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Phenotypic correlations among relatives and variability in reproductive performance in populations of… Anderson, Judith L. 1975

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PHENOTYPIC CORRELATIONS AMONG RELATIVES AND VARIABILITY IN REPRODUCTIVE PERFORMANCE IN POPULATIONS OF THE VOLE KICROTUS TOSNSENDII by JUDITH L. ANDERSON B.A.r Harvard U n i v e r s i t y , 1969 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Zoology We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER, 1975 In presenting th i s thesis in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It i s understood that copying or pub l i ca t i on of th is thes i s for f i nanc ia l gain sha l l not be allowed without my wr i t ten permission. Department of Zoology  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT The purpose o f t h i s study was to i n v e s t i g a t e the p o t e n t i a l of a p o p u l a t i o n of v o l e s (Microtus townsendii) t o respond g e n e t i c a l l y to n a t u r a l s e l e c t i o n upon e c o l o g i c a l l y important t r a i t s . Reproductive performance of i n d i v i d u a l v o l e s was observed i n s m a l l outdoor e n c l o s u r e s , and t h e i r o f f s p r i n g were monitored a f t e r r e l e a s e i n t o n a t u r a l p o p u l a t i o n s . Among the p o s s i b l e f a c t o r s i n f l u e n c i n g success of l i t t e r s , maternal behavior proved to be an important determinant of l i t t e r s i z e at rec r u i t m e n t . A measure of the c o n t r i b u t i o n by i n d i v i d u a l parents to the next g e n e r a t i o n ' s gene pool r e v e a l e d a s e r i o u s r e d u c t i o n i n e f f e c t i v e numbers between J u l y and September f o r t h i s p o p u l a t i o n . H e r i t a b i l i t y a n a l y s i s was performed on the f o l l o w i n g t r a i t s : j u v e n i l e growth r a t e , maximum body s i z e , tendency to breed i n winter, age at puberty, tendency to leave a p o p u l a t i o n , a c t i v i t y , and a g o n i s t i c behavior. None of these t r a i t s manifested a strong g e n e t i c i n f l u e n c e . However, c o r r e l a t i o n s between o f f s p r i n g and mothers were s i g n i f i c a n t f o r maximum s i z e , a c t i v i t y , and a g o n i s t i c behavior, and there was evidence that common environment e f f e c t s tend to make s i b l i n g s resemble one another i n j u v e n i l e growth r a t e , age at puberty, and d i s p e r s a l tendency. i i CONTENTS LIST OF FIGURES .., i v LIST OF TABLES v i ACKNOWLEDGMENTS . . . . v i i i SECTION I: INTRODUCTION 1 SECTION I I : QUANTITATIVE GENETICS THEORY 10 SECTION I I I : METHODS 21 A. Trapping techniques 30 B. F i e l d breeding techniques .......................... 33 C. Behavior tests 36 D. General treatment of the data 38 SECTION IV: RESULTS — POPULATION STRUCTURE AND REPRODUCTIVE VARIATION 41 A. L i t t e r size 4 2 B. Unsuccessful l i t t e r s ............................... 53 C. Variation i n a f i t n e s s measure 68 D. Effect i v e population si z e 69 E. Discussion 80 SECTION V: RESULTS—CORRELATIONS AMONG RELATIVES 90 A. Body s i z e 90 Growth rate 91 Maximum body siz e 104 i i i D i s c u s s i o n . 114 B. Reproductive c h a r a c t e r s 121 Winter breeding 121 age at puberty ......... 122 D i s c u s s i o n 130 C. D i s p e r s a l tendency 133 D i s c u s s i o n . . 134 D. Behavior 139 General treatment of data 139 ' C o r r e l a t i o n s among r e l a t i v e s 142 Behavior and r e p r o d u c t i v e success 143 D i s c u s s i o n 147 SECTION VI: EVALUATION, FURTHER WORK 159 SECTION V I I : CONCLUSIONS 177 APPENDIX 181 REFERENCES ....196 i v LIST OF FIGURES Page 1. 14-day s u r v i v a l rate and minimum numbers a l i v e , Grid A A •••• 22 2. 14-day s u r v i v a l rate and minimum numbers a l i v e . Grid 0 24 3. 14-day su r v i v a l rate and minimum numbers a l i v e . Grid L 26 4. Diagram of the Haney study area 28 5. Frequency d i s t r i b u t i o n s of l i t t e r sizes 44 6. Cumulative o f f s p r i n g f i r s t captures 46 7. Frequency d i s t r i b u t i o n of parental f i t n e s s 71 8. Weight as a function of s k u l l width 93 9. Regression of juvenile growth rate on maximum size of s i r e 103 10. Regression of offspring maximum size on maximum size of dam ....110 11. Regression of maximum siz e on juvenile growth rate ...112 12. Frequency d i s t r i b u t i o n of s k u l l width at f i r s t capture 161 13. Growth curves of littermates 163 14. Growth curves of littermates 164 15. Growth curves of littermates ..165 16. Growth curves of littermates .....166 17. Growth rate as a function of siz e .....169 V 18. Frequency d i s t r i b u t i o n of residence times for enclosure-born vs native animals ...............171 A-1. Functional relationships of the non-overlapping generations model 184 A-2. Functional relationships of the overlapping generations model , . . 188 A-3. Simulated vole population cycle, non-overlapping generations .....190 A-4. Simulated vole population cycle, overlapping generations 193 A-5. Relative f i t n e s s of simulated phenotype classes .....195 v i LIST OF TABLES Table Page 1. Estimation of h 2 from correlations among r e l a t i v e s 17 2. Repeatability of l i t t e r size 50 3. Recruited l i t t e r s i z e vs season of b i r t h 52 4. Frequency d i s t r i b u t i o n of stage of f a i l u r e of unsuccessful l i t t e r s 55 5. Association of l i t t e r success with b i r t h i n traps 56 6. Association of l i t t e r success with mother's t r a p p a b i l i t y ... 57 7. Association of l i t t e r success with season of b i r t h .... 61 8. Number of successful and unsuccessful l i t t e r s over seasons , . . 62 9. Association of l i t t e r success with presence of male ...64 10. Association of l i t t e r success with source of parents . 65 11. Association of l i t t e r success with source of parents (pooled data) 66 12. Estimated parameters of the frequency d i s t r i b u t i o n of parental f i t n e s s 72 13. Estimated parameters of the frequency d i s t r i b u t i o n of parental f i t n e s s , by seasons and sexes 73 14. Formulae for estimating variance e f f e c t i v e numbers ... 74 15. Coefficients for estimating e f f e c t i v e number for the v i i e n c losure-born p o p u l a t i o n 77 1 6 . Estimated v a l u e s o f e f f e c t i v e number 7 8 17. Estimated i n d i c e s of j u v e n i l e s u r v i v a l 86 18. Components of v a r i a n c e f o r j u v e n i l e growth r a t e — l i t t e r s , 9 7 1 9 . Components of v a r i a n c e f o r j u v e n i l e growth r a t e - - l i t t e r s w i t h i n h a l f - s i b f a m i l i e s 9 9 20. Components of v a r i a n c e . f o r j u v e n i l e growth r a t e — l i t t e r s w i t h i n matings ......101 21. Summary of j u v e n i l e growth r a t e and maximum s i z e a n a l y ses 1 0 8 22. Components of v a r i a n c e f o r age at p u b e r t y — l i t t e r s ...121 23. Components of va r i a n c e f o r age at p u b e r t y - - l i t t e r s w i t h i n h a l f - s i b f a m i l i e s ...126 24. Components of v a r i a n c e f o r age at p u b e r t y — l i t t e r s w i t h i n matings ........128 2 5. Components of va r i a n c e f o r l e n g t h of r e s i d e n c e i n p o p u l a t i o n s ..136 26. R e p e a t a b i l i t y of behavior v a r i a b l e s 141 27. R e l a t i o n s h i p s of o f f s p r i n g behavior to maternal behavior . 144 28. R e l a t i o n s h i p s of l i t t e r success t o maternal behavior .145 29. S t a t i s t i c s f o r r e g r e s s i o n s of growth r a t e on s i z e ....172 v i i i ACKNOWLEDGMENTS I would l i k e t o extend my g r a t i t u d e to a l l the people who a s s i s t e d me with t h i s p r o j e c t . Dr. C h a r l e s Krebs i n p a r t i c u l a r provided generous i n t e l l e c t u a l , f i n a n c i a l , and l o g i s t i c a l support. His example of p a t i e n t p e r s i s t e n c e i n the fa c e of an amazing range of o b s t a c l e s to f i e l d work was a source of i n s p i r a t i o n to me. Pat H i l s o n , Irene Wingate, Dr. Alan B i r d s a l l , Dr. James R e d f i e l d , J a n i c e LeDuc, Pam Fraker, Rob Powell, Tom S u l l i v a n , Suzanne Robertson, Rudy Boonstra, Dr. Bay H i l b o r n , and Dr. C h a r l e s Krebs a l l helped with the f i e l d work. In a d d i t i o n , Rudy Boonstra and Ray H i l b o r n provided me with some of t h e i r data. The U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t provided the study area. Dr. Conrad Wehrhahn, Dr. Ch a r l e s Krebs, Dr. Dennis C h i t t y , Dr. R a n d a l l Peterman, and Daphne F a i r b a i r n a l l took the time t o read the manuscript and provide h e l p f u l comments. I r e c e i v e d f e l l o w s h i p support from a te a c h i n g a s s i s t a n t s h i p and a f e l l o w s h i p from the N a t i o n a l Science Foundation, U. S. A. 1 SECTION I: INTRODUCTION The genetic and phenotypic v a r i a b i l i t y w i t h i n populations i s the m a t e r i a l upon which e v o l u t i o n by n a t u r a l s e l e c t i o n depends. Populations of microtine rodents are proving e s p e c i a l l y i n t e r e s t i n g i n t h i s r e s p e c t , f o r v a r i a b i l i t y appears to be i n t i m a t e l y connected with t h e i r population dynamics as we l l as with t h e i r long-term e v o l u t i o n a r y p o t e n t i a l . The purpose of my research has been to explore phenotypic v a r i a b i l i t y i n the vole Microtus t p ^ n s e n d i i , i n both a general and a more s p e c i f i c context. The general problem concerns the d e s c r i p t i o n and p r e d i c t i o n of phenotypic and genotypic changes under n a t u r a l s e l e c t i o n . My goal was to explore the u t i l i t y of q u a n t i t a t i v e g e n e t i c s as an e c o l o g i c a l t o o l f o r p r e d i c t i n g short-term population responses to n a t u r a l s e l e c t i o n . With respect to the s p e c i f i c problem, the causation of microtine population f l u c t u a t i o n s , my goals were ( 1 ) to i n v e s t i g a t e the i n h e r i t a n c e , under n a t u r a l c o n d i t i o n s , of some e c o l o g i c a l l y important t r a i t s of the sp e c i e s , and (2) to describe the v a r i a t i o n i n reproductive performance among i n d i v i d u a l v o l e s. THE GENERAL PROBLEM One of the major problems i n the f i e l d of e c o l o g i c a l genetics i s the p r e d i c t i o n of population responses to n a t u r a l 2 selection pressures. a t h e o r e t i c a l approach to t h i s problem has been largely worked out. It consists of a description of relationships between the functions of single genes and the dynamics of population gene pools; these r e l a t i o n s h i p s constitute much of the theory of population genetics. However, there i s a serious obstacle to the application of t h i s theory to natural populations. This obstacle i s the p o s s i b i l i t y that descriptions of the dynamics of independent genes may be i r r e l e v a n t to evolutionary processes, because natural selection pressures probably do not work upon the products of single l o c i , but rather upon the whole phenotype. What i s needed, then, i s a theory which can r e l a t e the phenotype to the genotype. a t t h i s time, no such theory exists; i n f a c t , i t i s unclear even what variables and parameters one would need to put together a workable theory. Thus, there i s a serious gap in the t h e o r e t i c a l structure necessary to predict phenotypic population responses to natural selec t i o n . On the one hand, we have population genetics theory: given a gene pool, we could predict what the next generation would look l i k e genotypically, i f we could actually measure selection pressures acting upon the elements of the gene pool. However, at present we cannot measure selection at t h i s l e v e l . As Lewontin (1974, Chapter 6) has pointed out, the observation of the dynamics of i n d i v i d u a l l o c i may y i e l d estimates of selection pressures, but these estimates are often i n s u f f i c i e n t to explain population response even under controlled laboratory conditions. On the other hand, we have ecology: from a description of 3 the phenotypes i n the population and a thorough knowledge of th e i r responses to the environment, we can quantify the f i t n e s s of d i f f e r e n t phenotypes. However, ecology at present includes no theory which can predict, from t h i s information on phenotypes and th e i r f i t n e s s , what the population w i l l look l i k e phenotypically i n the next generation. There are several approaches to f i l l i n g the gap between the detailed theory on the l e v e l of single genes and the ecological understanding of the phenotype. One i s to try to develop new genetic models* which would describe both selection pressures and genotypes i n measurable terms, bridging the gap between genotype and phenotype. Such attempts have characterized the f i e l d of ecological genetics, and have led to constant r e v i s i o n of models of the genome and of the action of natural s e l e c t i o n . For example, the paradox of genetic load (Lewontin and Hubby, 1966) has been central to a p r o l i f e r a t i o n of points of view concerning two major problems: (1) The p o s s i b i l i t y that genetic variation might be s e l e c t i v e l y neutral has been argued at great length (e.g., Kimura and Ohta, 1971; Johnson, 1972; Wills, 1973; Tracey and Ayala, 1974). (2) The i d e n t i f i c a t i o n of the units on which selection acts has also been disputed, with suggestions ranging from single genes (Morgan, 1975) to control sequences (Britten and Davidson, 1971) to linkage groups and chromosome *I s h a l l refer to "hypotheses" and "models" somewhat interchangeably. A model refers to a statement of a hypothesis i n which the causal mechanisms and t h e i r i n t e r r e l a t i o n s are described with some s p e c i f i c i t y . A quantitative extension of such a "verbal" model would be a "mathematical" or "simulation" model. I 4 segments (Marshall and A l l a r d , 1969; Lewontin, 1974) to phenotypic c h a r a c t e r s (Antonovics and Bradshaw, 1970). S i m i l a r l y , there i s disagreement among e c o l o g i c a l g e n e t i c i s t s as to which b i o l o g i c a l u n i t best d e s c r i b e s l a r g e - s c a l e e v o l u t i o n a r y change. ' Patterns of molecular v a r i a t i o n are f r e q u e n t l y d i f f e r e n t from those of phenotypic v a r i a t i o n a t a l l taxonomic l e v e l s , from the p o p u l a t i o n (Soule and Yang, 197.3) to i n c i p i e n t s p e c i e s (Zouros, 1973) to genera (King and Wilson, 1975). For each p o t e n t i a l u n i t of e v o l u t i o n , s e v e r a l models of n a t u r a l s e l e c t i o n have been proposed, which v a r i o u s l y i n c l u d e p a t t e r n s of environmental h e t e r o g e n e i t y , l e v e l s of c o m p e t i t i o n , gene f r e q u e n c i e s , and parameters of p o p u l a t i o n growth (Levins, 196 8; Temptleton and Eothman, 1974; Wallace, 1968; Milkman, 1967; Sved et a l . , 1967; C l a r k e , 1972; G a d g i l and S o l b e r g , 1972; Roughgarden, 1971; Pianka, 1972; Kojima and Yarbrough, 1967). I am e x p l o r i n g here another approach to the e s t a b l i s h m e n t of a l i n k between the phenotype and the g e n e t i c s of p o p u l a t i o n s . My approach i s to adapt q u a n t i t a t i v e g e n e t i c s theory to the problems of e c o l o g i c a l g e n e t i c s . The methods of q u a n t i t a t i v e g e n e t i c s enable one to avoid d e s c r i b i n g the genome a l t o g e t h e r , but r a t h e r to p r e d i c t the next generation p h e n o t y p i c a l l y from a purely phenotypic d e s c r i p t i o n of the p a r e n t a l p o p u l a t i o n and a knowledge of i t s r e l a t i o n s with the environment. T h i s approach has been mentioned from time to time i n the e c o l o g i c a l l i t e r a t u r e (Long, 1974; Roughgarden, 1972; Lewontin, 1974), but r e l a t i v e l y few s t u d i e s have been c a r r i e d out i n an e c o l o g i c a l (as opposed to a g r i c u l t u r a l or l a b o r a t o r y ) context (Morris and F u l t o n , 1970; M c l n t y r e and Blanc, 1973; C a l a p r i c e , 1967, 1971; 5 Ayles, 1974; Perrins and Jones, 1974; Dingle, 1968; Doyle, 1974; Caldwell and Hegmann, 1969). 6 THE SPECIFIC PROBLEM Po p u l a t i o n f l u c t u a t i o n s i n m i c r o t i n e r o d e n t s , g e n e r a l l y d e s c r i b e d as " c y c l e s " , are widespread, and are a s s o c i a t e d with a more-or-less c o n s i s t e n t set of demographic changes: M i c r o t u s p o p u l a t i o n s t y p i c a l l y e x h i b i t peaks i n numbers a t i n t e r v a l s of two to fou r years, though the p r e c i s e d u r a t i o n of each of the phases of the c y c l e ( i n c r e a s e , peak, d e c l i n e , and low numbers) i s v a r i a b l e . The r e p r o d u c t i v e v a r i a b l e s most c l o s e l y a s s o c i a t e d with phases of the c y c l e are age at puberty and l e n g t h of breeding season. S u r v i v a l of a d u l t s t y p i c a l l y drops d u r i n g the d e c l i n e and low phases, while s u r v i v a l o f n e s t l i n g s and j u v e n i l e s . i s low durin g the peak and d e c l i n e . These demographic p a t t e r n s have been reviewed i n d e t a i l by Krebs and Myers (1974). A v a r i e t y of phenotypic and genotypic c o v a r i a t e s of f l u c t u a t i n g numbers i n d i c a t e that f o r c e s of n a t u r a l s e l e c t i o n may vary throughout the c y c l e . For example, i n c r e a s e s i n mean body weight i n peak po p u l a t i o n s have f r e q u e n t l y been observed ( C h i t t y , 1952; Krebs, K e l l e r , and Tamarin, 1969; Krebs, 1966; C h i t t y and C h i t t y , 1962; B a t z i i and P i t e l k a , 1971). Body p r o p o r t i o n s vary over the c y c l e i n lemmings (Krebs, 1964). A g o n i s t i c behavior and tendency to c o l o n i z e vacant h a b i t a t a l s o change over the c y c l e (Krebs, 1970; Myers and Krebs, 1971; Krebs et a l . , 1975). Genotypic changes, i n d i c a t e d by the f r e q u e n c i e s of s e v e r a l v a r i a b l e l o c i d e t e c t a b l e through e l e c t r o p h o r e s i s , are a l s o a s s o c i a t e d with changes i n numbers (Tamarin and Krebs, 1969, 1973; Gaines and Krebs, 1971; LeDuc and Krebs, 1975). In 7 a d d i t i o n , d i s p e r s i n g v o l e s are not a random g e n e t i c sample of the p o p u l a t i o n (Myers and Krebs, 1971, Krebs e t a l . , 1975), and m o r t a l i t y among j u v e n i l e s i s a s s o c i a t e d with genotype ( B i r d s a l l , 1974) . Hypotheses which have been proposed t o e x p l a i n m i c r o t i n e p o p u l a t i o n c y c l e s can be c l a s s i f i e d i n two c a t e g o r i e s : t h a t causes are e x t r i n s i c t o the p o p u l a t i o n , such as n u t r i t i o n , p r e d a t o r s , or weather; and t h a t causes are i n t r i n s i c t o the po p u l a t i o n , such as g e n e t i c or p h y s i o l o g i c a l changes i n the v o l e s . I t appears that no e x t r i n s i c f a c t o r i s both necessary and s u f f i c i e n t t o e x p l a i n the phenomenon ( C h i t t y , 1960, 1967; Krebs and Myers, 1974). However, any i n t r i n s i c f a c t o r proposed t o cause the f l u c t u a t i o n s must meet at l e a s t one i n t e r e s t i n g requirement: i t must provide a mechanism f o r s t o r i n g i n f o r m a t i o n , a "memory". ftt a given d e n s i t y , the p o p u l a t i o n must "know" whether i t should be i n c r e a s i n g or d e c r e a s i n g . T h i s i n f o r m a t i o n must be s u f f i c i e n t l y l o n g - l i v e d to e x p l a i n prolonged p e r i o d s of low or high numbers, as w e l l . Two hypothesized causes of m i c r o t i n e population f l u c t u a t i o n s f i t the above c r i t e r i a , both based on a g o n i s t i c behavior as the c r u c i a l i n t r i n s i c v a r i a b l e . C h r i s t i a n and Davis (1964) proposed t h a t phenotypic changes i n behavior and r e p r o d u c t i v e s u c c e s s , mediated by hormones and passed to subsequent g e n e r a t i o n s through the mother, are r e s p o n s i b l e f o r the c y c l e . C h i t t y (1960, 1967) suggested that the v a r i a t i o n i n behavior was g e n e t i c r a t h e r than phenotypic, and co u l d be a s s o c i a t e d with changes i n s u r v i v a l , p a r t i c u l a r l y i n young v o l e s . Both models, then, share the b a s i c components of (1) i n c r e a s i n g l e v e l of 8 a g o n i s t i c i n t e r a c t i o n i n the p o p u l a t i o n with i n c r e a s i n g numbers, (2) lowered i n t r i n s i c r a t e of i n c r e a s e a s s o c i a t e d with i n t e n s i t y of a g o n i s t i c encounters, (3) i n a b i l i t y of the p o p u l a t i o n to recover immediately from the i n i t i a l drop i n numbers. The "memory" component i s the most important d i f f e r e n c e between the two models. To be pa r t of a p l a u s i b l e e x p l a n a t i o n of the c y c l e , the "memory" must s a t i s f y two p a r t i a l l y -c o n f l i c t i n g requirements. F i r s t , i n f o r m a t i o n about the pop u l a t i o n ' s immediate h i s t o r y must be a c c u r a t e l y t r a n s m i s s i b l e from one generation to the next. Second, the system as a whole must be able to respond to changes w i t h i n the time s c a l e of a few gene r a t i o n s . The phenotypic changes proposed by C h r i s t i a n and Davis c l e a r l y f i t the second c r i t e r i o n ( r a p i d response to change), and may, be a b l e to meet the f i r s t through maternal e f f e c t s ( C h r i s t i a n and LeMunyan, 1957). The ge n e t i c hypothesis e a s i l y s a t i s f i e s the f i r s t c r i t e r i o n , but the second c r i t e r i o n seems to r e q u i r e a r e s t r i c t i v e s e t of c o n d i t i o n s : strong s e l e c t i o n pressures, i n h e r i t e d behavior, and a mechanism f o r mainta i n i n g v a r i a b i l i t y i n the p o p u l a t i o n . To t e s t whether these requirements were l o g i c a l l y c o n s i s t e n t with r e a l i s t i c p o p u l a t i o n parameters and a two-to-three year c y c l e , I have w r i t t e n a s i m u l a t i o n model of the b e h a v i o r - g e n e t i c hypothesis. The model i s d i s c u s s e d , along with i t s r e s u l t s , i n the Appendix; i t shows that the b e h a v i o r - g e n e t i c hypothesis can indeed produce po p u l a t i o n c y c l e s on the c o r r e c t time s c a l e . T h i s study i s an e x p l o r a t i o n of s e v e r a l questions suggested by C h i t t y ' s b e h a v i o r - g e n e t i c h y p o t h e s i s : (1) I f str o n g n a t u r a l s e l e c t i o n occurs over the po p u l a t i o n c y c l e , then there ought to 9 be differences in fitness among individuals in the population. Could these differences be detected by comparing individual reproductive performances and survival of families? (2) To what degree i s behavior inherited? Are other attributes involved with the population fluctuations strongly inherited (e.g., growth rate, body size, age at puberty, winter breeding, dispersal tendency)? (3) Are behavior and some components of fitness linked within individual voles? 10 SECTION I I : QUANTITATIVE GENETICS THEORY The body of genetical theory which deals with continuously variable t r a i t s i n populations has two purposes which are relevant here: f i r s t , to estimate the r e l a t i v e influences of genotypic and environmental variation upon phenotypic variance for a t r a i t within a population; and second, to predict the short-term phenotypic response of the population to selection for the t r a i t under consideration. The following discussion presents the basic ideas and assumptions used i n the analysis of phenotypic c o r r e l a t i o n s among r e l a t i v e s in t h i s study. My understanding of the ideas and assumptions comes largely from Falconer (1960a) and Moran and Smith (1966). Methods of analysis were taken from Falconer (1960a) and Becker (1967). The basic assumptions and concepts of quantitative genetics theory used in t h i s study can be summarized as follows. 1. The "phenotypic value" of an i n d i v i d u a l ( i . e . , i t s measurement for the given t r a i t ) i s a simple additive function of the following: P = G + E + I where P i s the phenotypic value of the i n d i v i d u a l , G i s the e f f e c t of genes upon the phenotypic value, E i s the e f f e c t of the environment upon the phenotypic value, and I i s the e f f e c t of interactions between genes and environment. 11 2 . A number of genes i n f l u e n c e the t r a i t , and they f o l l o w simple Mendelian laws. Thus, though genes at a l o c u s may i n t e r a c t , r e s u l t i n g i n dominance, the l o c i are independent i n t h e i r e f f e c t s . Suppose B and b are two a l l e l e s at a l o c u s . I n d i v i d u a l s homozygous f o r b are assigned an a r b i t r a r y "genotypic v a l u e " of -a, and i n d i v i d u a l s with genotype BB are assigned the value +a. The value of Bb heterozygotes w i l l be d, and i n the case where there i s no dominance, d = 0 . The sum of the genotypic values f o r a l l l o c i i n f l u e n c i n g the t r a i t under c o n s i d e r a t i o n i s "G" i n the above e x p r e s s i o n . When we adjust a and d f o r the gene f r e q u e n c i e s i n the p o p u l a t i o n , we can then c a l c u l a t e the "average e f f e c t " of each of the genes, i . e . , the mean d e v i a t i o n (from the p o p u l a t i o n ' s phenotypic mean) of i n d i v i d u a l s r e c e i v i n g the gene from one parent, with the other parent drawn randomly from the p o p u l a t i o n . The sum, f o r an i n d i v i d u a l , of the average e f f e c t s of a l l the genes i n f l u e n c i n g the t r a i t i s the i n d i v i d u a l ' s "breeding value" (A), a l s o c a l l e d • the " t o t a l a d d i t i v e e f f e c t s " o f the genes. The dominance d e v i a t i o n (D) i s d e f i n e d as G minus A, and can be w r i t t e n i n terms of the heterozygote genotypic value and the gene f r e q u e n c i e s of a l l l o c i which a f f e c t the t r a i t . Thus, the sum of the a d d i t i v e and dominance e f f e c t s of the a l l e l e s present at each l o c u s determines the g e n e t i c component (G) of the ex p r e s s i o n , P = G + E + I , y i e l d i n g : P = A + D + E + I Both E and I can a l s o be decomposed, so the ex p r e s s i o n f o r 1 2 the phenotypic value can be w r i t t e n : P = A + D + Es + Ec + Igg + leg where A i s the sum of the a d d i t i v e e f f e c t s of the r e l e v a n t genes upon the phenotypic value. D i s the sum of the dominance e f f e c t s . Es i s " s p e c i a l environment" e f f e c t s , environmental i n f l u e n c e s which tend to make each i n d i v i d u a l unique, e.g., a d u l t n u t r i t i o n a l i n t a k e . Ec i s "common environment" e f f e c t s , environmental i n f l u e n c e s which tend to make fami l y members s i m i l a r , e.g., q u a l i t y of the mother's milk i n mammals, or the e f f e c t of the s i t u a t i o n of an egg mass i n i n s e c t s . Igg i s e f f e c t s of i n t e r a c t i o n among l o c i , e.g., c a n a l i z a t i o n . l e g i s e f f e c t s of i n t e r a c t i o n s among g e n e t i c and environmental i n f l u e n c e s , e x e m p l i f i e d by cases i n which the r e l a t i v e e f f e c t s of genotypes are reversed i n d i f f e r e n t environments. Because of the property of a d d i t i v i t y o f v a r i a n c e s , the phenotypic variance of the p o p u l a t i o n with r e s p e c t to a given t r a i t may be w r i t t e n V(P) = V (A) + V(D) + V{Ec) + V(Es) + V (Igg) + V (leg) 1 3 An important assumption at t h i s point i s that both V (Igg) and V (leg) are small r e l a t i v e to the other terms i n t h i s expression. In practice, such interactions tend to be included with sp e c i a l environment e f f e c t s , unless the experiment i s s p e c i f i c a l l y designed to detect them. This error can be important i f questions are asked concerning the actual genetic mechanisms (such as quantification of dominance deviations or the number of l o c i involved). However, the inc l u s i o n of interactions with environmental "noise" may s t i l l give reasonable predictions of the phenotypic response of the population to a few generations of select i o n . Such a short time frame i s , fortunately, useful in t h i s and many other eco l o g i c a l studies. Another important point concerns genotype-environment interactions. They are undoubtedly widespread, but the following examples describe situations which are sometimes mistakenly thought of as genotype-environment interactions. Both these examples can be described adequately under the assumptions of a d d i t i v i t y and l i n e a r i t y : f i r s t , changes in fi t n e s s of a phenotype in di f f e r e n t environments do not necessarily imply genotype-environment interactions in the sense used here. For example, suppose that in one environment, large i n d i v i d u a l s of a population are at a s e l e c t i v e advantage, while i n another environment, small sizes have the advantage. Clearly the r e l a t i v e f i t n e s s of a large animal w i l l be di f f e r e n t i n the two environments, but as long as the same genotypes tend to be large r e l a t i v e to the population mean in both environments, there i s no genotype-environment i n t e r a c t i o n . Second, changes 1 4 i n the p o p u l a t i o n Phenotypic mean i n d i f f e r e n t environments do not n e c e s s a r i l y imply s i g n i f i c a n t values of l e g . For example, c o n s i d e r two c o h o r t s of animals, one born i n s p r i n g , another i n f a l l . The growth r a t e of the s p r i n g cohort may be hig h e r than that of the f a l l c o h o r t . There i s no i n t e r a c t i o n between genotype and environment, however, as long as a p a r t i c u l a r genotype produces a growth r a t e which i s f a s t r e l a t i v e t o the cohort mean i n both s p r i n g and f a l l . Let us now re f o r m u l a t e the ques t i o n s asked at the beginning of t h i s s e c t i o n . The measure of the r e l a t i v e e f f e c t s of genes and environment on the phenotypic e x p r e s s i o n of the t r a i t w i l l be V(G)/V(P), the r a t i o of the varia n c e accounted f o r by genes to the t o t a l phenotypic v a r i a n c e i n the p o p u l a t i o n . T h i s q u a n t i t y i s o f t e n r e f e r r e d to as " h e r i t a b i l i t y i n the broad sense". However, f o r the purposes of p r e d i c t i n g immediate p o p u l a t i o n responses to s e l e c t i o n , a narrower d e f i n i t i o n of h e r i t a b i l i t y i s used: h 2 = V(fi)/V(P), the r a t i o of the v a r i a b i l i t y accounted f o r by a d d i t i v e g e n e t i c v a r i a n c e to t o t a l phenotypic v a r i a b i l i t y . T h i s e x p r e s s i o n f o r h 2 i s e q u i v a l e n t to: h* = V(A) V (G) + V (E) + V(I) T h i s d e f i n i t i o n i s u s e f u l because i t i s the a d d i t i v e e f f e c t s of genes which r e s u l t i n p r e d i c t a b l e r e l a t i o n s h i p s between phenotype and genotype. 