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Adaptive divergence and the evolution of trophic diversity in the threespine stickleback Lavin, Patrick A. 1985

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ADAPTIVE DIVERGENCE AND THE EVOLUTION OF TROPHIC DIVERSITY IN THE THREESPINE STICKLEBACK by PATRICK A. LAVIN B . S c , U n i v e r s i t y Of B r i t i s h C o l u m b i a 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department o f Z o o l o g y ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNlVESSXT-Y-^OF BRITISH COLUMBLX O c t o b e r 1985 @ P a t r i c k A. L a v i n , 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Ẑ g>oVc, The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date C3c3r to } I 7 K DE-6(3/81) i i ABSTRACT Five populations of the threespine stickleback, Gasterosteous aculeatus,from the upper Cowichan River system (Vancouver Island, B r i t i s h Columbia) were surveyed to assess interpopulation levels of v a r i a b i l i t y in trophic morphology. Phenotypic divergence i s assumed to be a p o s t - g l a c i a l event. Nine characters were scored; eight were related to feeding and the ninth character was l a t e r a l plate number. A l l populations surveyed were the low plate morph; however populations of Gasterosteus in lakes lacking piscivorous f i s h had s i g n i f i c a n t l y fewer l a t e r a l plates than populations in lakes with predatory f i s h species. Three trophic 'morphotypes' were i d e n t i f i e d , each associated with one of three lake environments. Populations inhabiting benthic dominated environments ('benthic morph') were found to possess reduced g i l l raker number and reduced g i l l raker length but increased upper jaw length r e l a t i v e to populations from l e n t i c environments ('limnetic morph'). An intermediate morph may also exist and i s characterized by a morphology suitable to either trophic regime. Analysis of -stomach contents showed diet type (benthic or limnetic) to be s i g n i f i c a n t l y dependent on morph. The functional s i g n i f i c a n c e of differences in trophic morphology was investigated in three feeding experiments using a representative population from each morphotype. The longer jaw of the benthic and intermediate morphs allowed them to ingest a larger benthic prey than the limnetic. No behavioural component to benthic foraging success between populations was i d e n t i f i e d , although increased jaw length shortened the time spent manipulating prey. Both the intermediate and limnetic morphs were better foragers on an experimental limnetic prey than was the benthic. Head length, snout length, g i l l raker density and g i l l raker number were strongly correlated with limnetic foraging success. The quantitative genetics governing the eight trophic characters were investigated using the same three representative populations. Broad sense estimates of character h e r i t a b i l i t i e s ranged from 0.132 to 0.677; a l l estimates were s i g n i f i c a n t . Character genetic c o r r e l a t i o n s were reasonably strong (0.3 < j rG| ^ 0.9), while character correlations a r i s i n g through environment tended to be lower. Cluster analyses of the genetic c o r r e l a t i o n matrices defined two character suites, the f i r s t grouped measures of head shape, the second grouped measures of g i l l raker structure. The patterns of genetic correlations suggest the three populations are d i s t i n c t races. Selection gradients for divergence between morphotype indicated that d i r e c t i o n a l selection had operated hardest on head length, snout length, g i l l raker number, head depth and upper jaw length; hence selection has operated to modify characters related to food s i z e . The benthic-limnetic and intermediate- limnetic morphs were separated by the greatest selection distance while the intermediate-benthic morphs were separated by the shortest selection distance. These results support the conclusion that d i r e c t i o n a l selection, a r i s i n g from trophic resource differences between i v l a k e s , has o r g a n i z e d i n t e r p o p u l a t i o n v a r i a b i l i t y f o r G a s t e r o s t e u s w i t h i n t h e upper Cowichan d r a i n a g e . The r a c i a l d i s t i n c t i o n o f e a c h p o p u l a t i o n c o u p l e d w i t h t h e f u n c t i o n a l s i g n i f i c a n c e of some components o f t r o p h i c m o r p h o l o g y i n d i c a t e t h a t a t l e a s t t h e b e n t h i c and l i m n e t i c morphs must be c o n s i d e r e d ' e c o t y p e s ' . V TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES - . v i i LIST OF FIGURES ix ACKNOWLEDGEMENTS x General Introduction 1 Chapter 1 4 Introduction 4 Materials and Methods 5 Cowichan Lake 5 S t a t i s t i c a l Methods 10 Results 12 Discussion 28 Chapter 2 34 Introduction 34 Materials and Methods 36 Establishment and Fostering of Progeny 36 Estimation of Character H e r i t a b i l i t i e s and Correlations . 38 Reconstructing the Pattern of Trophic Divergence .... 41 Results 42 H e r i t a b i l i t y and Genetic Correlations 42 Selection Gradients' 59 Discussion 60 Chapter 3 65 v i Introduction 65 Materials and Methods 67 Trophic Morphology 67 Gape Experiments 68 Amphipod Manipulation Experiments 70 Limnetic Foraging T r i a l s 73 Results 75 Trophic Morphology 75 Maximum Gape 7 6 Amphipod Manipulation Experiments 81 Limnetic Foraging T r i a l s 86 Discussion , 88 General Discussion 99 References 102 v i i LIST OF TABLES Table 1. Morphometry data for lakes in the upper Cowichan drainage 8 Table 2. Means and standard deviations on adjusted data for each variable and population 18 Table 3. PCA from adjusted data 23 Table 4. Component correlations from the co r r e l a t i o n matrix of adjusted data 24 Table 5. Experimental design of nested ANOVA on component scores 28 Table 6 . Design of f u l l s i b ANOVA for the estimation of Vg. 37 Table '7. Descriptive s t a t i s t i c s for wild c o l l e c t i o n s and laboratory reared progeny 43 Table 8. H e r i t a b i l i t i e s for the three representative trophic morphs 46 Table 9. Genetic, phenotypic and environmental c o r r e l a t i o n matrices for Bear Lake 49 Table 10. Genetic, phenotypic and environmental c o r r e l a t i o n matrices for Caycuse 51 Table 11. Genetic, phenotypic and environmental c o r r e l a t i o n matrices for Grant Lake 53 Table 12. Spearman rank co r r e l a t i o n s between the elements of the genetic, environmental and phenotypic c o r r e l a t i o n matrices 57 Table 13. Selection gradients for population t r a n s i t i o n s . . 59 v i i i T a b l e 14. ANCOVA r e s u l t s f o r g i l l r a k e r d e n s i t y on s t a n d a r d l e n g t h 75 T a b l e 15. Gut c o n t e n t d a t a from w i l d p o p u l a t i o n s a m p l e s . .. 77 T a b l e 16. ANCOVA r e s u l t s f o r amphipod s i z e on s t a n d a r d l e n g t h and upper jaw l e n g t h 79 T a b l e 17. C e l l means and s t a n d a r d d e v i a t i o n s f o r ANOVA on b e n t h i c f o r a g i n g s u c c e s s 84 T a b l e 18. M u l t i p l e r e g r e s s i o n summary o f f o r a g i n g s u c c e s s on b e h a v i o u r 85 T a b l e 1 9 . C o r r e l a t i o n c o e f f i c i e n t s f o r a v e r a g e s u c c e s s f u l m a n i p u l a t i o n t i m e on UPJL 86 T a b l e 20. Summary of l i m n e t i c f e e d i n g e x p e r i m e n t s 87 T a b l e 21. I n t r a p o p u l a t i o n c o r r e l a t i o n s f o r c h a r a c t e r and t h e p r o p o r t i o n o f l i m n e t i c f o r a g i n g 87 T a b l e 22. I n t e r p o p u l a t i o n c o r r e l a t i o n c o e f f i c i e n t s f o r c h a r a c t e r and l i m n e t i c s u c c e s s 88 LIST OF FIGURES Figure 1 . The Cowichan drainage system and the S t r a i t of Georgia region 6 Figure 2. Dendrogram summary of lake groupings based on lake chemistry '. 13 Figure 3. V a r i a b i l i t y p r o f i l e s for the nine sampling s i t e s in the Cowichan drainage 15 Figure 4. Dendrogram summary of lake groupings based on population morphology . .. 20 Figure 5. Bivariate mean component scores, for each population, plotted on the f i r s t two p r i n c i p a l components 26 Figure 6. Dendrogram summary of character genetic c o r r e l a t i o n matrices 57 Figure 7. Plot of amphipod size vs UPJL for each morph. ... 82 Figure 8. Plots of bivariate means for the proportion of limnetic foraging and adjusted character 89 Figure 9. Plots of bivariate means for the proportion of limnetic foraging and GRL, GRN and GRDENS 91 X ACKNOWLEDGMENTS My i n i t i a l interest in the stickleback and evolutionary problems was stimulated by Dr. J.D. McPhail. I wish to express my most sincere thanks for his creative insight and patient support in a l l aspects of thi s project. Melanie Mad i l l , Andrew Simons, E r i c Taylor and Gary Birch kindly provided of their time for assistance in the f i e l d . Melanie Madill deserves special recognition for suffering through boring hours of data recording and key punching. Drs. Dolph Schluter, Jack Maize and C. Wehrhan led (dragged) me through the mysteries of multivariate s t a t i s t i c s . I would p a r t i c u l a r l y l i k e to thank Dolph Schluter for the many hours he devoted to discussing my work, on and off the squash court. Discussions and arguments with E r i c Taylor were always enlightening and this work was improved by them. Comments from Drs. Judy Myers, C. Wehrhan and Nick Giles added c l a r i t y to my thinking and thi s t h e s i s . Bob Carveth's c r i t i c i s m s greatly improved the figures. A l i s t a i r Blachford, Susan E r t i s and the s t a f f of the b i o l o g i c a l sciences data center provided invaluable aid in data analysis. 