper Germany western North America New Brunswick western North America western l a r c h Ponderosa pine a l l pines western hemlock white spruce western hemlock 1974 to present 12-16 10-20 10-16 8-16 10-16 8- 12 9- 14 11111111 8-16 6-16 2-3 2-3 2-3 2-3 2-3 para -s i t e s p a ra-s i t e s p a r a -s i t e s , f o l i a g e q u a l i t y ?? ?? B B B B Table I I I : continued PRIMARY PERIOD CAUSES HOST OF OUTBREAK OF OTHER FOREST PEST LOCATION SPECIES INTEREST PERIOD LENGTH DECLINE FACTORS EFFECTS Western F a l s e Hemlock Looper Western Hemlock Looper Western Spruce Budworm Western Spruce Budworm Western Tent C a t e r p i l l a r western North America western North America western North America Vancouver I s l a n d Vancouver Island Douglas-f i r western hemlock Douglas-f i r , grand f i r , sub-a l p i n e f i r Douglas-f i r , grand f i r , sub-a l p i n e f i r Garry oak 1 0 - 1 6 1 0 - 1 2 6 - 1 1 6 - 1 4 1 2 - 2 0 5 - 3 3 8 - 1 2 2 - 3 2 - 3 5 - 1 0 2 - 3 v i r u s , i n d i v i -d ual d i f f e r -ences b i r d s , ants ?? d i s p e r s a l B B B B Table I I I : continued PEST LOCATION PRIMARY HOST SPECIES PERIOD OF INTEREST OUTBREAK PERIOD LENGTH CAUSES OF DECLINE OTHER FACTORS FOREST EFFECTS Winter Moth Nova S c o t i a red oak before 1958 K111111 11 11 B Winter Moth Nova S c o t i a red oak a f t e r 1958 6-8 2-3 par a -s i t e s A Winter Moth England oaks * 6-8 2-3 para-s i t e s s mall mammals A - 49 -Table IV: L i t e r a t u r e sources used i n documenting p a t t e r n s of i n s e c t / f o r e s t system behavior (Table I I I ) . INSECT LITERATURE USED D o u g l a s - f i r tussock moth Eastern Hemlock Looper Eastern Blackheaded Budworm Eastern Spruce Budworm European Pine Sawfly European Spruce Sawfly G r e e n - s t r i p e d F o r e s t Looper Gypsy Moth Jack Pine Budworm Jack Pine Sawfly Sugden (1957), Brookes et a l . (1979), Tunnock (1973), M o r r i s (1963), Clendenon (1975), Mason and Torgerson (1977), Shepherd and Otvos (1986) Mason and Torgerson ( i n p r e s s ) , Mason (1981), Mason and Torgerson (1983) Wickman ( 1986a,b), Wickman et. a l . ( 1986) C a r r o l l (1954), Canada (1939 to present) M i l l e r (1966), M i l l e r and M a r s h a l l (1970), Canada (1939 to present) Morris (1963), B l a i s (1968, 1974), M i l l e r (1975), C l a r k (1979), C l a r k and H o l l i n g (1979), M o rris (1958), Wotton and Jones (1975), Canada (1939 to present) Lyons et a l . (1972) N e i l s o n and M o r r i s (1964), Balch and B i r d (1944) Dawson (1970), Evans (1962) Bess (1961), Campbell and Sloan (1978), Campbell et a l . (1977), Kaya (1976), Maksimovic (1953), Simionescu (1973) Canada (1939 to present) McLeod (1972, 1974, 1975, 1976b), T r i p p (1965) - 50 -Table IV: continued INSECT LITERATURE USED Larch Budmoth Larch Sawfly Pine B u t t e r f l y Pine Looper Saddlebacked Looper Spruce Budmoth Western Blackheaded Budworm Western F a l s e Hemlock Looper Western Hemlock Looper Western Spruce Budworm Western Tent C a t e r p i l l a r Winter Moth B a l t e n s w e i l e r (1968), B a l t e n s w e i l e r e t a l . (1977), F i s c h l i n and B a l t e n s w e i l e r (1977) Canada (1939 to p r e s e n t ) , Turnock (1972), Graham (1952), Coppel and L e i u s (1955) Cole (1971), Weaver (1961), F u r n i s s and C a r o l i n (1977) Klomp (1966), V a r l e y (1949) S i l v e r (1961), Canada (1939 to present) Carrow (1985) Canada (1939 to p r e s e n t ) , McCambridge and Downing (1960) K l e i n and Minnoch (1969), Canada (1939 to present) F u r n i s s and C a r o l i n (1977), Canada (1939 to present) Johnson and Denton (1975), Canada (1939 to p r e s e n t ) , Torgerson and Campbell (1982), Campbell and Torgerson (1983), Campbell et. a_l. (1983) Canada (1939 to p r e s e n t ) , W e l l i n g t o n (1957, 1960, 1964) Embree (1965), Cuming (1961), Canada (1939 to p r e s e n t ) , V a r l e y and Gradwell (1965), H a s s e l l (1976) - 5 1 -1. a l a c k of outbreaks; 2. a c o n t i n u a l outbreak; 3. s p o r a d i c outbreaks; and 4. outbreaks ranging i n p e r i o d i c i t y from 2 years to about 90 y e a r s . The preponderance of outbreak p e r i o d i c i t i e s appear to be at 6-12 years (or 6-12 d e f o l i a t o r g e n e r a t i o n s i n the case of d i v o l t i n e d e f o l i a t o r s ) . V i r a l d i s e a s e or p a r a s i t i s m are f a c t o r s most o f t e n i m p l i c a t e d i n the d e c l i n e of outbreaks, although s t a r v a t i o n of d e f o l i a t o r s i s mentioned o f t e n as a ca u s a l mechanism f o r outbreak d e c l i n e . Other f a c t o r s , such as f o l i a g e q u a l i t y and i n d i v i d u a l d i f f e r e n c e s are c i t e d , although much l e s s o f t e n than the above f a c t o r s . Host f o r e s t s g e n e r a l l y s u f f e r e i t h e r l i t t l e or no mor-t a l i t y from outbreaks or very heavy m o r t a l i t y . Furthermore, the type of host damage i n c u r r e d does not seem to depend on the outbreak p e r i o d i c i t y . F o r e s t s i n systems which have experienced c o n t i n u a l outbreaks can experience l i t t l e mor-t a l i t y (e.g., gypsy moth) while f o r e s t s i n systems which experience s p o r a d i c outbreaks can s u f f e r very heavy m o r t a l -i t y (e.g., e a s t e r n hemlock l o o p e r , D o u g l a s - f i r tussock moth) . A l s o , jack pine can s u f f e r very heavy m o r t a l i t y when d e f o l i a t e d by jack pine sawfly, but only moderate m o r t a l i t y when d e f o l i a t e d by jack pine budworm. - 52 -P r e d a t i o n , p a r t i c u l a r l y v e r t e b r a t e p r e d a t i o n by b i r d s and small mammals, i s c i t e d very o f t e n as a f a c t o r which i n f l u e n c e s d e f o l i a t o r p o p u l a t i o n s . In most systems i n which i t i s understood, v e r t e b r a t e p r e d a t i o n has the g r e a t e s t e f f e c t on the d e f o l i a t o r at low p o p u l a t i o n l e v e l s . The p i c t u r e from t h i s review, t h e r e f o r e , i s one of a small number of d i f f e r e n t c l a s s e s of d e f o l i a t o r p o p u l a t i o n behavior, a l b e i t with a wide v a r i e t y of outbreak p e r i o d i c i -t i e s . A l s o , i t appears that o n l y a small set of v a r i a b l e s and processes have been i m p l i c a t e d i n the dynamics of d e f o l i a t o r p o p u l a t i o n s : a d e f o l i a t o r whose dynamics i s i n f l u e n c e d by s t a r v a t i o n , v e r t e b r a t e p r e d a t i o n , p a r a s i t i s m , and v i r a l d i s e a s e s . The f a c t o r s which i n f l u e n c e the dynam-i c s of the f o r e s t are l e s s c e r t a i n . - 53 -3.0 THE EASTERN BLACKHEADED BUDWORM SYSTEM 3.1 I n t r o d u c t i o n Chapter 2 d e s c r i b e d the methods of a n a l y s i s which w i l l be used i n t h i s t h e s i s , provided an overview of some of the important h i s t o r i c a l t h e o r i e s f o r the behavior of i n s e c t / f o r e s t systems, and d e s c r i b e d the types of behavior e x h i b i t e d by i n s e c t / f o r e s t systems. T h i s and the f o l l o w i n g two chapters develop evidence which w i l l be used to develop the i n t e g r a t i v e theory f o r the behavior of i n s e c t / f o r e s t systems. T h i s evidence i s i n the form of d e t a i l e d analyses of three d e f o l i a t i n g i n s e c t systems and models: the e a s t e r n blackheaded budworm; the e a s t e r n spruce budworm; and the jack pine sawfly. 3.2 The Eas t e r n Blackheaded Budworm System Eas t e r n blackheaded budworm i s a n a t i v e d e f o l i a t i n g i n s e c t of the e a s t e r n North American c o n i f e r o u s f o r e s t . I t s favored host t r e e i s balsam f i r , Abies balsamea; i t w i l l a l s o feed on white spruce, P i c e a g l a u c a , i n l a t e r i n s t a r s but i t does not s u r v i v e w e l l on other t r e e s p e c i e s ( M i l l e r 1966). The budworm i s found from northern Manitoba south and east to Newfoundland (McCambridge and Downing 1960). Inten-s i v e p o p u l a t i o n s t u d i e s commenced on blackheaded,budworm as an o f f s h o o t to the Green R i v e r e a s t e r n spruce budworm pro-j e c t i n New Brunswick i n the 1950s and 1960s. No management a c t i v i t i e s have been d i r e c t e d at t h i s d e f o l i a t o r , although - 54 -po p u l a t i o n s of the i n s e c t have undoubtedly been a f f e c t e d by the a p p l i c a t i o n of i n s e c t i c i d e s f o r c o n t r o l of eastern spruce budworm i n New Brunswick. 3.2.1 Documented Behavior The system has e x h i b i t e d e s s e n t i a l l y two d i f f e r e n t types of behavior (Canada 1939 to 1982, M i l l e r 1966, Table I I I ) . F i r s t , outbreaks have been observed r e g u l a r l y i n the Maritimes s i n c e the e a r l y 1900s. A l l recorded outbreaks have f o l l o w e d a s i m i l a r p a t t e r n . P o p u l a t i o n s i n c r e a s e to outbreak l e v e l s every 12 to 16 years and p e r s i s t at these high l e v e l s f o r 2 to 4 y e a r s . These outbreaks cause heavy d e f o l i a t i o n and consequent growth r e d u c t i o n of mature host t r e e s . However, they cause very l i t t l e m o r t a l i t y of mature o v e r s t o r y timber. P a r a s i t i s m r a t e s are u s u a l l y low i n a l l p a r t s of the i n s e c t p o p u l a t i o n c y c l e except i n the d e c l i n i n g years of outbreaks, when r a t e s may reach 80% to 97% ( M i l l e r 1966). A second type of behavior occurs over much of the geo-g r a p h i c a l range of the i n s e c t . In these areas the i n s e c t i s r e g u l a r l y recovered i n F o r e s t Insect Survey samples, but p e r s i s t e n t l y remains at endemic l e v e l s . N a t u r a l l y , i n these areas, d e f o l i a t i o n i s low and there i s no t r e e damage. - 55 -3.3 System D e s c r i p t i o n 3.3.1 The D e f o l i a t o r The l i f e h i s t o r y of e a s t e r n blackheaded budworm has been d e s c r i b e d by s e v e r a l authors (Morris 1958, McCambridge and Downing 1960, M i l l e r 1966). The i n s e c t i s u n i v o l t i n e . Eggs are l a i d i n the e a r l y f a l l and the budworm passes the winter as a d i a p a u s i n g egg. F i r s t i n s t a r l a r v a l emergence occurs i n l a t e May the f o l l o w i n g year. There are f i v e f e e d -ing l a r v a l i n s t a r s and pupation occurs i n l a t e J u l y i n the s i t e s where the f i f t h i n s t a r l a r v a e l a s t f e d . The i n s e c t p r e f e r s the c u r r e n t year's f o l i a g e but w i l l feed on o l d e r f o l i a g e i f necessary. Some l a r v a l drop and d i s p e r s a l has been observed ( M i l l e r 1966) but i t does not appear to be an o b l i g a t o r y process f o r the s p e c i e s . A d u l t moth d i s p e r s a l has a l s o been o c c a s i o n a l l y observed ( M i l l e r 1966) but i t s importance i n the s p a t i a l dynamics of the p o p u l a t i o n are not known. 3.3.2 N a t u r a l Enemies A l a r g e complex of p a r a s i t o i d s p e c i e s has been recovered from e a s t e r n blackheaded budworm ( M i l l e r 1966). P a r a s i t i s m r a t e s have been recorded to vary from 3% i n the e a r l y stages of an outbreak to 97% i n the d e c l i n e phase of i n f e s t a t i o n s . A s p e c i e s of Ascogaster appears to be the most important s p e c i e s , as i t i s the most common sp e c i e s recovered d u r i n g outbreak d e c l i n e s . B i r d p r e d a t i o n has been e x t e n s i v e l y s t u d i e d (Gage e_t - 56 -a l . 1970, M i l l e r and Mook 1970). Avian p r e d a t i o n occurs on a l l l i f e stages of the budworm, but i s concentrated on the l a r g e f i f t h i n s t a r and pupal stages. Avian p r e d a t i o n r a t e s are much higher at low budworm d e n s i t i e s than at high ( M i l l e r and Mook 1970). 3.3.3 The F o r e s t and F o l i a g e Balsam f i r i s the dominant t r e e s p e c i e s of the b o r e a l f o r e s t of e a s t e r n North America and i s a co-dominant s p e c i e s , along with white, red, and black spruce, of the ea s t e r n North American c o n i f e r o u s f o r e s t (Bakuzis et a l . 1965). Balsam f i r i s a shade t o l e r a n t s p e c i e s (Bakuzis et a l . 1965), and appears to e x i s t on a " p a t h o l o g i c a l r o t a t i o n " of 70 to 100 years (Marchand 1984) and d e c l i n e of balsam f i r from b i o t i c or a b i o t i c events occurs i n mature stands from e a s t e r n spruce budworm ( B l a i s 1968), wind (Sprugel 1976) or root d i s e a s e s and r o t s (Blum et. al_. 1983). Removal of the o v e r s t o r y i n p a t h o l o g i c a l r o t a t i o n d r a m a t i c a l l y i n c r e a s e s growth of p r e v i o u s l y suppressed balsam f i r ( B l a i s 1952). Balsam f i r and white spruce r e t a i n approximately e i g h t year c l a s s e s of f o l i a g e . The complement of new f o l i a g e f l u s h e s i n l a t e A p r i l or e a r l y May, very near the time e a s t e r n blackheaded budworm emerge from diapause. White spruce f o l i a g e f l u s h e s approximately 2 weeks l a t e r than b a l -sam f i r ( M i l l e r 1963) . 3.4 Model D e s c r i p t i o n An i n i t i a l s i m u l a t i o n model of the dynamics of the - 57 -system was c o n s t r u c t e d as p a r t of a bac c a l a u r e a t e t h e s i s (McNamee 1977, pp. 80-100). The model was subsequently r e v i s e d and e l a b o r a t e d ; a summary of the f i n a l model i s given i n McNamee (1979). 3.4.1 S p a t i a l And Temporal C h a r a c t e r i s t i c s The model mimics system behavior i n a uniform stand of balsam f i r l a r g e enough that p o p u l a t i o n l o s s e s or ga i n s due to i n s e c t movement i n t o and out of the stand are n e g l i g i b l e . Budworm h a b i t a t w i t h i n the stand i s d e s c r i b e d i n square meters of branch s u r f a c e area. F o r e s t and f o l i a g e dynamics are simulated a n n u a l l y but most of the i n t e r a c t i o n s between budworm and i t s environment occur on s p e c i f i c i n s t a r s d u r i n g the model year. 3 . 4 . 2 F o r e s t Dynamics The model uses the f o r e s t and f o l i a g e submodels developed by Jones (1977a) f o r the eas t e r n spruce budworm s i m u l a t i o n model. The r a t i o n a l e f o r t h i s i s that both d e f o l i a t o r s occupy the same f o r e s t h a b i t a t , p r e f e r the same host t r e e s p e c i e s and age c l a s s e s of f o l i a g e , and feed on the host s p e c i e s at s i m i l a r time of the year (McNamee 1977). Responses of the f o l i a g e and the f o r e s t to the same l e v e l s of d e f o l i a t i o n by both f o r e s t i n s e c t s i s t h e r e f o r e l i k e l y to be s i m i l a r , assuming there are no d i f f e r e n c e s i n t r e e response f o r a giv e n l e v e l of d e f o l i a t i o n by e i t h e r budworm. The f o r e s t i s represented as 75 age c l a s s e s of host t r e e s Each tr e e age c l a s s i s c h a r a c t e r i z e d by three r e l e v a n t - 58 -a t t r i b u t e s : the p r o p o r t i o n of the land area i t occupies (Jones 1977a, p.101); the branch s u r f a c e area per acre of f o r e s t i f each acre were e n t i r e l y i n t r e e s of that age c l a s s (Jones 1977a, p. 103); and s u s c e p t i b i l i t y of the age c l a s s to m o r t a l i t y from budworm d e f o l i a t i o n (Jones 1977a, p. 113). Trees l e s s than 22 years of age are assumed to be immune to budworm a t t a c k . The r a t i o of e x i s t i n g branch s u r f a c e area to the branch s u r f a c e area of a 40 year o l d stand i s used as a measure of the degree of f o r e s t m a t u r i t y . F o r e s t growth i s simulated by an n u a l l y aging the age c l a s s p a r c e l s of land a f t e r accounting f o r n a t u r a l and budworm-induced m o r t a l i t y . Aging i n v o l v e s changes i n branch area, while area occupied by an age c l a s s changes only due to m o r t a l i t y . A l l m o r t a l i t y i s placed i n t o the youngest age c l a s s , implying immediate r e g e n e r a t i o n . The f r a c t i o n of t r e e s k i l l e d by budworm i n each age c l a s s i s a f u n c t i o n of the a g e - s p e c i f i c f o r e s t s u s c e p t i b i l -i t y from budworm m o r t a l i t y (Jones 1977a, p.113) and the d e f o l i a t i o n s t r e s s caused by budworm d e f o l i a t i o n (Jones 1977a, p.112). Older f o r e s t age c l a s s e s have a higher sus-c e p t i b i l i t y to m o r t a l i t y to budworm d e f o l i a t i o n , while younger age c l a s s e s are completely immune to d e f o l i a t i o n and t h e r e f o r e to t h i s m o r t a l i t y . A l s o , d e f o l i a t i o n s t r e s s does not begin to occur u n t i l o l d f o l i a g e biomass begins to d e c l i n e . 3.4.3 F o l i a g e Dynamics - 59 -Although balsam f i r and white spruce r e t a i n a p p r o x i -mately 8 year c l a s s e s of f o l i a g e (Bakuzis e_t a_l. 1965), the model c o n s i d e r s o n l y dynamics of two c l a s s e s : c u r r e n t year's f o l i a g e ; and an aggregated c l a s s of o l d f o l i a g e (1+ years o l d ) . F o l i a g e i s measured i n r e l a t i v e u n i t s , as p r o p o r t i o n of maximum p o s s i b l e new f o l i a g e biomass per m of branch. Non-susceptible age c l a s s e s are assumed to always have a f u l l complement of f o l i a g e . New f o l i a g e biomass f o r sus-c e p t i b l e f o r e s t age c l a s s e s produced at the s t a r t of each year i s p r o p o r t i o n a l to the t o t a l f o l i a g e biomass l e f t at the end of the pre v i o u s year (Jones 1977a, p.107). Old f o l i a g e biomass i s updated using density-dependent s u r v i v a l f u n c t i o n s f o r remaining o l d and new f o l i a g e (Jones 1977a, p. 107). Old f o l i a g e dynamics are s t r u c t u r e d so t h a t a tre e w i l l r e t a i n a higher p r o p o r t i o n of i t s new f o l i a g e as d e f o l -i a t i o n i n c r e a s e s . The f o r e s t , i n e f f e c t , compensates f o r d e f o l i a t i o n by r e t a i n i n g a higher p r o p o r t i o n of remaining f o l i a g e from the c u r r e n t year. New f o l i a g e l e v e l s i n budworm s u s c e p t i b l e age c l a s s e s are mod i f i e d to account f o r the re c r u i t m e n t of newly s u s c e p t i b l e age c l a s s e s , using a branch s u r f a c e area-weighted average of f o l i a g e biomass i n the s u s c e p t i b l e and newly s u s c e p t i b l e age c l a s s e s . 3.4.4 Insect Dynamics Base P o p u l a t i o n Parameters M i l l e r (1966) presents a s u r v i v o r s h i p curve f o r eastern blackheaded budworm and documents unpublished f i n d i n g s of - 60 -other workers on budworm m o r t a l i t y r a t e s . The a d u l t , egg, e a r l y l a r v a l , and pupal stages are c h a r a c t e r i z e d by r e l a -t i v e l y low and constant m o r t a l i t y r a t e s . The l a r g e l a r v a l stage i s c h a r a c t e r i z e d by h i g h l y v a r i a b l e m o r t a l i t y r a t e s . M i l l e r (1966) a t t r i b u t e s the changes i n l a r g e l a r v a l m o r t a l -i t y to avian p r e d a t i o n and p a r a s i t i s m . I t i s impossible to disaggregate the p u b l i s h e d l a r g e l a r v a l s u r v i v a l r a t e s i n t o "predator and p a r a s i t o i d induced" and " n a t u r a l " . The p u b l i s h e d r a t e s , however, were taken from s t u d i e s done i n mature f o r e s t stands i n an i n t e r -outbreak p e r i o d . P a r a s i t i s m r a t e s are l i k e l y to have been low ( M i l l e r 1966) and avian p r e d a t i o n l e v e l s are a l s o l i k e l y lower than i n younger stands ( S e c t i o n 3.4.5). I t h e r e f o r e adopted the r a t e s from M i l l e r (1966) as b a s e l i n e s u r v i v a l r a t e s (Table V) . The sex r a t i o of a d u l t s i s r e l a t i v e l y constant i n non-outbreak s i t u a t i o n s ( M i l l e r 1966). Although evidence from other i n s e c t / f o r e s t systems i n d i c a t e the sex r a t i o would l i k e l y change under c o n d i t i o n s of low f o l i a g e because female l a r v a e must consume g r e a t e r amounts of f o l i a g e f o r egg development (Brookes e_t a_l 1979, Doane and McManus 1981, M o r r i s 1963), I assumed i t remains constant, i r r e s p e c t i v e of the c o n d i t i o n of the budworm (Table V ) . M i l l e r (1966) p u b l i s h e d a number of f e c u n d i t y estimates f o r the budworm i n non-outbreak s i t u a t i o n s i n a s e r i e s of stands. The mean of these f e c u n d i t i e s i s used as the max-- .61 -Table V: B a s e l i n e p o p u l a t i o n parameters f o r e a s t e r n blackheaded budworm. Parameters d e r i v e d from M i l l e r (1966). PARAMETER VALIJF 1. Egg S u r v i v a l Rate 0.85 2. Small L a r v a l S u r v i v a l Pate 0.60 3. Large L a r v a l S u r v i v a l Rate 0.25 4. Pupal S u r v i v a l Rate 0.71 5. A d u l t S u r v i v a l Rate 1.0 6. A d u l t Sex Ra t i o 0.53 7. Maximum Fe c u n d i t y 88 8. B a s e l i n e Generation S u r v i v a l (product o f 1 through 6) 0.048 9. B a s e l i n e P o p u l a t i o n Recruitment (product o f 1 through 7) 4.22 - 62 -imum f e c u n d i t y i n the model (Table V ) . This assumes that n u t r i t i o n a l c o n d i t i o n s f o r budworm w i l l be most f a v o r a b l e at low p o p u l a t i o n l e v e l s . Weather e f f e c t s on budworm are simulated by randomly v a r y i n g the l a r g e l a r v a l s u r v i v a l between 0.76 and 1.29 as i s done i n the e a s t e r n spruce budworm model (Jones 1977a, p. 121). The b a s e l i n e g e n e r a t i o n s u r v i v a l i s 0.048 and the max-imum r e c r u i t m e n t , the product of the g e n e r a t i o n s u r v i v a l and maximum f e c u n d i t y , i s 4.22, given the s u r v i v a l r a t e s , sex r a t i o , and maximum f e c u n d i t y (Table V ) . T h i s means t h a t , i n the absence of any other f a c t o r s , budworm p o p u l a t i o n s i n the model w i l l i n c r e a s e approximately 4 - f o l d per year. Feeding And Feeding E f f e c t s E astern blackheaded budworm meets most of i t s f o l i a g e requirements f o r maturation i n the l a s t l a r v a l stage. M i l l e r (1966) r e p o r t s lowered l a r v a l s u r v i v a l and f e c u n d i t y at high p o p u l a t i o n l e v e l s . I n t r a - s p e c i f i c c o m p e t i t i o n i s hypothesized to be the cause of these two phenomena. The feeding submodel i s a predator-prey model. I t i s assumed that an i n d i v i d u a l l a r v a has a f u n c t i o n a l response to i t s "prey", the f o l i a g e . T h i s response i s shaped by the requirements of the l a r v a f o r maintenance, growth, and r e p r o d u c t i o n . Competition among l a r v a e f o r f o l i a g e m o d i f i e s t h i s response. - 63 -The instantaneous f u n c t i o n a l response i s : q = m, where (1) q i s the per l a r v a consumption of f o l i a g e ; and m i s the number of f o l i a g e u n i t s ( S e c t i o n 3.4.3) r e q u i r e d by a l a r v a f o r s u r v i v a l and maximum growth and r e p r o d u c t i o n . Equation 1 i m p l i e s that food requirements are constant over a l l f o l i a g e d e n s i t i e s . The t o t a l food requirement (A) of the whole p o p u l a t i o n (N) i s t h e r e f o r e : A = (q) (N), where * 2^ No estimates of q are a v a i l a b l e from previous work on b l a c k -headed budworm. I e l e c t e d to use an estimate m o d i f i e d from the e a s t e r n spruce budworm model. Eas t e r n spruce budworm i s assumed to r e q u i r e .0074 f o l i a g e u n i t s . q f o r blackheaded budworm was estimated as: q = .00 74HCW b h b / HCW e s b, where (3) HCW i s the l a s t i n s t a r head capsule width f o r each s p e c i e s . HCW i s 1.36 mm ( M i l l e r 1966) and HCW i s 1.44 mm (Morris 1963); q i s set to .007. Equation 3 assumes a l i n e a r r e l a -t i o n s h i p between food requirements and head capsule width, - 64 -e v e n t h o u g h t h e r e l a t i o n s h i p i s l i k e l y t o be a l l o m e t r i c . T h i s i s a . r e a s o n a b l e a s s u m p t i o n , s i n c e t h e d i f f e r e n c e s i n h ead c a p s u l e w i d t h b e t w e e n t h e s p e c i e s i s l e s s t h a n 6%. A random c o m p e t i t i o n m o d e l , a n a l o g o u s t o t h a t d e v e l o p e d by Thompson ( 1 9 2 4 ) f o r p a r a s i t o i d s , i s u s e d t o compute r e a l i z e d i n t a k e o f f o l i a g e : E = F (1 - e " A / F ) , w h e r e ( 4 ) E i s t h e u n i t s o f f o l i a g e consumed by a l l l a r -v a e ; and F i s t h e f o l i a g e d e n s i t y . E q u a t i o n 4 i s a p p l i e d t w i c e , f i r s t f o r f e e d i n g on new f o l i -age and s e c o n d f o r f e e d i n g on o l d f o l i a g e w h i c h o c c u r s i f f o o d r e q u i r e m e n t s have n o t been met by c o n s u m p t i o n o f new f o l i a g e . The budworm p o p u l a t i o n ' s f o o d r e q u i r e m e n t s f o r o l d f o l i a g e (A') a r e : A' = A - E ( 5 ) and o l d f o l i a g e ( F ' ) c o n s u m p t i o n (E ' ) i s c a l c u l a t e d a s : E' = F' (1 - e " A ' / F ' ) (6) T h e r e a r e no d a t a i n t h e l i t e r a t u r e on t h e e x a c t r e l a -t i o n s h i p b e t w e e n t h e q u a n t i t y o f f o l i a g e consumed and - 65 -s u r v i v a l and f e c u n d i t y f o r e a s t e r n blackheaded budworm. I assumed both r e l a t i o n s h i p s to be simple l i n e a r ones. T h e r e f o r e , l a r g e l a r v a l s u r v i v a l i s mo d i f i e d f o r s t a r v a t i o n e f f e c t s by: s = (E + 0.8E')/(qN), where ( 7) s i s a s u r v i v a l r a t e a p p l i e d to l a r g e l a r v a e , and •8 i s a p r o p o r t i o n to account f o r the assumed lower q u a l i t y of o l d e r f o l i a g e to budworm. A c t u a l f e c u n d i t y , b, i s c a l c u l a t e d by: b = sB, where (8) B i s the maximum p o s s i b l e f e c u n d i t y (Table V ) . 3.4.5 N a t u r a l Enemy Dynamics  P a r a s i t i s m The m a j o r i t y of p a r a s i t o i d s p e c i e s which respond numer-i c a l l y to changing blackheaded budworm d e n s i t i e s attack the young l a r v a e and emerge from the l a r g e l a r v a e ( M i l l e r 1966). Of these, a s p e c i e s of Ascogaster appears to be the most important. I modelled the dynamics of t h i s s p e c i e s and assumed i t to be r e p r e s e n t a t i v e of the g u i l d of p a r a s i t o i d s t h a t a t t a c k small l a r v a e and emerge from l a r g e ones. - 66 -U n f o r t u n a t e l y , I could f i n d no data on the bionomics of the s p e c i e s . Cox (1928) presents a d e t a i l e d a n a l y s i s of the b i o l o g y and behavior of a c o n s p e c i f i c , Ascogaster carpo- capse. The b i o l o g y and behavior of t h i s p a r a s i t o i d was used as a surrogate f o r the s p e c i e s that a t t a c k s budworm. The model of p a r a s i t o i d dynamics i s very simple. The number of a d u l t female p a r a s i t o i d s a t t a c k i n g e a r l y budworm l a r v a e i n year t (P*. ) i s given by: aTN tp a t-1 t-1 P =. S S, N t p h t-1 N t-1 1 -1 + ahN t-1 N t - 1 k where (9) i s the number of host l a r v a e i n year t-1; i s the s u r v i v a l r a t e of budworm from the time of p a r a s i t o i d a t t a c k to p a r a s i t o i d progeny emergence; and i s the s u r v i v a l r a t e of p a r a s i t o i d s from emergence to at t a c k ( i n c l u d e s sex r a t i o ) ; i s the r a t e of s u c c e s s f u l search by the p a r a s i t o i d f o r budworm; i s the t o t a l time the p a r a s i t o i d searches f o r budworm; i s the handling time, or the time taken by the p a r a s i t o i d from the beginning of attack to the resumption of search; and - 67 -k i s the d i s p e r s i o n c o e f f i c i e n t of the negative binomial d i s t r i b u t i o n . Equation 9 i s an instantaneous f u n c t i o n a l response, a com-p e t i t i o n submodel to account f o r s u p e r - p a r a s i t i s m e f f e c t s ( G r i f f i t h s and H o l l i n g 1969, Mace et. a_l. 1978), and a s e r i e s of s u r v i v a l f u n c t i o n s which compute the number of a t t a c k i n g p a r a s i t o i d s from the number of p a r a s i t i z e d budworm i n the prev i o u s g e n e r a t i o n . S i s c a l c u l a t e d i n the d e f o l i a t o r submodel from n a t u r a l and s t a r v a t i o n m o r t a l i t y . Budworm feedi n g r a t e s and s u s c e p t i b i l i t y to other forms of p r e d a t i o n are assumed to be the same f o r p a r a s i t i z e d and non-p a r a s i t i z e d h o s t s . :The F u n c t i o n a l Response I used the Type 2 f u n c t i o n a l response form r e p r e s e n t a -t i v e of a predator s e a r c h i n g f o r a s i n g l e prey type ( H o l l i n g 1959 , but see H a s s e l l e_t a l . 