1 5 The true value of h 2 v a r i e s between 0 and 1, and i t becomes the c o e f f i c i e n t of the p r e d i c t e d p o p u l a t i o n response to s e l e c t i o n , when s e l e c t i o n i s formulated i n terms of the phenotypic mean of the p o p u l a t i o n . Thus, i n the s i m p l e s t s e l e c t i o n design, E = h 2S where R i s the change i n po p u l a t i o n phenotypic mean i n one ge n e r a t i o n , and S i s the s e l e c t i o n pressure measured by the d i f f e r e n c e between the po p u l a t i o n mean and the mean of the subset of i n d i v i d u a l s which a c t u a l l y c o n t r i b u t e to the next g e n e r a t i o n . MEASUREMENT OF H 2 Because h 2 i s a po p u l a t i o n parameter, one cannot speak merely of the h e r i t a b i l i t y of a t r a i t , but r a t h e r of the h e r i t a b i l i t y of a t r a i t i n a p a r t i c u l a r p o p u l a t i o n , d e f i n e d by i t s mating s t r u c t u r e , i t s gene p o o l , and i t s environmental m i l i e u . T h i s l a s t p o p u l a t i o n c h a r a c t e r i s t i c , the environment, i s p a r t i c u l a r l y c r u c i a l f o r e c o l o g i c a l a p p l i c a t i o n s of h e r i t a b i l i t y , s i n c e many e c o l o g i c a l l y important t r a i t s i n n a t u r a l p o p u l a t i o n s have a measurable V (E) component. The parameter h 2 i s s e n s i t i v e to changes i n the V (E) component, which i s one of the terms i n i t s denominator. I t i s t h i s aspect which makes l a b o r a t o r y determinations of h 2 p r a c t i c a l l y u s e l e s s 1 6 when a p p l i e d to n a t u r a l p o p u l a t i o n s i n v a r i a b l e environments, unless d e t a i l e d knowledge i s a v a i l a b l e concerning the e f f e c t s of a l l the environmental v a r i a b l e s upon the value of h 2 . Most methods of e s t i m a t i n g h 2 depend upon phenotypic resemblances among r e l a t i v e s , s i n c e r e l a t i v e s share a known p r o p o r t i o n of t h e i r genes. The g e n e r a l p r i n c i p l e , then, i s : t o the e x t e n t t h a t two r e l a t i v e s resemble one another i n a given t r a i t , t h a t t r a i t i s determined by the genes they share. To the extent t h a t they d i f f e r p h e n o t y p i c a l l y , the t r a i t i s i n f l u e n c e d by the environment. Thus h 2 i s estimated by the d i f f e r e n c e between the observed phenotypic c o r r e l a t i o n between two r e l a t i v e s , and the expected c o r r e l a t i o n between them i f the va r i a n c e i n the t r a i t were e n t i r e l y a d d i t i v e g e n e t i c . Table 1 presents the expected v a l u e s of phenotypic c o v a r i a n c e and the parameters from which they are estima t e d , f o r the r e l a t i o n s h i p s analyzed i n t h i s study. The o f f s p r i n g - p a r e n t r e l a t i o n s h i p i s the most s t r a i g h t f o r w a r d and r e l i a b l e way of e s t i m a t i n g h 2 . Because o f f s p r i n g share 1 / 2 t h e i r genes with each parent, the g e n e t i c c o v a r i a n c e between o f f s p r i n g and one parent or o f f s p r i n g and midparent (mean of both ^parents) i s 1 / 2 . I f we assume t h a t the t o t a l phenotypic v a r i a n c e i s the same f o r both o f f s p r i n g and parents, and that no s e l e c t i o n i s o p e r a t i n g i n the p o p u l a t i o n , then the slope of the r e g r e s s i o n of o f f s p r i n g phenotypic values on the phenotypic value of one parent i s equal to 1 / 2 h 2 . The s l o p e of the r e g r e s s i o n on midparent measures the h e r i t a b i l i t y d i r e c t l y , because the va r i a n c e of midparental values i s 1 / 2 that of the set of s i n g l e parents. Under the above assumptions, the r e g r e s s i o n s l o p e i s equal t o the 17 TABLE 1 Phenotypic resemblances among r e l a t i v e s and t h e i r a p p l i c a t i o n i n e s t i m a t i n g h e r i t a b i l i t y (from F a l c o n e r , 1960). R e l a t i v e s Phenotypic c o v a r i a n c e Parameter f o r e s t i m a t i o n of V(A)/V(P) (= h 2) O f f s p r i n g vs one parent 1/2 V(A) Regression s l o p e b = 1/2 h 2 O f f s p r i n g vs midparent 1/2 V(A) Regression slope b = h 2 H a l f - s i b s 1/4 V(A) I n t r a - f a m i l y c o r r e l a t i o n t = 1/4 h 2 F u l l s i b s 1/2 7(A) + 1/4 V(D) + V (Ec) I n t r a - f a m i l y c o r r e l a t i o n t > 1/2 h 2 18 c o r r e l a t i o n c o e f f i c i e n t between o f f s p r i n g and p a r e n t a l phenotypic values. When the a n a l y s i s i n c l u d e s only s i b l i n g s , i t i s more i n d i r e c t and complex. H a l f - s i b s share 1/4 of t h e i r genes, and t h e i r phenotypic c o v a r i a n c e f o r a t r a i t measures 1/4 of the a d d i t i v e g e n e t i c v a r i a n c e f o r that t r a i t i n the p o p u l a t i o n . F u l l s i b s share 1/2 t h e i r genes, but a l s o a re p h e n o t y p i c a l l y s i m i l a r owing to e f f e c t s of common environment and dominance. The phenotypic c o v a r i a n c e f o r s i b l i n g s i s commonly estimated by the s t a t i s t i c " t " , the i n t r a f a m i l y c o r r e l a t i o n . " t " i s d e f i n e d as s 2 ( B ) / s 2 { T ) , where s 2 (B) i s the between-family component of v a r i a n c e , and s 2 (T) i s the t o t a l p o p u l a t i o n v a r i a n c e , the sum of the between- and w i t h i n - f a m i l y components. These v a r i a n c e components are estimated from an a n a l y s i s of va r i a n c e i n which h a l f - s i b o r f u l l - s i b f a m i l i e s r e p r e s e n t the treatments, and the Y v a r i a t e i s the phenotypic value of the t r a i t under c o n s i d e r a t i o n f o r each animal. H a l f - s i b f a m i l i e s y i e l d an unbiased estimate of h 2 by t h i s method, under the assumptions mentioned above. However, the h e r i t a b i l i t y e s t imated from f u l l - s i b f a m i l i e s must be c o n s i d e r e d an upper l i m i t , because both the common environment and dominance e f f e c t s are i n c l u d e d i n the numerator. In mammals, i t must be expected that at l e a s t the common environment e f f e c t s are l i k e l y t o be s u b s t a n t i a l . Both kinds of s i b l i n g a n a l y s i s are a s s o c i a t e d with l a r g e standard e r r o r s owing to the in a c c u r a c y of estimates of v a r i a n c e ; t h i s problem i s more s e r i o u s f o r h a l f - s i b a n a l y ses. Q u a n t i t a t i v e g e n e t i c s theory depends h e a v i l y upon 19 assumptions of l i n e a r i t y and a d d i t i v i t y , as do many s t a t i s t i c a l procedures. I t has been proven u s e f u l f o r the assessment of f e a s i b i l i t y of s e l e c t i o n programs i n animal and plant breeding, and i s probably at l e a s t on par with much of e c o l o g i c a l theory i n the r e l i a b i l i t y of i t s p r e d i c t i o n s . However, the l i t e r a t u r e i s f u l l of c a u t i o n a r y examples of complex responses to s e l e c t i o n i n l a b o r a t o r y s t u d i e s , which b e l i e the g e n e r a l i t y of the assumptions i n v o l v e d . F i r s t , response to s e l e c t i o n u s u a l l y stops a f t e r some ge n e r a t i o n s , u s u a l l y more than t e n . When the response ceases, i t can sometimes be shown that there i s s t i l l a d d i t i v e g e n e t i c v a r i a n c e f o r the s e l e c t e d t r a i t i n the p o p u l a t i o n . F r e q u e n t l y the c e s s a t i o n i s a f u n c t i o n of some c o r r e l a t e d t r a i t which i s c l o s e l y t i e d to f i t n e s s . Second, the response to s e l e c t i o n o f t e n i s a f f e c t e d by the d i r e c t i o n , s t r e n g t h , and design of the s e l e c t i o n , because of dominance e f f e c t s or c o r r e l a t e d f i t n e s s t r a i t s . T h i r d , unexpected maternal or other common environment e f f e c t s , or a r t i f a c t s of the experimental design, may r e s u l t i n very s m a l l estimates of h 2 , whereas the p o p u l a t i o n i s s t i l l capable of response t o s e l e c t i o n . These problems are d i s c u s s e d i n Falconer (1954, 1960a, 1970, 1965), Clayton et e l . , (1957a, b, c ) , D e f r i e s and Hegmann (1970), Hurnik et a l . , (1973), and J i n k s and Broadhurst (1965), to name only a few r e f e r e n c e s . While h e r i t a b i l i t y has proven u s e f u l i n a p p l i e d breeding of p l a n t s and animals, i t remains to be seen whether t h i s p o p u l a t i o n parameter can p r e d i c t response to s e l e c t i o n i n e c o l o g i c a l s i t u a t i o n s . In summary, then, the p o p u l a t i o n parameter h 2 f o r a given a t t r i b u t e does t h r e e t h i n g s : i t p r e d i c t s the p o p u l a t i o n ' s 20 phenotypic response to selection; i t describes to what extent members of families resemble each other more clos e l y than unrelated i n d i v i d u a l s ; and i t measures the extent to which the phenotype of an i n d i v i d u a l r e f l e c t s i t s genotype with respect to that t r a i t . 21 / SECTION I I I : METHODS T h i s r e s e a r c h was conducted on p o p u l a t i o n s of the v o l e Microtus townsendii a t the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , at Haney, B.C. The study area was a h i l l s i d e from which the climax v e g e t a t i o n of Douglas f i r and cedar had been logged i n the past and c l e a r e d of second growth the year before. The area was f e r t i l i z e d and seeded with a mixture of grasses and herbs i n the s p r i n g of 1971, and was maintained i n an e a r l y s u c c e s s i o n a l stage by freguent h a n d - c l e a r i n g of a l d e r s a p l i n g s . 1 while Microtus townsendii does occur i n such patches of g r a s s l a n d , the h a b i t a t appears to be marginal f o r the s p e c i e s . Annual p r e c i p i t a t i o n at the Haney study area i s ample (around 200 cm); however, there i s a p e r i o d of s i x to e i g h t weeks i n J u l y and August of hot weather and drought. T h i s p e r i o d was always accompanied by massive disappearance of animals and c e s s a t i o n of breeding and recruitment i n the p o p u l a t i o n s (Figures 1, 2, and 3). The marked seasonal f l u c t u a t i o n s i n numbers may have obscured any t y p i c a l p e r i o d i c f l u c t u a t i o n s . Also present i n the study area were Peromy_scus maniculatus, l i c r o t u s oregoni ( s p o r a d i c a l l y ) , and Zapus sp_. Weasels, owls, hawks, f e r a l c a t s , black bears, and raccoons frequented the area. The l a s t t h r e e o c c a s i o n a l l y learned to open t r a p s . The study area was d i v i d e d i n t o s e v e r a l t r a p p i n g g r i d s (Figure 4). In t h i s study three kinds of areas were trapped: 22 Figure 1. 14-day survival rate and minimum numbers a l i v e on unfenced Grid AA, September, 1973 - August, 1974. NUMBERS SURVIVAL i—» i—> • ~ • a c n a o o o c n c/i c n ZZ 24 Figure 2. 14-day s u r v i v a l rate and minimum numbers a l i v e on fenced Grid 0, July, 1972 - August, 1973. Population was cropped during weeks 107 to 113. 26 Figure 3. 14-day su r v i v a l rate and minimum numbers a l i v e on fenced Grid L, July, 1972 - August, 1974. Population was cropped during weeks 107 - 109, and 155 - 163. 2 8 Figure 4 . Diagram of the Haney study area. Only the f i r s t eight breeding enclosures are shown; the other eight (completed later) continue along the border of Grid 0 . 29 30 1. Unfenced g r i d . G r i d AA, an area of 2 a c r e s , was h a b i t a t f o r an unmanipulated p o p u l a t i o n of v o l e s . One hundred trap s t a t i o n s were placed i n a 20 X 5 p a t t e r n , 7.2 m a p a r t . T h i s area was trapped from J u l y , 1973 through August, 1974. 2. Fenced g r i d s . G r i d s L and 0, a l s o of 2 a c r e s each, were surrounded by "mouse-proof" f e n c i n g , ,5-cm wire mesh buried .5 m i n the ground and topped with a f l a n g e of aluminum s h e e t i n g to prevent animals from c l i m b i n g over. G r i d L was trapped c o n t i n u o u s l y from J u l y , 1972 through August, 1974; the po p u l a t i o n on G r i d 0 was trapped from J u l y , 1972 through J u l y , 1973. Each g r i d c o n s i s t e d of 100 t r a p s t a t i o n s i n a 10 X 10 p a t t e r n , 7.2 m a p a r t . 3. Breeding e n c l o s u r e s . S i x t e e n s m a l l e n c l o s u r e s , surrounded by the same "mouse-proof" f e n c i n g , housed the experimental animals. A p a i r of a d u l t v o l e s was placed i n each e n c l o s u r e , and they and t h e i r o f f s p r i n g were trapped at f o u r s t a t i o n s spaced around the breeding e n c l o s u r e . E i g h t e n c l o s u r e s were stocked beginning i n November, 1972, and by the f o l l o w i n g June, a l l s i x t e e n were being u t i l i z e d . The d e t a i l s o f the breeding procedure are given below. TRAPPING TECHNIQUES The l a r g e g r i d s were trapped o v e r n i g h t f o r two c o n s e c u t i v e n i g h t s every two weeks. The 100 Longworth t r a p s were provided with oats and n e s t i n g m a t e r i a l and set the f i r s t a f t e r n o o n , then checked the next morning. During c o o l weather, they were l e f t 31 s e t and checked a g a i n the next a f t e r n o o n . The f o l l o w i n g morning, they were l o c k e d open f o r p r e b a i t i n g between t r a p p i n g s e s s i o n s . When f i r s t captured, i n d i v i d u a l animals were marked with numbered f i n g e r l i n g f i s h tags i n one ear. During most of the study, a blood sample was taken from the s u b o r b i t a l s i n u s at or soon a f t e r the f i r s t capture, f o r e l e c t r o p h o r e t i c t y p i n g of the LAP ( l e u c i n e amino-peptidase) l o c u s , as d e s c r i b e d i n Leduc and Krebs (1975). At each c a p t u r e , weight, s k u l l width (zygomatic breadth), and l o c a t i o n of capture were re c o r d e d . Number of wounds, s i z e of f l a n k gland, and r e p r o d u c t i v e c o n d i t i o n were a l s o noted. For t h i s l a s t category, the f o l l o w i n g s t a t e s were recorded: i n males, t e s t e s s c r o t a l or abdominal; i n females, vagina p e r f o r a t e or not, n i p p l e s s m a l l or enlarged f o r l a c t a t i o n , and pubic symphysis open, c l o s e d , or s l i g h t l y open. Most animals were r e l e a s e d immediately a f t e r c a p t u r e , except i n two circumstances: 1. The f i r s t day of each t r a p p i n g s e s s i o n , s e v e r a l randomly s e l e c t e d i n d i v i d u a l s were taken i n t o the l a b o r a t o r y f o r behavior t e s t s . 2. During times of r a p i d p o p u l a t i o n growth, randomly s e l e c t e d animals were removed from the fenced g r i d s i n order to maintain those p o p u l a t i o n s a t l e s s than s i x t y animals, thus a v o i d i n g some of the a b n o r m a l i t i e s of s o c i a l s t r u c t u r e which occur among very dense c o n f i n e d p o p u l a t i o n s of J l i c r o t u s (Krebs, K e l l e r , and Tamarin, 1969). The p o p u l a t i o n s served as a m i l i e u i n which the animals born i n the breeding e n c l o s u r e s l i v e d t h e i r post-weaning l i v e s . Thus, i t was important that the r a t i o of e x p e r i m e n t a l l y - i n t r o d u c e d animals t o r e s i d e n t s remain low, a requirement n e c e s s i t a t i n g the 32 maintenance of s e v e r a l g r i d s . The fenced g r i d s i n p a r t i c u l a r served the purpose of i n s u r i n g . t h a t l o s s e s of experimental animals would not be too d r a s t i c immediately a f t e r the trauma of i n t r o d u c t i o n . In a d d i t i o n , the numbers of animals i n the fenced g r i d s could be manipulated so t h a t , during the summer d e c l i n e s and p e r i o d s of peak re c r u i t m e n t , a r e l a t i v e l y c onstant p o p u l a t i o n c o u l d be maintained by means of i n t r o d u c t i o n s and removals. In s p i t e of the unnatural aspects of the fenced p o p u l a t i o n s , d e n s i t i e s w i t h i n the fences were low enough t h a t the worst e f f e c t s of f e n c i n g (Krebs, K e l l e r , and Tamarin, 1969) were avoided. I wanted to r a i s e animals of known parentage i n a t o t a l l y unmanipulated p o p u l a t i o n , as w e l l as i n the fenced ones. In t h i s c a p a c i t y , the unfenced g r i d (Grid AA) served as a more r e p r e s e n t a t i v e environment f o r animals of known parentage; i t d i d , however, c a r r y the disadvantage of a s l i g h t l y higher l o s s r a t e than t h a t i n the fenced g r i d s . The p o p u l a t i o n s on a l l t h r e e g r i d s provided a base f o r e s t i m a t i o n of means f o r d i f f e r e n t seasons, p o p u l a t i o n s , and sexes, with r e s p e c t to the t r a i t s under c o n s i d e r a t i o n . The two fenced g r i d s were stocked i n J u l y , 1972, with twenty animals each from the Serpentine Fen study area i n the F r a s e r D e l t a , about 35 km from Haney. At t h a t time, there were no Microtus townsendii i n evidence o u t s i d e the fences. I t seems l i k e l y that the p o p u l a t i o n s o u t s i d e may have been founded l a r g e l y or e n t i r e l y by e a r l y escapees from the fences. T h e r e f o r e , most of the animals i n t h i s study can be c o n s i d e r e d to be of the same b a s i c stock. . 3 3 TECHNIQUES OF BREEDING MICROTUS TOWNSENDII IN THE FIELD Adjacent to the large grids were a number of small enclosures ( 6 m X 6 m),,made of the same kind of fencing used for the fenced grids. The grass inside each enclosure was f e r t i l i z e d at the time of the completion of the fence; otherwise the habitat inside was unmanipulated. An adult male and female Microtus townsendii were maintained in each enclosure throughout the year. Owing to the sporadic disappearance of animals native to the Haney study area, i t was necessary to draw on the Serpentine study area for one-third of the potential parents. Two other study areas contributed small numbers of voles (8.4%). The remainder were natives of the Haney study area. By the arguments stated above, Haney animals were probably not very d i f f e r e n t from those from the Serpentine area. Because i t was important to keep close control over events i n the breeding enclosures, and yet to avoid i n t e r f e r i n g with reproductive a c t i v i t y as much as possible, the usual censusing procedure had to be modified s l i g h t l y . Each breeding enclosure was supplied with four Longworth traps, which were prebaited with oats between trapping sessions. Laboratory mouse chow was provided in the traps during the winter to supplement the limited grass i n the enclosures. Every second week, the traps were set for two nights, and, weather permitting, one day, as on the large grids. In addition, the breeding enclosure traps were set for one night during alternate weeks. Data on i n d i v i d u a l animals were gathered i n a fashion similar to that described 34 above. During the trapping sessions i n which there was more than one check, information about which animals were s t i l l present i n an enclosure and about their breeding condition was seldom complete u n t i l after the t h i r d check. Therefore, adult males and females which were not ac t i v e l y reproducing were held i n the lab with an extra supply of fresh vegetable food u n t i l the t h i r d check, aft e r which, reorganization of potential parents was carried out i f necessary. V i s i b l y pregnant, recently parturient, and l a c t a t i n g females were always returned to t h e i r enclosures immediately after capture, and, i f i t was judged necessary to avoid jeopardizing a l i t t e r , trapping i n that enclosure was abandoned for the week. Offspring from l i t t e r s were weighed and, i f less than 20 g, were also returned immediately to t h e i r enclosures. Offspring weighing more than 20 g were immediately released at.randomly chosen trap stations on one of the large grids. Littermates were released onto the same large grid. There were disadvantages to th i s method of breeding animals. F i r s t , the trapping did i n t e r f e r e with breeding success to some extent, as w i l l be discussed below. Second, i t was d i f f i c u l t to know whether the f a i l u r e of an adult to be caught was a t t r i b u t a b l e to i t s avoidance of traps or to i t s death. I f an animal had not been caught for three weeks, i t was assumed dead; th i s c r i t e r i o n was usually, but not always, adequate. It resulted, however, i n an inevitable time lag between the death of a potential parent and i t s replacement. Third, the f a i l u r e of a pair to breed could not be detected for 3 5 at l e a s t s i x weeks, and -the reasons f o r the f a i l u r e were n e a r l y always obscure. Fourth, i t was i m p o s s i b l e to c o n t r o l the age a t f i r s t capture of o f f s p r i n g . F i n a l l y , v o l e s o c c a s i o n a l l y t u n n e l l e d beneath the f e n c e s and escaped. To avert t h i s behavior, I i n s p e c t e d the fences f r e q u e n t l y and packed g r a v e l i n t o any i n c i p i e n t escape t u n n e l s . F o r t u n a t e l y , t h i s k i n d of t u n n e l l i n g was p o s s i b l e only i n the d r i e s t few weeks of the year owing to the high l e v e l of ground water at other times, and during those p e r i o d s , breeding ceased almost e n t i r e l y . There was doubt about male parentage ( e i t h e r because of escapes or because a male was thought dead but was a c t u a l l y s t i l l present) i n 9% of l i t t e r s . LAP genotypes enabled me to i d e n t i f y f a t h e r s i n most of these c a s e s . In s p i t e of the disadvantages, there were s e v e r a l compelling reasons f o r adopting t h i s kind of breeding technique f o r t h i s study. F i r s t , Microtus townsendii s u r v i v e s only p o o r l y , and w i l l not breed r e l i a b l y , i n the l a b o r a t o r y . Second, the cage environment causes other obvious changes i n the animals' metabolism and behavior. Caged Microtus townsendii grow f a t on almost any d i e t ; a u t o p s i e s a f t e r only a few days i n c a p t i v i t y r e v e a l t h a t t h i s process has a l r e a d y begun. P r e l i m i n a r y t e s t s convinced me that caged animals were l e s s a g g r e s s i v e and showed a s m a l l e r range of behavior than f i e l d animals. C l e a r l y , when one hopes to p r e d i c t phenotypes i n a f i e l d s i t u a t i o n , the c l o s e s t p o s s i b l e approach to n a t u r a l c o n d i t i o n s w i l l ensure the most normal e x p r e s s i o n of growth r a t e and b e h a v i o r a l t r a i t s , which appear to be s e r i o u s l y a f f e c t e d i n 36 the l a b o r a t o r y environment. The breeding e n c l o s u r e s appear to be a reasonable compromise between the need to i d e n t i f y f a m i l y members, and the importance o f n a t u r a l h a b i t a t and food c o n d i t i o n s . BEHAVIOR TESTS During each r e g u l a r t r a p p i n g s e s s i o n beginning i n August, 1973, I s e l e c t e d e i g h t to twelve a d u l t animals from the l a r g e g r i d s and e n c l o s u r e s f o r a behavior t e s t intended to measure a c t i v i t y and aggre s s i v e n e s s . An attempt was made to t e s t every a d u l t i n the breeding e n c l o s u r e s , as well as every e n c l o s u r e -born animal t h a t had reached s e x u a l maturity a f t e r being r e l e a s e d i n a g r i d p o p u l a t i o n . In a d d i t i o n , I t e s t e d a random sample of s e x u a l l y mature animals from the g r i d s i n order to provide a b a s e l i n e f o r determining s e a s o n a l , g r i d , and sexual e f f e c t s on behavior. Males with t e s t e s abdominal and females v i s i b l y pregnant or l a c t a t i n g were excluded from the sample, as was any animal which had been t e s t e d l e s s than f o u r weeks p r e v i o u s l y . A f t e r the morning check, candidates f o r behavior t e s t s were kept i n the l a b o r a t o r y i n i n d i v i d u a l g l a s s j a r s with mesh covers. Each animal was provided with c l e a n wood shavings, f r e s h v e g e t a b l e s , and l a b o r a t o r y mouse chow. Since a l l behavior t e s t s were run between 2000 and 2300 hours on the evening of the f i r s t check, each animal had ten to twelve hours to become f a m i l i a r with i t s i n d i v i d u a l c o n t a i n e r and was allowed t o recover from any lack of food or moisture i t had s u f f e r e d i n the 37 t r a p . For the t e s t s , each animal was matched a g a i n s t an opponent of the same sex and from a d i f f e r e n t g r i d o r, o c c a s i o n a l l y , from the opposite end of i t s g r i d . Beyond these c o n s t r a i n t s opponents were chosen randomly. Each mouse was placed, s t i l l i n i t s c o n t a i n e r , on one s i d e of a wooden b a r r i e r i n the g l a s s - f r o n t e d arena under red l i g h t . The arena f l o o r was marked o f f i n t o d i v i s i o n s ; d u r i n g f i v e minutes be f o r e the b a r r i e r was l i f t e d , the number of d i v i s i o n s through which each animal moved was recorded. The b a r r i e r was l i f t e d , and duri n g the next ten minutes the number and t i m i n g of the f o l l o w i n g behaviors were recorded f o r each animal: I n i t i a t i v e behaviors 1. I n i t i a t i o n of i n v e s t i g a t i o n , (abbreviated " I I " ) — approach wi t h i n 10 cm of the other mouse, nose or t a i l o u t s t r e t c h e d , s n i f f i n g of the other. 2 . F i g h t i n i t i a t o r ( " F I " ) — a t t a c k e r i n w r e s t l i n g , b i t i n g , c h a s i n g , e t c . 3. A c t i v e t h r e a t ("AT")— t a i l l a s h i n g , l u n g i n g at other animal, lowered posture with head turned sideways. Response behaviors 4 . Mutual u p r i g h t ("MO")—taking part i n mutual u p r i g h t stance. , 5 . R e t a l i a t i o n ( " R e t " ) — b i t i n g back, w r e s t l i n g when at t a c k e d , e t c . 6. Submission/avoidance ("Sub")--animal backs away 38 or runs away i n response to i n i t i a t i v e behavior by o t h e r , submissive posture. 7. Defensive posture ( " D P " ) — u p r i g h t stance, b a t t i n g with forepaws, u s u a l l y accompanied by v o c a l i z a t i o n . A c t i v i t y measures 8. A c t i v i t y ("Act")—number of d i v i s i o n s moved through d u r i n g the encounter. 9. Latency to approach ("Lat")--number of seconds be f o r e approaching the other animal w i t h i n 10 cm. For a n a l y s i s , each behavior was a d j u s t e d to counts per minute, except f o r L a t , which was expressed i n seconds and s u b t r a c t e d from 600 (the t o t a l d u r a t i o n of the t e s t , i n seconds). The three behaviors which occurred only as responses to the other animal, Ret, Sub, and DP, were adjusted to the number of i n v e s t i g a t i v e and a g g r e s s i v e behaviors by the opponent. Before the next t e s t , the arena was cleaned out, and f r e s h shavings were spread on the f l o o r . Each animal was returned i n the morning to the t r a p l o c a t i o n at which i t had been caught the day b e f o r e . GENERAL TREATMENT OF THE DATA The data f o r t h i s study were c o l l e c t e d i n three neighboring p o p u l a t i o n s of v o l e s , over changing seasons. The sample s i z e s 39 were not l a r g e enough f o r me to estimate h 2 s e p a r a t e l y f o r each block of data, so a l l measurements were adjus t e d to make them comparable in a s i n g l e a n a l y s i s . T h i s was done i n the f o l l o w i n g way. F i r s t , I c o n s i d e r e d the r e l e v a n t m i l i e u f o r a v o l e to be the other animals present i n h i s p o p u l a t i o n d u r i n g a three-month segment* of the year. When p o s s i b l e , the year was d i v i d e d i n t o s h o r t e r segments. Within t h i s d e f i n e d p o p u l a t i o n , I wanted to r e t a i n a l l v a r i a b i l i t y among i n d i v i d a l s , f o r reasons d i s c u s s e d above. T h e r e f o r e , i n order to compare animals from separate b l o c k s , a l l data were adjusted to d e v i a t i o n s from block means, and, where necessary, o b s e r v a t i o n s were a d j u s t e d f o r d i f f e r e n c e s between the sexes, as w e l l . Some of the t r a i t s r e q u i r e d a more complex treatment, which w i l l be d i s c u s s e d where a p p r o p r i a t e . *A d i v i s i o n of the year i n t o b i o l o g i c a l l y r e l e v a n t seasons f o r the p o p u l a t i o n s i n t h i s study i s not a simple matter. There was no c l e a r d i v i s i o n between breeding and non-breeding season on any of the g r i d s . P e r i o d s of good and poor s u r v i v a l were dominated by the y e a r l y summer d e c l i n e s i n numbers, and these were not c o n s i s t e n t i n timing from g r i d t o g r i d . D i v i s i o n s of the year f o r any of the l a r g e g r i d s would have only q u e s t i o n a b l e relevance f o r the breeding e n c l o s u r e s . T h e r e f o r e the year was d i v i d e d i n t o f o u r p e r i o d s of approximately three months each, which c o u l d be f u r t h e r broken down i n t o 4-week segments. Though a r b i t r a r y , these p e r i o d s represent f a i r l y w e l l the seasonal changes which occur i n weather p a t t e r n s , v e g e t a t i o n growth, and p o p u l a t i o n processes. 40 In general, the expression for within-population v a r i a b i l i t y in the t r a i t s can be summarized: Y = H + A (I) + B (J) + C (K) + E where Y i s the observation on an in d i v i d u a l for the t r a i t under consideration, M i s the o v e r a l l mean for a l l the data, A i s the season constant, I i s the season i n which the observation was made, B i s the population constant, J i s the population in which the observation was made, C i s the sex constant, K i s the sex of the i n d i v i d u a l , E i s the remainder. It i s the unexplained remainders E which have been analyzed in this study. 