Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Parental investment in threespine stickleback, Gasterosteus aculeatus Pressley, Peter Harold 1976

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1976_A6_7 P74.pdf [ 4.35MB ]
Metadata
JSON: 831-1.0093705.json
JSON-LD: 831-1.0093705-ld.json
RDF/XML (Pretty): 831-1.0093705-rdf.xml
RDF/JSON: 831-1.0093705-rdf.json
Turtle: 831-1.0093705-turtle.txt
N-Triples: 831-1.0093705-rdf-ntriples.txt
Original Record: 831-1.0093705-source.json
Full Text
831-1.0093705-fulltext.txt
Citation
831-1.0093705.ris

Full Text

PARENTAL INVESTMENT IN THSEESPINE STICKLEBACK, GASTEROSTEUS ACULEATUS by PETER HAROLD PRESSLEY B, A. , U n i v e r s i t y of C a l i f o r n i a , 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STODIES Department of Zoology We accept t h i s t h e s i s as conforming to the r e g u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1976 / ? \ Peter Harold Pressley, 1976 In p resent ing t h i s t he s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and study. I f u r t h e r agree that permiss ion for ex tens i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r ep re sen ta t i ve s . It i s understood that copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t ten pe rm i ss i on . Department of 2<yo ( The U n i v e r s i t y of B r i t i s h Columbia 20 75 Wesbrook Place Vancouver, Canada V6T 1W5 i Abstract Parental investment, defined as any parental a c t i v i t y that 1 increases the survival of offspring at a cost to the parent, i s a useful concept for examining the sel e c t i v e bases of parental behavior. To maximize i t s lifetime production of surviving offspring, a parent should adjust i t s l e v e l of r i s k i n a parental investment depending on the value of i t s future "prospects" in r e l a t i o n to i t s present young. as present young increase i n value, either by number or age, a parent should expend more r i s k in a parental investment so long as the effectiveness of i t s behavior does not diminish. This w i l l often be the case for a parent that defends a nest containing eggs. The prediction of an increase in parental r i s k f o r more eggs or older eggs has been tested using two natural populations of threespine stickleback, Gasteros teus- acule^tus L. Male sticklebacks that were guarding nests were presented with a dummy predator, the pr i c k l y sculpin Cottus asper, and th e i r responses were measured. Those males that remained within t h e i r nest area and attacked the dummy sculpin had a larger number of eggs or older eggs than those males that deserted t h e i r nests and never attacked the dummy. In the population that i s sympatric with sculpins, males that i n i t i a l l y attacked the sculpin's head had older eggs than those which avoided the head but attacked the t a i l area. i i The l e v e l of the male's respo n s i v e n e s s , and a s s o c i a t e d r i s k , was recorded i n a s e r i e s of q u a n t i t a t i v e measures. The time i t took a male t o r e t u r n to i t s nest, as w e l l as the time to a t t a c k the s c u l p i n dummy, was s h o r t e r f o r males with a l a r g e r number of eggs or o l d e r eggs. The number of b i t e s at the dummy i n the f i r s t minute a f t e r the i n i t i a l a t t a c k i n c r e a s e d as the egg number and egg age i n c r e a s e d . Changes i n male r i s k were i n the p r e d i c t e d d i r e c t i o n and none of the responses c o u l d be a s s o c i a t e d with any s i n g l e b i o l o g i c a l or environmental f a c t o r other than the number or age of the eggs. i i i T able of Contents A b s t r a c t i Table of Contents i i i L i s t o f Tables v L i s t of F i g u r e s v i i Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . V i i i CHAPTER I . INTRODUCTION 1 CHAPTER I I . NATURAL SELECTION AND PARENTAL INVESTMENT .. 4 1. In t r o d u c t i o n <4 2. Reproductive E f f o r t and P a r e n t a l Investment ......... 4 3. Reproductive Value and Reproductive Success ......... 6 5. P r e d i c t i o n s 18 6. Changing Environments 21 7. A Re-examination of the I n i t i a l Model ............... 23 8. D i s c u s s i o n .......................................... 27 CHAPTER I I I . NEST DEFENSE BY MALE STICKLEBACKS ......... 31 1.I n t r o d u c t i o n 31 2. The Parent - Gasterosteus a c u l e a t u s . . . . . . . . . . . . . . . . . . 32 3. The Threat - Cottus asger............................ 36 4. F i g h t or F l i g h t - Choosing a F i e l d Test 38 5. Experimental R e s u l t s 43 CHAPTER IV. DISCUSSION 57 i v LITERATURE CITED 66 APPENDIX I. THE CHRONOLOGICAL EGG AGE 72 APPENDIX I I . ALL-OR-NONE RISK MEASURES 74 APPENDIX I I I . QUANTITATIVE RISK MEASURES 75 APPENDIX IV. MULTIPLE REGRESSION RESULTS 77 V L i s t of Tables TABLE I . A comparison between the number of eggs for males i n the high and low r i s k category for each a l l -or-none response ..................................... 45 TABLE I I . A comparison between the physiological age of the eggs for males i n the high and low r i s k category for each all-or-none response 46 TABLE I I I . A comparison between the chronological age of the eggs for males in the high and low ris k category for each all-or-none response ........................ 47 TABLE IV. A comparison between the two populations f o r the number and egg age of males that attacked the sculpin dummy 48 TABLE V. Regression results for each quantitative r i s k measure as a function of the number of eggs i n the nest 50 TABLE VI. Regression r e s u l t s for each quantitative r i s k measure as a function of the physiological age of the eggs in the nest 51 TABLE VII. Regression results for each guantitative r i s k measure as a function of the chronological age of the eggs in the nest ..................................... 52 v i TABLE V I I I . Regression r e s u l t s c a l c u l a t e d f o r the combined p o p u l a t i o n s counting only those males with eggs i n t h e i r n e s t s .................................. 53 TABLE IX. Responses of males guarding f r y .............. 56 List of Figures v i i FIGURE 1. The Influence of the Cost of a Parental Investment 11 FIGURE 2. The Optimal Cost of a Parental Investment .... 13 FIGURE 3. The Effectiveness of a Parental Investment ... 15 FIGURE 4. The Incorporation of a Parental Investment into a Population .................................... 25 v i i i Acknowledgements Numerous people in the I n s t i t u t e of Animal Resource Ecology have been helpful during the course of t h i s study. I would especially l i k e to thank my supervisor, J . D . McPhail, f o r his cheerful encouragement and generous support. Kim Hyatt, B i l l N e i l l , and Derek Soff provided useful c r i t i c i s m and encouragement from the begining of the study u n t i l i t s completion. Steve Borden, N e i l G i l b e r t , Clyde Murray, Ross McMurtrie, Judy Myers, Gaile Ramey, Jamie Smith, Neal Smith, and Steve Stearns also contributed s i g n i f i c a n t l y to the development of th i s thesis. 1 CHAPTER I. INTRODUCTION "The pervasive role of natural selection in shaping a l l classes of t r a i t s in organisms can be f a i r l y c a l l e d the central dogma of evolutionary biology." In t h i s statement E. 0. Wilson (1975) points out the emphasis b i o l o g i s t s place on discerning the adaptive features of b i o l o g i c a l phenomena-By o u t l i n i n g the s e l e c t i v e basis of b i o l o g i c a l patterns, evolutionary studies seek to develop p r i n c i p l e s of adaptation. P r i n c i p l e s that generate testable hypotheses not only provide an understanding of nature, but can be used to evaluate the precision of natural selection. In t h i s thesis I attempt to produce and test some hypotheses that explain certain behavioral t r a i t s involved i n parental care.1 The primary focus i s on the ultimate rather than the proximate factors that regulate the expression of parental behavior. An evolutionary interpretation of parental cars has begun to emerge within a general theory of s o c i a l behavior (Alexander 1974; Best Eberhard 1975; Wilson 1975). The period of parental care i s usually viewed as a composite of responses selected to maximize the i n d i v i d u a l parent's contribution to the gene pool of subsequent generations. Theoretical work primarily focuses on the genetic consequences of a parent's " a l t r u i s t i c " behavior, following an outline provided by Hamilton (1964). The s e l f - s a c r i f i c i n g nature of parental care i s emphasized i n the concept of parental investment introduced by Trivers (1972,1974), Parental investment i s defined as any 2 behavior toward o f f s p r i n g t h a t i n c r e a s e s the o f f s p r i n g ' s chance of s u r v i v i n g at the c o s t of the parent's a b i l i t y to i n v e s t i n other o f f s p r i n g . . Any p a r e n t a l investment, such as f e e d i n g or guarding the young, w i l l be adjusted by n a t u r a l s e l e c t i o n t o maximize the parent's l i f e t i m e p r oduction of s u r v i v i n g o f f s p r i n g . A c o n s i d e r a t i o n of the changes that occur i n de v e l o p i n g o f f s p r i n g suggests t h a t the expre s s i o n of a p a r e n t a l investment might vary throughout the pe r i o d of p a r e n t a l care. The p r o b a b i l i t y , of the o f f s p r i n g s u r v i v i n g t o reproduce w i l l g e n e r a l l y i n c r e a s e as they get o l d e r . One would expect s e l e c t i o n t o f a v o r a parent i n c r e a s i n g i t s r i s k of m o r t a l i t y as l o n g as t h i s i n c r e a s e i n the " v a l u e " of the o f f s p r i n g i s not accompanied by an i n c r e a s e i n the o f f s p r i n g ' s a b i l i t y to s u r v i v e without the parent's a s s i s t a n c e . T h i s would be the case when the developing o f f s p r i n g a re eggs and remain completely dependent on p a r e n t a l p r o t e c t i o n u n t i l h a t c h i n g . As the o f f s p r i n g become i n c r e a s i n g l y independent a f t e r h a t c h i n g , the i n c r e a s e i n t h e i r s u r v i v a l r e s u l t i n g from a given l e v e l of p a r e n t a l r i s k w i l l o f t e n d e c l i n e . T h i s decrease i n the e f f e c t i v e n e s s of a p a r e n t a l response w i l l o f t e n f a v o r a c u r t a i l m e n t of the parent's investment i n the o f f s p r i n g , as observed i n the weaning process i n some s p e c i e s . The l e v e l of r i s k d i s p l a y e d by a parent w i l l a l s o depend on the number of o f f s p r i n g r e c e i v i n g the b e n e f i t of the parent's a s s i s t a n c e . For a p a r e n t a l investment that enhances the s u r v i v a l of a l l the o f f s p r i n g e g u a l l y , such as the defense 3 of a nest, the int e n s i t y of the parent's commitment w i l l be proportional to the number of offspring involved. The parent's response w i l l also be influenced by i t s c a p a b i l i t y of acquiring more offspring in the future. Thus the l e v e l of ri s k displayed i n a parental investment w i l l be a function of (1) the present number of offspring compared to the parent's expectation of future offspring, (2) the potential increase in offspring s u rvival r e s u l t i n g from any given l e v e l of r i s k , and (3) the pro b a b i l i t y that the offspring w i l l survive to reproduce i r r e s p e c t i v e of the parental investment. In the next chapter I formally develop these predictions in a model that considers the evolution of parental investment within the framework of l i f e history theory. The model assesses the expression of a parental investment i n terms of the fundamental demographic parameters of populations, thus generating a wide range of predictions for organisms with parental care. Chapter III describes a f i e l d test of some of these predictions in natural populations of threespine stickleback, Gasterosteus aculeatus L. The l a s t chapter gives a general discussion of the test r e s u l t s and reviews some other studies of parental care that are relevant to the model of parental investment. The reader more interested i n the f i e l d experiment with sticklebacks, and s a t i s f i e d with the arguments presented so f a r , may turn d i r e c t l y to Chapter III and skip the more general theory. CHAPTER I I . NATURAL SELECTION AND PARENTAL INVESTMENT l i l S t E o d u c t i o n In r e c e n t years t h e r e has been an i n c r e a s i n g i n t e r e s t i n the e v o l u t i o n of l i f e h i s t o r y phenomena ( f o r an e x t e n s i v e review see Stearns 1976). B i o l o g i s t s are attempting to e x p l a i n how n a t u r a l s e l e c t i o n i n t e r a c t s with the environment to mold an organism's s u r v i v a l , age a t f i r s t r e p r o d u c t i o n , f e c u n d i t y , and r e p r o d u c t i v e . l i f e s p a n . The e v o l u t i o n of any component of an organism's l i f e h i s t o r y i s assumed to depend on i t s e f f e c t on the i n d i v i d u a l ' s f i t n e s s , d e f i n e d as i t s g e n e t i c c o n t r i b u t i o n to f u t u r e g e n e r a t i o n s . T h e o r e t i c a l work i s p r i m a r i l y focused on n o n - s o c i a l l i f e h i s t o r y t r a i t s , as these are a n a l y t i c a l l y more t r a c t a b l e i n mathematical models of e v o l u t i o n . A common approach i s t o c o n s i d e r the e x i s t i n g demographic s t r u c t u r e of a p o p u l a t i o n as a major i n f l u e n c e on the s e l e c t i o n of a s p e c i f i e d t r a i t . Here I extend t h i s approach to c o n s i d e r the maintenance and e v o l u t i o n of c e r t a i n a s p e c t s of p a r e n t a l c a r e . 