1 GENERAL INTRODUCTION The threespined stickleback (Gasterosteous aculeatus) i s a polytypic species (Bell 1976) exhibiting v a r i a b i l i t y i n: breeding colours (e.g. McPhail 1969; Moodie 1972); behaviour (e.g. Hay and McPhail 1975; McLean 1980; McPhail and Hay 1983); body morphology (e.g. Hagen and Gilbertson 1972; McPhail 1977; Gross and Anderson 1984); and in biochemistry (Withler and McPhail 1985). Despite the range of characters which show a propensity to vary, the most extensive surveys of variation have concentrated on body armature, p a r t i c u l a r l y with respect to the l a t e r a l plates or scutes (e.g. Munzing 1963; M i l l e r and Hubbs 1969; Gross 1977). Recent studies have also examined the loss of skeletal parts including pelvic g i r d l e elements (Giles 1983) and dorsal and pelvic spines (Reimchen 1980b). Investigations of the three commonly described 'plate morphs' (Hagen and Gilbertson 1972) have generated two hypotheses concerning the origins of freshwater d i v e r s i t y in resident ( i . e . nonanadromous) populations of Gasterosteus. The model outlined by M i l l e r and Hubbs (1969) proposes the maintenance of v a r i a b i l i t y by gene flow. The authors suggest that the d i s t r i b u t i o n of plate phenotypes results from continual introgression of freshwater genomes by genetic input from anadromous populations, in t h i s case most of the variation would be neutral. Studies at contact zones however, do not support introgression as hybrids appear to be s e l e c t i v e l y disfavoured (Hagen 1967). This observation led to the alternate hypothesis proposed by Hagen and McPhail (1970) which describes selection, 2 as the primary agent organizing freshwater d i v e r s i t y . Later empirical work i l l u s t r a t e d the selective advantage of di f f e r e n t plate phenotypes (Moodie et a l . 1973), while recent studies of coastal A t l a n t i c populations suggest that the p a r t i a l l y plated morph (once thought to be a hybrid) -may be at a selective advantage in some situations and represent d i s t i n c t populations (Hagen and Moodie 1982; Wootton 1984). Although gene flow may not contribute s i g n i f i c a n t l y to patterns of interpopulation v a r i a b i l i t y , forces other than selection may s t i l l y i e l d detectable v a r i a t i o n . Changes in sea- l e v e l with temperature minima and maxima during the Pleistocene, afforded anadromous populations saltwater routes into g l a c i a l lakes. Freshwater populations are generally thought to be derived from these marine founder stocks (Bell 1976) following the invasion of previously uncolonized habitat; selection subsequently organizes the founder genetic v a r i a t i o n . McPhail (1984) has suggested that such founder invasions are responsible for the evolution of the Gasterosteus species pair in Enos Lake, Vancouver Island. These b i o l o g i c a l species exhibit extreme i n t e r s p e c i f i c divergence in morphology thought to be associated with trophic ecology, and the differences are congruent with diet type. One species, the so c a l l e d 'benthic' is a bottom browser feeding on macroinvertebrates, while the 'limnetic' feeds almost e n t i r e l y on planktonic prey. Bentzen and McPhail (1984) have shown differences in jaw morphology, between the two species, to be in part responsible for the dietary d i s t i n c t i o n . This i s one of the few studies involving freshwater populations 3 of Gasterosteus in which the significance of morphological v a r i a b i l i t y has been c l e a r l y defined, but more importantly i t indicates a potential mechanism for the evolution of d i f f e r e n t i a t i o n - adaptive divergence (Bentzen 1982). Although the species pairs are of great interest they may be evolutionary anomalies and hence provide l i t t l e generality in describing the origins of r a c i a l differences ( i . e . variation preserved below the l e v e l of b i o l o g i c a l species). Is there any significance to interpopulation differences or i s t h i s v a r i a t i on neutral, a r i s i n g largely from the e f f e c t s of history? If adaptive divergence is a common mode of evolution in the stickleback then we must be able to ascribe a si g n i f i c a n c e to the observed v a r i a t i o n . This thesis investigates the adaptive divergence in freshwater populations of Gasterosteus. The study was designed to address three questions relevant to adaptive divergence. 1. How much morphological v a r i a t i o n exists within and between resident populations of lake-dwelling Gasterosteus? 2. Does the morphological v a r i a t i o n appear to be under genetic control? 3. If selection can be implicated in s h i f t i n g population morphology, which characters have been s e l e c t i v e l y modified? The three chapters which follow focus on each of these questions in turn. 4 CHAPTER 1 Introduction The extensive phenotypic v a r i a t i o n exhibited by the threespine stickleback Gasterosteous aculeatus, together with the dichotomy between the freshwater and marine forms, has generated two hypotheses to account for the evolution of t h i s d i v e r s i t y . M i l l e r and Hubbs (1969) suggest that much of the phenotypic v a r i a t i o n found in freshwater habitats arises from continual introgression from the marine form; whereas, Hagen and McPhail (1970) argue that most freshwater v a r i a t i o n i s due to l o c a l selection. The l a t t e r hypothesis i s supported by a number of empirical investigations that have i d e n t i f i e d l o c a l adaptations (e. g. Hagen and Gilbertson 1973). Many of these studies focus on body armature, p a r t i c u l a r l y the l a t e r a l plate phenotype. This character i s e a s i l y scored and differences between populations in plate count frequencies are often obvious. Thus, much of the perceived complexity within the Gasterosteous aculeatus complex arises from investigations of plate count frequencies, or the frequencies of d i f f e r e n t plate morphs. Although t h i s concentration on l a t e r a l plates has been productive, i t has led to confusion (see Hagen and Moodie 1982 for a discussion of t h i s problem) and, more importantly, i t has obscured the extensive morphological v a r i a b i l i t y in other characters, p a r t i c u l a r l y those involved in trophic resource exp l o i t a t i o n . This v a r i a t i o n is probably adaptive, and i f so selection on trophic t r a i t s may be a dr i v i n g force behind 5 population divergence. Recent studies emphasize the ecological and evolutionary significance of variation in teleost head morphology (e.g. Witte 1984) and in Gasterosteus, differences in head morphology in the Enos Lake species pair appear to be appropriate to their resource use (Bentzen and McPhail 1984). This chapter describes the degree of variation in trophic morphology between populations from five lakes within the Cowichan drainage, Vancouver Island, B r i t i s h Columbia. If interpopulation variation i s a response to d i f f e r e n t selective regimes between lakes, one would predict an association between lake characters and s i t e - s p e c i f i c Gasterosteus morphologies. Thus, I have attempted to identi f y extant differences in lake c h a r a c t e r i s t i c s and associate these with divergence in trophic morphology. Materials and Methods Cowichan Lake Cowichan Lake is a large, oligotrophic lake on south- central Vancouver Island, B r i t i s h Columbia. The lake drains through the Cowichan River into the Straight of Georgia (Fig. 1). A recent geologic u p l i f t has caused the river to sink into i t s own floodplain, confining the r i v e r to a narrow, steep channel containing a number of f a l l s (Carl 1953). The anadromous form of Gasterosteus enters the lower Cowichan system but i s excluded from my study area by Skutz F a l l s , a 5.5 metre drop over a 91 metre run. The entire Cowichan Valley was 6 Figure 1. The Cowichan drainage system and the S t r a i t of Georgia region. (1 = Kwassin Lake, 2 = Grant Lake, 3 = Beaver Lake, 4 = Mesachie Lake, 5 = Bear Lake, 6 = Honeymoon Bay, 7 = Gordon Bay, 8 = Caycuse, 9 = Bay 10; 6,7,8, and 9 are a l l s i t e s within Cowichan Lake.) 7 8 glaciated during the last (Fraser) g l a c i a t i o n and in the i n i t i a l stages of deglaciation (about 10,000 BP) the study area was covered by a single g l a c i a l lake (Alley and Chatwin 1979). This area now contains Cowichan Lake and four smaller lakes (Fig. 1). A l l of the lakes are interconnected and there are no obvious barriers to stickleback dispersal between the lakes. Thus, gene flow is possible between populations in di f f e r e n t lakes. Data on lake morphometry are presented in Table 1. Table 1. 1 Morphometry data for lakes in the upper Cowichan drainage system. Lake Area Maximum Elevat ion (Hectares) Depth(m) (m) Cowichan 6176.9 45.7 1 63 Bear 28.0 5.5 1 63 Beaver 33.0 5.0 181 Grant 2.2 2.5 1 75 Kwassin 1 .4 2.5 175 Mesachie 76.0 10.1 1 68 The lakes, and sites within the lakes, were grouped by chemical s i m i l a r i t y ; these groups were then compared to population groupings achieved by morphological a n a l y s i s , on the sticklebacks c o l l e c t e d from each s i t e . Five chemical measures were made at each sampling locat i o n : dissolved oxygen, t u r b i d i t y , conductivity, pH, and a l k a l i n i t y . Dissolved oxygen was measured in the f i e l d , and the four remaining measures were made on water samples returned to the Environmental Engineering Laboratory (U. B. C. ). Using Euclidean distance as the s i m i l a r i t y c r i t e r i o n the five variables were then entered into a 9 cluster analysis. Each variable was given equal weight in computing the distance matrix. , Euclidean distance i s affected by changes in variable scaling; consequently a l l data were standardized by d i v i d i n g the i t h s i t e datum of the kth variable by the standard deviation of the kth variable (Everitt 1974). Ward's method (Everitt 1974) was used to generate a dendrogram of lake s i t e s (Fig. 2). E i l e r s et a l . (1983) employed a similar c l a s s i f i c a t i o n analysis using three variables to group separate lakes r e l a t i v e to their s u s c e p t i b i l i t y to a c i d i f i c a t i o n . Sticklebacks were co l l e c t e d using pole-seines and minnowtraps from the nine locations during May 1983. A l l f i s h were preserved in 10% buffered formalin for one week, washed and then stained in a solution of a l i z a r i n red and KOH. F i n a l preservation was in 37.5% isopropyl alcohol. Nine morphological measures were made on each individual (21 < N < 40) with d i a l c a l i p e r s (+ 0.05mm) and where necessary an ocular micrometer. These measures include: standard length (STDLEN), head length (HEAL), snout length (SNOL), eye diameter (EYED), upper jaw length (UPJL), g i l l raker number (GRN) , g i l l raker length (GRL), head depth (HEAD), inner o r b i t a l width (INOW), and plate number (PLN). Except for plate number a l l measurments follow Hubbs and Lagler (1958). Plates were scored according to Hagen and Gilbertson (1972). A l l of these variables, except plates, are associated with trophic exploitation (Kliewer 1970; Fryer and l i e s 1972; Northmore et a l . 