1977) because Ascogaster i s capable of causing heavy m o r t a l i t y to i t s host ( M i l l e r 1966) and i s t h e r e f o r e l i k e l y to be monophagous and an o b l i g a t o r y p a r a s i t o i d of the budworm ( P r i c e 1975). H o l l i n g (1965) and McLeod (1976) show that the func-t i o n a l response parameters can be estimated from simple b i o -l o g i c a l knowledge about the behavior of the predator and prey. Ascogaster females are l o n g - l i v e d with a mean l i f e span of 36 days. The a d u l t s search only by day; I set T to 288 hours, assuming 8 hours per day i s spent searching (J.M. McLeod, pe r s . comm.). The p a r a s i t o i d f e c u n d i t y i s 360 eggs - 68 -(Cox 1928). T h i s means that h, the handling time, i s 288/360 hours, or 0.8 hours. H o l l i n g (1965) showed that a can be estimated by: (V) (D) (PR) (PA), where (10) V i s the v e l o c i t y of the p a r a s i t o i d while s e a r c h i n g ; D i s the r e a c t i v e f i e l d of the p a r a s i t o i d , the d i s t a n c e w i t h i n which prey r e c o g n i t i o n can occur; PR i s the p r o b a b i l i t y the prey w i l l be recog-nized once i t i s i n the p a r a s i t o i d ' s r e a c t i v e f i e l d ; and PA i s the p r o b a b i l i t y of attack once the prey has been r e c o g n i z e d . The p a r a s i t o i d , when se a r c h i n g f o r h o s t s , walks along the branch of the t r e e , tapping i t s antennae on the f o l i a g e . When i t touches a l a r v a i t stops, taps the l a r v a with i t s antennae, turns around, and o v i p o s i t s i n the host. Antennae are .0043 meters long and extend to the s i d e of the female (Cox 1928). Thus the r e a c t i v e f i e l d , D, g i v e n that search i s t a c t i l e , i s .0086 meters. J.M. McLeod (p e r s . comm.) has observed s i m i l a r - s i z e d p a r a s i t o i d s s e a r c h i n g f o r prey i n a s i m i l a r manner and estimates speed of search, V, to be 20 to 90 meters per hour. He a l s o estimates t h a t , f o r s i m i l a r p a r a s i t o i d s he has observed, the p r o b a b i l i t y of a t t a c k , PR, i s 0.1 to 0.3. Cox's (1928) d e s c r i p t i o n of o v i p o s i t i o n i n d i c a t e s that the a d u l t female i s p e r s i s t e n t i n her attack i n t h at she w i l l continue s e a r c h i n g f o r the host even i f e a r l i e r attempts have f a i l e d ; I set PA to 1.0. A f e a s i b l e range f o r a can now be d e f i n e d using Equation 10: (90) ( .0086) ( .3)( 1 .0) = .23 ( 20)( .0086)( .1)( 1.0) = .017 Equation 10 only c a l c u l a t e s t o t a l p a r a s i t o i d eggs o v i -p o s i t e d per square meter of branch area. Cox (1928) s t a t e s t h a t , although o n l y one egg i s o v i p o s i t e d i n each a t t a c k , the a d u l t female p a r a s i t o i d does not d i s c r i m i n a t e between unattacked and p r e v i o u s l y attacked h o s t s . A l s o , only one p a r a s i t o i d progeny emerges from each host, i r r e s p e c t i v e of the number of p a r a s i t o i d eggs l a i d i n that host. Therefore host l a r v a e p a r a s i t i z e d does not equal p a r a s i t o i d eggs o v i -p o s i t e d . I used a c o mpetition submodel developed by G r i f -f i t h s and H o l l i n g (1969) to c a l c u l a t e the number of l a r v a e p a r a s i t i z e d , g i v e n the number of p a r a s i t o i d eggs o v i p o s i t e d (Equation 9). The frequency d i s t r i b u t i o n of a t t a c k s by i n d i v i d u a l p a r a s i t o i d s are needed to a c c u r a t e l y estimate k, the d i s p e r -s i o n c o e f f i c i e n t of the a t t a c k d i s t r i b u t i o n ; such data do not e x i s t f o r A scogaster.. I chose a range of k values from 0.5 to 1.5 (J.M. McLeod, p e r s . comm.). - 70 -S u r v i v a l of p a r a s i t o i d progeny remains to be estimated. Cox (1928) g i v e s no estimate of t h i s , nor does he r e p o r t where or how emerged p a r a s i t o i d s e x i s t over the w i n t e r . I assumed a constant d a i l y m o r t a l i t y i n the range of 0.5% to 1%. Emergence occurs about 270 days before a t t a c k the f o l -lowing s p r i n g ; p a r a s i t o i d progeny s u r v i v a l r a t e i s t h e r e f o r e 0.07 to 0.26. I know of no f i e l d s t u d i e s which can be used to more a c c u r a t e l y estimate t h i s parameter. A summary of p a r a s i t o i d p o p u l a t i o n dynamics parameters used i n the model i s given i n Table VI; these values are used i n the f o l l o w i n g analyses unless otherwise s p e c i f i e d . The values f o r search r a t e , d i s p e r s i o n c o e f f i c i e n t , and p a r a s i t o i d s u r v i v a l r a t e are means of the ranges i d e n t i f i e d above. Avian P r e d a t i o n The equation used to represent avian p r e d a t i o n e f f e c t s i s : 3 B. A. N D I. — - , where (11) i = l , -c.N q. + e 1 g,c,A are parameters of " F u j i i " f u n c t i o n a l response form (Mace et a l . 1978); D i s the number of days budworm i s preyed upon; and B . l i s the number of b i r d s per square meter of - 7 1 -Table VI: P a r a s i t o i d dynamics parameters. Values below are used unless otherwise s t a t e d . PARAMETER VALUE 1. T o t a l Time Spent Searching 288 hours 2. Handling Time 0.8 hours 3. Rate o f S u c c e s s f u l Search .124 m2 4. D i s p e r s i o n C o e f f i c i e n t Of 1.0 Att a c k D i s t r i b u t i o n 5. P a r a s i t o i d Progeny S u r v i v a l Rate .16 - 72 -b r a n c h . T h i s f o r m c a l c u l a t e s an i n s t a n t a n e o u s a t t a c k r a t e u s i n g t h e f u n c t i o n a l r e s p o n s e e q u a t i o n , and u s e s t h e a t t a c k r a t e i n an e x p l o i t a t i o n e q u a t i o n t o a p p r o x i m a t e d e p l e t i o n o f p r e y t h r o u g h t h e s e a s o n (D d a y s ) . I assumed t h a t a l l p r e d a t i o n l o s s e s o c c u r r e d on l a r g e l a r v a e b e f o r e p a r a s i t o i d e m e r g e n c e , b u t t h a t t h e a t t a c k p e r i o d c o v e r e d t h e e n t i r e l a r g e l a r v a l and p u p a l s t a g e . A v i a n p r e d a t o r s a r e assumed t o s e a r c h a v o l u m e o f f o l i a g e ; t h a t i s , t h e y f l y among t h e t r e e c r o w n s s e a r c h i n g f o r budworm. T h e r e f o r e , b i r d d e n s i t y p e r s q u a r e m e t e r o f b r a n c h c h a n g e s w i t h c h a n g i n g f o r e s t b i o m a s s . The e a s t e r n s p r u c e budworm m o d e l u s e s t o t a l b r a n c h s u r f a c e a r e a f o r c r o w n v o l u m e ; I u s e t h e same m e t r i c t o d e r i v e B: B. = M. / SURF, w h e r e ( 1 2 ) 1 1 M i s t h e number o f b i r d s p e r a c r e ; and i SURF i s t h e s q u a r e m e t e r s o f b r a n c h s u r f a c e a r e a p e r a c r e . Gage e_t a l ^ . ( 1970) r e p o r t e d o b s e r v i n g no n u m e r i c a l r e s p o n s e by t h e b i r d c o m p l e x t o c h a n g i n g budworm d e n s i t i e s . I t h e r e -f o r e u s e d t h e b i r d d e n s i t i e s g i v e n i n H o l l i n g ( u n p u b l . manus.) f o r e s t i m a t e s o f M. F u n c t i o n a l r e s p o n s e d a t a have been c o l l e c t e d f o r some - 73 -b i r d s p e c i e s f e e d i n g on e a s t e r n blackheaded budworm (Gage et a l . 1970, M i l l e r and Mook 1970). On 8 sampling days i n each of J u l y and August of 1965, 1966, and 1967 i n a stand of mature balsam f i r c o n t a i n i n g approximately 24,000 square meters of branch s u r f a c e area per a c r e , b i r d s were shot and t h e i r stomach contents analyzed. Simultaneously, the den-s i t y of blackheaded budworm l a r v a e or pupae i n the stands was estimated by sampling a mid-crown branch from 300 t r e e s . Nine b i r d s p e c i e s were considered s u f f i c i e n t l y abundant to c o n s i d e r i n t h e i r a n a l y s i s . The raw data g i v e the number of mandibles (from l a r v a e ) and cremasters (from pupae) per b i r d stomach. I converted these to a t t a c k s per b i r d per day by the f o l l o w i n g formula from Gage et al_. ( 1970): K ( MAN / 2 + CRE), where ^ 1 MAN, CRE are the number of mandibles ( 2 / l a r v a ) and cremasters (1 per pupa) recovered from the b i r d stomachs; and K i s a f a c t o r (= 9.14) to convert stomach sam-p l e s to estimates of consumption i n an 8 hour p e r i o d . The above uses " s u c c e s s f u l " a t t a c k i n f o r m a t i o n (gut contents) to d e r i v e " a t t a c k " i n f o r m a t i o n (number of a t t a c k s ) . The l a r v a l and pupal stage of blackheaded budworm - 74 -are present f o r about a month. I have, i n t h i s d e r i v a t i o n , assumed that attack i n f o r m a t i o n over a d a i l y p e r i o d i s , i n r e l a t i v e terms, instantaneous when compared to the e n t i r e p r e d a t i o n p e r i o d . T h i s may not be v a l i d i f the b i r d popula-t i o n can s i g n i f i c a n t l y d e p l e t e l o c a l budworm p o p u l a t i o n s i n l e s s than a s i n g l e day. I w i l l come back to t h i s assumption below. The f u n c t i o n a l response data gathered by M i l l e r and Mook (1970) are presented i n Fig u r e 9. I f i t t e d equation 11, s c a l e d to a t t a c k s per b i r d per day, to the data i n F i g -ure 9 using n o n - l i n e a r parameter e s t i m a t i o n , minimizing the sums of squares of the d e v i a t i o n s between the estimated f u n c t i o n and the data. The r e s u l t s are shown as the s o l i d l i n e i n Fig u r e 9. The f i t i s not a good one. I t should be noted that the parameter estimates d e r i v e d using t h i s procedure may be h i g h l y b i a s e d . The independent v a r i a b l e i n Fig u r e 9, budworm d e n s i t y , was not known with c e r t a i n t y , but was estimated with sampling. T h i s i s a t y p i c a l " e r r o r s i n v a r i -a b l e s " problem f o r which the measurement e r r o r s i n the independent v a r i a b l e w i l l tend to make the response ( b i r d f e e d i n g r a t e ) appear independent of i t . In t h i s case, the parameter e s t i m a t i o n overestimates the r a t e of e f f e c t i v e search (the slope of the ascending limb of the response) and underestimates the maximum at t a c k r a t e (the asymptote of the response). - 75 -Budworm Prey/m Branch Figure 9: Functional response of birds to eastern blackheaded budworm. Points are from M i l l e r and Mook (1970); s o l i d l i n e i s f i t t e d curve using Equation 11. - 76 -A summary of nominal parameter values f o r avian preda-t i o n used i n the f o l l o w i n g analyses i s given i n Table V I I . With these parameters, the maximum d a i l y p r e d a t i o n r a t e i n a mature f o r e s t with 24,000 square meters of branch s u r f a c e area i s 6% of the budworm p o p u l a t i o n . I t i s 13.5% i n a f o r e s t with 10,000 square meters of branch s u r f a c e area ( t h i s i s a 10 year o l d f o r e s t i n the budworm model). B i r d s can d e p l e t e t h e i r prey p o p u l a t i o n q u i c k l y i n an immature stand. The assumption that d a i l y s u c c e s s f u l attack informa-t i o n can be used to d e r i v e an instantaneous f u n c t i o n a l response i s t h e r e f o r e reasonable f o r mature f o r e s t s but becomes more tenuous i n younger stands. 3.5 Model E q u i l i b r i u m S t r u c t u r e I w i l l now d e s c r i b e the r o l e of p a r t i c u l a r processes i n shaping the e q u i l i b r i u m s t r u c t u r e d e s c r i b e d above. A l l v a r i a b l e s p l o t t e d i n the f i g u r e s are per m2 of branch sur-face area. 3.5.1 The D e f o l i a t o r The budworm recruitment curve with a l l processes i n c l u d e d ( F i g u r e 10a) has 2 p o t e n t i a l s t a b l e e q u i l i b r i a ; one at very low d e n s i t i e s , the other at very high d e n s i t i e s , separated by an unstable e q u i l i b r i u m . Avian p r e d a t i o n on budworm c r e a t e s the p o t e n t i a l lower s t a b l e e q u i l i b r i u m because that e q u i l i b r i u m disappears when avian p r e d a t i o n i s removed from the model (Figure 10b). The p o t e n t i a l unstable e q u i l i b r i u m disappears when a l l p a r a s i t o i d s are removed from - 77 -Table V I I : Avian p r e d a t i o n parameters f o r e a s t e r n blackheaded budworm model. See Equation 11 f o r e x p l a n a t i o n o f parameters. PARAMETER VALUE 1. D e n s i t y 10.2/acre 2. A 11.42 3. g 9.21 4. c .58 5. Feeding P e r i o d 28 days - 78 -F i g u r e 10: Recruitment curves f o r e a s t e r n blackheaded budworm. a - a l l processes i n c l u d e d , b - a v i a n p r e d a t i o n removed. c - avian p r e d a t i o n and p a r a s i t i s m removed. d - with changing p a r a s i t o i d d e n s i t i e s ; top l i n e has i n t r a - s p e c i f i c c o m p e t i t i o n removed. - 79 -the model ( F i g u r e 10c). The d i p i n the recru i t m e n t curve at low budworm d e n s i t i e s , t h e r e f o r e , i s caused by avian preda-t i o n and p a r a s i t i s m , while the e x i s t e n c e of the lower poten-t i a l s t a b l e e q u i l i b r i u m i s caused by avian p r e d a t i o n alone. The upper s t a b l e e q u i l i b r i u m disappears when a l l e f f e c t s of i n t r a - s p e c i f i c c o m petition (lowered l a r v a l sur-v i v a l and a d u l t female f e c u n d i t y ) are removed from the model (top l i n e i n Fig u r e l O d ) . I n t r a - s p e c i f i c competition c r e a t e s the upper s t a b l e e q u i l i b r i u m f o r budworm. However, budworm i n the r e a l world, and i n the model, are not faced with a constant environment. For example, i n s e c t r e c r u i t m e n t i s dependent upon p a r a s i t i s m r a t e s which are i n tu r n a f u n c t i o n of a d u l t female p a r a s i t o i d d e n s i t y (Equation 9 ) . Changing p a r a s i t o i d d e n s i t i e s changes the p o s i t i o n of the recruitment curve ( F i g u r e l O d ) . I n c r e a s i n g p a r a s i t o i d d e n s i t i e s lower the recru i t m e n t curve while d e c r e a s i n g p a r a s i t o i d d e n s i t i e s r a i s e i t . The e f f e c t i s most pronounced at low budworm d e n s i t i e s because of the depensatory nature of the p a r a s i t i s m process ( S e c t i o n 2.4.1) . An i s o r e c r u i t m e n t curve of budworm as a f u n c t i o n of a d u l t p a r a s i t o i d d e n s i t y ( F i g u r e 11) shows the i n s e c t curve has 2 s t a b l e s u r f a c e s , an upper and lower, separated by an unstable s u r f a c e ; these correspond d i r e c t l y to the a p p r o p r i a t e e q u i l i b r i a of F i g u r e 10a. Two p o i n t s i n Fig u r e 11 w i l l be of i n t e r e s t i n f u r t h e r - 80 -10000 1000 100 . 0) to to 10 -.1 41 .01 P a r a s i t o i d A d u l t s F i g u r e 1 1 : Budworm i s o r e c r u i t m e n t curve as a f u n c t i o n o f p a r a s i t o i d d e n s i t y , m i s maximum p a r a s i t o i d d e n s i t y f o r epidemic budworm; n i s minimum p a r a s i t o i d d e n s i t y f o r endemic budworm. - 8 1 -a n a l y s e s : p o i n t m, the p a r a s i t o i d d e n s i t y above which the upper s t a b l e s u r f a c e f o r budworm d i s a p p e a r s , and p o i n t n, the p a r a s i t o i d d e n s i t y below which the lower s t a b l e s u r f a c e f o r budworm d i s a p p e a r s . 3.5.2 The P a r a s i t o i d The p a r a s i t o i d e q u i l i b r i u m s t r u c t u r e ( F i g u r e 12) has a s i n g l e s t a b l e s u r f a c e . The bending over of the s u r f a c e at high p a r a s i t o i d d e n s i t i e s i s caused by i n c r e a s i n g super-p a r a s i t i s m r a t e s with high p a r a s i t o i d d e n s i t i e s (Appendix I I ) , simulated using a com p e t i t i o n equation ( G r i f f i t h s and H o l l i n g 1969). The p o s i t i o n of the s u r f a c e i s s e t by the numerical response of the p a r a s i t o i d to budworm d e n s i t i e s and i s determined by four parameters (Equation 9 ) : p a r a s i -t o i d f e c u n d i t y ; r a t e of s u c c e s s f u l search; p a r a s i t o i d pro-geny s u r v i v a l from the time of emergence from the host to the time of a t t a c k the f o l l o w i n g g e n e r a t i o n ; and the d i s p e r -s i o n c o e f f i c i e n t of a t t a c k s . The e f f e c t s of a l t e r n a t e parameter values on e q u i l i b r i u m s t r u c t u r e and model behavior w i l l be d i s c u s s e d i n S e c t i o n 3.10. 3.5.3 The F o l i a g e The e q u i l i b r i u m s t r u c t u r e f o r the f o l i a g e i n r e l a t i o n to budworm d e n s i t y ( F i g u r e 13) i s complicated. There i s a s t a b l e s u r f a c e at high f o l i a g e biomass (Figure 13a) and a lower s t a b l e s u r f a c e with low branch d e n s i t y ( i . e . , young f o r e s t s ) which changes i n t o an unstable s u r f a c e as branch d e n s i t y i n c r e a s e s . F o l i a g e e q u i l i b r i u m s t r u c t u r e i s depen-- 82 -100 EGGS F i g u r e 12: P a r a s i t o i d r e c r u i t m e n t curve as a f u n c t i o n o f budworm d e n s i t y . The bending o f the curve i s caused by the c o m p e t i t i o n equation (Appendix I I ) . - 83 -1 0 0 0 0 1 0 . 0 1 E G G S / m B R A N C H Figure 13: Foliage isorecruitment curves as a function of budworm density. a - for three forest types, b - with low, model, and high old foliage natural mortality. c - with low, model, and high new foliage natural mortality. - 84 -dent on branch d e n s i t y because i t i s assumed that budworm do not a t t a c k t r e e s l e s s than 21 years o l d (Jones 1977a). These age c l a s s e s provide a refuge of f u l l f o l i a g e . T h i s refuge forms a l a r g e p r o p o r t i o n of the t o t a l f o r e s t f o l i a g e when the f o r e s t i s young but decreases as branch d e n s i t y i n c r e a s e s . The dynamics of o l d f o l i a g e (Jones 1977a, p. 109) are the primary processes which c r e a t e the upper s t a b l e s u r f a c e f o r f o l i a g e i n the model (F i g u r e 13b). Changing new f o l i a g e dynamics has no observable i n f l u e n c e on the f o l i a g e e q u i l i b r i u m s t r u c t u r e (Figure 13c). 3.5.4 The F o r e s t The branch area e q u i l i b r i u m s t r u c t u r e i n r e l a t i o n to f o l i a g e biomass co n t a i n s a s i n g l e s t a b l e s u r f a c e ( F i g u r e 14). The maximum branch s u r f a c e area i s s e t by the amount of branch s u r f a c e area at each age (Jones 1977a, p. 103, Figu r e 14a). The slope of the i s o r e c r u i t m e n t curve i s set by the s u s c e p t i b i l i t y to m o r t a l i t y of the f o r e s t (Jones, 1977a, p. 114) (Figure 14b). Lower s u s c e p t i b i l i t y to low f o l i a g e l e v e l s means that the f o r e s t w i l l be able to keep a high branch d e n s i t y with heavy r e d u c t i o n s i n f o l i a g e . 3.6 Processes Which Keep Budworm C h r o n i c a l l y Endemic Ea s t e r n blackheaded budworm remains at low p o p u l a t i o n l e v e l s f o r many years i n many p a r t s of i t s range (Canada 1939 to 1982, M i l l e r 1966, Table I I I ) . In t h i s s e c t i o n , I w i l l demonstrate the c o n d i t i o n s i n the model which can give r i s e to t h i s type of behavior. Such behavior w i l l occur i f - 85 -1 0 J 1 0 3 . 8 2 F O L I A G E U N I T S / m B R A N C H F i g u r e 1 4 : F o r e s t i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f f o l i a g e d e n s i t y . a - w i t h l o w , m o d e l , a n d h i g h b r a n c h s u r f a c e a r e a g r o w t h r a t e , b - w i t h l o w , m o d e l , a n d h i g h s u s c e p t i b i l i t y t o m o r t a l i t y f r o m d e f o l i a t i o n . - 8 6 -the p o i n t n of Fig u r e 11 i s moved to the extreme r i g h t and past the maximum or minimum value of any v a r i a b l e d e f i n i n g the X a x i s . Poor weather c o n d i t i o n s , (poorer than that d e f i n e d as "normal" i n the model, S e c t i o n 3.4.4) low branch d e n s i t y , high p a r a s i t o i d d e n s i t i e s and low f o l i a g e biomass can move p o i n t n to the f a r r i g h t of the i s o r e c r u i t m e n t curves ( F i g -ure 15) and t h e r e f o r e have the p o t e n t i a l to keep budworm numbers endemic. But, the p a r a s i t o i d d e n s i t y r e q u i r e d (about .04/m2 branch, from Fi g u r e 15c) to keep budworm numbers on the lower s t a b l e s u r f a c e (about 3 budworm eggs/m 2 branch, p o i n t o i n Fig u r e 15c) cannot be supported by such, an "endemic" number of budworm (F i g u r e 12), as 3 budworm/m2 branch can support only .015 p a r a s i t o i d s / m 2 b r a n c h ( F i g u r e 12) . 3.7 The Role Of Weather The preceding s e c t i o n showed that low weather-induced l a r v a l s u r v i v a l can make the lower s t a b l e s u r f a c e f o r budworm, c r e a t e d by avian p r e d a t i o n , e x i s t even though other c o n d i t i o n s i n the model may be f a v o r a b l e f o r budworm recrui t m e n t (e.g., low p a r a s i t o i d d e n s i t i e s ) . However, nor-mal v a r i a t i o n i n weather ( S e c t i o n 3.4.4) cannot prevent out-breaks from o c c u r r i n g (Figure 16). I f other c o n d i t i o n s i n the model are f a v o r a b l e f o r budworm re c r u i t m e n t , both the - 87 -F o l i a g e 3 . 8 Foliage IOOOOT 1 0 0 0 1 0 0 0 Foliage b ' 1 0 0 0 0 1 0 0 0 1 0 0 3 . 8 R e l a t i v e Branch Surface Area F i g u r e 15: C o n d i t i o n s p o t e n t i a l l y c r e a t i n g c h r o n i c a l l y endemic budworm p o p u l a t i o n s . a - poor weather induced l a r v a l s u r v i v a l . b - low f o r e s t biomass. c - h i g h p a r a s i t o i d d e n s i t i e s , d - low f o l i a g e biomass. See t e x t f o r an e x p l a n a t i o n o f p o i n t o i n 15c. - 88 -F i g u r e 16: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n of f o l i a g e biomass with d i f f e r e n t l e v e l s o f weather induced l a r v a l s u r v i v a l . - 89 -lower and upper e q u i l i b r i a d i s a p p e a r , i r r e s p e c t i v e of weather c o n d i t i o n s , , and budworm d e n s i t i e s can move from endemic to epidemic and from epidemic to endemic l e v e l s . T h e r e f o r e , the major e f f e c t of weather i n the model i s to d e l a y or advance budworm outbreak formation and c o l l a p s e which would occur i n e v i t a b l y anyway. Because of t h i s con-c l u s i o n , a l l f u r t h e r analyses below w i l l use average weather c o n d i t i o n s ; the r e s u l t s of the analyses would be the same under any weather c o n d i t i o n . 3.8 The Role of P a r a s i t o i d s Budworm p a r a s i t o i d s cannot c r e a t e a s t a b l e lower e q u i l i b r i u m d e n s i t y f o r budworm ( F i g u r e s 12 and 15c) and keep budworm endemic because s u f f i c i e n t p a r a s i t o i d s cannot be supported by such low budworm p o p u l a t i o n s . Can the p a r a s i t o i d cause the c o l l a p s e of budworm outbreaks? Two se t s of i s o r e c r u i t m e n t curves, one f o r budworm as a f u n c t i o n of p a r a s i t o i d d e n s i t y , the other f o r the p a r a s i -t o i d s as a f u n c t i o n of budworm d e n s i t y , both generated f o r d i f f e r e n t f o l i a g e l e v e l s ( F i g u r e 17) show that the p a r a s i -t o i d i s o r e c r u i t m e n t curves i n t e r s e c t the budworm curves to the l e f t of the prey ( i . e . , budworm) i s o r e c r u i t m e n t curve peak. T h i s should t h e r e f o r e cause i n c r e a s i n g o s c i l l a t i o n s (Rosenzweig and MacArthur 1963; Fig u r e 3 ) . Assuming constant high f o l i a g e and branch d e n s i t y f o r the moment, budworm and the p a r a s i t o i d begin moving from low - 90 -P a r a s i t o i d A d u l t s F i g u r e 17: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f p a r a s i t o i d d e n s i t y and p a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y f o r d i f f e r e n t f o l i a g e l e v e l s . The system can have t r a j e c t o r y SI o r S2, depending on the p a r a s i t o i d numerical response. The n o t a t i o n i n t h i s f i g u r e w i l l be fo l l o w e d throughout Chapters 3, 4, 5. B - d e f o l i a t o r ; P - p a r a s i t o i d ; Fo - f o l i a g e ; F - f o r e s t . L - low l e v e l s o f v a r i a b l e whose d e n s i t y i s being v a r i e d ; M - medium l e v e l s ; H - high l e v e l s . - 91 -l e v e l s of each. Budworm w i l l begin i n c r e a s i n g f i r s t , as p a r a s i t o i d s are lagged to budworm by one year (Equation 9). I t i s d i f f i c u l t to say what the nature of the behavior of the system w i l l be once i t has moved from low budworm and p a r a s i t o i d l e v e l s . C e r t a i n l y , i n c r e a s e d budworm d e n s i t i e s w i l l cause some d e f o l i a t i o n and s h i f t i n g of the budworm curves to the r i g h t and p a r a s i t o i d curves downward. Two extreme p o s s i b i l i t i e s can be e n v i s i o n e d and both are dependent on the r e l a t i v e numerical responses of the budworm and the p a r a s i t o i d . I f the budworm has a more r a p i d numerical response than the p a r a s i t o i d the t r a j e c t o r y would l i k e l y be SI i n Figure 17. I f the p a r a s i t o i d has a more r a p i d numerical response than the budworm, the t r a j e c t o r y would l i k e l y be S2. The outcomes are l i k e l y to be much d i f -f e r e n t under case SI than S2. A s e t of f o l i a g e i s o r e c r u i t -ment curves as a f u n c t i o n of budworm d e n s i t y and a set of budworm i s o r e c r u i t m e n t curves as a f u n c t i o n of f o l i a g e den-s i t y i l l u s t r a t e t h i s p o i n t ( F i g u r e 18) (the f o l i a g e i s o r e -cruitment curve does not change as a f u n c t i o n of p a r a s i t o i d d e n s i t y because no d i f f e r e n t i a l f e e d i n g between p a r a s i t i z e d and u n p a r a s i t i z e d budworm i s assumed). The upper s t a b l e s u r f a c e s f o r budworm and f o l i a g e do not i n t e r s e c t ; t h a t i s , there i s no j o i n t e q u i l i b r i u m between budworm and f o l i a g e at high l e v e l s of each. Under t r a j e c t o r y SI budworm reach s u f f i c i e n t l y high l e v e l s so that the upper f o l i a g e e q u i l i b r i u m d i s a p p e a r s . Under t r a j e c t o r y - 92 -F i g u r e 18: F o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y and budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e biomass with d i f f e r e n t p a r a s i t o i d d e n s i t i e s . - 93 -S2, p a r a s i t o i d s have a s u f f i c i e n t l y f a s t numerical response to stop budworm from reaching l e v e l s which would cause the upper f o l i a g e e q u i l i b r i u m to di s a p p e a r . D e c l i n e s i n f o l i a g e caused by high budworm d e n s i t i e s ( F i g u r e 18) would cause high f o r e s t m o r t a l i t y and d e c l i n e s i n f o r e s t branch d e n s i t y (Figure 19). Whether the system t r a j e c t o r y i s SI or S2 ( e s s e n t i a l l y , whether p a r a s i t o i d s can cause c o l l a p s e of outbreaks) cannot be determined by simple a n a l y s i s of e q u i l i b r i u m s t r u c t u r e and model s i m u l a t i o n must be used. The determining f a c t o r i s the r e l a t i v e numerical responses of the paras'itoid and the budworm. I f changes i n p a r a s i t o i d numbers are f a s t e r than those of budworm we should expect to see short l a s t i n g i n f e s t a t i o n s with l i t t l e d e c l i n e s i n f o l i a g e or f o r e s t l e v -e l s . I f p a r a s i t o i d s change slowly r e l a t i v e to budworm, budworm i n f e s t a t i o n s should cause l a r g e d e c l i n e s i n f o l i a g e and branch d e n s i t y l e v e l s and i n t e r - o u t b r e a k p e r i o d s should be c h a r a c t e r i z e d by r e g e n e r a t i o n of f o l i a g e and f o r e s t to high l e v e l s . 