41 SECTION IV: RESULTS—POPULATION STRUCTURE AND VARIATION IN REPRODUCTIVE PERFORMANCE A number of s t u d i e s of m i c r o t i n e p o p u l a t i o n s have attempted to i d e n t i f y the importance of v a r i o u s components of the r e p r o d u c t i v e process to demographic changes. Among these components are pregnancy r a t e , b i r t h r a t e , and s u r v i v a l of the young duri n g t h e i r p e r i o d of dependence upon the mother. L i v e -t r a p p i n g a p o p u l a t i o n provides at best only i n d i r e c t estimates of any of these parameters of r e p r o d u c t i o n . Autopsies of k i l l e d animals can e l u c i d a t e aspects which are ev i d e n t i n morphological changes, but such a method i n e v i t a b l y i n t e r f e r e s with normal p o p u l a t i o n dynamics. Observation of r e p r o d u c t i v e performance i n the l a b o r a t o r y g i v e s a b e t t e r d e s c r i p t i o n of the b e h a v i o r a l a s p e c t s of r e p r o d u c t i o n , but i s of q u e s t i o n a b l e r e l e v a n c e t o n a t u r a l p o p u l a t i o n s . Data on i n d i v i d u a l r e p r o d u c t i v e performance i n the breeding e n c l o s u r e s provide answers to s e v e r a l q u e s t i o n s which have been d i f f i c u l t to approach. The f o l l o w i n g questions are p a r t i c u l a r l y important i n d e s c r i b i n g the breeding s t r u c t u r e of m i c r o t i n e p o p u l a t i o n s : What i s the v a r i a t i o n i n l i t t e r s i z e at recruitment? What f a c t o r s i n f l u e n c e success of a mother at r a i s i n g her l i t t e r t o independence? Do these f a c t o r s a f f e c t s u r v i v a l of the whole l i t t e r or of i n d i v i d u a l o f f s p r i n g ? 42 Are some mothers c o n s i s t e n t l y more s u c c e s s f u l than o t h e r s ? I s presence of other a d u l t s d e t r i m e n t a l to n e s t l i n g and j u v e n i l e s u r v i v a l ? what i s the v a r i a n c e among parents i n c o n t r i b u t i o n t o the next generation? In the f o l l o w i n g s e c t i o n , I s h a l l d e s c r i b e the r e s u l t s concerning l i t t e r s from which at l e a s t one o f f s p r i n g was r e c r u i t e d . The subsequent s e c t i o n , e n t i t l e d " U n s u c c e s s f u l L i t t e r s " , w i l l d e a l with l i t t e r s which f a i l e d completely. LITTER SIZE F i g u r e 5 shows the frequency d i s t r i b u t i o n of l i t t e r s i z e f o r females at the Haney study area, sampled dur i n g three stages of the r e p r o d u c t i v e process. Counts of p l a c e n t a l s c a r s and numbers of embryos were obtained d u r i n g a u t o p s i e s of animals from the breeding e n c l o s u r e s .and those removed from my g r i d s ; s i x t e e n of the animals were obtained from other g r i d s at the Haney study area, at the t e r m i n a t i o n of an experiment by Rudy Boonstra. A l l animals were sampled during s p r i n g and summer, 1974. Counts of p l a c e n t a l s c a r s r e p r e s e n t numbers of young born i n past l i t t e r s ; u s u a l l y i t i s p o s s i b l e to d i s t i n g u i s h between recent and o l d e r s c a r s . Included i n embryo counts were a l l v i s i b l e embryos. These data have been pooled as " a u t o p s i e s " i n F i g u r e 5. Data on l i t t e r s i z e a t b i r t h were pooled from two sources: 43 Figure 5. Frequency d i s t r i b u t i o n of l i t t e r s i z e s from pooled autopsy data, b i r t h s , and r e c r u i t s from l i t t e r s which were born i n the breeding enclosures. FREQUENCY FREQUENCY FREQUENCY r o — r — C O — r — r o + C O c n + V -J II —I 70 r n o x> C O C O 12 m II x> C D •—• C O • II C O O C O C D c n r o C O - f -4^ a C O i— i — i x C O c n 3: m II X C O CD a C O -4-C O X C —I C 3 X ) C O i—i m C O co is rn II x co >— c o 4^ c o C O 77 45 Figure 6. Cumulative numbers of offspring f i r s t captures, as a function of the number of weekly trapping sessions a f t e r the f i r s t member of each l i t t e r was captured. 100 80 f 60 f 40 t N = 230 20 t 0 0 1 2 # TRRPPING SESSIONS RFTER " F I R S T RECRUIT OF L I T T E R 47 l i v e l i t t e r s born i n t r a p s , and l i t t e r s born i n the l a b o r a t o r y . L i t t e r s born i n t r a p s may provide an underestimate of the true l i t t e r s i z e f o r two reasons: the l i t t e r may not a l l have been born when the t r a p was opened, and the mother may have eaten some of the young. T h i s second b i a s i s probably not too s e r i o u s , as th e r e was u s u a l l y evidence of such c a n n i b a l i s m when i t was known to have occurred i n the l a b o r a t o r y . L i t t e r s i z e i n the breeding e n c l o s u r e s could be estimated only when the young f i r s t entered the t r a p s . I s h a l l r e f e r to t h i s measure as " l i t t e r s i z e at recru i t m e n t " . Because the age a t f i r s t capture was v a r i a b l e , the f o l l o w i n g c r i t e r i a were used f o r a s s i g n i n g to l i t t e r s any untagged animals trapped i n breeding e n c l o s u r e s : presence i n the same e n c l o s u r e , f i r s t appearance at a reasonably s m a l l s i z e (when there was any doubt about the i n t e g r i t y of the f e n c e ) , and c o n s i s t e n c y of LAP genotype with that of the parents. Of 233 animals tagged i n the breeding e n c l o s u r e s , only t h r e e had to be d i s c a r d e d from the a n a l y s i s because of s e r i o u s u n c e r t a i n t y about which l i t t e r they belonged t o . I f e l t some doubt concerning another 19 animals which were f i r s t captured at a l a r g e s i z e , but i n every case I checked the LAP genotype f o r c o n s i s t e n c y before i n c l u d i n g the animal i n the most probable l i t t e r . As F i g u r e 6 i n d i c a t e s , about 1/2 the young were caught at the same time as the f i r s t r e c r u i t s i n t h e i r l i t t e r s , and 90% had been caught by the end of the t h i r d (weekly) t r a p p i n g s e s s i o n t h e r e a f t e r . The post-partum l i t t e r s i z e d i s t r i b u t i o n s (Figure 5) d i f f e r from the autopsy data both at b i r t h (G = 16.09, P < .005) and a t rec r u i t m e n t (G = 21.16, P < .005). The comparison of the 48 frequency d i s t r i b u t i o n of l i t t e r s i z e at b i r t h with that at rec r u i t m e n t i s j u s t on the b o r d e r l i n e of s i g n i f i c a n c e (G = 7.42, P = .06). One would expect a £riori that they ought t o d i f f e r simply by v i r t u e of the f a c t t h a t the p e r i o d of b i r t h to rec r u i t m e n t i s one of apparently high m o r t a l i t y (Hoffman, 1958, Krebs and Delong, 1965, C h i t t y , 1952, C h i t t y and Phipps, 1966, Krebs and Myers, 1974). There are t r e n d s , too, i n the parameters of the frequency d i s t r i b u t i o n s ; the mean of the frequency d i s t r i b u t i o n becomes p r o g r e s s i v e l y s m a l l e r , while the va r i a n c e i n c r e a s e s (Figure 5 ) . At the stage of r e c r u i t m e n t , the variance of the d i s t r i b u t i o n i s s i g n i f i c a n t l y l a r g e r than the autopsy v a r i a n c e (F (62,68) = 2. 32, p < .005). Despite the trend toward r e d u c t i o n of the mean during t h i s p e r i o d , i t appears t h a t the l a r g e s t l i t t e r s are about as w e l l represented at recruitment as they are before b i r t h . Two c o n c l u s i o n s can be drawn from t h i s evidence: 1. P a r t i a l f a i l u r e of l i t t e r s d uring the period from b i r t h to r ecruitment i s r e s p o n s i b l e f o r the l o s s of 25% of the p o t e n t i a l young as measured i n embryo and sca r counts (mean of recruits/mean of a u t o p s i e s = .748). 2. T h i s p a r t i a l f a i l u r e appears to a f f e c t most s e r i o u s l y l i t t e r s of average s i z e , r e s u l t i n g i n a spread from very s m a l l to very l a r g e l i t t e r s i z e s at re c r u i t m e n t . a t a b i l i t y of l i t t e r s i z e . 49 The r e p e a t a b i l i t y (R) of a t r a i t i s a measure of the c o n s i s t e n c y of t h a t t r a i t over time w i t h i n an i n d i v i d u a l . I t i s c a l c u l a t e d from estimated components of v a r i a n c e , as the r a t i o of v a r i a n c e between i n d i v i d u a l s to the t o t a l v a r i a n c e of a l l the o b s e r v a t i o n s , when more than one o b s e r v a t i o n has been made on each i n d i v i d u a l : R = s 2 (B) / s 2 (T) where s 2 (B) i s the between i n d i v i d u a l component of v a r i a n c e , and s 2 ( T ) i s the t o t a l v a r i a n c e , f o r repeated measurements (Becker, 1967). R e p e a t a b i l i t y i s of p a r t i c u l a r i n t e r e s t i n t h i s c o n t e x t f o r two reasons. F i r s t , i t g i v e s an upper l i m i t f o r the h e r i t a b i l i t y of the t r a i t (Falconer, 1960a). Second, because va r i a n c e i n the number of progeny i s a l i k e l y component of v a r i a n c e i n f i t n e s s , i t i s u s e f u l to know how w e l l the s i z e of one l i t t e r can p r e d i c t the s i z e of the next l i t t e r and hence the t o t a l number of o f f s p r i n g a female w i l l bear i n her l i f e . The r e p e a t a b i l i t y provides j u s t such an i n d i c a t i o n . Table 2 g i v e s estimates of R f o r l i t t e r s i z e before b i r t h and a t r e c r u i t m e n t . The estimates f o r l i t t e r s i z e during pregnancy were made from autopsy data i n which two s e t s of s c a r s of c l e a r l y d i f f e r e n t age, or embryos i n a d d i t i o n to s c a r s , were v i s i b l e . I c a l c u l a t e d estimates of the r e p e a t a b i l i t y of l i t t e r s i z e at recruitment from breeding e n c l o s u r e mothers which produced more than one l i t t e r d u r i n g the study. The d i f f e r e n c e between the r e p e a t a b i l i t y of l i t t e r s i z e 50 TABLE 2 Estimated r e p e a t a b i l i t y of l i t t e r s i z e at two stages o f the r e p r o d u c t i v e process. Standard e r r o r of estimate i s i n parentheses. Autopsies | R e c r u i t s .j R = .479 (. 165) | R = -.046 (. 146) Number of | Number of females = 20 | females = 14 I 1 51 before b i r t h and t h a t at re c r u i t m e n t could be i n t e r p r e t e d to mean that the female has r e l a t i v e l y good phenotypic or genotypic c o n t r o l over the number of embryos she produces, but r e l a t i v e l y l i t t l e over the events or c o n d i t i o n s which determine how many of her young w i l l a c t u a l l y be r e c r u i t e d . F a c t o r s determining l i t t e r s i z e at r e c r u i t m e n t . Seasons. In many m i c r o t i n e s p e c i e s l i t t e r s i z e v a r i e s over seasons, though i t may not be an important component i n demographic changes over the c y c l e (Hoffman, 1958; Kott and Robinson, 1963; K e l l e r and Krebs, 1970; Krebs and Myers, 1974; C h r i s t i a n , 1971a). In my data, r e c r u i t e d l i t t e r s i z e v a r i e d with season of b i r t h , with the l a r g e s t l i t t e r s i z e s o c c u r r i n g i n the f a l l (Table 3) . Si z e and p a r i t y of mother. Many s t u d i e s suggest t h a t l i t t e r s i z e at b i r t h d i f f e r s between primiparous and multiparous females, and other o b s e r v a t i o n s show t h a t i t i s a f u n c t i o n of the s i z e of the mother at the time of b i r t h (Kott and Robinson, 1963, Hoffman, 1958, K e l l e r and Krebs, 1970). There i s not complete agreement as to the magnitude and d i r e c t i o n of these e f f e c t s among pu b l i s h e d s t u d i e s ; however, a reasonable hypothesis might be t h a t i n e x p e r i e n c e and s m a l l body s i z e could reduce both the s i z e and the success of l i t t e r s born to smal l (young) females. Among females which r a i s e d l i t t e r s i n the breeding e n c l o s u r e s , the mean r e c r u i t e d l i t t e r s i z e f o r primiparae was 3.77 (standard e r r o r = 1.42, N = 13) and t h a t f o r multiparae was 3.62 (standard e r r o r = 1.90, N = 39). The TABLE 3 Recruited l i t t e r s i z e vs season of b i r t h Season of b i r t h T 1 Mean L i t t e r Size January -March A p r i l June July -September October -December 3. 363 3.520 2.400 4.765 11 25 10 -+-17 Analysis of variance: F = 4.615 P < .01 53 e x p e c t a t i o n t hat l i t t e r s i z e should be s m a l l e r f o r primiparous females i s not supported; i n f a c t , the means d i f f e r i n the oppo s i t e d i r e c t i o n . The c o r r e l a t i o n between r e c r u i t e d l i t t e r s i z e and body s i z e ( s k u l l width) of the mother i s a l s o i n the unexpected d i r e c t i o n , but i s not s i g n i f i c a n t (r - -.119, N=60, P > .0 5) . LAP aenotyjDe. Another p o s s i b l e f a c t o r a f f e c t i n g r e c r u i t e d l i t t e r s i z e i s the LAP genotype of e i t h e r or both of the parents. In other s t u d i e s , genotype a t a s i n g l e l o c u s ( t r a n s f e r r i n i n Microtus pennsylyanicus and M i c r o t u s ochroqasterl. has been shown to be a s s o c i a t e d with f i t n e s s a t d i f f e r e n t phases of the c y c l e (Tamarin and Krebs, 1969, Gaines and Krebs, 1971); i n Microtus townsendii, LAP genotype appears to be a s s o c i a t e d with other r e p r o d u c t i v e parameters (LeDuc and Krebs, 1975)., However, LAP genotype of the parent i s not a s s o c i a t e d with d i f f e r e n c e s i n r e c r u i t e d l i t t e r s i z e ( C h i 2 = 2.408, d . f . = 4, P > . 5) . Behavior. The r e l a t i o n s h i p between behavior and l i t t e r s i z e at recruitment w i l l be d i s c u s s e d i n d e t a i l i n the s e c t i o n on behavior. Maternal behavior can account f o r as much as 50% of the va r i a n c e among mothers i n mean number of o f f s p r i n g r e c r u i t e d per l i t t e r . UNSUCCESSFUL LITTERS Of the 107 l i t t e r s born i n the breeding e n c l o s u r e s d u r i n g the course of the study, 44 (41.1%) never produced any r e c r u i t s . These f a i l u r e s were detected when the female was observed to be 54 v i s i b l y pregnant or l a c t a t i n g , without subsequent appearance of o f f s p r i n g i n the e n c l o s u r e . T h i s percent i s probably an underestimate; i t does not i n c l u d e l i t t e r s which were resorbed or aborted at an e a r l y stage, nor cases i n which s i g n s of r e p r o d u c t i v e a c t i v i t y were missed. Every s u c c e s s f u l l i t t e r , on the other hand, co u l d be detected unambiguously toy the presence of young, even though o c c a s i o n a l l y there was no s i g n of r e p r o d u c t i v e a c t i v i t y on the p a r t of the mother. Table 4 Shows the frequency d i s t r i b u t i o n of the stages of the r e p r o d u c t i v e process at which the l i t t e r s apparently f a i l e d , i . e . , the l a s t r e p r o d u c t i v e a c t i v i t y seen i n the mother during the supposed p e r i o d of pregnancy and l a c t a t i o n f o r that l i t t e r . Though t h i s t a b l e i n d i c a t e s that l a t e pregnancy and p a r t u r i t i o n are the most hazardous time f o r the l i t t e r , s e v e r a l c o n s i d e r a t i o n s modify t h i s c o n c l u s i o n . F i r s t , l a c t a t i o n i s f a r more demanding on the energy reserves of the mother , than i s pregnancy ( S a d l e i r , 1969a,b). In t h i s study, too, u n s u c c e s s f u l l i t t e r s were a s s o c i a t e d with the disappearance (presumably death) of the mother more f r e q u e n t l y during l a c t a t i o n than dur i n g pregnancy. A second reason why l a t e p r e g n a n c y - p a r t u r i t i o n may not be as d i f f i c u l t a stage as Table 4 i n d i c a t e s , i s t h a t at l e a s t some of the f a i l u r e s are a t t r i b u t a b l e to a r t i f a c t s of t r a p p i n g . In Table 5, we see t h a t l i t t e r s born i n l i v e - t r a p s are almost always u n s u c c e s s f u l . However, the amount of time a female spends i n t r a p s does not seem to a f f e c t l i t t e r success a t any other stage. Table 6 shows the contingency t a b l e f o r t r a p p a b i l i t y of mothers vs success of t h e i r l i t t e r s . The number of t r a p - n i g h t s and number of captures were t a l l i e d f o r the 5 5 TABLE 4 Frequency d i s t r i b u t i o n of stage of f a i l u r e of unsuccessful l i t t e r s . N=49. T r # Failures Last stage observed Late pregnancy, p a r t u r i t i o n Lactation - week 1 30 -+-68.2 13.6 Lactation - week 2 Lactation - week 3 + , 9. 1 9. 1 56 TABLE 5 A s s o c i a t i o n of s u c c e s s f u l and unsuccessful l i t t e r s with b i r t h i n t r a p s . N = 107. T 1 Unsuccessful l i t t e r s | Successful | l i t t e r s I Born i n trap I 1 I I Born outside I 62 37 P = .008 (Fisher exact test) 57 TABLE 6 A s s o c i a t i o n of l i t t e r success with t r a p p a b i l i t y during the l a t e -pregnancy to weaning p e r i o d . | U n s u c c e s s f u l | l i t t e r s I S u c c e s s f u l l i t t e r s Number t r a p n i g h t s I 1 -+-28 169 I Number captures | 14 128 C h i * = 1.44 P > .1 58 period of late pregnancy to weaning for successful l i t t e r s , and l a t e pregnancy to l a s t v i s i b l e reproductive a c t i v i t y f o r mothers of unsuccessful l i t t e r s . Only mothers which were exposed to more than one trap-night during the relevant period were included in the analysis, since detection of an unsuccessful l i t t e r depended upon at least one capture during that period. Inclusion of ''mothers exposed to only one trap-night would bias the number of captures per trap-night for these animals. The conclusion i s that mothers of unsuccessful l i t t e r s are not more trappable than mothers of successful l i t t e r s during the period of v u l n e r a b i l i t y . From this sample they appear, in f a c t , to be s l i g h t l y less trappable. To what extent can we generalize on these results from the breeding enclosures to an undisturbed Microtus townsgndii population, or to a population being trapped by the technique used on the large grids? F i r s t , for an undisturbed population, we must revise downward the estimate of unsuccessful ..litters, which was 41.1% of the t o t a l (95% confidence l i m i t s , 31.3% -51.3%). Seven of the forty-four unsuccessful l i t t e r s were born i n traps; one of these survived at least to the second week of l a c t a t i o n . If we assume bi r t h in the trap to be the cause of the f a i l u r e of these l i t t e r s — a plausible but untested assumption from the a s s o c i a t i o n — t h e n the estimate of t o t a l l i t t e r f a i l u r e rate not associated with trapping would be 37/107 = 34.6% .('95% confidence l i m i t s , 24.8% - 44.2%). Insofar as the breeding enclosures protected l i t t e r s from other sources of mortality, t h i s may be a minimum estimate. For a trapped population, the estimate of 34.6% i s probably reasonable as a 59 basic f a i l u r e r a t e , with an added separate estimate of m o r t a l i t y fo r l i t t e r s born i n tr a p s of 7/8 = 87.5% (95% confidence l i m i t s , 54.3% - 99.7%). Unfortunately, l i t t l e can be done to reduce t h i s unnatural source of l i t t e r m o r t a l i t y , except to increase the frequency of checks, o r , as I d i d , to avoid trapping i n breeding enclosures which contained females near p a r t u r i t i o n . Natural f a c t o r s a f f e c t i n g l i t t e r success. With s i x and p o s s i b l y seven of the unsuccessful l i t t e r s accounted f o r by b i r t h s i n t r a p s , the remaining 37 or 38 must be explained. Because a s s o c i a t i o n of unsuccessful l i t t e r s with t r a p b i r t h s does not n e c e s s a r i l y imply c a u s a t i o n , I have i n c l u d e d those l i t t e r s i n most of the subsequent analyses, where i t seemed reasonable that there might be another f a c t o r a f f e c t i n g both t r a p p a b i l i t y of the female and success of the l i t t e r . Disappearance of the mother. In the breeding enclosures, disappearance of the mother i n d i c a t e d t h a t she died at some point a f t e r her l a s t capture. Disappearance of the mother during the period from b i r t h to recruitment i s not s i g n i f i c a n t l y a s s o c iated with l i t t e r success, though i t does occur i n a higher proportion of the unsuccessful cases than of s u c c e s s f u l ones ( C h i 2 = .613, d.f. = 1, P > .1). D i s t r i b u t i o n of unsuccessful l i t t e r s among females. I n d i v i d u a l females produced as many as f i v e l i t t e r s ( s u c c e s s f u l and unsuccessful) during t h e i r time i n the breeding enclosures. S u f f i c i e n t numbers produced one, two, and three l i t t e r s f o r me 60 to t e s t whether s u c c e s s f u l and u n s u c c e s s f u l l i t t e r s are d i s t r i b u t e d randomly among females. I compared the observed frequency d i s t r i b u t i o n s with the expected values under the n u l l h y pothesis t h a t s u c c e s s f u l and u n s u c c e s s f u l l i t t e r s are d i s t r i b u t e d b i n o m i a l l y among females, and co u l d not r e j e c t the n u l l hypothesis (Kolmogorov-Smirnov t e s t ; N = 29 f o r mothers with one l i t t e r , 1 9 f o r those with 2 l i t t e r s , 9 f o r those with t h r e e l i t t e r s ; P >.05 f o r a l l t h r e e t e s t s ) . Table 7 shows changes i n the d i s t r i b u t i o n of s u c c e s s f u l to u n s u c c e s s f u l l i t t e r s over the seasons, with p e r i o d s of r e l a t i v e l y high success i n both s p r i n g and autumn. These d i f f e r e n c e s are not s i g n i f i c a n t at the .05 l e v e l , however. Table 8 presents the s u c c e s s f u l and u n s u c c e s s f u l l i t t e r s per en c l o s u r e f o r four-week p e r i o d s throughout the study. The only seasonal e f f e c t which emerges i s the i n d i c a t i o n t h a t l i t t e r s born during l a t e March to A p r i l have a high p r o b a b i l i t y of f a i l u r e , and t h a t l i t t e r s born during May and October are almost u n i f o r m l y s u c c e s s f u l . Reproductive a c t i v i t y a p p a r e n t l y ceases almost e n t i r e l y d u r i n g January and February. P§rifl of. lSOfk§£* B v "the same arguments o u t l i n e d above concerning r e c r u i t e d l i t t e r s u c c ess, i t might be expected t h a t u n s u c c e s s f u l l i t t e r s should occur more f r e q u e n t l y among primiparous than among multiparous females. There i s no d i f f e r e n c e between the two groups, however ( C h i 2 = .486, d.f. = 1 , P > . 1) . LAP genotype of mother and f a t h e r the LAP genotype of n e i t h e r f a t h e r nor mother i s s i g n i f i c a n t l y a s s o c i a t e d with l i t t e r success. (Chi* = 1-544, d . f . = 2, P > . 1 ) . 61 TABLE 7 Frequency d i s t r i b u t i o n s of successful and unsuccessful l i t t e r s associated with period of b i r t h Successful l i t t e r s Unsuccessful l i t t e r s January March 1 1 15 A p r i l -June 25 10 July -September -+-1 0 1 0 October -December 17 C h i 2 = 6.33 df = 3 . 0 5 < P < . 1 N = 1 0 7 62 TABLE 8 Numbers of successful and unsuccessful l i t t e r s per breeding enclosure during four-week periods of the study. t • - — i ._ . _ - T 1 | Successful | UnsuccessfulJ | l i t t e r s per | l i t t e r s per j | enclosure | enclosure J } Four-week periods | 1 9 7 2 - 1 1 9 7 3 - | 1 9 7 2 - J 1 9 7 3 1 j 1 9 7 3 | 1 9 7 4 | 1 9 7 3 I 1 9 7 4 | I 1 September I . 3 3 | 0 . 0 | 0 . 0 1 . 1 0 | I 2 | . 3 3 | . 2 0 | 0 . 0 I 0 . 0 | \ 3 I - 5 5 | . 1 3 | 0 . 0 J . 1 3 J I 4 I . 2 9 1 0 . 0 | . 1 4 | . 0 7 | j 5 Dec - Jan 1 . 1 3 | . 2 5 | 0 . 0 | . 3 1 | I 6 I 0 . 0 | 0 . 0 | 0 . 0 | . 0 7 | ! 7 I . 3 8 | . 1 9 | . 2 5 | . 0 7 | i 8 March \ . 1 3 | . 2 5 | . 5 0 | . 4 4 | I 9 I . 3 8 J . 1 9 J 0 . 0 I . 3 1 | | 1 0 I . 5 0 I . 4 4 | 0 . 0 j 0 . 0 J | 1 1 June | . 2 2 | . 3 8 | . 1 1 | . 2 5 | | 1 2 | . 4 4 | . 1 9 | 0 . 0 J . 1 9 | t 1 3 I . 1 0 | . 0 6 | . 1 0 | . 3 1 | ... i i _ - L - _. J,... j 6 3 Presence of father or other male. Nothing i s known about the role of the male parent with respect to his offspring during the period from b i r t h to recruitment, in Hierotus townsendii. There i s no evidence to indicate any sort of pair bond, and parental care by the father i s unusual in rodents, though i t has been reported in Microtus ochrogaster by Scudder, Karczmar, and Lockett (1967"). On the supposition that presence of a male i n a small enclosure might be deleterious to s u r v i v a l of the l i t t e r , I attempted to remove the father whenever I knew that a l i t t e r had been born. This was not always possible, however, either because I f a i l e d to capture the male, or because I was unaware of the l i t t e r u n t i l late in the period of l a c t a t i o n . In some cases in which I was unaware of the l i t t e r ' s existence, another male was introduced to the enclosure before recruitment took place. These three treatments allow a test of the following predictions: the presence of the father should a f f e c t l i t t e r success, the di r e c t i o n of the ef f e c t being dependent upon the role of the father i n the early history of the young. On the other hand, a non-paternal male, i f he had any eff e c t at a l l , would probably be harmful to the l i t t e r . The results of testing these predictions appear i n Table 9. Neither the father nor any other male apparently influences the sur v i v a l of the l i t t e r when present i n the breeding enclosure. Source of parents. Parents in t h i s study were obtained from several populations, for reasons outlined i n the Methods section. Among the parents which did attempt reproduction, there i s no association between l i t t e r success and source (Table 64 TABLE 9 Freguency d i s t r i b u t i o n of successful and unsuccessful l i t t e r s associated with presence of the father or other male i n the breeding enclosure during the period from b i r t h to recruitment. r . . . T , | Father j present - T " . " - " j Father | absent I i Unsuccessful l i t t e r s | 18 20 1 • j i Successful l i t t e r s \ 29 34 i i j Chi* = .02 5 df = 1 P > .5 N = 101 Other male present Other male absent Unsuccessful l i t t e r s 34 Successful l i t t e r s 20 43 Chi* = 2.077 df = 1 P > .05 N = 105 65 TABLE 10 Association of frequency d i s t r i b u t i o n of successful and unsuccessful l i t t e r s with sources of parents. Voles which made no reproductive e f f o r t are excluded from the analysis. SOUECE OF MOTHER Haney Other sources pooled Unsuccessful l i t t e r s 18 26 Successful l i t t e r s 27 36 C h i 2 = .040 df = 1 P > .5 N = 107 SOURCE OF FATHER Haney Other sources pooled -I Unsuccessful l i t t e r s 24 20 Successful l i t t e r s 40 23 C h i 2 = .862 df = 1 P > . 1 N = 107 6 6 TABLE 11 A s s o c i a t i o n of frequency d i s t r i b u t i o n of s u c c e s s f u l r e p r o d u c t i v e e f f o r t with source of parents. Data f o r mothers and f a t h e r s pooled. Source of parent i : 1 1 1 ~\ I i l l ) | 1 Haney | Serpentine| D e l t a | 1 1 1 1 1 j . H _! H 4 j + H -j ^ i i i I I I S u c c e s s f u l r e p r o d u c t i o n | 47 | 37 I 4 | I (at l e a s t 1 r e c r u i t ) | | j | I I I I I I .j .j .j ^ I I I I I I U n s u c c e s s f u l \ | I I | r e p r o d u c t i o n | 57 | 22 I 12 | | or no r e p r o d u c t i o n | | | | I I I I I L 1 i I J G = 8.946 df = 2 P < .025 N = 179 67 1 0 ) . However, when I Include a l l potential parents in the sample and pool unsuccessful breeders with animals which apparently made no reproductive effort at a l l , there is a significant association of origin of parent with successful reproduction (Table 1 1 ) . Surprisingly, though one would expect animals native to the Haney study area to be the most f i t in that environment, i t appears that animals from the Serpentine study area are the best reproducers. This result may be confounded with seasonal effects, since reliance on animals from other sources was heaviest just after the periods when Haney animals had become unavailable owing to the seasonal fluctuations in numbers. CONCLUSIONS Of the factors discussed so far, neither LAP genotype nor parity of the mother i s associated with l i t t e r size at recruitment, while season of birth can account for some of the variance in this quantity in Microtus townsendii. Of l i t t e r s which f a i l completely, the majority appear to do so shortly after birth. Birth in traps nearly always i s associated with failure of the l i t t e r , and may be the direct cause, though several l i t t e r s born in traps survived for some time after birth. Other than at this stage, however, trapping does not interfere with l i t t e r success. Successful and unsuccessful l i t t e r s are randomly distributed among mothers, and are not associated with parity or LAP genotype. Neither the father nor any other male seems to affect weaning success when 68 present. Parents from d i f f e r e n t p o p u l a t i o n s which reproduced do not d i f f e r i n l i t t e r success, but there i s a d i f f e r e n c e among sources i n o v e r a l l r e p r o d u c t i v e e f f o r t . Both l i t t e r s u ccess and r e c r u i t e d l i t t e r s i z e vary over seasons. In both years, there was a strong tendency f o r l i t t e r s born i n March t o f a i l c ompletely, and f o r those born i n May and October to be r e c r u i t e d s u c c e s s f u l l y . These c o n c l u s i o n s apply to animals breeding under semi-n a t u r a l c o n d i t i o n s . T h i s p o p u l a t i o n d i f f e r e d from an unmanipulated one i n t h a t the animals were not part of a normal s o c i a l s t r u c t u r e d u r i n g t h e i r r e p r o d u c t i v e a c t i v i t y i n the breeding e n c l o s u r e s , they may have been p r o t e c t e d from some pre d a t o r s , and they were s u p p l i e d with some e x t r a food d u r i n g the winter. Normal d i s p e r s a l of the young may have been i n t e r f e r e d with s l i g h t l y , though most o f f s p r i n g were f i r s t caught and removed at about the s i z e a t which they would normally enter a t r a p p a b l e p o p u l a t i o n . To the extent t h a t these f a c t o r s might i n c r e a s e or decrease t o t a l or p a r t i a l f a i l u r e of l i t t e r s , the r e s u l t s should be a p p l i e d to unmanipulated p o p u l a t i o n s only with c a u t i o n . For the most p a r t , the v a r i a b i l i t y among i n d i v i d u a l s i n r e p r o d u c t i v e performance i s probably greater i n a normal p o p u l a t i o n than i n the breeding e n c l o s u r e p o p u l a t i o n . VARIATION IN A MEASURE OF FITNESS In a d d i t i o n performance i n to de the br s c r i b i n g v a r i a b l i t y i n rep eeding e n c l o s u r e . p o p u l a t i o n . r o d u c t i v e we may 69 c a l c u l a t e a more i n c l u s i v e measure of f i t n e s s , which may d e s c r i b e reasonably w e l l the p r o p o r t i o n a l c o n t r i b u t i o n of a parent to the next g e n e r a t i o n ' s gene p o o l . The t o t a l number of weeks l i v e d by a l l the o f f s p r i n g of a parent are summed, and d i v i d e d by the number of weeks the parent was present i n the breeding e n c l o s u r e s . A l l o f f s p r i n g which disappeared at l e s s than s i x weeks of age, i . e . , before they would have had a chance t o reproduce, were e l i m i n a t e d from the sum of " t o t a l number of o f f s p r i n g mouse-weeks". In F i g u r e 7 and Table 12, we see histograms and parameters of the frequency d i s t r i b u t i o n o f t h i s f i t n e s s measure, which I s h a l l r e f e r to as "offspring-weeks per week". There i s a s i g n i f i c a n t d i f f e r e n c e between the sexes i n the v a r i a n c e of t h i s f i t n e s s measure (Table 12). The d i f f e r e n c e i n means, though not s i g n i f i c a n t a t the .05 l e v e l , i s i n the expected d i r e c t i o n , because males can p o t e n t i a l l y mate many times during the time a female i s occupied with a s i n g l e l i t t e r . W ithin sexes and between seasons, there i s s i g n i f i c a n t h e t e r o g e n e i t y of v a r i a n c e f o r t h i s f i t n e s s measure, as w e l l , and seasonal changes are p a r a l l e l f o r the two sexes (Table 13). Variance among i n d i v i d u a l s i s highest during October - December; i t i s high d u r i n g the peak of breeding, ( A p r i l - June), as w e l l . EFFECTIVE POPULATION SIZE Many ques t i o n s asked i n p o p u l a t i o n g e n e t i c s theory, p a r t i c u l a r l y those concerned with s t o c h a s t i c changes i n gene f r e q u e n c i e s (genetic d r i f t ) i n v o l v e assumptions about the 70 Figure 7. Frequency d i s t r i b u t i o n of a measure of parental f i t n e s s : the t o t a l number of weeks l i v e d by a l l offspring of the parent are summed and divided by the number of weeks the parent spent i n the breeding enclosure population. Animals in the "zero" category include both parents of l i t t e r s which were en t i r e l y unsuccessful, and parents which evidently made no reproductive e f f o r t during their time i n the breeding enclosures. D 0 T CO C E I P 4 + 12 + | 1 MRLES-FEMRLES- N=79 0 0 + TO 5 5+ 0 10 10 + JO 15 15 + TO 20 20 + TO 25 25 + 0 30 30 + TOTRL OFFSPRING-WEEKS PER WEEK IN ENCLOSURES Figure 7 TABLE 12 Parameters of the d i s t r i b u t i o n of the f i t n e s s measure: offspring-weeks ^ 6 // weeks in breeding enclosures Including a l l p o t e n t i a l parents: Males Females Mean =2.467 Mean = 1.924 s 2 = 32.254 s 2 = 11.447 N = 93 N = 79 F(92,78) = 2.818 p < .002 t = .774 df =. 