1978; Hyatt 1979; Wright et a l . 1983).. 10 S t a t i s t i c a l Methods In animals with indeterminate growth, growth related differences in body size frequently account for the majority of both inter and intrapopulation v a r i a b i l i t y (Thorpe 1976). To remove such size e f f e c t s each variable was adjusted to a standard length of 40mm. This adjustment uses the linear regression of the log of each variable on the log of standard length (Steele and Torrie 1980). The basic form of the regression i s , Yijk = Yjk - 0 j k ( L i k - 40) where Yijk i s the i t h adjusted case of the jt h variable in the kth population, Yjk i s the sample mean of the j t h variable, (Lik 40) i s the standard length of the i t h individual minus the grand mean, and /3jk i s the c o e f f i c i e n t of allometry for the j t h variable on standard length within each population. Although other authors have adjusted their data sets to a standard length of 50mm (Hagen and Gilbertson 1973; McPhail 1984), some of the populations contained many small individuals (< 35mm) and thus I reduced the adjusted length to 40mm. If the r e l a t i v e growth curves of two populations are similar, but c u r v i l i n e a r ; individuals sampled e a r l i e r in development y i e l d a steeper function than larger individuals whose growth rate has slowed. As a re s u l t , adjusting a sample consisting of many small individuals to a standard length beyond the sample mean, may exaggerate morphological differences between.populations. Site s p e c i f i c regression c o e f f i c i e n t s were used to adjust each character (Thorpe 1976). 11 Using Sheffe's test, multiple comparisons of sample means were made for each variable. Many of these univariate contrasts were s i g n i f i c a n t (p < 0.05), while others suggested certain s i t e s might be grouped by morphological s i m i l a r i t y . This p o s s i b i l i t y was investigated by clu s t e r i n g morphometric data. The methods of t h i s analysis are the same as those used for clustering the lake chemistry data. An element by element co r r e l a t i o n of the two Euclidean distance matrices, was used to test for congruence of the two dendrograms. Patterns of morphological v a r i a t i o n were summarized by p r i n c i p a l components derived from the character c o r r e l a t i o n matrix (Pimentel 1979). A l l characters, except plate number, were entered into the analysis. The contribution of each variable to each component was evaluated by component correlations (Pimentel 1979). To define the r e l a t i v e contributions of intra and i n t e r l o c a l i t y variances to morphological d i f f e r e n t i a t i o n , an ANOVA was performed on the component scores from the f i r s t three components. The i n t e g r i t y of the inferred groupings (see results) was investigated by nesting the populations within the groups suggested by thi s ANOVA. The sampling program within the Cowichan drainage was not a survey of putative microhabitats; therefore nesting the populations within groups does not vi o l a t e the assumption of random assignment within a subordinate l e v e l (Sokal and Rohlf 1981). Unless otherwise noted, a l l s t a t i s t i c a l procedures were performed using MIDAS (Fox and Guire 1976). 1 2 Results The r e s u l t s of the cluster analysis of s i t e chemistry are summarized in Figure 2. The four Cowichan Lake s i t e s form a d i s t i n c t group as do Grant and Kwassin lakes. One should note that Bear Lake i s more closely related to Beaver Lake even though the former i s a small bay off the main body of Cowichan Lake and so might have been expected to group with the Cowichan s i t e s . These re s u l t s indicate the existence of two lake types defined by chemistry, with the Bear-Beaver pair possibly forming a t h i r d type. For each character and population the c o e f f i c i e n t s of va r i a t i o n on the unadjusted data are plotted in Figure 3. Such ' v a r i a b i l i t y p r o f i l e s ' (Yablokov 1974) provide two important insights into the nature of evolutionary responses: (a) an indication of character c o r r e l a t i o n , and (b) the mechanism by which a p a r t i c u l a r species interacts with selective constraints. Concordance of peaks and troughs, but differences in peak amplitudes, suggests that the species i s responding to l o c a l selection with a common genetic architecture. This i s in contrast to genome reorganization as a response to l o c a l selection (Sokal 1978). These concepts are treated in d e t a i l below. For each variable and each population the adjusted means and standard deviations are reported in Table 2. There were no s i g n i f i c a n t differences (p > 0 . 0 5 ) between subsamples within Cowichan Lake; however, a l l Cowichan subsamples were s i g n i f i c a n t l y d i f f e r e n t (p < 0 . 0 5 ) from a l l other lakes in at 13 F i g u r e 2 . Dendrogram summary o f l a k e g r o u p i n g s b a s e d on l a k e c h e m i s t r y . 9 BAY 10 8 CAYCUSE GORDON BAY 6 HONEYMOON BAY MESACHIE BEAR BEAVER GRANT- 1 KWASSIN- 0.0 20 3 0 DISTANCE 1 5 - F i g u r e 3. V a r i a b i l i t y p r o f i l e s f o r t h e n i n e s a m p l i n g s i t e s i n t h e C o wichan d r a i n a g e . lO HEAL SNOL EYED UPJL GRN CHARACTER Legend O BAY10 A BEAR O BEAVER V CAYCUSE GORDON O GRANT • HONEYMOON • KWASSIN © MESACHIE GRL HEDP INOW 1 7 least one variable. Mean plate number i s also presented in Table 2 for each population. A l l populations, including s i t e s within Cowichan Lake, are c l e a r l y the "low plate morph" (Hagen and Gilbertson 1972), although there are s i g n i f i c a n t differences between populations in mean plate number. For both Beaver and Bear lakes mean plate numbers do not d i f f e r from any of the Cowichan Lake s i t e s or from Mesachie Lake; however the plate means for both Grant and Kwassin lakes are lower than a l l other samples (p < 0.0001). Neither Grant nor Kwassin Lakes contain any species of piscivorous f i s h although stickleback populations in both lakes are subject to avian predation. A l l of the other lakes contain a variety of f i s h species known to prey on Gasterosteus. These univariate comparisons suggested that populations within the smaller lakes (Bear, Beaver, Grant and Kwassin) were morphologically d i s t i n c t from both the Cowichan Lake s i t e s and the Mesachie Lake sample. The dendrogram derived from the character data support t h i s conclusion (Figure 4). The Cowichan Lake s i t e s and Mesachie Lake form one cluster while the smaller lakes form a second c l u s t e r . Interestingly, the analysis preserves the grouping of Bear and Beaver lakes produced by the c l u s t e r i n g of s i t e data, although in t h i s instance the pair c l u s t e r more clos e l y with the Kwassin-Grant group. The distance matrices were reasonably strongly correlated (r = 0.653). Cl e a r l y , within the upper Cowichan system there exist at least two morphologically distinguishable groups. Is t h i s grouping s i t e - s p e c i f i c or are the populations simply components 18 T a b l e 2. Means and s t a n d a r d d e v i a t i o n s on a d j u s t e d d a t a f o r e a c h v a r i a b l e and p o p u l a t i o n . A l l d a t a a d j u s t e d t o 40mm s t a n d a r d l e n g t h . S t a n d a r d d e v i a t i o n s a r e g i v e n i n b r a c k e t s . 19 T a b l e 2. P o p u l a t i o n means and s t a n d a r d d e v i a t i o n s f o r a l l a d j u s t e d v a r i a b l e s . P o p u l a t i o n N HEAL SNOL EYED UPJL GRN GRL HEAD I NOW Bay 1 0 2 1 1 1 .98 3 . 7 3 3 . 9 4 2 .89 2 0 . 1 0 0 .84 5 . 5 5 2 . 4 5 ( .51 ) ( .15) ( . 16) ( .25) ( 1 . 3 3 ) ( .09) ( .25) (. 13) Bear 30 1 2 . 4 7 3 .67 3 .81 3 .04 1 7 .86 0 .80 5 . 5 5 2 . 38 ( 1 .27) ( .24) ( . 2 1 ) ( . 2 0 ) ( 1 . 13) ( . 1 1 ) ( .32) (. 16) B e a v e r 23 1 1 . 9 3 3 .71 3 . 7 3 2 . 9 4 18 .60 0 . 7 3 5 . 4 7 2 . 1 6 ( .50) ( . 2 0 ) ( . 16) ( .19) ( 1 . 3 7 ) ( .08) ( .27) (. 14) C a y c u s e 30 1 1 .68 3 .62 3 . 9 5 2 . 9 5 1 9 .70 0 .85 5 .50 2 . 3 7 ( .42) ( .25) ( . 16) ( . 2 0 ) ( 1 .08) ( . 1 0 ) ( .26) ( . 15) Gordon 29 1 1 .84 3 . 7 5 3 . 9 7 2 .83 2 0 . 1 7 0 .84 5 .36 2 . 3 7 (. 4 5 ) ( . 2 1 ) ( .17) ( .18) ( 1 . 13) ( . 1 0 ) ( .27) (. 14) G r a n t 30 1 2 .60 3 .62 4 .06 3 . 3 9 17 .46 0 .69 5 .70 2 . 2 1 ( .60) ( .32) ( .17) ( . 2 2 ) ( .86) ( . 1 1 ) ( .36) ( . 16) Honeymoon 2 1 1 1 .25 3 .50 3 .88 2 .80 19 . 3 5 0 .83 5 .31 2 . 3 5 ( .56) ( . 3 3 ) ( .19) ( .28) ( 1 . 1 1 ) ( .08) ( .31 ) ( . 17) K w a s s i n 30 1 2 .24 3 . 9 9 3 . 9 5 3 . 3 3 17 .30 0 .71 5 . 7 9 2 . 3 5 ( .67) ( . 3 3 ) ( . 2 0 ) ( .27) ( 1 .46) ( . 15) ( . 3 4 ) (. 1 9 ) M e s a c h i e 30 1 2 . 1 2 3 . 7 3 3 .85 3 . 1 0 19 .06 0 . 9 7 5 . 7 5 2 . 