3.9 Temporal Model Behavior The preceding s e c t i o n s have presented 2 s e t s of e q u i l i -brium s t r u c t u r e s f o r the model ( F i g u r e s 15a and 17 to 19). Th i s s e c t i o n presents the numerical r e s u l t s generated by each s e t of e q u i l i b r i u m s t r u c t u r e s . 3.9.1 Temporal Behavior With C h r o n i c a l l y Poor Weather The f i r s t e q u i l i b r i u m s t r u c t u r e ( F i g u r e 15a), should - 9 4 -Figure 19: Forest isorecruitment curves as a function of foliage biomass and foliage isorecruitment curves as a function of forest biomass for d i f f e r e n t budworm densi t i e s . - 95 -generate a behavior which i s c h a r a c t e r i z e d by an absence of outbreaks, c o n t i n u a l low p a r a s i t o i d numbers, and c o n t i n u a l high f o l i a g e biomass and branch d e n s i t y . T h i s behavior should occur poor weather c o n d i t i o n s i n the model cause the low d e n s i t y s t a b l e e q u i l i b r i u m to remain, i r r e s p e c t i v e of any other c o n d i t i o n . A s i m u l a t i o n of the model made with weather-induced l a r g e l a r v a l s u r v i v a l set at 0.35 ( F i g u r e 20) shows the gen-er a t e d behavior i s c o n s i s t e n t with that expected from an a n a l y s i s of e q u i l i b r i u m s t r u c t u r e ( F igure 15a). There are no budworm outbreaks over a 60 year time span. P a r a s i t o i d l e v e l s remain low and f o l i a g e and f o r e s t l e v e l s remain high f o r the 60 year p e r i o d . T h i s generated behavior has good q u a l i t a t i v e correspondence with the behavior of the r e a l world system i n some cases ( M i l l e r 1966, Canada 1939 to 1982). 3.9.2 Temporal Model Behavior With Normal Weather I was unable to deduce what behavior the second e q u i l i -brium s t r u c t u r e ( F i g u r e s 17 to 19) w i l l generate without a c t u a l l y g e n e r a t i n g the s i m u l a t i o n r e s u l t s . S i m u l a t i o n r e s u l t s generated with model parameters set so as to g i v e the e q u i l i b r i u m s t r u c t u r e of F i g u r e s 17 to 19 (Figure 21) show budworm outbreaks o c c u r r i n g about every 16 years and l a s t i n g 2 to 3 y e a r s . Outbreaks cause moderate d e c l i n e s i n f o l i a g e l e v e l s and very l i t t l e l o s s of f o r e s t biomass. P a r a s i t o i d l e v e l s reach a peak i n the d e c l i n i n g phase of - 96 -4 0 0 T to to w 0 0 3 . 8 0) fc/J <3 •H H O 0 0 -I 1 1 1 1 YERR 60 H 1 1 1 1 1 YEAR 60 20 •rl o <n +» +> •H H m 3 (fl T3 r, < DM 0 0 1 T X! u o c v 00 o> u •rl W -H U2 <D Pi 0 0 H 1 1 1 1 YEAR 60 —I 1 1 1 1 H YEAR 60 F i g u r e 20: Model be h a v i o r f o r c h r o n i c a l l y low weather induced l a r v a l s u r v i v a l . See F i g u r e 15a f o r e q u i l i b r i u m s t r u c t u r e . - 97 -F i g u r e 2 1 : M o d e l b e h a v i o r u n d e r n o r m a l w e a t h e r c o n d i t i o n s . S e e F i g u r e s 1 7 , 1 8 , a n d 1 9 f o r e q u i l i b r i u m s t r u c t u r e . - 98 -budworm outbreaks. T h i s behavior i s very much l i k e the behavior of the system i n New Brunswick documented by the F o r e s t Insect and Disease Survey (Canada 1939 to 1982) and s t u d i e d by M i l l e r (1966, Table I I I ) . The s i m u l a t i o n r e s u l t s a l s o demonstrate that the model p a r a s i t o i d i s able to respond q u i c k l y enough to i n c r e a s e s i n budworm numbers to prevent budworm from reaching even higher l e v e l s and i n f l i c t i n g heavy d e c l i n e s of both f o l i a g e and f o r e s t ; t h a t i s , i t can c o l l a p s e outbreaks. A f u r t h e r demonstration that the c a p a b i l i t y of the p a r a s i t o i d to q u i c k l y respond n u m e r i c a l l y to host numbers i s c r i t i c a l to model behavior i s shown i n Figure 22. The p a r a s i t o i d progeny s u r v i v a l was s e t to .05 f o r the f i n a l 100 years of a 150 year s i m u l a t i o n shown i n Figure 22. Model behavior i n the f i r s t 50 years i s l i k e that shown i n Figure 21. The f i n a l 100 y e a r s , however, are marked by i n f r e q u e n t but very heavy budworm i n f e s t a t i o n s causing l a r g e d e c l i n e s i n f o l i a g e and f o r e s t , a behavior much l i k e t h a t f o r the unmanaged e a s t e r n spruce budworm system ( B l a i s 1968, Table I I I ) . The p a r a s i t o i d numerical response i s o b v i o u s l y very c r i t i c a l i n determining the behavior of the model. 3.10 E f f e c t s Of A l t e r n a t e P a r a s i t o i d Attack Parameters Many of the p a r a s i t o i d a t t a c k parameters were estimated without any e m p i r i c a l evidence. Minima and maxima f o r three parameters: r a t e of s u c c e s s f u l search; the d i s p e r s i o n coef-f i c i e n t f o r the d i s t r i b u t i o n of a t t a c k s ; and the p a r a s i t o i d - 99 -F i g u r e 2 2 : M o d e l b e h a v i o r f o r a 1 5 0 y e a r s i m u l a t i o n w i t h n o r m a l w e a t h e r c o n d i t i o n s . P a r a s i t o i d p r o g e n y s u r v i v a l i s t h a t g i v e n i n T a b l e V I f o r f i r s t 5 0 y e a r s a n d t h r e e t i m e s l o w e r f o r f i n a l 1 0 0 y e a r s . - 100 -progeny s u r v i v a l r a t e (Equation 9) were e s t a b l i s h e d . The analyses of the preceding s e c t i o n s were made with averages of the minimum and maximum d e f i n e d f o r each parameter. T h i s s e c t i o n t e s t s the s e n s i t i v i t y of the model e q u i l i b r i u m s t r u c t u r e and behavior to extreme values of these parame-t e r s . 3 . 1 0 . 1 Good Searcher, High S u r v i v a l , Low S u p e r p a r a s i t i s m T h i s parameter s e t i n c r e a s e s the c a p a b i l i t y of the p a r a s i t o i d to respond n u m e r i c a l l y . The new parameter set s h i f t s the budworm i s o r e c r u i t m e n t curves to the r i g h t and the p a r a s i t o i d i s o r e c r u i t m e n t curves downward i n F i g u r e 23a (compare to Figure 17). The e f f e c t i s to s h i f t the common e q u i l i b r i a f a r t h e r down to lower budworm l e v e l s . The model behavior generated by t h i s e q u i l i b r i u m s t r u c -ture ( F i g u r e 24) i s very s i m i l a r to that f o r the base model under normal weather c o n d i t i o n s ( F i g u r e 21). However, out-breaks are l e s s frequent and p a r a s i t o i d numbers generated from outbreaks are much hig h e r . Both these c o n d i t i o n s are generated by the i n c r e a s e d numerical response c a p a b i l i t i e s of the p a r a s i t o i d . 3 .10.2 Poor Searcher, Low S u r v i v a l , High S u p e r p a r a s i t i s m T h i s parameter set decreases the a b i l i t y of the p a r a s i -t o i d to n u m e r i c a l l y respond to i n c r e a s i n g budworm. T h i s has the o p p o s i t e e f f e c t to the parameter set d e s c r i b e d i n the above s e c t i o n ( F i g u r e 25, compare to F i g u r e 17 f o r the "nor-mal" and 23 f o r the "super" p a r a s i t o i d ) . Budworm - 1 0 1 -P a r a s i t o i d Adults F i g u r e 23: Model e q u i l i b r i u m s t r u c t u r e f o r "super" p a r a s i t o i d . Compare with e q u i l i b r i u m s t r u c t u r e i n F i g u r e 17. - 10 2 -H y-^ i > — i H YERR 60 - i — i — i — i — i — i — i — i — i — i YEAR 60 60 •H O ID -P -P •H H (0 3 (0 -o-U < flj O (0 CQ 0> O > <C •H W »H (0 3 H O) 0 4 — H 0 1 T YEAR 60 0 H 1 1 1 1 1 1 1 1 1 0 YERR 60 M o d e l b e h a v i o r g e n e r a t e d w i t h " s u p e r " p a r a s i t o i d . C o m p a r e w i t h m o d e l b e h a v i o r i n F i g u r e 21. - 1 0 3 -Figure 25: Model equilibrium structure for "slow" p a r a s i t o i d . Compare with equilibrium structure i n Figure 17 and Figure 23. - 1 0 4 -i s o r e c r u i t m e n t curves are s h i f t e d to the l e f t and p a r a s i t o i d i s o r e c r u i t m e n t curves are s h i f t e d upward. The common e q u i l i b r i a are now on the upper s t a b l e budworm s u r f a c e . T h i s means that model behavior should be determined by f o l i -age and f o r e s t growth processes as i n the l a s t 100 years of model s i m u l a t i o n i n Figure 22. The model behavior generated ( F i g u r e 26), i s what i s expected given the e q u i l i b r i u m s t r u c t u r e with outbreaks causing l a r g e d e c l i n e s i n f o l i a g e and f o r e s t biomass and p e r i o d s between outbreaks marked by r e g e n e r a t i o n of f o l i a g e and f o r e s t . These l a s t two se t s of e q u i l i b r i u m s t r u c t u r e s and simu-l a t i o n s i l l u s t r a t e very c l e a r l y the no t i o n that the r e l a t i v e numerical responses of the p a r a s i t o i d and the budworm are c r i t i c a l i n determining the behavior of the model. 3.11 Summary The analyses i n the preceding s e c t i o n s have i d e n t i f i e d a small s et of processes which c r e a t e the e q u i l i b r i u m s t r u c -t u r e s f o r i n d i v i d u a l components of the e a s t e r n blackheaded budworm system: 1. avian p r e d a t i o n on budworm l a r v a e ; 2. e f f e c t s of i n t r a - s p e c i f i c c o m petition on budworm; 3. p a r a s i t o i d f e c u n d i t y , p a r a s i t o i d progeny s u r v i v a l , r a t e of s u c c e s s f u l search, and i n t r a - s p e c i f i c com-- 1 0 5 -2 6 : M o d e l b e h a v i o r g e n e r a t e d w i t h " s l o w " p a r a s i t o i d . C o m p a r e w i t h m o d e l b e h a v i o r i n F i g u r e 2 1 . - 1 0 6 -p e t i t i o n among developing p a r a s i t o i d s caused by s u p e r - p a r a s i t i s m ; 4. density-dependent f o l i a g e growth; and 5. density-dependent f o r e s t growth. In a d d i t i o n , there are a s e t of processes which d e t e r -mine how the p a r t i c u l a r e q u i l i b r i u m s t r u c t u r e s f o r the sy s -tem components i n t e r a c t to generate model behavior which i s c o n s i s t e n t with observed system behavior: 1. weather induced l a r v a l s u r v i v a l ; 2. the p a r a s i t o i d a t t ack parameters which d e f i n e i t s numerical response to budworm; and 3. the s u s c e p t i b i l i t y of f o r e s t branch d e n s i t y to low f o l i a g e l e v e l s . The p a r a s i t o i d a t t a c k parameters are most important, f o r they determine the r a t e of p a r a s i t o i d numerical response. S u f f i c i e n t l y r a p i d p a r a s i t o i d numerical response generates behavior which i s c o n s i s t e n t with the observed p a t t e r n of outbreaks. S u f f i c i e n t l y slow p a r a s i t o i d numeri-c a l response generates behavior not observed i n t h i s system, but found i n the e a s t e r n spruce budworm system. The a n a l y s i s has shown that e q u i l i b r i u m s t r u c t u r e s f o r model components are s e t by s p e c i f i c model processes, and that the c o n f i g u r a t i o n and i n t e r a c t i o n of e q u i l i b r i u m s t r u c -- 1 0 7 -t u r e s of system components, along with time s c a l e s of response by key v a r i a b l e s , generate model behaviors which are q u a l i t a t i v e l y s i m i l a r to r e a l world behavior under s i m i -l a r c o n d i t i o n s (Table I I I ) . - 10 8 -4.0 THE EASTERN SPRUCE BUDWORM SYSTEM Eastern spruce budworm i s the major d e f o l i a t i n g i n s e c t of the e a s t e r n c o n i f e r o u s f o r e s t of North America. I t i s found throughout the Canadian Maritimes and northern New England and westward and northward through middle Canada up to the b o r e a l f o r e s t (Davidson and P r e n t i c e 1967). I t s favored host t r e e s p e c i e s are balsam f i r and white spruce. Outbreaks of the budworm have been documented through t r e e r i n g a n a l y s i s back to the 1700's ( B l a i s 1968). I n t e n s i v e i n s e c t i c i d e s p r a y i n g on the d e f o l i a t o r commenced i n many p a r t s of e a s t e r n North America i n the e a r l y 1950*s (Prebble 1975) and conti n u e s at p r e s e n t . The behavior of t h i s system has been analyzed exhaus-t i v e l y by a number of workers ( B a s k e r v i l l e 1976, C l a r k 1979, C l a r k and H o l l i n g 1979) using a d e t a i l e d s i m u l a t i o n model of the system (Jones 1977a). The purpose of t h i s chapter i s to complement, r a t h e r than redo these a n a l y s e s . T h e r e f o r e , t h i s chapter c o n t a i n s a d e s c r i p t i o n of the r e a l system, a summary of pre v i o u s workers' analyses of system s t r u c t u r e and behavior, and analyses r e l e v a n t to t h i s t h e s i s which were not c a r r i e d out by previous workers. The reader i s r e f e r r e d to a p p r o p r i a t e r e f e r e n c e s f o r more d e t a i l e d r e p o r t s of model s t r u c t u r e and behavior. 4.1 Documented Behavior T h i s system e x h i b i t s e s s e n t i a l l y 3 d i f f e r e n t types of behavior (Table I I I ) . F i r s t , there have been no recorded - 109 -outbreaks by the budworm i n the extreme northern p a r t s of i t s d i s t r i b u t i o n , although budworm are present there because they can u s u a l l y be recovered i n F o r e s t Insect Sur-vey t r e e b e a t i n g samples (Canada 1939 to p r e s e n t ) . A second type of behavior i s c h a r a c t e r i s t i c of the l a r g e areas of the system before i n t e n s i v e p e s t i c i d e a p p l i -c a t i o n p o l i c i e s were adopted i n the e a r l y 1950's. T h i s behavior i s c h a r a c t e r i z e d by i r r e g u l a r i n f e s t a t i o n s occur-r i n g every 20 to 90 years over l a r g e areas of the host f o r e s t ( B l a i s 1954, 1968). These i n f e s t a t i o n s l a s t e d 5 to 11 years i n any one s i t e ( M i l l e r 1975) and caused very high m o r t a l i t y of mature balsam f i r and a s s o c i a t e d white spruce. Between outbreaks, evidence i n d i c a t e s t hat the budworm was extremely r a r e but u s u a l l y r e c o v e r a b l e i n t r e e - b e a t i n g s u r -veys (Greenbank 1963). The t h i r d type of behavior has occurred i n stands e i t h e r composed mainly of white spruce or subjected to i n t e n s i v e i n s e c t i c i d e s p r a y i n g s i n c e the e a r l y 1950s (Morris 1958, B l a i s 1974, Wotton and Jones 1976). T h i s behavior i s c h a r a c t e r i z e d by l o n g - l a s t i n g i n f e s t a t i o n s o c c u r r i n g every 10 to 15 years and causing low or moderate t r e e m o r t a l i t y . 4.2 System D e s c r i p t i o n 4.2.1 The D e f o l i a t o r The l i f e h i s t o r y of the i n s e c t i s w e l l documented (Mor r i s 1958, Davidson and P r e n t i c e 1967, Greenbank 1963). Eggs are l a i d i n the l a t e summer and emerge about 2 weeks - 110 -l a t e r . Emerging l a r v a e d i s p e r s e a e r i a l l y on s i l k t hreads, then s p i n h i b e r n a c u l a e where they diapause over w i n t e r . The second i n s t a r l a r v a e emerge from diapause i n e a r l y May. D i s p e r s a l occurs again i n the same manner as i n the f a l l , whereupon fee d i n g commences on the new f o l i a g e of the host t r e e . Old f o l i a g e i s consumed i f a l l the new f o l i a g e i s gone. The i n s e c t passes through 4 more i n s t a r s u n t i l e a r l y J u l y when the mature l a r v a pupates f o r about 10 days i n the f i n a l f e e d i n g s i t e s on the host t r e e . A d u l t s emerge i n l a t e J u l y and may d i s p e r s e . I f d i s p e r s a l does occur, i t may extend 10 to 100 k i l o m e t e r s . 4.2.2 N a t u r a l Enemies The budworm i s attacked by a l a r g e complex of p a r a s i -t o i d s on e a r l y l a r v a e ( M i l l e r 1977). Apanteles fumiferanae and G l y p t a fumiferanae are the most important s p e c i e s of the complex ( M i l l e r 1959, 1960), being the most completely h o s t - s p e c i f i c and causing the h i g h e s t m o r t a l i t y r a t e s on the host ( M i l l e r 1963). These two p a r a s i t o i d s p e c i e s attack budworm i n the f a l l , g e n e r a l l y a f t e r the f i r s t l a r v a l d i s p e r s a l , and emerge from the host when the host i s i n the f i f t h or s i x t h l a r v a l i n s t a r . L a t e r l a r v a l and pupal stages are attacked by a l a r g e complex of b i r d s (Morris e_t a_l 1958) and evidence i n d i c a t e s that t h e i r e f f e c t on budworm p o p u l a t i o n s may be g r e a t e s t at low budworm d e n s i t i e s (Morris 1963). 4.2.3 The F o r e s t - I l l -A ge n e r a l d e s c r i p t i o n of the balsam f i r / s p r u c e f o r e s t i s given i n the a n a l y s i s of the ea s t e r n blackheaded budworm/balsam f i r system i n Chapter 4. Eas t e r n spruce budworm i s i d e n t i c a l to e a s t e r n black-headed budworm i n terms of the ages of t r e e p r e f e r r e d as d e f o l i a t o r h a b i t a t and the ages of f o l i a g e p r e f e r r e d f o r f e e d i n g . 4.3 Model D e s c r i p t i o n The s i m u l a t i o n model used i n my study i s d e s c r i b e d i n Jones (1977a). I t i s a s i n g l e stand model of the system and has been used as a t o o l f o r p o l i c y and re s e a r c h d esign by f o r e s t managers and s c i e n t i s t s i n New Brunswick ( C l a r k e_t a_l 1979). The model simulates the annual dynamics of the i n s e c t , n a t u r a l enemies, and host t r e e s i n a stand of f i r and spruce f o r e s t . Many of the i n t e r a c t i o n s simulated between the budworm and i t s n a t u r a l enemies and host f o l i a g e occur during s p e c i f i c budworm l i f e h i s t o r y stages. There are four major components to the model: the f o r e s t , the f o l i a g e , the budworm, and budworm n a t u r a l enemies ( b i r d s and p a r a s i t o i d s ) . The reader i s r e f e r r e d to Jones (1977a) and Cl a r k (1979) f o r a complete model d e s c r i p t i o n . 4.4 Model E q u i l i b r i u m S t r u c t u r e 4.4.1 The Insec t With a l l processes i n c l u d e d , under c e r t a i n f o r e s t con-d i t i o n s budworm can have 2 p o t e n t i a l s t a b l e e q u i l i b r i a ( F i g -ure 27). One i s at high budworm d e n s i t i e s , the other i s at low budworm d e n s i t i e s . An unstable e q u i l i b r i u m l i e s between - 1 1 2 -F i g u r e 27: Recruitment curves f o r e a s t e r n spruce budworm. a - a l l p r o c e s s e s . b - i n t r a - s p e c i f i c competi-t i o n e f f e c t s removed. c - p a r a s i t i s m and pre-d a t i o n removed. d - with low, medium, and h i g h f o l i a g e biomass. - 1 1 3 -these 2 s t a b l e e q u i l i b r i a . The upper s t a b l e e q u i l i b r i u m d isappears when i n t r a - s p e c i f i c c o mpetition e f f e c t s (on l a r g e l a r v a l s u r v i v a l , sex r a t i o , or f e c u n d i t y ) are removed from the model (Figure 27b). Only the upper s t a b l e e q u i l i b r i u m remains with avian p r e d a t i o n and p a r a s i t i s m removed from the model (F i g u r e 27c). The unstable e q u i l i b r i u m i s crea t e d by the s a t u r a t i o n of the f u n c t i o n a l responses of these a t t a c k -ing s p e c i e s . However, t h i s i s a s t a t i c p i c t u r e of the model. For example, the budworm recruitment curve depends on f o l i a g e biomass through the i n t e n s i t y of i n t r a - s p e c i f i c c o mpetition and the s u r v i v a l r a t e of d i s p e r s i n g l a r v a e (Figure 27d). The p o s i t i o n of the curve changes as the f o l i a g e d e n s i t y changes, and the p o s i t i o n of the e q u i l i b r i a s h i f t s as the p o s i t i o n of the recruitment curve changes. Under extreme f o l i a g e d e n s i t i e s , the e q u i l i b r i a disappear and reappear. T h i s s h i f t i n g of e q u i l i b r i a i s b e t t e r captured i n an i s o r e c r u i t m e n t curve (Figure 28). Budworm has an e q u i l i -brium s t r u c t u r e with an upper and lower s t a b l e domain; these correspond to the movement of the upper and lower s t a b l e e q u i l i b r i a i n response to changing f o l i a g e biomass. The unstable domain intermediate to the two s t a b l e s u r f a c e s corresponds to the unstable e q u i l i b r i u m . 4.4.2 The P a r a s i t o i d The i s o r e c r u i t m e n t curve f o r the budworm p a r a s i t o i d ( F i g u r e 29) has one s t a b l e e q u i l i b r i u m . The bending over of - 1 1 4 -1 0 0 0 0 T o t a l F o l i a g e Units/m Branch F i g u r e 28: Budworm i s o r e c r u i t m e n t curve as a f u n c t i o n o f f o l i a g e biomass. P o i n t m i s the minimum f o l i a g e f o r epidemic budworm; p o i n t n i s the maximum f o l i a g e f o r endemic budworm. - j.15 -F i g u r e 29: P a r a s i t o i d i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y . a - low, model, and h i g h f e c u n d i t y . b - low, model, and h i g h p a r a s i t o i d progeny s u r v i v a l . - 1 1 6 -the s u r f a c e at high p a r a s i t o i d d e n s i t i e s i s caused by the i n c r e a s i n g s u p e r - p a r a s i t i s m r a t e s with high p a r a s i t o i d den-s i t i e s simulated using a competition equation ( G r i f f i t h s and H o l l i n g 1969) (Appendix I I ) . The p o s i t i o n of the curve i s set by the p a r a s i t o i d f e c u n d i t y , the p a r a s i t o i d progeny sur-v i v a l from the time of emergence from the host to the time of a t t a c k the f o l l o w i n g g e n e r a t i o n , and the d i s p e r s i o n coef-f i c i e n t of the competition equation (Appendix I I ) . 4.4.3 The F o l i a g e And The Fo r e s t The f o l i a g e e q u i l i b r i u m s t r u c t u r e f o r e a s t e r n spruce budworm i s the same as that f o r e a s t e r n blackheaded budworm (Fi g u r e 13). I t c o n t a i n s a lower s t a b l e f o l i a g e e q u i l i b r i u m at young f o r e s t branch area which disappears as the f o r e s t grows and an upper s t a b l e e q u i l i b r i u m s et by the dynamics of ol d f o l i a g e . The appearance of a low d e n s i t y s t a b l e s u r f a c e f o r f o l i a g e at low f o l i a g e biomass l e v e l s occurs because the younger f o r e s t age c l a s s e s are not fed upon by budworm i n the model (Jones 1977a). These younger age c l a s s e s t h e r e -f o r e a ct as a f o l i a g e refuge which disappears under c o n d i -t i o n s of high f o r e s t biomass. The f o r e s t e q u i l i b r i u m s t r u c t u r e f o r e a s t e r n spruce budworm i s the same as that f o r e a s t e r n blackheaded budworm (F i g u r e 14). The f o r e s t e q u i l i b r i u m i n c r e a s e s with i n c r e a s -ing f o l i a g e biomass and the maximum branch s u r f a c e area i s set by the amount of branch s u r f a c e area at each age (Jones 1977a, p. 103). The slope of the i s o r e c r u i t m e n t curve i s - 1 1 7 -s e t by the s u s c e p t i b i l i t y to m o r t a l i t y of the f o r e s t (Jones 1977a, p. 113). Lower s u s c e p t i b i l i t y to low f o l i a g e l e v e l s means that the f o r e s t w i l l be able to ma i n t a i n a high biomass with heavy r e d u c t i o n s i n f o l i a g e . 4.5 Review Of Previous Model Analyses C l a r k (1979) and C l a r k and H o l l i n g (1979) concentrated on model analyses which would help e x p l a i n the two d i f f e r e n t outbreak behaviors e x h i b i t e d by the r e a l budworm system i n New Brunswick. They t h e r e f o r e concentrated on the i n t e r a c -t i o n s between the f o r e s t , f o l i a g e , and budworm v a r i a b l e s , and o n l y examined p a r a s i t o i d and weather e f f e c t s o n l y i n a cu r s o r y manner. I w i l l review the e s s e n t i a l p o i n t s of the prev i o u s model analyses and w i l l then turn to a more d e t a i l e d a n a l y s i s of the r o l e of the p a r a s i t o i d and weather. 4.5.1 Model Behavior Under Normal C o n d i t i o n s We w i l l begin the system at low budworm, high f o l i a g e , and high branch s u r f a c e area. F i g u r e 30 shows t h a t , under normal weather c o n d i t i o n s , the lower s t a b l e e q u i l i b r i u m f o r budworm disappears under s u f f i c i e n t l y high f o l i a g e l e v e l s and branch s u r f a c e area. Under these c o n d i t i o n s , budworm begins moving to the upper s t a b l e e q u i l i b r i u m . Above about 600 eggs/m 2 , f o l i a g e begins to d e c l i n e very r a p i d l y from i t s upper s t a b l e s u r f a c e . T h i s d e c l i n e i n f o l i a g e l e v e l s causes f o r e s t branch s u r f a c e area to begin d e c r e a s i n g as w e l l ( F i g -ure 31). The d e c l i n e i n these two v a r i a b l e s causes the budworm to move o f f i t s upper s t a b l e e q u i l i b r i u m and c o l -- 1 1 8 -10000 10 .01 Eggs gure 30: Budworm i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e d e n s i t y and f o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f budworm d e n s i t y , f o r d i f f e r e n t f o r e s t biomasses (Low, Medium, High). - 1 1 9 -F i g u r e 31: F o r e s t i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o l i a g e l e v e l s and f o l i a g e i s o r e c r u i t m e n t curves as a f u n c t i o n o f f o r e s t biomass, f o r d i f f e r e n t budworm l e v e l s . - 120 -l a pse to low l e v e l s . T h i s allows both the f o l i a g e and, more sl o w l y , the f o r e s t to regenerate. T h i s g i v e s a temporal behavior l i k e that shown i n Figure 32, with i n f r e q u e n t , long l a s t i n g outbreaks r e s u l t i n g i n e x t e n s i v e f o l i a g e and f o r e s t l o s s . The i n t e r - o u t b r e a k p e r i o d i s c h a r a c t e r i z e d by regen-e r a t i o n of f o l i a g e and f o r e s t . T h i s behavior i s e s s e n t i a l l y a d e f o l i a t o r / f o r e s t c y c l e and i s s i m i l a r to the system behavior i n the Canadian Maritimes before h i s t o r i c a l manage-ment p r a c t i c e s were i n i t i a t e d i n the 1950s ( B l a i s 1968, Table I I I ) . 4.5.2 Model Behavior With Reduced F o r e s t S u s c e p t i b i l i t y A d i f f e r e n t behavior emerges when the f o r e s t i s made l e s s s u s c e p t i b l e to budworm d e f o l i a t i o n , i n t h i s case by s p r a y i n g to reduce budworm p o p u l a t i o n s and m a i n tain high f o l i a g e l e v e l s to i n turn reduce t r e e and f o r e s t m o r t a l i t y . ( F i g u r e s 33, 34). T h i s has been the f o r e s t p r o t e c t i o n s t r a -tegy adopted by New Brunswick s i n c e the e a r l y 1950s (Prebble 1975). A s i m i l a r e q u i l i b r i u m s t r u c t u r e would emerge i f the f o r e s t were made l e s s v u l n e r a b l e to d e f o l i a t i o n , as i s the case with white spruce ( M i l l e r 1975). The movement of e q u i l i b r i a d e s c r i b e d above i s the same, except that the movement of the budworm from i t s upper s t a b l e e q u i l i b r i u m i s accompanied by d e c l i n e s i n f o l i a g e but not d e c l i n e s i n f o r e s t branch s u r f a c e area. T h i s means that the next out-break can occur when f o l i a g e again reaches high l e v e l s but i s not delayed by slower f o r e s t r e g e n e r a t i o n . T h i s i s e s s e n t i a l l y a d e f o l i a t o r / f o l i a g e c y c l e ( F igure 35) and i s - 1 2 1 -3 5 0 0 T •H 0) to 0] o 0 1/ . 1 •H o to +> + » •H H ^ < (0 0 , Q i — I I — i — — i — • i l - i — i — i ! — i 0 150 Y E A R 3 . 8 u C (Q ^ < e o fl > •H <H H 10 - t — i — i — i — i 0 YEAR 150 YEAR F i g u r e 32: Model be h a v i o r f o r the unmanaged system. s i m u l a t i o n was made with the e q u i l i b r i u m s t r u c t u r e d e s c r i b e d i n F i g u r e s 30 and 31 - 1 2 2 -o 4 1 1 1 1 1 1 1 0 0 0 0 10 . 0 1 Eggs F i g u r e 33: Budworm and f o l i a g e i s o r e c r u i t m e n t curves f o r d i f f e r e n t f o r e s t biomasses under the h i s t o r i -c a l budworm spray r u l e . Dotted d i s c o n t i n u i t i e s r e f l e c t the spray t h r e s h o l d . - 1 2 3 -F o l i a g e U n i t s F i g u r e 34: F o r e s t and f o l i a g e i s o r e c r u i t m e n t curves f o r d i f f e r e n t budworm d e n s i t i e s under the h i s -t o r i c a l budworm spray r u l e . Dotted d i s c o n -t i n u i t i e s r e f l e c t the spray t h r e s h o l d . - 1 2 4 -3 5 0 0 tn to to w 0 0 3 . 8 •H C to « •rl i-H 0 fe. 0 ii Y E A R . 