170 p ; .5 Including only parents with successful reproduction: Males Females Mean =5.735 Mean = 3.942'.. s 2 = 56.861 s 2 = 15.539 N = 40 N ='.41 F(39,40) = 3.659 p < .002 t = 1.336 df = 79 p> .1 73 T A B L E 13 Estimated parameters of the frequency d i s t r i b u t i o n s of the p a r e n t a l f i t n e s s measure ' o f f spring-weeks per week': Breakdown by seasons and sexes. Only parents with a t l e a s t one r e c r u i t e d o f f s p r i n g are i n c l u d e d . P e r i o d i n t r o d u c e d Males Females January -March mean = 3.101 s 2 = 7.102 N = 10 mean = 1.715 s 2 = 1.728 N = 6 A p r i l -June mean = 3.440 sz = 32.515 N = 11 I mean = 3.347 | s 2 = 16.033 j N = 16 I J u l y -September mean = 8.367 s^ = 30.633 N = 6 mean = 3.702 sz = 3.611 N = 9 mean = 5.486 J sz = 31.780 | N = 10 j October -December mean = 8.489 sz = 117.323 N = 13 Fmax = 16.50 P < .01 Fmax = 18.39 P < .05 TAB LIS 14 74 Formulae for variance e f f e c t i v e number ( N £ V ) > from Crow and Kimura, (1970) Di f f e r e n t expected numbers of progeny: N. = 2N - (k/2) t_ M ^ . ev Where N = actual population s i z e next generation V = variance i n expected number of progeny 1 + V /k -k k = mean number of progeny If k and V, are d i f f e r e n t for the two sexes: k N = 4 H C N ev i ef em Where N = N calculated f o r females ef ev N + N •' ef em N = N calculated for males em ev 75 breeding s t r u c t u r e of the p o p u l a t i o n . The number of animals i n the p o p u l a t i o n , randomness of mating, d i s t r i b u t i o n of progeny among parents, sex r a t i o , and degree of i n b r e e d i n g are parameters of p o p u l a t i o n s t r u c t u r e whose p a t t e r n s i n r e a l p o p u l a t i o n s f r e q u e n t l y d i f f e r from those assumed by the theory. The " e f f e c t i v e p o p u l a t i o n s i z e " i s an adjustment of the a c t u a l p o p u l a t i o n s i z e , t o c o r r e c t f o r v i o l a t i o n s of s e v e r a l of these assumptions. In a g e n e r a l way, a r e a l p o p u l a t i o n of s i z e N should behave s i m i l a r l y to an " i d e a l " p o p u l a t i o n of s i z e Ne, where Ne i s the e f f e c t i v e p o p u l a t i o n s i z e f o r that p a r t i c u l a r set of breeding s t r u c t u r e parameters. I have estimated v a r i a n c e i n offspring-weeks per week and i n p o t e n t i a l number of o f f s p r i n g ("progeny s i z e " ) , as d i s c u s s e d above i n the s e c t i o n on l i t t e r s i z e . These q u a n t i t i e s are u s e f u l i n e s t i m a t i n g the " v a r i a n c e e f f e c t i v e number" and the " s e x - r a t i o e f f e c t i v e number" of the p o p u l a t i o n , parameters which summarize the way i n which variance i n progeny s i z e i n f l u e n c e s the breeding s t r u c t u r e (Crow and Kimura, 1970, 1972). Table 14 summarizes the formulae f o r c a l c u l a t i n g the v a r i a n c e e f f e c t i v e number and the sex r a t i o e f f e c t i v e number. The a p p l i c a t i o n of the formula f o r the v a r i a n c e e f f e c t i v e number (Nev) assumes d i s c r e t e generations and random mating. Of these, the second i s approximately true f o r the breeding e n c l o s u r e p o p u l a t i o n , i n t h a t parents were p a i r e d a t random from the a v a i l a b l e pool. The composition of t h i s pool,' however, n e c e s s a r i l y v a r i e d over the seasons. Micrqtus townsendii p o p u l a t i o n s do not have d i s c r e t e g e n e r a t i o n s , but the formula i s s t i l l approximately v a l i d i n v i o l a t i o n of t h i s assumption (Crow 76 and Kimura, 1972). In any case, the a n a l y s i s w i l l g ive us some id e a of the r e l a t i v e importance of d i f f e r e n t sources of v a r i a b i l i t y i n f i t n e s s . Under the above assumptions, the expected value of Nev i s equal to N, the census number, i f the v a r i a n c e i n progeny number i s the b i n o m i a l v a r i a n c e , i . e . , i f the l i t t e r s i z e s are randomly d i s t r i b u t e d among parents. When a l l parents c o n t r i b u t e egual numbers of progeny, then Nev approaches i t s upper bound, 2N. I f the v a r i a n c e i n progeny number i s g r e a t e r than the b i n o m i a l v a r i a n c e , Nev w i l l be l e s s than N (Crow and Kimura, 1970). Table 15 shows est i m a t e s of Nev f o r the breeding e n c l o s u r e p o p u l a t i o n and t h e i r o f f s p r i n g , using t h r e e d i f f e r e n t , e s t i m a t o r s of Vk: autopsy l i t t e r s i z e , r e c r u i t e d l i t t e r s i z e , and the f i t n e s s measure "number of offspring-weeks per week ". When the v a r i a n c e in l i t t e r s i z e before b i r t h i s used as a measure of Vk (the v a r i a n c e i n progeny number), then the e f f e c t i v e p o p u l a t i o n s i z e i s c o n s i d e r a b l y higher than the census number. Even at rec r u i t m e n t , although the frequency d i s t r i b u t i o n of l i t t e r s i z e has changed (Figure 5), the Nev i s not s i g n i f i c a n t l y reduced. However, a d i f f e r e n t p a t t e r n emerges when estimates of Nev are based on a more comprehensive measure of the c o n t r i b u t i o n s made by i n d i v i d u a l parents. I f we take "offspring-weeks per week" as the measure of Vk, and i f we assume each parent l i v e s an equal l e n g t h of time, then, the Nev of the o f f s p r i n g v a r i e s depending upon the season of the parent's i n t r o d u c t i o n to the breeding e n c l o s u r e p o p u l a t i o n . For both sexes of parents, there are p o t e n t i a l b o t t l e n e c k s i n numbers during autumn and s p r i n g , and r e l a t i v e l y high Nev i n winter and summer. TABLE ;15 7 7 Calculations of variance e f f e c t i v e numbers for the breeding enclosure population, using d i f f e r e n t estimates of k and V •. " . *8P V, and k estimated'from k autopsy data: N = 1.56N - 1.900 ev V and k estimated from re c r u i t e d l i t t e r s i z e : k N = 1.06N - .971 ev For parental f i t n e s s measure: offspring-weeks/week i n breeding enclosures: Season N —females ev N —males ev January - March N = .996N - .427 ev N = .873N - .677 ev A p r i l - June N = .345N - .289 ev N = .19 IN - .165 ev July - September N = 1.012N - .937 ev N = .429N - .897 ' ev October - December N = .294N - .404 ev N = .135N - .286 ev . 78 TABLE 16 .. Calculations of N for the actual number of offspring weaned in the breeding ev enclosures during each season. (Formulae and parameters are shown in Tables 14 and 15,.) , Period N ' N ev July - September, 1972 6 2.53 October - December, 1972 38 6.68 January - March, 1973 12 10.59 April - June, 19 73 35 8.40 July - September, 1973 9 4.55 October - December, 1973 43 7.61 January - March, 1974 25 22.69 April - June, 1974 54 13.07 July - September, 1974 7 3.14 Total 230 79.25 79 I f we c a l c u l a t e Nev from the a c t u a l number of o f f s p r i n g born i n these seasons, we can see {Table 16) t h a t the p e r i o d i n which the s m a l l e s t number of o f f s p r i n g were born (July -September) i s a l s o the g r e a t e s t r e a l i z e d g e n e t i c b o t t l e n e c k , whereas another p e r i o d of low r e p r o d u c t i v e output (January -March) corresponds t o the highest r a t i o of r e a l i z e d Nev to N. The seasonal c o h o r t s of o f f s p r i n g i n Microfus t o w n s e n d i i p o p u l a t i o n s do not r e a l l y correspond to generations.*. F i r s t , the young j o i n a p o p u l a t i o n i n which a d u l t s are c o n t i n u i n g to breed. Second, most of the young i n the J u l y - September and October -December cohor t s do not breed u n t i l the next s p r i n g , except i n years when there i s winter breeding. The values i n Table 16 are probably overestimates of Nev f o r two reasons: F i r s t , with the c o n s i d e r a t i o n that parents do not l i v e equal l e n g t h s of time i n a n a t u r a l p o p u l a t i o n , the Nev w i l l be reduced even more, unless number and v i a b i l i t y of o f f s p r i n g are c o r r e l a t e d with l e n g t h of l i f e of a d u l t s . Second, t h i s a n a l y s i s i n c l u d e d only parents which produced some o f f s p r i n g s u c c e s s f u l l y . A l a r g e p r o p o r t i o n of a d u l t s i n the breeding e n c l o s u r e s never produced any r e c r u i t s . When these u n s u c c e s s f u l breeders are i n c l u d e d , the mean l i t t e r s i z e (k) i s reduced more than Vk (Table 12). Again, the e f f e c t w i l l be to reduce Nev. CONCLUSIONS Because a sample of o f f s p r i n g of known parentage was monitored throughout the l i v e s of the animals, i t i s p o s s i b l e to 80 estimate the f i t n e s s of the parents i n terms of the proportional representation of t h e i r genes i n the offspring gene pool. Both autopsy l i t t e r size and recruited l i t t e r s i z e are d i s t r i b u t e d among parents i n such a way that the e f f e c t i v e number i s close to the census number, but the estimate from a more comprehensive f i t n e s s measure r e s u l t s i n a small r a t i o of e f f e c t i v e number to actual number, during several seasons. The most serious bottleneck in e f f e c t i v e number occurs during July - September; t h i s period, however, may be important only in years when breeding continues through the winter. DISCUSSION The study of v a r i a b i l i t y in reproductive performance of voles under the semi-natural conditions of the breeding enclosures has provided information relevant to several important questions concerning vole population structures. F i r s t , I have been able to estimate in d i f f e r e n t ways one parameter describing the breeding structure of Microtus townsendii populations, the variance e f f e c t i v e number. In combination with the extensive sampling of migration rates and gene frequencies i n Microtus townsendii populations currently being carried out, t h i s estimate of Nev w i l l permit evaluation of the effects of fluctuations in numbers and in reproductive rates upon the gene freguency dynamics of t h i s species. The fact that Nev was small at some times and large at others implies that there are major differences in s u r v i v a l among families. Thus, the a b i l i t y of a female vole to nurture 81 her o f f s p r i n g to t r a p p a b l e age, and the e f f e c t s of t h e i r common environment upon t h e i r subsequent s u r v i v a l may be as important t o her f i t n e s s as i s her f e r t i l i t y . As we have seen, d i f f e r e n c e s i n f i t n e s s among parents are great enough t h a t the e f f e c t i v e number of o f f s p r i n g i n t h i s study was reduced t o one-t h i r d of the t o t a l number born (Table 16). These measurements of Nev were made only upon parents which a c t u a l l y produced o f f s p r i n g , s i n c e the variance e f f e c t i v e number r e a l l y a p p l i e s to the o f f s p r i n g g e n e r a t i o n , r a t h e r than t o the p a r e n t a l generation. Two other aspects of breeding s t r u c t u r e are a p p l i c a b l e to vole p o p u l a t i o n s , as w e l l . F i r s t , s u b d i v i s i o n of the breeding p o p u l a t i o n can have d r a s t i c e f f e c t s upon the e f f e c t i v e numbers (Petras, 1967), and may be important i n some h a b i t a t s even f o r Migrotus. However, the high r a t e s of m i g r a t i o n and g e n e r a l l y homogeneous h a b i t a t s of most m i c r o t i n e p o p u l a t i o n s probably o f f s e t the r e d u c t i o n i n e f f e c t i v e number, much as i n the Mus p o p u l a t i o n s s t u d i e d by Berry and Jakobson (1974). Second, the segment of the p o p u l a t i o n which does not produce o f f s p r i n g s u c c e s s f u l l y must be d e s c r i b e d i n any d e t a i l e d model of m i c r o t i n e breeding s t r u c t u r e . Non-breeding animals play an important p a r t i n b u f f e r i n g p o p u l a t i o n s a g a i n s t sudden f l u c t u a t i o n s , i n s p e c i e s such as marmots (Svendsen, 1974), grouse (Watson and J e n k i n s , 1968), and p a s s e r i n e b i r d s ( J . Krebs, 1971). Noting the numbers of r e p r o d u c t i v e a d u l t s , non-reproductive a d u l t s , and r e c r u i t s i n a p o p u l a t i o n of M i c r o f u s a q r e s t i s , C h i t t y and Phipps (1966) detected an e v i d e n t g e n e t i c b o t t l e n e c k , even without knowing the r e l a t i v e c o n t r i b u t i o n s of the breeding animals. J 82 Greenwood (1974) estimated the e f f e c t i v e numbers of Cejaaea nemoralis, under s e v e r a l p l a u s i b l e s e t s of parameters. He concluded from h i s experimental v a r i a t i o n of parameters t h a t the estimate of Nev/N i s q u i t e robust with r e s p e c t to v a r i a n c e of both f e c u n d i t y of the mother and s u r v i v a l of the young. Only when s u r v i v a l of young was s t r o n g l y homegeneous w i t h i n f a m i l i e s was the Nev/N r a t i o s i g n i f i c a n t l y lowered. The range of r a t i o s of Nev/N which he obtained (.19 - .65) w a s n o t as wide as the range over seasons found i n t h i s study. From t h i s r e s u l t we may conclude that the s e a s o n a l f l u c t u a t i o n s i n Nev/N probably represent s i g n i f i c a n t seasonal changes i n w i t h i n - and between-f a m i l y s u r v i v a l p a t t e r n s among n e s t l i n g s and young j u v e n i l e s . Other estimates of e f f e c t i v e number i n n a t u r a l p o p u l a t i o n s are few. F e l s e n s t e i n (1971), T i n k l e (1965), K e r s t e r (1964), Petras (1967), and M e r r e l l (1968) have p u b l i s h e d estimates f o r v a r i o u s v e r t e b r a t e p o p u l a t i o n s . The s i g n i f i c a n c e and g e n e r a l p a t t e r n of t h i s parameter w i l l be e v i d e n t , however, only a f t e r a number of e c o l o g i c a l l y d i v e r s e s p e c i e s have been s t u d i e d i n t h i s r e s p e c t . The second group of questions which I have attempted to answer concern: Which stages of the r e p r o d u c t i v e process c o n t r i b u t e most to the variance i n f i t n e s s among parents? What f a c t o r s i n f l u e n c e the r e l a t i v e success at each of these stages? I have i d e n t i f i e d the p e r i o d from b i r t h to recruitment as an important component i n the r e p r o d u c t i v e performance of M i c r o t u s townsendii parents. T h i s o b s e r v a t i o n agrees with the c o n c l u s i o n s of Krebs and Myers (1974) and B i r d s a l l (1974), t h a t s u r v i v a l of very young v o l e s i s a s i g n i f i c a n t aspect of the 83 g e n e t i c and numerical f l u c t u a t i o n s of H i c r o t u s p o p u l a t i o n s . I have e l i m i n a t e d s e v e r a l promising f a c t o r s which might i n f l u e n c e r e c r u i t m e n t from a l i t t e r : p a r i t y , s i z e of the mother, t r a p p a b i l i t y of the mother, presence of the f a t h e r and other males, LAP genotype, and o r i g i n of e i t h e r parent. In a d d i t i o n , we can conclude t h a t there must be s e v e r a l d i f f e r e n t kinds of m o r t a l i t y working upon the l i t t e r s r a i s e d i n the breeding e n c l o s u r e s . Hoffmann (1958) recognized t h a t some agents would tend to e l i m i n a t e e n t i r e l i t t e r s , e.g., p r e d a t o r s , death of the mother, while others would k i l l i n d i v i d u a l o f f s p r i n g , e.g., i n h e r e n t weakness, d i s e a s e . Losses of both types are important i n the breeding e n c l o s u r e s , an o b s e r v a t i o n which m i l i t a t e s a g a i n s t simple e x p l a n a t i o n s of m o r t a l i t y before r e c r u i t m e n t . The p a t t e r n s of r e p r o d u c t i v e performance i n the breeding e n c l o s u r e s may gi v e us f u r t h e r i n s i g h t i n t o the e f f e c t s of seasons and the s o c i a l environment upon n e s t l i n g and j u v e n i l e s u r v i v a l . The i n t e r a c t i o n o f these two f a c t o r s has been i m p l i c a t e d i n s u r v i v a l of young Microtus i n s e v e r a l s t u d i e s . C h i t t y (1952) and C h i t t y and Phipps (1966), o b s e r v i n g the f a i l u r e of r e c r u i t m e n t during the e a r l y p a r t of the breeding season and i t s recovery upon the disappearance of many l a r g e males l a t e r , concluded that a d u l t a g g r e s s i o n a g a i n s t j u v e n i l e s might be r e s p o n s i b l e f o r the e a r l y l o s s e s . A s i m i l a r , p a t t e r n has been observed i n other p o p u l a t i o n s of Microtus townsendii i n the Vancouver area, and heavy m o r t a l i t y of j u v e n i l e s , e s p e c i a l l y during p o p u l a t i o n d e c l i n e s , i s c h a r a c t e r i s t i c of s e v e r a l m i c r o t i n e s p e c i e s (Godfrey, 1955, Krebs, K e l l e r , and Tamarin, 84 1969) . In Peromy.scus, as w e l l , Healey (1967) showed t h a t aggressiveness of a d u l t males was c l o s e l y a s s o c i a t e d with j u v e n i l e l o s s e s . T h i s study c a s t s some doubt upon the p o s s i b i l i t y t h a t i n t e r f e r e n c e o r ag g r e s s i o n by r e s i d e n t a d u l t s (other than the mother) i s a necessary f a c t o r f o r poor s u r v i v a l of n e s t l i n g s and j u v e n i l e s . We have already seen evidence t h a t the males i n the breeding e n c l o s u r e s do not i n f l u e n c e t o t a l f a i l u r e r a t e of l i t t e r s . In a d d i t i o n , males have been i n c l u d e d i n cages i n s e v e r a l l a b o r a t o r y s t u d i e s of r e p r o d u c t i o n i n other s p e c i e s of v o l e s . I f the male's i n t r o d u c t i o n i s c a r e f u l l y timed, there need be no i l l e f f e c t s (fianson, 1941, L e s l i e e t a l . , 1955, L e s l i e and Hanson, 1940, H. C h i t t y , 1957). Young o f f s p r i n g i n the breeding e n c l o s u r e s were exposed to no a d u l t s other than t h e i r mother and one male, between b i r t h and recruitment. Even without a f l u c t u a t i n g s o c i a l environment, however, there were str o n g s e a s o n a l changes i n the s u r v i v a l of l i t t e r s , i n v o l v i n g c o n s i s t e n t f a i l u r e of recruitment e a r l y i n the breeding season. While the s o c i a l c l i m a t e i n an unmanipulated p o p u l a t i o n undoubtedly does vary throughout the breeding season, i t i s c l e a r l y not a necessary f a c t o r f o r the production o f t h i s t y p i c a l p a t t e r n of n e s t l i n g and j u v e n i l e s u r v i v a l . A comparison of s u r v i v a l t o t r a p p a b l e age du r i n g t h i s p e r i o d among the breeding e n c l o s u r e s , the unfenced g r i d AA, and the fenced g r i d L helps e l u c i d a t e the r o l e of the s o c i a l environment i n j u v e n i l e m o r t a l i t y . I n d i c e s of e a r l y j u v e n i l e s u r v i v a l were c a l c u l a t e d f o r g r i d AA and g r i d L by the method of 85 Krebs and Delong (1965): U S = the number of young animals recruited (<35 g) in week t, divided by the number of females l a c t a t i n g in week t-4. The index of juvenile survival for the breeding enclosures was calculated from the mean number of r e c r u i t s per l i t t e r born during the corresponding period. The results for 1974 appear in Table 17. If we make the c r u c i a l assumptions that estimates of survival between bi r t h and recruitment are not seriously biased by differences i n t r a p p a b i l i t y or dispersal potential among the three treatments (fenced gr i d , unfenced g r i d , and breeding enclosures), then the two populations and the breeding enclosures d i f f e r e d c h i e f l y i n apparent habitat q u a l i t y , in movements and density of adults, and possibly i n l e v e l of predation. The assumption that dispersal of the early juvenile age group i s unaffected by fencing can be supported by the f a c t that voles appearing i n areas of empty habitat are nearly a l l reproductively mature, indicating that very young Micrqtus do not move great distances (Krebs and Myers, 1974). From Table 17 we can see that the index of juvenile s u r v i v a l i s consistently higher i n the fenced grid L; only at the height of the breeding season does the index i n the breeding enclosures approach those l e v e l s . This information i s not s u f f i c i e n t to enable us to draw strong inferences about the eff e c t s of fencing and i s o l a t i o n of fam i l i e s , but i t does suggest the following conclusions. 1. The pattern of poor juvenile and nestling s u r v i v a l early in the breeding season can occur in the absence of any adults other than the parents, in the breeding enclosures. 86 TABLE 17 I n d i c e s o f e a r l y j u v e n i l e s u r v i v a l f o r two-week i n t e r v a l s , January - J u l y , 1974. r -Week ._T_ T " G r i d AA | \ E n c l o s u r e s | i G r i d L I ! 137 January j 1.00 | 0.00 j | 139 | 1.67 | 0.00 | 1 I 141 j 0.00 J 0.00 | 1.00 | | 143 February j 0.50 J 1.00 2.00 | | 145 j 0.50 | 2.67 | 2.00 I | 147 | 2.00 J 0.33 j 2.50 j J 149 | 0.33 | 1. 88 ] 4.50 \ J 151 A p r i l j 0.58 | 1.33 | 1.56 j I 153 j 1.00 J 1.20 | 4.00 | | 155 j 1.40 | 4.25 j 6.00 | | 157 | 0.63 | 4.50 j 0.71 j | 159 June | 1.80 | 1.63 j 5.25 | | 161 | 1.50 | 0.50 | 3.33 J | 163 | 0.67 1 0.75 | 0.40 | | 165 I 1.67 | 0.50 I | j . . . j_ * 1 t Mean r i . 1.02 | 1,,. 1.69 - + j . i 2.77 | j 87 2. The p o s s i b i l i t y exists that being enclosed i n a small space upsets the normal maternal care patterns; however, t h i s e f f e c t i s not serious enough to keep the index of juvenile s u r v i v a l consistently low i n the breeding enclosures. 3. The major differences between grids L and AA were in habitat quality (better on Grid L), and amount of immigration of strange adults (lower on Grid L). Density of adults and emigration rates were similar on the two grids. One or both of these factors, habitat quality and adult immigration, may be responsible for the difference i n the U S values for the two grids. These observations agree with re s u l t s from other studies of fenced grids. Krebs, Keller and Tamarin (1969) found that fencing populations improved juvenile survival dramatically, but that cropping of adults every two weeks on one of the fenced grids did nothing to increase the index further, in Microtus pennsylvanicus. Hilborn (1974) calculated the index of juvenile s u r v i v a l , adult s u r v i v a l rate, and rate of immigration for f i v e periods on unfenced grids at Haney. He made two c r u c i a l assumptions for h i s estimates of immigration rates: (1) that t r a p p a b i l i t y of young juveniles i s no higher on fenced than on unfenced grids, and (2) that growth rates of young animals are no lower on fenced than on unfenced grids. If one accepts these assumptions, then over f i v e demographic periods in his study, there i s a strong negative c o r r e l a t i o n (-.82) between juvenile s u r v i v a l and adult immigration, contrasted with a positive c o r r e l a t i o n (-77) between juvenile s u r v i v a l and resident adult s u r v i v a l . This r e s u l t suggests, again, that immigration of 88 strange a d u l t s may be a.n important f a c t o r i n reducing j u v e n i l e s u r v i v a l below the l e v e l s i t can a t t a i n i n enclosed p o p u l a t i o n s . In s e v e r a l other rodent s p e c i e s , the importance of immigration by strange a d u l t s to the s o c i a l and demographic processes of r e s i d e n t p o p u l a t i o n s has been documented (Wolfe and Suramerlin, 1968; S c o t t , 1966; Howe and Redfern, 1969; Petrusewicz, 1963; Ginsburg and A l l e e , 1942). However, t h i s i n t e r p r e t a t i o n , t h a t immigration of strange a d u l t s i s a major f a c t o r i n m i c r o t i n e p o p u l a t i o n dynamics, i s at va r i a n c e with the p a t t e r n s observed when movement i s monitored i n areas of empty h a b i t a t . In Microtus pennsylvanicus, Myers and Krebs (1971) found that d i s p e r s a l , measured by c o l o n i z a t i o n of such an area, was freguent d u r i n g the i n c r e a s e phase and r a r e during the d e c l i n e , when j u v e n i l e s u r v i v a l i s lowest. Krebs et a l . , (1975) and H i l b o r n (1974) have rep o r t e d s i m i l a r o b s e r v a t i o n s i n Microtus townsendii. Because r e c r u i t e d l i t t e r s i z e i s at l e a s t p a r t l y a f u n c t i o n of l i t t e r s i z e at b i r t h , a d i s c u s s i o n of the g e n e t i c s of l i t t e r s i z e at b i r t h i n other s p e c i e s may shed some l i g h t upon the p o s s i b i l i t i e s f o r s e l e c t i v e changes i n t h i s t r a i t i n Microtias t o w n s e n d i i . To my knowledge, on l y one study has attempted to measure h e r i t a b i l i t y of l i t t e r s i z e i n a w i l d s p e c i e s . P e r r i n s and Jones (1974) estimated h e r i t a b i l i t y of c l u t c h s i z e i n Great T i t s as .51. (This estimate may, however, be i n f l a t e d by maternal e f f e c t s ) . T h i s value i s c l o s e to the upper l i m i t f o r h e r i t a b i l i t y s e t by the r e p e a t a b i l i t y of l i t t e r s i z e at b i r t h f o r both Microtus townsendii (.48, t h i s study) and Mus (.45, F a l c o n e r , 1960a). In f a c t , however, h e r i t a b i l i t y of l i t t e r s i z e 89 i n Mus i s c o n s i d e r a b l y below t h i s upper l i m i t . F a l c o n e r (1960b), studying a l a b o r a t o r y p o p u l a t i o n of Mus, found a negative estimate of h e r i t a b i l i t y of f i r s t l i t t e r s i z e , owing to maternal e f f e c t s . Only when these e f f e c t s were removed e x p e r i m e n t a l l y c o u l d he i n c r e a s e the estimate of h e r i t a b i l i t y t o .12. Dadlani and Prabhu (1971) found a s i m i l a r s i t u a t i o n with r e s p e c t to l i t t e r weight at b i r t h , a t r a i t c l o s e l y c o r r e l a t e d with l i t t e r s i z e . Within the p o p u l a t i o n , while r e p e a t a b i l i t y of l i t t e r weight was .32, the h e r i t a b i l i t y was only .06. By c o n t r o l l i n g f o r l i t t e r s i z e i n which the mother grew up, they i n c r e a s e d the estimate of h e r i t a b i l i t y to .32. In both these cases, i t i s d o u b t f u l whether the l a r g e r values of h e r i t a b i l i t y f o r l i t t e r s i z e would ever be r e a l i z e d i n a w i l d p o p u l a t i o n of Mus. They appear to be simply a r t i f a c t s of experimental design. 