2 t E e E E o d u c t i v e _ E f f o r t _and_Pa rent al_Investm§n t R. A. F i s h e r (1930) f i r s t c a l l e d a t t e n t i o n to the problem of determining how n a t u r a l s e l e c t i o n w i l l i n f l u e n c e an organism's a l l o c a t i o n of resources t o r e p r o d u c t i v e versus non-r e p r o d u c t i v e a c t i v i t i e s . His i n s i g h t l e d to the notion of r e p r o d u c t i v e e f f o r t , which has been a c e n t r a l concept i n 5 r e c e n t s t u d i e s o f l i f e h i s t o r y e v o l u t i o n ( W i l l i a m s 1966a,1966b; T i n k l e 1969; Goodman 1974; H i r s h f i e l d a n d T i n k l e 1975; P i a n k a and P a r k e r 1975). R e p r o d u c t i v e e f f o r t i s d e f i n e d as t h e f r a c t i o n o f t h e t o t a l amount o f t i m e and e n e r g y a v a i l a b l e t o an i n d i v i d u a l t h a t i s d e v o t e d t o r e p r o d u c t i o n ( G a d g i l and B o s s e r t 1970), and i s u s u a l l y q u a n t i f i e d by some measure o f r e p r o d u c t i v e t o n o n r e p r o d u c t i v e t i s s u e s ( H i r s h f i e l d and T i n k l e 1975) . R e p r o d u c t i v e e f f o r t i s d i f f i c u l t t o q u a n t i f y when r e p r o d u c t i v e a c t i v i t i e s i n c l u d e p a r e n t a l c a r e . F u r t h e r m o r e when c o n s i d e r i n g t h e e v o l u t i o n o f p a r e n t a l b e h a v i o r , t i m e and e n e r g y may n o t be a r e l e v a n t measure o f e f f o r t . A p a r e n t a l a c t i v i t y t h a t r e q u i r e s l i t t l e e x p e n d i t u r e o f t i m e and e n e r g y , y e t i n v o l v e s a h i g h r i s k o f m o r t a l i t y f o r t h e p a r e n t , i s u n d e r s t r o n g e r s e l e c t i v e p r e s s u r e t h a n would be i m p l i e d by a c o r r e s p o n d i n g measure o f r e p r o d u c t i v e e f f o r t b a s e d o n l y on t i m e and e n e r g y expended. Any m e a n i n g f u l measure o f t h e r e p r o d u c t i v e e f f o r t i n v o l v e d i n p a r e n t a l c a r e s h o u l d i n c o r p o r a t e t h e r i s k o f m o r t a l i t y t o t h e p a r e n t ( H i r s h f i e l d and T i n k l e 1975; P i a n k a and P a r k e r 1975). P a r e n t a l i n v e s t m e n t ( T r i v e r s 1972,1974) i s a u s e f u l c o n c e p t f o r e v a l u a t i n g t h e r i s k i n v o l v e d i n p a r e n t a l a c t i v i t i e s . A p a r e n t a l i n v e s t m e n t i s d e f i n e d as any p a r e n t a l a c t t h a t i n c r e a s e s an o f f s p r i n g ' s c hance o f s u r v i v i n g w h i l e d e c r e a s i n g t h e p a r e n t ' s a b i l i t y t o i n v e s t i n o t h e r o f f s p r i n g . The p e r i o d o f p a r e n t a l c a r e i s composed o f numerous p a r e n t a l i n v e s t m e n t s , t h e s i z e o f e a c h b e i n g measured by i t s e f f e c t on 6 the parent's a b i l i t y to produce other offspring (Trivers 1972). The decrease in a parent's p r o b a b i l i t y of future offspring gives a better measure of the importance of a parental a c t i v i t y than reproductive e f f o r t . The concept of parental investment may allow one to determine how natural selection w i l l adjust parental a c t i v i t i e s to increase a parent's contribution to future generations. 3_.S§EE2_iilctive_Value_a Fisher (1930) also introduced the notion of reproductive value, which has been widely used in evolutionary theory (Williams 1957, 1966b; Medawar 1957; HacArthur and Wilson 1967; Emlen 1970; Cody 1971). In a stable population, reproductive value (Vx) i s defined as an organism's age-s p e c i f i c expectation of future offspring (Pianka 1974) and i s given by the eguation: The term 1-fc/lx represents the probability of l i v i n g from age x to age t, and i s the expected number of female offspring produced in the time i n t e r v a l t to { t+dt ) per female aged t (or an equivalent measure fo r males, Warner 1975). In a population changing i n s i z e , the equation includes exponential terms that weight the r e l a t i v e importance of future offspring by the population's i n t r i n s i c rate of increase (Fisher 1930). 7 Because i t r e p r e s e n t s an organism's expected p r o d u c t i o n of o f f s p r i n g throughout the remainder of i t s l i f e , r e p r o d u c t i v e value i s o f t e n used as a measure of f i t n e s s i n t h e o r i e s of l i f e h i s t o r y e v o l u t i o n {Williams 1966b; Hamilton 1966; Pianka and Parker 1975). T a y l o r e t a l . (1974) have mathematically demonstrated t h a t maximizing the r e p r o d u c t i v e value at age zero i s e g u i v a l e n t t o maximizing the u l t i m a t e r a t e of i n c r e a s e , another common measure of f i t n e s s (Mertz 1971; Charlesworth 1973; B e l l 1976). Since most theory c o n s i d e r s the e v o l u t i o n a r y t r a d e - o f f between s u r v i v a l (If) and f e c u n d i t y (m^) at each i n s t a n t i n an organism's l i f e t i m e , n a t u r a l s e l e c t i o n i s assumed to f a v o r the p a r t i t i o n i n g of r e s o u r c e s so t h a t r e p r o d u c t i v e value i s maximized at every age ( H i l l i a m s 1966b; S c h a f f e r 1974a; T a y l o r e t a l . 1974). However, as f i r s t pointed out by F i s h e r (1930), r e p r o d u c t i v e value i s not an adeguate measure of f i t n e s s f o r organisms with p a r e n t a l c a r e . A parent can devalue i t s e x p e c t a t i o n of f u t u r e o f f s p r i n g while i n c r e a s i n g i t s g e n e t i c c o n t r i b u t i o n t o f u t u r e g e n e r a t i o n s . Consider the o r i g i n of a p a r e n t a l response t h a t i n v o l v e s a " s a c r i f i c e " f o r the young (aged y) such that the parent (aged x) decreases i t s chance of s u r v i v a l ( i . e . a p a r e n t a l investment). The response i n c r e a s e s the o f f s p r i n g ' s s u r v i v a l a t that age ( l y ) , and w i l l be i n c o r p o r a t e d i n t o the p o p u l a t i o n i f the genotype that d i s p l a y s the response has a l a r g e r u l t i m a t e r a t e of i n c r e a s e ( r e p r o d u c t i v e value a t age zero) than the other genotypes i n the p o p u l a t i o n (Mertz 1971). Since the response i n c r e a s e s the 8 s u r v i v a l of o f f s p r i n g bo rn i n t h e pas t i t w i l l not be a c c o u n t e d f o r by an i n c r e a s e i n t h e measure o f the p a r e n t ' s p r e s e n t p r o d u c t i o n o f o f f s p r i n g , m t . T h e r e f o r e , t h e d e c r e a s e i n t he p a r e n t ' s a g e - s p e c i f i c s u r v i v a l (1-t) w i l l r e s u l t i n a l o w e r r e p r o d u c t i v e v a l u e (V x ) f o r t h e p a r e n t a t t h a t a ge . Thus , n a t u r a l s e l e c t i o n can f a v o r p a r e n t a l a c t i v i t i e s t h a t d e c r e a s e a p a r e n t ' s r e p r o d u c t i v e v a l u e . Because a p a r en t can i n f l u e n c e t he s u r v i v a l of i t s young, any measure o f f i t n e s s f o r a p a r e n t s h o u l d i n c l u d e t he p o t e n t i a l c o n t r i b u t i o n t o f u t u r e g e n e r a t i o n s by o f f s p r i n g s t i l l under i t s c a r e , as w e l l as any c o n t r i b u t i o n by i t s e x p e c t e d f u t u r e o f f s p r i n g . I d e f i n e a p a r e n t ' s r e p r o d u c t i v e s u c c e s s , S , as i t s e x p e c t a t i o n o f f u t u r e g r a n d c h i l d r e n . The r e p r o d u c t i v e s u c c e s s o f a p a r e n t i n c l u d e s t h e number o f g r a n d c h i l d r e n t h a t w i l l be p roduced by t h e p a r e n t ' s f u t u r e o f f s p r i n g as w e l l as t he o f f s p r i n g p r e s e n t l y under i t s i n f l u e n c e . F o l l o w i n g W i l l i a m s (1966b) , r e p r o d u c t i v e s u c c e s s (S) can be p a r t i t i o n e d i n t o p r e s e n t (P) and f u t u r e (F) components such t h a t : S = P + F The p r e s e n t component, p , i s e q u a l t o the sum o f t he r e p r o d u c t i v e v a l u e s o f each o f t h e o f f s p r i n g p r e s e n t l y under p a r e n t a l c a r e . T h i s i s e q u i v a l e n t t o the number o f Ergs_n.t young t i m e s t h e i r a ve rage e x p e c t a t i o n o f f u t u r e o f f s p r i n g . The f u t u r e component, F , i s d e t e rm ined by t he sum o f t h e p a r e n t ' s g r a n d c h i l d r e n t h a t w i l l be p roduced by i t s £utur.e o f f s p r i n g . In a p o p u l a t i o n w i t h a s t a b l e age d i s t r i b u t i o n t h e 9 f u t u r e component i s egual to the parent's r e p r o d u c t i v e value ( V x j , s i n c e the eguation f o r r e p r o d u c t i v e value accounts f o r the c o n t r i b u t i o n by f u t u r e o f f s p r i n g to subseguent g e n e r a t i o n s ( L e s l i e 1948). is. P a r e n t a l Investment and Reproductive Success The p e r i o d of p a r e n t a l care can now be c o n s i d e r e d as a composite of p a r e n t a l investments, each adjusted by n a t u r a l s e l e c t i o n t o maximize the parent's r e p r o d u c t i v e success (S). For any s p e c i f i e d p a r e n t a l investment, I determine i t s e f f e c t on the present (P) and f u t u r e (F) p o r t i o n s of the parent's r e p r o d u c t i v e success by i s o l a t i n g i t from the r e s t of the parent's l i f e h i s t o r y . In t h i s way the maintenance and e v o l u t i o n of a p a r e n t a l investment i s i n f l u e n c e d by demographic f a c t o r s that are independent of the investment. Consider a p a r e n t a l investment t h a t i n v o l v e s a r i s k of m o r t a l i t y f o r the parent, such as the defense of i t s young a g a i n s t a predator. F o l l o w i n g Williams (1966b), the p a r e n t a l investment has a c o s t , C , measured as the p r o p o r t i o n a t e decrease i n the f u t u r e component (F) of the parent's r e p r o d u c t i v e success (S). I f a more inte n s e defense r e s u l t s i n a higher r i s k of m o r t a l i t y f o r the parent, then the s i z e of the c o s t w i l l depend on the i n t e n s i t y of the parent's response. The i n c r e a s e i n the o f f s p r i n g ' s s u r v i v a l as a r e s u l t of the response i s the b e n e f i t , B , measured as the p r o p o r t i o n a t e i n c r e a s e i n the present component (P) of the 10 parent's reproductive success. The amount of increase in the offspring's survival w i l l often depend on the level of risk taken by the parent. Thus, for a parental investment I consider the benefit as a function of the cost ( B = B (C) ) . For any parental investment, I assume there i s a l i m i t to the extent that a parent can increase the survival of i t s offspring (Trivers 1972,1974; Smith and Fretwell 1974). Figure 1a shows a hypothetical relation between the benefit and cost of a parental investment. The reproductive success (S) of a parent resulting from a parental investment can now be considered as a function of the investment's cost (Figure 1b), such that S(C) = ( 1 + B(C) ) P + ( 1 - C ) F (1) The reproductive success (S) w i l l be at a maximum where S' (C) = 0 (Figure 2a) and S''(C) i s negative. I define the cost associated with this point as the optimal cost, designated C^,. Solving from equation (1) , the optimal cost for a parental investment i s the cost that s a t i s f i e s the relation F BMC) = (2) P Hhen the benefit i s . a sigmoidal function of the cost (Brockelraan 1975), B ' ' ( c m ) ^ s necessarily negative. Figure 2a shows that C m corresponds to the point where the slope equal to F/P i s tangent to the curve for benefit as a function of cost. As F/p decreases (the tangent line becomes more 11 FIGURE 1 The I n f l u e n c e o f t h e C o s t o f a P a r e n t a l I n v e s t m e n t F i g . 1 a : A h y p o t h e t i c a l r e l a t i o n between t h e b e n e f i t ( t h e p r o p o r t i o n a t e i n c r e a s e i n t h e p r e s e n t component o f a p a r e n t ' s r e p r o d u c t i v e s u c c e s s ) and t h e c o s t ( t h e p r o p o r t i o n a t e d e c r e a s e i n t h e f u t u r e component) o f a p a r e n t a l i n v e s t m e n t - The b e n e f i t i s c o n s i d e r e d as a f u n c t i o n o f t h e c o s t , B ( C ) , and a p p r o a c h e s an a s y m p t o t e b e c a u s e t h e r e i s a l i m i t t o t h e e x t e n t t h a t a p a r e n t can i n c r e a s e t h e s u r v i v a l o f i t s o f f s p r i n g - I n t h i s f i g u r e i n i t i a l i n c r e a s e s i n c o s t have t h e l a r g e s t e f f e c t on t h e b e n e f i t , a l t h o u g h t h e f u n c t i o n c o u l d a l s o be s i g m o i d a l a t low l e v e l s o f c o s t . F i g . 1 b : A p a r e n t ' s r e p r o d u c t i v e s u c c e s s ( e x p e c t a t i o n o f f u t u r e g r a n d c h i l d r e n ) c o n s i d e r e d a s a f u n c t i o n o f t h e c o s t , S(C) , o f a p a r e n t a l i n v e s t m e n t . The r e p r o d u c t i v e s u c c e s s i s t h e sum o f a p r e s e n t component ( P ) , r e p r e s e n t i n g t h e young p r e s e n t l y u n d e r p a r e n t a l c a r e , and a f u t u r e component ( F ) , w h i c h r e p r e s e n t s t h e p a r e n t ' s e x p e c t a t i o n o f f u t u r e o f f s p r i n g . The r e s u l t i n g r e p r o d u c t i v e s u c c e s s f o r t h e r e l a t i o n o f b e n e f i t and c o s t shown i n F i g . 1a i s a t a maximum f o r an i n t e r m e d i a t e l e v e l o f c o s t . R E P R O D U C T I V E S U C C E S S 13 FIGURE 2 The Optimal Cost of a Parental Investment Fig 2a.: The optimal cost, C*,, i s the l e v e l of cost at which the parent's reproductive success i s at a maximum, S'{C)=0. This cost corresponds to the point where the slope egual to the r a t i o of the future (F) to the present (P) component, F/P, i s tangent to the curve for benefit as a function of cost. Fig 2b: As F/P decreases (the slope i n Fig. 2a becomes more horizon t a l ) , either by an increase i n the number or reproductive value of the young or by a decrease i n the parent's expectation of future of f s p r i n g , the optimal cost of the parental investment increases. 14 15 FIGURE 3 The Effectiveness of a Parental Investment For a parental investment that r e s u l t s i n more benefit for a given l e v e l of cost, the optimal cost (Cm) w i l l be higher for a given value of F/P. S i m i l a r l y , any decrease i n the effectiveness of a parental investment (e. g. i f the young become less dependent on the parent's assistance) w i l l favor a lower cost. 17 h o r i z o n t a l ) , C m i n c r e a s e s (Figure 2b). Thus, as the value of the present component (P) i n c r e a s e s (F/P decreases) , the response t h a t maximizes a parent's r e p r o d u c t i v e s u c c e s s (S) has a higher c o s t . A decrease i n a parent's e x p e c t a t i o n of f u t u r e o f f s p r i n g (lower F) a l s o f a v o r s a p a r e n t a l response i n v o l v i n g a higher r i s k t o the parent. During the period of p a r e n t a l care, the a b i l i t y of a parent to e f f e c t the s u r v i v a l of i t s young may change ( f o r example, as the young become independent). The b e n e f i t of a p a r e n t a l investment may vary f o r any given l e v e l of c o s t (Figure 3). As the b e n e f i t i n c r e a s e s , the optimal c o s t (C m) of a response i n c r e a s e s ( f o r parents with egual v a l u e s of F/P). S i m i l a r l y , a decrease i n a parent's e f f e c t i v e n e s s f a v o r s l e s s p a r e n t a l r i s k . So f a r I have co n s i d e r e d p a r e n t a l investments t h a t vary i n the i n t e n s i t y of the parent's response. For a p a r e n t a l investment t h a t i n v o l v e s an a l l - o r - n o n e response (such as whether the parent defends i t s young at a l l ) , the problem i s to determine a t what p o i n t the response becomes j u s t i f i e d (Williams 1966b). An a l l - o r - n o n e response i n c r e a s e s a parent's r e p r o d u c t i v e success i f S (C), the r e p r o d u c t i v e success r e s u l t i n g from the response, i s g r e a t e r than S (0), the r e p r o d u c t i v e success i n the absence of the response (zero c o s t ) . Combining S (C) > S(0) with equation (1) g i v e s 18 B F > (3) C P The b e n e f i t i n r e l a t i o n to the c o s t of an a l l - o r - n o n e response must be gr e a t e r than a parent's f u t u r e prospects (F) d i v i d e d by i t s present prospects (P) f o r i t to i n c r e a s e the parent's r e p r o d u c t i v e success (S). During the pe r i o d of p a r e n t a l c a r e , an a l l - o r - n o n e response w i l l not be j u s t i f i e d u n t i l F/P i s exceeded by the b e n e f i t - c o s t r a t i o of the response (Williams 1966b; Goodman 1974). ^ P r e d i c t i o n s The model of p a r e n t a l investment and r e p r o d u c t i v e success l e a d s to a number of p r e d i c t i o n s f o r p a r e n t a l a c