1 T O <Q +> +> •rl M 0) 3 U < (3 150 O C u m S3 i2 o <3 •rl <H +» 3 C/3 H 1 1 1 1 1 1-0 Y E A R 150 0 0 1 T •A — t — i — i — i — i — i — i — i — i — i YEAR 150 0 H 1 1 1 1 1 1 0 YEAR 150 F i g u r e 35: Model be h a v i o r with h i s t o r i c a l budworm spray r u l e s . T h i s s i m u l a t i o n was made with the e q u i l i b r i u m s t r u c t u r e d e s c r i b e d i n Fi g u r e s 3 3 and 34. Compare with F i g u r e 32. - 125 -c h a r a c t e r i z e d by more frequent outbreaks causing u s u a l l y moderate d e c l i n e s i n branch s u r f a c e area. T h i s behavior i s q u a l i t a t i v e l y s i m i l a r to that observed by M o r r i s (1958) and Wotton and Jones (1976) on white spruce and to that e x h i -b i t e d by the system under h i s t o r i c a l i n s e c t i c i d e a p p l i c a -t i o n s ( B l a i s 1974). 4.6 C h r o n i c a l l y Endemic D e f o l i a t o r P o p u l a t i o n s The budworm, i n many p a r t s of i t s range, c o n t i n u a l l y remains at low p o p u l a t i o n l e v e l s (Table I I I ) . T h i s s e c t i o n demonstrates which processes i n the model can gi v e r i s e to t h i s type of system behavior. Endemic f o r the budworm case i s d e f i n e d as a p o p u l a t i o n which does not cause f o l i a g e to d e c l i n e from i t s high d e n s i t y s t a b l e s u r f a c e ( F i g u r e 18); t h i s i s about 600 eggs/m2 . Po i n t n i n Fig u r e 18 i s the maximum f o l i a g e biomass, given the other c o n d i t i o n s d e f i n i n g the model, which can keep budworm on i t s lower s t a b l e s u r f a c e ; that i s , to keep i t from moving from the endemic to the epidemic s t a t e . T h e r e f o r e , any process which moves p o i n t n to and past the maximum number of f o l i a g e u n i t s i n the model can keep budworm numbers endemic. H y p o t h e t i c a l l y , low f o r e s t branch s u r f a c e area, poor s u r v i v a l of l a r g e l a r v a e , and high numbers of a d u l t p a r a s i t e s can each keep budworm p o p u l a t i o n s endemic (Figure 36). Under any of these three c o n d i t i o n s , p o i n t n d i s a p -pears, and f o l i a g e l e v e l s can never become high enough to - 126 -<10000 1 0 . 0 1 a H i g h / I ' 1 0 0 0 0 o o w 0 3 . 8 1 0 1 0 0 0 0 . 0 1 3 . 8 . 0 1 3.8 F O L I A G E U N I T S F i g u r e 3 6 : P r o c e s s e s p o t e n t i a l l y c r e a t i n g c h r o n i c a l l y e n d e m i c b u d w o r m . a - l o w f o r e s t b i o m a s s . b - p o o r w e a t h e r - i n d u c e d l a r v a l s u r v i v a l , c - h i g h p a r a s i t o i d d e n s i t i e s . S e e t e x t f o r e x p l a n a t i o n o f p o i n t o . - 127 -permit budworm to move from i t s lower s t a b l e e q u i l i b r i u m . However, because p a r a s i t o i d d e n s i t y i s a dynamic model v a r i a b l e and because p a r a s i t o i d p o p u l a t i o n s are coupled to budworm p o p u l a t i o n s i n the model, we must make sure that low budworm p o p u l a t i o n s ( p o i n t o i n Fig u r e 36c, about 24 eggs/m2 ) can s u s t a i n the high p a r a s i t o i d p o p u l a t i o n s needed (about 1 per m2 branch s u r f a c e from F i g u r e 20c) to keep budworm on i t s lower s t a b l e s u r f a c e . F i g u r e 29, however, shows that the s u s t a i n a b l e p o p u l a t i o n of p a r a s i t o i d s i s .02 adults/m 2 from 24 budworm eggs/m2 . T h i s i s f a r l e s s than that needed to keep budworm endemic ( F i g u r e 36c). P a r a s i -t o i d s by themselves are incapable of keeping budworm popula-t i o n s endemic. The annual r e p o r t s of the Canadian F o r e s t Insect and Disease Survey (Canada 1939 to 1982) show that areas with c h r o n i c a l l y endemic budworm c o n t a i n mature f o r e s t with high f o l i a g e l e v e l s ; these c o n d i t i o n s i n the model cannot keep budworm endemic ( F i g u r e 36a). The e x p l i c i t f a c t o r i n the model m o d i f i e d i n Fig u r e 36b i s r e l a t e d to weather i n f l u -ences. T h i s i s supported by model s i m u l a t i o n s ( F i g u r e 37), made with very low s u r v i v a l of l a r g e l a r v a e , which show an absence of outbreaks and c h r o n i c a l l y high f o l i a g e and f o r e s t biomass (the s h i f t s i n f o r e s t biomass are a g e - s t r u c t u r e e f f e c t s ) . The hy p o t h e s i s , then, i s that weather f a c t o r s i n d u c i n g poor l a r v a l s u r v i v a l are necessary f o r c r e a t i n g c h r o n i c a l l y endemic budworm p o p u l a t i o n s . - 128 -3500 T .1 in w to a •H o « •p -p •rl H (0 3 fl T3 ^ < a. 0 H 1 1 1 1 1 1 1 1 1 0 3 . 8 Y E A R 150 to -p •rl c w •H i—I o 0 o fl ti V a u u < cc O u > « •H <H •P u fl 3 H U) H 1 1 1 1 1 1 1 1 1 0 Y E A R 150 Q i — i — i — i — i — i — i — i — i — i — i 0 150 YEAR 0 H 1 1 1 1 1 1 1 1 1 0 YEAR 150 F i g u r e 37: Model behavior f o r c h r o n i c a l l y low weather-induced l a r v a l s u r v i v a l . T h i s was made with the e q u i l i b r i u m s t r u c t u r e d e s c r i b e d i n Fi g u r e 36b. Compare with F i g u r e s 32 and 35. - 129 -4.7 The Role Of Weather In The Budworm System Very poor weather c o n d i t i o n s can prevent budworm from moving o f f i t s lower s t a b l e s u r f a c e ( F i g u r e 36b). The e f f e c t s of normal l e v e l s of weather-induced l a r g e l a r v a l s u r v i v a l ( F i g u r e 38) shows th a t "normal" poor weather (weather-induced s u r v i v a l r a t e s used i n the model) cannot by i t s e l f prevent i n i t i a t i o n of outbreaks i f other c o n d i t i o n s are a p p r o p r i a t e f o r outbreak i n i t i a t i o n ; p o i n t n does not disappear under normally v a r y i n g weather c o n d i t i o n s . The weather-induced s u r v i v a l r a t e s i n the model only have the e f f e c t of advancing or d e l a y i n g i n i t i a t i o n of outbreaks that w i l l e v e n t u a l l y occur, independent of weather f a c t o r s . 4.8 The Role Of P a r a s i t o i d s In The Budworm System P a r a s i t o i d s i n the model cannot keep budworm popula-t i o n s endemic. The other r o l e which they may have i n the model i s to c o l l a p s e an outbreak that has begun. Two s e t s of i s o r e c r u i t m e n t curves, one f o r the budworm, the other f o r the p a r a s i t o i d , f o r d i f f e r e n t f o l i a g e biomass l e v e l s ( F i g u r e 39), show that the j o i n t d e f o l i a t o r / p a r a s i t o i d e q u i l i b r i u m i s at the upper s t a b l e e q u i l i b r i u m f o r budworm, at about 2000 eggs/m2 of branch. F i g u r e 18 i n d i c a t e s that r a p i d d e c l i n e s i n f o l i a g e l e v e l s should occur at about 600 eggs/m2 , and d e c l i n e s i n f o l i a g e b r i n g about d e c l i n e s i n f o r e s t branch d e n s i t y ( F i g u r e 19). The r e f o r e , before the p a r a s i t o i d can c o l l a p s e an outbreak, some very d i f f e r e n t processes are s e t i n motion to b r i n g - 1 3 0 -1 0 0 0 0 F o l i a g e U n i t s F i g u r e 3 8 : B u d w o r m i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f f o l i a g e b i o m a s s w i t h d i f f e r e n t n o r m a l l e v e l s o f w e a t h e r - i n d u c e d l a r v a l s u r v i v a l . A h i g h f o r e s t b i o m a s s i s a s s u m e d . - 1 3 1 -P a r a s i t o i d A d u l t s F i g u r e 3 9 : B u d w o r m i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f p a r a s i t o i d d e n s i t y a n d p a r a s i t o i d i s o r e c r u i t -m e n t c u r v e s a s a f u n c t i o n o f b u d w o r m d e n s i t y , w i t h d i f f e r e n t f o l i a g e l e v e l s . - 132 -about t h i s c o l l a p s e . The p a r a s i t o i d has too slow a numeri-c a l response to be important i n the dynamics of the model budworm system. 4.9 Summary The analyses i n the preceding s e c t i o n s have i d e n t i f i e d a small set of processes which c r e a t e the e q u i l i b r i u m s t r u c -t u r e s f o r i n d i v i d u a l components of the e a s t e r n spruce budworm model: 1. avian p r e d a t i o n on budworm l a r v a e ; 2. e f f e c t s of i n t r a - s p e c i f i c c o m petition on budworm s u r v i v a l and f e c u n d i t y ; 3. p a r a s i t o i d f e c u n d i t y , p a r a s i t o i d progeny s u r v i v a l , and i n t r a - s p e c i f i c c o m petition among developing p a r a s i t o i d s caused by s u p e r - p a r a s i t i s m ; 4. density-dependent f o l i a g e growth; and 5. density-dependent f o r e s t growth. In a d d i t i o n , there i s a set of processes which d e t e r -mine how the p a r t i c u l a r e q u i l i b r i u m s t r u c t u r e s f o r the sy s -tem components i n t e r a c t to generate model behavior which i s c o n s i s t e n t with observed system behavior: 1. weather induced l a r v a l s u r v i v a l ; 2. the p a r a s i t o i d a t t ack parameters which d e f i n e i t s - 133 -numerical response to budworm; and 3. the s u s c e p t i b i l i t y of f o r e s t branch d e n s i t y to low f o l i a g e l e v e l s . The a n a l y s i s has shown that e q u i l i b r i u m s t r u c t u r e s f o r model components are s e t by s p e c i f i c model p r o c e s s e s , and that the c o n f i g u r a t i o n and i n t e r a c t i o n of e q u i l i b r i u m s t r u c -t u r e s of system components, along with time s c a l e s of response by key v a r i a b l e s , generate model behaviors which are q u a l i t a t i v e l y s i m i l a r to r e a l world behavior under s i m i -l a r c o n d i t i o n s . - 134 -5.0 THE JACK PINE SAWFLY SYSTEM The jack pine sawfly i s a n a t i v e d e f o l i a t i n g i n s e c t of the e a s t e r n b o r e a l f o r e s t of North America. I t i s found wherever jack p i n e , Pinus banksiana (Lamb.), o c c u r s , p r i -m a r i l y i n O n t a r i o and Quebec. The sawfly i s the major pest of jack p i n e , and w i l l not s u r v i v e on other host t r e e s (McLeod 1970) . 5.1 Documented Behavior The system e x h i b i t s e s s e n t i a l l y three types of behavior (McLeod 1970 1977a, Table I I I ) . F i r s t , over l a r g e areas of jack pine f o r e s t , outbreaks never occur and the i n s e c t i s never an economic concern. The i n s e c t can o f t e n be recovered i n F o r e s t Insect Survey samples i n these areas (Canada 1939 to p r e s e n t ) . These low sawfly numbers, of course, i n f l i c t l i t t l e d e f o l i a t i o n and the host f o r e s t grows l a r g e l y u n a f f e c t e d by the presence of the sawfly (Canada 1939 to present; McLeod 1970). T h i s type of behavior a l s o occurs i n immature jack pine f o r e s t s , as sawfly outbreaks are extremely r a r e i n young jack pine stands (McLeod, pers. comm.) . Second, i n some stands of jack p i n e , sawfly numbers become s u f f i c i e n t l y high to cause heavy d e f o l i a t i o n and some r e d u c t i o n of t r e e growth every 8 to 10 y e a r s . Tree m o r t a l -i t y i s r a r e . High sawfly p o p u l a t i o n s p e r s i s t f o r a maximum of 3 y e a r s , then c o l l a p s e . McLeod (1977a) found t h a t , between these outbreaks, the sawfly causes minor d e f o l i a t i o n - 135 -of the upper crowns of the dominant pine t r e e s i n stands. T h i r d , i n very r a r e cases, sawfly numbers reach extremely high l e v e l s . These very high p o p u l a t i o n s remove much of the f o l i a g e from the host t r e e s and i n f l i c t very heavy t r e e m o r t a l i t y . Whole stands of mature jack pine are l o s t and, unless f i r e r e l e a s e s the seed crop, are not r e p l a c e d . Sawfly p o p u l a t i o n s c o l l a p s e once t r e e d e f o l i a t i o n becomes high (McLeod 1977a). 5.2 System D e s c r i p t i o n 5.2.1 The D e f o l i a t o r The l i f e h i s t o r y of jack pine sawfly i s w e l l documented (McLeod 1968). The i n s e c t i s u n i v o l t i n e ; a d u l t emergence commences i n the e a r l y s p r i n g from puparia t h a t have overwintered i n the ground. A d u l t d i s p e r s a l i s minimal, as the female i s a very poor f l i e r . Larvae develop through 4 i n s t a r s . There i s no l a r v a l d i s p e r s a l . Larvae feed on f o l i a g e produced i n p r e v i o u s years f i r s t , but w i l l consume the c u r r e n t year's f o l i a g e supply i f the o l d f o l i a g e supply becomes d e p l e t e d . Once feed i n g i s f i n i s h e d i n the e a r l y f a l l , l a r v a e drop from the f o l i a g e to the ground to pupate; the pupal stage l a s t s f o r about 9 months. Weather i s a strong determinant of l a r v a l s u r v i v a l . T r i p p (1965) found that s u f f i c i e n t l y c o l d temperatures i n the l a t e summer and f a l l w i l l slow completion of l a r v a l f e e d i n g . - 136 -5.2.2 N a t u r a l Enemies A l a r g e complex of p a r a s i t o i d s has been recovered from the sawfly (McLeod 1975). The most important s p e c i e s attack l a r g e l a r v a e i n l a t e summer and emerge from the pupal stage i n the s p r i n g s h o r t l y before a d u l t emergence begins. The sawfly i s preyed upon by p r i m a r i l y 3 g u i l d s of ver-t e b r a t e p r e d a t o r s . Small n e s t i n g b i r d s consume the sawfly while they are i n the l a r g e l a r v a l stage and l a r g e f l o c k i n g b i r d s prey on a d u l t sawfly f o l l o w i n g a d u l t emergence i n the l a t e s p r i n g (McLeod 1974). F i n a l l y , small mammals, p r i -m a r i l y the common shrew, Sorex c i n e r e u s c i n e r e u s , prey on the sawfly d u r i n g i t s 9 month pupal stage (McLeod 1966). 5.2.3 The F o r e s t Jack pine stands are f i r e - o r i g i n a t e d and t h e r e f o r e are l a r g e l y of a s i n g l e or a very few age c l a s s e s (Rowe 1971). Jack pine r e t a i n s 4 years of f o l i a g e growth (McLeod 1977a). Jack pine grows best on poor sandy s o i l s and i s outcompeted on r i c h e r s i t e s . Young stands grow very q u i c k l y , and s t a g -n a t i o n of the stand begins to s e t i n very e a r l y , at about 35 y e a r s , with d e c l i n i n g volume and t r e e v i g o r . I f l e f t u ndis-turbed, jack pine i s slowly r e p l a c e d by climax black spruce (Rudolph 1958) . 5.3 Model D e s c r i p t i o n The s i m u l a t i o n model I used i n the f o l l o w i n g analyses i s d e s c r i b e d i n McLeod (1977a, 1977b); a d e t a i l e d monograph - 137 -about the system i s c u r r e n t l y being prepared (McLeod, i n p r e p . ) . The s i m u l a t i o n model r e p r e s e n t s a s y n t h e s i s of a 19 year r e s e a r c h program on the system i n northern Quebec. 5.3.1 S p a t i a l and Temporal C h a r a c t e r i s t i c s of The Model The model sim u l a t e s system dynamics on a uniform stand of jack pine f o r e s t . F o r e s t and f o l i a g e dynamics are simu-l a t e d once a year, while i n s e c t development and many of the processes a f f e c t i n g sawfly dynamics occur d u r i n g s p e c i f i c sawfly i n s t a r s . 5.3.2 F o r e s t Dynamics A s i n g l e age c l a s s of t r e e i s simulated from the time of f i r e i n i t i a t i o n . There i s no simulated r e g e n e r a t i o n of the f o r e s t with other t r e e s p e c i e s . Stand b a s a l area i s used i n the model as a surrogate f o r avian predator h a b i t a t and as an index of p o t e n t i a l f o l i a g e development. There are b a s e l i n e age-dependent t r e e s u r v i v a l and diameter growth r a t e s which change stand b a s a l area through time. These b a s e l i n e r a t e s are mo d i f i e d downward with the l e v e l of budworm f e e d i n g , measured as the percent d e f o l i a -t i o n of a l l f o l i a g e . 5.3.3 F o l i a g e Dynamics Four f o l i a g e age c l a s s e s are maintained and are meas-ured i n b a s a l area u n i t s . The number of u n i t s of new f o l i -age produced i n a year i s equal to the b a s a l area of the stand. A l l f o l i a g e g r e a t e r than f o u r years o l d i s dropped - 138 -from the t r e e . 5.3.4 D e f o l i a t o r and N a t u r a l Enemy Dynamics The major processes i n the model which i n f l u e n c e sawfly p o p u l a t i o n s are: 1. i n t r a - s p e c i f i c competition f o r f o l i a g e r e s o u r c e s ; 2. p r e d a t i o n , modelled using Type I I I f u n c t i o n a l responses, by b i r d s on l a r g e l a r v a e and a d u l t s ; 3. p r e d a t i o n , modelled using a Type I I I f u n c t i o n a l response, by small mammals on pupae; 4. p a r a s i t o i d attack on l a r g e l a r v a e and p a r a s i t o i d emergence from f u l l y - d e v e l o p e d pupae; and 5. weather i n f l u e n c e s modelled as a lognormally d i s -t r i b u t e d random v a r i a t e a c t i n g on young l a r v a e . The f o l l o w i n g d e s c r i p t i o n w i l l be important f o r the d i s c u s -s i o n s l a t e r i n the chapter. Larvae consume o l d f o l i a g e f i r s t , without p r e f e r e n c e f o r any of the three o l d f o l i a g e age c l a s s e s . Larvae make up r e s i d u a l f o l i a g e demand on new f o l i a g e i f necessary. Large l a r v a l s u r v i v a l and a d u l t female f e c u n d i t y i s l i n e a r l y p r o p o r t i o n a l to the f r a c t i o n of f o l i a g e demand that i s met durin g f e e d i n g . I t i s assumed that b i r d s search the t r e e crowns f o r - 139 -sawfly l a r v a e and a d u l t s , so that avian p r e d a t i o n i s simu-l a t e d on a t r e e volume b a s i s . On the other hand, because small mammals search the f o r e s t f l o o r f o r sawfly pupae, small mammal p r e d a t i o n i s simulated on an a r e a l b a s i s . F i n a l l y , p a r a s i t o i d s a t t a c k the l a s t i n s t a r l a r v a e and emerge from the pupae j u s t before a d u l t emergence. In the model, p a r a s i t o i d a t t a c k i s simulated a f t e r l a r v a l s t a r v a -t i o n m o r t a l i t y ( i f any) has been a p p l i e d , before a v i a n pre-d a t i o n on l a r v a e i s sim u l a t e d . P a r a s i t o i d emergence occurs a f t e r small mammal p r e d a t i o n i s c a l c u l a t e d . In the f i g u r e s used i n the f o l l o w i n g analyses, sawfly and sawfly p a r a s i t o i d p o p u l a t i o n s are expressed i n numbers/m2 of ground, f o l i a g e i s expressed i n f o l i a g e u n i t s , and f o r e s t b a s a l area i s expressed i n square meters/hectare. 5.4 Model E q u i l i b r i u m S t r u c t u r e 5.4.1 The D e f o l i a t o r A sawfly recruitment curve with a l l model processes i n c l u d e d and other v a r i a b l e s h e l d constant (Figure 40a) has 3 p o t e n t i a l s t a b l e e q u i l i b r i a ; each p a i r i s separated by a p o t e n t i a l u nstable e q u i l i b r i u m . The lowest p o t e n t i a l s t a b l e e q u i l i b r i u m disappears when avian p r e d a t i o n i s removed from the model ( F i g u r e 40b), the uppermost p o t e n t i a l s t a b l e e q u i l i b r i u m disappears when the e f f e c t s of i n t r a - s p e c i f i c c o m p e t i t i o n on l a r v a l s u r v i v a l and a d u l t female f e c u n d i t y are removed ( F i g u r e 40c), and the middle p o t e n t i a l s t a b l e e q u i l i b r i u m disappears when small mammal p r e d a t i o n on sawfly - 1 4 0 -EGGS Figure 40: Recruitment curve for jack pine sawfly. a - A l l processes included. b - Avian predation and parasitism removed, c - I n t r a - s p e c i f i c competition e f f e c t s removed. d - Small mammal predation removed. - 141 -pupae i s removed (Figure 40d). T h e r e f o r e , as with both pre-v i o u s models, avian p r e d a t i o n c r e a t e s the p o t e n t i a l f o r a s t a b l e e q u i l i b r i u m at very low d e n s i t i e s , and e f f e c t s of i n t r a - s p e c i f i c c o m petition c r e a t e the p o t e n t i a l f o r a s t a b l e e q u i l i b r i u m at very high d e n s i t i e s . In a d d i t i o n , small mam-mal p r e d a t i o n c r e a t e s the p o t e n t i a l s t a b l e e q u i l i b r i u m f o r sawfly at intermediate d e n s i t i e s . Avian p r e d a t i o n on sawfly i n the model i s c l o s e l y cou-p l e d to f o r e s t m a t u r i t y as measured by stand b a s a l area. The e q u i l i b r i u m s t r u c t u r e f o r the sawfly changes with chang-ing b a s a l area of stands ( F i g u r e 41), and t h i s e f f e c t i s most extreme at low sawfly d e n s i t i e s , where avian p r e d a t i o n has i t s g r e a t e s t e f f e c t . The e f f e c t of changing f o r e s t biomass on sawfly e q u i l i -brium s t r u c t u r e i s more e a s i l y p i c t u r e d i n an i s o r e c r u i t m e n t curve ( F i g u r e 42). An i s o r e c r u i t m e n t curve f o r the model with a l l processes i n c l u d e d has 3 s t a b l e s u r f a c e s separated by unstable s u r f a c e s . There i s a d i r e c t correspondence between the e q u i l i b r i a of Figure 40a and the domains of F i g -ure 42. P o i n t s k and 1, under the c o n d i t i o n s used to gen-er a t e t h i s i s o r e c r u i t m e n t curve, r e p r e s e n t the minimum b a s a l area f o r which the 2 uppermost s t a b l e s u r f a c e s remain, and p o i n t s m and n represent the maximum bas a l area f o r which the 2 lowermost s t a b l e s u r f a c e s remain. These p o i n t s w i l l be used i n the analyses below. 5.4.2 The P a r a s i t o i d - 142 -1 0 T 1 0 0 0 0 E g g s F i g u r e 4 1 : R e c r u i t m e n t c u r v e f o r j a c k p i n e s a w f l y f o r l o w t o h i g h f o r e s t b i o m a s s , r e p r e s e n t e d b y b a s a l a r e a . - 143 -1 0 0 0 0 150 B a s a l Area F i g u r e 42: Sawfly i s o r e c r u i t m e n t curve as a f u n c t i o n o f f o r e s t b a s a l area. P o i n t s k and 1 are the minimum b a s a l areas f o r which sawfly can remain on the uppermost s t a b l e s u r f a c e s . P o i n t s m and n are the maximum b a s a l areas under which sawfly can remain on the lowermost s t a b l e s u r f a c e s . - 144 -The p a r a s i t o i d has a s i n g l e s t a b l e domain (F i g u r e 43). The e q u i l i b r i u m p a r a s i t o i d d e n s i t y i n c r e a s e s as host d e n s i t y i n c r e a s e s . T h i s i s caused by i n c r e a s i n g s u p e r - p a r a s i t i s m r a t e s with high p a r a s i t o i d d e n s i t i e s (Appendix I I ) . The p o s i t i o n of the i s o r e c r u i t m e n t curve i s s e t by the numerical response of the p a r a s i t o i d to budworm d e n s i t i e s and i s determined by four parameters: p a r a s i t o i d f e c u n d i t y ; r a t e of s u c c e s s f u l search; p a r a s i t o i d progeny s u r v i v a l from the time of emergence from the host to the time of a t t a c k the f o l l o w -ing g e n e r a t i o n ; and the d i s p e r s i o n c o e f f i c i e n t of the nega-t i v e b i n o m i a l d i s t r i b u t i o n d e s c r i b i n g the degree of super-p a r a s i t i s m (Appendix I I ) . 5.4.3 The F o l i a g e F o l i a g e has a s i n g l e s t a b l e domain (Figure 44) and the e q u i l i b r i u m f o l i a g e biomass at low sawfly d e n s i t i e s (the f o l i a g e biomass i n a jack pine f o r e s t without sawfly) i n c r e a s e s with i n c r e a s i n g b a s a l area of stands. Very sim-p l y , f o l i a g e biomass i n stands without d e f o l i a t i o n i n c r e a s e s with i n c r e a s i n g f o r e s t m a t u r i t y . S i g n i f i c a n t f o l i a g e d e c l i n e occurs at a d e f o l i a t o r d e n s i t y of about 300 sawfly eggsm2/ . 5.4.4 The F o r e s t L i k e f o l i a g e , the f o r e s t a l s o has a s i n g l e s t a b l e e q u i l i b r i u m (Figure 45). F o r e s t d e c l i n e from d e f o l i a t i o n begins to occur i f f o l i a g e biomass decreases below about 350 u n i t s per h e c t a r e . - 145 -1 0 0 0 0 EGGS F i g u r e 4 3 : P a r a s i t o i d i s o r e c r u i t m e n t curve as a f u n c t i o n sawfly d e n s i t y . See S e c t i o n 5.5 f o r an explana-t i o n o f p o i n t s o and p. a - changing p a r a s i t i o d f e c u n d i t y . b - changing p a r a s t i o i d search r a t e . c - changing s u r v i v a l r a t e o f p a r a s i t o i d progeny. - 1 4 6 -10000 E g g s F i g u r e 4 4 : F o l i a g e i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f s a w f l y d e n s i t y w i t h h i g h , m o d e l , a n d l o w f o r e s t b a s a l a r e a . - 147 -l6o 600 F o l i a g e Biomass F i g u r e 4 5 : F o r e s t i s o r e c r u i t m e n t curve as a f u n c t i o n o f f o l i a g e biomass. - 148 -5.5 Model C o n d i t i o n s Which Keep Sawfly C h r o n i c a l l y Endemic S e c t i o n 5.2 o u t l i n e d 2 observed c o n d i t i o n s which keep sawfly endemic. F i r s t , young f o r e s t s never experience sawfly outbreaks (McLeod 1970). Second, extremely poor weather c o n d i t i o n s slow l a r v a l development i n extreme p a r t s of the i n s e c t ' s range ( T r i p p 1965). Is o r e c r u i t m e n t curves ( F i g u r e 46) show that the model produces both these s i t u a t i o n s . F i r s t , the lowest s t a b l e e q u i l i b r i u m e x i s t s under c o n d i t i o n s of low stand b a s a l area. Second, s u f f i c i e n t l y poor e a r l y l a r v a l s u r v i v a l , even i n a f o r e s t with a high b a s a l area which would o r d i n a r i l y be able to generate an outbreak, moves p o i n t n (see Figure 42) to the f a r r i g h t of the graph and past the maximum p o s s i b l e stand b a s a l area. S u f f i c i e n t l y high p a r a s i t o i d l e v e l s can a l s o move p o i n t n past the maximum p o s s i b l e stand b a s a l area and t h e r e f o r e p o t e n t i a l l y keep sawfly p o p u l a t i o n s c h r o n i c a l l y endemic ( F i g u r e 47a). However, u n l i k e the budworm models, low f o l i -age biomass does not move p o i n t n past the maximum p o s s i b l e f o r e s t biomass (Figure 47b). Low f o l i a g e l e v e l s i n t h i s model, then, cannot p o t e n t i a l l y keep sawfly c h r o n i c a l l y endemic. As i n the previous models, the q u e s t i o n remains whether, i n a mature f o r e s t , the number of p a r a s i t o i d s r e q u i r e d (the rightmost curve i n Fig u r e 47a, about .07 adults/m 2 ) to keep sawfly c h r o n i c a l l y endemic (endemic i s - 149 -Figure 46: Sawfly isorecruitment curves as a function of basal area with normal to extremely poor early l a r v a l s u r v i v a l . - 1 5 0 -loooo O o 10000 1000 100 10 . 1 150 BASAL AREA Figure 4 7 : Sawfly isorecruitment curves as a function of basal area. a - With d i f f e r e n t adult parasitoid d e n s i t i e s . b - With d i f f e r e n t foliage biomass l e v e l s . - 151 -about 3.2 eggs/m 2, from Figure 47a) can be supported by that d e n s i t y of sawfly. F i g u r e 43a shows that o n l y about .012 a d u l t p a r a s i t o i d s / m 2 ( p o i n t p) can be supported when the sawfly d e n s i t y i s 3.2 sawfly eggs/m 2 ( p o i n t o ) . P a r a s i -t o i d s , then, cannot keep sawfly endemic. The r e s u l t of t h i s a n a l y s i s show that low stand b a s a l area and low weather-induced e a r l y l a r v a l s u r v i v a l are the two c o n d i t i o n s i n the model which can keep sawfly p o p u l a t i o n s c h r o n i c a l l y endemic. 5.6 The Role Of Weather The preceeding a n a l y s i s showed that very poor weather-induced l a r v a l s u r v i v a l can remove any p o s s i b i l i t y of the sawfly having upper e q u i l i b r i u m ( i . e . outbreak) d e n s i t i e s ( F i g u r e 46). Normal v a r i a t i o n i n weather (Figure 48) s h i f t s the sawfly i s o r e c r u i t m e n t curve to the l e f t and r i g h t of the curve f o r normal weather c o n d i t i o n s , but the lower s t a b l e e q u i l i b r i u m never d i s a p p e a r s . T h e r e f o r e , normal weather v a r i a t i o n i n the model can advance or delay major s h i f t s i n sawfly p o p u l a t i o n s but i t cannot cause those s h i f t s . The r e s u l t s of t h i s a n a l y s i s means that weather e f f e c t s can be ignored i n any remaining model analyses and that constant normal weather c o n d i t i o n s w i l l be used i n the f o l l o w i n g ana-l y s e s . The r e s u l t s would be the same under any normal f l u c -t u a t i o n i n weather e f f e c t s . 