90 SECTION V: RESULTS—CORRELATIONS AMONG RELATIVES IN ECOLOGICALLY IMPORTANT TRAITS BODY SIZE The body s i z e of each animal i n t h i s study was monitored r e g u l a r l y through two measures: width of the s k u l l at i t s widest p a r t , and weight. The f o l l o w i n g a n a l y s i s of some determinants of growth r a t e and body s i z e deals only with the s k u l l width measure, because i t overcomes three of the problems associated with i n t e r p r e t i n g weight changes i n mice. F i r s t , pregnancy causes f l u c t u a t i o n s i n weight. Second, changes i n c o n d i t i o n of the vole f r e q u e n t l y r e s u l t i n weight l o s s , which can make i t d i f f i c u l t to estimate an animal's maximum s i z e from i t s growth curve. The s k u l l width never gets s m a l l e r , though growth rates do f l u c t u a t e i n time. T h i r d , voles tend t o l o s e weight i n l i v e -t r a p s { C h i t t y , pers. com., Iverson and Turner, 1974). The s k u l l width measure i s accurate ( r e p e a t a b i l i t y i s .976, standard e r r o r of r e p e a t a b i l i t y estimate = .008). I t p r e d i c t s body length of both sexes w e l l (the c o r r e l a t i o n c o e f f i c i e n t i s .974 f o r a sample of 31 males, .973 f o r 42 females); and i t i s high l y c o r r e l a t e d with weight i n males during the breeding season (r = .971, d.f. = 28). The c o r r e l a t i o n with weight i n females that were not v i s i b l y pregnant during the breeding 91 season i s not so high, probably because of the weight changes a s s o c i a t e d with e a r l y pregnancy (r = .897, d.f. = 38). Brown (1973) a l s o concludes t h a t s k e l e t a l measures are more u s e f u l than weight i n s t u d y i n g growth p a t t e r n s i n s m a l l mammals. F i g u r e 8 i s a graph of weight as a f u n c t i o n of s k u l l width. Using s k u l l width as an i n d i c a t o r of body s i z e , I asked the f o l l o w i n g q u e s t i o n s i n t h i s a n a l y s i s : 1. What i s the h e r i t a b i l i t y of maximum body s i z e ? 2. What i s the h e r i t a b i l i t y of e a r l y growth r a t e ? 3. Can r e l e v a n t environmental f a c t o r s be i d e n t i f i e d which a f f e c t these t r a i t s ? GROWTH RATE The d a i l y instantaneous growth r a t e f o r each i n t e r v a l between captures was c a l c u l a t e d f o r a l l animals marked i n the study, except when the i n t e r v a l between capt u r e s was g r e a t e r than f o u r weeks. I then t e s t e d f o r e f f e c t s of the f o l l o w i n g f a c t o r s upon a l l d a i l y growth r a t e e s t i m a t e s : sex, p o p u l a t i o n of r e s i d e n c e , three-month p e r i o d , and s k u l l width of the animal at the end of the i n t e r v a l . There was a l i n e a r r e l a t i o n s h i p between the l o g a r i t h m s of instantaneous growth r a t e and s i z e ; a n a l y s i s of c o v a r i a n c e r e v e a l e d t h a t t h i s r e l a t i o n s h i p v a r i e d between the g r i d p o p u l a t i o n s and the breeding e n c l o s u r e animals, and among seasons, but was u n a f f e c t e d by sex. The model f o r d e t e r m i n a t i o n of i n d i v i d u a l estimates of i n s t a n t a n e o u s d a i l y growth r a t e , then, became: 92 Figure 8. Relationship between weight and s k u l l width for a sample of Microtus townsendii taken i n spring, 1974. Obviously pregnant females were excluded. Both regression l i n e s are s i g n i f i c a n t (p < .001) and d i f f e r e n t from one another (p < .001). Standard errors of the regression c o e f f i c i e n t s are given i n parentheses. 9 3 1.1 1 . 2 1 . 3 1 . 4 1 . 5 1 . 6 1 . 7 1 . 8 1 . SKULL WIDTH (CM) Figure 8 94 Growth r a t e •= B(I) x ( s k u l l width) + A (I) + C (J) + E where A i s the p e r i o d constant, I i s the index of the p e r i o d i n which the measurement was made, B i s the s l o p e of the l i n e , J i f the index of the p o p u l a t i o n i n which the animal l i v e d , C i s the p o p u l a t i o n c o n s t a n t , and E i s the d e v i a t i o n of the measurement from the block mean. Having c o r r e c t e d f o r the e f f e c t s of major f a c t o r s a f f e c t i n g growth r a t e , I expressed a l l growth r a t e s as d e v i a t i o n s from the block means (E i n the above formul a ) . I estimated " j u v e n i l e growth r a t e " f o r each animal born i n the e n c l o s u r e s by averaging a l l the o b s e r v a t i o n s f o r that animal duri n g the p e r i o d when i t s s k u l l width was s m a l l e r than 1.60 cm (males) or 1.55 cm (females). These boundaries were chosen f o r two reasons. F i r s t , i t i s at about these s i z e s t h a t the standard e r r o r of the measurement of s k u l l width ceases t o be n e g l i g i b l e with r e s p e c t to the change i n s i z e between c a p t u r e s . Second, p l o t s of untransformed i n s t a n t a n e o u s growth r a t e vs s i z e begin to l e v e l o f f at t h i s p o i n t . Because each estimate of growth r a t e r e q u i r e d at l e a s t two captures f a i r l y c l o s e together i n time, a number of breeding enclosure o f f s p r i n g c o u l d not be i n c l u d e d i n t h i s a n a l y s i s . A l s o , because t h e r e was no e a r l y i n f o r m a t i o n on many of the parents, sample s i z e s were too s m a l l f o r an o f f s p r i n g - o n -midparent r e g r e s s i o n to be worthwhile. However, I c a l c u l a t e d 95 r e g r e s s i o n s f o r j u v e n i l e growth r a t e of o f f s p r i n g on the j u v e n i l e growth r a t e s of dams and s i r e s s e p a r a t e l y . N e i t h e r of these r e g r e s s i o n s was s i g n i f i c a n t , but there was a d i f f e r e n c e between the two r e l a t i o n s h i p s which suggests t h a t maternal e f f e c t s may be important. The c o r r e l a t i o n between o f f s p r i n g and dam i s .147 (19 d.f.) whereas t h a t between o f f s p r i n g and s i r e s i s -.040 (22 d . f . ) . The i n t r a f a m i l y c o r r e l a t i o n t w i t h i n l i t t e r s g i v e s an estimate of h 2 of .455 f o r j u v e n i l e growth r a t e (Table 18). As was d i s c u s s e d above, t h i s estimate of h 2 may be i n f l a t e d by s e v e r a l f a c t o r s — d o m i n a n c e d e v i a t i o n s and e f f e c t s of common environment, i n c l u d i n g maternal e f f e c t s . In order to s o r t out these f a c t o r s , I grouped o f f s p r i n g i n two other ways. F i r s t , i n seven f a m i l i e s , a dam was mated to two or three s i r e s . From a nested a n a l y s i s of v a r i a n c e , I estimated the components of var i a n c e f o r dams and f o r s i r e s w i t h i n dams (Table 19). The component f o r s i r e s c o n t a i n s a l l dominance and common environment e f f e c t s while that f o r dams should be i n f l a t e d by maternal e f f e c t s . Though the varian c e e s t i m a t e s are not s i g n i f i c a n t l y d i f f e r e n t , the d i r e c t i o n of the d i f f e r e n c e i m p l i e s t h a t maternal e f f e c t s are s m a l l . A second approach a l s o helped t o c l a r i f y the c o n t r i b u t i o n of dominance and environmental f a c t o r s to the f u l l - s i b estimate of h 2 . There were growth r a t e o b s e r v a t i o n s f o r f i v e groups of f u l l s i b s , each of which c o n s i s t e d o f two separate l i t t e r s . These f u l l - s i b groups w i l l be r e f e r r e d t o as "mating" groups. To the extent that the estimate of h 2 from l i t t e r s i s i n f l a t e d by common environment e f f e c t s , t h e r e should be a d i f f e r e n c e 96 Table 18. Estimated components of variance f o r juvenile growth rate: within and among l i t t e r s . Standard error of h 2 in parentheses. TABLE 18 Analysis of variance: Source d.f. MS Expected MS Litters 29 .056 2 ^ 2 o l i t t e r s Within 60 .030 a-2 w Components of variance: s 2 = .030 w s 2 . = .009 l i t t e r s t. . = .227 l i t t e r s h 2 ~ .455 (.244) 98 Table 19. Estimated components of variance for juvenile growth rate: l i t t e r s nested within h a l f - s i b f a m i l i e s . Standard errors of estimates in parentheses. TABLE 19 Analysis of variance: Source d.f. MS Expected MS Dams 6 .415 9 ? 2 IT + n'o- . +nb c / , w w o sires o dams Sires 9 .671 rj + n (T . v w o sires Within 17 .332 c r 2 w Components of variance: s 2 = .020 (.006) w s 2. = .032 (.019) sires s 2 = -.006 (.020) dams . 100 Table 20. Estimated components of variance for juvenile growth rate: l i t t e r s nested within matings. Standard errors of estimates i n parentheses. TABLE 20 Analysis of variance: Source d.f. MS Expected MS Matings 4 .046 ? 2 2 C + n' crt. +nbCT „. *w o u l i t t e r s o matings .066 2 , 2 Litters 5 w o l i t t e r s Within 14 .021 w Components of variance: s 2 = .021 (.007) w = -.008 (.010) matings 1 0 2 Figure 9. Regression of juvenile growth rate upon maximum s k u l l width reached by father. Juvenile growth rate i s expressed as deviation from population mean as discussed i n the text. Intercept = -.915 Slope = .541 P < .025 103 104 between the estimate of the l i t t e r s component of va r i a n c e and t h a t of the matings component of v a r i a n c e . Any covar i a n c e of f u l l - s i b s a t t r i b u t a b l e to dominance, however, should i n c r e a s e the components of v a r i a n c e e q u a l l y f o r matings and f o r l i t t e r s . From Table 20 i t appears t h a t the estimate of the component of v a r i a n c e f o r l i t t e r s i s s t r o n g l y i n f l a t e d by common environment e f f e c t s . The l i t t e r s component of va r i a n c e i s comparable i n magnitude to the unexplained component;~however, when groups of v o l e s share the same parents but are heterogeneous i n time of b i r t h , as are the "mating" groups, the a s s o c i a t e d component of v a r i a n c e becomes s m a l l . In an attempt to f i n d the environmental f a c t o r s which might i n f l u e n c e j u v e n i l e growth r a t e i n Microtus townsendii, I t e s t e d the f o l l o w i n g , none of which has an e f f e c t : l i t t e r s i z e at rec r u i t m e n t , s k u l l width of the dam during the l a c t a t i o n p e r i o d , maximum s i z e of the dam, ove r l a p of l a c t a t i o n with subseguent pregnancy, d i f f e r e n t e n c l o s u r e s , and s e v e r a l f i n e r temporal d i v i s i o n s of the year. In a d d i t i o n , the LAP genotype of a vol e does not i n f l u e n c e i t s j u v e n i l e growth r a t e . There was a s i g n i f i c a n t c o r r e l a t i o n , s u r p r i s i n g l y , of j u v e n i l e growth r a t e with the maximum s i z e of the f a t h e r (r = .240, d.f.= 84, P < .025; see Figure 9). T h i s r e s u l t i s anomalous with r e s p e c t to both the other r e s u l t s concerning h e r i t a b i l i t y of j u v e n i l e growth r a t e , and the a n a l y s i s of maximum body s i z e below. MAXIMUM BODY SIZE Microtus townsendii i n the f i e l d never r e a l l y reach an 105 asymptotic body s i z e , as i t i s i n d i c a t e d by s k u l l width, though t h e i r s i z e changes only slowly once they become l a r g e . Because many of the animals born i n the breeding e n c l o s u r e s disappeared while s t i l l growing, I attempted to f i n d an i n d i c a t o r of maximum s i z e which would allow me to i n c l u d e the l i m i t e d data from such i n d i v i d u a l s , while s t i l l d i f f e r e n t i a t i n g them from animals which d i d s u r v i v e long enough to l e v e l o f f i n growth. F o r t u n a t e l y , the time of b i r t h of n e a r l y a l l the enclosure-born animals was known to the nearest week. T h i s made i t p o s s i b l e to compare the maximum s i z e reached by an animal with the s i z e of others i t s own age. The maximum s i z e achieved by an animal was always the l a s t or among the l a s t o b s e r v a t i o n s recorded f o r i t , s i n c e growth r a t e of a s k e l e t a l c h a r a c t e r must be a monotonically i n c r e a s i n g f u n c t i o n . Thus one o b s e r v a t i o n was chosen f o r each animal, the l a r g e s t , c orresponding to i t s age at l a s t capture. In order to compare animals of d i f f e r e n t ages, I regressed t h i s maximum s i z e on age at disappearance, with both v a r i a t e s transformed to lo g a r i t h m s . Analyses of covar i a n c e and v a r i a n c e q u a n t i f i e d the d i f f e r e n c e s among p o p u l a t i o n s and saxes. The model of v a r i a t i o n i n i n d i v i d u a l o b s e r v a t i o n s was thus: Maximum s i z e = B (I) x (age at l a s t capture) + A (I) + C {J) + E where B i s the s l o p e of the r e g r e s s i o n , I i s the index of the p o p u l a t i o n i n which the animal was l i v i n g , A i s the po p u l a t i o n c o n s t a n t . 106 C i s the sex constant, J i s the index o f / t h e i n d i v i d u a l ' s sex, and E i s the remainder. A l l maximum s i z e measures were converted t o the d e v i a t i o n (E) from the expected value f o r an animal of the given sex, age c l a s s , and p o p u l a t i o n . For o b s e r v a t i o n s on s k u l l width of parents i n the -breeding e n c l o s u r e s , t h i s s t a n d a r d i z a t i o n was i m p o s s i b l e , s i n c e t h e i r ages were not known. However, most parents were beyond the stage of r a p i d growth when l a s t captured, so an estimate of maximum s i z e c ould be made from the l a s t f i v e or s i x ob s e r v a t i o n s on each animal. Parents whose s k u l l widths were s t i l l changing r a p i d l y were not i n c l u d e d i n the a n a l y s i s . In a d d i t i o n t o her maximum s i z e , the mother's average s k u l l width at the time of b i r t h and l a c t a t i o n of each l i t t e r was recorded. Table 21 summarizes the r e s u l t s of comparisons among r e l a t i v e s f o r maximum s i z e . Neither the r e g r e s s i o n of o f f s p r i n g on midparent nor t h a t on the s i r e was s i g n i f i c a n t . However, there was a s i g n i f i c a n t r e g r e s s i o n of o f f s p r i n g maximum s i z e on the maximum s i z e of the dam. Suspecting t h a t t h i s might r e p r e s e n t some s o r t of maternal environmental i n f l u e n c e , I d i v i d e d the data up i n t o blocks by the age of the o f f s p r i n g when l a s t captured. There were s i g n i f i c a n t d i f f e r e n c e s i n the s l o p e s of the r e g r e s s i o n of o f f s p r i n g on mother between these b l o c k s , i n d i c a t i n g t h a t t h e maternal i n f l u e n c e does indeed decrease as the o f f s p r i n g grow o l d e r (Figure 10). A simple mechanism by which the mother's s i z e might 1 0 7 Table 21. Relationships among offspring juvenile growth rate, offspring maximum s i z e , and parental s i z e , using s k u l l width as an indicator of body s i z e . Blocks are offspring less than or greater than median age at l a s t capture {see tex t ) . TABLE 21-X variate Y. variate Differences among blocks. Overall regression Overall correlation coefficient Dam's maximum size Offspring maximum . size .< median: a = -.760 b = .434 ^median: a = -.134 b = .079 P < .005 a = -.445 b = .256 P < .001 r = .314 Sire's maximum size Offspring maximum size N.S. N.S. r = .121 Offspring juvenile =growth rate Offspring maximum size Intercepts differ, •• P 4 . -005 a = -.013 b = .093 P < .001 r = .451 Dam's size at time of birth Offspring maximum size N.S. a = -.234 h = .137 P < .01 r = .182 Dam's :•: maximum size Offspring juvenile growth' rate — N.S. r = -.010 Dam's size at time of birth Offspring juvenile growth rate — . N.S. r = -.002 Sire's maximum . size Offspring juvenile growth rate a = -.915 b = .541 P < .025 r = . 2 4 0 109 Figure 10. Regression of maximum s k u l l width reached by offspring upon maximum s k u l l width reached by mother. Offspring values are corrected to deviations from the population mean as described in the text. Upper graph includes offspring which l i v e d to an age of 10 weeks or more: Intercept = -.134 Slope = .079 lower graph includes offspring which were l a s t captured at 9 weeks or l e s s : Intercept = -.760 Slope = .434 P of ov e r a l l regression < .001 P of difference between slopes < .005. 110 . 1 0 5 : .057 00830 - . 0 4 0 4 0890 ca az o_ >—< c n > u _ L U feQ - . 1 3 7 OFFSPRING > MEDIAN AGE AT LAST CAPTURE + + +.+ + + t + 4-• 4 -+ + + + . 105 T - . 1 3 7 OFFSPRING < MEDIAN AGE AT LAST CAPTURE 1 . 6 2 1 . 6 6 1 .7 1 . 7 4 1 .78 MAXIMUM SKULL WIDTH OF DAM (CM) 1 . 8 2 Figure 10 111 Figure 11. Regression of maximum s k u l l width reached by voles born i n the breeding enclosures upon juvenile growth rate. Both variates are expressed as deviations from population means as discussed in the text. Intercept = -.013 Slope = .093 P < .001 112 + + + + 4" 4" + + 4" + + .+++ 4- + + 4-+ ++ > 4~. 4-+ 4-4- + •++ + + + ++• • , 4- •  T + + + + + 4-4- 4-4-+ 4-4-4--H-4-4-4-H h - . 2 6 9 - . 0 9 4 9 0 7 9 1 . 2 5 3 4 2 7 JUVENILE GROWTH RATE (DEVIATION FROM POPULATION MEAN) Figure 11 113 i n f l u e n c e the s i z e of her o f f s p r i n g e a r l y i n t h e i r l i v e s suggested i t s e l f : l a r g e mothers might produce more milk than s m a l l mothers, r e s u l t i n g i n f a s t e r growing n e s t l i n g s . T h i s advantage i n s i z e would c a r r y through the f i r s t few months of independent l i f e . In a d d i t i o n to t h e i r s i z e s , the growth r a t e s of w e l l - n o u r i s h e d j u v e n i l e s might continue to be above average f o r some time a f t e r weaning. From t h i s h y p o t h e s i s , one would p r e d i c t the f o l l o w i n g ; f i r s t , t h a t the s i z e of the mother a t the time of b i r t h and l a c t a t i o n should be more c l o s e l y r e l a t e d to o f f s p r i n g s i z e than should her maximum s i z e . Second, j u v e n i l e growth r a t e should be s t r o n g l y c o r r e l a t e d with both the mother's s i z e and the ,size of the o f f s p r i n g , p a r t i c u l a r l y i n young animals. The r e s u l t s summarized i n Table 21 do not support t h i s h y p o t h e s i s . F i r s t , while j u v e n i l e growth r a t e does indeed p r e d i c t the maximum s i z e of an animal (see Figure 11), i t s p r e d i c t i o n i s e q u a l l y as good f o r o f f s p r i n g which disappeared when o l d as f o r those which disappeared when young. T h i s p a t t e r n of i n f l u e n c e d i f f e r s from that manifested by the r e g r e s s i o n on maximum s i z e of the mother. In a d d i t i o n , the c o r r e l a t i o n of o f f s p r i n g maximum s i z e with t h a t of the mother at the time of b i r t h and l a c t a t i o n i s weaker r a t h e r than s t r o n g e r than the c o r r e l a t i o n with the maximum s i z e of the mother. U n l i k e the c o r r e l a t i o n between maximum s i z e measures, t h i s r e l a t i o n s h i p does not change s i g n i f i c a n t l y with the age at l a s t c apture of the o f f s p r i n g , though the slope i s s m a l l e r f o r o f f s p r i n g which disappear when o l d . F i n a l l y , though j u v e n i l e growth r a t e i s r e l a t e d to the s i z e of an animal at a l l ages. 1 14 there i s no correlation at a l l between juvenile growth rate and the size of the mother, either at her maximum size or at the time of birth. Indeed, the only influence on juvenile growth rate by either parent appears to be the sire's maximum size (Figure 9) . This weak relationship i s d i f f i c u l t to reconcile with the rest of the pattern, because any genetic or environmental influence which makes offspring juvenile growth rate predictable from the father's phenotype should result in a relationship at least as strong with the mother's phenotype. Table 21 shows that this is not the case. DISCUSSION This study has identified two c r i t i c a l periods in a vole's l i f e which are important in determining i t s body size relative to that of other animals of the same sex and age group in the population. During i t s period of dependence on i t s mother (the f i r s t two to three weeks of i t s l i f e ) , the animal's growth i s determined in part by the mother's size, or perhaps more accurately, by some factor whih also influences her maximum size. The effect of this factor is evident until some point between nine and twelve weeks of age. The residual influence does not operate by increasing the growth rate of the animal after weaning, but rather simply by determining the baseline from which i t s post-weaning growth continues. After weaning, some other factor, uncorrelated with the size of the mother, determines the juvenile growth rate of the 115 animal. Together, between the ages of three and ten or eleven weeks, the mother's maximum s i z e and the j u v e n i l e growth r a t e account f o r 33% of the v a r i a t i o n i n s i z e (N = 42, P of m u l t i p l e c o r r e l a t i o n < .005). However, a f t e r t h i s p e r i o d , the i n f l u e n c e of the mother's maximum s i z e d i m i n i s h e s , while the j u v e n i l e growth r a t e remains p r e d i c t i v e ' of body s i z e throughout the animal's l i f e . There are two p o s s i b l e reasons f o r the c o r r e l a t i o n between j u v e n i l e growth r a t e and maximum s i z e . F i r s t , a r a p i d j u v e n i l e growth r a t e could r e s u l t i n an animal which i s al r e a d y l a r g e r than i t s c o h o r t s and remains so simply because they do not catch up. Growth r a t e s l a t e r i n l i f e c o u l d be completely u n c o r r e l a t e d with j u v e n i l e growth r a t e . F a c t o r s which might cause such a r e l a t i o n s h i p are n u t r i t i o n or s o c i a l i n t e r a c t i o n s d u r i n g t h i s period of e a r l y growth. Second, some f a c t o r i n t r i n s i c to the i n d i v i d u a l might cause i t to grow more r a p i d l y than average throughout i t s l i f e . Mechanisms at the p h y s i o l o g i c a l l e v e l i n c l u d e hormonal l e v e l s or e f f i c i e n c y at using food; these might be i n f l u e n c e d by the animal's genotype, or by i t s s o c i a l s t a t u s , i f t h a t were f a i r l y c o nstant over time. In f a c t , both these reasons f o r the c o r r e l a t i o n between j u v e n i l e growth r a t e and maximum s i z e appear to be v a l i d i n Microtus townsendii. When j u v e n i l e growth r a t e , expressed here as d e v i a t i o n s from the p o p u l a t i o n and sea s o n a l means, i s compared with o b s e r v a t i o n s from l a t e i n l i f e , the r e p e a t a b i l i t y of growth r a t e i s .257 (standard e r r o r of r e p e a t a b i l i t y estimate = .119, N = 78). T h i s value of r e p e a t a b i l i t y g i v e s the upper l i m i t of the g e n e t i c d etermination of growth r a t e , and i n d i c a t e s 1 1 6 that genes and other f a c t o r s i n t r i n s i c to the animal are r e s p o n s i b l e f o r about 25% of the v a r i a b i l i t y i n s i n g l e measurements of growth rate d e v i a t i o n . In l i g h t of the obvious complexity of the d e t e r m i n a t i o n of both body s i z e and growth r a t e s , we might not expect to f i n d much a d d i t i v e g e n e t i c v a r i a n c e f o r maximum s i z e . Despite t h i s e x p e c t a t i o n , the upper l i m i t s f o r h e r i t a b i l i t y of both j u v e n i l e growth r a t e ( f u l l - s i b h 2 = .455) and o v e r a l l growth r a t e (H = .257) suggest t h a t t h e r e may be some g e n e t i c v a r i a t i o n f o r these t r a i t s i n the p o p u l a t i o n . The most f r u i t f u l l e v e l f o r g e n e t i c a n a l y s i s may w e l l be the p h y s i o l o g i c a l one, when the determinants of growth have been i d e n t i f i e d . However, n a t u r a l s e l e c t i o n a c t s on phenotypes, and not on the simple components of t r a i t s which are amenable to g e n e t i c a n a l y s i s . At t h i s g r o s s e r l e v e l , even without a good measure of V(A)/?(P) , i t may be p o s s i b l e i n a l i m i t e d way to p r e d i c t responses to s e l e c t i o n f o r body s i z e and growth r a t e , s i n c e o f f s p r i n g do tend to resemble t h e i r mothers i n maximum s i z e and t h e i r s i b l i n g s i n growth r a t e . In the case of maximum s i z e , p r e d i c t i o n of the o f f s p r i n g phenotypic d i s t r i b u t i o n from t h a t of the breeding mothers, using the offspring-dam r e g r e s s i o n above, would be most u s e f u l during the f i r s t ten or eleven weeks of l i f e of the o f f s p r i n g . P r e d i c t i o n of responses to repeated or c o n t i n u o u s l y a p p l i e d s e l e c t i o n pressures would be u n r e l i a b l e , s i n c e the other f a c t o r s which i n f l u e n c e growth r a t e overwhelm the maternal i n f l u e n c e s i n o l d e r o f f s p r i n g . In the case of growth r a t e , we can estimate the extent to 1 17 which s e l e c t i o n pressures on t h i s t r a i t w i l l tend t o f a v o r or e l i m i n a t e whole f a m i l i e s of s i b l i n g s ; however, the weak c o r r e l a t i o n between o f f s p r i n g and dams f o r t h i s t r a i t i s probably not u s e f u l f o r p r e d i c t i o n s of response a c r o s s g e n e r a t i o n s . C o n c l u s i o n s concerning. E2£uiiition c y c l e s . D i f f e r e n c e s i n body s i z e between peak and d e c l i n i n g p o p u l a t i o n s have been noted i n numerous s t u d i e s of m i c r o t i n e p o p u l a t i o n s . U s u a l l y , overwintered v o l e s from peak p e r i o d s are heavier than those from d e c l i n i n g p o p u l a t i o n s , though o c c a s i o n a l l y " i n c r e a s e " animals are heavy, as w e l l . T h i s p a t t e r n cannot be e x p l a i n e d as a simple f u n c t i o n of d i f f e r i n g s u r v i v a l r a t e s , but may i n v o l v e v a r i a t i o n i n both growth r a t e s and maximum s i z e (Krebs and Myers, 1974). T h i s v a r i a t i o n i n s i z e might suggest that animals i n d i f f e r e n t phases of the c y c l e are g e n e t i c a l l y d i f f e r e n t . C h i t t y and Phipps (1966) and Newson and C h i t t y (1962) d e s c r i b e s e v e r a l experiments i n which v a r i a t i o n i n growth p a t t e r n appeared to-be maintained i n the l a b o r a t o r y , even i n o f f s p r i n g of f i e l d animals. Krebs (1964) found s i g n i f i c a n t d i f f e r e n c e s i n the parameters of the s k u l l - b o d y r e g r e s s i o n among phases of a lemming c y c l e , and Tamarin and Krebs (1969) c i t e changes i n the growth r a t e - s i z e r e g r e s s i o n over the c y c l e . Another mechanism f o r the c y c l i c s i z e changes, which i s not incompatible with genotypic v a r i a t i o n , has been suggested by Iverson and Turner (1974): that growth i n a d u l t voles takes place only when hormone l e v e l s are e l e v a t e d during the breeding season. Because the breeding season i s t y p i c a l l y prolonged during the i n c r e a s e and 118 e a r l y peak phases, v o l e s would tend to be l a r g e r during these p e r i o d s . Krebs, K e l l e r , and Tamarin (1969), Brown (1973), and Krebs (196 6) have a l l reported an a s s o c i a t i o n of t h i s nature. How r e a l i s t i c i s the hypothesis t h a t the v a r i a t i o n i n s i z e i n m i c r o t i n e p o p u l a t i o n s i s l a r g e l y g e n e t i c a l l y mediated, i n l i g h t of the r e s u l t s of t h i s and other s t u d i e s ? S t u d i e s of the growth of l a b o r a t o r y mice and r a t s c o n f l i c t i n t h e i r e s t i m a t i o n s of the r e l a t i v e importance of a d d i t i v e g e n e t i c v a r i a n c e and maternal e f f e c t s on growth r a t e and body s i z e . Both f a c t o r s appear to be important under c e r t a i n c o n d i t i o n s . However, the subsequent common environmental i n f l u e n c e s on j u v e n i l e growth r a t e which t h i s study has detected i n Microtus townsendii have not been observed i n l a b o r a t o r y mice. Falconer (1954) estimated an o v e r a l l r e a l i z e d h e r i t a b i l i t y of .346 In an experiment i n which he s e l e c t e d f o r both l a r g e and s m a l l body s i z e . The response d i f f e r e d i n the two l i n e s , however, and F a l c o n e r r e p o r t e d s i g n i f i c a n t dominance d e v i a t i o n s f a v o r i n g l a r g e s i z e . He a l s o found c o r r e l a t e d responses i n l i t t e r s i z e , t a i l l e n g t h , and l a c t a t i o n e f f i c i e n c y . J i n k s and Broadhurst (1965) r e p o r t an average value of .65 f o r h e r i t a b i l i t y of body weight i n r a t s , u s i n g s e v e r a l d i f f e r e n t methods of e s t i m a t i o n . K i d w e l l and Howard, (1969), K i d w e l l , Howard, and L a i r d (1969), K i d w e l l (1973), and K i d w e l l and Howard (1970), i n a d i a l l e l a n a l y s i s of f i v e i n b r e d s t r a i n s of Mus, r e p o r t e d s i g n i f i c a n t maternal e f f e c t s i n the f i r s t seven weeks of l i f e , which accounted f o r as much as 26% of the v a r i a n c e i n weight and 33% of the growth r a t e v a r i a n c e . A d d i t i v e g e n e t i c v a r i a n c e f o r 1 1 9 weight at a given age, however, was estimated as e s s e n t i a l l y n i l by these authors. This r e s u l t agrees rather well with the pattern discussed here, but not with that described by Falconer. Falconer ( 1 9 6 5 ) discusses another si t u a t i o n in which a population showed rapid response to selection i n spite of an i n i t i a l estimate of h 2 as zero for a t r a i t ( l i t t e r s i z e ) , owing to maternal effects in the opposite d i r e c t i o n from genetic influences. Such disparate r e s u l t s point up the d i f f i c u l t i e s i n comparing studies c a r r i e d out with d i f f e r e n t experimental designs in the laboratory, where no attempt i s made to follow the guidelines suggested by natural population structures and selection pressures.. Christian and LeMunyan ( 1 9 5 7 ) have reported another study of the importance of maternal effects upon growth rates of young mice. They showed that extreme crowding for six weeks reduced the e f f i c i e n c y of l a c t a t i o n in females and that t h i s e f f e c t carried through two generations of offspring, as well, though at a diminishing rate. This study suggests again that the hormonal responses which serve as s t i m u l i to growth are largely determined by the l i t t e r ' s common environment. Similar results are reported by Widdowson and Kennedy ( 1 9 6 2 ) and Widdowson and McCance ( 1 9 6 3 ) . From the re s u l t s of t h i s work and the laboratory studies discussed above, we can conclude that the size differences observed in adult voles i n cycling populations are probably determined by common environment factors which influence the juvenile growth rate and thus the subsequent body s i z e , rather than by additive genetic variance. 120 SUMMARY Two factors, common to littermates, influence body size. One, associated with the mother's maximum s i z e , a f f e c t s offspring size in the f i r s t two to three months of l i f e . The other factor determines juvenile growth rate, and hence body size throughout the vole's l i f e . There seems to be l i t t l e additive genetic contribution to v a r i a b i l i t y in these t r a i t s , which suggests that changes i n body size over population fluctuations are not genetically mediated i n Microtus 1ownsendii. 