t i v i t i e s . For any p a r e n t a l investment, circumstances i n the parent's l i f e h i s t o r y and environment that are independent of the investment w i l l determine the i n t e n s i t y of the parent's response. A number of f a c t o r s can be co n s i d e r e d that w i l l i n f l u e n c e the p a t t e r n of p a r e n t a l investment throughout the p e r i o d of p a r e n t a l care. The model a l s o p r e d i c t s trends i n p a r e n t a l investment f o r v a r i o u s parents w i t h i n the same p o p u l a t i o n as w e l l as d i f f e r e n c e s between separate p o p u l a t i o n s and s p e c i e s . The components of a parent's r e p r o d u c t i v e success (S) are major determinants of a parent's behavior. For any p a r e n t a l investment the r a t i o of f u t u r e t o present p r o s p e c t s , F/P , w i l l i n f l u e n c e the i n t e n s i t y of a parent's response (Figure 2b). During the pe r i o d of p a r e n t a l care the f o l l o w i n g may 19 change the value of F/P and af f e c t the optimal cost of a parental investment. (1) As the offspring get older t h e i r p r o b a b i l i t y of surviving to reproduce increases, r e s u l t i n g i n a larger average reproductive value for the offspring (larger P). Increases i n the age of the young w i l l generally favor parental responses that involve a higher r i s k . (2) The number of offspring under parental care can increase (due to subseguent breeding) or decrease (due to mortality or fledging). A gain (larger P) or loss (smaller P) of young w i l l favor a corresponding increase or decrease i n parental r i s k for a given l e v e l of F . (3) As the parent ages i t s reproductive value w i l l often decrease, es p e c i a l l y i n seasonal breeders (Pianka and Parker 1975). A decrease i n a parent's expectation of future offspring during the period of parental care w i l l favor the parent increasing i t s r i s k for the young. In addition to influencing the optimal cost of a parental investment, the value of F/P w i l l determine the timing of an all-or-none response during the period of parental care (eguation 3). Thus, as the offspring get older (larger P), the value of F/P w i l l decrease to a point where a " r i s k y " a l l -or-none response w i l l become j u s t i f i e d . The rate at which the optimal cost of a parental investment changes w i l l also depend on the rate of change in the value of F/P. For any comparison of parents within a population, the age and number of young as well as the reproductive value of the parent w i l l influence the optimal cost for a parental investment. In addition, the sex of the parent may be 20 important in species where both sexes take part i n parental a c t i v i t i e s , since the age-specific expectation of future offspring may d i f f e r between sexes. Variation in adult and juvenile s u r v i v a l , as well as adult fecundity, w i l l result i n d i f f e r e n t patterns of parental investment for d i f f e r e n t populations and species. The e f f e c t of resource a v a i l a b i l i t y , predation, and competition on the present (P) and future (F) components of a parent's reproductive success (S) w i l l favor d i f f e r e n t l e v e l s of parental r i s k . For any prediction of an environment's e f f e c t on the optimal cost of a parental investment i t w i l l be necessary to delimit the environment's effect on offspring s u r v i v a l (P) separately from i t s e f f e c t on parent s u r v i v a l (F) . Another major determinant of parental investment i s the effectiveness of a parent's response, which i s the benefit r e s u l t i n g from a given l e v e l of cost (Figure 3). During the period of parental care, the a b i l i t y of a parent to influence the survival of i t s young may decrease as the offspring become independent. The r e s u l t i n g decrease i n the benefit of a parental investment w i l l favor a lower parental r i s k (Figure 3). A circumstance that a l t e r s the effectiveness of a response, such as the offspring becoming older and more independent, may simultaneously a f f e c t the value of F/P. The influence of the change in F/P on the optimal cost may act counter to the influence of the change i n the effectiveness of a response, making i t d i f f i c u l t to predict the f i n a l outcome. 21 Any prediction of a pattern of parental investment w i l l have to account for changes i n the effectiveness of a response, as well as changes i n F/P. This w i l l be especially true for comparisons of d i f f e r e n t populations where, for example, the benefit-cost function of a parental investment might vary due to the presence of d i f f e r e n t predators. £i£ha,S3i23_E.nyironments Fisher's eguation for reproductive value (V x) assumes that age-specific survivorship ( l t ) and fecundity (mt) are invariant over time and that the age d i s t r i b u t i o n within the population i s stable (Caughley 1970). In most natural s i t u a t i o n s , environmental fluctuations w i l l cause s u r v i v a l and fecundity to vary, r e s u l t i n g i n d i f f e r e n t measures of age-s p e c i f i c reproductive value at any one time. When considering the reproductive value of a parent and i t s offspring as a major determinant of parental investment, the simplest solution i s to assume that any pattern of parental investment i s a r e s u l t of selection acting on the long-term average reproductive values. However, i f environmental f l u c t a t i o n s af f e c t offspring s u r v i v a l d i f f e r e n t l y than parent s u r v i v a l , then selection may favor changes in parental investment to compensate for the difference. A fluctuating environment that has i t s major impact on juvenile mortality w i l l favor decreases i n the optimal cost of a parental investment, while fluctuations that primarily a f f e c t a parent's s u r v i v a l w i l l 22 s e l e c t f o r i n c r e a s e s i n p a r e n t a l r i s k . (Murphy 1968; S c h a f f e r 1974b) . Seasonal f l u c t u a t i o n s t h a t a f f e c t a g e - s p e c i f i c s u r v i v a l and f e c u n d i t y , such as seasonal v a r i a t i o n i n o f f s p r i n g s u r v i v a l , may r e s u l t i n a corresponding pattern of p a r e n t a l investment. Thus, f o r a p o p u l a t i o n i n a seasonal environment, the p a t t e r n of p a r e n t a l investment might be best determined by c o n s i d e r i n g the time of year as w e l l as the age of the parent and i t s o f f s p r i n g . The seasonal change i n s u r v i v a l c o u l d be i n c o r p o r a t e d i n t o the measure of r e p r o d u c t i v e value by i n c l u d i n g a v a r i a b l e s p e c i f y i n g the time of year. T h i s would be s i m i l a r to the "organism s t a t e v a r i a b l e " i n t r o d u c e d by T a y l o r e t a l . (1974), and would be u s e f u l f o r p r e d i c t i n g changes i n p a r e n t a l investment t h a t r e s u l t from seasonal changes i n s u r v i v a l and f e c u n d i t y . The e v o l u t i o n of any p a t t e r n of p a r e n t a l investment i n a changing environment may a l s o be i n f l u e n c e d by the parent's a b i l i t y to p r e d i c t the q u a l i t y of a given year f o r j u v e n i l e and a d u l t s u r v i v a l (Cohen 1967; H i r s h f i e l d and T i n k l e 1975). A parent t h a t can c o r r e l a t e environmental cues with a f a v o r a b l e year f o r o f f s p r i n g w i l l be s e l e c t e d to i n c r e a s e i t s r i s k i n a p a r e n t a l a c t i v i t y . A p a r e n t a l response may a l s o depend on the parent's a b i l i t y t o p r e d i c t a change i n the e f f e c t i v e n e s s of a p a r e n t a l investment, which might r e s u l t from d i f f e r e n t r e s o u r c e or p r e d a t i o n l e v e l s . The demographic determinants of a p a r e n t a l investment w i l l l i e between the long-term average values of the components of a parent's 23 reproductive success (S) and the actual values that would be known by a parent with "perfect knowledge". IiA_Re-examination_of_the_rnitial_Model So far I have considered the optimal response of a parental investment as a r e s u l t of demographic circumstances that are independent of the investment. However, once a pattern of parental investment i s incorporated into a population, the investment w i l l i n turn mold tha population's demography. although circumstances that are independent of a parental investment w i l l maintain i t at a certain l e v e l , a parental investment w i l l not evolve in i s o l a t i o n from the remainder of an organism's l i f e history. Considering t h i s i n t e r a c t i o n may be useful for evaluating the f e a s i b i l i t y of the i n i t i a l model. The e f f e c t of a parental investment being incorporated into a population w i l l be to increase P and decrease F (eguation 1 ) . This decrease i n F/P w i l l favor a larger optimal cost (C M) for the investment (Figure 2 b ) , which w i l l i n turn decrease F/P. This interaction w i l l r e s u l t i n continual selection for higher l e v e l s of cost. However, one would not expect the optimal cost to increase i n d e f i n i t e l y but to approach some stable l e v e l . To determine i f the i n i t i a l model leads to a f i n a l optimal cost, I simulated the i n t e r a c t i o n between C m and F/P. 24 Beginning with i n i t i a l values of the present (P0 ) and future (F 0) components of the parent's reproductive success (S), I determined the optimal cost (eguation 2) of the benefit-cost r e l a t i o n shown in Figure 1a. This optimal cost (C,) then modified the present and future components such that Ft = ( 1-(C, -C0) ) Fa and P, = ( 1-(B,-B0) ) P 0 where C0= 0 and Ba= 0 , since the i n t e r a c t i o n represents the f i r s t appearance of the parental investment. This was repeated a number (n) of times such that the r e s u l t i n g optimal cost, Cn , s a t i s f i e s the r e l a t i o n Fn-i d - t C ^ - C ^ ) ) F n. a B' (C„) = = Pn-1 (1-(B f t. 1-B-. a) ) P n. a Figure 4a shows that C h approaches an asymptote, demonstrating that the optimal cost does not increase i n d e f i n i t e l y . In a natural population, the rate at which C n increases w i l l depend on the b i o l o g i c a l circumstance. The purpose of the exercise was merely to determine i f the evolution of a new parental investment might lead to a stable response l e v e l . The influence of the i n i t i a l values, T0 and P 0 , on the f i n a l optimal cost, designated C/ , was also considered. The value of Cf was determined by setting i t egual to C n when the difference, C„ - C-.1,was less than a s p e c i f i e d value at which the optimal cost was considered to no longer be appreciably changing. The r e s u l t s are shown in Figure 4b. The f i n a l optimal cost (Cf) i s lower for a higher i n i t i a l r a t i o of future to present prospects (F^/P^,). In addition, as the 25 FIGURE 4 The I n c o r p o r a t i o n of a P a r e n t a l Investment i n t o a P o p u l a t i o n F i g . 4a: The r e s u l t s of a s i m u l a t i o n r e p r e s e n t i n g the change i n the optimal c o s t , C n , as a p a r e n t a l investment with a b e n e f i t - c o s t f u n c t i o n s i m i l a r to F i g , 1a becomes e s t a b l i s h e d i n a p o p u l a t i o n . The optimal c o s t at each r e i t e r a t i o n , n, remolds the p o p u l a t i o n ' s demography, by i n c r e a s i n g the value of the present component (P) and decreasing the value of the f u t u r e component ( F ) , r e s u l t i n g i n a new l e v e l of c o s t being f a v o r e d . The r a t e of i n c r e a s e i n the optimal c o s t g r a d u a l l y d e c l i n e s and reaches a s t a b l e l e v e l , designated the f i n a l o p timal cost ( C f ) . F i g . 4b: The f i n a l o p t i m a l c o s t , Cf, f o r a number of s i m u l a t i o n s s t a r t i n g with d i f f e r e n t i n i t i a l v alues of the present (P 0) and f u t u r e (F e) components. When the b e n e f i t f o r a given l e v e l of c o s t i n c r e a s e s , or when the value of F 0 / P 0 decreases, the f i n a l optimal c o s t i s higher, which i s the same q u a l i t a t i v e r e s u l t p r e d i c t e d by the i n i t i a l model shown i n F i g . 2 and F i g . 3. 26 ( b ) 27 effectiveness of a response increases (larger benefit for a given cost), Cf increases. These results are g u a l i t a t i v e l y the same as those predicted from the i n i t i a l model. 8-.Discussion Rather than trying to specify a minimum number of b i o l o g i c a l and environmental conditions that determine parental care, I have attempted to predict how the expression of a parental investment w i l l be influenced by the demography of a population. A parent's response i s considered a r e s u l t of natural selection acting on a range of parental behaviors, selecting the optimal response f o r a particular circumstance-Thus I have primarily focused on how the pattern of parental investment i n a population i s maintained and how i t w i l l evolve in d i f f e r e n t circumstances, rather than the o r i g i n of the investment. The cost of a parental investment serves as a measure of reproductive e f f o r t for a parental a c t i v i t y . By stressing the ris k of mortality, the concept of parental investment can be used to determine the s e l e c t i v e bases of parental behavior. To understand the evolution of any reproductive a c t i v i t y , the measure of reproductive e f f o r t should incorporate the r i s k of mortality ( H i r s h f i e l d and Tinkle 1975; Pianka and Parker 1975). In addition, the benefit of a parental investment i s considered a major determinant of a parent's response. The 28 benefit i s the proportionate increase in the present component (P) r e s u l t i n g from the parent's response. For a parental response that a f f e c t s the survival of offspring d i f f e r e n t i a l l y , such as feeding some young while starving others, the benefit i s measured by the average increase in offspring s u r v i v a l . The model only considers parent-offspring r e l a t i o n s from the standpoint of the parent. T r i v e r s (1974) has discussed i n d e t a i l circumstances in which the offspring can e l i c i t more benefit than the parent should optimally give. The optimal cost of a parental investment corresponds to the parental response that maximizes a parent's contribution to future generations. Thus, I have considered the expression of a parental investment as a function of selection acting to maximize future " p r o f i t s " rather than as a function of cumulative or past investment (Trivers 1972; Barash 1975). The notion of reproductive success (S) was introduced as a f i t n e s s measure because the eguation for reproductive value does not account f o r parental care. . Hamilton (1966) suggested redefining the measure of fecundity (mt) in species with parental care so that " b i r t h " i s the time when the offspring become independent of the parent. However, this i s not the usual method of c a l c u l a t i n g fecundity and would lead to complications in species with extended periods of parental care. Schaffer (1974a,1974b) considers fecundity as the number of offspring that survive to f i r s t breeding. While