5.7 The Role Of The P a r a s i t o i d S e c t i o n 5.5 demonstrated that the p a r a s i t o i d could not keep sawfly c h r o n i c a l l y endemic ( F i g u r e s 43, 47). There - 152 -Figure 48: Sawfly isorecruitment curves as a function of basal area with normal v a r i a t i o n i n weather-induced early l a r v a l s u r v i v a l . - 153 -remains the p o s s i b i l i t y t h a t the p a r a s i t o i d can b r i n g sawfly to endemic l e v e l s once i t has moved o f f i t s lower s t a b l e e q u i l i b r i u m . An o v e r l a y of sawfly and p a r a s i t o i d i s o r e c r u i t m e n t curves f o r d i f f e r e n t f o l i a g e l e v e l s ( F igure 49) shows that the curves i n t e r s e c t j u s t where the lowest unstable curve (set by the d e c l i n i n g m o r t a l i t y from avian p r e d a t i o n ) becomes the middle s t a b l e curve ( s e t by small mammal preda-t i o n ) . The common e q u i l i b r i u m does not s h i f t with changing f o l i a g e l e v e l s because the p a r a s i t o i d a t t a c k s sawfly a f t e r sawfly has consumed f o l i a g e and s u f f e r e d any s t a r v a t i o n mor-t a l i t y . S i g n i f i c a n t d e c l i n e i n f o l i a g e begins to occur above about 300 sawfly eggs/m 2 ; t h i s i s only s l i g h t l y above the sawfly d e n s i t y at the common p a r a s i t o i d / s a w f l y e q u i l i b r i u m ( F i g u r e 49). Furthermore, moderate d e c l i n e s i n f o l i a g e can cause very l a r g e d e c l i n e s i n f o r e s t l e v e l s ( F i g u r e 45). The p a r a s i t o i d numerical response i s c r u c i a l i n determining the behavior of the model. The behavior of the model would l i k e l y be very d i f -f e r e n t with d i f f e r e n t p a r a s i t o i d numerical responses. With a slow p a r a s i t o i d , sawfly would i n c r e a s e to the upper e q u i l i b r i u m d e f i n e d by food l i m i t a t i o n (about 2000 eggs/m2 ; Fig u r e 49). Once sawfly reach about 300/m2 , f o l i a g e biomass begins to d e c l i n e very q u i c k l y ( F i g u r e 44) and d e c l i n i n g f o l i a g e l e v e l s , c r e a t e very quick d e c l i n e s i n stand b a s a l 1 0 0 0 0 B - H P a r a s i t o i d A d u l t s F i g u r e 4 9 : S a w f l y i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f p a r a s i t o i d d e n s i t y a n d p a r a s i t o i d i s o r e c r u i t m e n t c u r v e s a s a f u n c t i o n o f s a w f l y d e n s i t y f o r d i f f e r e n t f o l i a g e l e v e l s . - 155 -area (Figure 45). T h e r e f o r e , a slow p a r a s i t o i d i n the model would permit higher outbreak sawfly p o p u l a t i o n s and cause heavy d e c l i n e s i n f o l i a g e biomass and f o r e s t b a s a l area. The d e c l i n e i n f o l i a g e biomass would remove the upper e q u i l i b r i u m ( F i g u r e 49b) and sawfly would d e c l i n e to i t s lowest s t a b l e e q u i l i b r i u m . The process determining the p e r i o d i c i t y of d e f o l i a t o r p o p u l a t i o n s would be the r a t e of f o r e s t growth i n that another i n f e s t a t i o n c o u l d not be gen-erated u n t i l a new f o r e s t had regrown. The behavior sug-gested by the e q u i l i b r i u m s t r u c t u r e with a slow p a r a s i t o i d i s much l i k e the second type of system behavior d e s c r i b e d i n S e c t i o n 5.1. On the other hand, a p a r a s i t o i d with a r a p i d numerical response would cause t i g h t c y c l i n g around the common e q u i l i -brium ( F i g u r e 49). This would cause l i t t l e d e c l i n e s i n f o l i a g e and f o r e s t . In t h i s case, system behavior would be determined by the p a r a s i t o i d numerical response. The r a t e of numerical response of the p a r a s i t o i d cannot be induced from simple examination of i s o r e c r u i t m e n t curves. I f the p a r a s i t o i d has a r a p i d numerical response, f o l i a g e and f o r e s t d e c l i n e s from peak budworm p o p u l a t i o n s should be minimal. T h i s behavior would be much l i k e the second type of system behavior d e s c r i b e d i n S e c t i o n 5.1. However, I must r e s o r t to model s i m u l a t i o n to f i n d out the type of numerical response the p a r a s i t o i d has and, t h e r e f o r e , which behavior the model w i l l e x h i b i t with a normal p a r a s i t o i d . - 156 -We have reached the l i m i t s of the a n a l y s i s p o s s i b l e using e q u i l i b r i u m s t r u c t u r e alone. The f o l l o w i n g s e c t i o n s examine the behavior generated from the model. 5.8 Temporal Model Behavior 5.8.1 C h r o n i c a l l y Poor Weather C o n d i t i o n s F i g u r e 46 showed that very poor e a r l y l a r v a l s u r v i v a l c ould keep sawfly numbers at a lower s t a b l e e q u i l i b r i u m and t h e r e f o r e endemic. Model behavior under t h i s c o n d i t i o n (Figure 50) shows that sawfly numbers do remain endemic. The i n i t i a l years of endemic sawfly p o p u l a t i o n s are gen-e r a t e d because of the low f o r e s t biomass ( F i g u r e 46). Endemic sawfly remain endemic i n s p i t e of the high f o r e s t biomass ( F i g u r e 50d) because of the poor weather-induced e a r l y l a r v a l s u r v i v a l . The c h r o n i c a l l y endemic sawfly popu-l a t i o n s allow f o r unhindered f o l i a g e and f o r e s t growth ( F i g -ure 50c,d). T h i s behavior i s very s i m i l a r to observed behavior of the system i n many p a r t s of i t s range (Table I I I , McLeod 1970), e s p e c i a l l y i n extreme northern areas ( T r i p p 1965) . 5.8.2 Normal Weather C o n d i t i o n s Under normal weather c o n d i t i o n s , the model can generate 2 d i f f e r e n t b e h a v i o r s , depending upon the p a r a s i t o i d numeri-c a l response. F i g u r e 51 shows the model behavior when the p a r a s i t o i d has a f a s t numerical response to sawfly a f t e r the s a w f l y 1 s lowest s t a b l e e q u i l i b r i u m has disappeared due to high stand b a s a l area. The system o s c i l l a t e s around the - 157 -F i g u r e 5 0 : M o d e l b e h a v i o r w i t h c h r o n i c a l l y p o o r w e a t h e r -i n d u c e d e a r l y l a r v a l s u r v i v a l . - 158 -Figure 51: Model behavior with normal va r i a t i o n i n weather-induced early l a r v a l s u r v i v a l . - 159 -common d e f o l i a t o r / p a r a s i t o i d e q u i l i b r i u m of Fig u r e 49. Sawfly outbreaks are generated about every 8 to 10 years ( F i g u r e 51a); these outbreaks cause some d e c l i n e i n f o l i a g e l e v e l s ( F igure 51c), but very l i t t l e d e c l i n e i n f o r e s t biomass (Figure 51d). P a r a s i t o i d numbers o s c i l l a t e with changes i n host l e v e l s with a 1 year l a g (F i g u r e 51b). T h i s behavior generated by the model i s very s i m i l a r to the com-mon behavior of the system when the sawfly does e x h i b i t out-breaks (Table I I I , S e c t i o n 5.1, McLeod 1977a). The behavior generated by the model with a slower p a r a s i t o i d ( F i g u r e 52, made with a p a r a s i t o i d progeny s u r -v i v a l r a t e which i s 50% of normal), c o n t a i n s a s i n g l e mas-s i v e sawfly outbreak when the f o r e s t b a s a l area becomes high enough f o r the lowest s t a b l e e q u i l i b r i u m to disappear ( F i g -ure 46). T h i s l a r g e outbreak causes heavy l o s s of f o l i a g e and subsequent d e c l i n e s of f o r e s t ( F i g u r e s 52c,d). P a r a s i -t o i d numbers remain very low throughout the s i m u l a t i o n ( F i g -ures 52b). T h i s behavior i s very s i m i l a r to the rare type of behavior (Table I I I , S e c t i o n 5.2, McLeod 1977a, Canada 1939 to p r e s e n t ) . C o n d i t i o n s f o r producing massive outbreaks i n the r e a l system have not been documented. My a n a l y s i s suggests that some event may have a d v e r s e l y a f f e c t e d the p a r a s i t o i d popu-l a t i o n and reduced i t s e f f e c t i v e n e s s i n some way, s i n c e the only way to generate t h i s type of behavior i n the model i s to slow the p a r a s i t o i d numerical response to prevent c y c l i n g around the j o i n t p a r a s i t o i d - s a w f l y e q u i l i b r i u m . - 1 6 0 -H * YERR YERR Model behavior with pa r a s i t o i d progeny survival at 50% of normal and normal v a r i a t i o n i n weather-induced early l a r v a l s u r v i v a l . - 161 -5.9 A Fourth Type of Behavior The reason f o r the c o l l a p s e of f o l i a g e biomass and f o r e s t b a s a l area from a massive sawfly outbreak (when the model p a r a s i t o i d i s made slow) i s t h a t the f o r e s t i s s e n s i -t i v e to l o s s of f o l i a g e ( F i g u r e 45). F o r e s t b a s a l area d e c l i n e s very q u i c k l y with only moderate l o s s of f o l i a g e . In t h i s s e c t i o n , I w i l l a l t e r the e q u i l i b r i u m s t r u c t u r e of the f o r e s t to generate another type of model behavior. I a l t e r e d the model f u n c t i o n s r e l a t i n g d e f o l i a t i o n to r e d u c t i o n i n r a d i a l growth and i n c r e a s e i n t r e e m o r t a l i t y , so that more d e f o l i a t i o n was needed to cr e a t e growth and m o r t a l i t y e f f e c t s . T h i s , i n e f f e c t , makes the jack pine l e s s v u l n e r a b l e to m o r t a l i t y from a given l e v e l of d e f o l i a -t i o n . T h i s m o d i f i e d the f o r e s t e q u i l i b r i u m s t r u c t u r e as shown i n Fig u r e 53 (compare to Fig u r e 45); a very l a r g e d e c l i n e i n f o l i a g e biomass i s now needed to decrease the s t a b l e f o r e s t b a s a l area. The e q u i l i b r i u m s t r u c t u r e now d e f i n e d by F i g u r e s 42, 44, and 53 i s d i f f e r e n t to any p r e v i o u s l y d e f i n e d . Given a mature f o r e s t , the lowest s t a b l e e q u i l i b r i u m f o r sawfly d i s a p p e a r s , l e a v i n g the d e f o l i a t o r f r e e to i n c r e a s e to the upper s t a b l e e q u i l i b r i u m (the p a r a s i t o i d i s assumed again to have a slow numerical response). F o l i a g e l e v e l s begin to d e c l i n e very q u i c k l y once sawfly i n c r e a s e to about 300/m , and the s t a b l e f o l i a g e l e v e l i s extremely low once sawfly reach t h e i r upper e q u i l i b r i u m . But, f o r e s t b a s a l area - 162 -Figure 5 3 : Forest equilibrium structure with lowered v u l n e r a b i l i t y to d e f o l i a t i o n . Compare with Figure 4 5 . - 163 -remains high over a l a r g e range of f o l i a g e biomass ( F i g u r e 53). The uppermost e q u i l i b r i u m f o r sawfly d i s a p p e a r s with s u f f i c i e n t l y low f o l i a g e l e v e l s , and these low f o l i a g e l e v -e l s generated by high sawfly i n t u r n c o l l a p s e the sawfly p o p u l a t i o n . The middle s t a b l e e q u i l i b r i u m remains under low f o l i a g e c o n d i t i o n s and sawfly d e n s i t i e s should decrease to t h i s l e v e l . Stand b a s a l area should s t i l l be high at the end of the outbreak, and the low ( r e l a t i v e l y ) sawfly d e n s i -t i e s and s t i l l high b a s a l area should allow the f o l i a g e l e v -e l s to recover ( F i g u r e 44). Sawfly numbers should i n c r e a s e once again a f t e r f o l i a g e l e v e l s have regenerated. The p i c t u r e t h at emerges from t h i s e q u i l i b r i u m s t r u c -t ure i s that model behavior i s s e t by the r e c r u i t m e n t and dynamics of f o l i a g e . The behavior that should r e s u l t should be one where the d e f o l i a t o r p o p u l a t i o n moves from the middle s t a b l e e q u i l i b r i u m to the upper s t a b l e e q u i l i b r i u m and back with the growth and d e c l i n e of f o l i a g e . Because the p a r a s i -t o i d has a slow numerical response to sawfly, they should remain at low l e v e l s throughout the s i m u l a t i o n . T h i s i s e x a c t l y the behavior generated by the model (Fi g u r e 54). Movement of sawfly p o p u l a t i o n s from 300 eggs/m2 to higher l e v e l s appears to occur at i n t e r v a l s of about 10 y e a r s . These cause l a r g e d e c l i n e s i n f o l i a g e , but l i t t l e to moderate d e c l i n e i n f o r e s t b a s a l area. The p e r i o d i c i t y of outbreaks i n t h i s s i t u a t i o n i s very s i m i l a r to that i n the f a s t p a r a s i t o i d case ( F i g u r e 51). - 164 -Figure 54: Model behavior with parasitoid progeny survival at 50% of normal, normal v a r i a t i o n i n weather-induced early l a r v a l s u r v i v a l , and reduced forest v u l n e r a b i l i t y to d e f o l i a t i o n . - 165 -The evidence from e x i s t i n g long term sawfly p o p u l a t i o n data (Table I I I , Appendix I) suggests t h a t the 6 to 10 year out-break p e r i o d i s determined by a f a s t p a r a s i t o i d . Model r e s u l t s suggest t h a t , i f the 6 to 10 year outbreak p e r i o d i s determined by a d e f o l i a t o r / f o l i a g e c y c l i n g , sawfly popula-t i o n s would r e g u l a r l y reach g r e a t e r than 1000 eggs/m2 and that the p o p u l a t i o n would r a r e l y drop below about 300 eggs/m 2 ( F i g u r e 54). However, i f the 6 to 10 year outbreak p e r i o d i s determined by a d e f o l i a t o r / p a r a s i t o i d c y c l i n g , sawfly p o p u l a t i o n s would reach 300 eggs/m2 during outbreak peaks and would d e c l i n e to l e s s than 100 eggs/m2 between outbreaks. The jack pine sawfly data i n Appendix I show th a t the l a t t e r i s a more r e a l i s t i c d e s c r i p t i o n of the d e f o l i a t o r p o p u l a t i o n behavior. But, t h i s f o u r t h type of behavior does i n d i c a t e t h a t d e f o l i a t o r / f o l i a g e c y c l i n g may produce q u a l i t a t i v e behaviors that are d i f f i c u l t to d i s t i n g u i s h from behaviors generated by d e f o l i a t o r / p a r a s i t o i d c y c l i n g on the b a s i s of d e f o l i a t o r p o p u l a t i o n behavior alone. I w i l l r e t u r n to t h i s i s s u e i n development of the i n t e g r a t i v e theory i n Chapter 6. 5.10 Summary The analyses i n the preceding s e c t i o n s have i d e n t i f i e d a s m a l l s e t of processes which c r e a t e the e q u i l i b r i u m s t r u c -t u r e s f o r i n d i v i d u a l components of the jack pine sawfly sys-tem: - 166 -1. avian p r e d a t i o n on sawfly l a r v a e and a d u l t s ; 2. e f f e c t s of i n t r a - s p e c i f i c c o m petition on sawfly s u r v i v a l and f e c u n d i t y ; 3. p a r a s i t o i d f e c u n d i t y , p a r a s i t o i d progeny s u r v i v a l , r a t e of s u c c e s s f u l search, and i n t r a - s p e c i f i c com-p e t i t i o n among developing p a r a s i t o i d s caused by s u p e r - p a r a s i t i s m ; 4. density-dependent f o l i a g e growth; and 5. density-dependent f o r e s t growth. In a d d i t i o n , there i s a set of processes which d e t e r -mine how the p a r t i c u l a r e q u i l i b r i u m s t r u c t u r e s f o r the sy s -tem components i n t e r a c t to generate model behavior which i s c o n s i s t e n t with observed system behavior: 1. weather induced l a r v a l s u r v i v a l ; 2. the p a r a s i t o i d a t t a c k parameters which d e f i n e i t s numerical response to sawfly; and 3. the s u s c e p t i b i l i t y of f o r e s t branch d e n s i t y to low f o l i a g e l e v e l s . The p a r a s i t o i d a t t a c k parameters are most important, f o r they determine the r a t e of p a r a s i t o i d numerical response. S u f f i c i e n t l y r a p i d p a r a s i t o i d numerical response generates behavior which i s c o n s i s t e n t with the observed - 16 7 -common p a t t e r n of outbreaks (Figure 51). S u f f i c i e n t l y slow p a r a s i t o i d numerical response generates behavior r a r e l y observed i n t h i s system (Figure 52). The a n a l y s i s has shown that e q u i l i b r i u m s t r u c t u r e s f o r model components are set by s p e c i f i c model p r o c e s s e s , and that the c o n f i g u r a t i o n and i n t e r a c t i o n of e q u i l i b r i u m s t r u c -t u r e s of system components, along with time s c a l e s of response by key v a r i a b l e s , generate model behaviors which are q u a l i t a t i v e l y s i m i l a r to r e a l world behavior under s i m i -l a r c o n d i t i o n s . - 168 -6.0 THE INTEGRATIVE THEORY 6.1 I n t r o d u c t i o n The d e t a i l e d a n a l y s i s of the s t r u c t u r e and behavior of three d e f o l i a t i n g i n s e c t models i n Chapters 3 to 5 showed that the models mimic w e l l the q u a l i t a t i v e behavior of the systems they r e p r e s e n t (Table I I I ) . T h i s chapter i n t e g r a t e s these a n a l y s e s , with p e r t i n e n t o b s e r v a t i o n s presented i n Table I I I , i n t o a g e n e r a l theory of the s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems. Before developing t h i s theory, i t i s worthwhile to r e i t e r a t e the o b j e c t i v e s of t h i s t h e s i s : 1. d e f i n e a set of components, or s t a t e and d r i v i n g v a r i a b l e s which are necessary and s u f f i c i e n t to p r e d i c t the q u a l i t a t i v e p r o p e r t i e s of d e f o l i a t i n g i n s e c t system behavior; 2. c o l l a p s e the p l e t h o r a of d e f o l i a t i n g i n s e c t system behaviors i n t o a s m a l l s e t of c l a s s e s , each i d e n -t i f i e d by c h a r a c t e r i s t i c temporal p r o p e r t i e s of the components; 3. show how the c l a s s e s of behavior can be deduced from a s e t of key i n t e r a c t i o n s among the com-ponents ; 4. show that the s t a t e components each e x h i b i t one of a small number of d i f f e r e n t e q u i l i b r i u m s t r u c -t u r e s ; and - 1 6 9 -5. show that the key i n t e r a c t i o n s among the com-ponents which determine system behavior and the e q u i l i b r i u m s t r u c t u r e s of the components i n any d e f o l i a t i n g i n s e c t system can be p r e d i c t e d with a minimum s e t of i n f o r m a t i o n about the components themselves. Each o b j e c t i v e above w i l l be d e a l t with i n a separate sec-t i o n below. 6 . 2 Elements Of Observed Behavior Not In Model Analyses There are important elements of Table I I I which were not a p a r t of any of the d e t a i l e d system analyses of Chapters 3 to 5 and which have to be c o n s i d e r e d i n the development of the i n t e g r a t i v e theory. The most obvious one i s the f a c t t h a t the outbreaks i n many of the systems d e s c r i b e d i n Table I I I are terminated by d i s e a s e e p i z o o t i c s but d i s e a s e i s not a v a r i a b l e i n any of the three systems analyzed i n the p r e v i o u s three c h a p t e r s . In t r u t h , d e f o l i a -t o r d i s e a s e s occur i n a l l d e f o l i a t i n g i n s e c t systems. They happen to be unimportant i n determining the behavior of the three systems I analyzed i n d e t a i l . I w i l l have to r e l y on work of other s c i e n t i s t s i n order to i n c o r p o r a t e disease i n t o the i n t e g r a t i v e theory. The temporal behavior of the systems i n which d i s e a s e e p i z o o t i c s have been observed to terminate d e f o l i a t o r outbreaks i s very s i m i l a r to the tem-p o r a l behavior of those systems i n which p a r a s i t i s m has been observed to terminate outbreaks. I w i l l t h e r e f o r e assume - 1 7 0 -that the behavior of systems i n which d i s e a s e terminates outbreaks w i l l be the same as the behavior of systems i n which p a r a s i t o i d s terminate outbreaks. A l s o , i t i s not c l e a r whether d e f o l i a t i n g i n s e c t system behavior s e t by a d e f o l i a t o r / p a r a s i t o i d c y c l e can always be d i s t i n g u i s h e d from one which i s s e t by a d e f o l i a t o r / f o l i a g e c y c l e (see Chapter 5 ) . T h i s i s s u e w i l l be d i s c u s s e d i n Sec-t i o n 6.5.3. The major elements of the i n t e g r a t i v e theory are presented i n b o l d f a c e below. 6 . 3 System Components The e s s e n t i a l q u a l i t a t i v e p r o p e r t i e s of d e f o l i a t i n g i n s e c t system behavior can be captured with v a r i a b l e s r e p r e s e n t i n g the dynamics of the d e f o l i a t o r , the f o r e s t , the f o l i a g e , the p a r a s i t o i d , and the d i s e a s e , and a v a r i a b l e r e p r e s e n t i n g the e f f e c t of weather on the d e f o l i a t o r The three models analyzed i n Chapters 3 to 5 were con-s t r u c t e d with a minimum number of s t a t e v a r i a b l e s r e q u i r e d to r e p r e s e n t the dynamics of the systems: the d e f o l i a t o r d e n s i t y , the f o r e s t biomass or l e v e l of m a t u r i t y , the f o l i -age biomass, and the p a r a s i t o i d d e n s i t y . In a d d i t i o n , Table I I I i n d i c a t e s t h a t d i s e a s e i s o f t e n an important determinant of b e h a v i o r . A d r i v i n g v a r i a b l e , r e p r e s e n t i n g weather e f f e c t s on d e f o l i a t o r s u r v i v a l , completes the l i s t of com-ponents. The s i m u l a t i o n of the 5 s t a t e v a r i a b l e s p l u s the e f f e c t s of a d r i v i n g v a r i a b l e s i m u l a t i n g weather-induced d e f o l i a t o r m o r t a l i t y , and a s e t of processes d e f i n i n g - 171 -i n t e r a c t i o n among them, can capture the e s s e n t i a l q u a l i t a -t i v e p r o p e r i t e s of d e f o l i a t i n g i n s e c t systems. 6.4 C l a s s e s of Behavior There are 4 qualitatively different classes of defoliating insect system behavior In a l l the behaviors generated by the 3 models, 4 d i s -t i n c t c l a s s e s can be i d e n t i f i e d ( F i g u r e 55). 6.4.1 C l a s s 1; Chronic Endemic T h i s c l a s s of behavior i s c h a r a c t e r i z e d by an absence of d e f o l i a t o r outbreaks with no v i s i b l e d e f o l i a t i o n or f o r e s t m o r t a l i t y . The e a s t e r n spruce budworm, e a s t e r n black-headed budworm, and jack pine sawfly models and s y s -tems e x h i b i t t h i s behavior, as do probably most d e f o l i a t i n g i n s e c t systems i n some p a r t s of t h e i r range. 6.4.2 C l a s s 2: D e f o l i a t o r / P a r a s i t o i d - D i s e a s e Cycle T h i s c l a s s of behavior i s c h a r a c t e r i z e d by short dura-t i o n , frequent d e f o l i a t o r outbreaks with high p a r a s i t i s m or dise a s e m o r t a l i t y r a t e s i n the d e c l i n e phase of outbreaks. F o l i a g e and f o r e s t biomass are l a r g e l y u n a f f e c t e d by i n s e c t l e v e l s d u r i n g outbreaks. The jack pine sawfly and e a s t e r n black-headed budworm models and systems e x h i b i t t h i s b e h avior. 6.4.3 C l a s s 3: D e f o l i a t o r / F o l i a g e C y c l e T h i s c l a s s of behavior i s c h a r a c t e r i z e d by p e r i o d i c outbreaks causing l a r g e d e c l i n e s of f o l i a g e but r e l a t i v e l y - 172 -CLASS I CLASS 2 TIME — T I M E — * - TIME — T I M E DEFOLIATOR FOLIAGE PARASITE FOREST F i g u r e 55: The 4 c l a s s e s of i n s e c t / f o r e s t system b e h a v i o r , shown i n s t y l i z e d f a s h i o n . - 173 -s m a l l d e c l i n e s i n f o r e s t b i o m a s s . T h i s b e h a v i o r was g e n -e r a t e d i n t h e e a s t e r n s p r u c e budworm/balsam f i r s p r u c e and t h e j a c k p i n e s a w f l y / j a c k p i n e m o d e l s and has been o b s e r v e d i n t h e e a s t e r n s p r u c e budworm s y s t e m i n p u r e s t a n d s o f w h i t e s p r u c e . 6.4.4 C l a s s 4; D e f o l i a t o r / F o r e s t C y c l e T h i s c l a s s o f b e h a v i o r i s c h a r a c t e r i z e d by l o n g - l a i n f e s t a t i o n s o c c u r i n g w i t h low f r e q u e n c y . I n f e s t a c a u s e l a r g e d e c l i n e s i n f o l i a g e and f o r e s t b a s a l a r e a b o t h r e c o v e r t o h i g h l e v e l s between o u t b r e a k s , b e h a v i o r was g e n e r a t e d i n a l l m o d e l s . 6.5 P r o c e s s e s D e t e r m i n i n g System B e h a v i o r The p a r t i c u l a r c l a s s o f b e h a v i o r a s y s t e m e x h i b i t s i s d e t e r m i n e d by w e a t h e r e f f e c t s on d e f o l i a t o r s u r v i v a l , t h e s p e e d o f t h e p a r a s i t o i d n u m e r i c a l r e s p o n s e , t h e s p e e d o f t h e d i s e a s e n u m e r i c a l r e s p o n s e , and t h e s e n s i t i v i t y o f t h e f o r e s t t o low f o l i a g e l e v e l s The b e h a v i o r o f any p a r t i c u l a r d e f o l i a t i n g i n s e c t s y s -tem i s d e t e r m i n e d by a s m a l l s e t o f p r o c e s s e s . 6.5.1 C l a s s 1 B e h a v i o r C l a s s 1 b e h a v i o r i s a s s o c i a t e d i n t h e m o d e l s w i t h h i g h d e f o l i a t o r m o r t a l i t y f r o m w e a t h e r e f f e c t s w h i c h m a i n t a i n s a b e l o w - o u t b r e a k s t a b l e e q u i l i b r i u m d e n s i t y f o r t h e d e f o l i a t o r ( F i g u r e s 15, 36, 4 6 ) . 6.5.2 C l a s s 2 B e h a v i o r s t i n g t i o n s and T h i s T h i s b e h a v i o r i n t h e m o d els i s a s s o c i a t e d w i t h n o r m a l - 174 -r a t e s of weather-induced l a r v a l s u r v i v a l and a p a r a s i t o i d which has a r a p i d numerical response to changes i n d e f o l i a -t o r d e n s i t i e s , r e l a t i v e to d e f o l i a t o r r e c r u i t m e n t . The tem-p o r a l p a t t e r n s of behavior i n t h i s c l a s s occur because of the i n t e r a c t i o n between the f a s t v a r i a b l e , the d e f o l i a t o r , and another f a s t v a r i a b l e , the p a r a s i t o i d or the d i s e a s e . The p e r i o d i c i t y of behavior i s s e t by the numerical response of the p a r a s i t o i d or d i s e a s e . The p a r a s i t o i d or d i s e a s e i s a s u f f i c i e n t l y f a s t v a r i a b l e that the f o l i a g e or f o r e s t e q u i l i b r i u m s t r u c t u r e has no i n f l u e n c e on the temporal behavior. 6.5.3 C l a s s 3 Behavior T h i s behavior i n the models i s a s s o c i a t e d with normal r a t e s of weather-induced d e f o l i a t o r s u r v i v a l , a slow p a r a s i -t o i d and d i s e a s e ( r e l a t i v e to the d e f o l i a t o r ) , and a f o r e s t which i s i n v u l n e r a b l e to d e c l i n e s i n f o l i a g e biomass. The p e r i o d i c i t y of events i s determined by the growth and replacement of the f o l i a g e v a r i a b l e . T h i s means that the temporal p a t t e r n of t h i s behavior w i l l be i n d i s t i n g u i s h a b l e from that of a C l a s s 2 system f o r p a r t i c u l a r f o l i a g e r ecovery times and i m p l i e s that simply examining the out-break frequency i s i n s u f f i c i e n t to determine what c l a s s of behavior the system i s e x h i b i t i n g . The p a r a s i t o i d and d i s e a s e are s u f f i c i e n t l y slow v a r i a b l e s that they have no i n f l u e n c e on system behavior. The f o r e s t v a r i a b l e i s insen-s i t i v e to l o s s of f o l i a g e and t h e r e f o r e a l s o does not i n f l u -ence the behavior of the system. - 175 -6.5.4 C l a s s 4 Behavior T h i s behavior i s a s s o c i a t e d with normal l e v e l s of weather-induced l a r v a l s u r v i v a l , a slow p a r a s i t o i d and di s e a s e ( r e l a t i v e to the d e f o l i a t o r ) , and a f o r e s t which i s v u l n e r a b l e to d e c l i n e s i n f o l i a g e l e v e l s . The behavior i s determined by the i n t e r a c t i o n of the the d e f o l i a t o r and the f o r e s t . The p a r a s i t o i d and d i s e a s e v a r i a b l e s are too slow to have any i n f l u e n c e on system behavior, and the s e n s i -t i v i t y of the f o r e s t v a r i a b l e to low f o l i a g e l e v e l s means that the p e r i o d i c i t y of events i s s e t by the growth and replacement of the f o r e s t . 6.6 Information Required To P r e d i c t System Behavior 6 . 6 . 1 Weather E f f e c t s Weather e f f e c t s can be p r e d i c t e d by knowing comparative d e f o l i a t o r developmental r a t e s Weather c o n d i t i o n s w i l l i n v a r i a b l y cause some m o r t a l i t y to the d e f o l i a t o r . I t i s the amount of m o r t a l i t y that weather f a c t o r s i n f l i c t which determines whether a C l a s s 1, C l a s s 5, or some other behavior w i l l r e s u l t . Weather-induced r e d u c t i o n i n l a r v a l s u r v i v a l s h i f t s the i s o r e c r u i t -ment curves, whatever t h e i r c o n f i g u r a t i o n may be, such that only the lowest s t a b l e e q u i l i b r i u m remains. The e f f e c t s of weather on d e f o l i a t o r s u r i v a l may may be estimated using i n d i c e s such as comparative developmental r a t e s ( T r i p p 1965). 