3 3 ( . 4 5 ) ( .15) ( . 16) ( . 1 1 ) ( 1 .25) ( .07) ( . 2 1 ) (. 2 2 ) 20 Figure 4. Dendrogram summary of lake groupings based on population morphology. BAY10-? 7 GORDON B A Y J C A Y C U S E - HONEYMOON B A Y 6 M E S A C H I E 4 B E A R 5 BEAVER 3 G R A N T 2 KWASSIN 1 I 0.0 .02 .044 DISTANCE 22 of a linear array that has arisen through stochastic events? Linear c l i n a l v a r i a t i o n could result from gene-flow between subpopulations that possess d i f f e r e n t a l l e l e frequencies as a result of genetic d r i f t or founder effect (Endler 1977). The interpopulation phenotypic c o r r e l a t i o n matrix contained only eight (of a possible 28) s i g n i f i c a n t (p < 0.05) corr e l a t i o n s . This suggests that certain phenotypic characters might be responding to similar influences (genetic, environmental, or both) across habitats and therefore acting as a character s u i t e . In contrast to the interpopulation character correlations, a l l the intrapopulation c o r r e l a t i o n matrices contained at least eight, and as many as twenty, s i g n i f i c a n t correlations. This pattern strongly suggests that the population phenomes are responding to some s i t e - s p e c i f i c influence. Further, the pattern of reduced interpopulation character covariance indicates that population divergence in thi s system may be the result of d i r e c t i o n a l selection acting on a limited suite of correlated characters. As a result, the next issue addressed was the i d e n t i f i c a t i o n of phenotypic character suites and an investigation of their r e l a t i v e contribution to the observed population d i f f e r e n t i a t i o n . I n i t i a l l y , p r i n c i p a l components were extracted from the individual populations and variable loadings compared for the f i r s t component'. The f i r s t p r i n c i p a l component accounted for 40-70% of the t o t a l variance across the nine populations with HEAL, SNOL, UPJL and HEAD consistantly having the highest c o e f f i c i e n t s . As a re s u l t , the populations were pooled and 23 components extracted from the t o t a l pooled correlation matrix. Table 3 summarizes the results of this p r i n c i p a l components analysis. Table 3. PCA from adjusted data ( a l l variables except plate number). Pr i n c i p a l Components Var iable Axis 1 Axis 2 Axis 3 HEAL 0. 41 699 -0. 18473 0. 10923 SNOL 0. 45125 0. 1 4857 0. 1 9395 EYED 0. 31298 0. 00425 -0. 83628 UPJL 0. 43590 -0. 29276 0. 05008 GRN -o. 1 071 8 0. 60835 -0. 27465 GRL 0. 16016 0. 55495 0. 39478 HEAD 0. 45600 -0. 03063 0. 09243 I NOW 0. 29907, 0. 42317 -0. 09353 Eigenvalue 3. 5524 1 . 7035 0. 7939 %variance 44 .40 21 .50 9. 92 The f i r s t three components account for 75.62% of the t o t a l variance. As a result of the i n i t i a l adjustment of the data set to a grand mean of 40mm, a l l components must be representations of shape differences. Table 4 presents the co r r e l a t i o n c o e f f i c i e n t s between the i t h o r i g i n a l variable and the j t h component. Head depth, snout length, upper jaw length and head length are a l l highly correlated with the f i r s t component which may be thought of as a summary variable describing head shape. Character correlations tend to decrease on the following two components. The component co r r e l a t i o n i s often considered to be the i t h variable's response to the j t h stimulus (Morrison 1967) ; consequently as the proportion of variance accounted for 24 Table 4. Correlation c o e f f i c i e n t s between each character and p r i n c i p a l component. Eigenvector Var iable Axis 1 Axis2 Axis3 HEAL 0.7859 -0.2411 0.0973 SNOL 0.8505 0. 1939 0.1728 EYED 0.5899 0.0056 -0.7452 UPJL 0.8215 -0.3821 0.0446 GRN -0.2020 0.7940 -0.2447 GRL 0.3018 0.7243 0.3518 HEAD 0.8594 -0.0474 0.0824 I NOW 0.5636 0.5523 -0.0833 decreases ( i . e. the effect of the major stimuli are removed) correlations of any given variable are l i k e l y to decline. There remain however, three r e l a t i v e l y high correlations on the next two axes: g i l l raker number and g i l l raker length on the second axis and, eye diameter on the t h i r d axis. These responses should not be dismissed as they may be the features producing the group d i f f e r e n t i a t i o n outlined below. The d i s t r i b u t i o n of variance summarized by the f i r s t three components was examined by ANOVA. PCI accounts for 44.4% of the t o t a l v a r i a t i o n ; 21.0% of t h i s proportion i s a result of variation among populations and the remainder i s due to within population variance. PCII accounts for 21.5% of the t o t a l v a r i a t i o n : 63.9% results from differences among populations and suggests that g i l l raker number and length, may be important aspects of population divergence. Upper jaw length contrasts with g i l l r a k e r number and length on t h i s component (Table 3). Populations from the small shallow lakes (Bear, Beaver and Grant) tend to have longer jaws but reduced g i l l r a k e r number and 25 length (Table 2) compared to populations from the larger, deeper lakes (Cowichan and Mesachie). F i n a l l y , PCIII accounts for 9.9% of the t o t a l v a r i a t i o n ; 34.7% of t h i s proportion results from differences among populations. In summary, 26.5% of the variance summarized by the f i r s t three components, arises from differences among populations. The means and standard deviations of the component scores are plotted in Figure 5. Although the intrapopulation variation reduces group discrimination on the f i r s t axis, the second axis appears to y i e l d the separation of at least two groups. The intermediate populations may, or may not, represent a t h i r d grouping. To investigate the i n t e g r i t y of these inferred groups, a nested ANOVA was performed on component scores, nesting populations within lake groupings (UBC:GENLIN). The design of thi s analysis i s given in Table 5. Since B a r t l e t t ' s test indicated that the variance among the lake groupings did not v i o l a t e the assumption of homoscedasticity; Tukey's multiple range test was used to id e n t i f y differences among s i t e s . Tukey's HSD i d e n t i f i e d two homogeneous subsets among PCI scores - [2,1] and [3], (p < .05). Si g n i f i c a n t v a r i a t i o n was also found among si t e s nested within groups. This result was expected as the i n i t i a l single c l a s s i f i c a t i o n ANOVA had already demonstrated s i g n i f i c a n t within group variance on PCI. Nested ANOVA on the scores from PCII yielded s i g n i f i c a n t differences among groups (p = 0.000) with much reduced within s i t e variation ( 0.0 < p < 0.05). In this instance Tukey's test indicated 26 F i g u r e 5. B i v a r i a t e mean c o m p o n e n t s c o r e s , f o r e a c h p o p u l a t i o n , p l o t t e d on t h e f i r s t two p r i n c i p a l c o m p o n e n t s . G l y p h s i n d i c a t e mean p o s i t i o n f o r e a c h p o p u l a t i o n ; b l a c k b a r s i n d i c a t e one s t a n d a r d d e v i a t i o n on e i t h e r s i d e o f t h e m e a n . 3.5 CO X < L U z o CL s o o Q z o o LU CO 7 1 1 1  9 H 1 -3.5 0 FIRST COMPONENT AXIS ro 28 Table 5. Design of the nested ANOVA on component scores from the f i r s t three eigenvectors. Lake Group 1 2 3 Caycuse Beaver Grant Bay 10 Bear Kwassin Gordon Bay Honeymoon Bay Mesachie three homogeneous subsets - [3], [2], and [1]. Scores from PCI11 produced s i g n i f i c a n t differences both between and within lake groups (p = 0.000) and two subsets were indicated - [3,1] and [2]. Discussion Here I have attempted to address two issues: (a) the multivariate response of Gasterosteus populations to some organizing forces, and (b) the characterization of these forces as l o c a l selective e f f e c t s . There i s c l e a r l y a multivariate, s i t e - s p e c i f i c , morphological d i f f e r e n t i a t i o n within the Cowichan drainage system and the d i s t r i b u t i o n of these morphologies is congruent with lake differences. Given t h i s r e s u l t , to what subset of lake differences are the phenomes responding? A l l the variables scored, except l a t e r a l plates, are associated with teleost trophic ecology. Consequently the 'latent factor variables' (Morrison 1967), described by the three axes must be multivariate summaries of trophic morphology. Hence, the observed population divergence indicated by these summaries i s the phenotypic response of each population to some inherent 29 ( s i t e - s p e c i f i c ) stimulus. G i l l raker architecture has been implicated in planktivory in a variety of teleosts (Kliewer 1970; Magnuson and Heitz 1971; Wright, et a l . 