t h i s accounts for the e f f e c t s of parental care on the population's ultimate rate of increase, i t provides no insight 29 i n t o how a parent might a d j u s t i t s behavior throughout the pe r i o d of p a r e n t a l c a r e . By d e f i n i n g r e p r o d u c t i v e s u c c e s s and p a r t i t i o n i n g i t i n t o present and f u t u r e components, d i f f e r e n t p a t t e r n s of p a r e n t a l investment can be p r e d i c t e d . The f u t u r e component (F) i s comparable to an organism's r e s i d u a l r e p r o d u c t i v e value (Williams 1966), which i s u s e f u l i n p r e d i c t i n g the a l l o c a t i o n of energy t o r e p r o d u c t i v e t i s s u e s up to the time of b i r t h (Pianka and Parker 1975). The present component (P) allows one to c o n s i d e r a parent's i n f l u e n c e on the s u r v i v a l of i t s o f f s p r i n g , which would not be accounted f o r i n the u s u a l measure of a g e - s p e c i f i c f e c u n d i t y . The concept of r e p r o d u c t i v e success (S) shares the same problems as any other a v a i l a b l e measure of f i t n e s s (Kempthorne and P o l l a k 1970). The assumptions of a s t a b l e age d i s t r i b u t i o n and i n v a r i a n t s u r v i v a l and f e c u n d i t y l e a d to d i f f i c u l t i e s i n making p r e c i s e p r e d i c t i o n s f o r n a t u r a l p o p u l a t i o n s . , The us e f u l n e s s of the model presented here i s i n making q u a l i t a t i v e p r e d i c t i o n s that can be t e s t e d i n f i e l d s i t u a t i o n s . I t s main value l i e s i n accounting f o r d i f f e r e n c e s or p r e d i c t i n g changes i n p a r e n t a l behavior based on known b i o l o g i c a l circumstances. For example, an i n c r e a s e i n the number of o f f s p r i n g i n a nest can le a d to a p r e d i c t i o n of an i n c r e a s e i n p a r e n t a l r i s k , without r e q u i r i n g exact measures of a l l the demoqraphic parameters of the p o p u l a t i o n . Some b i o l o g i c a l circumstances w i l l l e a d t o more g e n e r a l p r e d i c t i o n s than o t h e r s . When changes i n F/P are not confounded by simultaneous changes i n the e f f e c t i v e n e s s of a response, the 30 change in parental investment w i l l be more predictable. For example, as eggs i n a nest get older the value of F/P w i l l decrease, but the ef f e c t of a parent's defense on increasing the eggs' survival w i l l remain constant. Thus a mora general prediction of increased parental care with increasing age of offspring can be made for situations where the offspring are eggs than in situations where the offspring have hatched and are becoming more independent as they age. In t h i s l a t t e r s i t u a t i o n , the benefit of a parental defense may decrease over time favoring less parental r i s k . The model of parental investment and reproductive success w i l l be most useful when applied to p a r t i c u l a r circumstances. 31 CHAPTER I I I . NEST DEFENSE BY MALE STICKLEBACKS Production The concept of p a r e n t a l investment l e a d s to a number of hypotheses, some which are more t e s t a b l e than o t h e r s . P a r e n t a l a c t i v i t i e s t h a t a l l e v i a t e a s e r i o u s t h r e a t t o the young while c o n s t i t u t i n g c o n s i d e r a b l e r i s k f o r the parent are obvious examples of p a r e n t a l investment and can be used to t e s t these hypotheses. The circumstance i n which a parent defends i t s young a g a i n s t a predator t h a t i s a t h r e a t t o both the young and the parent, provides a u s e f u l s t a r t i n g p o i n t f o r e v a l u a t i n g the i n f l u e n c e of the o f f s p r i n g on the l e v e l of r i s k undertaken by the parent. To e l i m i n a t e any e f f e c t of the age or number of young on the e f f e c t i v e n e s s of the parent's defense, i t i s necessary to choose a s i t u a t i o n i n which the parent's a b i l i t y t o defend i t s o f f s p r i n g i s independent of t h e i r abundance or age. T h i s i s o f t e n the case when a parent defends eggs i n a nest. The parent's a b i l i t y t o chase a predator away from the nest w i l l u s u a l l y be independent of the number of o f f s p r i n g i f they are a l l concealed w i t h i n the nest. I f the o f f s p r i n g are eggs, they w i l l g e n e r a l l y remain dependent on the parent's a s s i s t a n c e u n t i l h a tching, and t h e i r age w i l l not a f f e c t the b e n e f i t r e s u l t i n g from any g i v e n l e v e l of p a r e n t a l r i s k . Thus I chose the circumstance of a parent defending a nest with eggs t o examine the i n f l u e n c e of the o f f s p r i n g on the i n t e n s i t y of the parent's defense. My 32 o p e r a t i o n a l h y p o t h e s i s was t h a t the parent would i n c r e a s e i t s r i s k f o r a l a r g e r number or o l d e r average age of eggs i n the n e s t . 2iThe_Parent_-_Gasterosteus_ac A v a r i e t y of organisms t h a t e x h i b i t p a r e n t a l care o f f e r p o t e n t i a l o p p o r t u n i t i e s f o r t e s t i n g hypotheses of p a r e n t a l investment. To t e s t the p a r e n t a l defense hypothesis i n t h i s study I have used the t h r e e s p i n e s t i c k l e b a c k , G_a.steroste^s a c u l e a t u s . In t h i s f i s h s p e c i e s , females enter breeding areas only to spawn and males assume p a r e n t a l r e s p o n s i b i l i t i e s , defending the eggs and newly hatched f r y . The r e p r o d u c t i v e behavior of male s t i c k l e b a c k s i n l a b o r a t o r y s i t u a t i o n s has been d e s c r i b e d i n d e t a i l (Tinbergen 1952; van I e r s e l 1958; van den Assera 1967). Here I w i l l only add some ob s e r v a t i o n s of male s t i c k l e b a c k s i n t h e i r n a t u r a l environment t h a t may be r e l e v a n t to the f i e l d experiment. , For t h i s study two i s o l a t e d p o p u l a t i o n s were chosen on S e c h e l t Peninsula north of Vancouver, B r i t i s h Columbia. Both were i n low e l e v a t i o n l a k e s , Trout Lake and Garden Bay Lake, which have c l e a r waters s u i t a b l e f o r o b s e r v a t i o n s from shore. In the s p r i n g t i m e male s t i c k l e b a c k s move i n t o shallow areas along the l a k e shores, where they e s t a b l i s h t e r r i t o r i e s and b u i l d nests of algae and other p l a n t d e b r i s . Baggerman (1957) found t h a t breeding i n G A agulaatus i s t r i g g e r e d by i n c r e a s i n g temperatures and l o n g e r day l e n g t h s . Males e n t e r i n g breeding 33 condition can usually be i d e n t i f i e d by t h e i r c h a r a c t e r i s t i c development of bright red throats and blue i r i s e s . In 1975, the f i r s t breeding males in Trout Lake were observed i n the second week of May. These were tending nests in shallow areas where the water temperature had climbed to 16° C. Males gradually began to se t t l e i n shore areas adjacent to deeper parts of the lake as the main lake temperature increased- In Garden Bay Lake, males with breeding coloration were also f i r s t observed i n the middle of May. The male stickleback c o l l e c t s plant debris and constructs a c y l i n d r i c a l nest that l i e s f l a t on the lake bottom.. Most of the nests observed i n Trout Lake (n=103) and Garden Bay Lake (n=66) were i n well exposed areas open to the main body of the lake. Nests were not uniformly di s t r i b u t e d along the shore; some areas had a larger concentration of males than others. The mean distance to i t s nearest neighbor's nest was 1.61 m (standard error (SE) =.095) for Trout Lake males and 1.26 m (SE=.088) for males from Garden Bay Lake. Nests were generally close to shore, except where shallow areas extended far out into the lakes. The mean distance of nests from shore was less i n Trout Lake (x=.86 m, SE=.050) than in Garden Bay Lake (x=1.85 m, SE=.164), which has more gradual sloping shallows than Trout Lake. The mean depth of water over the nests (x=.38 m, SE=.015) in Trout Lake did not vary u n t i l the l a s t part of the breeding season. By mid July water temperatures had climbed to 25° C. (measured at .4 m depth) and most sticklebacks had stopped breeding. In 34 contrast, males i n Garden Bay Lake continued to breed through July, when water temperatures exceeded 25° C , u n t i l the f i r s t week of August when the water temperature had dropped back to 22° C. The mean depth of nests i n Garden Bay Lake increased during t h i s period, with a mean nest depth of .39 m (SE=.012) in the f i r s t week of July and a mean depth of .70 m (SE=.190) at the end of July. Laboratory studies of threespine sticklebacks have characterized males as being highly active i n t e r r i t o r i a l defense (van den Assent 1967) and courtship of females (van Ier s e l 1953). However males i n Trout Lake were s t r i k i n g l y passive i n defending their nest areas and seldom displayed the well known zig-zag dance, in which the male courts a female by abruptly jumping from side to side. In addition, males i n the early stages of the reproductive cycle were often lacking bright throat coloration, which appears to function in aggression between males and in the courtship of females (ter Pelkwijk and Tinbergen 1937). In contrast, males i n Garden Bay Lake vigorously defended t e r r i t o r i e s , a c t i v e l y courted females, and displayed bright red throats throughout the reproductive cycle. Many of the differences i n reproductive behavior between Trout Lake males and males from Garden Bay Lake may be the re s u l t of a difference i n the a v a i l a b i l i t y of gravid females. Gravid females were freguently observed along the shores of Trout Lake, but were seldom seen i n Garden Bay Lake. This d i s p a r i t y i n female a v a i l a b i l i t y i s reflected by the number of 35 eggs found In males' nests. In Trout Lake 79 per cent of the nests co l l e c t e d contained eggs compared to 55 per cent i n Garden Bay Lake. Of those nests containing eggs, the mean number of eggs per nest in Trout Lake was 349.9 (SE=34.42, n=58). This represents approximately six successive spawnings by di f f e r e n t females, whose mean fecundity i n Trout Lake was 58.1 eggs per spawning (SE=5.29, n=21). The mean number of eggs per nest i n Garden Bay Lake was l e s s than half the mean in Trout Lake (5=151.7, SE=13.94, n=26) . This difference in the mean number of eggs per nest might be attributed to egg production by females. Trout Lake develops a summer a l g a l bloom and has a mud bottom i n contrast to the clearer waters and gravel bottom of Garden Bay Lake. If t h i s affects the a v a i l a b i l i t y of food i t might account f o r a higher production of eggs by Trout Lake females, since food l e v e l s influence the number of eggs per spawning and the length of the inter-spawning i t e r v a l in acul.ea.tus (wootton 1973). My main purpose in pointing out t h i s variation between sticklebacks from Trout Lake and Garden Bay Lake has been to give some s p e c i f i c information on the populations used to test the parental defense hypothesis, while providing a general background on male reproductive behavior. Some of these differences w i l l also be useful for interpreting the res u l t s of the f i e l d experiment. 36 1 tThe_Threat_-_Cqt tus_asp_er To t e s t the p a r e n t a l defense hypothesis i t was necessary to f i n d a common predator of both the male s t i c k l e b a c k and i t s eggs., The p r i c k l y s c u l p i n , Cottus asger , i s a b e n t h i c f i s h commonly found i n low e l e v a t i o n l a k e s and streams along the coast of B r i t i s h Columbia. S c u l p i n s are abundant i n Garden Bay Lake and absent from Trout Lake. Moodie (1972) found s t i c k l e b a c k eggs i n over 30 per cent of the a d u l t p r i c k l y s c u l p i n s he examined from Hayer Lake i n the Queen C h a r l o t t e I s l a n d s . In a study of Harewood Lake on Vancouver I s l a n d , Hurray (unpublished data) found t h a t s c u l p i n s ware pr e y i n g i n t e n s e l y on both a d u l t s t i c k l e b a c k s and t h e i r eggs. In a d d i t i o n , 7 out of 12 s c u l p i n s c o l l e c t e d at the beginning of the s t i c k l e b a c k breeding season i n Mix a l Lake, one h a l f mile from Garden Bay Lake, contained remains of ad u l t s t i c k l e b a c k s . The i n t e r a c t i o n of s t i c k l e b a c k s and s c u l p i n s c o l l e c t e d from Garden Bay Lake was observed i n the l a b o r a t o r y . In a 40 l i t e r aguarium a s c u l p i n as small as 98.4 mm (standard length) could s u c c e s s f u l l y capture and i n g e s t an a d u l t s t i c k l e b a c k 61.5 mm i n l e n g t h . S c u l p i n s were ambush pr e d a t o r s of s t i c k l e b a c k s ; they were never observed to chase t h e i r prey. A s c u l p i n would t y p i c a l l y l i e i n wait on the bottom u n t i l a s t i c k l e b a c k swam w i t h i n the area surrounding i t s head, a t which point the s c u l p i n would lunge at the s t i c k l e b a c k by u t i l i z i n g i t s l a r g e p e c t o r a l f i n s . S c u l p i n s never a t t a c k e d a s t i c k l e b a c k over t h e i r t a i l a rea, but would t u r n to f a c e the 37 s t i c k l e b a c k before s t r i k i n g . S i m i l a r predatory behavior has been r e p o r t e d f o r other s p e c i e s of Cottus ( H i k i t a and Nagasawa 1960; P h i l l i p s and C l a i r e 1966; Patten 1975). The method by which s c u l p i n s prey on s t i c k l e b a c k eggs i n nature i s unknown. P r e d a t i o n was observed i n the l a b o r a t o r y by i n t r o d u c i n g a s c u l p i n t o an aguarium c o n t a i n i n g a male s t i c k l e b a c k with i t s nest, When the male returned to fanning a f t e r the i n i t i a l d i s t u r b a n c e , the s c u l p i n began to approach the nest i n a s e r i e s of jumps along the bottom. With each forward movement of the s c u l p i n , the male would leave the nest and approach the s c u l p i n . The male would o c c a s i o n a l l y a t t a c k the s c u l p i n , d r i v i n g i t away from the nest, and sometimes the s c u l p i n would s t r i k e at the male. E v e n t u a l l y the s c u l p i n lunged f o r the nest, and i n a r o c k i n g motion r e p e a t e d l y s e i z e d and spat out the nest contents. A l l the eggs were i n g e s t e d before the male was able to d r i v e the s c u l p i n from the nest area. A number of f i e l d o b s e r v a t i o n s were made of s t i c k l e b a c k and s c u l p i n i n t e r a c t i o n s i n Garden Bay Lake. Males f r e q u e n t l y chased s c u l p i n s out of t h e i r nest areas. I f the s c u l p i n was a p o t e n t i a l predator of the male ( l a r g e r than 100 mm), the male would o f t e n approach the s c u l p i n from behind and b i t e i t on the t a i l . In one i n s t a n c e a male at the s t a r t of nest b u i l d i n g s u c c e s s i v e l y chased f i v e s c u l p i n s , a l l l e s s than 100 mm, from i t s t e r r i t o r y . P r e d a t i o n by s c u l p i n s was never d i r e c t l y observed, although a male and female s t i c k l e b a c k swimming toward a nest during c o u r t s h i