6 . 6 . 2 P a r a s i t o i d Numerical Response - 176 -The speed of the parasitoid variable can be predicted by knowing the l i f e stage of the host attacked, the d i s t r i b u t i o n of attacks, the rate of e f f e c t i v e search, the progeny survival rate, and the de f o l i a t o r recruitment P a r a s i t o i d Fecundity P a r a s i t o i d f e c u n d i t y can be determined i f the l i f e h i s -t o r y stage of the d e f o l i a t o r t h a t i s atta c k e d i s known. T h i s i s because P r i c e (1975), i n an e x t e n s i v e a n a l y s i s of p a r a s i t o i d f e c u n d i t y data, found a very good c o r r e l a t i o n and s i g n i f i c a n t r e g r e s s i o n between p a r a s i t o i d f e c u n d i t y and the l i f e h i s t o r y stage of the host a t t a c k e d . D i s t r i b u t i o n of A t t a c k s The d i s p e r s i o n c o e f f i c i e n t of the d i s t r i b u t i o n of a t t a c k s i s a l s o r e l a t i v e l y simple to estimate with s h o r t l a b o r a t o r y or i n - s i t u f i e l d s t u d i e s of p a r a s i t o i d egg d i s -t r i b u t i o n i n hosts which have been attacked by a s i n g l e p a r a s i t o i d . T h i s has been done f o r a number of important p a r a s i t o i d s i n a number of d e f o l i a t i n g i n s e c t systems such as Apantales fumiferanae and Gl y p t a fumiferanae on e a s t e r n spruce budworm ( M i l l e r 1959) and Pleolophus basizonus on European pine sawfly ( G r i f f i t h s and H o l l i n g 1969). Rate Of E f f e c t i v e Search H o l l i n g (1965 1966) has shown that the r a t e of e f f e c -t i v e search can be estimated from a number of b e h a v i o r a l a t t r i b u t e s of the se a r c h i n g p a r a s i t o i d : speed of search; r e a c t i v e d i s t a n c e ; p r o b a b i l i t y of d e t e c t i o n g i v e n the host e n t e r s the p a r a s i t o i d ' s r e a c t i v e f i e l d ; and the p r o b a b i l i t y - 177 -of a t t a c k g i v e n d e t e c t i o n . These procedures were used to estimate the r a t e of e f f e c t i v e search f o r the e a s t e r n black-headed budworm p a r a s i t o i d u sing simple b e h a v i o r a l i n f o r m a t i o n about the p a r a s i t o i d (Chapter 3 ) . F i e l d estima-t i o n of t h i s parameter may be more d i f f i c u l t than l a b o r a t o r y e s t i m a t i o n because of the problems i n v o l v e d i n o b s e r v i n g the a t t a c k behavior of p a r a s i t o i d s under f i e l d c o n d i t i o n s (J.M. McLeod, p e r s . comm.). P a r a s i t o i d Progeny S u r v i v a l The e s t i m a t i o n of p a r a s i t o i d progeny s u r v i v a l i s l i k e l y to be time-consuming. I t s e s t i m a t i o n r e q u i r e s d e t a i l e d f i e l d s t u d i e s to d e r i v e p a r a s i t o i d l i f e t a b l e s , or at l e a s t , s u r v i v o r s h i p curves. In a d d i t i o n , t h i s i n f o r m a t i o n must be coupled with d e f o l i a t o r l i f e t a b l e or s u r v i v o r s h i p s t u d i e s designed to estimate d e f o l i a t o r r e c r u i t m e n t . Once a l l t h i s i s known, the p a r a s i t o i d r e c r u i t m e n t can be compared to the d e f o l i a t o r r e c r u i t m e n t to determine the speed of the p a r a s i t o i d v a r i -able r e l a t i v e to the speed of the d e f o l i a t o r v a r i a b l e (Huf-f a k e r e t a l . 1977) . 6.6 . 3 The Disease The speed of the disease variable can be predicted by knowing disease pathogenicity, length of the i n f e c t i v e stage, and d e f o l i a t o r recruitment Disease was not a p a r t of any of the three systems analyzed i n d e t a i l . However, Anderson(1979) and Anderson and May (1980) have found that d i s e a s e s which have a high - 178 -p a t h o g e n i c i t y , d e f i n e d as high host m o r t a l i t y r a t e from i n f e c t i o n , and a l o n g - l i v e d i n f e c t i v e stage are capable of c r e a t i n g e p i z o o t i c s . T h e r e f o r e , I w i l l d e f i n e these f a c t o r s as the minimum set of i n f o r m a t i o n necessary to determine the speed of the d i s e a s e v a r i a b l e . As with the p a r a s i t o i d v a r i -a b l e , however, d e f o l i a t o r l i f e t a b l e or s u r v i v o r s h i p s t u d i e s must a l s o be conducted to determine the speed of the d i s e a s e v a r i a b l e r e l a t i v e to that of the d e f o l i a t o r . 6.6.4 F o r e s t V u l n e r a b i l i t y To D e f o l i a t i o n F o r e s t v u l n e r a b i l i t y to d e f o l i a t i o n can be p r e d i c t e d by knowing the t r e e m o r t a l i t y r a t e f o r a range of d e f o l i a t i o n r a t e s at the time d e f o l i a t o r f e e d i n g occurs T h i s can be gathered using e i t h e r a r t i f i c i a l d e f o l i a -t i o n (Craighead 1940) or d e f o l i a t i o n by the i n s e c t (Wickman 1978). I t i s important that the a r t i f i c i a l d e f o l i a t i o n experiments be done duri n g the season that the d e f o l i a t o r consumes most of i t s r a t i o n . Craighead (1940), f o r example, found that the t i ming of f o l i a g e removal was c r i t i c a l i n determining whether a t r e e l i v e d or d i e d . 6.7 A l t e r n a t e S t r u c t u r e s And Necessary Information 6.7.1 The D e f o l i a t o r The d e f o l i a t o r can e x h i b i t one of f o u r d i f f e r e n t e q u i l i b r i u m s t r u c t u r e s , and the d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e i s determined by the presence, absence, and form of p r e d a t i o n by crown-searching p r e d a t o r s , p r i m a r i l y b i r d s , p r e d a t i o n by ground-searching p r e d a t o r s , p r i m a r i l y s m a l l mammals, and i n t r a - s p e c i f i c c o m p e t i t i o n I n t r a - s p e c i f i c Competition I n t r a - s p e c i f i c c o m petition always occurs and - 179 -creates a stable equilibrium at a high d e f o l i a t o r density I n t r a - s p e c i f i c c o m petition occurs i n a l l 3 models and c r e a t e s a s t a b l e s u r f a c e i n a l l d e f o l i a t o r i s o r e c r u i t m e n t curves at high d e n s i t i e s ( F i g u r e s 10, 27, 40). I t i s axiomatic that a l l p o p u l a t i o n s would be, at some p o i n t , l i m -i t e d by t h e i r food supply; I t h e r e f o r e assume t h a t t h i s s t a b l e e q u i l i b r i u m must be present i n a l l d e f o l i a t i n g i n s e c t systems. Another System Before examining the remaining processes, I must present evidence from another d e f o l i a t i n g i n s e c t system, European pine sawfly, Neodiprion s e r t i f e r , f o r the sake of completeness (Wallace and G r i f f i t h s , i n p r e p . ) . I have not i n c l u d e d t h i s system i n my p r e v i o u s analyses because the European pine s a w f l y / r e d pine model has a f o r e s t submodel which i s not amenable f o r the a n a l y t i c a l approach I have taken i n t h i s t h e s i s . F i g u r e 56, an i s o r e c r u i t m e n t curve f o r the d e f o l i a t o r from the European pine sawfly model, shows t h a t an upper s t a b l e e q u i l i b r i u m caused by the e f f e c t s of i n t r a - s p e c i f i c c o m p e t i t i o n e x i s t s at a high i n s e c t d e n s i t y and a s t a b l e e q u i l i b r i u m caused by small mammal p r e d a t i o n e x i s t s at an i n t e r m e d i a t e i n s e c t d e n s i t y . T h i s d e n s i t y i s very s i m i l a r to the intermediate s t a b l e e q u i l i b r i u m i n the jack pine s a w f l y / j a c k pine model. There i s no low d e n s i t y s t a b l e e q u i l i b r i u m . - 1 8 0 -Low High FOREST BIOMASS Fi g u r e 56: A r e p r e s e n t a t i v e i s o r e c r u i t m e n t curve from the European pine sawfly/ red pine model. The upper s t a b l e s u r f a c e i s s e t by i n t r a - s p e c i f i c c o m p e t i t i o n ; the lower s t a b l e s u r f a c e i s set by s m a l l mammal p r e d a t i o n . - 181 -Avian P r e d a t i o n Avian predation, i f i t occurs, creates a stable d e f o l i a t o r equilibrium at a low density, and the presence of avian predation can be predicted by knowing the effectiveness of d e f o l i a t o r predator defense mechanisms The lower s t a b l e e q u i l i b r i u m i n the e q u i l i b r i u m s t r u c -tures of the two budworm and of jack pine sawfly i s c r e a t e d by avian p r e d a t i o n , and avian p r e d a t i o n always c r e a t e s a s t a b l e s u r f a c e at a very low d e f o l i a t o r d e n s i t y i n the models. T h i s s t a b l e s u r f a c e does not e x i s t i n the e q u i l i -brium s t r u c t u r e f o r European pine sawfly. European pine sawfly i s the only system of the fou r i n which p r e d a t i o n by b i r d s i s minimal. European pine sawfly l a r v a e are c o l o n i a l and are capable of a c t i v e l y r e p e l l i n g a vian p r e d a t o r s (Prop 1960). Ea s t e r n spruce budworm (M o r r i s 1963) and e a s t e r n black-headed budworm ( M i l l e r 1966) are s o l i t a r y as l a r v a e , while jack pine sawfly, although c o l o n i a l , i s not able to e f f e c t i v e l y defend i t s e l f a g a i n s t avian p r e d a t i o n (McLeod 1977a). The presence or absence of avian p r e d a t i o n on the d e f o l i a t o r t h e r e f o r e determines presence or absence of a s t a b l e d e f o l i a t o r e q u i l i b r i u m at a very low d e f o l i a t o r den-s i t y . The above suggests that b i r d p r e d a t i o n , i f i t i s pres e n t , w i l l c r e a t e a low d e n s i t y s t a b l e e q u i l i b r i u m f o r the d e f o l i a t o r . T h i s depends c r i t i c a l l y on two d e f i n i t i o n s . F i r s t , the s t a b l e e q u i l i b r i u m c r e a t e d by avian p r e d a t i o n must always be at a very low d e n s i t y ("low" i n t h i s case i s d e f i n e d r e l a t i v e to what outbreak d e n s i t i e s normally a r e ) . - 182 -Second, the form of the predator f u n c t i o n a l response must be Type I I I ( H o l l i n g 1959), so that the m o r t a l i t y r a t e due to them must i n c r e a s e over some i n c r e a s i n g range of d e f o l i a t o r d e n s i t i e s as the predator switches to the d e f o l i a t o r s from some other food source. To t e s t whether both these c o n d i t i o n s are v a l i d , I gathered d e f o l i a t o r m o r t a l i t y data from avian p r e d a t i o n from as many sources as p o s s i b l e with d e f o l i a t o r d e n s i t i e s meas-ured i n the same u n i t s as each o t h e r . U n f o r t u n a t e l y , such data have been c o l l e c t e d f o r very few cases. The data s e t s I could f i n d are presented i n Fi g u r e 57, along with m o r t a l -i t y curves f i t t e d using n o n - l i n e a r parameter e s t i m a t i o n (UBC 1975). The m o r t a l i t y curve i s d e r i v e d from the g e n e r a l i z e d f u n c t i o n a l response presented i n Mace et a_l. (1978). The peak m o r t a l i t i e s f o r the three cases occur from 0.5 to 5 larvae/m 2 of ground. T h i s i s a wide range of d e f o l i a -t o r d e n s i t y , but a l l peak p r e d a t i o n r a t e s occur at d e n s i t i e s which are low r e l a t i v e to outbreak d e n s i t i e s f o r these d e f o l i a t o r s . Furthermore, i n 2 out of 3 data s e t s , there i s a range of d e f o l i a t o r d e n s i t i e s over which m o r t a l i t y from avian p r e d a t i o n i n c r e a s e s . T h i s l i m i t e d evidence does i n d i -cate t h a t avian p r e d a t o r s of d e f o l i a t o r s have t h e i r g r e a t e s t e f f e c t at very low d e f o l i a t o r d e n s i t i e s and they may crea t e a p o t e n t i a l s t a b l e e q u i l i b r i u m a t those d e n s i t i e s . Small Mammal P r e d a t i o n Small mammal p r e d a t i o n , i f i t o c c u r s , c r e a t e s a d e f o l i a t o r e q u i l i b r i u m a t an int e r m e d i a t e d e f o l i a t o r - 183 -DENSITY F i g u r e 5 7 : A v i a n p r e d a t i o n d a t a f r o m v a r i o u s i n s e c t / f o r e s t s y s t e m s . E a s t e r n b l a c k h e a d e d b u d w o r m d a t a a r e f r o m M i l l e r a n d M o o k ( 1 9 7 0 ) . J a c k p i n e s a w f l y d a t a a r e f r o m M c L e o d ( 1 0 7 6 b ) . • - b l a c k h e a d e d b u d w o r m , 1 9 6 5 . + - b l a c k h e a d e d b u d w o r m , 1 9 6 6 . • - j a c k p i n e s a w f l y . - 184 -d e n s i t y and the presence of s m a l l mammal p r e d a t i o n can be p r e d i c t e d by knowing the l o c a t i o n of d e f o l i a t o r pupation The intermediate s t a b l e e q u i l i b r i u m f o r jack pine sawfly and European pine sawfly i s caused by small mammal p r e d a t i o n . An intermediate s t a b l e s u r f a c e does not e x i s t f o r e i t h e r budworm. Both budworm s p e c i e s pupate at the p o i n t of t h e i r f i n a l f e e d i n g , i n the t r e e crowns (Morris 1963, M i l l e r 1966); they are t h e r e f o r e r e l a t i v e l y i n v u l n e r -able to p r e d a t i o n by small mammals which i n h a b i t the f o r e s t f l o o r . Both s a w f l i e s pupate on the ground below the f o r e s t canopy (McLeod 1966, Wallace and G r i f f i t h s , i n pr e p ) ; they are t h e r e f o r e v u l n e r a b l e to p r e d a t i o n by the small mammals which i n h a b i t the f o r e s t f l o o r . L o c a t i o n of pupation, then, determines presence or absence of p r e d a t i o n by small mammals which, i n t u r n , determines presence or absence of a s t a b l e s u r f a c e f o r the d e f o l i a t o r at intermediate d e n s i t i e s . As with avian p r e d a t i o n , my c l a i m about small mammal pr e d a t i o n depends on two c o n d i t i o n s . F i r s t , the peak of small mammal p r e d a t i o n must be at s i m i l a r d e n s i t i e s f o r a l l d e f o l i a t o r s . Second, the form of the f u n c t i o n a l response by small mammal pred a t o r s must be Type I I I ( H o l l i n g 1959) so that the m o r t a l i t y r a t e due to them w i l l i n c r e a s e over an i n c r e a s i n g range of d e f o l i a t o r d e n s i t y . I gathered s u i t a b l e small mammal p r e d a t i o n data s e t s from as many d e f o l i a t i n g i n s e c t systems as p o s s i b l e . L i k e the a v i a n p r e d a t i o n data s e t s , there are very few cases i n which the proper data f o r t h i s a n a l y s i s have been c o l l e c t e d . - 185 -I used the p u b l i s h e d m o r t a l i t y curves i n cases where I could not get the raw data. Both these c o n d i t i o n s are met, however, f o r the three examples I could f i n d ( F i g u r e 58). Th i s l i m i t e d evidence shows that small mammal p r e d a t i o n , i f i t oc c u r s , can c r e a t e a p o t e n t i a l s t a b l e s u r f a c e at an intermediate d e f o l i a t o r d e n s i t y . Summary Of the fou r processes d e s c r i b e d above, i n t r a - s p e c i f i c c o m petition always occurs and avi a n and small mammal preda-t i o n are e i t h e r present or absent. T h e r e f o r e , there are 2 , or 4 p o s s i b l e d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e s (Figure 59). 6.7.2 The Other V a r i a b l e s The f o l i a g e , p a r a s i t o i d , d i s e a s e , and f o r e s t v a r i a b l e s have the same e q u i l i b r i u m s t r u c t u r e i n a l l d e f o l i a t i n g i n s e c t systems In a l l 3 models, f o l i a g e , p a r a s i t o i d , and f o r e s t have a s i n g l e s t a b l e e q u i l i b r i u m , the p o s i t i o n of which i n c r e a s e s with d e c r e a s i n g d e f o l i a t o r , i n c r e a s i n g d e f o l i a t o r , and i n c r e a s i n g f o l i a g e d e n s i t i e s , r e s p e c t i v e l y . T h e r e f o r e , there i s no need to determine what f a c t o r s w i l l g i v e r i s e to a l t e r n a t e e q u i l i b r i u m s t r u c t u r e s f o r these v a r i a b l e s . The e q u i l i b r i u m s t r u c t u r e of the d i s e a s e models developed by Anderson (1979) and Anderson and May (1980) have a s i n g l e s t a b l e s u r f a c e , much l i k e t h a t i n Figure 3. Th e r e f o r e , I w i l l assume that the d i s e a s e v a r i a b l e has a - 186 -200 COGOONS PER M' OF GROUND Fi g u r e 58': Small mammal p r e d a t i o n data from varfio'ite d e f o l i a t i n g i n s e c t systems. • - European spruce sawfly data from N e i l s o n and Mo r r i s (1964). JPS - f i t t e d curve to jack pine sawfly data from McLeod (unpublished d a t a ) . EPS - f i t t e d curve to European pine sawfly data from H o l l i n g (1959). - 187 -s i n g l e s t a b l e e q u i l i b r i u m , and t h a t the p o s i t i o n of t h i s e q u i l i b r i u m i s set by the p a t h o g e n i c i t y of the d i s e a s e , and the l e n g t h of the i n f e c t i v e stage. 6 . 7 Summary I have d e r i v e d an i n t e g r a t i v e theory f o r the s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems. The key e l e -ments of the theory ar e : 1. the s t r u c t u r e and behavior of an d e f o l i a t i n g i n s e c t system can be e x p l a i n e d with f i v e dynamic v a r i a b l e s — the d e f o l i a t o r , the f o l i a g e , the f o r e s t , the p a r a s i t o i d , and the d i s e a s e — and the e f f e c t s of weather a c t i n g on the d e f o l i a t o r ; 2. there are 4 c l a s s e s of d e f o l i a t i n g i n s e c t system behavior; 3. the behavior that an d e f o l i a t i n g i n s e c t system w i l l e x h i b i t i s determined by the magnitude of weather e f f e c t s on d e f o l i a t o r s u r v i v a l and r e c r u i t m e n t , the p a r a s i t o i d numerical response to changing d e f o l i a t o r d e n s i t i e s , the d i s e a s e numeri-c a l response to changing d e f o l i a t o r d e n s i t i e s , and the v u l n e r a b i l i t y of the f o r e s t to d e f o l i a t i o n ; 4. there are 4 s t r u c t u r e s the d e f o l i a t o r can e x h i b i t , and one each f o r the p a r a s i t o i d , the f o l i a g e , the f o r e s t , and the d i s e a s e ; and - 188 -5. d e f o l i a t i n g i n s e c t system s t r u c t u r e and behavior can be p r e d i c t e d with a p a r t i c u l a r , w e l l - d e f i n e d s e t of i n f o r m a t i o n (Table V I I I ) . - 189 -Table V I I I : i n f o r m a t i o n necessary to p r e d i c t the s t r u c t u r e and behavior o f i n s e c t / f o r e s ^ systems. INFORMATION REQUIRED TO PREDICT V a r i a b l e S t r u c t u r e Behavior D e f o l i a t o r E f f e c t i v e n e s s o f l a r v a l predator defense mechanisms L o c a t i o n of pupation P a r a s i t o i d Comparative development r a t e s i n d i f f e r e n t g e o g r a p h i c a l l o c a t i o n s 1. Fecundity 2. Rate of e f f e c t i v e search 3 . Progeny s u r v i v a l r a t e 4. Attack d i s t r i b u t i o n 5. D e f o l i a t o r recruitment r a t e Disease 1. P a t h o g e n i c i t y 2. Length of i n f e c t i v e stage 3 . D e f o l i a t o r recruitment r a t e F o l i a g e Time to f u l l f o l i a g e f o r d i f f e r e n t d e f o l i a t i o n l e v e l s F o r e s t 1. Tree m o r t a l i t y f o r d i f f e r e n t d e f o l i a t i o n l e v e l s - 1 9 0 -7.0 TESTING THE THEORY 7.1 I n t r o d u c t i o n The i n t e g r a t i v e theory f o r the s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems developed i n Chapter 6 cannot be proved c o r r e c t . I t can onl y be d i s p r o v e n . However, i f the theory stands up i n the face of i n v a l i d a t i o n attempts, one's confidence should i n c r e a s e t h a t the theory p r o v i d e s a u s e f u l and p r e d i c t i v e method f o r a n a l y z i n g the dynamics of d e f o l i a t i n g i n s e c t systems. The most c o n v i n c i n g t e s t s of e c o l o g i c a l hypotheses are f i e l d experiments. Too many models are c o n s t r u c t e d with l i t t l e or no e m p i r i c a l b a s i s or cannot be t e s t e d or parameterized with d i r e c t e x p e r i m e n t a t i o n . The theory I have developed, however, can be t e s t e d e m p i r i c a l l y . The most c o n v i n c i n g f i e l d experiments are those which would t e s t whether an experimental p e r t u r b a t i o n to a d e f o l i a t i n g i n s e c t system d i d indeed have the consequences f o r e q u i l i b r i u m s t r u c t u r e and system behavior that the theory p r e d i c t e d . Because of the time s c a l e s of the system components i n v o l v e d , these experiments would not be t r i v i a l . Years, perhaps even decades, would be needed before the theory could be t e s t e d . However, as a c t u a l f i e l d experiments pro-v i d e the best mechanism f o r e v a l u a t i n g the theory, I w i l l o u t l i n e and d e s c r i b e s p e c i f i c f i e l d experiments which would t e s t the theory. In the absence of f i e l d experiments to t e s t the theory, - 191 -e x i s t i n g data c o l l e c t e d on d e f o l i a t i n g i n s e c t system can be used f o r simple i n v a l i d a t i o n t e s t s . These data can be exam-ined f o r p a r t i c u l a r behaviors or s t r u c t u r e s p r e d i c t e d by the theory. T h i s approach presents some problems and some oppor-t u n i t i e s . F i r s t , there i s s t i l l the problem of time s c a l e s . Such long term d a t a , f o r C l a s s 4 systems f o r example, would have to span approximately 100 g e n e r a t i o n s f o r them to be remotely u s e f u l . Even then, only one d e f o l i a t o r outbreak may be r e p r e s e n t e d . These types of data s e t s simply do not e x i s t . Second, most long term data c o l l e c t e d on d e f o l i a t i n g i n s e c t systems c o n s i s t almost e n t i r e l y of d e f o l i a t o r popula-t i o n e s t i m a t e s . The other 3 system components which the theory uses have never been censused with the r e g u l a r i t y that d e f o l i a t o r p o p u l a t i o n s have, l e t alone with the regu-l a r i t y needed to t e s t the theory. However, these long term d e f o l i a t o r p o p u l a t i o n data could be used to t e s t s p e c i f i c hypotheses r e l a t i n g to d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e and behavior d e r i v e d from the theory. A p a r t of my i n v a l i d a t i o n w i l l use these long term p o p u l a t i o n data to t e s t p a r t s of the i n t e g r a t i v e theory r e l a t e d to the d e f o l i a t o r . A l s o , i n s p i t e of the absence of long term data on a l l 4 components of d e f o l i a t i n g i n s e c t systems used i n the theory, 2 sources c o n t a i n extremely good q u a l i t a t i v e accounts of the temporal behavior of a l l components of - 192 -d e f o l i a t i n g i n s e c t systems: the annual r e p o r t s of the Cana-dia n F o r e s t Insect and Disease Survey, beginning i n 1939 and c o n t i n u i n g to the p r e s e n t , and review a r t i c l e s of major d e f o l i a t i n g i n s e c t system s t u d i e s (e.g., e a s t e r n spruce budworm, M o r r i s 1963, European spruce sawfly, N e i l s o n and M o r r i s 1964). These s t u d i e s and r e p o r t s w i l l be used to t e s t how w e l l the q u a l i t a t i v e p a t t e r n s of behavior p r e d i c t e d by the theory compare with the accounts of d e f o l i a t i n g i n s e c t system behavior r e p o r t e d i n these sources. 7.2 F i e l d Experiments The core of the theory i s t h a t i t i s p o s s i b l e to p r e d i c t e q u i l i b r i u m s t r u c t u r e and behavior of d e f o l i a t i n g i n s e c t systems from simple s e t s of i n f o r m a t i o n . There are 2 f i e l d experiments which need to be undertaken to t e s t t h i s n o t i o n . The f i r s t r e l a t e s to the idea that a simple i n f o r -mation s e t can be used to p r e d i c t e q u i l i b r i u m s t r u c t u r e , the second r e l a t e s to the idea t h a t a simple i n f o r m a t i o n s e t can be used to p r e d i c t temporal behavior. 7.2.1 A F i e l d Experiment For T e s t i n g E q u i l i b r i u m S t r u c t u r e The theory p r e d i c t s that d e f o l i a t o r s which have poor or no l a r v a l defense mechanisms and pupate on the ground w i l l have 3 s t a b l e e q u i l i b r i a , one at a very low d e n s i t y s e t by avian p r e d a t o r s , one at an i n t e r m e d i a t e d e n s i t y set by small mammal p r e d a t o r s , and one at a very high i n s e c t d e n s i t y s e t by l i m i t a t i o n i n the food supply. Beginning with a d e f o l i a -t o r at very low p o p u l a t i o n l e v e l s , removal of the 2 r e l e v a n t - 19 3 -sources of p r e d a t i o n should cause the d e f o l i a t o r p o p u l a t i o n to i n c r e a s e . Furthermore, once the d e f o l i a t o r p o p u l a t i o n had i n c r e a s e d , adding the sources of p r e d a t i o n back i n to the system should not cause the d e f o l i a t o r p o p u l a t i o n to d e c l i n e . T h e r e f o r e , t h i s experiment should take the f o l l o w i n g form ( F i g u r e 60). A system should be chosen f o r which the theory p r e d i c t s the d e f o l i a t o r has 3 e q u i l i b r i a ; t h a t i s , the d e f o l i a t o r must have no l a r v a l predator defense mechan-isms and must pupate i n the ground. D e f o l i a t o r p o p u l a t i o n s should be at very low l e v e l s ( l e s s than 10 eggs/m 2 ). D e f o l i a t o r p o p u l a t i o n s i n the stands i n which the experiment are to be done should be censused f o r a number of i n s e c t g e n e r a t i o n s before the p e r t u r b a t i o n s are done to make sure that experimental behaviors are a cause of the p e r t u r b a t i o n and not standard behaviors f o r the system i n those stands. The experiment should occur i n stands of mature host f o r e s t to remove e f f e c t s of f o r e s t immaturity on system dynamics ( F i g u r e s 15, 31, 47). The experiment should be i n stands where outbreaks have occu r r e d p r e v i o u s l y so the experimenter can be sure the e f f e c t s of heavy l a r v a l m o r t a l i t y from weather c o n d i t i o n s can be removed. F i n a l l y , each treatment should be on a s u f -f i c i e n t l y l a r g e s p a t i a l s c a l e to remove e f f e c t s of d e f o l i a -t o r d i s p e r s a l ( C l a r k 1979) or p r e d a t o r aggregation ( B l a i s and Parks 1964, Mattson et a l . 1968). - 194 -f j _ Remove b i r d s on B Allow r e c o l o n i z a t i o n Remove s m a l l mammals on B and C on C igure 60: Experiment to t e s t f o r d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e . B i r d s are removed from Stand B and b i r d s and small mammals are removed from Stand C. Stand A i s a c o n t r o l . - 195 -One stand (A) should be a c o n t r o l , with no predator removal. The f i r s t treatment (B) should c o n s i s t of removing avian p r e d a t o r s . The second treatment (C) should c o n s i s t of removing both a v i a n and small mammal p r e d a t o r s . The theory p r e d i c t s t h at d e f o l i a t o r p o p u l a t i o n s i n A should remain at very low l e v e l s , p o p u l a t i o n s i n B should i n c r e a s e t o i n t e r -mediate l e v e l s (100 to 200 eggs/m 2), and p o p u l a t i o n s i n C should i n c r e a s e to very high l e v e l s (about 1000 eggs/m 2). These l e v e l s should be reached 2 to 4 years a f t e r the i n i -t i a t i o n of predator removal. When these s h i f t s i n p o p u l a t i o n have been demonstrated, about 5 years a f t e r i n i t i a l p r e d a tor removal, pr e d a t o r s should be allowed back i n t o the treatment areas. D e f o l i a t o r p o p u l a t i o n s should not d e c l i n e to c o n t r o l l e v e l p o p u l a t i o n s , but should remain at t h e i r r e s p e c t i v e i n c r e a s e d l e v e l s . T h i s f i n a l step i s necessary to c o n t r o l f o r the p o s s i b i l i t y that the i n i t i a l i n c r e a s e s i n p o p u l a t i o n were simply due to removal of m o r t a l i t y sources. I f the theory i s not i n v a l i d , a l l o w i n g the predator g u i l d s to r e c o l o n i z e the treatment stands should not cause d e f o l i a t o r p o p u l a t i o n s to d e c l i n e . The t o t a l time p e r i o d of t h i s t e s t would be about 15 yea r s , from i n i t i a l censusing of d e f o l i a t o r p o p u l a t i o n s . S i m i l a r experiments have been attempted i n the gypsy moth/oak system (Campbell and. Sloan 1977). Both b i r d s and small mammals were removed from p a r t s of red oak stands and d e f o l i a t o r p o p u l a t i o n s censused. However, the predator g u i l d s were allowed back i n to the stands too soon a f t e r - 196 -removal and the r o l e of these p r e d a t o r s i n d e f i n i n g the d e f o l i a t o r e q u i l i b r i u m s t r u c t u r e was not c o n c l u s i v e l y demon-s t r a t e d . 