121 REPRODUCTIVE CHARACTERS WINTER BREEDING An index of tendency to breed during winter was calculated, where possible, f o r a l l parents and offspring from the breeding e n c l o s u r e s . This index, the "index of winter reproductive c o n d i t i o n " , was the p r o p o r t i o n of captures between November 1 and February 28 at which the v o l e was breeding: males with s c r o t a l t e s t e s ; females l a c t a t i n g , pregnant, or with p e r f o r a t e v a g i n a l o r i f i c e . The p o p u l a t i o n was v a r i a b l e i n t h i s t r a i t ; observed values ranged from 0 to 1. In a d d i t i o n to the above index of c o n d i t i o n , an "index of winter r e p r o d u c t i v e e f f o r t " was c a l c u l a t e d f o r each parent. T h i s index was the number of l i t t e r s (both s u c c e s s f u l and unsuccessful) produced by t h a t i n d i v i d u a l per week, between November and February. These i n d i c e s were a l t e r e d by the angular transform and t e s t e d f o r e f f e c t s of p o p u l a t i o n of r e s i d e n c e and sex. There were d i f f e r e n c e s only between the sexes, and a l l i n d i c e s were t r e a t e d as d e v i a t i o n s from the means. Because the data were f a r from normally d i s t r i b u t e d , I could not estimate h e r i t a b i l i t y of the index of winter r e p r o d u c t i v e c o n d i t i o n by the u s u a l parametric procedures. However, the r e s u l t s from non-parametric t e s t s were unambiguous. F i r s t , a K r u s k a l - W a l l i s a n a l y s i s of v a r i a n c e r e v e a l e d t h a t there were no d i f f e r e n c e s among l i t t e r s i n the index of winter 122 r e p r o d u c t i v e c o n d i t i o n (P = .84, d.f. = 58). Second, K e n d a l l and Spearman c o r r e l a t i o n c o e f f i c i e n t s ranged between -.03 and -.09 f o r c o r r e l a t i o n s between o f f s p r i n g index of winter r e p r o d u c t i v e c o n d i t i o n and the i n d i c e s of both e f f o r t and c o n d i t i o n f o r e i t h e r or both parents (N = 40). C l e a r l y the tendency of an i n d i v i d u a l Microtus townsendii to breed during winter i s not i n h e r i t e d to any s i g n i f i c a n t e x t e n t . AGE AT PUBERTY Because the week of b i r t h of the animals born i n the breeding enclosures was known, i t was p o s s i b l e to estimate the age at puberty f o r most of them. T h i s was d e f i n e d as the age at which an animal f i r s t reached breeding c o n d i t i o n , e i t h e r p e r f o r a t e v a g i n a l o r i f i c e i n females or t e s t e s s c r o t a l i n males. E f f e c t s of season of b i r t h , p o p u l a t i o n of r e s i d e n c e , and sex were a l l s i g n i f i c a n t , and each o b s e r v a t i o n was adjus t e d a c c o r d i n g l y . A f t e r e f f e c t s of three-month seasons were removed, t h e r e were s t i l l s i g n i f i c a n t d i f f e r e n c e s among f i n e r d i v i s i o n s of time. Therefore an a n a l y s i s of varia n c e with l i t t e r s nested w i t h i n t h e i r four-week p e r i o d s of b i r t h provided s t a t i s t i c s f o r e s t i m a t i o n of components of v a r i a n c e and i n t r a f a m i l y c o r r e l a t i o n s . Table 22 shows t h a t , even w i t h i n these four-week p e r i o d s , members of l i t t e r s tend t o resemble one another s t r o n g l y , with an estimated h e r i t a b i l i t y of .549. T h i s i s onl y an upper bound f o r the true h e r i t a b i l i t y , however, because i t i s i n f l a t e d by both dominance d e v i a t i o n s and e f f e c t s of common environment. 123 Table 22. Estimated components of variance for age at puberty: l i t t e r s nested within four-week periods. Standard error of h 2 in parentheses. TABLE 22 Analysis of variance: Source d.f. MS'. Expected MS 4-week period 10 32.783 2 2 2 (f + n' rr^ . + nb <T . j o w l i t t e r s o period Litters • 40 15.121 2 2 w o l i t t e r s Within 88 8.175 2 ^w Components of variance: S w = 8-l75 s 2 ers 3-507 8 2 Periods = *-093 1Utters = -275 h £ .549 (.203) 1 2 5 Table 23. Estimated components of variance for age at puberty l i t t e r s nested within h a l f - s i b f a m i l i e s . Standard errors o estimates in parentheses. TAELE 23 Analysis of variance: Source d.f. MS Expected MS Dams 7 .359 2 2 2 <r + n'o- . + nb c r , w o s i r e s o dams Sires 10 .486 2 , _2 v w o s i r e s Within 31 .320 Components of variance: s 2 = .320 (.079) w s 2 . = .073 (.093) s i r e s s 2 =-.033 (.085) dams 127 Table 24. Estimated components of variance f o r age at puberty: l i t t e r s nested within matings. Standard errors of estimates i n parentheses. TABLE 24 Analysis of variance: Source d.f. MS . Expected MS Matings 4 .597 *l + l i t t e r s + n b o ^ matings 2 ' 2 Litters 5 .590 O'w + V l i t t e r s Within 15 .360 Components of variance: s 2 = .360 (.123) w s 2 . = .102 (.150) l i t t e r s z . = -.003 (.219) matings 129 The r e a l i z e d breeding design was inadequate to d i s t i n g u i s h c o n c l u s i v e l y between these causes of high i n t r a - f a m i l y c o r r e l a t i o n (dominance, common environment, and a d d i t i v e g e n e t i c d e v i a t i o n s ) . However, two l i n e s of evidence suggest t h a t most of the resemblance among f u l l - s i b s i s a t t r i b u t a b l e to common environment e f f e c t s . F i r s t , i n e i g h t f a m i l i e s the mother was mated with two or th r e e d i f f e r e n t males. A n a l y s i s of v a r i a n c e with s i r e s nested w i t h i n dams y i e l d e d the components of va r i a n c e i n Table 23. The i n t r a f a m i l y c o r r e l a t i o n " t " f o r h a l f s i b s a s s o c i a t e d with dams estimates 1/4 of the h e r i t a b i l i t y , while t h a t f o r s i r e s i s e s s e n t i a l l y a f u l l - s i b c o r r e l a t i o n , i n f l a t e d by both dominance and common environment. The l a r g e standard e r r o r on the s i r e component of v a r i a n c e prevents us from c o n c l u d i n g t h a t the s i r e component and dam component are s i g n i f i c a n t l y d i f f e r e n t . However, the d i r e c t i o n of the d i f f e r e n c e suggests the f o l l o w i n g i n t e r p r e t a t i o n s : (1) Because the dam component c o n t a i n s both V(A) and any maternal e f f e c t s which are c o n s i s t e n t over time, these are probably s m a l l ; (2) The s i r e component contains' V (A) , V(Ec ) , and V (D), of which the l a s t two are probably l a r g e r e l a t i v e to V (A) . The second piece of evidence which l e a d s us to suspect t h a t common environment e f f e c t s might be r e s p o n s i b l e f o r most of the f u l l - s i b c o r r e l a t i o n i s a comparison of l i t t e r s which shared both parents. Table 24 presents the r e s u l t s of an a n a l y s i s of va r i a n c e i n which l i t t e r s were nested w i t h i n matings. Again, though we cannot show s i g n i f i c a n t d i f f e r e n c e s between the component of va r i a n c e f o r l i t t e r s and that f o r f u l l - s i b groups. 130 a t e n t a t i v e c o n c l u s i o n , c o n s i s t e n t with the above a n a l y s e s , can be drawn: the f u l l s i b groups are s i m i l a r to l i t t e r s i n V(A), V (D) , and r e p e a t a b l e maternal e f f e c t s . However, l i t t e r s alone share other common environment e f f e c t s . I t appears, then, t h a t the r a t h e r l a r g e estimate of h 2 from l i t t e r s {Table 22) i s almost e n t i r e l y a t t r i b u t a b l e t o the e f f e c t s of the shared environment of l i t t e r m a t e s . Maternal i n f l u e n c e s may be important here, but they are not c o n s i s t e n t over time, w i t h i n a mother. DISCUSSION Both the aspects of r e p r o d u c t i o n analyzed here (tendency to breed i n winter and age at puberty) have been d i f f i c u l t t o measure i n most m i c r o t i n e p o p u l a t i o n s . Enough evidence has accumulated, though, to suggest that they may be important i n causing population c y c l e s i n M i c r o t u s . Winter breeding f r e q u e n t l y , but not always, accompanies the i n c r e a s e phase (Krebs and Myers, 1974), and i t i s not e a s i l y e x p l a i n a b l e by any of the obvious f a c t o r s e x t r i n s i c t o the p o p u l a t i o n ( K e l l e r and Krebs, 1970)., From t h i s study, i t appears u n l i k e l y t h a t the tendency f o r winter reproduction i s a g e n e t i c a l l y determined a t t r i b u t e . Estimates of age at puberty i n c y c l i n g p o p u l a t i o n s have u s u a l l y depended upon weight as an i n d i c a t o r of age; however, such measures confound growth r a t e and maturation r a t e . Krebs and Myers (1974) conclude that age at puberty does i n c r e a s e i n peak p o p u l a t i o n s , though there i s no c o n c l u s i v e evidence t h a t 131 expanding p o p u l a t i o n s d i f f e r from d e c l i n i n g ones i n t h i s r e s p e c t . C h r i s t i a n (1971a) has proposed the hypothesis t h a t age at puberty may be a c r u c i a l v a r i a b l e causing p o p u l a t i o n c y c l e s . The c o n c l u s i o n drawn from the present study, that age at puberty i s i n f l u e n c e d by the e a r l y environment of an animal, i s c o n s i s t e n t with s e v e r a l published o b s e r v a t i o n s . Environmental i n f l u e n c e s upon maturation are well-documented i n mammals ( S a d l e i r , 1969a, 1969b), but the f a c t o r s of i n t e r e s t here are those shared s p e c i f i c a l l y by the members of a l i t t e r . N u t r i t i o n , e i t h e r pre- or post-weaning, can i n f l u e n c e age a t puberty i n s e v e r a l s p e c i e s ( S a d l e i r , 196 9b; C h r i s t i a n and LeMunyan, 1957). Maternal hormones c r o s s i n g the pl a c e n t a might have permanent e f f e c t s on o f f s p r i n g r e p r o d u c t i o n s i m i l a r t o those observed i n r a t s by G o r s k i and Barraclough (1963). The b e h a v i o r a l m i l i e u of the f a m i l y , e s p e c i a l l y the mother's behavior, may be i n v o l v e d , as w e l l . Age at puberty i s important both t o i n d i v i d u a l f i t n e s s and to p o p u l a t i o n dynamics (Schaffer and Tamarin, 1973). Nat u r a l s e l e c t i o n upon t h i s t r a i t may t h e r e f o r e s t i l l be an important f o r c e i n the g e n e t i c s t r u c t u r e o f Microtias townsendii ( p o p u l a t i o n s , i n s o f a r as i t w i l l tend t o a c t upon whole f a m i l i e s . Whether or not the response to s e l e c t i o n i s d i r e c t i o n a l , however, depends upon the c o r r e l a t i o n between o f f s p r i n g and parents, r a t h e r than t h a t among s i b l i n g s , estimated here. SUMMARY An important component of the demography of m i c r o t i n e 1 3 2 populations, tendency of individuals to breed i n winter, appears to have no s i g n i f i c a n t genetic basis, and littermates do not resemble one another i n t h i s a t t r i b u t e . However, the common environment s p e c i f i c to l i t t e r s does influence age at puberty, with the r e s u l t that s i b l i n g s are more s i m i l a r than unrelated in d i v i d u a l s for t h i s t r a i t . Selection upon age at puberty may thus have interesting genetic consequences, but would not necessarily r e s u l t in a d i r e c t i o n a l response. / 1 3 3 ESTIMATION OF CORRELATIONS AMONG RELATIVES IN DISPERSAL TENDENCY D i s p e r s a l tendency i s here d e f i n e d as the p r o b a b i l i t y t h a t an i n d i v i d u a l w i l l a t some p o i n t move o u t s i d e the area sampled by the t r a p p i n g g r i d . No d i r e c t measure of d i s p e r s a l tendency was made on the i n d i v i d u a l v o l e s i n t h i s study; however, an i n d i r e c t measure was made p o s s i b l e by the f a c t t h at o f f s p r i n g from the breeding e n c l o s u r e s were r e l e a s e d on both fenced and unfenced g r i d s : i f d i s p e r s a l tendency i s a t r a i t shared by s i b l i n g s , then one ought to observe a higher w i t h i n - f a m i l y c o r r e l a t i o n f o r l e n g t h of r e s i d e n c e i n the po p u l a t i o n on the unfenced g r i d than on the fenced g r i d s . The f o l l o w i n g e x p r e s s i o n s show the reason f o r t h i s p r e d i c t i o n : on a fenced g r i d , disappearance of an animal must be due to i t s death, but on an unfenced g r i d , disappearance can be caused by e i t h e r death or movement o f f the g r i d . Now, the i n t r a f a m i l y c o r r e l a t i o n t f o r l e n g t h of r e s i d e n c e on the g r i d w i l l be t (LR) = s 2 (B) / s 2 (T) where s 2(B) i s the between-family component of va r i a n c e i n l e n g t h of re s i d e n c e and s 2 (T) i s the t o t a l v a r i a n c e i n length of r e s i d e n c e . On a fenced g r i d , s 2 (B) f o r l e n g t h of r e s i d e n c e equal to s 2(B,death) i . e . , the component expressing the tendency of l i t t e r m a t e s to d i e at a s i m i l a r age. However, on an unfenced g r i d , s 2 (B) i s the sum of two components: s 2(B,death) and s 2 ( B , d i s p e r s a l ) , where the l a t t e r expresses the tendency f o r l i t t e r m a t e s to d i s p e r s e at a s i m i l a r age. I t i s t h i s second 134 term which w i l l i n c r e a s e the value of t (LR) on an unfenced g r i d , i f l i t t e r m a t e s are s i m i l a r i n t h e i r tendency to leave the g r i d . Table 25 presents the estimates of components of variance and the i n t r a f a m i l y c o r r e l a t i o n among l i t t e r m a t e s . Two estimates are given f o r the fenced g r i d s : the f i r s t i n c l u d e s only the period during which l i t t e r s were being released e q u a l l y on unfenced G r i d AA and fenced G r i d L. The second i n c l u d e s a l l data from the fenced g r i d s . This second estimate, though not s t r i c t l y comparable to that from Grid AA because i t covers a longer span of time (two f u l l years i n s t e a d of one) has the advantage of having a considerably smaller standard e r r o r associated with t . The value of t estimated from g r i d AA i s indeed higher than e i t h e r of the fenced g r i d estimates, and i t d i f f e r s from the second fenced g r i d estimate by more than two standard e r r o r s . These r e s u l t s are c o n s i s t e n t with the hypothesis that f a m i l y members resemble one another i n tendency to leave a population. D I S C U S S I O N Movements of i n d i v i d u a l s i n t o vacant h a b i t a t have been shown to be non-random with respect to phase of the c y c l e , and age, sex, and e l e c t r o p h o r e t i c genotype of i n d i v i d u a l s of s e v e r a l species (Myers and Krebs, 1971). The pattern appears to hold f o r Microtias tpwnsendii, as w e l l , (Krebs et a l . , 1975). Movement ( e s p e c i a l l y i n t o poor habitat) may i n c r e a s e the r i s k of death. Even i f i t i s not associated with m o r t a l i t y , i t c e r t a i n l y plays an important r o l e i n determining the genetic 1 3 5 Table 25. Estimated components of v a r i a n c e f o r length of r e s i d e n c e on a g r i d , w i t h i n and between l i t t e r s . F i r s t a n a l y s i s i n v o l v e s o f f s p r i n g r e l e a s e d on unfenced G r i d AA, from September, 1973, through August, 1974. Second a n a l y s i s i n v o l v e s o f f s p r i n g r e l e a s e d on fenced G r i d L, from September, 1973, through August, 1974. T h i r d a n a l y s i s i n c l u d e s a l l o f f s p r i n g r e l e a s e d on the fenced g r i d s , from September, 1972, through August, 1974. Standard e r r o r s of i n t r a f a m i l y c o r r e l a t i o n s (tj given i n parentheses. TABLE 25 UNFENCED GRID, September, 1973-August, 1974 Source d.f. MS ' . Expected MS Components of variance Between l i t t e r s Within l i t t e r s 18 37 .152 .041 2 2 v w 0 l i t t e r s c r 2 w s 2 . „ = .067 l i t t e r s s 2 = .041 w t = .623 (.115) FENCED GRID L, September, 1973 - August, 1974 Source d.f. MS Expected MS Components of variance Between j 2 2 l i t t e r s 21 .193 + n 0 a l i t t e r s s,. = .047 l i t t e r s Within 0 s 2 = .052 w t = .476 (.127) l i t t e r s • 45 .052 FENCED GRIDS L AND 0, September, 1972 - August, 1974 Source d.f. MS Expected MS Components of variance Between l i t t e r s 44 .134 °"w + V l i t t e r s s 2 , = .026 l i t t e r s Within l i t t e r s 109 .044 s 2 = .044 w t = .375 (.082) 137 s t r u c t u r e of the p o p u l a t i o n . The "fence e f f e c t " d e s c r i b e d by Krebs, K e l l e r , and Tamarin (1969) may be a t t r i b u t a b l e t o the f a i l u r e of animals to leav e the p o p u l a t i o n or to the l a c k of d i s r u p t i o n by a d u l t s moving i n t o and through the p o p u l a t i o n . T h e r e f o r e , i t i s s i g n i f i c a n t that groups of s i b l i n g s are a l i k e i n tendency to l e a v e the trapped p o p u l a t i o n . I f t h i s i s only a common environment e f f e c t , i t w i l l s t i l l have a profound i n f l u e n c e upon p a t t e r n s o f gene flow and d r i f t i n M i c r o t u s £ oiaiLSMii p o p u l a t i o n s , and i f i t does i n v o l v e e i t h e r a phenotypic or a genot y p i c resemblance among o f f s p r i n g and parents, i t may prove to be a powerful f o r c e f o r d i r e c t i o n a l s e l e c t i o n , as w e l l . These r e s u l t s should be i n t e r p r e t e d with c a u t i o n , f o r s e v e r a l reasons. F i r s t , a proper experimental design would i n v o l v e r e p l i c a t e s f o r both the fenced and unfenced g r i d s , with c o r r e s p o n d i n g l y l a r g e r sample s i z e s . As i t i s , there i s no estimate of within-treatment (fenced vs unfenced) v a r i a n c e f o r the parameter t . Second, there are probably other d i f f e r e n c e s between fenced and unfenced g r i d s , p o s s i b l y i n l e v e l s and kinds of p r e d a t i o n , and almost c e r t a i n l y i n s o c i a l s t r u c t u r e . In p a r t i c u l a r , the f l u i d i t y of the s o c i a l s t r u c t u r e i n terms of numbers of t r a n s i e n t voles (immigrants) moving through the p o p u l a t i o n must be q u i t e d i f f e r e n t . Therefore we cannot conclude t h a t e m i g r a t i o n i s e n t i r e l y r e s p o n s i b l e f o r the d i f f e r e n c e s i n i n t r a -f a m i l y c o r r e l a t i o n s between the p o p u l a t i o n s . Whatever the mechanism may be, however, i t appears to i n f l u e n c e r e s i d e n c e time i n the p o p u l a t i o n d i f f e r e n t i a l l y among 1 3 8 f a m i l i e s . Fencing a p o p u l a t i o n , then, e v i d e n t l y has the e f f e c t of reducing the d i f f e r e n c e s i n f i t n e s s among f a m i l i e s . T h i r d , the data are i n s u f f i c i e n t i n t h i s case to allow t e s t i n g of groups of s i b l i n g s or h a l f - s i b s beyond l i t t e r s . Hence, we are unable t o determine how much of the l a r g e i n t r a f a m i l y c o r r e l a t i o n i s a t t r i b u t a b l e to a d d i t i v e g e n e t i c v a r i a n c e , how much t o the common environment of the l i t t e r , and how much to dominance. I s h a l l d i s c u s s below evidence f o r i n t e r a c t i o n s among mothers and young, which may i n f l u e n c e movement from the nest soon a f t e r weaning. Though the d i s p e r s a l tendency measured here manifests i t s e l f at a l a t e r age and probably i n v o l v e s l o n g e r movements, i t may w e l l be s u b j e c t to s i m i l a r maternal and common environment i n f l u e n c e s . SUMMARY Voles r e l e a s e d onto an unfenced g r i d resemble t h e i r s i b l i n g s more s t r o n g l y i n l e n g t h of r e s i d e n c e than do vo l e s r e l e a s e d onto fenced g r i d s . T h i s r e s u l t could be i n t e r p r e t e d to mean that tendency to move from an area i s shared among f a m i l y members. T h i s phenomenon may have profound i m p l i c a t i o n s f o r the po p u l a t i o n s t r u c t u r e of Microtus f o w n s e n d i i . 1 3 9 BEHAVIOR The t e s t used to measure a c t i v i t y and a g o n i s t i c behavior of a d u l t v o l e s has been d e s c r i b e d i n the Methods s e c t i o n . The purposes of the a n a l y s i s d i s c u s s e d below were to estimate the h e r i t a b i l i t y of these behavior v a r i a b l e s , to look f o r c o r r e l a t i o n s between them and other v a r i a b l e s measured i n t h i s study, and to ask whether the measured behaviors are r e l a t e d t o the success of a female i n r a i s i n g her l i t t e r . GENERAL TREATMENT OF THE DATA Because of the l a r g e number of zero counts i n the data, no t r a n s f o r m a t i o n c o u l d produce a frequency d i s t r i b u t i o n which s a t i s f i e d the requirements of parametric t e s t s , f o r s e v e r a l of the v a r i a b l e s measured. Th e r e f o r e , whenever p o s s i b l e , the r e s u l t s of parametric t e s t s were checked with non-parametric ones. There was never any s e r i o u s disagreement. A l l voles were r e p r o d u c t i v e l y mature and l a r g e r than 40 gm when t e s t e d ; t h e r e f o r e , I considered t h e s t a t e of maturity to be homogeneous f o r the t e s t e d animals. However, I d i d t e s t the data f o r e f f e c t s of p o p u l a t i o n s , sexes, and seasons; because t h e r e were no s i g n i f i c a n t e f f e c t s of p o p u l a t i o n s on any of the v a r i a b l e s , a two-way a n a l y s i s of v a r i a n c e provided the c e l l means f o r the sexes and four-week p e r i o d s . Only a few v a r i a b l e s were s i g n i f i c a n t l y a f f e c t e d by e i t h e r of these f a c t o r s . Seasonal v a r i a t i o n s were weakly c o r r e l a t e d with b r e e d i n g 1 4 0 a c t i v i t y i n the p o p u l a t i o n s . A f t e r adjustment f o r sex and f o u r -week p e r i o d of t e s t i n g , a l l v a r i a b l e s were expressed as d e v i a t i o n s from the r e l e v a n t c e l l mean. In a d d i t i o n t o c o r r e c t i n g f o r the above f a c t o r s , I looked f o r the e f f e c t s of repeated t e s t i n g . Only AT ( a c t i v e threat) and Lat ( l a t e n c y to approach) were s i g n i f i c a n t l y i n f l u e n c e d by t e s t order, but the means of a l l v a r i a b l e s changed i n a f a s h i o n c o n s i s t e n t with the i n t e r p r e t a t i o n t h a t animals become more a g g r e s s i v e , l e s s submissive, and more a c t i v e with repeated t e s t i n g . The e f f e c t of previous exposure i s remarkable i n l i g h t of the f a c t that a l l repeated t e s t s were conducted at l e a s t f o u r weeks a f t e r the preceding ones. A f t e r removing t e s t - o r d e r e f f e c t s , I computed r e p e a t a b i l i t i e s of the behavior v a r i a b l e s (Table 26). My e s t i m a t e s of r e p e a t a b i l i t y are s i m i l a r to those of Krebs (1970), f o r behavior v a r i a b l e s i n two other s p e c i e s of Microtus. As upper bounds on the h e r i t a b i l i t y of the t r a i t s , these estimates of r e p e a t a b i l i t y g ive a good i n d i c a t i o n of the s o r t s of r e s u l t s to be expected from the d i f f e r e n t v a r i a b l e s . Another component of v a r i a n c e , not measurable here, i s important to the r e p e a t a b i l i t y a n a l y s i s . There i s a " t e s t e r r o r " term, s i n c e the behavior v a r i a b l e s are only i n d i r e c t i n d i c a t o r s of the i n d i v i d u a l ' s a c t u a l b e h a v i o r a l s t a t e , and v o l e s were matched with d i f f e r e n t opponents f o r the repeated t e s t s . Because t e s t e r r o r w i l l tend to i n f l a t e w i t h i n -i n d i v i d u a l v a r i a n c e , the estimates of R should be c o n s i d e r e d underestimates of the true r e p e a t a b i l i t y f o r behavior of Microtus townsendii i n the f i e l d . 141 TABLE 26 Estimated r e p e a t a b i l i t y of the behavior v a r i a b l e s measured i n repeated arena encounters. Standard e r r o r s i n parentheses. r " "• T- i | Behavior v a r i a b l e | Repeatab i l i t y j J I i i | A c t i v e t h r e a t (AT) | . 196 (- 179) | Approach l a t e n c y (Lat) | . 320 (• 168) | I n i t i a t e i n v e s t i g a t i o n (II) j .037 (. 184) | F i g h t i n i t i a t o r (FI) | .001 (• 184) | Defensive posture (DP) | .200 (. 179) | Mutual u p r i g h t (MO) | -.001 ( .184) | R e t a l i a t i o n (Ret) | .02 2 (• 184) | Submissive posture (Sub) | .156 (• 181) J A c t i v i t y (Act) | .470 (- 147) i - — _ — i — j 1 4 2 F a c t o r a n a l y s i s was not p a r t i c u l a r l y u s e f u l i n s i m p l i f y i n g the behavior data. The f i r s t three f a c t o r s accounted f o r only 55% of the v a r i a n c e , though they grouped the behavior v a r i a b l e s i n an i n t u i t i v e l y s a t i s f y i n g way: AT ( a c t i v e thr.eat) , FI ( f i g h t i n i t i a t o r ) , MU (mutual u p r i g h t ) , and Ret ( r e t a l i a t i o n ) as i n d i c a t o r s o f ag g r e s s i v e n e s s ; I I ( i n i t i a t o r of i n v e s t i g a t i o n ) , Lat ( l a t e n c y t o approach o t h e r ) , and Act ( a c t i v i t y ) as measures of a c t i v i t y ; and DP (defensive posture) and Sub (submissive posture) as measures of submissiveness. To avoid s a c r i f i c i n g i n f o r m a t i o n , I analyzed each behavior v a r i a b l e s e p a r a t e l y . RESULTS C o r r e l a t i o n s among; r e l a t i v e s i n behavior. with the i n t e n t i o n of e s t i m a t i n g h e r i t a b i l i t y from r e g r e s s i o n s of o f f s p r i n g on parents, I measured the c o r r e l a t i o n s between o f f s p r i n g and s i r e , dam, and midparent f o r each behavior v a r i a b l e s e p a r a t e l y . Of these, only one a s s o c i a t i o n was s i g n i f i c a n t a t the .05 l e v e l — the c o r r e l a t i o n of o f f s p r i n g AT with the dam's AT (r = .356, P < .05). Th i s r e s u l t was i n c o n c l u s i v e , but, i n c o n t r a s t to the t o t a l l a c k of a s s o c i a t i o n between o f f s p r i n g and s i r e , i t d i d suggest that maternal e f f e c t s might i n f l u e n c e the development of behavior. I f t h i s were the case, then the e n t i r e range of maternal behaviors c o u l d be expected to i n f l u e n c e the o f f s p r i n g . 