p were both s t r u c k at by 38 a l a r g e s c u l p i n . i£^Fig tht_or_Flig Lht_-_Choos^ To t e s t the p r e d i c t i o n of i n c r e a s e d p a r e n t a l r i s k with a l a r g e r number of eggs or o l d e r eggs i n the nest, I decided to measure a male's response to a choice s i t u a t i o n . The o b j e c t i v e was to determine the i n f l u e n c e of the eggs on the l e v e l of r i s k taken by a male i n defending i t s nest a g a i n s t a s c u l p i n predator. A dummy, s c u l p i n was prepared from a l a r g e specimen (138.3 mm standard length) of C.. 4§E§£. T h i s was w e l l beyond the s i z e of s c u l p i n t h a t c o u l d e a s i l y prey on the s t i c k l e b a c k s i n Trout Lake and Garden Bay Lake ( a l l males t e s t e d were l e s s than 60 mm), thus minimizing any e f f e c t o f male s i z e on the response. The dummy was preserved i n ethanol and g l y c e r i n e (to prevent drying) and was washed before each t e s t . Transparent f i s h i n g l i n e was attached through the head and caudal area so t h a t the dummy could be suspended and c o n t r o l l e d from the end of two pole s , each 2.5 meters i n l e n g t h . The experimental procedure was to move q u i e t l y along the shore u n t i l a male with a nest was observed. I f the male was f r i g h t e n e d from h i s nest area by my approach, I waited u n t i l i t had resumed normal fanning before I began a t e s t . The model was then lowered down over the nest. The d i s t u r b a n c e at the water s u r f a c e o f t e n f r i g h t e n e d the male from the nest area 39 and I observed the d i r e c t i o n t h a t the male escaped. Since males u s u a l l y r e t u r n from the same d i r e c t i o n i n which they escape, I was able to o r i e n t the dummy so t h a t i t s head was f a c i n g the d i r e c t i o n from which the male was most l i k e l y to r e t u r n . In t h i s way the t e s t was s t a n d a r d i z e d so th a t the r e t u r n i n g male always faced the mouth end of the s c u l p i n dummy. Upon r e t u r n the male c h a r a c t e r i s t i c a l l y stopped a t the pe r i p h e r y of i t s t e r r i t o r y where i t c o u l d view the nest. At t h i s p o i n t I would g e n t l y bob the dummy i n a simulated f e e d i n g motion of approximately one bob per second. T h i s motion was s i m i l a r to the f e e d i n g behavior observed i n the Q l a b o r a t o r y , although the amplitude was s l i g h t l y exaggerated to ensure t h a t the male would spot the dummy. The bobbing motion was continued throughout the t e s t , making i t p o s s i b l e to keep the dummy's head o r i e n t e d t o the male i f i t attempted t o swim around to the dummy's t a i l . The male's response to the s c u l p i n dummy was recorded as a s e r i e s of d i f f e r e n t " r i s k measures". Responses were c a t e g o r i z e d i n t o t h r e e separate " a l l - o r - n o n e " measures, as e i t h e r a high r i s k or low r i s k response (see D i s c u s s i o n ) . The p r e d i c t i o n was t h a t f o r each a l l - o r - n o n e measure, males i n the high r i s k category would have more eggs or o l d e r eggs than males i n the low r i s k category. Upon r e t u r n i n g t o i t s nest area and s p o t t i n g the s c u l p i n dummy, the male would u s u a l l y e i t h e r desert the nest area again or a t t a c k the dummy. Th i s was recorded as an "Att a c k " or "No Attack", with the a t t a c k response r e p r e s e n t i n g a hi g h e r 40 r i s k . Males t h a t r e - d e s e r t e d t h e i r nest never r e t u r n e d and at t a c k e d the s c u l p i n dummy ( t e s t s were terminated a f t e r three minutes). Of those males t h a t d i d a t t a c k the dummy, the l o c a t i o n on the s c u l p i n 1 s body t h a t was f i r s t b i t t e n was recor d e d , s i n c e some males were ab l e to swim around the dummy and a t t a c k i t from behind before i t could be r e o r i e n t e d . I f the male f i r s t a t t a c k e d the s c u l p i n * s head the response was recorded as "Head", and any a t t a c k on the body behind the s c u l p i n ' s operculum was recorded as " T a i l " . O c c a s i o n a l l y a male would not desert i t s nest area when the dummy was f i r s t i n t r o d u c e d i n t o the water, but would remain w i t h i n an area approximately one h a l f meter from the nest. T h i s response was recorded as "Remain", i n c o n t r a s t to the more common "Desert" response. Remaining i n the nest area was c o n s i d e r e d a hi g h e r r i s k response than d e s e r t i n g the nest, and every male t h a t remained w i t h i n i t s immediate nest area subseguently a t t a c k e d the dummy. In a d d i t i o n to the a l l - o r - n o n e measures, a number of " q u a n t i t a t i v e " r i s k measures of the male's response were recorded u t i l i z i n g two stopwatches. Each g u a n t i t a t i v e measure accounted f o r a range o f i n t e n s i t y i n the male's response, and the p r e d i c t i o n was t h a t the l e v e l of r i s k d i s p l a y e d would be higher f o r males with l a r g e r numbers of eggs or o l d e r eggs i n t h e i r nests. The i n i t i a l time i t took a male to r e t u r n t o a l o c a t i o n where i t could view i t s nest was designated the "Return Time", and a qui c k e r r e t u r n time was considered a hi g h e r r i s k 41 response. If the male then attacked the dummy, the "Time to Attack" was recorded as the time between the male's return to a stationary position at the periphery of i t s t e r r i t o r y and i t s f i r s t bite at the dummy. For those males that never deserted the nest area, the Return Time was assigned as one second and the Time to Attack was measured from the time the male had turned and faced the dummy u n t i l i t s f i r s t b i t e . After the i n i t i a l attack, the number of bites at the dummy in the next 60 seconds was recorded (Bites per Min), and males with a larger number of eggs or older eggs were expected to attack the dummy more f i e r c e l y , r e s u l t i n g in a larger number of recorded bites per minute. The sculpin dummy was also presented to males that were guarding f r y , which remain in a swarm over the nest for approximately a week after hatching. The dummy was placed over the remains of the nest i f i t was v i s i b l e , or i n the midst of the swarm i f no nest was spotted. , The same male responses were recorded. At the end of each test the male was captured with a dip net ( i f possible), measured, and subsequently released. , Nests were coll e c t e d and the eggs were preserved in 10% formalin. After tests on males guarding f r y , a small sample of f r y was col l e c t e d . In addition, a number of nest measures were recorded after each test: (1) the depth of water over the nest, (2) the distance from the nest to shore, (3) the temperature of the water at the nest, (4) the distance of the nest from the nearest rock or plant cover that could shelter 42 the male, (5) the d i s t a n c e to the male's n e a r e s t neighbor's nest, (6) the presence of s u n l i g h t or shade on the nest d u r i n g the t e s t , (7) d i s t u r b a n c e of the water s u r f a c e by wind, (8) the date, and (9) the time of day. The nest contents were t r a n s f e r r e d to 30% a l c o h o l i n the l a b o r a t o r y and the number of eggs i n each nest was counted. The eggs were c l a s s i f i e d by e m b r y o l o g i c a l stage and assigned a " p h y s i o l o g i c a l age" (Swarup 1958). T h i s age was the time i n hours t h a t the eggs used i n Swarup's study took to reach each e m b r y o l o g i c a l stage a t 18° C. The mean p h y s i o l o g i c a l age of the eggs was c a l c u l a t e d f o r each nest, as w e l l as the v a r i a n c e i n egg age w i t h i n the nest. An estimate of the mean " c h r o n o l o g i c a l age" of the eggs i n each nest was determined (see Appendix I ) , based on water temperatures and the development r a t e of eggs from a s t i c k l e b a c k p o p u l a t i o n on Vancouver I s l a n d ( H c P h a i l , unpublished d a t a ) . Hales were t e s t e d u n t i l the end of the breeding season i n both l a k e s . A t o t a l of 51 males were t e s t e d i n Trout Lake and 57 males i n Garden Bay Lake. Only males t h a t had n e s t s were t e s t e d , and no male was t e s t e d more than once, thus e l i m i n a t i n g any p o s s i b i l i t y of h a b i t u a t i o n to the dummy. Sometimes the contents of the nest were s p i l l e d d u r i n g c o l l e c t i o n (most o f t e n when the eggs were i n l a t e s t a g e s and l e s s c o h e s i v e ) , so that the number of eggs could not be determined. For these s i t u a t i o n s the egg number was not counted, but i f the remaining sample was l a r g e , the eggs were used to estimate the mean egg age. Any other measurements 43 t h a t were suspected of obvious e r r o r (e. g, i f I f r i g h t e n e d the male by f a l l i n g i n t o the water) were not i n c l u d e d i n the a n a l y s i s . 5«.Ex£erimental_Results The p a r e n t a l defense hypothesis p r e d i c t e d t h a t males with a l a r g e r number of eggs or o l d e r eggs would d i s p l a y more r i s k i n defending t h e i r n e s t s from the s c u l p i n predator. For each a l l - o r - n o n e measure, the male's response was c a t e g o r i z e d as e i t h e r high or low r i s k , and the p r e d i c t i o n was that males i n the high r i s k category would have a s i g n i f i c a n t l y (p<.05) l a r g e r number of eggs, or average egg age per nest, than males i n the low r i s k category. The Attack, Head, or Remain response was co n s i d e r e d to c o n s t i t u t e higher r i s k than the corresponding No Atta c k , T a i l , or Desert response. A comparison of the mean number of eggs i n each response category f o r the t h r e e a l l - o r - n o n e r i s k measures i s shown i n Table I . The r e s u l t s g e n e r a l l y support the hy p o t h e s i s f o r both Trout Lake and Garden Bay Lake males. In both l a k e s , the number of eggs f o r males t h a t a t t a c k e d the dummy and remained w i t h i n t h e i r immediate nest area at the beginning of the t e s t i s s i g n i f i c a n t l y l a r g e r (Mann-Whitney 0" tes t ) than f o r those males that d i d n ' t attack the dummy and deserted t h e i r nest area. The mean number of eggs per nest of males t h a t i n i t i a l l y a t t a c k e d the s c u l p i n ' s head i s a l s o l a r g e r than the mean f o r males t h a t swam around t o the s c u l p i n ' s t a i l , however un the d i f f e r e n c e i s not s t a t i s t i c a l l y s i g n i f i c a n t . The d i f f e r e n c e i n the mean age of eggs f o r males i n each r i s k category i s shown i n Table I I f o r the p h y s i o l o g i c a l egg age and Table I I I f o r the c h r o n o l o g i c a l egg age. The r e s u l t s are q u a l i t a t i v e l y the same f o r e i t h e r measure of egg age. Males from both l a k e s t h a t a t t a c k e d the dummy had s i g n i f i c a n t l y o l d e r eggs than males t h a t d i d n ' t a t t a c k , and males with o l d e r eggs g e n e r a l l y remained i n the nest area more o f t e n . In both l a k e s the mean age of eggs f o r males t h a t a t t a c k e d the s c u l p i n ' s head was g r e a t e r than the mean egg age f o r males t h a t a t t a c k e d the t a i l a r e a , but the d i f f e r e n c e was only s i g n i f i c a n t i n Garden Bay Lake. A comparison of the two p o p u l a t i o n s {Table IV) i n d i c a t e s t h a t the mean number of eggs f o r males t h a t a t t a c k the dummy i s s i g n i f i c a n t l y l a r g e r f o r Trout Lake males than f o r males from Garden Bay Lake. T h i s d i f f e r e n c e can not be e n t i r e l y a t t r i b u t e d to the g r e a t e r frequency of males without any eggs i n Garden Bay Lake, as shown by a comparison of means c a l c u l a t e d from o n l y those nests t h a t contained eggs. A s i m i l a r d i f f e r e n c e was found f o r the mean age of eggs f o r males from both l a k e s . . Both the p h y s i o l o g i c a l and c h r o n o l o g i c a l egg age f o r males t h a t attacked the s c u l p i n dummy i s l a r g e r i n Trout Lake than Garden Bay Lake, however t h i s d i f f e r e n c e i s onl y s i g n i f i c a n t f o r c h r o n o l o g i c a l egg age. There were no other s i g n i f i c a n t d i f f e r e n c e s between the two pop u l a t i o n s f o r the other a l l - o r - n o n e r i s k measures. The mean number and age o f eggs f o r these other r i s k c a t e g o r i e s . 45 TABLE I. A comparison between the number of eggs f o r males i n the high and low r i s k category f o r each a l l - o r - n o n e response I 1 1 T 3 1 I I I I I I | SISK MEASURE | MEAN | SE | N | PROB* | I I I I I I \ J 1 1 1 J I Trout Lake I 1 f }- f 1- i | Attack | 257.3 | 50.52 | 21 | .001 | | No Attack | 76.2 | 42.25 | 16 | I 1 f 1- +• + i | Head | 217.9 | 39.07 | 16 | p>.10 | I T a i l I 139.7 | 111.48 | 3 | I r + f + f 1 | Remain I 434.7 f 113.12 | 6 | .002 | | Desert ] 126.4 | 31.04 | 32 J f j j 1 . _ J i | I Garden Bay. Lake I \ Attack t 118.0 ~ t 17.60 } 25 t -001 ] | No Attack j 21.1 | 12.95 | 21 I I I Head | 146.4 | 21.90 | 14 ~ | ,05<p<.10 | | T a i l j 90.0 | 26.99 | 10 | | }. +— 1- 1- + i | Remain I 202.5 | 18.50 | 2 | .047 | | Desert I 66.7 | 13.42 | 43 | \ i 1 1 j i i 1. Mann-Whitney U t e s t 46 TABLE I I . A comparison between the p.hy.siglogical age of the eggs f o r males i n the high and low r i s k category f o r each a l l -or-none response RISK MEASURE "T™ I i MEAN SE I I P R O B 2 Attack No Attack Head T a i l Remain Desert Trout Lake -+ 1 I -+-80.4 26. 2 11.68 10.63 93.9 37.0 13. 20 29.51 I 25 17 001 19 3 | .05<p<.10 I . j 123. 1 43.3 18. 31 8. 83 8 33 .001 H Attack No Attack Head T a i l Remain Desert Garden Bay. Lake -f-I 62.7 10. 1 11.19 6. 51 32 21 84.0 29.6 14.72 12.32 20 11 .001 I p<.025 I I 138.9 33.9 19.88 7.47 3 48 006 1. Sample s i z e f o r egg age i s o f t e n l a r g e r than egg number (TABLE I.) because estimates of egg age i n c l u d e d eggs from s p i l l e d n e s ts, which were not used i n the a n a l y s i s of egg number. 2. Mann-Whitney U t e s t 47 TABLE I I I . A comparison between the c h r o n o l o g i c a l age of the-eggs f o r males i n the high and low r i s k category f o r each a l l -or-none response RISK MEASURE 1 I MEAN Trout Lake SE | PROB* Attack No Attack Bead T a i l Remain Desert Attack No Attack Head T a i l Remain Desert 56.7 18.0 8. 17 7.21 I I -+-65.8 27.0 9. 24 21.56 79.7 30.5 12.66 6.21 Garden Bay. Lake 37.6 6.0 6.64 3.81 50.4 17.6 8. 73 7. 17 82. 1 21.8 10.04 5.00 25 17 I 001 19 3 "| .05<p<.10~1 8 33 32 21 -+ | .001 I 001 20 11 t~ P<-01 3 48 T .006 I 1. Hann-Shitney U t e s t 48 TABLE IV. A comparison between the two po p u l a t i o n s f o r the number and egg age of males that a t t a c k e d the s c u l p i n dummy NEST MEASURE Number of Eggs A l l Nests Only with Eggs E l u s i o l o g i c a l Age A l l ~ N e s t s ~ Only with Eggs C h r o n o l o g i c a l Age ""111 Nests Only with Eggs TROUT LAKE Mean ±SE(n) GARDEN BAY LAKE Mean ±SE(n) 257.3 ± 5 0 . 5 2 (21) 286.0 ± 5 1 . 5 5 ( 1 9 ) 80.4 ± 1 1 . 6 8 (25) 91.4 ± 1 1 . 