1983); populations inhabiting pelagic regions are found to possess long and numerous rakers, while populations in habitats dominated by benthic production are characterized by shorter and fewer rakers. This pattern has been noted for Gasterosteus both in North America (Hagen and Gilbertson 1972) and Europe (Gross and Anderson 1984). In the Cowichan system g i l l raker architecture and head morphology are associated with s i t e type and I suggest that the observed differences, although small compared to intrapopulation variance, are a response to trophic differences between s i t e s . Both Cowichan and Mesachie lakes are dominated by l e n t i c environments with comparatively l i t t l e l i t t o r a l development. Gasterosteus in these lakes are open water pelagic foragers, rarely found close to shore except during the breeding season. The diet of these animals i s dominated by copepods and cladocerans (Carl 1953). In contrast Grant and Kwassin lakes are very shallow with no appreciable l e n t i c regions, and these populations feed primarily on macroinvertebrates (Chapter 3). Feeding studies have shown that the jaw morphology of individuals from Grant Lake allows them to ingest s i g n i f i c a n t l y larger prey than those from Cowichan Lake (Chapter 3). The differences in trophic morphology between populations therefore appear to be ecotypic. At t h i s point however, I w i l l forego the use of the term 'ecotype' and instead define three morphotypes: 30 a limnetic, a benthic and an intermediate. The limnetic morph includes a l l samples from Cowichan Lake in addition to the Mesachie Lake population; the benthic morph includes both Grant and Kwassin lakes; while the intermediate morph describes populations from Bear and Beaver lakes. The patterns of character covariance summarized by the PCA are p a r t i c u l a r l y interesting as they give a s t a t i s t i c a l measure of the degree to which the phenotype i s integrated (Sokal 1978). G i l l raker number and g i l l raker length appear to form a character suite independent of head shape described by the f i r s t component. However, to extend evolutionary arguments from patterns of phenotypic covariance, i t i s necessary to have some indication that the pattern has a genetic basis. The v a r i a b i l i t y p r o f i l e s (Fig 3.) in t h i s study suggest that there i s a genetic component to each of the characters scored. It i s unlikel y that the observed concordance of p r o f i l e s between populations would exist without a genetic component, as t h i s would require similar sets of environmental constraints acting simultaneously on a l l populations. Sokal (1978) considers i t u n l i k e l y that one could find f u n c t i o n a l l y independent characters under simultaneous selection across populations, due to the 'cost of selection' argument. Populations are thought to be unable to suffer the genetic load associated with simultaneous selection on a host of g e n e t i c a l l y independent characters (Futuyma 1979). If the genotype in a given population i s integrated by linkage disequilbrium and/or pleiotropy, the number of selective deaths per generation decreases r e l a t i v e to 31 a population containing genotypes controlled by large numbers of independent genes. Pleiotropy and linkage lead to character c o r r e l a t i o n (Falconer 1981), hence we have an i n i t i a l indication that these trophic characters are probably at least in part, genetically correlated. Correlations are treated in greater d e t a i l in Chapter 2. Although plate numbers vary between the lakes, plate phenotype i s an inadequate descriptor of the interpopulation va r i a t i o n within the Cowichan drainage. Within the system, selection on plates appears to be independent of selection on trophic morphology. This suggests two independently evolved character suites. Unfortunately t h i s result may be biased. No predatory f i s h occur in either Grant or Kwassin lakes and.thus the conclusion that plate phenotype evolved independently of the trophic character suite i s dependent on the questionable intermediate morphology of the Beaver and Bear lakes populations. Perhaps plate phenotype i s p l e i o t r o p i c a l l y linked to trophic morphology. Within populations both scute and spine phenotypes appear to d i s t r i b u t e themselves d i f f e r e n t i a l l y among s i t e s within populations (Moodie 1972; Larson 1976; Reimchen 1980a). These d i s t r i b u t i o n s may indicate selection for s p e c i a l i s t phenotypes each adapted to a r e s t r i c t e d segment of the t o t a l lake habitat ( i . e . 'Niche va r i a t i o n hypothesis', Van Valen 1965). This may be the mechanism preserving r e l a t i v e l y high intrapopulation variation in Gasterosteus (Reimchen 1980b). At a l l s i t e s , with the exception of Grant and Kwassin, l a t e r a l plate number shows a strong mode at seven. This 32 arrangement i s associated with the presence of piscivorous f i s h (Hagen and Gilbertson 1973), and plate phenotype has a modest h e r i t a b i l i t y (Hagen 1973). The low plate numbers in Grant and Kwassin lakes are associated with the absence of predatory f i s h species; however, both lakes contain high densities of invertebrate predators (Lethocerus americanus, Dytiscus sp., Aeshna sp. and L i b e l l u l a sp.) and I have observed invertebrate attacks on Gasterosteus in both lakes. Recently, Reimchen (1980b) has suggested that reduced body armature may be a response to invertebrate predation. Very l i t t l e of the less obvious morphological v a r i a t i o n has been investigated in Gasterosteus, and evolutionary narratives for t h i s species usually extend from more d i s t i n c t differences. The biology of Gasterosteus, however, is such that inferences based on plate phenotypes and plate frequencies may confuse the effects of selection, hybridization and history on v a r i a t i o n . The concordance of morphology and habitat described above, suggests that interpopulation d i f f e r e n t i a t i o n in t h i s system i s a response to d i f f e r e n t selective regimes. Two predictions originate from th i s hypothesis. 1. The characters measured must have a genetic component i f they are to evolve in response to s e l e c t i o n . 2. If a given trophic character(s) has been organized by selection between populations, one should be able to demonstrate the functional significance of that character by contrasting i t s performance in d i f f e r e n t environments. Both of these predictions are tested in the following 33 chapters . 34 CHAPTER 2 Introduction Recent c r i t i c i s m s of the i n a b i l i t y of evolutionary studies to c l e a r l y define the target features of natural selection (Lewontin 1978; Gould and Lewontin 1979), has led to a reexamination of organismal design. Studies that atomize the phenotype into smaller and smaller subunits may obscure the processes of selection active at the interface of phenotype and environment (Bock 1980; Mayr 1984). Hence, some degree of 'holism' i s demanded i f one i s to properly define processes of morphological evolution. Methodologies for such an approach have only recently been described and are based on the recognition of organisms as integrated functional units which evolve (Gould and Lewontin 1979). Consequently a l l phenotypic characters (despite the organizational l e v e l at which they are defined) necessarily evolve only within the context of the organism (Cheverud 1982). The implications of phenotypic integration are not newly recognized, Darwin f i r s t suspected t h e i r existence in 1859, "...the whole organism i s so t i e d together... that when s l i g h t variations in one part occur, and are accumulated through natural selection, other parts become modified. This is a very important subject, most imperfectly understood." pl82. Morphological integration i s thought to ari s e primarily through the e f f e c t s of pleiotropy and linkage (Falconer 1981), which y i e l d character c o r r e l a t i o n s . In most studies, workers have 35 sought to ide n t i f y patterns of character correlations in polygenic characters, for which pleiotropy may be most important. Working with polygenic characters has two advantages: most e v o l u t i o n a r i l y important characters are thought to be polygenic (Leworitin 1974); the genetics of polygenetic systems has been extensively treated in the l i t e r a t u r e , and is based largely on parametric s t a t i s t i c s . This s t a t i s t i c a l background has become the foundation for testing hypotheses concerned with character integration. Indeed, Cheverud (1982) feels strongly that the 'degree of integration' may be measured by the s t a t i s t i c a l association of the phenotype, and several workers (Leamy 1977; Atchley and Rutledge 1980; Atchley 1981; Cheverud 1981, 1982; Leamy and Atchley 1984) have concentrated e f f o r t s on describing these associations. In t h i s chapter I present the results of a laboratory breeding program which was designed to address three questions: 1. How much genetic v a r i a t i o n is present within each morphotype; 2. How are the characters organized to respond to selective constraints; and, 3. How have characters responded to selection during the course of the population's evolution? 36 Materials and Methods Establishment and Fostering of Progeny L o g i s t i c s prevented ra i s i n g progeny from a l l f i v e lakes, I therefore chose to l i m i t the breeding study to three populations; one from each of the proposed morphotypes. The limnetic representative was from the north end of Cowichan Lake (Caycuse), the benthic form was from one of the small bog lakes (Grant), and the intermediate form was taken from the small bay off the main body of Cowichan (Bear Lake). Mature adults were coll e c t e d from three s i t e s in June and July (1984) using minnow traps and pole-sienes. Adults were chosen without bias from the f i s h collected at each s i t e , but some e f f o r t was made to choose individuals which represented the observed range of standard lengths in the breeding population. F e r t i l i z a t i o n of eggs was done on si t e following the methodology outlined by B e l l (1984), but using dechlorinated water transported from the laboratory, rather than lake water. This precaution was taken in order to reduce possible e f f e c t s of lake water on development, p a r t i c u l a r l y those e f f e c t s r e s u l t i n g from differences in temperature and/or the possible introduction of fungus. I attempted to make a minimum of 12 crosses from each population; 14 families were obtained from Grant Lake, 12 families from Bear Lake and 12 families from Caycuse. Although laboratory mortality was generally low, fungus k i l l e d 2 families from Caycuse leaving only 10. The paucity of breeding adults at this s i t e precluded the replacement of these two fam i l i e s . 