143 In order t o d e t e c t such an a s s o c i a t i o n , I c a l c u l a t e d stepwise m u l t i p l e r e g r e s s i o n s of o f f s p r i n g behavior v a r i a b l e s on a l l maternal and p a t e r n a l v a r i a b l e s . The p a t t e r n d e s c r i b e d above was confirmed; the s i r e ' s behavior c o u l d not p r e d i c t any of the o f f s p r i n g behavior v a r i a b l e s , and t h i s was e q u a l l y t r u e f o r s i r e s which were present i n or absent from the breeding e n c l o s u r e s , and f o r any other male present. In c o n t r a s t , f o u r of the nine o f f s p r i n g behavior v a r i a b l e s c o u l d be p r e d i c t e d to a s i g n i f i c a n t extent by va r y i n g combinations of the dam's behavior v a r i a b l e s (Table 27). Behavior and r e p r o d u c t i v e success. To answer the g u e s t i o n , " I s p a r e n t a l behavior a s s o c i a t e d with the number of o f f s p r i n g r e c r u i t e d from a l i t t e r ? " I c a l c u l a t e d three measures of r e p r o d u c t i v e success, and r e l a t e d each of them to the behavior v a r i a b l e s of the dam or the s i r e , when he was present, using a stepwise m u l t i p l e r e g r e s s i o n . The t h r e e measures of r e p r o d u c t i v e success were (1) mean number of o f f s p r i n g per s u c c e s s f u l l i t t e r (2) mean number of o f f s p r i n g per s u c c e s s f u l or u n s u c c e s s f u l l i t t e r (3) t o t a l number of o f f s p r i n g r e c r u i t e d l e s s the number l o s t , assuming a mean of four o f f s p r i n g i n each u n s u c c e s s f u l l i t t e r . The three measures, while c l e a r l y c o r r e l a t e d , r e p r e s e n t somewhat d i f f e r e n t a s p e c t s of r e p r o d u c t i o n . The l a s t measure i n c o r p o r a t e s the idea that r e p r o d u c t i o n i s a s s o c i a t e d with a c o s t , so an animal which produced no young and made no 144 TABLE 27 Multiple regressions of offspring behavior variables upon mother's behavior. H 2 estimates the proportion of the variance in Y explained by the X variates. + indicate the signs of the p a r t i a l regression c o e f f i c i e n t s . N = 38. X variates I P a 2 AT I AT+, Act + , Lat+, I I - j <.025 ,259 t .06 I Act Lat+, M0- 135 MU I Act+, FI-, AT+, Sub-| <.025 I .299 I FI AT+, I I - +-I <.025 I _i .199 145 TABLE 28 M u l t i p l e r e g r e s s i o n s of three measures of l i t t e r success upon maternal behaviors. R 2 estimates the p r o p o r t i o n of va r i a n c e i n Y accounted f o r by the X v a r i a t e s . + ,- i n d i c a t e the s i g n s of the p a r t i a l r e g r e s s i o n c o e f f i c i e n t s . L i t t e r success measures are as f o l l o w s : 1 = mean number of o f f s p r i n g per s u c c e s s f u l l i t t e r 2 = mean number of o f f s p r i n g per l i t t e r , r e g a r d l e s s of l i t t e r success 3 = number o f f s p r i n g r e c r u i t e d - number l o s t before recruitment L i t t e r success measure P a r e n t a l behaviors (X) R 2 Act+, DP-, MU+ M0+ Act-, AT+, MU+, L a t -<.005 <.05 <.025 509 136 34 3 22 32 32 | 146 r e p r o d u c t i v e e f f o r t r e c e i v e s a higher s c o r e than one which weaned no young but had u n s u c c e s s f u l l i t t e r s . The second measure takes u n s u c c e s s f u l l i t t e r s i n t o account, but not so s e v e r e l y as the t h i r d . The f i r s t measure i s independent of u n s u c c e s s f u l l i t t e r s . T able 28 p r e s e n t s the r e s u l t s of these m u l t i p l e r e g r e s s i o n s . The behavior of the s i r e makes no s i g n i f i c a n t c o n t r i b u t i o n toward p r e d i c t i n g any of the three measures of success of h i s o f f s p r i n g d u r i n g the p e r i o d of b i r t h to r e c r u i t m e n t . However, the dam's behavior i s e v i d e n t l y an important f a c t o r i n p r e d i c t i n g both the f i r s t and t h i r d measures, and i s weakly a s s o c i a t e d with the second. In the most powerful case, three of the dam's behavior v a r i a b l e s can account f o r 50% of the v a r i a n c e among mothers i n mean l i t t e r s i z e at r e c r uitment. The f i r s t and t h i r d measures d i f f e r i n t h e i r r e l a t i o n s h i p s with the behavior v a r i a b l e s . Both are p o s i t i v e l y c o r r e l a t e d with MU and AT, which measure a g g r e s s i v e n e s s , and the number of o f f s p r i n g per l i t t e r i s n e g a t i v e l y a s s o c i a t e d with DP, which rep r e s e n t s submissiveness. However, more a c t i v e mothers tend to have l a r g e numbers of o f f s p r i n g per l i t t e r (Measure #1), while the t h i r d measure of r e p r o d u c t i v e success i s low f o r a c t i v e mothers. Other c o r r e l a t e s of behavior. * Both age at puberty and which l i t t e r m a t e s tend to j u v e n i l e growth r a t e are t r a i t s i n resemble one another, a p p a r e n t l y 1 4 7 because of t h e i r shared environment at some time between b i r t h and recruitment. Adult behavior, a l s o determined i n part d u r i n g t h a t p e r i o d , might be expected to be c o r r e l a t e d with age at puberty and with j u v e n i l e growth r a t e , e s p e c i a l l y i n view of the o b s e r v a t i o n that a l l three t r a i t s vary on a p o p u l a t i o n l e v e l throughout the c y c l e s . However, f o r n e i t h e r sex are there any s i g n i f i c a n t c o r r e l a t i o n s with the behavior v a r i a b l e s . T h i s l a c k of phenotypic a s s o c i a t i o n i m p l i e s t h a t these t r a i t s are not c l o s e l y l i n k e d e i t h e r g e n e t i c a l l y or p h y s i o l o g i c a l l y , w i t h i n an i n d i v i d u a l v o l e. DISCUSSION The behaviors observed i n Microtus townsendii resemble the a g o n i s t i c behavior i n other m i c r o t i n e s p e c i e s , d e s c r i b e d by Turner and Iverson (1973), Krebs (1970), Murie (1971), Novak and Getz (1969), Getz (1962), C l a r k e (1956), and C o l v i n (1973). However, Microtus townsendii does appear to be more a g g r e s s i v e than most of the other s p e c i e s (C. Krebs, pers. com.). In a d d i t i o n , I d i d not observe s t r o n g s e a s o n a l changes i n behavior l i k e those recorded by Turner and Iverson (1973) i n flicrotus E ^ n n s Y lvanicus. Probably t h i s d i f f e r e n c e i s r e l a t e d to the l a c k of a w e l l - d e f i n e d breeding season i n the p o p u l a t i o n s of Microtus townsendii I s t u d i e d . The l a c k of c o r r e l a t i o n , w i t h i n an i n d i v i d u a l v o l e , among j u v e n i l e growth r a t e , age a t puberty, and a d u l t behavior i s somewhat s u r p r i s i n g , s i n c e a l l three t r a i t s appear to be p a r t i a l l y determined by the e a r l y common environment of the 148 l i t t e r . I t i m p l i e s t h a t the search f o r i d e n t i f y i n g a t t r i b u t e s of " i n c r e a s e " or " d e c l i n e " types of v o l e s w i l l have t o be c a r r i e d on a t the i n d i v i d u a l l e v e l , s i n c e these t r a i t s have been shown t o covary i n the p o p u l a t i o n as a whole. In a d d i t i o n , the importance of maternal and common environment e f f e c t s demands c a r e f u l a t t e n t i o n to the causes of c o r r e l a t i o n s between t r a i t s w i t h i n i n d i v i d u a l s , f o r i t cannot be assumed t h a t such c o v a r y i n g t r a i t s , even w i t h i n i n d i v i d u a l s , are g e n e t i c a l l y mediated. The nature of the c o r r e l a t i o n between o f f s p r i n g and maternal behavior d e s c r i b e d here was not unexpected from the l i t e r a t u r e . C h r i s t i a n and Davis (1964) reviewed evidence f o r l a s t i n g e f f e c t s of the maternal environment upon behavior of o f f s p r i n g . These i n f l u e n c e s have been demonstrated at a l l stages of the r e p r o d u c t i v e and n u r t u r i n g process i n l a b o r a t o r y r a t s and mice. J o f f e (1965) demonstrated that s t r e s s ( e l e c t r i c shock) upon the mother before mating changed the o p e n - f i e l d a c t i v i t y of her o f f s p r i n g . O f f s p r i n g behavior can be i n f l u e n c e d i n utero by e l e c t r i c shock ( J o f f e , 1965), i n j e c t i o n of s t r e s s -r e l a t e d hormones (Lie.berman, 1963) , and extreme crowding of the mother (Keeley, 1962). The a d u l t a g g r e s s i v e n e s s of mice can be a f f e c t e d by v i s u a l o b s e r v a t i o n of a g g r e s s i v e encounters around the time of weaning (DeGhett, 1975), or by d e p r i v a t i o n of s o c i a l s t i m u l a t i o n soon a f t e r weaning (Scott, 1966). In Mus, these e f f e c t s are s e n s i t i v e to age and t i m i n g of the s o c i a l e xperiences (King, 1957). A s i m i l a r e f f e c t was r e p o r t e d by Svendsen (1974) upon marmots i n n a t u r a l l y - i s o l a t e d f a m i l i e s . On the other hand, i t might have been expected t h a t behavior would e x h i b i t a measurable a d d i t i v e g e n e t i c component 149 i n M icrotus townsendii p o p u l a t i o n s , as w e l l . S e v e r a l b e h a v i o r a l t r a i t s of l a b o r a t o r y mice have been shown to respond - to s e l e c t i o n , and t h e r e f o r e to have some a d d i t i v e g e n e t i c b a s i s . DeFries and Hegmann (1970) and D e F r i e s , Hegmann, and Halcomb (1974) r e p o r t e d a r e a l i z e d h e r i t a b i l i t y (estimated from the s e l e c t i o n response) of .25 f o r o p e n - f i e l d a c t i v i t y . Hurnik, B a i l e y , and Jerome (1973) repo r t e d a r e a l i z e d h e r i t a b i l i t y f o r r e t r i e v i n g behavior of .26 to .44, depending upon the d i r e c t i o n of s e l e c t i o n . Estimates of .46 and .68 r e s p e c t i v e l y f o r h e r i t a b i l i t y of open f i e l d d e f e c a t i o n and a c t i v i t y have been publi s h e d by J i n k s and Broadhurst (1965) i n l a b o r a t o r y r a t s ; while Broadhurst (1965) has shown t h a t avoidance l e a r n i n g responds to s e l e c t i o n i n t h a t s p e c i e s . Plomin and Manosevitz (1974) found that o f f s p r i n g of w i l d Mus from d i f f e r e n t g e o g r a p h i c a l areas d i f f e r e d i n behavior when r a i s e d under l a b o r a t o r y c o n d i t i o n s . The authors concluded t h a t the d i f f e r e n c e s were caused by ge n e t i c d r i f t r a t h e r than s e l e c t i o n . From comparisons among s t r a i n s of mice, Parsons (1974) deduced that o p e n - f i e l d a c t i v i t y and e m o t i o n a l i t y , e x p l o r a t o r y a c t i v i t y , and avoidance c o n d i t i o n i n g performance were g e n e t i c a l l y i n f l u e n c e d . Crosses among s t r a i n s have y i e l d e d e s t i m a t e s of .15 f o r h e r i t a b i l i t y of sex u a l behavior i n male mice, and have pointed out the importance of i n t e r a c t i o n s between genotype and environment f o r hoarding behavior and open-f i e l d behavior ( M c G i l l , 1970). Laboratory s t u d i e s of Mus behavior g e n e t i c s have p r a c t i c a l l y ignored most aspects of s o c i a l b ehavior, and have been l a r g e l y r e s t r i c t e d to inbred s t r a i n s . S t i l l , i t i s ) 150 somewhat s u r p r i s i n g to f i n d no evidence f o r g e n e t i c i n f l u e n c e upon a c t i v i t y , at l e a s t , i n the Microtus t o w n s e n d i i p o p u l a t i o n s t u d i e d here, c o n s i d e r i n g the l i t e r a t u r e mentioned above. The i n d i c a t o r s of a c t i v i t y i n t h i s study, however, were measured i n the encounter s i t u a t i o n , and are t h e r e f o r e not s t r i c t l y comparable to those of o p e n - f i e l d behavior. The demonstration that the behavior of a mother i s r e l a t e d to her r e p r o d u c t i v e output i s c o n s i s t e n t with both the hypothesis of C h i t t y (1960,1967) and t h a t of C h r i s t i a n and Davis (1964). In a s p e c i e s i n which maternal i n f l u e n c e s can be shown t o operate throughout the l i v e s of animals, and i n which i t i s d i f f i c u l t to d e t e c t , i n the f i e l d , when maternal care ceases and independent j u v e n i l e s u r v i v a l begins, the o p e r a t i o n a l d i s t i n c t i o n between " p a r e n t a l r e p r o d u c t i v e a b i l i t y " and " o f f s p r i n g s u r v i v a l " becomes unclea r . The p e r i o d between b i r t h and r e c r u i t m e n t i s e v i d e n t l y an important one i n the demography of p o p u l a t i o n c y c l e s , and i t i s p r e c i s e l y t h i s p e r i o d during which p a r e n t a l r e p r o d u c t i o n and o f f s p r i n g s u r v i v a l o v e r l a p i n l i v e - t r a p p i n g s t u d i e s . Thus, the general r e l a t i o n s h i p "behavior i s c o r r e l a t e d with r e c r u i t m e n t " i s supported whether the mechanism i s p r e c i s e l y n u r t u r i n g a b i l i t y of the mother, or s u r v i v a l of the young. The maternal e f f e c t s on o f f s p r i n g behavior d e s c r i b e d are c o n s i s t e n t with the model f o r the i n t e r a c t i o n of behavior and p o p u l a t i o n c y c l e s proposed by C h r i s t i a n and Davis (1964), except perhaps f o r the f a i l u r e to demonstrate a c o r r e l a t i o n between a d u l t behavior and j u v e n i l e growth r a t e or age at puberty. In p a r t i c u l a r , the t r a n s m i s s i o n of maternal experience to the 1 5 1 o f f s p r i n g , i n terms of both behavior and body s i z e , c o r r o b o r a t e s r e l a t i o n s h i p s i n t h e i r model which seemed l i k e l y to be a r t i f a c t s of the l a b o r a t o r y environment. To my knowledge, t h i s i s the f i r s t e x p l o r a t i o n of these r e l a t i o n s h i p s i n a rodent s p e c i e s under f i e l d c o n d i t i o n s . The demonstration of maternal e f f e c t s p r o v i d e s , however, no assurance that the exact p h y s i o l o g i c a l mechanisms suggested by C h r i s t i a n and Davis a c t u a l l y operate i n Microtus townsendii. Though the r e s u l t s of t h i s study do not agree with p r e d i c t i o n s from the g e n e t i c - b e h a v i o r hypothesis, they are not s u f f i c i e n t grounds f o r r e j e c t i n g i t . F i r s t , the c o r r e l a t i o n s among r e l a t i v e s f o r behavior were measured i n a h a b i t a t i n which the Microtus townsendii d e f i n i t e l y did not undergo " t y p i c a l " m i c r o t i n e p o p u l a t i o n f l u c t u a t i o n s . In a d d i t i o n , i t i s s t i l l not c l e a r whether Microtus townsendii p o p u l a t i o n s i n any h a b i t a t e x h i b i t such two- or three-year f l u c t u a t i o n s . Second, there i s no guarantee t h a t the behaviors measured are the ones which a c t u a l l y might cause p o p u l a t i o n c y c l e s . However, the f a c t t h a t p a t t e r n s i n behavior can be demonstrated ( t h i s study; Krebs, 1970; Turner and I v e r s o n , 1973) i n d i c a t e s that the observed v a r i a b l e s probably r e p r e s e n t some b e h a v i o r a l or p h y s i o l o g i c a l s t a t e important to the animals. On one l e v e l , the important r e l a t i o n s h i p s of C h i t t y ' s b e h a v i o r - g e n e t i c h y p o t h e s i s , the m a t e r n a l - e f f e c t s hypothesis of C h r i s t i a n and Davis, and the s i m u l a t i o n model d e s c r i b e d i n the Appendix have been upheld: that there must be a c o r r e l a t i o n (1) between behavior of o f f s p r i n g and t h a t of at l e a s t one parent (Table 27), and (2) between behavior of mothers and t h e i r 152 o v e r a l l c o n t r i b u t i o n to the r e c r u i t i n g age c l a s s e s (Table 28). Whether the estimated values of these c o r r e l a t i o n s are c o n s i s t e n t with p o p u l a t i o n c y c l e s c o u l d be t e s t e d with the s i m u l a t i o n model, a f t e r e s t i m a t i o n of some of the model's other f u n c t i o n a l r e l a t i o n s h i p s . * Whether or not i t i s r e l a t e d to behavior, n a t u r a l s e l e c t i o n appears to work on Microtus townsendii p o p u l a t i o n s as they f l u c t u a t e In numbers. A l l e l e f r e q u e n c i e s at the LAP l o c u s are c o r r e l a t e d with d e n s i t y , though they do not appear to cause d e n s i t y changes (LeDuc and Krebs, 1975). Any model of n a t u r a l s e l e c t i o n i n Microtus townsendii p o p u l a t i o n s w i l l be complicated by the f a c t t h a t , t o some exten t , s e l e c t i o n on the t r a i t s s t u d i e d here w i l l be a c t i n g on e n t i r e f a m i l i e s as w e l l as on I n d i v i d u a l s . T h i s alone could r e s u l t i n gene frequency changes, e s p e c i a l l y when numbers are low, but the d i r e c t i o n of the changes should be random unless t h e r e i s some l i n k a g e between the LAP locu s and s e g r e g a t i n g l o c i which i n f l u e n c e the t r a i t s under s e l e c t i o n . Since m u l t i p l e r e g r e s s i o n s have been used t o determine which p a r e n t a l b e h a v i o r s c o u l d p r e d i c t both l i t t e r success and o f f s p r i n g behavior, i t i s important t o examine the assumptions behind t h i s a p p l i c a t i o n of the technique ( G i l b e r t , 1973). F i r s t , r e g r e s s i o n a n a l y s i s assumes t h a t the x v a r i a t e s are * P r e l i m i n a r y experimentation with the s i m u l a t i o n model, using i n t e l l i g e n t guesses f o r the ranges of the parameters, demonstrated that c y c l i n g would occur only i f the o f f s p r i n g -midparent c o r r e l a t i o n i n behavior were at l e a s t .8. T h i s was true over a number of t r i a l s i n which other parameters were v a r i e d w i t h i n the ranges suggested by the l i t e r a t u r e . 1 5 3 measured without e r r o r . E r r o r s of measurement i n the X v a r i a t e s tend to r e s u l t i n p a r t i a l r e g r e s s i o n c o e f f i c i e n t s which underestimate the t r u e s l o p e of the f u n c t i o n a l r e l a t i o n s h i p between the v a r i a b l e s . While the a c t u a l counts and d u r a t i o n s of b e h a v i o r s i n the arena t e s t s are q u i t e a c c u r a t e , they represent the t r u e behavior s t a t e of the animal to an extent which i s e n t i r e l y unknown. The v i o l a t i o n of t h i s assumption i s important c h i e f l y i n the a p p l i c a t i o n of the r e g r e s s i o n equation to a p r e d i c t i v e a s s o c i a t i o n . Since such an a p p l i c a t i o n would undoubtedly be made with data acguired i n a s i m i l a r f a s h i o n , the best p r e d i c t i o n s would s t i l l come from these underestimates. Second, a l l the important X v a r i a t e s must be i n c l u d e d i n the a n a l y s i s , unless they are u n c o r r e l a t e d , because omission of an X v a r i a t e can r e s u l t i n i n f l a t i o n of the importance of oth e r s . Since we r e a l l y have no idea of the c a u s a l mechanism i n t h i s r e l a t i o n s h i p , i t i s d i f f i c u l t to s p e c i f y the s e t of l i k e l y X v a r i a t e s , but a l l the behavior v a r i a t e s with s a t i s f a c t o r y frequency d i s t r i b u t i o n s were i n c l u d e d i n the m u l t i p l e r e g r e s s i o n s . Other p o t e n t i a l determinants have been e l i m i n a t e d i n the case of o f f s p r i n g behavior; these were age at puberty and j u v e n i l e growth r a t e . Other p o t e n t i a l i n f l u e n c e s on l i t t e r s i z e have been d e s c r i b e d above, and a l l e l i m i n a t e d except f o r seasons. Because the behavior data have been c o r r e c t e d f o r seasonal v a r i a t i o n s , they s a t i s f y t h i s assumption. T h i r d , the r e g r e s s i o n a n a l y s i s assumes t h a t the e f f e c t s of the X v a r i a b l e s are l i n e a r and a d d i t i v e . T h i s i s perhaps a weak (though commonly made) assumption with r e s p e c t to behavior data. I t can be defended here by the o b s e r v a t i o n t h a t the parametric 1 5 4 analyses used to d e t e c t d i f f e r e n c e s among seasons, p o p u l a t i o n s , and sexes sere c o n s i s t e n t l y s u b s t a n t i a t e d when checked a g a i n s t noa-parametric t e s t s . In a d d i t i o n to r e c o g n i z i n g the above assumptions, one should i n t e r p r e t with c a u t i o n m u l t i p l e r e g r e s s i o n s on o b s e r v a t i o n a l data such as these, because there i s no reason to assume a c a u s a l r e l a t i o n s h i p . On t h i s p o i n t , l e t us c o n s i d e r some of the mechanisms by which the observed r e l a t i o n s h i p s can be e x p l a i n e d . O f f s p r i n g behavior could resemble maternal behavior f o r a number of reasons: 1. The observed behaviors might be s e x - l i n k e d g e n e t i c c h a r a c t e r s . T h i s remote p o s s i b i l i t y can be r e j e c t e d by the o b s e r v a t i o n that the r e g r e s s i o n s of sons on dams do not d i f f e r from those' of daughters on dams. 2. O f f s p r i n g might l e a r n behavior from t h e i r mothers by observing i n t e r a c t i o n s . I t i s u n l i k e l y t h a t t h i s i s the case i n the breeding e n c l o s u r e s , where at most one other a d u l t was present, and the behavior of that male has been shown to be u n c o r r e l a t e d with that of the o f f s p r i n g . However, DeGhett (1975) r e p o r t s that v i s u a l l e a r n i n g of t h i s s o r t does occur i n Mus under l a b o r a t o r y c o n d i t i o n s . T h i s might be a f r u i t f u l area of r e s e a r c h i n Microtus townsendii. 3. Some aspect of the dam's past experience, e i t h e r n u t r i t i o n a l or b e h a v i o r a l , might cause her to pass a p h y s i o l o g i c a l f a c t o r on to her young through l a c t a t i o n , which would i n t u r n modify t h e i r behavior. The i n f l u e n c e would have to be l o n g - l i v e d i n order to be c o n s i s t e n t with the o b s e r v a t i o n s 1 5 5 of t h i s study, s i n c e the behavior of o f f s p r i n g was measured a f t e r they had reached adulthood, i n some cases months a f t e r weaning.. 4. Young Microtus townsendii might l e a r n behavior d i r e c t l y from t h e i r own i n t e r a c t i o n s with the mother. However, t h i s h y p o t h e s i s suggests the c r i t i c i s m t h a t the c o r r e l a t i o n s among r e l a t i v e s could be a r t i f a c t s of prolonged exposure to the mother i n the breeding e n c l o s u r e s . There are two arguments a g a i n s t t h i s c r i t i c i s m . F i r s t , the enc l o s u r e s were trapped twice as o f t e n as were the g r i d s . T h e r e f o r e , young animals, when removed from the breeding e n c l o s u r e s , o f t e n were s m a l l e r , and t h e r e f o r e probably younger, than those f i r s t captured i n unmanipulated p o p u l a t i o n s . Second, i n normal p o p u l a t i o n s , groups of young v o l e s , s i m i l a r i n s i z e and e v i d e n t l y l i t t e r m a t e s , o f t e n f i r s t e nter l i v e - t r a p s w i t h i n 20 m of one another. Such groups of young can be captured even e a r l i e r , and o f t e n with an a d u l t female, i n p i t f a l l t r a p s . These o b s e r v a t i o n s i n d i c a t e t h a t o f f s p r i n g do not normally wander f a r from the nest immediately a f t e r weaning. However, l e t us assume f o r the moment the most c o n s e r v a t i v e i n t e r p r e t a t i o n , that the c o r r e l a t i o n s among dams and o f f s p r i n g are indeed an a r t i f a c t of confinement i n the breeding e n c l o s u r e s . An i n t e r e s t i n g c o n c l u s i o n could s t i l l be drawn: that there i s a c r i t i c a l p e r i o d sometime between weaning and recruit m e n t , during which i n t e r a c t i o n s with a d u l t s are c r u c i a l to the formation of behavior p a t t e r n s which the vole w i l l r e t a i n throughout i t s l i f e . T h i s hypothesis i s p o t e n t i a l l y t e s t a b l e through v a r i a t i o n i n s i z e of breeding e n c l o s u r e s and the use of 156 p i t f a l l t r a p s , which would allow capture of the young at e a r l i e r ages. A s i m i l a r s e t of hypotheses can be suggested t o e x p l a i n the c o r r e l a t i o n between maternal behavior and mean l i t t e r s i z e at r e c r u i t m e n t : 1. The dam's performance i n the behavior t e s t s might i n d i c a t e her a b i l i t y t o defend her l i t t e r a g a i n s t other a d u l t s . T h i s seems u n l i k e l y In the breeding e n c l o s u r e s , where only one other a d u l t was present, and n e i t h e r h i s behavior nor h i s presence a f f e c t s the o v e r a l l success or s i z e at recruitment of the l i t t e r . 2. Past experience or her n u t r i t i o n a l s t a t e might a l t e r e i t h e r the dam's f e r t i l i t y or her a b i l i t y t o nurture her l i t t e r s . Examples of t h i s mechanism i n other s p e c i e s have been mentioned above. 3. The mother h e r s e l f might harry her young or k i l l them d i r e c t l y . While t h i s i s perhaps the s i m p l e s t e x p l a n a t i o n , i t r a i s e s again the s u s p i c i o n that the r e s u l t s are a r t i f a c t s of the breeding e n c l o s u r e s . I f t h i s were the case, however, we should expect t o f i n d a lower number of o f f s p r i n g per l i t t e r i n the breeding e n c l o s u r e s than i n the unmanipulated p o p u l a t i o n on G r i d A l . Instead, the breeding e n c l o s u r e s n e a r l y always produce a s l i g h t l y g r e a t e r number per l i t t e r , the d i f f e r e n c e being s u b s t a n t i a l during May (Table 17). In a d d i t i o n , we have d i s c u s s e d above s e v e r a l reasons f o r b e l i e v i n g t h a t young v o l e s were removed from the breeding e n c l o s u r e s at about the same age as they would normally have f i r s t wandered from the nest. I f we were t o assume the observed r e l a t i o n s h i p between 1 5 7 maternal behavior and l i t t e r s i z e at recruitment t o be an a r t i f a c t , the f o l l o w i n g arguments are probably s t i l l v a l i d . F i r s t , the a r t i f a c t i s probably not caused by abnormal behavior on the part of the mother, f o r no d i f f e r e n c e s i n behavior could be found between females i n the breeding e n c l o s u r e s and those o u t s i d e . Second, i f young Microtus townsendii i n the breeding e n c l o s u r e s are unable to l e a v e the nest q u i c k l y enough to avoid harassment by t h e i r mothers, then we have i d e n t i f i e d a period of i n t e n s e i n t e r a c t i o n s between mothers and o f f s p r i n g , which may be i n t i m a t e l y i n v o l v e d with d i s p e r s a l . Probably the same i n t e r a c t i o n s go on i n unfenced p o p u l a t i o n s , with d i s p e r s a l from the nest r a t h e r than death as the r e s u l t , The s p e c i f i c maternal b e h a v iors i d e n t i f i e d here may w e l l be u s e f u l i n f i e l d s t u d i e s , f o r p r e d i c t i n g which females are l i k e l y to c o n t r i b u t e the most young to the immediate gene p o o l . In a d d i t i o n , we would have evidence f o r a mechanism by which d i s p e r s a l tendency (at the j u v e n i l e stage) could be h i g h l y c o r r e l a t e d among s i b l i n g s . with a l a r g e p r o p o r t i o n of the v a r i a n c e i n l i t t e r s i z e at recruitment e x p l a i n e d by maternal behavior, we must q u e s t i o n the low estimate f o r r e p e a t a b i l i t y of l i t t e r s i z e (Table 2 ) . I f maternal behavior i s c o n s i s t e n t over time, then we must conclude that the l a r g e standard e r r o r on the estimate of r e p e a t a b i l i t y f o r l i t t e r s i z e at recruitment i s r e s p o n s i b l e f o r the negative estimate, and r e p e a t a b i l i t y i s a c t u a l l y d i f f e r e n t from zero. The d i f f e r e n c e s among the three measures of l i t t e r success c a r r y an i n t e r e s t i n g i m p l i c a t i o n . The measure most s t r o n g l y c o r r e l a t e d with maternal behavior i s the mean number of o f f s p r i n g per s u c c e s s f u l l i t t e r . When l i t t e r s which produced no 158 o f f s p r i n g at a l l are i n c l u d e d (Measure #2) , the c o r r e l a t i o n with behavior i s reduced. T h i s suggests t h a t l o s s e s of e n t i r e l i t t e r s are not a s s o c i a t e d with maternal behavior, e i t h e r d i r e c t l y or through some common c o r r e l a t e such as nest defense or l a c t a t i o n a b i l i t y . Rather, they may have some l a r g e l y separate set of causes, e.g., weather or p r e d a t i o n , as Hoffmann (1958) has suggested. Such an i n t e r p r e t a t i o n i s c o n s i s t e n t with the random d i s t r i b u t i o n of u n s u c c e s s f u l l i t t e r s among females and the o b s e r v a t i o n that most of them appear to f a i l s h o r t l y a f t e r b i r t h . I t a l s o i m p l i e s t h a t the maternal behavior which i s a s s o c i a t e d with p a r t i a l l o s s of l i t t e r s here i s not of the same s o r t as that observed i n the "rogue" females d e s c r i b e d by Banson (1941), which ca n n a b a l i z e d t h e i r e n t i r e l i t t e r s . SUMMARY Thi s study of b e h a v i o r a l i n f l u e n c e s w i t h i n f a m i l i e s has l e d to the f o l l o w i n g c o n c l u s i o n s : 1. The behavior of the mother can p r e d i c t the o f f s p r i n g ' s a d u l t behavior. 2. The behavior of the mother can p r e d i c t her r e p r o d u c t i v e success, both i n terms of the mean number of o f f s p r i n g r e c r u i t e d per l i t t e r , and i n terms of a measure which i n c l u d e s the c o s t of her r e p r o d u c t i v e e f f o r t . 3 . No c o r r e l a t i o n could be shown between a vol e ' s behavior and e i t h e r i t s j u v e n i l e growth r a t e or i t s age at puberty. 159 SECTION VI: AN EVALUATION, AND SUGGESTIONS FOB FURTHER WORK The relevance of these r e s u l t s to n a t u r a l p o p u l a t i o n s of Microtus townsendii might be questioned from two p o i n t s of view. F i r s t , how r e p r e s e n t a t i v e of the whole p o p u l a t i o n are the animals born i n the breeding e n c l o s u r e s ? Second, to what extent are the r e s u l t s concerning phenotypic c o r r e l a t i o n s among r e l a t i v e s merely a r t i f a c t s of the experimental design? To e x p l o r e these i s s u e s , I have compared the p a t t e r n s i n s e v e r a l t r a i t s between enclosure-born and g r i d - b o r n v o l e s . F i g u r e 12 compares the s i z e at recruitment of the two groups. The somewhat s m a l l e r s i z e d i s t r i b u t i o n at f i r s t capture f o r enclosure-born animals i s expected from the i n c r e a s e d frequency of t r a p p i n g i n the breeding e n c l o s u r e s ; the two d i s t r i b u t i o n s are not s i g n i f i c a n t l y d i f f e r e n t ( c h i 2 = 8.59, p > .1). I t i s reasonable to conclude that j u v e n i l e behavior toward t r a p s and probably s i z e at the time of weaning and d i s p e r s a l from the nest are not a f f e c t e d by the breeding e n c l o s u r e s . F i g u r e s 13 through 16 show some r e p r e s e n t a t i v e growth curves f o r l i t t e r s born i n the breeding e n c l o s u r e s . Since l i t t e r m a t e s d i f f e r e d i n t h e i r age at f i r s t c apture and the age at which they were removed from the breeding e n c l o s u r e , i t i s p o s s i b l e t o compare an i n d i v i d u a l ' s growth a f t e r r e l e a s e with t h a t of i t s s i b l i n g s which remained l o n g e r i n the breeding e n c l o s u r e . In a d d i t i o n , the growth of a randomly s e l e c t e d animal, n a t i v e t o the g r i d p o p u l a t i o n , has been p l o t t e d i n these 160 F i g u r e 12. Frequency d i s t r i b u t i o n of s k u l l width at f i r s t capture f o r v o l e s born i n the breeding e n c l o s u r e s and those born on fenced G r i d L. Note that the breeding e n c l o s u r e s were trapped twice as o f t e n as the g r i d s ; t h e r e f o r e i t i s expected t h a t the d i s t r i b u t i o n of f i r s t capture s i z e s i n the e n c l o s u r e s should be skewed i n f a v o r of s m a l l s i z e s . FREQUENCY FREQUENCY o \(\ to o t o I—' I O Lo 1 o -e-I Ln O Ln I—* I o I IV) c o jv» O 2 1 CD II PD CO 4^  O IV) CO 2 : m CD o o r -a c o c z X ) m c o o T9T 162 Figures 13 to 16. Comparison of the growth curves of littermates before and after removal from the breeding enclosures. A l l littermates begin with the same hypothetical size at b i r t h . Each l i n e represents the early growth history of an i n d i v i d u a l from the l i t t e r . Dashed l i n e s and +'s indicate growth t r a j e c t o r i e s and data points in the breeding enclosure; s o l i d l i n e s and o's indicate growth and data points after removal from the enclosure. One i n d i v i d u a l of si m i l a r size was selected at random from the appropriate g r i d , for comparison with the breeding enclosure-born voles. That animal's growth i s represented by t r i a n g l e s . 163 1 . 6 T LITTER 31 BORN A P R I L . 1974 1 . 5 + 1 . 4 + i — . Q ZD CO 1 . 3 + 1-2 + 1.1 + 0 2 3 4 5 WEEKS AFTER BIRTH 6 Figure 13 7 164 LITTER 4 4 BORN SEPTEMBER. 1973 l Y-—-+- 1 — : — i 1 1 - h ^ — — i — • — i 1 1 1 0 1 2 3 4 5 6 7 8 9 10 11 WEEKS AFTER BIRTH Figure 14 165 Figure 15 166 LITTER 55 BORN FEBRUARY. 