3 7 ( 2 2 ) 56.7 ± 8.17(25) 64.4 ± 7.94 (22) 118.0 ± 1 7 . 6 0 (25) 163.9 ± 1 2 . 8 6 ( 1 8 ) 62.7 ± 1 1 . 1 9 ( 3 2 ) 80.2 ± 1 2 . 1 8 ( 2 5 ) 37.6 ± 6.64 (32) 48.1 ± 7.20 (25) PROB* 013 025 112 226 037 065 Mann-Whitney U t e s t U9 c a l c u l a t e d f o r only those n e s t s t h a t contained eggs, i s given i n Appendix I I . The i n f l u e n c e of the number and age of eggs on each of the g u a n t i t a t i v e measures of the male's response was examined by r e g r e s s i o n a n a l y s i s . The p r e d i c t i o n was t h a t with l a r g e r numbers or o l d e r eggs i n a male's nest, the Return Time and Time t o Attack would decrease, and the number of Bit©s per Min would i n c r e a s e . The slope f o r each g u a n t i t a t i v e r i s k measure as a f u n c t i o n of egg number or egg age was c a l c u l a t e d and t e s t e d f o r s i g n i f i c a n c e . The r e l a t i o n between the number of eggs per male's nest and each g u a n t i t a t i v e r i s k measure i s shown i n Table V . For both l a k e s the male's response i s i n the p r e d i c t e d d i r e c t i o n , and a l l the s l o p e s are s i g n i f i c a n t . The i n f l u e n c e of the mean age of eggs per male's nest on each g u a n t i t a t i v e measure i s shown i n Table VI f o r p h y s i o l o g i c a l egg age and Table VII f o r c h r o n o l o g i c a l age, both measures of egg age g i v i n g the same q u a l i t a t i v e r e s u l t s . In the two p o p u l a t i o n s , the r e t u r n time and the time t o a t t a c k decreases f o r males with o l d e r eggs i n the nest, while the number of b i t e s per minute i n c r e a s e s . There are no s i g n i f i c a n t d i f f e r e n c e s between the two l a k e s f o r the s l o p e s or i n t e r c e p t s of any of the r e g r e s s i o n s . C o n s i d e r i n g only those males t h a t had eggs i n t h e i r n e s t s , the changes i n the q u a n t i t a t i v e responses f o r the combined p o p u l a t i o n s are s t i l l i n the p r e d i c t e d d i r e c t i o n s (Table V I I I ) . The r e s u l t s f o r each separate l a k e , and more complete r e g r e s s i o n s t a t i s t i c s , are given i n Appendix I I I . 50 TABLE V. Regression r e s u l t s f o r each q u a n t i t a t i v e r i s k measure as a f u n c t i o n of the number of eggs i n the nest r T i r r T 1 RISK MEASURE1 I PREDICTED | OBSERVED j SE | N | PROB2 I | SLOPE | SLOPE J SLOPE | | i _ i J . L 1 L I Trout Lake | Return Time I - } - .005 ~t .00 14 } 27~t -001 | Time to Attack | - | - .003 | .0011 | 20 | .003 r b -I f f -I \ B i t e s per Min 1 + I +.027 | .0076 | 22 J .001 ] : 1 1 1 i i .j I G§.E4®E Bay Lake r h - f — 1 r f + i j Return Time 1 - I - .008 | .0025 | 35 | .003 j Time to Attack | - | - .006 | .0026 | 24 | .022 1 f r f f r ~ 1 1 B i t e s per Min 1 + I +.043 | .0246 | 23 J .046 1. Time measures are l o g transformed 2. P r o b a b i l i t y that the slope i s not i n the p r e d i c t e d d i r e c t i o n ( o n e - t a i l e d F t e s t ) \ 51 TABLE VI. Regression r e s u l t s f o r each g u a n t i t a t i v e r i s k measure as a f u n c t i o n of the E h y s i o l o g i c a l age of the eggs i n the nest RISK MEASURE1 I I | PREDICTED | OBSERVED | SLOPE | SLOPE 1 SE | H SLOPE | I I | PROB2 I _J Trout Lake | Return Time (-1 ._ 1 _._ -1— 1 , i .... , -.020 f -1 f .0050 | | Time to Attack i .-.„._„.„,„__ , 1 1 1 -1 1 . . 1 -.014 (--1 _ _ i ., j .0043 | i | B i t e s per Min L i 1 _ J + 1 1 J + .086 T 1 j. .0320 | | .001 t -002 | .006 1 Return Time Garden Bay. Lake t - ~T~ -.011 t .0034 | 42 Time to Attack -.011 B i t e s per Min + + .070 | .0031 | 31 t .0290 | 30 | .011 1. Time measures are l o g transformed 2. P r o b a b i l i t y that the slope i s not i n the p r e d i c t e d d i r e c t i o n ( o n e - t a i l e d F t e s t ) / 52 TABLE V I I . Regression r e s u l t s f o r each g u a n t i t a t i v e r i s k measure as a f u n c t i o n of the c h r o n o l o g i c a l age of the eggs-in the nest _____ ., 1 T , 1  I I I I I RISK MEASURE* | PREDICTED | OBSERVED | SE | N ] PROB* | SLOPE | SLOPE | SLOPE | | 1 ! I l l r- H- H- f 1 Return Time ! - I -.030 1 .0072 | 30 -| .001 ! 4- f r f + j Time to Attack | - I -.020 | .0062 | 23 | .002 I B i t e s per Min ' | + I +.126 | .0453 | 25 | .005 j 1 1 1 j 1 | Garden Bay. Lake j F _ _ I Z _ _ I " J : _ _ I H F +  i Return Time I - I -.018 | .0057 | 42 | .002 1 r r f f 1-| Time to Attack | - ! -.018 | .0053 | 31 | .001 r +- 1 f r r | B i t e s per Min | + | +.116 | .0492 J 30 | .012 i 1 i i 1 1 i 1. Time measures are l o g transformed 2. P r o b a b i l i t y that the slope i s not i n the p r e d i c t e d d i r e c t i o n ( o n e - t a i l e d F t e s t ) 53 TABLE V I I I . Regression r e s u l t s c a l c u l a t e d f o r the combined p o p u l a t i o n s counting only those males with eggs i n t h e i r n e s t s . The s l o p e and p r o b a b i l i t y i s given f o r each r i s k measure as a f u n c t i o n of the number or age of the eggs. 1 1 3—; 1—• 1 |RISK MEASURE1 j NUMBER OF EGGS | PHYS. AGE | CH RON. AGE | "Return Time 1 -.002 | -.007 I -.011 I j I p=.046 | p=.038 | p=.038 | I '• 1- + J- i |Time to Attack | -.003 | -.010 J -.016 J | | p=.006 | p=.002 | p=.002 | , f j | B i t e s per Min | +.023 f +.059 i +.092 \ | I P=-013 j p=.015 | p=.016 | 1. Time measures are l o g transformed 54 The influence on the male's response of the d i f f e r e n t nest measures (nest depth, water temperature, etc.)., as well as the number of eggs, physiological egg age, male s i z e , and variance in egg age, was examined by multiple regression for those males in which there were no missing values for any of the various measures. For the all-or-none r i s k measures the influence of the egg and nest measures was determined by discriminant analysis, which i s a special case of multiple regression (Gilbert 1973), using only those nest measures that were normally d i s t r i b u t e d . None of the various measures contributed consistently to the prediction of the male's response besides the number or age of the eggs (Appendix IV). In Trout Lake the distance of the nest from shore contributed s i g n i f i c a n t l y to the prediction of the Time to Attack i n addition to the egg number, and in Garden Bay Lake the depth of the nest added to the prediction of the Return .Time. Although the cor r e l a t i o n between egg number and egg age for males that had eggs was low in both Trout Lake (r=.1166) and Garden Bay Lake (r=-.0711), the number of eggs i s s u f f i c i e n t to predict the male's response i n a l l the r i s k measures except the male's tendency to desert i t s nest, which i s best predicted by the age of the eggs. However t h i s may underestimate the influence of egg age on the male's response, since nests with older eggs had a higher freguency of s p i l l a g e during c o l l e c t i o n and were not included in the multiple regression analysis. For a l l the r i s k measures, only a small proportion (<55%) of the variance i n the male's response i s 5 5 accounted for (R2) by the egg number or age. The experimental results for males that were guarding f r y are given i n Table IX. Only six males were tested but there i s a clear trend of decreasing r i s k with larger f r y . The mean length of f r y represents the time since hatching, and t h i s r e l a t i o n i s probably s i m i l a r i n both populations, since the mean diameter of eggs i n Trout Lake (x=16.9, SE=.307, n=20) i s approximately the same as in Garden Bay Lake (x=17.0, SE=.16 2, n=20). Those males that attacked the dummy sculpin had s i g n i f i c a n t l y smaller fry than those that didn't, and the time to attack increased for males with older f r y , while the number of bites per minute decreased. 56 TABLE IX. Responses of males guarding f r y 1 MEAN LENGTH OF FRY I 5.7 j 6.7*7 6.8~T 7.5 ] ~ 9.2 T~"7o. 0 ] 1 + -I r 1- 1- r 1 1 MALE RESPONSE |Att a c k | A t t a c k | A t t a c k | No | No | No | j I I I |Attack|Attack J Attack| r + -1 1- 1- + H 1 ! Time to Attack | 1.2 | 3.0 | 8.0 | — I — I — I I B i t e s per Min | 36 | 23 ) 19 | — I — | — I i 1 a 1 I ATTACK | NO ATTACK I PROBABILITY | | Mean Fry Length ± SE | Mean Fry Length ± SE | U Test I 1 6.4 ± .35 | 8.9 ± 1.63 | .05 j i 1 i I j 1. Male from Garden Bay Lake 57 CHAPTER IV. DISCUSSION The r e s u l t s of the f i e l d experiment demonstrate an i n c r e a s e i n the i n t e n s i t y of a male's defense f o r a l a r g e r number or o l d e r eggs i n the nest. The unde r l y i n g m o t i v a t i o n and responsiveness i n f l u e n c i n g the s t r e n g t h of a parent's response to a nest predator has been d i s c u s s e d i n d e t a i l by Cu r i o ( 1 9 7 5 ) , who a l s o found a temporal change d u r i n g the breeding c y c l e i n the mobbing i n t e n s i t y of pied f l y c a t c h e r s . Other s t u d i e s have d e s c r i b e d s i m i l a r changes i n the i n t e n s i t y of d i s t r a c t i o n d i s p l a y s by n e s t i n g b i r d s (Armstrong 1 9 5 6 ; Simmons 1 9 5 5 ; Stephens 1 9 6 3 , Gramza 1 9 6 7 ) , but have p r i m a r i l y focused on the proximate f a c t o r s i n f l u e n c i n g the behavior (however see Barash 1 9 7 5 ) . Many of these a n t i - p r e d a t o r responses are d i f f i c u l t t o assess i n terms of t h e i r c o s t to the parent, and e v a l u a t i o n s based on time or energy expended make the i m p l i c i t assumption that these " c u r r e n c i e s " are l i m i t i n g . In t h i s study I have attempted to measure responses which i n v o l v e an i n c r e a s e d r i s k of m o r t a l i t y to the parent f o r an i n c r e a s e i n the i n t e n s i t y of i t s defense. Each of the a l l - o r - n o n e r i s k measures c a t e g o r i z e s the male's response t o the s c u l p i n dummy as c o n s t i t u t i n g e i t h e r a high or low r i s k f o r the male, based on ob s e r v a t i o n s of the predatory behavior of s c u l p i n s . Those males t h a t a t t a c k the s c u l p i n are assumed t o take more r i s k than males which never approach the dummy, s i n c e s c u l p i n s never pursue t h e i r prey and only a t t a c k when a s t i c k l e b a c k i s i n c l o s e p r o x i m i t y . A male 58 t h a t a t t a c k s the s c u l p i n ' s head has entered a c r i t i c a l s t r i k e a r e a , and should have a higher p r o b a b i l i t y of being captured than a male which a c t i v e l y avoids the s c u l p i n ' s head and a t t a c k s i t s t a i l - S i m i l a r l y , males which remain i n t h e i r immediate nest area a f t e r the s c u l p i n i s f i r s t i n t r o d u c e d are i n c l o s e p r o x i m i t y to the s c u l p i n , and would have a h i g h e r p r o b a b i l i t y of being captured than males which i n s t a n t l y d e s e r t t h e i r nest area a f t e r a d i s t u r b a n c e . The g u a n t i t a t i v e measures of the male's response r e f l e c t the i n t e n s i t y of i t s defense, and would a l s o i n v o l v e an i n c r e a s e d r i s k of m o r t a l i t y f o r the male with a l i v e s c u l p i n p r e d a t o r . Although the decrease i n the Return Time and the Time to Attack mostly r e p r e s e n t an i n c r e a s e d r e a d i n e s s t o defend the nest, the p r o b a b i l i t y of being captured by a nest predator i n c r e a s e s with a s h o r t e r time away from the nest. A l a r g e r number of B i t e s per Min r e p r e s e n t s repeated c o n t a c t s with the s c u l p i n ' s head, which was kept o r i e n t e d to the male throughout the t e s t , and would r e s u l t i n a higher p r o b a b i l i t y of capture by a l i v e s c u l p i n . The mechanism by which a male r e c o g n i z e s the number and age of the eggs i n i t s nest was not examined. Males f r e g u e n t l y have d i r e c t c o n t a c t with the eggs, o f t e n poking and r e a r r a n g i n g the egg mass i n the n e s t . A number of l a b o r a t o r y s t u d i e s i n d i c a t e t h a t p a r e n t a l behavior i n &c_!±__a._us i s d i r e c t l y i n f l u e n c e d by s t i m u l i from the eggs. The p r o p o r t i o n of time a male spends f a n n i n g the eggs i n c r e a s e s with egg number and age, and nest s w i t c h i n g experiments have I 59 demonstrated that t h i s behavior i s d i r e c t l y influenced by the eggs, rather than the seguence or number of past f e r t i l i z a t i o n s (van l e r s e l 1953; Beune, unpublished MS). Increases i n fanning are stimulated by an increase i n the carbon dioxide concentration of the water surrounding the nest (Sevenster 1961), and the changes in fanning through the developmental period correlate with changes in the metabolism of the eggs (Jones 1966). In t h i s study both the physiological and chronological age of the eggs were egually s i g n i f i c a n t predicters of a male's response. Experiments with eggs developing at di f f e r e n t rates indicate that a male's fanning behavior i s a response to the embryological stage of the eggs rather than the time since f e r t i l i z a t i o n (van l e r s e l 1953). Thus i t i s most l i k e l y that males are responding to the physiological age of the eggs, rather than t h e i r chronological age. The r e s u l t s of thi s and other studies of parental care correspond to many of the predictions generated by the model of parental investment and reproductive success. For each of the quantitative r i s k measures, there was an increase i n the in t e n s i t y , and associated r i s k , of the male's defense as the number or age of the eggs increased., During, the incubation period of many b i r d species a s i m i l a r increase occurs i n the conspicuousness of the d i s t r a c t i o n displays by parents (Stephens 1963; Gramza 1967; Barash 1975), and i n the in t e n s i t y of the mobbing response to nest predators (Smith and Hosking 1955; Curio 1963,1975; Curio et. a l . .1969). These 6 0 i n c r e a s e s i n the i n t e n s i t y of p a r e n t a l defense can be a s s o c i a t e d with the l a r g e r r e p r o d u c t i v e value of o l d e r eggs, which f a v o r s a parent t a k i n g a higher r i s k i n a p a r e n t a l investment (Figure 2) . Each of the a l l - o r - n o n e r i s k measures c a t e g o r i z e s the male's response t o the s c u l p i n dummy as c o n s t i t u t i n g e i t h e r a high or low r i s k f o r the male. However only the Attack-No Attack measure a c t u a l l y r e p r e s e n t s an a l l - o r - n o n e response; the Head-Tail and Remain-Desert measures were developed as a means of g u a n t i f y i n g responses t h a t are v a r i a b l e i n i n t e n s i t y , but d i f f i c u l t to measure. The s i g n i f i c a n t l y l a r g e r number and age of the eggs f o r males t h a t a t t a c k e d the dummy r e p r e s e n t s an i n c r e a s e d p r o b a b i l i t y of t h i s response o c c u r r i n g as the "v a l u e " of the eggs i n the nest i n c r e a s e s . T h i s corresponds g u a l i t a t i v e l y to the model's p r e d i c t i o n of c e r t a i n high r i s k responses not becoming " j u s t i f i e d " u n t i l the value of the present young ( i n r e l a t i o n t o the parent's f u t u r e prospects) exceeds a t h r e s h o l d (eguation 3). T h i s has a l s o been observed f o r the attack response o f willow warblers to a predatory cuckoo (Edwards e t . a l . 