37 F e r t i l i z e d eggs and parents were returned to the laboratory. Egg batches were incubated in a water bath at 17.5°C u n t i l hatch (approximately seven days after f e r t i l i z a t i o n ) . Newly hatched fry were l e f t in the incubator for three days following hatch, and then moved into the l i g h t for swimup. After swimup, individual families were placed in 20 l i t r e aquaria. Illumination was by fluorescent l i g h t s mounted eight inches above the tanks. A constant light-dark cycle (16 hours l i g h t : 8 hours dark) was maintained for the entire l i f e t i m e of the progeny. Fry were fed an infusoria culture for approximately one week, or u n t i l the fry could ingest Artemia n a u p l i i . Once the fry attained approximately 20 millimetres standard length, their diet was switched to a mixture of Tubifex, chopped l i v e r , and frozen Artemia. Large families ( > 40 individuals) were s p l i t into subfamilies by removing f i s h at random and placing them in other tanks. This subdivision provided the advantage of reducing the . e f f e c t s of common environment on the estimate of h e r i t a b i l i t y (Falconer 1981). A l l families were maintained u n t i l February (1985) and then s a c r i f i c e d and preserved. Progeny and parents were scored for the same set of characters as those given in Chapter 1. Standard lengths of progeny varied widely, within and between populations, hence a l l measures were again adjusted to 40 millimetres. A l l adjusted data were log (base e) transformed before proceeding with any analysis. 38 Estimation of Character H e r i t a b i l i t i e s and Correlations The h e r i t a b i l i t y of any polygenic character i s defined as the r a t i o of additive genetic variance (Va) to the character's phenotypic variance (Vp). H e r i t a b i l i t y in the 'narrow sense' i s given as Va/Vp and may be estimated by a variety of experimental designs (Falconer 1981). I n i t i a l l y I had hoped to determine a narrow sense h e r i t a b i l i t y for each character using midparent- off s p r i n g regression (Falconer 1981). Unfortunately the int r a c l a s s c o r r e l a t i o n c o e f f i c i e n t (described below) was found to be low for most characters and as a consequence 10-14 families were not enough to obtain a reasonable estimate of Va by regression. H e r i t a b i l i t y was therefore estimated from ANOVA using the progeny of the single pair matings (Becker 1975). Table 6 outlines the design of the analysis and the expected mean squares. Table 6 Design of f u l l s i b ANOVA for the estimation of Vg. Source of Variation Expected Mean Square Among Families c52w + No(ct2a) Within Families(error: among individuals) * No i s the weighted average family s i z e . In t h i s design H 2 i s estimated from the in t r a c l a s s c o r r e l a t i o n c o e f f i c i e n t (t) where: t = S 2 / S 2 + S2w, and S 2 estimates a 2a while S2w estimates a2w. In thi s instance H 2 i s given as : H 2 < 2t (Falconer 1981). The inequality results from 39 the estimate of a 2 a . S 2a estimates 1/2 the additive genetic variance but also 1/4 of the dominance variance (Becker 1975). The measure of h e r i t a b i l i t y i s therefore defined as 'broad sense' and given as Vg/Vp, where Vg = l/2(Va) + l/4(Vd) + V i . Vi is a measure of a l l variance a r i s i n g from non-additive effects (Hartl 1979). As a consequence of t h i s estimate, H 2 (obtained) sets only an upper l i m i t to H 2 (population) . If the. dominance deviations are zero then the estimate approximates the measure of narrow-sense h e r i t a b i l i t y , except for the additional interactions. Nevertheless, the broad sense estimate of H 2 provides the basis for , the construction of evolutionary inference. The estimation of additive genetic covariance between characters proceeds in the same manner as the estimation of genetic variance, but in this instance the sums of cross- products are partitioned rather than the sums of squares. Becker's computational formulae (1975) were used for pa r t i t i o n i n g the sums of cross-products. Three correlations were estimated for each character pair (x,y), within each population: 1. Genetic: r(G) = 2cov(a) (2a 2a(x) * 2 a 2 a ( y ) ) ' 5 , 2. Phenotypic : r(P) = cov(w) + cov(a) R a M x ) + rj 2a(x)) * (o 2w(y) + a 2 a ( y ) ) ] ' 5 , 3. Environmental: r(E) = cov(w) - cov(a) [(a 2w(x) - a 2a(x)) * U 2w(y) + a 2 a ( y ) ) ] - 5 , where cov(a) estimates the covariance between characters among families and cov(w) estimates the covariance between characters within f a m i l i e s . The variance terms are the same as those 40 estimated in the previous ANOVA. Again, as in the estimation of H 2, the numerator in these equations contains dominance and epi s t a t i c e f f e c t s , in addition to additive e f f e c t s . Interpreting patterns of single correlations between pairs of characters i s hindered by two factors. The f i r s t i s that single genetic correlations w i l l vary due to differences in gene frequencies, selective regimes and evolutionary history (Atchley et a l . 1981). The second d i f f i c u l t y results simply from the i n a b i l i t y to define and describe patterns a r i s i n g from multiple effects (in thi s case 28 genetic correlations, within each population); hence i t i s preferable to apply some kind of summary technique (Oxnard 1978).' Boag (1983) has extracted p r i n c i p a l components d i r e c t l y from the c o r r e l a t i o n matrix, however t h i s method i s not favoured as genetic c o r r e l a t i o n matrices are often i l l s u i t e d for PCA (Leamy 1977 ; Boag 1983). In contrast to PCA, c l u s t e r analysis may be used with many kinds of s i m i l a r i t y matrices, including genetic c o r r e l a t i o n s , and i s less r i g i d in i t s assumptions concerning the nature of the input matrix. Cluster analysis was therefore used to summarize patterns of genetic correlations using 'complete linkage' as the clu s t e r i n g algorithm (Everitt 1977). Boag (1983) has used 'average linkage' to cluster correlation data, but both average linkage and single linkage gave results very similar to those of complete linkage using my data. The s t a t i s t i c a l package 'S' (Becker and Chambers 1984) was used to compute the character linkages. 41 Reconstructing the Pattern of Trophic Divergence In the past the process of reconstructing h i s t o r i c a l patterns of morphological divergence has been complicated by the observation that continuously varying t r a i t s tend to covary; consequently, i t i s d i f f i c u l t to ide n t i f y those characters which might be considered the targets of natural selection (Arnold 1983). If the targets of selection can not be elucidated, then the processes of morphological evolution necessarily remain obscure (Gould and Lewontin 1979 ; Bock 1980). Recently Russell Lande (1979) has provided a multivariate solution for describing the evolution of correlated characters. He.defines a selection gradient for the evolution of mean phenotype as: /3 = G" 1[z(0) - z ( t ) ] , where G"1 i s the inverse of the symmetric matrix of character variances and covariances; z(0) and z(t) are vectors of character means for the population at times '0' and ' t ' . If the structure of the character complex, as described by 'G', i s constant over evolution, then the net selection gradient i s the sum of /3 = G~ 'Az over the generations '0' to 't - 1'. This measure of selection i s independent of the path taken between z(0) and z(t) and i s therefore robust to changes in the rate and dir e c t i o n of evolution (Lande 1979). Given the assumption of the constancy of 'G', we may calculate selection gradients between populations (or species). In thi s instance vectors of character means for population's 'a' and 'b' are substituted for z(0) and z ( t ) . If the individual vectors z(a) and z(b) are transformed such that: 42 z* = G"1 then, 0 = z*(a) - z*(b) (Schluter 1984). The elements /3i of the selection gradient are the net forces of natural selection which have acted on each character independent of the correlated responses to selection on the other characters measured. Recently Schluter (1984) has defined the length of the vector 0 as the Euclidean distance B = [Z(z'i(a) - z ' i ( b ) ) 2 ] . B then, i s the net force of d i r e c t i o n a l selection which would be required to s h i f t mean morphology from z(a) to z(b). If 'G' is known, selection gradients between pairs of populations may be calculated under the assumptions that 'G' has been determined without error, and that i t has remained constant through time (Price et a l . 1984). Given the preceding assumptions, I have calculated net selection gradients for population t r a n s i t i o n s from the pooled within populations matrix of genetic variances and covariances (Schluter 1984). Results H e r i t a b i l i t y and Genetic Correlations The means and standard deviations of both the adjusted progeny values and the wild population values are given in Table 7. For the progeny data, there are four more s i g n i f i c a n t (p < 0.05) character contrasts between populations than for the wild data. This suggests that selection and/or environment may be masking some interpopulation differences in gene frequencies. 43 Table 7. D e s c r i p t i v e s t a t i s t i c s for w i l d c o l l e c t i o n s and l a b o r a t o r y reared progeny. i i T a b l e 7. Means and s t a n d a r d d e v i a t i o n s of a d j u s t e d d a t a f o r e a c h c h a r a c t e r and p o p u l a t i o n . * I . W i l d P o p u l a t i o n s P o p u l a t i o n C h a r a c t e r B e a r L a k e ( a ) N = 30 C a y c u s e ( b ) N = 30 G r a n t L a k e ( c ) N = 30 HEAL SNOL EYED UPJL GRL GRN HEAD I NOW (ac)b# (abc) a be ( a b ) c (ab) c (ac) b ( a b ) c ( a b ) c 2.52(0.092) 1 .29(0.065) 1 .34(0.058) 1.11 (0.065) -0.23(0.131) 17.86(1.130) 0.86(0.071) 2.88(0.063) 2.46(0.036) 1 .29(0.068) 1.37(0.042) 1.07(0.071 ) -0.16(0.126) 19.17(1.080) 0.86(0.067) 2.98(0.055) 2.53(0.053) 1 .28(0.090) 1.40(0.043) 1.22(0.066) -0.37(0.167) 17.46(0.860) 0.79(0.076) 2.86(0.049) I I . L a b o r a t o r y P r o g e n y P o p u l a t i o n C h a r a c t e r B e a r L a k e ( a ) N = 357 C a y c u s e ( b ) N = 179 G r a n t L a k e ( c ) N = 292 HEAL abc SNOL abc EYED (ab)c UPJL ( a b ) c GRL (ac)b GRN abc HEAD abc INOW abc 2.54(0.038) 1.45(0.061 ) 1.39(0.053) 1.13(0.072) -0.06(0.115) 19.25(1.070) 0.89(0.068) 2.96(0.055) 2.56(0.034) 1.49(0.067) 1 .39(0.063) 1.13(0.083) -0.01(0.120) 20.34(1.370) 0.95(0.060) 3.01(0.077) 2.56(0.049) 1.42(0.062) 1.41(0.052) 1.17(0.079) -0.07(0.104) 18.14(1.170) 0.93(0.061) 2.89(0.065) * A l l d a t a l o g ( b a s e e) t r a n s f o r m e d . # L e t t e r s i n b r a c k e t s i n d i c a t e no d i f f e r e n c e s between a d j u s t e d means. 