1974 0 2 3 4 5 WEEKS AFTER BIRTH 6 7 Figure 16 1 6 7 f i g u r e s (small t r i a n g l e s ) . I t i s evident t h a t removal from the enc l o s u r e does not s i g n i f i c a n t l y a l t e r an i n d i v i d u a l ' s subsequent growth; growth curves f o r young animals i n the breeding e n c l o s u r e s are s i m i l a r to those of animals i n the g r i d p o p u l a t i o n . However, th e r e i s a suggestion t h a t , i n some cases, growth i s i n h i b i t e d d u r i n g the f i r s t week a f t e r removal from the breeding e n c l o s u r e (cf l i t t e r s 31 and 44) . Although i n d i v i d u a l growth curves do not e x h i b i t marked d i f f e r e n c e s between the g r i d s and the e n c l o s u r e s , a d i f f e r e n c e can be shown when the e n t i r e p o p u l a t i o n i s c o n s i d e r e d . F i g u r e 17 and Table 29 present the r e g r e s s i o n of growth r a t e on s i z e f o r the voles present i n the breeding e n c l o s u r e s compared with those on the g r i d s . In the e n c l o s u r e s , a p p a r e n t l y , v o l e s have an advantage i n growth over those l i v i n g on the g r i d s , e s p e c i a l l y at smal l s i z e s . The d i f f e r e n c e s i n growth r a t e are l e s s important f o r l a r g e animals. Both between p o p u l a t i o n groups and among seasons, the r e g r e s s i o n l i n e s are s i g n i f i c a n t l y d i f f e r e n t (p < .01). During the period from January to March, when e x t r a food was s u p p l i e d i n the breeding e n c l o s u r e s , growth r a t e i n the two environments was almost i d e n t i c a l ; i t appears that the e x t r a food had no e f f e c t on growth r a t e . During the other seasons, the breeding e n c l o s u r e s provided a more f a v o r a b l e environment than the g r i d s f o r growth. A comparison of re s i d e n c e time i n the g r i d p o p u l a t i o n s , between n a t i v e and enclosure-born animals, can provide i n f o r m a t i o n concerning two ques t i o n s . F i r s t , how s e r i o u s i s the trauma a s s o c i a t e d with i n t r o d u c t i o n of young mice i n t o the g r i d p o p u l a t i o n s ? Second, are enclosure-born animals able t o s u r v i v e 168 Figure 17. Daily instantaneous growth rate i n s k u l l width, as a function of s k u l l width, for each three-month d i v i s i o n of the year. The ov e r a l l regression for the breeding enclosures d i f f e r s from that of the grids (p < .01), and differences among the seasons are s i g n i f i c a n t for both populations (p < .005). Coefficients of the regressions (Table 29) were estimated using the following transformation: Y' = log <100Y +1) X' = logX 169 .010 -f .005 -f 0.00 Breeding enclosures (N = 181) Grids AA, L, and 0 pooled (N = 605) JRNURRY - I \ MARCH i .010 + .005 0.00 H 1 APRIL JUNE \ \ \ \ N LU t — CE o CD .010, t 1.1 1 . 3 1 . 5 1.7 1 . 9 1.1 1 . 3 1 . 5 1.7 1 . 9 CE K .005 4 0.00 s- + JULY -SEPTEMBER .010 .005 0.00 \ OCTOBER -DECEMBER \ \ \ \ \ H—: : — h 1.1 1 . 3 1 . 5 1.7 1 . 9 1.1 1 . 3 1 . 5 1.7 1 . 9 SKULL WIDTH (CM) Figure 17 170 F i g u r e 18. Frequency d i s t r i b u t i o n s of r e s i d e n c e times i n the t r a p p a b l e p o p u l a t i o n of unfenced G r i d AA. The top graph r e p r e s e n t s animals born i n the breeding e n c l o s u r e s and r e l e a s e d on G r i d AA, the bottom graph r e p r e s e n t s animals f i r s t captured on G r i d AA. C h i 2 = 2.20, p> .5. 5 T 375 .25 + 125 4-0 5 T ENCLOSURE-BORN N=52 H 1 H 375 --' 25 --125 --0 NATIVE TO GRID AA N=143 _j ' i 1 = r 1-4 5-8 9-12 13-16 17-20 21-24 25-28 29-32 33+ RESIDENCE TIME (VKS) Figure 18 172 TABLE 29 S t a t i s t i c s for the regressions of growth rate vs s k u l l width (cf Figure 17) . C o e f f i c i e n t s of the regressions were estimated using the following transformation: Y» = log (100Y + 1) X' = logX i r Season Breeding enclosures J January -| March T 1 & = 1 B = . 6 3 9 - 1 . 0 8 6 I A = | B = . 6 6 8 | - 1 . 0 6 6 j I A p r i l - 1 A = 1 . 6 0 8 I A = 1 . 1 8 3 | | June 1 B = - 2 . 7 3 0 I B = - 1 . 9 1 0 j i 1 I t I July -I September i _ 1 A = | B = 1 . 0 3 3 - 1 . 7 6 4 | A = I B = . 7 0 3 | - 1 . 1 4 5 j Grids October -December A B 1.278 -2. 313 A B .602 -.748 j . ± 173 as well on the g r i d s as n a t i v e animals? F i g u r e 18 shows the frequency d i s t r i b u t i o n s f o r r e s i d e n c e time on the unfenced G r i d AA, f o r n a t i v e vs enclosu r e - b o r n v o l e s . The c l a s s of v o l e s which were never r e c a p t u r e d (residence time=0) i s only s l i g h t l y l a r g e r f o r enclosure-born voles than f o r n a t i v e animals. T h i s i n d i c a t e s t h a t i n t r o d u c e d animals were about as s u c c e s s f u l at e s t a b l i s h i n g themselves as those f i r s t caught on the g r i d i t s e l f , and t h e r e f o r e that i n t r o d u c t i o n i n t o an e s t a b l i s h e d p o p u l a t i o n was not unduly d i f f i c u l t f o r them. Because the two frequency d i s t r i b u t i o n s do not d i f f e r s i g n i f i c a n t l y (p > .5), we can a l s o assume that enclosure-born voles s u r v i v e d about as well as those f i r s t captured on G r i d AA. Neither the i n d i v i d u a l behavior v a r i a b l e s nor the " a g g r e s s i o n " and " a c t i v i t y " f a c t o r scores were i n f l u e n c e d by the place of b i r t h of an animal ( K r u s k a l - W a l l i s a n a l y s i s of v a r i a n c e , p > .05). However, the "submission" f a c t o r score d i f f e r e d s i g n i f i c a n t l y between v o l e s born i n the breeding e n c l o s u r e s and those f i r s t captured on the g r i d s ( K r u s k a l - W a l l i s anova, p < .01). The "submission" f a c t o r score i n c l u d e d only behavior v a r i a b l e s (Defensive Posture and Submission) which were r e l a t i v e l y unimportant i n the c o r r e l a t i o n s between o f f s p r i n g and mother (Tables 27 and 2 8). T h e r e f o r e , t h i s d i f f e r e n c e probably does not a f f e c t d i r e c t l y the v a l i d i t y of the c o r r e l a t i o n s , but i t does suggest that the breeding e n c l o s u r e s may i n f l u e n c e beha v i o r . From these r e s u l t s , we can conclude that the breeding e n c l o s u r e s do produce animals which may be d i f f e r e n t i n some ways from those n a t i v e to the ou t s i d e p o p u l a t i o n s . These 1 7 4 d i f f e r e n c e s might r e f l e c t e i t h e r (1) a d d i t i v e changes i n the p o p u l a t i o n means, or (2) r e a l i n t e r a c t i o n s between genotypes and the two environments ( g r i d vs breeding e n c l o s u r e ) . The f i r s t of these a l t e r n a t i v e s would not a f f e c t the v a l i d i t y of t h i s study's c o n c l u s i o n s f o r w i l d p o p u l a t i o n s of Microtus townsendii; genotype-environment i n t e r a c t i o n s , however, might be d i f f i c u l t to i n t e r p r e t without f u r t h e r experimental work on the problem. With the experimental design d e s c r i b e d here, i t i s impossible to decide which of these two i n t e r p r e t a t i o n s i s the c o r r e c t one, s i n c e a c o n t r o l would r e q u i r e that f a m i l y members be i d e n t i f i e d without c o n f i n i n g them together. S e v e r a l techniques might provide c o n t r o l data f o r s i m i l a r f i e l d s t u d i e s i n the f u t u r e , however. In an area with l e s s r a i n f a l l and a lower ground water l e v e l , p i t f a l l t r a p s would enable the experimenter c o n s i s t e n t l y t o remove young at an e a r l i e r age than was p o s s i b l e with Longworth t r a p s . A l t e r n a t i v e l y , techniques c o u l d be developed s i m i l a r to those of Rongstad (1965) by which o f f s p r i n g would become l a b e l e d with r a d i o i s o t o p e s i n j e c t e d i n t o t h e i r mothers. F i n a l l y , i f nests c o u l d be found and the d i s t u r b a n c e were t o l e r a t e d by mothers, c r o s s - f o s t e r i n g might be p o s s i b l e . l a t h e r q u e s t i o n s . Because of the d i f f i c u l t i e s i n manipulating and observing f a m i l i e s of Microtus townsendii, I f e e l t h a t s e v e r a l of the q u e s t i o n s suggested by t h i s study might b e t t e r be answered with a d i f f e r e n t s p e c i e s of M i c r o t u s . U n f o r t u n a t e l y , however, such a program would r e q u i r e another study s i m i l a r to t h i s one, as w e l l . Some f u t u r e problems might be: 1. How many and what kinds of b e h a v i o r a l i n t e r a c t i o n s take 1 7 5 p l a c e among l i t t e r m a t e s and t h e i r mothers? How do these i n t e r a c t i o n s i n f l u e n c e the a d u l t behavior of the o f f s p r i n g ? For a s p e c i e s which would r a i s e i t s young normally i n the l a b o r a t o r y , these gu e s t i o n s c o u l d be answered with a program of o b s e r v a t i o n and s t a n d a r d i z e d behavior t e s t s i n v o l v i n g both f a m i l y members and strange v o l e s . In a d d i t i o n , mechanisms of behavior l e a r n i n g c o u l d be i n v e s t i g a t e d ; f o r example, one could t e s t whether simple o b s e r v a t i o n of a g g r e s s i v e i n t e r a c t i o n s might induce changes i n the l a t e r behavior of a v o l e . 2. What are the n u t r i t i o n a l needs of the s p e c i e s , and, i n p a r t i c u l a r , how does maternal n u t r i t i o n i n f l u e n c e the subseguent growth of the o f f s p r i n g ? How can these growth-patterns be r e l a t e d to the weight changes 'associated with the p o p u l a t i o n c y c l e ? Again, a l a b o r a t o r y study would be necessary t o s o r t out the e f f e c t s of maternal n u t r i t i o n at d i f f e r e n t stages of development. C r o s s - f o s t e r i n g at va r i o u s ages, perhaps with i n b r e d l a b o r a t o r y mice as "standard" mothers, would f a c i l i t a t e the design of experiments r e l e v a n t t o these q u e s t i o n s . 3. Does the apparent l a c k of a d d i t i v e g e n e t i c v a r i a n c e i n Microtus townsendii, f o r the t r a i t s examined here, r e f l e c t the unusually s m a l l p r o p o r t i o n (Alan B i r d s a l l , pers. com.) of polymorphic l o c i d e t e c t e d through e l e c t r o p h o r e s i s i n t h i s s p e c i e s ? I t might be expected that measurements of h e r i t a b i l i t y f o r corresponding t r a i t s i n v a r i o u s m i c r o t i n e s p e c i e s would be c o r r e l a t e d with the p r o p o r t i o n of v a r i a b l e l o c i i n those s p e c i e s , i f the l o c i are indeed random genetic markers. 4. Given t h a t the mother can i n f l u e n c e the phenotypes of her o f f s p r i n g , to what degree does t h i s enable her to manipulate 176 them, as a group or individually? If she can exert such control, what might be her best strategy, in terms of her own fitness? The concept of parental manipulation has been applied to the phenotypic expression of altruism in social insects (Alexander, 1974); in this context, however, the mother's concern would be to prepare her offspring for survival in a future social and physical environment which is moderately predictable and might be very different from the one in which she has lived. 1 7 7 SECTION VII: CONCLUSIONS In terms of the o r i g i n a l g o als of t h i s study, the r e s u l t s have y i e l d e d some unexpected i n f o r m a t i o n and d i r e c t i o n s f o r f u r t h e r r e s e a r c h . The f i r s t g oal was to generate a p a r t i a l d e s c r i p t i o n of the breeding s t r u c t u r e of the Microtus townsendii p o p u l a t i o n a t the Haney study area, i n terms of e f f e c t i v e p o p u l a t i o n s i z e and var i a n c e i n f i t n e s s . I have concluded t h a t , during the p e r i o d between b i r t h and disappearance of a c o h o r t , the r a t i o of e f f e c t i v e p o p u l a t i o n s i z e to census number drops from approximately 1 to .33. T h i s i n d i c a t i o n of high v a r i a n c e i n f i t n e s s among parents and f a m i l i e s changes d r a m a t i c a l l y throughout the year. The v a r i a b i l i t y i n r e p r o d u c t i v e output, with i t s important i m p l i c a t i o n s f o r the g e n e t i c s t r u c t u r e of Microtus townsendii p o p u l a t i o n s , can be e x p l a i n e d to a c o n s i d e r a b l e extent by the behavior of the female parent. The s o c i a l behavior of Microtus t o S S s e n d i i females may thus be a u s e f u l i n d i c a t o r of i n d i v i d u a l r e p r o d u c t i v e success during some phases of the c y c l e . The second g o a l of the study, the e s t i m a t i o n of c o r r e l a t i o n s among r e l a t i v e s with r e s p e c t to s e v e r a l e c o l o g i c a l l y important t r a i t s , has pointed out the importance of common environment and e s p e c i a l l y maternal e f f e c t s i n the phenotypic expression of these t r a i t s . I t appears, on the other hand, that there i s r e l a t i v e l y l i t t l e a d d i t i v e g e n e t i c v a r i a n c e 178 f o r the t r a i t s , under f i e l d c o n d i t i o n s . Tendency to breed i n winter i s randomly d i s t r i b u t e d among f a m i l y members, while age at puberty i s h i g h l y c o r r e l a t e d among s i b l i n g s , e v i d e n t l y through a common environment e f f e c t s p e c i f i c to i n d i v i d u a l l i t t e r s . J u v e n i l e growth r a t e i s a l s o c o r r e l a t e d among s i b s , probably owing to another l i t t e r - s p e c i f i c common environment i n f l u e n c e . Body s i z e at a given age, however, i s s t r o n g l y r e l a t e d to the dam's maximum s i z e u n t i l a f t e r the n i n t h week of l i f e . A g o n i s t i c behavior and a c t i v i t y as measured by an encounter t e s t are a l s o c o r r e l a t e d with maternal behavior. F i n a l l y , the p r o b a b i l i t y of l e a v i n g a trapped p o p u l a t i o n appears to be s i m i l a r among l i t t e r m a t e s . These r e s u l t s do not imply that t h e r e are no genes s e g r e g a t i n g i n the pop u l a t i o n which i n f l u e n c e these c h a r a c t e r s . Had t h i s study been c a r r i e d out i n the l a b o r a t o r y , i t might w e l l have y i e l d e d r e s u l t s c o n s i s t e n t with the p u b l i s h e d l a b o r a t o r y s t u d i e s of h e r i t a b i l i t y of behavior, s i z e , and r e p r o d u c t i v e c h a r a c t e r i s t i c s on va r i o u s s p e c i e s . In many cases, a s i g n i f i c a n t g e n e t i c component has c o n t r i b u t e d to phenotypic v a r i a n c e i n the l a b o r a t o r y . However, i n n a t u r a l p o p u l a t i o n s of Microtus townsendii, i t can probably be concluded that h e r i t a b i l i t y f o r these t r a i t s i s low, though the phenotypic response of the p o p u l a t i o n to s e l e c t i o n may s t i l l be p r e d i c t a b l e to a l i m i t e d extent through maternal e f f e c t s . The i m p l i c a t i o n s of these r e s u l t s to p o t e n t i a l e x p l a n a t i o n s of v o l e p o p u l a t i o n c y c l e s depend upon t h e i r a p p l i c a b i l i t y to c y c l i n g p o p u l a t i o n s . The Microtus townsendii p o p u l a t i o n s at Haney d i d not e x h i b i t t y p i c a l p o p u l a t i o n - c y c l e s , though nearby 1 7 9 p o p u l a t i o n s appeared to resemble more c l o s e l y other m i c r o t i n e s i n t h e i r demography. I f the r e s u l t s of t h i s study are a p p l i c a b l e to a c y c l i c a l l y f l u c t u a t i n g Microtus townsendii p o p u l a t i o n , two c o n c l u s i o n s can be drawn: f i r s t , these r e s u l t s do not support the hypothesis that g e n e t i c change a s s o c i a t e d with s e l e c t i o n upon a g o n i s t i c behavior i s a major d r i v i n g f o r c e of p o p u l a t i o n f l u c t u a t i o n s i n Microtus t o w n s e n d i i . Rather, a hypothesis more c o n s i s t e n t with t h i s study suggests that changes i n s u r v i v a l , r e p r o d u c t i o n , and behavior c o u l d be mediated by and passed to o f f s p r i n g through p h y s i o l o g i c a l changes i n the mother. Second, s e l e c t i o n upon e c o l o g i c a l l y important t r a i t s may s t i l l r e s u l t i n g e n e t i c changes i n Microtus townsendii p o p u l a t i o n s , even though we may not be able t o p r e d i c t the phenotypic changes which should occur i n response. T h i s c o n c l u s i o n i s t r u e of the c h a r a c t e r s which have been shown to be c o r r e l a t e d among s i b s , but which are not p r e d i c t a b l e from the parents* phenotypes (e.g., j u v e n i l e growth r a t e , age at puberty); s e l e c t i o n upon such t r a i t s w i l l tend to f a v o r or e l i m i n a t e whole f a m i l i e s , and hence t h e i r shared genes. T h i s i n f o r m a t i o n i s u s e f u l i n d e s c r i b i n g the a c t u a l g e n e t i c s t r u c t u r e and dynamics of Microtus townsendii p o p u l a t i o n s , whether from a " s e l e c t i o n " or a " d r i f t " p o i n t of view. The t h i r d goal of the study has been to e v a l u a t e the u s e f u l n e s s of q u a n t i t a t i v e g e n e t i c s theory i n e c o l o g i c a l g e n e t i c s , a f i e l d which has h i t h e r t o been dominated by s t u d i e s of simply i n h e r i t e d t r a i t s , o f t e n of n e g l i g i b l e e c o l o g i c a l s i g n i f i c a n c e . Having found no c o r r e l a t i o n s among r e l a t i v e s which u n e q u i v o c a l l y estimate h e r i t a b i l i t y i n the s t r i c t sense 1 8 0 (V(A)/V(P)), I cannot test predictions of selection responses in th i s context. However, studies of t h i s sort may serve a d i f f e r e n t and more s i g n i f i c a n t role in ecological genetics, i n the long run. Since the existing models of evolutionary change i n populations involve guestionable assumptions and parameters which are d i f f i c u l t to measure, i t i s clear that new guestions must be asked and new models formulated i n the future. Lewontin (1974) has made one such attempt. One hopes that the new.models of ecological genetics theory w i l l be based partly upon a broad range of descriptions of the breeding structure and inheritance of e c o l o g i c a l l y important t r a i t s in populations of many species. Not only would t h i s kind of information suggest new directions for ecological genetics theory, but i t might also help to evaluate the importance of some of the existing models. I t i s possible- that many mammalian species share the pattern, seen here in Microtus townsendii, of low additive genetic variation and high intrafamily c o r r e l a t i o n for t r a i t s apparently under selection in fluctuating environments. In that case, models emphasizing genetic d r i f t , organization of the genome, and se l e c t i o n acting upon families might assume an important role i n predicting the genetics of evolutionary change within these populations. 181 APPENDIX I cre a t e d a s i m u l a t i o n model of a v o l e p o p u l a t i o n based on the b e h a v i o r - g e n e t i c hypothesis, i n order to e x p l o r e the f o l l o w i n g q u e s t i o n s : (1) Is the b e h a v i o r - g e n e t i c h y p o t h e s i s a s u f f i c i e n t e x p l a n a t i o n f o r r e g u l a r f l u c t u a t i o n s i n numbers, with no d r i v i n g v a r i a b l e e x t e r n a l t o the p o p u l a t i o n ? (2) How would a model based upon the assumptions of q u a n t i t a t i v e g e n e t i c s theory d i f f e r i n behavior from one assuming phenotypes to be determined by s i n g l e genes or other non-continuous mechanisms (e.g.,' Dekker, 1975)? (3) Over what ranges of parameters can i t produce p o p u l a t i o n c y c l e s ? I was p a r t i c u l a r l y i n t e r e s t e d i n t e s t i n g what values of the h e r i t a b i l i t y of behavior would produce c y c l e s . The model was w r i t t e n i n two v e r s i o n s , one with non-o v e r l a p p i n g g e n e r a t i o n s , the other with o v e r l a p p i n g g e n e r a t i o n s . I s h a l l d e s c r i b e f i r s t the s i m p l e r , non-overlapping g e n e r a t i o n s v e r s i o n , and l a t e r the v e r s i o n complicated by age s t r u c t u r e . No"~QY.?glapping qsn§£ations model. There i s one major s t a t e v a r i a b l e i n the model: the number of animals i n the, p o p u l a t i o n . Each animal i s d e s c r i b e d by i t s p o s i t i o n on an a r b i t r a r y phenotypic continuum, which p r e d i c t s i t s a b i l i t y to cope with i n t e r a c t i o n s with other animals, i . e . , i t s a g o n i s t i c behavior. The continuum of behavior types can be d i v i d e d up i n t o any number of phenotypic c l a s s e s . I found that d i v i s i o n of the continuum i n t o ten c l a s s e s gave r e s u l t s s i m i l a r to d i v i s i o n 1 8 2 i n t o any l a r g e r number of c l a s s e s . Therefore during most of my experimentation with the model, the behavior continuum was d i v i d e d i n t o ten to twenty phenotype c l a s s e s . S p a t i a l l y , the simulated vole p o p u l a t i o n e x i s t s i n a homogeneous h a b i t a t of constant area, so f l u c t u a t i o n s i n numbers re p r e s e n t f l u c t u a t i o n s i n d e n s i t y . The time-step of the non-o v e r l a p p i n g g e n e r a t i o n s model r e p r e s e n t s one g e n e r a t i o n (about s i x weeks i n simulated ti m e ) . Breeding i s assumed to c ontinue r e g u l a r l y throughout the year. During each time-step of the model, the f u n c t i o n a l r e l a t i o n s h i p s shown i n F i g u r e A-1 d e s c r i b e the changes i n the s t a t e v a r i a b l e , numbers of v o l e s i n each phenotype c l a s s . Note t h a t the a c t u a l r e l a t i o n s h i p s drawn are i n d i c a t i v e of the g e n e r a l shape which was assumed, and the parameters of each curve are e x p e r i m e n t a l l y v a r i a b l e . F i r s t , the number of o f f s p r i n g r e c r u i t i n g i n t o the p o p u l a t i o n per parent i s a f u n c t i o n of the phenotype of that parent (Figure A-1a). Thus f e r t i l i t y and s u r v i v a l of n e s t l i n g s and weanlings are combined i n t h i s f u n c t i o n a l r e l a t i o n s h i p . The g e n e r a l shape of the f u n c t i o n was such t h a t very a g g r e s s i v e animals (high on the phenotype scale) produced few r e c r u i t s r e l a t i v e to l e s s a g g r e s s i v e animals (low on the phenotype sc a l e ) . The second f u n c t i o n a l r e l a t i o n s h i p (Figure A-1b) d e s c r i b e s the phenotypes of the o f f s p r i n g from random matings among the a v a i l a b l e parents. T h i s r e l a t i o n s h i p i s the p r e d i c t i o n , from q u a n t i t a t i v e g e n e t i c s theory, t h a t the mean phenotype of o f f s p r i n g from a mating w i l l be a l i n e a r f u n c t i o n of the mean 1 8 3 F i g u r e A-1. F u n c t i o n a l r e l a t i o n s h i p s of the non-overlapping g e n e r a t i o n s model. Phenotype here r e f e r s to any a r b i t r a r y phenotypic c h a r a c t e r which s a t i s f i e s these r e l a t i o n s h i p s . A. Reproductive r a t e (measured i n terms of the number of o f f s p r i n g produced per g e n e r a t i o n ) , as a f u n c t i o n of phenotype. B. Mean phenotype of o f f s p r i n g as a f u n c t i o n of the mean phenotype of the two parents. The s m a l l normal curve r e p r e s e n t s the frequency d i s t r i b u t i o n of phenotypes around the mean of o f f s p r i n g f o r a p a r t i c u l a r mating. C. Aggressiveness as a f u n c t i o n of phenotype. D. S u r v i v a l r a t e to adulthood as a f u n c t i o n of two v a r i a b l e s : phenotype, and the t o t a l amount of ag g r e s s i o n i n the p o p u l a t i o n d u r i n g t h i s g e n e r a t i o n . T h i s l a t t e r value i s c a l c u l a t e d as the sum over a l l phenotype c l a s s e s of the number i n each c l a s s , m u l t i p l i e d by the aggressiveness of tha t c l a s s (cf Fig u r e A-1c) . OFFSPRING 185 phenotype of the two parents (midparent value). The slope of t h i s l i n e i s given by the parameter h 2. Offspring from a mating do not a l l have the mean phenotype, however. They are assigned phenotypes with a freguency which s a t i s f i e s the binomial d i s t r i b u t i o n about the offspring mean for that mating. The variance of t h i s d i s t r i b u t i o n could be treated in two ways. It could be set at the t h e o r e t i c a l expectation, proportional to 1 -h 2. However, in r e a l i t y , for any p a r t i c u l a r mating, the within-family variance w i l l be influenced by at least some of the following: (1) the phenotypic distance between the parents, (2) the number of l o c i involved in determining the t r a i t , (3) the h e r i t a b i l i t y of the t r a i t , (4) common environment e f f e c t s , and (5) dominance. Thus, the phenotypic variance i n offspring from a family may indeed deviate widely from the expected value. Experimental variation of this parameter showed that the behavior of the model i s i n fact quite s e n s i t i v e to the within-family phenotypic variance. Third, for the offspring generation, the aggressiveness of the entire population i s determined by summing the l e v e l of aggressiveness of a l l the animals in the population, where that l e v e l i s a function of the phenotype class of the animal (Figure A-1c). F i n a l l y , the number of offspring surviving to reproduce i s calculated for each phenotype c l a s s . The s u r v i v a l rate of an i n d i v i d u a l i s a function of both the t o t a l aggressiveness of the population in which he l i v e s , and his phenotype (Figure A-1d). QX££l3.22ifi3 3.§B6xa tions model. In the overlapping generations model, the p r i n c i p l e state variable becomes doubly 186 s u b s c r i p t e d : the number of v o l e s i n each age and phenotype c l a s s . The time-step r e p r e s e n t s the minimum time between l i t t e r s , ' or three weeks; maximum l e n g t h of l i f e i s twenty time-steps. Reproductive r a t e s are a d j u s t e d f o r ages, and each age c l a s s has a "memory" f o r the t o t a l amount of a g g r e s s i v e i n t e r a c t i o n i t has encountered over i t s l i f e . T h i s "memory" i s c a l c u l a t e d as a cumulative sum of the t o t a l a g g r e s s i v e n e s s of the p o p u l a t i o n , f o r a l l the time p e r i o d s the age c l a s s has experienced. The e f f e c t s of experience are weighted, so r e c e n t experience i s more important than past experience. Thus two of the f u n c t i o n a l r e l a t i o n s h i p s (Figure A-2) are a l t e r e d : r e p r o d u c t i v e r a t e s are determined by both age and phenotype c l a s s (Figure A-2a), and s u r v i v a l i s determined by phenotype and the t o t a l aggression experienced (Figure A-2d). S e l e c t i o n of exgerimental range of Earameters. S e v e r a l of the parameters of the model had to be s e t a r b i t r a r i l y . For example, no a b s o l u t e measure of aggressiveness has been p u b l i s h e d f o r i n d i v i d u a l s of a vole p o p u l a t i o n . S i m i l a r l y , no estimate was a v a i l a b l e of the r e l a t i v e importance of r e c e n t vs past exposure to a g g r e s s i o n . However, wherever p o s s i b l e , other parameters were s e t i n the neighborhood and range of p u b l i s h e d v a l u e s . R e s u l t s . A complete e x p l o r a t i o n of parameter space has not been c a r r i e d out with e i t h e r model, but p r e l i m i n a r y experimentation has r e v e a l e d the f o l l o w i n g c o n c l u s i o n s : 1. Within r e a l i s t i c parameter ranges, both models produce p o p u l a t i o n c y c l e s . With non-overlapping g e n e r a t i o n s , the peaks occur every f i v e t o s i x g e n e r a t i o n s (Figure A-3); with 1 8 7 F i g u r e A - 2 . F u n c t i o n a l r e l a t i o n s h i p s of the o v e r l a p p i n g g e n e r a t i o n s model. A. Reproductive r a t e , measured i n terms of the number of o f f s p r i n g produced per time s t e p , as a f u n c t i o n of two v a r i a b l e s : phenotype, and age. B. Mean phenotype of o f f s p r i n g as a f u n c t i o n of the mean phenotype of the two parents. The s m a l l normal curve r e p r e s e n t s the frequency d i s t r i b u t i o n of phenotypes around the mean of o f f s p r i n g f o r a p a r t i c u l a r mating. C. Aggressiveness as a f u n c t i o n of phenotype. D. S u r v i v a l r a t e t o adulthood as a f u n c t i o n of two v a r i a b l e s : phenotype, and the t o t a l amount of ag g r e s s i o n experienced by an age c l a s s , weighted such that recent experience i s more important than past experience. 189 Figure A-3. Simulated vole population cycle, with non-overlapping generations. The s o l i d l i n e represents t o t a l numbers; the dotted l i n e represents the t o t a l aggression of the population, measured on an a r b i t r a r y scale. 190 Figure A-3 NUMBERS TOTAL POPULATION AGGRESSION (ARBITRARY UNITS) 160 T 140 + 120 -f c o LU 03 ZD az h— o 100 4 80 + 60 + 40 0 10 20 GENERATIONS 30 1 9 1 o v e r l a p p i n g g e n e r a t i o n s , peaks are separated by about 120 weeks simulated time (Figure A-4). T h i s l a t t e r value agrees reasonably w e l l with n a t u r a l c y c l e s , s i n c e i t i s e q u i v a l e n t t o a l i t t l e more than two y e a r s . I f a non-breeding season ( u n i v e r s a l low recruitment and f a i r l y high s u r v i v a l ) were i n t r o d u c e d i n t o the model, the time between peaks would i n c r e a s e to three or f o u r years. Relevant v a r i a b l e s of the model, e.g., t o t a l a ggressiveness of the pop u l a t i o n or f i t n e s s of an extreme phenotype, a l s o c y c l e , but s l i g h t l y out of phase with numbers, as i s to be expected (Figure A-3) . 2. C y c l i n g appears to occur only when the r e l a t i o n s h i p s shown i n Fi g u r e A-5 hold between r e l a t i v e f i t n e s s and phenotype. Here, f i t n e s s i s measured as the number of o f f s p r i n g per parent which s u r v i v e t o reproduce. R e l a t i v e f i t n e s s of a phenotype during a time p e r i o d i s c a l c u l a t e d as the r a t i o of the f i t n e s s of that phenotype to the maximum f i t n e s s observed at t h a t time. Thus a l l r e l a t i v e f i t n e s s values are between 0 and 1, but the a c t u a l maximum f i t n e s s may change g r e a t l y . For example, during the i n c r e a s e phase, the maximum f i t n e s s must be g r e a t e r than 1, but during a d e c l i n e i n numbers, a l l phenotypes may have f i t n e s s l e s s than 1. The c r u c i a l aspect of t h i s r e l a t i o n s h i p i s t h a t i n t e r m e d i a t e phenotypes must be at an o v e r a l l disadvantage. I t i s t h i s requirement which prevents the p o p u l a t i o n from going to e q u i l i b r i u m with an i n t e r m e d i a t e phenotype dominant. 3. When h 2 i s l e s s than than .8, p o p u l a t i o n c y c l e s cease, and the system e x h i b i t s unstable behavior. 192 Figure A - 4 . Simulated vole population cycle, with overlapping generations. 193 Figure A-4 WEEKS 1 9 4 Figure A-5. 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