1950), and f o r the ontogeny of the d i s t r a c t i o n d i s p l a y s o f d i f f e r e n t b i r d s , which f o l l o w a s e q u e n t i a l p a t t e r n from l e s s t o more conspicuous as the age of the eggs i n c r e a s e s (Simmons 1955; Barash 1975). S i m i l a r l y , N. G. Smith (pers. com.) has observed t h a t oropendulas do not enter t h e i r n e sts a t ni g h t to incubate u n t i l l a t e r stages of egg development, a b e h a v i o r a l p a t t e r n which p r i m a r i l y appears to be a response to nest p r e d a t i o n r a t h e r than i n c r e a s e d 61 energy demands of the eggs ( R i c k l e f s 1969). Males i n c r e a s e d t h e i r r i s k i n nest defense u n t i l the eggs hatched, a f t e r which the freguency of a t t a c k i n g the s c u l p i n dummy, as w e l l as the i n t e n s i t y of the male's defense, d e c l i n e d . The decrease i n p a r e n t a l r i s k a f t e r h a t c h i n g , even though the value of the young continued to i n c r e a s e , can be a s s o c i a t e d with the decrease i n the e f f e c t i v e n e s s of the male's defense (Figure 3). As the f r y develop, t h e i r swimming a b i l i t y i n c r e a s e s and they become l e s s dependent on p a r e n t a l a s s i s t a n c e i n a v o i d i n g nest p r e d a t o r s . The b e n e f i t r e s u l t i n g from a given l e v e l of p a r e n t a l r i s k r a p i d l y d e c l i n e s , and outweighs the advantage to the parent of i n c r e a s i n g i t s r i s k f o r o l d e r young. Barash (1975) has given a s i m i l a r i n t e r p r e t a t i o n f o r the d i f f e r e n c e i n the t i m i n g of the most conspicuous d i s t r a c t i o n d i s p l a y s of p r e c o c i a l b i r d s , which occur s h o r t l y a f t e r h a t c h i n g , and the maximum d i s p l a y s of a l t r i c i a l b i r d s , which don't reach a peak u n t i l s e v e r a l days a f t e r h a t c h i n g . T h i s corresponds to the i n c r e a s e d independence of p r e c o c i a l young s h o r t l y a f t e r h a t c h i n g , while a l t r i c i a l young remain completely dependent on the parent's a s s i s t a n c e u n t i l j u s t before f l e d g i n g . Thus the d i f f e r e n t p a t t e r n of p a r e n t a l r i s k f o r the two groups can be a s s o c i a t e d with temporal changes i n the e f f e c t i v e n e s s of p a r e n t a l defense, although the i n f l u e n c e of the r e n e s t i n g c a p a b i l i t i e s of each group should a l s o be c o n s i d e r e d . 62 It i s in t e r e s t i n g to note that the inverted U-shaped trend over the breeding cycle in the intensity of the male's response to the sculpin dummy i s d i r e c t l y opposite to the temporal pattern of "aggression" to conspecifics found i n many laboratory studies of G. aculeatus (Segaar 1961; Symons 1965; Black 1971; Hootton 1971). In these studies the freguency of bi t i n g at a conspecific intruder (usually another male behind glass or a model) decreases as the eggs near hatching, and then subseguently increases as the fry develop. , Thus the pattern of male response to the dummy predator in t h i s study suggests discrimination of the dummy sculpin from other sticklebacks, an expected res u l t based on other studies of stimulus recognition i n Gj, aculeatus (ter Pelkwijk and Tinbergen 1937; Tinbergen 1952). Although sculpins are absent from Trout Lake, the pattern of response to the sculpin dummy in t h i s population was simi l a r to the response pattern of males i n Garden Bay Lake, where sculpins are present. Curio (1963,1969) also found a s i m i l a r i t y i n the response to a model predator by Darwin's finches on islands where the predator was absent and on islands where the finches were sympatric with the predator. A larger proportion of males from Garden Bay Lake than Trout Lake avoided the sculpin's head, and the increased tendency to attack the head area with more or older eggs was si g n i f i c a n t only i n Garden Bay Lake, which implies that males in t h i s population recognize the sculpin's s t r i k e zone. Thrushes have a si m i l a r tendency to avoid the front of a 63 s t u f f e d jay predator, and t r y t o a t t a c k i t from behind (Goodwin 1953). T h i s s p e c i f i c response to the s c u l p i n by males i n Garden Bay Lake may be i n f l u e n c e d by experience or coul d be a p o p u l a t i o n c h a r a c t e r i s t i c . Seghers (1970,1973) found a s i m i l a r v a r i a t i o n between p o p u l a t i o n s of the guppy P o e c i l i a r e t i c u l a t a i n t h e i r a n t i - p r e d a t o r behavior, and showed that t h i s may have evolved as a response t o the presence of d i f f e r e n t predators. The number of eggs f o r males t h a t attacked the s c u l p i n dummy i n Garden Bay Lake was s i g n i f i c a n t l y lower than the number f o r males i n Trout Lake. The i n c r e a s e d p r o b a b i l i t y of a male i n Garden Bay Lake a t t a c k i n g the s c u l p i n when there i s a s m a l l number of eggs i n the nest may be a r e s u l t of the lower number of eggs u s u a l l y r e c e i v e d by males i n t h i s p o p u l a t i o n . Thus i n r e l a t i o n t o the male's f u t u r e p r o s p e c t s , a given number of eggs i n the nest may be worth more i n Garden Bay Lake than i n Trout Lake and w i l l f a v o r a higher p a r e n t a l r i s k (eguation 3), although the absence o f s c u l p i n s from Trout Lake could a l s o i n f l u e n c e t h i s v a r i a t i o n i n the att a c k response t h r e s h o l d . None of the nest measures other than the number or age of the eggs added c o n s i s t e n t l y t o the p r e d i c t i o n of the male's response. The s i z e of the male d i d not s i g n i f i c a n t l y i n f l u e n c e i t s response to the s c u l p i n dummy, although male s i z e might be important with a s m a l l e r s c u l p i n t h a t would have d i f f i c u l t y h a n d l i n g a l a r g e s t i c k l e b a c k . a f t e r an i n i t i a l c o n s i d e r a t i o n one might expect there to be a s i g n i f i c a n t 64 increase in male r i s k as the breeding season progresses, since seasonal breeders often show a rapid decline in reproductive value (Pianka and Parker 1975) which would favor an increase i n parental r i s k f o r a given value of present young (Figure 2). However the model predicts that r i s k w i l l be proportional to the r a t i o of future to present prospects (F/P), and a corresponding decline over the summer i n the reproductive value (probability of survival) of the eggs would counteract the influence of the decline in parental reproductive value. Kynard (1972) found that 76.8 per cent (n=34) of the stickleback males i n wapato Lake,Washington were able to rear eggs in May, but the success rate of males i n August was only 2.4 per cent (n=82), which suggests that egg s u r v i v a l i s generally lower at the end of the breeding season. The reproductive value of sticklebacks hatched in late summer may also be lower I f a small s i z e decreases the p r o b a b i l i t y of surviving through the winter. Furthermore males appear to have been selected to avoid breeding in the early f a l l , even though there are often secondary r i s e s i n water temperature s i m i l a r to increases i n the springtime, by.an additional breeding requirement of increasing daylengths (Baggerman 1972) . There was a large degree of v a r i a b i l i t y i n the response of males to the dummy for any given number or age of eggs i n the nest. Thus many possible differences between the two populations in the l e v e l of r i s k undertaken by males could not be s t a t i s t i c a l l y resolved. The cause of t h i s v a r i a b i l i t y i n 65 the response l e v e l s i s d i f f i c u l t to determine. The v a r i a b i l i t y in the lake environment, as well as the nature of the experiment, made i t d i f f i c u l t to standardize the stimulus, and t h i s may have influenced the strength of a male's response (Curio 1975), The male's past experience, e s p e c i a l l y i n Garden Bay Lake where sculpins are present, may have also affected the male's response at the time of the t e s t . In addition, loss of the eggs shortly before the test (e. g. from predation by other sticklebacks) could have resulted i n a higher r i s k response than would have been predicted by the number of eggs i n the nest, since a male's responsiveness may slowly wane after egg loss. These and other possible f a c t o r s , such as basic behavioral differences among i n d i v i d u a l males (Black 1971), w i l l have to be examined before i t can be determined whether the v a r i a b i l i t y i n response i s a result of adaptation, or just a lack of precision i n the system. 66 LITERATURE CITED Alexander, R. D. 1974. The e v o l u t i o n of s o c i a l behavior. Ann. Rev. E c o l . Syst. 5:325-383. Assem, J . van den. 1967. T e r r i t o r y i n the t h r e e - s p i n e d s t i c k l e b a c k , Gasterosteus a c u l e a t u s L. Behavior Suppl. 16:1-164. Armstrong, E. A. 1956. D i s t r a c t i o n d i s p l a y and the human predator. I b i s 98:641-654. Baggerman, B. 1957. An experimental study on the t i m i n g of breeding and mi g r a t i o n i n the t h r e e - s p i n e d s t i c k l e b a c k (Gasterosteus a c u l e a t u s L . ) . Arch. N e e r l . de Z o o l o g i e . 12:105-318™ Baggerman, B. 1972. P h o t o p e r i o d i c responses i n the s t i c k l e b a c k and t h e i r c o n t r o l by a d a i l y rhythm of p h o t o s e n s i t i v i t y . Gen. Comp. E n d o c , Suppl. 3:466-476. Barash, D. P. 1975. E v o l u t i o n a r y a s p e c t s of p a r e n t a l behavior: d i s t r a c t i o n behavior of the A l p i n e Accentor. Wilson B u l l . 87:367-373. B e l l , G. 1976. On breeding more than once. Amer. Natur. 110:57-77. Black, W. R. 1971. Hatching success i n the t h r e e - s p i n e d s t i c k l e b a c k (Gasterosteus aculeatus) i n r e l a t i o n to changes i n behavior d u r i n g the p a r e n t a l phase. Anim. Behav. 19:532-541. Brockelman, W. Y. 1975. Competition, the f i t n e s s of o f f s p r i n g , and o p t i m a l c l u t c h s i z e . Amer. Natur. 109:677-699. Caughley, G. 1970. A comment on Vandermeer's "pseudo-r e p r o d u c t i v e value". Amer. Natur. 104:214-215. Charlesworth, B. 1973. S e l e c t i o n i n p o p u l a t i o n s with o v e r l a p p i n g g e n e r a t i o n s . V. N a t u r a l s e l e c t i o n and l i f e h i s t o r i e s . Amer. Natur. 107:303-311, Cody, M. L. 1971. E c o l o g i c a l a s p e c t s of r e p r o d u c t i o n , pp.462-512. In: D. S. Farner and J. R. King ( e d s . ) . Avian b i o l o g y . V o l . 1. Academic Press, New York. 67 Cohen, D. 1967. O p t i m i z i n g r e p r o d u c t i o n i n a randomly v a r y i n g environment. J . Theoret. Pop. B i o l . 16:1-14. C u r i o , E. 1963. Probleme des feinderkennens b e i vogeln. Proc. I n t e r n a t . Orn. Congr. 13:206-239. C u r i o , E. 1969. Funktionsweise und stammesgeschichte des fl u g f e i n d e r k e n n e n s e i n i g e r Darwinfinken ( G e o s p i z i n a e ) . , Z. T i e r p s y c h o l . 26:394-487. Cu r i o , E. 1975. The f u n c t i o n a l o r g a n i z a t i o n of a n t i - p r e d a t o r behaviour i n the pied f l y c a t c h e r : a study of a v i a n v i s u a l p e r c e p t i o n . Anim. Behav. 23:1-115. C u r i o , E., R. B l a i c h , and N. Reider. ,1969, Der funktionszusammenhang zwischen e i n e r handlung und der i h r zugrunde liegenden erregung a l s grundlage der ethometrie von s c h l u s s e l r e i z e n . Z. v e r g l . P h y s i o l . 62:301-317. Edwards, G., E- Hosking, and S. Smith 1949. Reactions of some pas s e r i n e b i r d s to a s t u f f e d cuckoo. B r i t . B i r d s . 42:13-19. Emlen, J. M. 1970. Age s p e c i f i c i t y and e c o l o g i c a l theory. Ecology 51:588-601. F i s h e r , R. A. 1930. The g e n e t i c a l theory of n a t u r a l s e l e c t i o n . Clarendon, Oxford. 272 pp. G a d g i l , M., and W. H. Bossert. 1970. L i f e h i s t o r i c a l conseguences of n a t u r a l s e l e c t i o n . Amer. Natur. 104:1-24. G i l b e r t , N. 1973. B i o m e t r i c a l i n t e r p r e t a t i o n . Clarendon P r e s s , Oxford. 125 pp. Goodman, D. 1974. Na t u r a l s e l e c t i o n and a c o s t c e i l i n g on r e p r o d u c t i v e e f f o r t . Amer. Natur. 108:247-268. Goodwin, D. 1953. The r e a c t i o n s of some n e s t i n g p a s s e r i n e s toward l i v e and s t u f f e d j a y s . B r i t . B i r d s . ,46: 193-200. Gramza, A.1967. Responses of brooding nighthawks t o a d i s t u r b a n c e s t i m u l u s . Auk. 84:72-86. Hamilton, W. D. 1964. The g e n e t i c a l e v o l u t i o n of s o c i a l behavior. J. Theor. B i o l . 7:1-52. Hamilton, W. D. 1966. The moulding of senescence by n a t u r a l s e l e c t i o n . J . Theoret. B i o l . 12:12-45. 68 H i k i t a , T,, and A. Nagasawa, 1960. B i o l o g i c a l o b s e r v a t i o n s of Memu Stream, Tokachi R i v e r System. The damage of salmon eggs and f r y by predaceous f i s h e s . S c i e n t i f i c Reports Hokkaido Salmon Hatchery ( T r a n s l . From Japanese) 15:69-83. T r a n s l . Program, Bur. Comm. F i s h . , S e a t t l e , Washington. H i r s h f i e l d , M. F., and D. W. T i n k l e . 1975. N a t u r a l s e l e c t i o n and the e v o l u t i o n of r e p r o d u c t i v e e f f o r t . Proc. Nat. Acad. S c i . 72:2227-2231. l e r s e l , J . A. A. van. 1953. An a n a l y s i s of the p a r e n t a l behavior of the male thre e - s p i n e d s t i c k l e b a c k (Gasterosteus a c u l e a t u s L . ) , Behavior, Suppl. 3:1-159. Jones, R. L . 1966, Embryonic r e s p i r a t i o n of the t h r e e s p i n e s t i c k l e b a c k (Gasterosteus a c u l e a t u s L,) with a comparison of r e s p i r a t i o n i n two g e n e t i c forms. C4.Sc. . T h e s i s , Dept. of Zoology, U n i v e r s i t y of Washington. Kempthorne, 0,, and E, P o l l a k . 1970, Concepts of f i t n e s s i n Mendelian p o p u l a t i o n s . Genetics 64:125-145., Kynard, B. E. 1972. Male breeding behavior and l a t e r a l p l a t e phenotypes i n the t h r e e s p i n e s t i c k l e b a c k (Gasterosteus a c u l e a t u s L . ) . Ph.D. T h e s i s , Dept. of Zoology, U n i v e r s i t y of Washington. L e s l i e , P. H. 1948. Some f u r t h e r notes on the use of m a t r i c e s i n p o p u l a t i o n mathematics, , Amer. Natur. 108:499-506. , MacArthur, R. H., and E. 0. Wilson. 1967. Theory of i s l a n d biogeography. P r i n c e t o n U n i v e r s i t y Press, P r i n c e t o n , 203 pp. Medawar, P. B. 1957. The unigueness of the i n d i v i d u a l . Metheun, London. 191 pp. Mertz, D. B. 1971. L i f e h i s t o r y phenomena i n i n c r e a s i n g and d e c r e a s i n g p o p u l a t i o n s , pp. 361-399. In G. P. P a t i l , E. C. P i e l o u , and W. E. Waters (Eds.), S t a t i s t i c a l ecology. V o l . 2. The Pennsylvania State U n i v e r s i t y Press, U n i v e r s i t y Park, Penn. Moodie, G. E. E. 1972. P r e d a t i o n , n a t u r a l s e l e c t i o n and a d a p t a t i o n i n an unusual t h r e e s p i n e s t i c k l e b a c k . Heredity 28:155-167. Murphy, G. I. 1968. P a t t e r n i n l i f e h i s t o r y and the environment, Amer. Natur. 