45 T h r e e p o i n t s c a n be e m p h a s i z e d i n t h e c o m p a r i s o n o f t h e two s e t s of d a t a , t h a t a r e of i n t e r e s t t o l a t e r d i s c u s s i o n : SNOL i s now s i g n i f i c a n t l y d i f f e r e n t between a l l p o p u l a t i o n s ; UPJL i s s i g n i f i c a n t l y g r e a t e r i n t h e G r a n t L a k e p o p u l a t i o n , but does not d i f f e r s i g n i f i c a n t l y between e i t h e r B e a r Lake o r C a y c u s e ; C a y c u s e has s i g n i f i c a n t l y l o n g e r r a k e r s t h a n e i t h e r Bear or G r a n t l a k e s . The r e s u l t s of t h e h e r i t a b i l i t y a n a l y s i s a r e g i v e n i n T a b l e 8. A l l c h a r a c t e r s , i n a l l p o p u l a t i o n s , had s i g n i f i c a n t h e r i t a b i l i t i e s (p < 0.05) a l t h o u g h t h e a v e r a g e h e r i t a b i l i t y f o r e a c h p o p u l a t i o n was low, s u g g e s t i n g t h e r e i s o n l y a moderate amount o f a d d i t i v e g e n e t i c v a r i a n c e w i t h i n e a c h p o p u l a t i o n . The e s t i m a t e of H 2 f o r GRN i s l o w e r t h a n t h a t r e p o r t e d e l s e w h e r e ( h 2 = 0.58, 21 ° C , Hagen 1973). C o m p a r i s o n s of H 2 v a l u e s a c r o s s p o p u l a t i o n s w h i c h have been r e a r e d under d i f f e r e n t c o n d i t i o n s , a r e i n g e n e r a l o f l i t t l e v a l u e , a s h 2 i s s p e c i f i c t o p o p u l a t i o n and e n v i r o n m e n t ( F a l c o n e r 1981). A l l g e n e t i c components a r e i n f l u e n c e d by gene f r e q u e n c i e s and t h e r e f o r e a r e l i k e l y t o v a r y between p o p u l a t i o n s a s a r e s u l t o f s e l e c t i o n and s t o c h a s t i c f o r c e s ( F a l c o n e r 1981). In a d d i t i o n t h e component of e n v i r o n m e n t a l v a r i a n c e depends on t h e c o n d i t i o n s under w h i c h t h e p r o g e n y were r a i s e d (a c o n s t a n t e n v i r o n m e n t t e n d s t o i n c r e a s e h e r i t a b i l i t y ) . I t i s f o r t h i s r e a s o n we seek t o r e d u c e t h e e f f e c t s of common e n v i r o n m e n t i n e s t i m a t i n g H 2 . Pr o g e n y w i t h i n f a m i l i e s r e a r e d t o g e t h e r , under c o n s t a n t e n v i r o n m e n t , t e n d t o be more s i m i l a r t h a n t h o s e r e a r e d a p a r t , w h i c h i n f l a t e s e s t i m a t e s o f S 2 a , and i n t u r n i n f l a t e s t h e v a l u e o f H 2 o b t a i n e d . 46 Table 8. H e r i t a b i l i t i e s for the three representative morphotypes. The standard error of the estimate i s give in brackets. T a b l e 8. H e r i t a b i l i t i e s f o r t h e t h r e e r e p r e s e n t a t i v e m o r p h o t y p e s . E s t i m a t e s a r e b a s e d on f a m i l y s i z e w e i g h t e d i n t r a c l a s s c o r r e l a t i o n s among f u l l s i b s . P o p u l a t i o n C h a r a c t e r Bear L a k e C a y c u s e G r a n t Lake HEAL .2173*** .2155** . 1436** ( .1243) 0.1375) ( . 1197) SNOL .1624*** .2614** . 1676** ( .0896) (.1534) (.1006) EYED .3229*** .2377** .7957*** ( .1381 ) ( . 1460) (.2112) UPJL .1489** .2170** .3822*** ( .0859) (.1393) (.1554) GRL . 1824*** .6777*** .1320* ( .0926) (.2420) (.0898) HEAD .1263** .1922** .2566*** ( .0798) (.1310) (.1254) I NOW .4570*** .4122*** . 4 5 4 4 * * * ( .1705) (.1946) (.1699) GRN .1438** .2210** .3577*** ( .0833) (.1406) (.1500) X .22 .30 .34 N 12,357 10, 176 14,292 N o t e : *** (p < .0001), ** (p < .001), * ( p < .01) 48 Estimates of h e r i t a b i l i t y may change d r a s t i c a l l y across environments even i f the expressed phenotypic variance remains constant (Hartl 1979). Hagen (1973) found the h e r i t a b i l i t y of l a t e r a l plates in the threespine stickleback to decrease from 0.83 to 0.5 with an increase of 4°C. Obviously then, h e r i t a b i l i t i e s depend strongly on population and circumstance. Nevertheless, the results presented here indicate that a s i g n i f i c a n t proportion of the phenotypic variance expressed within populations, arises as a result of variance among genotypes. Tables 9, 10 and 11 give the genetic, phenotypic and environmental correlations between characters for each population. Many of the genetic correlations within populations are reasonably strong (0.3 ̂  |rG| ̂  0.9), however the average correlation i s much lower as a result of the reduced covariance term for GRN with other characters. In a l l instances the genetic correlations are greater than the environmental co r r e l a t i o n s , suggesting the l a t t e r are largely residual (Leamy 1977). If the genetic correlations are moderate to high, and the phenotypic correlations are moderate, r(G) may be considered to contribute more to r(P) than does r(E) (Pirchner 1969). This conclusion i s supported by the Spearman rank-order c o r r e l a t i o n c o e f f i c i e n t s (Table 12) between elements of the three matrices. In the case of both Caycuse and Grant Lake, the rank-order correlations between r(G) and r(P) exceed those for r(E) , and r(P). The exception i s found for Spearman c o e f f i c i e n t s within Bear Lake, in which the co r r e l a t i o n between elements of r(P) and 49 T a b l e 9. G e n e t i c , p h e n o t y p i c a n d e n v i r o n m e n t a l c o r r e l a t i o n m a t r i c e s f o r B e a r L a k e . I = G e n e t i c c o r r e l a t i o n m a t r i x , I I = P h e n o t y p i c ( a b o v e t h e d i a g o n a l ) a n d e n v i r o n m e n t a l ( b e l o w t h e d i a g o n a l ) c o r r e l a t i o n m a t r i c e s . A l l v a r i a n c e s and c o v a r i a n c e s were c a l c u l a t e d f r o m l o g ( b a s e e) t r a n s f o r m e d d a t a . T a b l e 9 . G e n e t i c , p h e n o t y p i c a n d e n v i r o n m e n t a l c o r r e l a t i o n m a t r i c e s f o r B e a r L a k e . D i a g o n a l o f r G m a t r i x c o n t a i n s g e n e t i c v a r i a n c e ( * E - 3 ) f o r e a c h c h a r a c t e r . H E A L SNOL EYED U P J L GRL HEAD INOW GRN ( I ) H E A L . 3 3 0 6 SNOL . 9 1 5 . 6 0 3 6 EYED . 2 2 7 . 3 0 3 6 . 9 1 7 0 U P J L • - . 2 3 5 . 159 . 7 6 4 6 . 7 7 5 4 GRL • - . 1426 . 6 1 7 0 - . 4 3 0 4 . 3 5 9 E - 1 2 . 4 1 8 HEAD • - . 0 9 0 7 . 3 1 5 1 . 2 7 2 6 . 6 0 4 6 - . 3 2 6 4 . 4 3 4 6 INOW • - . 1 1 1 5 . 2 5 5 8 . 5 5 3 5 . 7 4 9 0 - . 4 2 8 2 . 8 7 5 3 2 . 122 GRN . 3 9 6 3 E - 3 . 8 5 5 E - 2 -- . 1 2 9 E - 1 . 1 2 0 E - 1 . 1 8 5 E - 1 - . 4 7 2 E - 1 - . 2 3 E - 1 166 . . 4 6 ( I D H E A L . 6 3 5 0 . 2 5 3 6 . 4 6 5 8 . 1684 . 2 1 7 1 . 6 2 3 E - 2 - . . 2 0 SNOL . 5 9 8 . 1 3 9 1 . 3 0 3 5 . 2 2 9 4 . 2 3 9 6 . 3 3 0 0 , 4 4 E - 2 EYED . 2 6 5 8 . 0 9 2 3 . 4 2 8 7 . 1223 . 281 1 . 2 8 1 6 4 2 E - 2 U P J L . 6 2 2 . 3 8 8 8 . 3 4 3 8 . 4 0 1 5 . 4 5 5 6 . 3 4 9 3 , 2 6 E - 2 GRL . 2 4 5 8 . 4 0 5 4 . 1644 . 4 7 5 4 . 2 8 1 5 . 0 6 8 7 , 2 3 E - 2 HEAD . 2 8 0 7 . 2 2 7 4 . 2 9 3 9 - . 4 3 2 1 . 3 9 1 7 . 3 1 4 8 4 5 E - 2 INOW -- . 0 4 4 0 . 3 8 5 6 . 1 192 . 2 2 6 6 . 2 8 7 7 . 1 5 2 1 2 6 E - 2 GRN -- . 0 0 5 9 . 0 0 3 7 . 0 5 8 3 -- . 0 0 5 1 - . 0 0 6 3 - . 0 0 2 1 . 0 0 4 9 51 T a b l e 10. G e n e t i c , p h e n o t y p i c and e n v i r o n m e n t a l c o r r e l a t i o n m a t r i c e s f o r C a y c u s e . I = G e n e t i c c o r r e l a t i o n m a t r i x , I I = P h e n o t y p i c (above t h e d i a g o n a l ) and e n v i r o n m e n t a l (below t h e d i a g o n a l ) c o r r e l a t i o n m a t r i c e s . A l l v a r i a n c e s and c o v a r i a n c e s were c a l c u l a t e d f r o m l o g ( b a s e e) t r a n s f o r m e d d a t a . T a b l e 1 0 . G e n e t i c , p h e n o t y p i c a n d e n v i r o n m e n t a l c o r r e l a t i o n s f o r C a y c u s e . D i a g o n a l o f r G c o n t a i n s t h e g e n e t i c v a r i a n c e ( * E - 3 ) f o r e a c h c h a r a c t e r . H E A L SNOL EYED U P J L GRL HEAD INOW GRN ( I ) H E A L . 2 8 3 4 SNOL . 7 8 9 9 1 . 2 8 6 0 EYED . 4 8 2 3 . 4 8 1 1 . 9 8 7 0 U P J L . 7 2 4 3 . 3 7 2 4 . 1256 1 . 5 2 8 0 GRL -• . 3 0 7 0 - . 1 9 1 2 . 6 4 9 9 - . 5 1 5 8 9 . 6 4 2 0 HEAD . 7 3 9 6 . 9 8 4 9 1 . 0 3 5 7 . 0 7 6 9 . 9 7 6 1 . 4 6 9 6 INOW . 5 2 5 8 - . 3 4 5 5 - . 2 7 3 2 . 2 9 8 3 - . 3 6 4 9 - . 0 4 1 7 1 . 6 9 4 0 GRN . 0 4 5 5 . 0 5 6 9 . 0 2 4 6 . 0 2 2 8 - . 0 1 0 7 - . 0 1 8 1 - . 0 0 9 5 4 3 0 . 6 ( I D H E A L . 6 3 5 0 . 2 5 3 6 . 4 6 5 8 . 1684 . 2 1 7 1 . 6 2 E - 2 - . 4 8 E - 2 SNOL . 5 9 8 0 . 1 3 9 1 . 3 0 3 5 . 2 2 9 4 . 2 3 9 6 . 3 3 0 0 - . 4 4 E - 2 EYED . 2 6 5 8 . 0 9 2 3 . 4 2 8 7 . 1223 . 28 1 1 . 2 8 1 6 . 0 4 16 U P J L . 6 2 2 0 . 3 8 8 8 . 3 4 3 8 . 4 0 1 5 . 4 5 5 6 . 3 4 9 3 - . 2 6 E - 2 GRL . 2 4 5 8 . 4 0 5 4 . 1644 . 4 7 5 4 . 2 8 1 5 . 0 6 8 7 - . 2 3 E - 2 HEAD . 2 8 0 7 . 2 2 7 4 . 2 9 3 9 . 4 3 2 1 . 3 9 1 7 . 3 1 4 8 - . 4 5 E - 2 I NOW - . 0 4 4 0 . 3 8 5 6 . 1 192 . 2 2 6 6 . 2 8 7 7 . 1521 - . 2 6 E - 2 GRN - . 0 0 5 9 - . 0 0 3 6 . 0 5 8 3 - . 0 0 5 1 - . 0 0 6 3 . 0 0 2 1 . 