7.2.2 A F i e l d Experiment For T e s t i n g System Behavior The i n t e g r a t i v e theory s t a t e s t h a t the d i f f e r e n c e between a C l a s s 3 or 4 system and a C l a s s 2 system i s simply the time s c a l e of the p a r a s i t o i d . C l a s s 3 and 4 systems have a slow p a r a s i t o i d , while C l a s s 2 systems have a f a s t p a r a s i t o i d , r e l a t i v e to the d e f o l i a t o r . I t should t h e r e f o r e be p o s s i b l e to s h i f t the behavior of a C l a s s 2 system to e i t h e r a C l a s s 3 or 4 by "slowing down" the p a r a s i t o i d . "Slowing down" the p a r a s i t o i d i s a r e l a t i v e l y easy t a s k . I t occurs o f t e n , f o r example, i n a g r i c u l t u r a l pest systems when ex c e s s i v e p e s t i c i d e a p p l i c a t i o n s are used and remove most of a p a r t i c u l a r p e s t ' s n a t u r a l enemy g u i l d (van den Bosch 1979) . The experiment should take the f o l l o w i n g form ( F i g u r e 61). A system should be chosen i n Which the h i s t o r i c a l e v i -dence shows the behavior to be C l a s s 2. Again, experimental stands should be s u f f i c i e n t l y l a r g e to remove p o t e n t i a l l y confounding e f f e c t s of d e f o l i a t o r d i s p e r s a l and predator a g g r e g a t i o n . The treatment (B) i n the second stand should c o n s i s t of reducing p a r a s i t o i d progeny s u r v i v a l f o r a number of y e a r s . T h i s could be achieved by r e l e a s e of s t e r i l e p a r a s i t o i d males ( i n non-parthenogenic s p e c i e s ) or t r a p p i n g p a r a s i t o i d - .197 -S T A N D A S T A N D B d e f o l i a t o r paras i t o i d f o l i a g e YV f o r e s t d e f o l i a t o r A A / V W p a r a s i t o i d AAAAiW f o l i a g e f o r e s t T I M E T I M E F i g u r e 61: Experiment to t e s t whether the i n t e g r a t i v e theory can p r e d i c t c l a s s o f behavior. Para-s i t o i d r e c r u i t m e n t i s reduced i n Stand A between time I and I I . The theory s t a t e s that system behavior should s h i f t to a C l a s s 3 o r Cla s s 4 from a C l a s s 2 system. - 198 -males with pheromones (again i n non-parthenogenic p a r a s i t o i d s p e c i e s ) . The hypothesis p r e d i c t s t h a t the system should immediately a c q u i r e the c h a r a c t e r i s t i c s of e i t h e r a C l a s s 3 or 4 system. The theory p r e d i c t s that i t i s p o s s i b l e to p r e d i c t the c l a s s of behavior by knowing p r o b a b i l i t y of t r e e m o r t a l i t y under low f o l i a g e c o n d i t i o n s . Once the new c l a s s of behavior has been c o n c l u s i v e l y demonstrated, the treatment causing the r e d u c t i o n i n p a r a s i -t o i d progeny s u r v i v a l should be terminated. The i n t e g r a t i v e theory p r e d i c t s that the behavior of the system should r e t u r n to that of a C l a s s 2. T h i s experiment would take approximately 20 years to complete. T h i s time frame allows f o r 1 outbreak c y c l e f o r each behavior c l a s s . F o r t u n a t e l y , the c l a s s i c examples of b i o l o g i c a l c o n t r o l p r ovide evidence that d i f f e r e n c e s i n the time s c a l e of the p a r a s i t o i d can c r e a t e dramatic s h i f t s from one c l a s s of behavior to another i n d e f o l i a t i n g i n s e c t systems (e.g., N e i l s o n and M o r r i s 1964, Turnock 1972, S e c t i o n 7.4). 7.3 E q u i l i b r i u m S t r u c t u r e In Long Term P o p u l a t i o n Data I f m u l t i p l e e q u i l i b r i a e x i s t i n d e f o l i a t o r p o p u l a t i o n s , then perhaps they can be r e v e a l e d i n long term p o p u l a t i o n data. There i s no c e r t a i n t y t h a t they can because the d e f o l i a t o r p o p u l a t i o n may have never moved i n t o the r e g i o n of one or more of the e q u i l i b r i a d u r i n g the time the data were c o l l e c t e d . The theory would be supported, though, i f analyses showed or suggested i n s e c t p o p u l a t i o n s contained - 199 -m u l t i p l e e q u i l i b r i a . I know of no s t a t i s t i c a l methods to t e s t f o r m u l t i p l e e q u i l i b r i a i n p o p u l a t i o n data. T h e r e f o r e , I w i l l i d e n t i f y p a t t e r n s which appear i n long term data f o r a d e f o l i a t o r which i s known to be m u l t i p l y s t a b l e and see i f these pat-t e r n s appear i n other d e f o l i a t o r p o p u l a t i o n data. I w i l l choose gypsy moth as the d e f o l i a t o r on which to i d e n t i f y these p a t t e r n s . Many gypsy moth s c i e n t i s t s agree that the d e f o l i a t o r i s m u l t i p l y s t a b l e and that t h i s m u l t i p l e s t a b i l -i t y i s r e f l e c t e d i n the h i s t o r i c a l p o p u l a t i o n data (Doane and McManus 1977, Campbell and Sloan 1978). Gypsy Moth P o p u l a t i o n Data A n a l y s i s The i n t e g r a t i v e theory p r e d i c t s that gypsy moth should have three e q u i l i b r i a , as i t pupates on the ground and has no l a r v a l p r e d a t o r defense mechanisms (Bess 1961). The long term p o p u l a t i o n data f o r gypsy moth (Appendix I) from 1911 to 1932 show a c o n s i s t e n t p a t t e r n c h a r a c t e r i z e d by an i n i -t i a l p e r i o d (1911-1921) of high p o p u l a t i o n l e v e l s f o l l o w e d by a r a p i d d e c l i n e to a lower p o p u l a t i o n s t a t e (1922-1932). The i n i t i a l p e r i o d was marked by high d e f o l i a t i o n r a t e s and reduced t r e e growth and f o r e s t v i g o r and the l a t t e r p e r i o d was marked by very l i t t l e d e f o l i a t i o n and higher gypsy moth p a r a s i t i s m r a t e s (Doane and McManus 1977). V e r t e b r a t e pre-d a t i o n r a t e s were not measured f o r t h i s p e r i o d . In a d d i -t i o n , more recent data from a s i t e i n which gypsy moth i s presen t but has never caused d e f o l i a t i o n (Figure 62) show - 20 0 --p -H W c (L) Q Cr> tn w O a § ' CI o 1965 1973 Year F i g u r e 62: Gypsy moth p o p u l a t i o n d a t a s e t from a non-outbreak l o c a t i o n i n New York. Data from Campbell and Sloan (1978). - 201 -extremely low p o p u l a t i o n l e v e l s . Campbell (1976) showed that p o p u l a t i o n s i n t h i s area were s u b j e c t to extremely high v e r t e b r a t e p r e d a t i o n . I performed a c l u s t e r a n a l y s i s on the f o u r d a t a s e t s from 1911-1932 coupled with the data from F i g u r e 62 using the SYSTAT s t a t i s t i c a l package (SYSTAT 1985). C l u s t e r a n a l y s i s i s an a n a l y t i c a l procedure f o r combining samples i n t o l i k e groups. There are many d i f f e r e n t types of c l u s t e r a n a l y s i s procedures, and d i f f e r e n t c l u s t e r i n g a l g o r i t h m s w i l l produce d i f f e r e n t sample groupings. In t h i s case, I used an a l g o r i t h m which c l u s t e r e d a c c o r d i n g to average E u c l i d e a n d i s t a n c e . The r e s u l t s show that c l u s t e r i n g i n t o 2 p o p u l a t i o n groups from 3 g i v e s the l a r g e s t i n c r e a s e i n the d i s t a n c e measure between p o p u l a t i o n groups. T h i s means that 3 popu-l a t i o n groups i s the most a p p r o p r i a t e l e v e l of c l u s t e r i n g . The data p o i n t s i n each of the 3 groups s e l e c t e d by the c l u s t e r a n a l y s i s r e p r e s e n t the 1911-1921, 1922-1932, and the data i n F i g u r e 62. A l s o , the i n c r e a s e i n the d i s t a n c e meas-ure when the p o p u l a t i o n s are c l u s t e r e d from 3 to 2 groups accounts f o r over 50% of the f i n a l d i s t a n c e measure. The g r e a t e r the p r o p o r t i o n of the f i n a l d i s t a n c e measure accounted f o r by a c l u s t e r i n g , the l a r g e r the d i f f e r e n c e s between the groups being c l u s t e r e d . F i n a l l y , the i n t e g r a -t i v e theory p r e d i c t s t h a t the d e f o l i a t o r should have 3 s t a b l e e q u i l i b r i a . The f a c t t h a t the c l u s t e r a n a l y s i s r e v e a l s 3 p o p u l a t i o n groups to be the most a p p r o p r i a t e - 202 -c l u s t e r i n g i s encouraging. But, i t i s important to emphasize what e x a c t l y the r e s u l t s of using t h i s s t a t i s t i c a l technique mean. The r e s u l t s show very c l e a r l y that h i s t o r i c a l gypsy moth popula-t i o n data can be aggregated i n t o a s m a l l s e t of groups and that the d i f f e r e n c e s between these groups are l a r g e . The r e s u l t s a l s o show th a t the number of c l u s t e r s p r e d i c t e d by the i n t e g r a t i v e theory are a l s o r e f l e c t e d i n the d a t a s e t s . T h i s does not mean, however, t h a t the processes hypothesized i n the i n t e g r a t i v e theory to c r e a t e m u l t i p l e e q u i l i b r i a were o p e r a t i n g at each of these p o p u l a t i o n l e v e l s . The r a t e s of v e r t e b r a t e p r e d a t i o n from 1922 to 1932 were not measured. Furthermore, the r e s u l t s do not p r o v i d e c o n c l u s i v e proof that the groups or c l u s t e r s are d i s t i n c t and separate popu-l a t i o n e q u i l i b r i a . Gypsy moth may have onl y a s i n g l e e q u i l i b r i u m which s h i f t s i n response to one of the f a c t o r s d e s c r i b e d i n Chapter 2, such a f o l i a g e q u a l i t y . Only the f i e l d experiments d e s c r i b e d above can p r o v i d e c o n c l u s i v e evidence. On the other hand, the r e s u l t s do show that the gypsy moth e x i s t s i n d i s t i n c t p o p u l a t i o n s t a t e s . They a l s o i n c r e a s e degree of b e l i e f i n the concept of m u l t i p l e s t a b i l -i t y i n gypsy moth p o p u l a t i o n s and t h a t the i n t e g r a t i v e theory does p r o p e r l y p r e d i c t gypsy moth e q u i l i b r i u m s t r u c -ture . The A n a l y s i s Procedure Given the above r e s u l t s f o r gypsy moth, a c l u s t e r - 203 -a n a l y s i s of the p o p u l a t i o n d a t a s e t s presented i n Appendix I should demonstrate t h a t the number of s t a b l e e q u i l i b r i a p r e d i c t e d by the i n t e g r a t i v e theory should be the same as the number of c l u s t e r s , or p o p u l a t i o n groupings, observed i n the d a t a s e t s . I performed a c l u s t e r a n a l y s i s f o r each p o p u l a t i o n d a t a s e t contained i n Appendix I, s e l e c t e d the most s i g n i f i -cant p o p u l a t i o n grouping as measured by the % of the f i n a l d i s t a n c e measure made by the next c l u s t e r i n g , and compared the number of groupings with the number of e q u i l i b r i a p r e d i c t e d by the i n t e g r a t i v e theory based on predator defense and l o c a t i o n of pupation. R e s u l t s Table IX shows that the m a j o r i t y of the p o p u l a t i o n d a t a s e t s c o n t a i n 2 or 3 p o p u l a t i o n groupings. 26% of the d a t a s e t s had s i g n i f i c a n t c l u s t e r i n g (Table X), using a s i g -n i f i c a n c e c r i t e r i o n of 50% of f i n a l d i s t a n c e measure. 40% of the d a t a s e t s f o r which 2 c l u s t e r s were p r e d i c t e d and 5% of the d a t a s e t s ( i . e . , o n l y one p o p u l a t i o n dataset) f o r which 3 were predicted, met t h i s 50% c r i t e r i o n . 57% of the d a t a s e t s f o r which the i n t e g r a t i v e theory p r e d i c t s 2 s t a b l e e q u i l i b r i a had 2 p o p u l a t i o n c l u s t e r s ( i r r e s p e c t i v e of l e v e l of s i g n i f i c a n c e ) , while 53% of the d a t a s e t s f o r which the i n t e g r a t i v e theory p r e d i c t s 3 s t a b l e e q u i l i b r i a had 3 popu-l a t i o n c l u s t e r s , again i r r e s p e c t i v e of l e v e l of s i g n i f i c a n c e (Table X I ) . - 204 -Table IX: Number of p o p u l a t i o n groups p r e d i c t e d by the cjluster a n a l y s i s . Number Of Number Of P o p u l a t i o n Groups Datasets 2 3 4 5 6 5 1 1 9 3 5 2 - 205 -Table X: S i g n i f i c a n c e of c l u s t e r a n a l y s i s r e s u l t s for d a t a s e t s i n which 2 or 3 p o p u l a t i o n groups were s e l e c t e d . S i g n i f i c a n c e i s d e f i n e d by the % of the t o t a l d i s t a n c e measure with the succeeding c l u s t e r ( c l u s t e r to 1 i n the case of 2 p o p u l a t i o n groups or to 2 i n the case of 3 p o p u l a t i o n g r o u p s ) . I assume 50% as being s i g n i f i c a n t . Number Of P o p u l a t i o n Groups % Of T o t a l D i s t a n c e Measure With Next C l u s t e r 2 3 0- 10 0 0 10- 20 4 5 20- 30 8 7 30- 40 9 4 40- 50 9 4 50- 60 5 0 6 0- 70 7 1 70- 80 3 0 80- 90 4 0 90-100 2 0 T o t a l 51 19 - 206 -Table XI: Comparison of number of p o p u l a t i o n groups s e l e c t e d by c l u s t e r a n a l y s i s with number p r e d i c t e d by i n t e g r a t i v e theory. Table e n t r i e s are number of d a t a s e t s . # P o p u l a t i o n Groups Number Of Groups P r e d i c t e d By Theory 2 3 > 3 2 3 34 12 14 4 4 2 - 207 -The r e s u l t s on a d e f o l i a t o r b a s i s (Table XII) show that there are d e f o l i a t o r s , p a r t i c u l a r l y gypsy moth and sa d d l e -back l o o p e r , f o r which the c l u s t e r i n g a n a l y s i s r e s u l t s match the p r e d i c t i o n s of the i n t e g r a t i v e theory, i n that the m a j o r i t y of t h e i r d a t a s e t s have h i g h l y s i g n i f i c a n t numbers of the p r e d i c t e d number of c l u s t e r s . In another group of d e f o l i a t o r s , i n c l u d i n g D o u g l a s - f i r tussock moth, western blackheaded budworm, western spruce budworm, western hemlock l o o p e r , European pine sawfly, a m a j o r i t y of da t a s e t s c o n t a i n the same number of p o p u l a t i o n groups s e l e c t e d by the c l u s t e r a n a l y s i s as the number p r e d i c t e d by the i n t e g r a t i v e theory, although fewer of these are s i g n i f i c a n t , using the 50% of f i n a l d i s t a n c e measure c r i t e r i o n . The r e s u l t s of a t h i r d group, i n c l u d i n g green s t r i p e d f o r e s t l o o p e r , western f a l s e hemlock l o o p e r , l a r c h sawfly, pine l o o p e r , jack pine sawfly, and European spruce sawfly do not match the p r e d i c t i o n s at a l l w e l l . The r e s u l t s show that the i n t e g r a t i v e theory has moderate success at p r e d i c t i n g the number of e q u i l i b r i a i n d e f o l i a t o r p o p u l a t i o n s using t h i s technique. 7.4 Test Of System Behavior The i n t e g r a t i v e theory holds t h a t 4 c l a s s e s of d e f o l i -a t i n g i n s e c t system e x i s t , and t h a t the p e r i o d i c i t i e s of v a r i o u s events, such as d e f o l i a t o r outbreaks, are d i f f e r e n t i n the d i f f e r e n t behavior c l a s s e s . I f the theory i s v a l i d , then d i f f e r e n c e s i n d e f o l i a t o r p o p u l a t i o n outbreak frequen-- 208 -T a b l e X I I : C l u s t e r a n a l y s i s r e s u l t s f o r e a c h d e f o l i a t o r . E n t r i e s a r e number o f d a t a s e t s . B o l d e n t r i e s i n d i c a t e t h e number o f p o p u l a t i o n g r o u p s p r e d i c t e d by t h e i n t e g r a t i v e t h e o r y . Numbers i n b r a c k e t s r e f e r t o t o t a l number o f d a t a s e t s . # P o p u l a t i o n Groups D e f o l i a t o r S i g n i f i c a n t 2 3 >3 S a d d l e b a c k Y 4 0 0 L o o p e r (7) N 2 0 1 G r e e n s t r i p e d Y 2 0 0 F o r e s t L o o p e r ( 1 2 ) N 4 3 3 D o u g l a s - f i r Y 2 0 0 T u s s o c k Moth(6) N 3 0 1 W e s t e r n F a l s e Y 2 0 0 Hemlock L o o p e r ( 1 2 ) N 3 6 1 W e s t e r n B l a c k - Y 1 0 0 headed Budworm(7) N 3 3 0 W e s t e r n S p r u c e Y 3 1 0 Budworm (15) N 7 4 0 L a r c h S a w f l y ( 5 ) Y 0 0 0 N 2 1 2 Gypsy Moth (4) Y 0 4 0 N 0 0 0 P i n e L o o p e r ( 2 ) Y 0 0 0 N 2 0 0 J a c K P i n e Y 1 0 0 S a w f l y ( l ) N 0 0 0 E u r o p e a n p i n e Y 0 0 0 S a w f l y ( 1 ) N 0 1 0 E u r o p e a n S p r u c e Y 0 0 0 S a w f l y ( 1 ) N 1 0 0 - 209 -c i e s should be apparent i n d e f o l i a t o r p o p u l a t i o n d a t a . U n f o r t u n a t e l y , none of the p o p u l a t i o n d a t a s e t s span a s u f f i -c i e n t p e r i o d of time to allow f o r any C l a s s 4 behavior to appear. Furthermore, I do not expect any outbreaks from C l a s s 1 systems. T h e r e f o r e , t h i s a n a l y s i s focused on C l a s s 2 and 3 systems, and the hypothesis I t e s t e d i s t h a t out-break f r e q u e n c i e s from C l a s s 2 and C l a s s 3 systems are d i f -f e r e n t . The procedure I used on the d a t a s e t s i n Appendix I i s : 1. p r e d i c t , using the i n t e g r a t i v e theory, the behavior c l a s s f o r each d e f o l i a t i n g i n s e c t system ( C l a s s 2 or 3); 2. using s p e c t r a l a n a l y s i s (Fox and McGuire 1975) determine the p e r i o d i c i t y of d e f o l i a t o r outbreaks, d e f i n e d by the p e r i o d i c i t y with the h i g h e s t spec-t r a l d e n s i t y (only those d a t a s e t s i n which the spectrum was s t a t i s t i c a l l y shown not to be f l a t , i . e . , the s p e c t r a l a n a l y s i s d i d not d i s t i n g u i s h a p e r i o d i c i t y as dominant) f o r each d a t a s e t ; and 3. t e s t , u sing a t - t e s t , whether the p e r i o d i c i t i e s from each behavior c l a s s are d i f f e r e n t . A t o t a l of 91 p o p u l a t i o n s e t s with s i g n i f i c a n t s p e c t r a l d e n s i t i e s were s e l e c t e d (there are more p o p u l a t i o n s e t s , 91, than d a t a s e t s , 80, because some of the d a t a s e t s , such as those f o r gypsy moth, could be d i v i d e d i n t o two or more - 210 -p e r i o d s ) . Frequency d i s t r i b u t i o n s of the p e r i o d i c i t i e s ( F i g u r e 63) show that there i s a s e p a r a t i o n i n d e f o l i a t o r outbreak f r e q u e n c i e s between C l a s s 2 and C l a s s 3 systems. 61 of the 91 d a t a s e t s were p r e d i c t e d to be Type 2 systems while 17 of the 91 d a t a s e t s were p r e d i c t e d to be Type 3 sys-tems. The t e s t of the hypothesis t h a t the 2 c l a s s e s do have d i f f e r e n t p e r i o d i c i t i e s gave a t value of 2.95. T h i s i s s i g n i f i c a n t (p < .01) and the 2 s e t s of p e r i o d i c i t i e s are s t a t i s t i c a l l y d i f f e r e n t . The r e s u l t of t h i s t e s t provides more evidence that the simple i n f o r m a t i o n s e t d e f i n e d i n the i n t e g r a t i v e theory can be used to p r e d i c t the proper c l a s s of behavior of d e f o l i a t i n g i n s e c t systems. A f e a t u r e of the outbreak p e r i o d i c i t i e s of the C l a s s 3 systems worth noting i s the h i g h number of d a t a s e t s which have a very low p e r i o d i c i t y (2-3 y e a r s ) . These samples are from the gypsy moth/red oak system. The gypsy moth feeds on red oak, a host t r e e which r e t a i n s o n l y one year of f o l i a g e at any time. The m a j o r i t y of the other samples from C l a s s 3 systems are from the western spruce budworm/Douglas f i r sys-tem. T h i s budworm feeds on Douglas f i r , a host t r e e which r e t a i n s 8 years of f o l i a g e ( S i l v e r 1960). The f o l i a g e v a r i -able has very d i f f e r e n t time s c a l e s i n these 2 systems, and these d i f f e r e n t time s c a l e s appear are r e f l e c t e d i n the dom-inant outbreak p e r i o d i c i t i e s . 7.5 T e s t s Using Information Set I t e s t e d the p r e d i c t i v e power of the i n t e g r a t i v e theory - 211 -2 0 x = 1 2 , 7 1 years V~ = 8 2 . 5 n = 6l n n n n 0 5 1 0 1 5 2 0 2 5 P e r i o d i c i t y (years) 2 0 k x = 2 3 , 6 years p~ = 2 0 ( i . 6 n = 17 J l 5 0 n 50 0 5 1 0 1 5 2 0 2 5 P e r i o d i c i t y (years) F i g u r e 63: Frequency d i s t r i b u t i o n s o f dominant p e r i o d i c i t i e s found i n long term d e f o l i a t o r p o p u l a t i q n data. a. From those systems p r e d i c t e d to be C l a s s 2. b. From those systems p r e d i c t e d to be C l a s s 3. - 212 -by using the minimum i n f o r m a t i o n s e t to p r e d i c t the c l a s s of behavior the system should e x h i b i t and comparing p r e d i c t e d behavior with documented behavior from annual r e p o r t s of the Canadian F o r e s t I n s e c t and Disease Survey and s y n t h e s i s a r t i c l e s of d e f o l i a t i n g i n s e c t systems. I had d i f f i c u l t y i n f i n d i n g evidence of weather-induced m o r t a l i t y e f f e c t s on d e f o l i a t o r p o p u l a t i o n s i n s p e c i f i c geo-g r a p h i c a l l o c a t i o n s . I f a system e x h i b i t e d 2 types of behavior, I could o n l y r a r e l y p o i n t to weather e f f e c t s as being the major d i f f e r e n c e . T h i s i s not s u r p r i s i n g , as most f o r e s t e n t o m o l o g i c a l work has been done on systems which have been managed f o r outbreak containment f o r some time. These are i n v a r i a b l y systems i n which the d e f o l i a t o r has caused outbreaks and some damage to the f o r e s t ; I t h e r e f o r e concentrated on those systems which were not C l a s s 1. I a l s o found that there are very few systems f o r which the minimum i n f o r m a t i o n s e t needed to p r e d i c t behavior e x i s t s . Of a l l the systems d e s c r i b e d i n Table I I I , o n l y s i x of them had a l l the r e q u i r e d i n f o r m a t i o n s e t . The i n f o r m a t i o n on the p a r a s i t o i d or d i s e a s e v a r i a b l e was u s u a l l y l a c k i n g . The r e s u l t s of t h i s t e s t (Table XIII) show that the i n t e g r a t i v e theory d e s c r i b e d i n Chapter 6, m o d i f i e d with the changes d e s c r i b e d above f o r f o l i a g e recovery times, has good p r e d i c t i v e power f o r a l l s i x d e f o l i a t i n g i n s e c t systems. I t p r e d i c t s n a t u r a l system dynamics, s h i f t s i n behavior caused by s u c c e s s f u l i n t r o d u c t i o n of b i o l o g i c a l c o n t r o l agents ( l a r c h s a wfly, 1921-1940; gypsy moth i n U.S.A a f t e r 1921), Table X I I I : Comparison o f p r e d i c t e d with documented behavior c l a s s . Unless mentioned, behavior i s f o r system i n Canada. Se_e Table XIV f o r references f o r t h i s i n f o r m a t i o n . De f o l i a t o r Host Tree Type Of Numerical Response Indicated By P a r a s i t e Or Disease Information Tree M o r t a l i t y With High De f o l i a t i o n P r e d i c t e d Behavior C l a s s Documented Behavior C l a s s Western Spruce Budworm Douglas-f i r p a r a s i t e , slow low 3 3 European Spruce Sawfly before 1938 White spruce no p a r a s i t e o r disease low 3 3 European Spruce Sawfly a f t e r 1938 White Spruce p a r a s i t e , r a p i d low 2 2 Larch Sawfly before 1912 tamarack no p a r a s i t e o r disease low 3 3 Larch Sawfly 1912-1940 tamarack p a r a s i t e , r a p i d low 2 2 Larch Sawfly a f t e r 1940 tamarack no, encapsula-t i o n of host low 3 3 T a b l e X I I I : C o n t i n u e d D e f o l i a t o r H o s t T r e e Type Of N u m e r i c a l Response I n d i c a t e d By P a r a s i t e Or D i s e a s e I n f o r m a t i o n T r e e M o r t a l i t y W i t h H i g h D e f o l i a t i o n P r e d i c t e d B e h a v i o r C l a s s Documented B e h a v i o r C l a s s D o u g l a s - f i r t u s s o c k moth D o u g l a s -f i r d i s e a s e , r a p i d h i g h 2 2 W i n t e r moth b e f o r e 1958 r e d oak no p a r a s i t e o r d i s e a s e low 3 3 Gypsy moth i n U.S.A b e f o r e 1922 w h i t e oak no p a r a s i t e o r d i s e a s e low 3 3 Gypsy moth i n U.S.A a f t e r 1922 w h i t e oak d i s e a s e , r a p i d low 2 2 Gypsy moth w h i t e oak d i s e a s e , r a p i d low 2 2 i n E urope - 216 -T a b l e X I V : L i t e r a t u r e s o u r c e s f o r t h e i n f o r m a t i o n c p . n t a i n e d i n T a b l e X I I I . De f o l i a t o r R e f e r e n c e s W e s t e r n S p r u c e B u d w o r m E u r o p e a n S p r u c e S a w f l y L a r c h S a w f l y D o u g l a s - f i r T u s s o c k M o t h W i n t e r M o t h G y p s y M o t h . D o d g e ( 1 9 6 1 ) , S i l v e r ( 1 9 6 0 ) , C a n a d a ( 1 9 3 9 - 1 9 8 2 ) , J o h n s o n a n d D e n t o n ( 1 9 7 5 ) R e e k s a n d B a r t e r ( 1 9 5 1 ) , N e i l s o n a n d M o r r i s ( 1 9 6 4 ) , W e b b e r ( 1 9 3 2 ) , R e e k s ( 1 9 5 3 ) C r a i g h e a d ( 1 9 4 0 ) , T u r n o c k ( 1 9 7 2 ) , G r a h a m ( 1 9 5 2 ) , M u l d r e w ( 1 9 5 3 ) T h o m p s o n ( 1 9 7 9 ) , S i l v e r ( 1 9 6 0 ) , S u g d e n ( 1 9 5 7 ) , S h e p h e r d a n d O t v o s ( 1 9 8 6 ) E m b r e e ( 1 9 6 5 ) , E m b r e e ( 1 9 6 6 ) , E m b r e e ( 1 9 6 7 ) C a m p b e l l a n d S l o a n ( 1 9 6 7 , 1 9 7 8 ) , B e s s ( 1 9 6 1 ) , R e a r d o n ( 1 9 7 8 ) D o a n e ( 1 9 7 6 ) , R o m a n y k ( 1 9 6 5 , c i t e d i n D o a n e a n d M c M a n u s ( 1 9 7 7 ) f a i l u r e s of those b i o l o g i c a l c o n t r o l agents ( l a r c h sawfly a f t e r 1940), and system behavior i n widely d i f f e r e n t geo-g r a p h i c a l areas (gypsy moth i n U.S.A and i n Europe). The e x c e p t i o n i s with D o u g l a s - f i r tussock moth. A l l the b i o l o g -i c a l i n f o r m a t i o n suggests i t should be a C l a s s 2 system, but the l e v e l of t r e e m o r t a l i t y i n some stands suggests that i t s impact on the host f o r e s t i s more l i k e t h a t e x h i b i t e d i n a C l a s s 4 system (Shepherd and Otvos 1986). These r e s u l t s , p l u s the r e s u l t s of the time s e r i e s a n a l y s i s , suggest that the theory i s , i n g e n e r a l , a good framework f o r understanding and e x p l a i n i n g the behavior of d e f o l i a t i n g i n s e c t systems. O b v i o u s l y , more t e s t i n g needs to be done to c l e a r l y i d e n t i f y where the framework does and does not work. - 218 -8 . 0 C O N C L U S I O N S A N D R E S E A R C H I M P L I C A T I O N S 8 . 1 C o n c l u s i o n s The major c o n c l u s i o n s of t h i s t h e s i s , i n terms of the o b j e c t i v e s s e t out i n S e c t i o n 1 . 2 are: 1 . the s t r u c t u r e and behavior of a d e f o l i a t i n g i n s e c t system can be e x p l a i n e d with f i v e dynamic v a r i -a b l e s — the d e f o l i a t o r , the f o l i a g e , the f o r e s t , the p a r a s i t o i d , and the d i s e a s e — and the e f f e c t s of weather a c t i n g on the d e f o l i a t o r ; 2. there are 4 c l a s s e s of d e f o l i a t i n g i n s e c t system behavior; 3. the behavior that a d e f o l i a t i n g i n s e c t system w i l l e x h i b i t i s determined by the magnitude of weather e f f e c t s on d e f o l i a t o r s u r v i v a l and r e c r u i t m e n t , the p a r a s i t o i d numerical response to changing d e f o l i a t o r d e n s i t i e s , the numerical response of the d i s e a s e to changing d e f o l i a t o r d e n s i t i e s , and the v u l n e r a b i l i t y of the f o r e s t to d e f o l i a t i o n ; 4. there are 4 e q u i l i b r i u m s t r u c t u r e s the d e f o l i a t o r can e x h i b i t , and one each f o r the p a r a s i t o i d , the f o l i a g e , the f o r e s t , and the d i s e a s e ; and 5. d e f o l i a t i n g i n s e c t system s t r u c t u r e and behavior can be p r e d i c t e d with a p a r t i c u l a r , w e l l - d e f i n e d set of i n f o r m a t i o n . - 219 -I must emphasize at t h i s p o i n t , however, that the con-cepts developed i n t h i s t h e s i s remain l a r g e l y u n t e s t e d , and must t h e r e f o r e s t i l l be viewed as simply an approach by which the s t r u c t u r e and behavior of d e f o l i a t i n g systems can perhaps be understood. The l a c k of data f o r t e s t i n g the components of the theory, so c l e a r l y demonstrated i n Chapter 7, preclu d e the concepts from being w e l l t e s t e d . T h i s means that i t i s d i f f i c u l t to c u r r e n t l y c l e a r l y d e f i n e those cases f o r where the concepts and theory do apply and those cases i n which they do not. Only experiments s i m i l a r to those d e s c r i b e d i n Chapter 7, and the c o l l e c t i o n of the minimum i n f o r m a t i o n s e t o u t l i n e d i n Chapter 6 w i l l be able to d e f i n -i t i v e l y t e s t the concepts. In a d d i t i o n , there are a t l e a s t two major areas which remain u n r e s o l v e d : hypotheses f o r d e f o l i a t i n g i n s e c t system behavior which are not a p a r t of t h i s theory; and the s p a t i a l dynamics of these systems. These are d i s c u s s e d below. 