102:390-404, 69 P a t t e n , B. G, 1975. C o m p a r a t i v e v u l n e r a b i l i t y o f f r y o f P a c i f i c s almon and s t e e l h e a d t r o u t t o p r e d a t i o n by t o r r e n t s c u l p i n i n s t r e a m a q u a r i a . F i s h . B u l l . U.S. 73:931-934. P e l k w i j k , J . J . t e r and N. T i n b e r g e n . 1937. E i n e r e i z b i o l o g i s c h e a n a l y s e e i n i g e r v e r h a l t e n s w e i s e n von G-Sterosteus a c u l e a t u s L. Z. T i e r p s y c h o l . 1:193 P h i l l i p s , R. W. And E . W. C l a i r e . 1966. I n t r a g r a v e l movement o f t h e r e t i c u l a t e s c u l p i n , C o t t u s £erp_lexus> and i t s p o t e n t i a l a s a p r e d a t o r on s a l m o n i d embryos. T r a n s a c t i o n s o f t h e A m e r i c a n F i s h e r i e s S o c i e t y . 95:210-212. P i a n k a , E. R. 1974, E v o l u t i o n a r y e c o l o g y . H a r p e r and Row, New Y o r k . 356 pp. P i a n k a , E. R., and W. S. P a r k e r . 1975. A g e - s p e c i f i c r e p r o d u c t i v e t a c t i c s . Amer. N a t u r . 109:453-464. R i c k l e f s , R. E. 1969. An a n a l y s i s o f n e s t i n g m o r t a l i t y i n b i r d s . S m i t h s o n i a n C o n t r i b . Z o o l . 9:1-48, S c h a f f e r , W. H. 1974a. S e l e c t i o n f o r o p t i m a l l i f e h i s t o r i e s : t h e e f f e c t s o f age s t r u c t u r e . E c o l o g y 55:291-303. S c h a f f e r , W. M. 1974b. O p t i m a l r e p r o d u c t i v e e f f o r t i n f l u c t u a t i n g e n v i r o n m e n t s . Amer. N a t u r . 108:783-790. S e g a a r , J . 1961. T e l e n c e p h a l o n and b e h a v i o r i n G a s t e r o s t e u s a c u l e a t u s m a l e s . B e h a v i o r 18:256-2 87. S e g h e r s , B. H. 1970. B e h a v i o r a l a d a p t a t i o n s o f n a t u r a l p o p u l a t i o n s o f t h e guppy, P o e c i l i a r e t i c u l a t a , t o p r e d a t i o n . Amer. Z o o l . 10:489-490. S e g h e r s , B. H. 1973. An a n a l y s i s o f g e o g r a p h i c v a r i a t i o n i n t h e a n t i - p r e d a t o r a d a p t a t i o n s o f t h e guppy, P o e c i l i a _________§.- Ph.D. T h e s i s , D ept. o f Z o o l o g y , U n i v e r s i t y o f B r i t i s h C o l u m b i a . S e v e n s t e r , P. 1961. A c a u s a l a n a l y s i s o f a d i s p l a c e m e n t a c t i v i t y ( f a n n i n g i n G a s t e r o s t e u s a c u l e a t u s ) . B e h a v i o r , S u p p l . 9:1-110. Simmons, K. E. L. 1955. The n a t u r e o f t h e p r e d a t o r r e a c t i o n s o f waders t o w a r d s humans. B e h a v i o r 8:130-173. S m i t h , C. C. , and S. D. F r e t w e l l . 1974. between s i z e and number o f N a t u r . 108:499-506. The o p t i m a l b a l a n c e o f f s p r i n g . Amer. 70 Smith, S. And S. Hoskings. 1955. B i r d s f i g h t i n g . Faber and Faber, london. Stearns, S. C. 1976. L i f e h i s t o r y t a c t i c s : A review of the i d e a s . Quart. Hev. B i o l . 51:3-47. Stephens, W. J . D. 1963. Some responses of female m a l l a r d s to d i s t u r b a n c e by man. J . W i l d l . Manage. 27:280-283. Swarup, H. 1958. Stages i n the development of the s t i c k l e b a c k Oasterosteus a c u l e a t u s ( L . ) . J. Embryol. exp. Morph.~6:373-383. Symons, P. E. K. 1965. A n a l y s i s of s p i n e - r a i s i n g i n the male t h r e e - s p i n e d s t i c k l e b a c k . Behavior 26:1-74. T a y l o r , H. M., R. S. Gourley, C. E. Lawrence, and R. S. Kaplan. 1974. N a t u r a l s e l e c t i o n o f l i f e h i s t o r y a t t r i b u t e s : an a n a l y t i c a l approach. Theoret. Pop. B i o l . 5:104-122. Tinbergen, N. 1952. vThe study of i n s t i n c t . Clarendon Press, Oxford, T i n k l e , D. W. 1969. The concept of r e p r o d u c t i v e e f f o r t and i t s r e l a t i o n to the e v o l u t i o n o f l i f e h i s t o r i e s of l i z a r d s . Amer. Natur. 103:501-516. T r i v e r s , R. L. 1972. P a r e n t a l investment and sexual s e l e c t i o n . Pp. 136-179. In B. G. Campbell (Ed.), Sexual s e l e c t i o n and the descent of man (1871-1971). A l d i n e -Atherton, Chicago. T r i v e r s , R. L. 1972.. P a r e n t - o f f s p r i n g c o n f l i c t . Amer, Z o o l . 14:249-264. Warner, R. R. 1975. The adap t i v e s i g n i f i c a n c e of s e g u e n t i a l hermaphroditism i n animals. Amer. Natur. 109:61-82. West Eberhard, M. J . 1975. The e v o l u t i o n of s o c i a l behavior by k i n s e l e c t i o n . Quart. Rev. B i o l . 50:1-33. W i l l i a m s , G. C. 1957. P l e i o t r o p y , n a t u r a l s e l e c t i o n , and the e v o l u t i o n of senescence. E v o l u t i o n 11:398-411. W i l l i a m s , G. C. 1 9 6 6 a . Adaptation and n a t u r a l s e l e c t i o n . P r i n c e t o n U n i v e r s i t y P ress, P r i n c e t o n , N. J . 307 pp. W i l l i a m s , G. C. 1966b. N a t u r a l s e l e c t i o n , the c o s t s of r e p r o d u c t i o n , and a refinement of Lack's p r i n c i p l e . Amer. Natur. 100:687-690. 71 Wilson, E. 0. 1975. Sociobiology: the new synthesis. Belknap Press, Cambridge, Mass. 697 pp. Wootton, R. J . 1971. Measures of the aggression of parental male three-spined sticklebacks. Behavior 40:228-262. Wootton, R. J . 1973. Fecundity of s t i c k l e b a c k , Gasterosteus a c u l e a t u s B i o l . 5:683-688. the t h r e e - s p i n e d (L. ) . J . F i s h . 72 APPENDIX I. THE CHRONOLOGICAL EGG AGE The c h r o n o l o g i c a l age of the eggs, the time from f e r t i l i z a t i o n to c o l l e c t i o n , was estimated by c a l c u l a t i n g the time the eggs take to reach a given e mbryological stage f o r the water temperature i n the lake at the date of c o l l e c t i o n . The average water temperature f o r each l a k e throughout the summer was estimated by averaging the e a r l y morning (lowest) and l a t e afternoon (highest) water temperatures, measured a t the mean nest depth (.4m). T h i s average temperature was combined with i n f o r m a t i o n on the development r a t e of s t i c k l e b a c k eggs at d i f f e r e n t temperatures, c a l c u l a t e d from data c o l l e c t e d by B c P h a i l (unpublished) on a p o p u l a t i o n from Harewood Lake, Vancouver I s l a n d . The time these eggs took t o reach each e m b r y o l o g i c a l stage, as d e s c r i b e d by Swarup(1958), had been measured at 15, 20, and 25° C. To determine the development r a t e , I used r e g r e s s i o n a n a l y s i s to c a l c u l a t e the slo p e f o r the development time at each temperature as a f u n c t i o n of the p h y s i o l o g i c a l age of the eggs, which i s the time the eggs i n Swarup's study took to reach each e m b r y o l o g i c a l stage. The f o l l o w i n g developmental s l o p e s were found at each water temperature: r T Temp. | 150 200 250 Slope | 1.262 .731 .581 | 73 The decreasing developmental s l o p e f o r high e r water temperatures i n d i c a t e s t hat the time to reach a c e r t a i n stage decreases with higher temperatures. However, the developmental s l o p e i s not a l i n e a r f u n c t i o n of the water temperature. To determine the developmental s l o p e f o r in t e r m e d i a t e temperatures, a g u a d r a t i c eguation was f i t t e d to the above data g i v i n g the developmental s l o p e as a f u n c t i o n of temperature: Slope = .0076 (temp) 2 - .373 (temp) + 5.15 Thus to c a l c u l a t e the c h r o n o l o g i c a l age of the eggs i n each nest, (1) the average temperature of the lake at the date of c o l l e c t i o n was estimated, (2) t h i s temperature was used i n the above eguation t o c a l c u l a t e the developmental s l o p e , and (3) the mean p h y s i o l o g i c a l age of the eggs was m u l t i p l i e d by the c a l c u l a t e d s l o p e , g i v i n g the mean c h r o n o l o g i c a l age of the eggs. 74 APPENDIX I I . ALL-OR-NONE RISK MEASURES Re s u l t s c a l c u l a t e d f o r only those nests with eggs •TT- T T " TROUT LAKE GARDEN BAY LAKE I I ++-RISK MEASURE|| MEAN ± SE (N) 1 I | PROB MEAN ± SE {N) - X X - X X -I I PROB I _ i Number of Eggs . X X . Attack 1| 286.0+ 51.55(19) |p<.10j| 163.9± 12.86(18) No Attack || 165.5± 74.80{ 8) | || 111.0± 50.41 ( 4) + 1 |p>.10 f Head | I 249.0± 37.63(14) |p>.10|| 170,8± 16.80(12) T a i l || 209.5±150.50( 2) | || 150.0± 19.62 ( 6) Remain I! 434. 7± 113. 12 ( 6) J.025 || 202.5± 18.50 ( 2) Desert || 205.7+ 40.74(20) | I I 151.1± 15.62(19) i-j i i_i H |p>.10 I H i |p>.10 I P h y s i o l o g i c a l Egg Age r X X . Attack No Attack Head T a i l — + + • Remain Desert | 91.4± 11.37 (22) J.041 || 80.2± 12.18(25) | 55.6± 17.76( 8) | II 52.?± 26.94 { 4) | 104.9± 12.11(17) |p>.10|| 93.3± 14.76(18) | 55.4± 39.85{ 2) | || 46.5± 16.32( 7) L X J- L X . r -| 123. 1± 18.31( 8) 1.012 || 152.4± 6.55( 3) | 68.0± 10.57(21) | || 65.3± 11.15(25) Jp>.10 I |p< . 10 I | .035 I £k£2H2l2ai£§l Egg Age Attack No Attack Head T a i l Remain Desert 64.4+ 7.94{22)~~t.041~tt 48.1± 7.20 (25) 38.4± 11.90( 8) | I! 31.7± 15.42( 4) + -T-r-73.5± 8.48(17) |p>.10|J 56.0± 8.74(18) 40.5± 29.11 ( 2) | || 27.7± 9.38 ( 7) + + 79.7± 12.66( 9) t T o i 2 ~ | t 47.9± 7.42(21) j || - X J I L X -82.1± 10.04 ( 3) 39.4± 6.66 (25) .206 1 .072 025 75 APPENDIX I I I . QUANTITATIVE RISK MEASURES A. Regression r e s u l t s f o r a l l nests t T T T T 1 1 ! 1 1 RISK MEASURE1 (CONST | SE |COEFF| SE | r | n ]PROB| I | A | A | B | B | 1 1 1 ) J J I I J J 1 1 | Number of Eggs I y + — 7~--—H + + + 1- 1 1 Return Time (TL) \ 3.8 | .44|-.005|.0014 |-567 127 1.001J j Time t o Attack (TL) | 3.5 | . 37|-. 003 | . 00 11 | - 595 | 20 J.003| | B i t e s per Min (TL) | 6.3 | 2. 531 -027J.0076 I .625 122 |.001| | Return Time (GB) | 3.3 | . 28 j - . 008| .00 25 J.493 135 |.001| | Time to Attack (GB) | 4.1 | .38\-.006|,0026 |.464 |24 |.011| | B i t e s per Min (GB) | 4.1 | 3.62| .043].0246 J.356 123 |.046| | Return Time (CO) | 3.3 | .24|-.004|.0010 |.476 |62 |.001f j Time to Attack (CO) | 3.7 | ,24|-.004|.0009 1.555 |44 |.001| I B i t e s per Min (CO) | 5.7 | 1.94| .029|.0075 1-510 |45 |.001| | 1 1 i i j j i | ! P h y s i o l o g i c a l Egg Age | r r — - — H - + + 1- 1 | Return Time (TL) | 3.9 | .43J-.020J.0050 | .599 i 30 |.001| | Time to Attack (TL) | 3.6 | .43J-.014|.0043 |- 591 |23 |.002| | B i t e s per Min (TL) | 7.2 | 3- 151 . 0861 .0320 J.489 125 |.006| | Return Time (GB) j 3.0 1 .26J-.011 J .0034 |.447 |42 |. 0 0 21 | Time to Attack (GB) | 3.7 | .28]-.011|.0031 I.535 131 |.001| | B i t e s per Min (GB) | 5.9 | 2- 621 .0701.0290 |.416 130 |.011| J Return Time (CO) I 3.3 I .23|-.014|.0029 |.504 J72 |.001| ! Time to Attack (CO) I 3.7 I .24|-.012l.0025 I.569 J54 |-001| | B i t e s per Min (CO) 1 6.4 | 1.981 .079J.0211 1.459 J55 I - 0011 { i i i i j i i j I C h r o n o l o g i c a l Egg Age I I- 1-"" H-- + + 1- r \ I Return Time (TL) 1 3.9 | .43J-.030J.0072 |.615 |30 |.0011 1 Time t o Attack (TL) | 3.6 1 .44]-.020|.0062 1.586 |23 |.003| 1 B i t e s per Min (TL) | 7.0 | 3.141 .1261-0453 |.502 125 |.005| | Return Time (GB) | 3.0 1 .261-.0181.0057 J.440 |42 J-0021 I Time to Attack (GB) I 3.7 \ - 28 J-- 018 J.0053 |.525 131 |.001J I B i t e s per Min (GB) | 6.0 J 2.64J .1161- 0492 1-405 j30 I.Q12J | Return Time (CO) I 3.3 | .231-.0221.0045 J.511 172 1.0011 | Time to Attack (CO) | 3.7 1 .241-.0201.0038 |-578 154 1.001J I B i t e s per Min (CO) l 6.3 | 1.971 -125|.0322 J.470 |55 |.0011 i i j '. i i j i i i 1. Time measures are l o g transformed (TL)-Trout Lake; (GBL)-Garden Bay Lake; (CO)-Combined Lakes 76 APPENDIX II I . QUANTITATIVE RISK MEASURES B. Regression results for only those nests with eggs 1 1 T T T 1 1 1 1 | RISK MEASURE1 JCONST j SE ICOEFF| SE ] r | n |PROB| 1 | A j A | B | B | 1 1 1 | i i i j j i i 1 I Number of Eggs I -+ - t - | L - f -+ -+ 1 Return Time (TL) | 2.6 | .65 -.002|.0017 | .296 I 19 |.108| Time to Attack (TL) I 3.3 | .48 -,003|.0013 1.515 |17 |.016| Bites per Min (TL) I 7.5 | 3. 23 .025J.0090 |.552 | 19 1.007| Return Time (GB) | 4.1 | 1. 07 -.012J.0061 1.496 | 15 1-029| Time to Attack (GB) | 3.5 | 1.01 -.003!.0058 1.147 I 17 1.2891 Bites per Min (GB) 112.3 ] 10.16 -.0011.0576 1-000 I 16 1.932J Return Time (CO) | 2.6 | .45 -.002|.0014 | .290 | 34 | .046| Time to Attack (CO) | 3.4 | . 34 -.003|.0012 I .426 | 34 |.006| Bites per Min (CO) | 8.1 j 2. 88 .0231.0099 1.374 I 35 l-013| 1 • i L i _ _ A. • i 1 Physiological Egg Age I • i j t _ i t i 1 1 I "1* I T l 1 Return Time (TL) | 2.6 1 .68 |-. 009J .0070 1 .289 121 1.1011 Time to Attack (TL) | 3.4 1 .59 -.013|.0050 | .487 | 20 1-0141 Bites per Min (TL) | 9.2 1 4. 15 .070|.0390 | .367 I 22 | .045| Return Time (GB) 1 2.4 1 .54 -.006|.0051 1.254 | 22 |-126| Time to Attack (GB) | 3.3 i .41 -.0071.003 9 I .373 |24 1.0351 Bites per Min (GB) | 8.5 1 3.97 .051J.0378 1 .283 | 23 |.0941 Return Time (CO) | 2.5 1 .42 -.007|.0040 1 .270 143 | .038| Time to Attack (CO) | 3.3 I .34 |-.0101.0032 | .427 | 44 1,002| Bites per Min (CO) I 8.9 1 2.82 .059|.0268 1 .322 1 45 1.0151 1 i • i 1 _ x i i I Chronological Egg Age 1 i i l— 4. — -+ -f H- J I i I r rReturn Time (TL) 1 2.6 1 . 68 I-,014J.0096 I .316 121 |.0801 Time to Attack (TL) | 3.4 1 .60 I-.018J.0080 | .480 I 20 |.0151 Bites per Min (TL) | 8.8 1 4. 15 .104|.0561 1 .384 J22 1-0371 Return Time (GB) 1 2.3 1 .55 -. 0091 .00 89 1.213 | 22 I.171J Time to Attack (GB) | 3.3 1 .41 |-.011|.0068 1.341 | 24 1-049| Bites per Min (GB) | 9.3 I 4. 04 | .0721.0660 I .230 | 23 | .1451 Return Time (CO) | 2.5 1 .42 I-.011|.0064 1.271 |43 |,038| Time to Attack (CO) | 3.3 1 ,34 I-.0161.0050 I .434 | 44 1-0021 Bites per Min (CO) | 9.0 1 2.82 | .0921.0417 1.318 I 45 |,016| L. J .. JL _ J — L . .i. . - .. • « 1. Time measures are log transformed (TL)-Trout Lake; (GBL)-Garden Bay Lake; (CO)-Combined Lakes 77 APPENDIX IV. MULTIPLE EEGEESSION RESULTS RISK MEASURE T I SIG IND VAR | COEFF I 1 i I SE J I 1 -J L. N |PROB | R 2 I I Trout Lake ~r~~ Return Time egg number | -0.385 nest depth | -0 .427 t . 0 8 3 l t I.98051 Time to Attack B i t e s per Min +  egg number 1-1.424 + Remain-Desert J egg number I 1 . 1 1 0 - f — • r I 1-1002J , | „| I .92821 Attack-No Attack egg age 1 0.669 -f r 1 egg number ] 4.492 _l_ f  + f -J.0011J 1 .09901 + r-Head-Tail 1 no sig var 1 I 35 1.001 |.370 i I ——j—-———I 1 23 1.018 J.236 22 J.046 |.181 19 j.011 |.320 20 |.001 |.493 17 t "--"I j i — Return Time Time to Attack B i t e s per Min l I Garden Bay. Lake -f-egg number |-0.821 egg number 1-2.565 shore d i s t J 1.035 }. 102et 27 t |.1338~t 19 I I .8498J | egg number 1 2.680 I1.056J H + r 1 f 20 J- -j .000 I-529 | i j .015 H 1 1.409 1 1 1 - f 1 Remain-Desert 1 egg number 1 0.091 I.0724J ,015 I.282 -+-Attack-No Attack Head T a i l -+ I no sig var -t r 26 I.020 J.194 1 f-I no sig var \ -+ SIG IND VAR are those independent variables that contributed s i g n i f i c a n t l y (p<.05) to the prediction of the r i s k measure. For the all-or-none r i s k measures the high r i s k response was assigned the value 1 and 0 was assigned to the low r i s k response. Only nests that contained eggs were used in the analysis of the a l l - o r -none measures, and the time measures and egg number are log transformed. PROB i s the p r o b a b i l i t y of obtaining a value of R 2 given that there i s no association between the dependent and independent variables. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0093705/manifest

Comment

Related Items