8.2 R e l a t i o n s h i p To Previous T h e o r i e s The i n t e g r a t i v e theory developed i n t h i s t h e s i s does not supplant any previous t h e o r i e s of d e f o l i a t i n g i n s e c t system s t r u c t u r e and behavior. No new c l a s s e s of explana-t i o n , such as p r e d a t i o n or food q u a l i t y , are proposed. How-ever, i t i s unusual i n the sense that i t does not e x p l a i n the s t r u c t u r e and behavior of simply one p a r t i c u l a r system on the b a s i s of f a c t o r s or processes s p e c i f i c to that system i n the way that p r e v i o u s analyses do (W e l l i n g t o n et a l . 1975, McLeod 1977a, Brookes f 2 e t a l . 1979, C l a r k and H o l l i n g - 220 -1979, F i s c h l i n and B a l t e n s w e i l e r 1979, McNamee 1979). Rather, i t i s a gen e r a l framework with unusual p r o p e r t i e s when viewed i n the l i g h t of pr e v i o u s t h e o r i e s . F i r s t , c e r t a i n p r e v i o u s t h e o r i e s have a w e l l d e f i n e d r o l e i n t h i s i n t e g r a t i v e t heory. The r o l e of p r e d a t i o n i s de f i n e d by a g u i l d of t r e e crown-searching n a t u r a l enemies and a g u i l d of ground-searching n a t u r a l enemies; these g u i l d s c r e a t e temporary s t a b l e d e f o l i a t o r p o p u l a t i o n s t a t e s at d e n s i t i e s w e l l below outbreak. The r o l e of weather i s to remove upper s t a b l e e q u i l i b r i a by reducing d e f o l i a t o r gen-e r a t i o n s u r v i v a l . P a r a s i t i s m and d i s e a s e i n f e c t i o n have the r o l e of p o t e n t i a l l y c o l l a p s i n g d e f o l i a t o r outbreaks. Second, the i n t e g r a t i v e theory i s s u f f i c i e n t l y g e n e r a l that i t i s able to d e f i n e s p e c i f i c c o n d i t i o n s under which p a r t i c u l a r s t r u c t u r e s and behaviors w i l l occur. I t t h e r e -f o r e can be used to p r e d i c t the s t r u c t u r e and behavior of a wide v a r i e t y of d e f o l i a t i n g i n s e c t systems. 8 . 3 F a c t o r s Not Included The i n t e g r a t i v e theory does not u t i l i z e a l l p r e v i o u s t h e o r i e s . In p a r t i c u l a r , the t h e o r i e s i n v o l v i n g f o l i a g e q u a l i t y , i n d i v i d u a l d i f f e r e n c e s i n d e f o l i a t o r s , and d e f o l i a -t o r d i s p e r s a l are not used i n the i n t e g r a t i v e theory. 8 . 3 . 1 D i s p e r s a l The process of d e f o l i a t o r d i s p e r s a l i s p a r t of the l a r g e r q u e s t i o n of d e f o l i a t i n g i n s e c t system s p a t i a l dynam-- 221 -i c s . I suspect that a comprehensive examination of the spa-t i a l dynamics of d e f o l i a t i n g i n s e c t systems can onl y be addressed by an approach s i m i l a r to the one taken i n t h i s t h e s i s . There i s c e r t a i n l y evidence that an i n t e g r a t i v e theory f o r the s p a t i a l dynamics of d e f o l i a t i n g i n s e c t s y s -tems can be developed. For example, there appear to be a few q u a l i t a t i v e l y d i f f e r e n t s p a t i a l b e h a v i o r s : 1. "spreading wave" - h i s t o r i c a l e a s t e r n spruce budworm (Cl a r k 1979), e a s t e r n black-headed budworm ( M i l l e r 1966), western spruce budworm (Shepherd et a l . 1979), 2. "synchronous l o c a l i z e d " - gypsy moth (Doane and McManus 1981), D o u g l a s - f i r tussock moth (Brookes et a l . 1979); and 3. "asynchronous l o c a l i z e d " - jack pine budworm (Canada 1939 to 1982), managed e a s t e r n spruce budworm ( C l a r k 1979). Such an i n t e g r a t i v e theory would o u t l i n e the minimum set of processes necessary to capture a l l the p o t e n t i a l spa-t i a l behaviors and the c o n d i t i o n s under which each behavior i s l i k e l y to occur. I suspect that the f o l l o w i n g components may be important i n developing t h i s i n t e g r a t i v e theory: 1. the primary l i f e stage i n which d i s p e r s a l occurs ( l a r v a as i n D o u g l a s - f i r tussock moth or gypsy - 222 -moth, or a d u l t as i n jack pine budworm or e a s t e r n spruce budworm); 2. the primary method of d i s p e r s a l ( p h y s i c a l f l i g h t as i n a l l s a w f l i e s , or w i n d - a s s i s t e d d i s p e r s a l as i n jack pine budworm or e a s t e r n spruce budworm); 3. q u a l i t a t i v e l y d i f f e r e n t "exodus" and " s e t t l i n g " f u n c t i o n s ( C l a r k 1979); and 4. the s p a t i a l p a t t e r n of the " h a b i t a t " ( d i s c o n t i n u -ous as i n the B r i t i s h Columbia mountain ranges, or homogeneous as i n the tamarack f o r e s t s of the North American midwest or p l a n t a t i o n f o r e s t s ) . I p o i n t out here, however, that C l a r k (1979) found that the behavior of the e a s t e r n spruce budworm system was e x p l a i n -able by l o c a l dynamics, m o d i f i e d to account f o r exodus and s e t t l i n g of d i s p e r s i n g budworm. Th i s must be c o n s i d e r e d as a c a u t i o n to anyone undertaking such a task. 8.3.2 I n d i v i d u a l D i f f e r e n c e s I n d i v i d u a l d i f f e r e n c e s have no r o l e i n the i n t e g r a t i v e theory of d e f o l i a t i n g i n s e c t systems, yet they have been shown to be c r i t i c a l l y important i n the dynamics of a number of f o r e s t i n s e c t p e s t s (Chapter 2). I t i s probable that the r o l e of i n d i v i d u a l d i f f e r e n c e s i s important i n s p a t i a l dynamics and i t i s there t h a t the r o l e of i n d i v i d u a l d i f f e r -ences would best be p l a c e d . For example, C l a r k (1979) used i t e x t e n s i v e l y i n developing a l t e r n a t e budworm d i s p e r s a l - 223 -f u n c t i o n s . 8 . 3 . 3 F o l i a g e Q u a l i t y As with i n d i v i d u a l d i f f e r e n c e s , f o l i a g e q u a l i t y i s not a p a r t of t h i s i n t e g r a t i v e theory. I suspect that the only a p p r o p r i a t e method of t e s t i n g whether f o l i a g e q u a l i t y can determine d e f o l i a t i n g i n s e c t / s y s t e m behavior would be to attempt to i n i t i a t e outbreaks by a l t e r i n g f o l i a g e q u a l i t y . 8.4 I m p l i c a t i o n s For I n s e c t / F o r e s t System Research The r e s u l t s of t h i s t h e s i s demonstrate c l e a r l y that i t i s not necessary to assume, as has been assumed i n the p a s t , that each d e f o l i a t i n g i n s e c t system i s unique and d i f f e r e n t from a l l o t h e r s . At the very l e a s t , the i n t e g r a t i v e theory i m p l i e s t h a t , with l e s s e f f o r t than has h i s t o r i c a l l y been thought necessary, the e q u i l i b r i u m s t r u c t u r e and the behavior of these systems can be induced. A l s o , the i n f o r -mation that i s needed to accomplish t h i s i s c l e a r . Once t h i s i n f o r m a t i o n i s known, very simple models of the system of concern can be developed using s p e c i f i c b i o l o g i c a l and b e h a v i o r a l data. These models can then used to d e f i n e r e s e a r c h q u e s t i o n s more s p e c i f i c to the p a r t i c u l a r system. The r e s u l t s of t h i s t h e s i s a l s o have p a r t i c u l a r i m p l i -c a t i o n s f o r the emphasis which needs to be p l a c e d on p a r t i c -u l a r types of r e s e a r c h i n f o r e s t entomology. 8 . 4 . 1 The D e f o l i a t o r D e f o l i a t o r r e s e a r c h need not be as e x t e n s i v e as i t has - 224 -been t r a d i t i o n a l l y . T y p i c a l l y , the m a j o r i t y of the budget i n f o r e s t pest r e s e a r c h programs i s a l l o c a t e d to studying the d e f o l i a t o r (e.g., M o r r i s 1963, Brookes et a l . 1979). T h i s i s not necessary. The r e s u l t s of t h i s t h e s i s suggest that e x t e n s i v e l i f e t a b l e s t u d i e s and d e t a i l e d p r e dator s t u -d i e s which census the types of pre d a t o r s and t h e i r e f f e c t s at d i f f e r e n t p o p u l a t i o n l e v e l s — r e s e a r c h which i s i n v a r i -a b l y undertaken at high c o s t — need not be done. What i s needed to induce the e q u i l i b r i u m s t r u c t u r e of the d e f o l i a t o r i s the l o c a t i o n of i t s v a r i o u s l i f e h i s t o r y stages and the e f f i c a c y of i t s predator defense mechanisms. 8.4.2 The P a r a s i t o i d And Disease Complexes The r e s u l t s of t h i s t h e s i s imply that a r i g o r o u s , quan-t i t a t i v e understanding of the dynamics of the p a r a s i t o i d and di s e a s e complexes of d e f o l i a t o r s i s c r i t i c a l to understand-ing d e f o l i a t i n g i n s e c t systems. U n f o r t u n a t e l y , the research i n t o these n a t u r a l enemy g u i l d s i s u s u a l l y d e s c r i p t i v e . In terms of these two n a t u r a l enemy complexes, the s t a t e of understanding i s as poor as the s t a t e of understanding of d e f o l i a t o r p o p u l a t i o n dynamics before the major d e f o l i a t o r r e s e a r c h programs of' the l a s t 25 y e a r s . Research i n t o p a r a s i t o i d and d i s e a s e g u i l d s should be 'popula t i o n dynamic* i n nature. For p a r a s i t o i d s , t h i s means l i f e t a b l e a n a l y s e s , b e h a v i o r a l s t u d i e s e s t i m a t i n g attack r a t e s and the l e v e l of s u p e r - p a r a s i t i s m and d i s c r i m i n a t i o n between p a r a s i t i z e d and n o n - p a r a s i t i z e d h o s t s . For disease - 225 -complexes, f u t u r e r e s e a r c h should i n t e g r a t e the c u r r e n t understanding of the dynamics of the pathogen w i t h i n the host with a good understanding of the dynamics while the pathogen i s o u t s i d e the host. 8 . 4 . 3 The F o l i a g e As with p a r a s i t o i d and d i s e a s e complexes, f o l i a g e r e s e a r c h tends to be minimal and r e s t r i c t e d to p r e d i c t i n g f o l i a g e biomass as a f u n c t i o n of v a r i o u s t r e e a t t r i b u t e s . F o l i a g e r e s e a r c h should concentrate on e s t i m a t i n g f o l i a g e recovery times a f t e r d e f o l i a t i o n . T h i s i n f o r m a t i o n i s c r u -c i a l to determining whether the system of i n t e r e s t i s a C l a s s 3 system, o p e r a t i n g on a d e f o l i a t o r : f o l i a g e c y c l e , or a C l a s s 4 system, o p e r a t i n g on a d e f o l i a t o r : p a r a s i t o i d or di s e a s e c y c l e . 8.4.4 The F o r e s t The r e s u l t s of t h i s t h e s i s imply that the e q u i l i b r i u m s t r u c t u r e of the f o r e s t can be induced by knowing the proba-b i l i t y of t r e e m o r t a l i t y when heavy d e f o l i a t i o n occurs dur-ing the time of year when the d e f o l i a t o r does the m a j o r i t y of i t s f e e d i n g . T h i s i n turn i m p l i e s t h a t the e q u i l i b r i u m s t r u c t u r e i s l a r g e l y a f u n c t i o n of c h a r a c t e r i s t i c s of the t r e e s themselves and i s somewhat independent of the d e f o l i a -t o r of concern. That i s , i f t h i s i n f o r m a t i o n i s known f o r a p a r t i c u l a r t r e e s p e c i e s and a p a r t i c u l a r d e f o l i a t o r , i t can be used f o r another system i n which a d i f f e r e n t d e f o l i a t o r feeds at the same time of the year. T h e r e f o r e , f o r e s t - 226 -r e s e a r c h need only be undertaken i f the t r e e s p e c i e s has never experienced heavy d e f o l i a t i o n d u r i n g the time of year when the d e f o l i a t o r of concern feeds. I f such a c o n d i t i o n o c c u r s , r e s e a r c h should be under-taken to f i n d out the p r o b a b i l i t y of t r e e m o r t a l i t y under these c o n d i t i o n s . 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S i l v i c a l c h a r a c t e r i s t i c s of jack pine. Lake Sta t e s For. Exp. S t a . Pap. No. 61: 31 pp. S c h a f f e r , W.M. and M. Kot. i n p r e s s . Nearly one dimensional dynamics i n an epidemic. J o u r . Theor. B i o l . Shepherd, R.F. and I.S. Otvos. 1986. Pest management of D o u g l a s - f i r tussock moth: procedures f o r i n s e c t - 238 -m o n i t o r i n g , problem e v a l u a t i o n , and c o n t r o l a c t i o n s . Canadian F o r e s t r y S e r v i c e . BC-X-270. 14 pp. S i l v e r , G.T. 1960. The r e l a t i o n of weather to p o p u l a t i o n trends of the black-headed budworm, A c l e r i s v a r i a n a Fern., ( L e p i d o p t e r a : T o r t r i c i d a e ) . Can. Ent. 95: 401-410. S i l v e r , G.T. 1961. Notes on the chemical c o n t r o l of E c t r o p i s c r e p u s c u l a r i a S c h i f f . at K i t i m a t , B.C. Proc. B.C. Entomol. Soc. 58: 13-16. S i l v e r , G.T. 1963. A f u r t h e r note on the r e l a t i o n of weather to p o p u l a t i o n trends of the black-headed budworm, A c l e r i s v a r i a n a Fern., ( L e p i d o p t e r a : T o r t r i c i -dae). Can. Ent. 98: 58-61. Simionescu, A. 1973. Development of g r a d a t i o n s of Lymantria  d i s p a r L. i n Rumania, and c o n t r o l measures. ( i n French, E n g l i s h summary). "Zast. B i l j a . 24: 275-284. Smith, H.R. 1985. W i l d l i f e and the gypsy moth. W i l d l . Soc. B u l l . 13: 166-174. Southwood T.R.E. 1977. The relevance of p o p u l a t i o n dynamics theory to pest s t a t u s . In: J.M. C h e r r e t t and G.R. Sager. eds. O r i g i n s Of Pest, P a r a s i t e , Disease, And Weed Problems. Proc. B r i t i s h E c o l . Soc. pp. 35-54. Southwood, T.R.E. 1975. The dynamics of i n s e c t p o p u l a t i o n s . In: D. Pimentel. ed. I n s e c t s , S c i e n c e , and S o c i e t y . Academic Press, New York. pp. 151-200. Southwood, T.R.E. and H.N. Comins. 1976. A s y n o p t i c popula-t i o n model. Jour. Anim. E c o l . 45: 949-965. Spr u g e l , D.G. 1976. Dynamic s t r u c t u r e of wave-generated Abies balsamea f o r e s t s i n the Northeastern United S t a t e s . J . E c o l . 65: 889-911. Stark, R.W. 1959. Recent trends i n f o r e s t entomology. Ann. Rev. Ent. 303-324. Sugden, B.A. 1957. A b r i e f h i s t o r y of D o u g l a s - f i r tussock moth, Hemerocampa pseudotsugata McD., i n B r i t i s h Colum-b i a . Proc. Ent. Soc. B.C. 54: 37-39. SYSTAT. 1985. User manual. SYSTAT Inc. 235 pp. Takahashi, F. 1964. Reproduction c u r v i e with two e q u i l i -brium p o i n t s : A c o n s i d e r a t i o n on the f l u c t u a t i o n of an i n s e c t p o p u l a t i o n . Res. Pop. E c o l . 6: 28-36. Thomson, A.J. e_t a l . 1984. R e l a t i n g weather to outbreaks of western spruce budworm Ch o r i s t o n e u r a o c c i d e n t a l i s - 239 -( L e p i d o p t e r a : T o r t r i c i d a e ) i n B r i t i s h Columbia. Can. Ent. 116: 375-381. Thompson, C.G. V i r u s . In: Brookes, M.A., R.M. Campbell, and R.A. Stark, eds. 1978. The D o u g l a s - f i r tussock moth: A s y n t h e s i s . U.S. Dept. Agr. For. Ser. Tech. B u l l . no. 1585. pp. 47-43. Torgerson, T.R. and R.W. Campbell. 1982. Some e f f e c t s of avian p r e d a t o r s on the western spruce budworm. E n v i r o n . Ent. 11: 429-431. T r i p p , H.A. 1965. The development of Neodiprion s w a i n e i i Middleton (Hymenoptera: D i p r i o n i d a e ) i n the p r o v i n c e of Quebec. Can. Ent. 97: 92-107. Tunnock, S. The D o u g l a s - f i r tussock moth i n the northern r e g i o n — a c a r t o g r a p h i c h i s t o r y of the outbreaks from 1928-1973. U.S. Dept. Agr. For. Serv. Div. State and P r i v . For. Rep 73-27. 18 pp. Turnock, W.J. 1972. Geographical and h i s t o r i c a l v a r i a b i l i t y i n p o p u l a t i o n parameters and l i f e systems of the l a r c h sawfly. Can. Ent. 104: 1893-1900. UBC, 1975. Nonlinear Function O p t i m i z a t i o n . U n i v e r s i t y of B r i t i s h Columbia Computing Center Manual. 137 pp. van den Bosch, I. 1979. The P e s t i c i d e C onspiracy. V a r l e y , G.C. 1949. S p e c i a l review: p o p u l a t i o n changes i n German f o r e s t p e s t s . J . Anim. E c o l . 18: 117-122. V a r l e y , G.C. and G.R. Gradwell. 1965. I n t e r p r e t i n g winter moth p o p u l a t i o n changes. Proc. 12th I n t . Congr. Ent. London, pp. 377-388. V o l t e r r a , V. 1928. V a r i a t i o n s and f l u c t u a t i o n s of the number of i n d i v i d u a l s i n animal s p e c i e s l i v i n g t o g e t h e r . In: R.N. Chapman. ed. Animal Ecology. McGraw-Hill. New York. pp. 409-448. Voute, A.D. 1947. R e g u l a t i o n of the d e n s i t y of the i n s e c t p o p u l a t i o n s i n v i r g i n f o r e s t s and c u l t i v a t e d woods. Arch. N e e r l . Z o o l . 7: 435-470. Wallace, D.R. and K.J. G r i f f i t h s . i n prep. A s i m u l a t i o n study of European pine sawfly/red pine dynamics. Wallner, W.E. and G.S. Walton. 1979. Host d e f o l i a t i o n : A p o s s i b l e determinant of gypsy moth p o p u l a t i o n q u a l i t y . Ann. Ent. Soc. Amer. 72: 62-67. Weaver, H. 1961. E c o l o g i c a l changes i n the ponderosa pine f o r e s t of Cedar V a l l e y i n southern Washington. E c o l . - 240 -42: 416-420. Webber, R.T. 1932. Sturmia i n c o n s p i c u a Meigen, a t a c h n i d p a r a s i t e of the gypsy moth. Can. J . Agr. Res. 45: 193-208. W e l l i n g t o n , W.G. 1957. I n d i v i d u a l d i f f e r e n c e s as a f a c t o r i n p o p u l a t i o n dynamics: The development of a problem. Can. Jour. Z o o l . 35: 293-323. W e l l i n g t o n , W.G. 1960. Q u a l i t a t i v e changes i n n a t u r a l popu-l a t i o n s d u r i n g changes i n abundance. Can. Jour . Z o o l . 38: 289-314. W e l l i n g t o n , W.G. 1964. Q u a l i t a t i v e changes i n p o p u l a t i o n s i n u n stable environments. Can. Ent. 96: 436-451. W e l l i n g t o n , W.G. et a l . 1975. A s t o c h a s t i c model f o r as s e s s i n g the e f f e c t s of e x t e r n a l and i n t e r n a l h e t e r o -g e n e i t y of an i n s e c t p o p u l a t i o n . Res. Pop. E c o l . 17: 1-29. White, T.C.R. 1969. An index to measure weather-induced s t r e s s of t r e e s a s s o c i a t e d with outbreaks of P s y l l i d s i n A u s t r a l i a . E c o l . 50: 909-909. White, T.C.R. 1974. A hypothesis to e x p l a i n outbreaks of looper c a t e r p i l l a r s , with s p e c i a l r e f e r e n c e to popula-t i o n s of Selidosema s u a v i s i n a p l a n t a t i o n of Pinus  r a d i a t a i n New Zealand. Oecol. 16: 279-301. White, T.C.R. 1976. Weather, food, and plagues of l o c u s t s . O ecol. 22: 119-134. White, T.C.R. 1978. The importance of a r e l a t i v e shortage of food i n animal ecology. O e c o l . 33: 71-86. Wickman, B.E. 1963. M o r t a l i t y and growth r e d u c t i o n of white f i r f o l l o w i n g d e f o l i a t i o n by the D o u g l a s - f i r tussock moth. U.S. Dept. Agr. For. Ser. Res. Pap. PSW-7. 15 pp. Wickman, B.E. 1978. Tree m o r t a l i t y and t o p - k i l l r e l a t e d to d e f o l i a t i o n by the D o u g l a s - f i r tussock moth i n the Blue Mountains outbreak. U.S. Dept. Agr. For. Serv. Res. Pap. PNW-233. 39 pp. Wickman, B.E. 1986a. R a d i a l growth of grand f i r and D o u g l a s - f i r 10 years a f t e r d e f o l i a t i o n by the Douglas-f i r tussock moth i n the Blue Mountains outbreak. U.S. Dept. Agr. For. Serv. Res. Pap. PNW-367. 11 pp. Wickman, B.E. 1986b. Growth of white f i r a f t e r D o u g l a s - f i r tussock moth outbreaks: Long term records i n the S i e r r a Nevada. U.S. Dept. Agr. For. Serv. Res. Note. PNW-440. - 241 -8 pp. Wickman, B.E., K.W. S e i d e l , and G. L. S t a r r . 1986. N a t u r a l r e g e n e r a t i o n 10 years a f t e r a D o u g l a s - f i r tussock out-break i n n o r t h e a s t e r n Oregon. U.S. Dept. Agr. For. Serv. Res. Pap. PNW-370. 15 pp. Wotton, D.L. and D.C. Jones. 1975. A r a t i o n a l i z a t i o n of spruce budworm c o n t r o l i n the Spruce Woods P r o v i n c i a l Park and F o r e s t , Manitoba. Manitoba Dept. Mines Resources, and Env. Manage. MS Report 76-1. - 242 -A . I A P P E N D I X I - T I M E S E R I E S A N D S P E C T R A L D E N S I T I E S F O R D E F O L I A T O R P O P U L A T I O N S The f o l l o w i n g f i g u r e s are the d e f o l i a t o r p o p u l a t i o n d a t a s e t s used i n the analyses throughout the t h e s i s . In a d d i t i o n , the s p e c t r a l d e n s i t i e s are giv e n f o r each d a t a s e t ; these were d e r i v e d from the d a t a s e t s by using the MIDAS s t a -t i s t i c a l package (Fox and Guire 1 9 7 6 ) . The s p e c t r a l d e n s i -t i e s are used i n Table I I I , Chapter 2, the review of i n s e c t / f o r e s t system behavior and i n Chapter 7 , t e s t i n g f o r c l a s s e s of i n s e c t / f o r e s t system behavior. The p o p u l a t i o n data are used i n Chapter 7 , i n the t e s t i n g f o r m u l t i p l e s t a b l e e q u i l i b r i a i n d e f o l i a t o r p o p u l a t i o n s . Table II l i s t s the data sources used i n the c o m p i l a t i o n of these d a t a s e t s . Each d a t a s e t has two graphs. The f i r s t a graph of the p o p u l a t i o n over time. The p o p u l a t i o n s were transformed to t h e i r common l o g a r i t h m before p l o t t i n g and a l l are s c a l e d from -3 (=.001) to 4 (=10,000). A v e r t i c a l bar f o r a given at the top of the graph s i g n i f i e s a year i n which the popu-l a t i o n estimate was 0. The absence of a v e r t i c a l bar or a p o p u l a t i o n p o i n t means no data were gathered. Most of these graphs r e p r e s e n t a s i n g l e r e g i o n or p l o t . A number of time s e r i e s are presented on the same graph i n those systems where the data are r e l a t i v e l y s h o r t term but from a s e r i e s of p l o t s (e.g., jack pine s a w f l y ) . Below each graph i s the normalized s p e c t r a l d e n s i t y f o r the dominant d a t a s e t i n each time s e r i e s . A r e p r e s e n t a t i v e s p e c t r a l d e n s i t y i s presented f o r those d a t a s e t s where the - 243 -data are r e l a t i v e l y s h o r t term but from a s e r i e s of p l o t s . - 24 5 -Western F a l s e Hemlock Looper - 246 -G r e e n - S t r i p e d F o r e s t Looper 247 - 248 -D o u g l a s - f i r TussocTc Moth - 249 -4 ISO 20 10 - S PERIODICITY - YEARS D o u g l a s - f i r Tussock Moth - 2 5 0 -Western Hemlock Looper - 251 -Larch Sawfly - 253 -Western Spruce Budworm - 254 -Western Spruce Budworm - 256 -4 Western Blackheaded Budworm Gypsy Moth - 261 -i ! ' ' • i 1,1,1 I I I , I I I I I I I I I I 1 I I I I 1 9 4 9 Y E A R 19." 1QQ 2 0 10 P E R I O D I C I T Y - Y E A R S Saddlebacked Looper - 262 -European Pine Sawfly Jack Pine Sawfly European Spruce Sawfly - 263 -A . I I A P P E N D I X I I - A N A L Y S I S OF P A R A S I T O I D I S O R E C R U I T M E N T CURVES The p a r a s i t o i d submodel i n the three i n s e c t / f o r e s t models can be c o l l a p s e d to the f o l l o w i n g g e n e r a l equation: Pt+1 = N ( 1 ~ ( ( ( a P t N ) / ( l + b N ) ) / ( k N ) ) ) " k c e , where (A.1) P^ +^ the p a r a s i t o i d d e n s i t y i n the succeeding gen-e r a t i o n ; P^_ the p a r a s i t o i d d e n s i t y i n the c u r r e n t genera-t i o n ; N ' host ( d e f o l i a t o r ) d e n s i t y ; a,b parameters o f the p a r a s i t o i d f u n c t i o n a l response to host d e n s i t y ; k the d i s p e r s i o n c o e f f i c i e n t o f the negative binomial equation; c the s u r v i v a l o f attacked hosts during the time before p a r a s i t o i d emergence; e the s u r v i v a l o f the p a r a s i t o i d from the time o f emergence from the host to the time of attack i n the next g e n e r a t i o n . - 264 -The components o f t h i s model are: 1. a Type 2 f u n c t i o n a l response to host d e n s i t y ( H o l -l i n g , 1959); 2. a competition equation (the negative binomial) which accounts f o r the e f f e c t s o f contagion i n the d i s t r i b u t i o n o f a t t a c k s among the prey. The nega-t i v e binomial zero term g i v e s the p r o p o r t i o n o f the host p o p u l a t i o n which i s not attacked by p a r a s i t o i d s . The assumption i s that p a r a s i t o i d s cannot o r do not d i s c r i m i n a t e between non-p a r a s i t i z e d and p r e v i o u s l y p a r a s i t i z e d hosts, and that o n l y one p a r a s i t o i d can emerge from an attacked host; i r r e s p e c t i v e o f the number of p a r a s i t o i d eggs o r i g i n a l l y l a i d i n that host; 3. a s u r v i v a l of hosts from the time o f attack by the p a r a s i t o i d to the time o f p a r a s i t o i d emergence from the host (parameter c ) ; and 4. a p a r a s i t o i d progeny s u r v i v a l r a t e (parameter e) from the time o f p a r a s i t o i d emergence from the host to the time those progeny r e - a t t a c k the i n the succeeding g e n e r a t i o n . Parameters c and e are simply s c a l a r s to the p a r a s i t o i d r e c r u i t m e n t f u n c t i o n . They do not determine the shape of the i s o r e c r u i t m e n t curve and w i l l t h e r e f o r e be l e f t out of - 265 -the remaining a n a l y s i s . We can look at the e f f e c t t h a t the p a r a s i t o i d func-t i o n a l response has on the shape of the i s o r e c r u i t m e n t curve by removing the competition equation from the model. Ignoring parameters c and e, the model t h e r e f o r e s i m p l i f i e s t o : P t + 1 / P t = a N / ( 1 + b N ) (A.2) I want to f i n d a l l values of N f o r which p t + i / p t = 1? that i s , a l l host d e n s i t y values from which there i s no change i n the p a r a s i t o i d p o p u l a t i o n from one g e n e r a t i o n to the next. These d e n s i t i e s form the p a r a s i t o i d i s o r e c r u i t m e n t curve. Rearranging equation A.2, one g e t s : aN/(l+bN) = 1 (A.3) - 266 -R e a r r a n g i n g t e r m s g i v e s : aN = 1 + bN bN - aN = 1 N(a-b) = 1 N = l / ( a - b) (A.4) T h e r e f o r e , w i t h o u t t h e c o m p e t i t i o n e q u a t i o n , t h e d e n s i t y o f h o s t s w h i c h c r e a t e e q u i l i b r i u m p a r a s i t o i d d e n s i t i e s i s l / ( b - a ) . The p a r a s i t o i d i s o r e c r u i t m e n t c u r v e u n d e r t h e s e c o n d i t i o n s i s a v e r t i c a l l i n e a t N = l / ( b - a ) and u n l i k e t h e i s o r e c r u i t m e n t c u r v e s d e r i v e d f r o m t h e t h r e e i n s e c t / f o r e s t m o d e l s . The i s o r e c r u i t m e n t c u r v e f o r e q u a t i o n A.2 ( w i t h o u t t h e c o m p e t i t i o n e q u a t i o n ) i s what t h e i s o r e c r u i t m e n t c u r v e w o u l d be i n t h e i n s e c t m o d e l s i f t h e r e were no e f f e c t s o f egg d i s t r i b u t i o n , and t h a t a l l p a r a s i t o i d e g g s l a i d w o u l d emerge f r o m t h e h o s t . The c o n c l u s i o n i s t h a t i t i s t h e c o m p e t i t i o n e q u a t i o n w h i c h c a u s e s t h e p a r a s i t o i d i s o r e c r u i t m e n t c u r v e s t o bend o v e r a t h i g h p a r a s i t o i d d e n s i t i e s . The r e a s o n f o r t h i s i s t h a t , w i t h i n c r e a s i n g number o f p a r a s i t o i d a t t a c k s ( w h i c h o c c u r s w i t h i n c r e a s e s i n p a r a s i t o i d d e n s i t i e s ) t h e number o f s u c c e s s f u l a t t a c k s , d e f i n e d by t h e number o f p a r a s i t o i d p r o -g e n y w h i c h emerge f r o m t h e h o s t s , r e l a t i v e t h e number o f a t t a c k s made by t h e p a r a s i t o i d s , d e c r e a s e s . I t d e c r e a s e s - 26 7 -because o f the assumption that o n l y one p a r a s i t o i d progeny can emerge from a host, i r r e s p e c t i v e o f the number o f eggs l a i d i n that host. 

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