0 0 4 9 53 T a b l e 1 1 . G e n e t i c , p h e n o t y p i c and e n v i r o n m e n t a l c o r r e l a t i o n m a t r i c e s f o r G r a n t L a k e . I = G e n e t i c c o r r e l a t i o n m a t r i x , I I = P h e n o t y p i c (above t h e d i a g o n a l ) and e n v i r o n m e n t a l (below t h e d i a g o n a l ) c o r r e l a t i o n m a t r i c e s . A l l v a r i a n c e s and c o v a r i a n c e s were c a l c u l a t e d f r o m l o g ( b a s e e) t r a n s f o r m e d d a t a . T a b l e 11. G e n e t i c , p h e n o t y p i c , and env i ronmenta l c o r r e l a t i o n s f o r G ran t Lake . The d i g o n a l of rG c o n t a i n s g e n e t i c v a r i a n c e s f o r each c h a r a c t e r . HEAL SNOL EYED UPJL GRL HEAD INOW GRN ( I ) HEAL . 3942 SNOL .8137 . 6534 EYED .6965 . 2621 2 . 208 UPJL . 8409 . 4626 . 8446 2.474 GRL .2106 - . 2 101 - . 1 0 0 7 - .3129 1 .425 HEAD . 2323 . 3049 . 4836 .3907 - .8535 1 .695 INOW - . 0 3 4 3 - . 0 8 6 7 8 .6279 .5797 - .6632 . 7499 1 . 735 GRN, .0283 .022 1 .01326 .0278 .0325 - .0252 -.0111 500.4 ( I I ) HEAL . 5 153 . 3535 .4748 . 3590 . 2566 . 1620 .41E-2 SNOL .4576 . 2421 .4915 . 3995 .2245 . 1908 - . 4 1 E - 2 EYED . 2794 . 3552 . 5352 . 2073 . 2495 . 3595 - .47E-2 UPJL . 3806 . 5221 . 1952 .3867 . 2344 .3148 - . 2 9 E - 2 GRL . 3829 . 5068 . 5699 .6241 .0702 -.0081 - . 8 2 E - 2 HEAD . 2657 . 1934 .0797 . 1654 . 2830 .2308 - . 6 7 E - 2 INOW . 2475 . 2476 - . 0 5 4 7 . 1262 . 2247 - .0398 - . 4 1E-2 GRN - .0031 - . 0 1 3 0 - . 0255 - . 0210 - .0205 .0014 .0008 55 r(E) exceeds that for r(P) and r(G). The l a t t e r result may be a consequence of Bear Lake having the lowest estimates of H 2 . If the phenotypic correlation i s expressed as: r(P) = r(G) * H 2 x * H 2 y + r(E) * [(1 - H 2 X ) ( 1 - H 2 y ) ] ' 5 (Pirchner 1969), where H 2 x and H 2 y are the h e r i t a b i l i t i e s of characters 'x' and 'y' respectively, the compound nature of r(P) becomes evident. In addition i t i s apparent that r(P) also Table 12. Spearman rank correlations between the elements of the genetic, environmental and phenotypic correlation matrices. Bear Lake r(G) r(E) r(P) r(G) 1 .0 0.0071 0.4347 r(E) 1 .0 0.8236 r(P) 1.0 x 0 .3048 0.2331 0.2156 Caycuse r(G) r(E) r(P) 1 .0 -0.2184 0.6021 1 .0 0.5362 1 .0 x 0 .3749 0.2191 0.1777 Grant r(G) r(E) r(P) 1 .0 -0.1598 0.5742 1 .0 0.5529 1 .0 x 0 .3544 0.2245 0.2249 depends on the h e r i t a b i l i t i e s of the two characters. When the h e r i t a b i l i t i e s are small, the environmental component contributes more to r(P), but i f the estimates of H 2x and H 2y are imprecise, the r e l a t i v e contributions of r(G) and r(E) remain questionable. This result however does not appear to have effected the overall structure of the c o r r e l a t i o n matrices 56 described below, and I have proceeded under the assumption that r(G) contributes s i g n i f i c a n t l y to r(P) within Bear Lake. Figure 6 shows the three dendrogram summaries of character cl u s t e r i n g implied by r(G) for each population. Patterns of character c l u s t e r s are very similar for Grant and Bear lakes. At the l e v e l of about r(G) = 0.2, two d i s t i n c t clusters are evident. The f i r s t contains two characters, GRN and GRL, and hence groups the two features of g i l l r a k e r structure which have been implicated in planktivory (e.g. Kliewer 1970; Lindsey 1981). The second grouping contains the remaining six characters and might be interpreted as a head shape c l u s t e r . Interestingly, the character structure of the two groups defined here, i s the same as that given by the f i r s t two p r i n c i p a l components derived from the wild population data (Chapter 1). This supports the conclusion that phenotypic covariance results largely from genotypic covariance. The character c l u s t e r s derived from r(G) for the Caycuse progeny are quite d i f f e r e n t than those described for Grant and Bear lakes. The only s i m i l a r i t y to the previous c l u s t e r s i s that the most distant grouping of GRL has been preserved, suggesting i t i s indeed a d i s t i n c t l y organized character ( i . e . i s not strongly integrated by pleiotropy, with the other characters measured). GRL has been separated from GRN in the present dendrogram, a result which appears i n t u i t i v e l y anamolous. GRN and GRL are both characters associated with a planktivorous existence and one might well expect them to form an integrated character. It is possible that the structure of 57 Figure 6. Dendrogram summary of character genetic c o r r e l a t i o n matrices . (A = Bear Lake, B = Caycuse, C = Grant Lake) 58 (A) -.2 .2 .6 1.0 i 1 1 1 1 1 1 8 5 3 fl 4 I 6 I z 1 2 (B) -.2 1.0 _4 J. _§ _2 _a 6 (C) -.2 1 2 3 4 5 6 7 HEAL SNOL E Y E D U P J L GRL HEAD INOW 8 GRN 1.0 — i 8 5 6 2 _1 _3 4 59 the dendrogram derived from the Caycuse cor r e l a t i o n matrix, results from low genetic variances and imprecise estimates of r(G). Bear Lake however, has lower average additive variances for each character than does Caycuse, yet the structure of r(G) for the former population is nearly i d e n t i c a l to that of the geographically disparate population - Grant Lake. It seems unlikely that the l a t t e r result could ar i s e by chance considering the number of correlations involved. If the structure of r(G) for Caycuse is r e a l , i t may indicate that the genome in t h i s population has been in part reorganized. Selection Gradients Selection gradients for tran s i t i o n s between population morphologies are given in Table 1 3 . The individual elements 0i of each gradient are dimensionless therefore only the r e l a t i v e magnitudes of each /3i are of inte r e s t . In the c a l c u l a t i o n of each gradient, z* for the second population was subtracted from z* for the f i r s t population, as a consequence, the sign of each /3i i s a result of the magnitude of the second term and not an indication of divergence on that character. The /3i's for each character averaged across a l l three populations indicate that the strongest d i r e c t i o n a l s e l e c t i o n has operated on HEAL and SNOL, followed by GRN. Average selection i n t e n s i t i e s for HEAD and UPJL are si m i l a r . Relative to these f i r s t f i v e characters, much weaker net forces of selection have acted on INOW, EYED and GRL. Net s e l e c t i o n distance, B, suggests that the Limnetic-Benthic and 60 Table 13. Selection gradients for the three representative morphotypes based on the pooled-within variance-covariance matrix. Population Transitions Bear/Caycuse Bear/Grant Caycuse/Grant HEAL 2174.64 -219.67 -2394.30 SNOL -1494.97 188.09 1682.07 EYED - 190.66 - 15.64 175.02 UPJL - 771.12 64.02 835.15 GRL 18.50 42.67 61.18 HEAD 902.33 - 76.24 - 978.50 INOW 367.93 - 7.28 - 375.22 GRN 1015.56 -141 .03 -1156.59 B 3093.90 259.40 3424.80 Intermediate-Limnetic populations are separated by the greatest selection distance, while the Intermediate-Benthic populations are separated by the shortest selection distance. Discussion The r e l a t i v e l y low h e r i t a b i l i t i e s observed for the characters scored, suggests there i s l i t t l e additive variance with which e c o l o g i c a l l y s i g n i f i c a n t characters may respond to sel e c t i o n . This paradox i s not uncommon in evolutionary ecology, and has in the past led to tenuous inference of adaptive s i g n i f i c a n c e . It is often assumed that characters with low h e r i t a b i l i t i e s , but which are d i r e c t l y related to f i t n e s s , l i e at equilibrium (an adaptive peak), and that their mean fi t n e s s i s no longer increasing (Futuyma 1979). However i t is equally l i k e l y that additive variance was.reduced by a founder event ( i . e . is the h i s t o r i c a l consequence of a population 61 bottleneck). If freshwater populations of Gasterosteus are p o s t - g l a c i a l derivatives of an anadromous marine form, as i s generally assumed (Bell 1976; Wootton 1984), then c e r t a i n l y the potential exists for the reduction of variance due to sampling error. Natural selection in turn i s thought to modify the patterns of extant v a r i a t i o n produced by these invasions (Hagen and McPhail 1970). Recently data from electrophoretic studies of the marine and freshwater forms of Gasterosteus, in B r i t i s h Columbia, have provided empirical support for t h i s model (Withler and McPhail 1984). If these estimates are reasonable r e f l e c t i o n s of Va, then freshwater populations may not be capable of response to a novel sele c t i v e regime should i t a r i s e , however the expressed v a r i a t i o n may not represent the scope of available additive variance. Large amounts of Va may be preserved as 'hidden variance' in negative genetic correlations (Lande 1975). Theoretical models suggest that s t a b i l i z i n g selection w i l l lead to the f i x a t i o n of p o s i t i v e l y correlated t r a i t s , but that under a constant regime of s t a b i l i z i n g s e lection, negative cor r e l a t i o n s w i l l evolve preserving variance (Lewontin 1964). Their e f f e c t s on the phenotype cancel producing small deviations from the mean. Perturbations of these complexes w i l l lead to the expression of that variance (Rose 1982). Thus i t i s possible that the genepools of freshwater Gasterosteus populations have preserved variance in coadapted gene complexes and may s t i l l respond to selection following a founder event. Population founder events (the establishment of daughter 62 populations from founder i n d i v i d u a l s ) , may or may not be followed by incipient i s o l a t i o n (which i s required i f the daughter population i s to emerge as a b i o l o g i c a l species). Not a l l ancestral populations are thought to possess the genomic architecture required for the evolution of i s o l a t i o n . Carson and Templeton (1984) distinguish between speciating and non- speciating lineages derived from ancestral populations. Non- speciating lineages may arise from the dispersal (or subdivision) of species which show a propensity to colonize - so c a l l e d 'weed species'. Such an organism probably possesses a generalist genome (Baker 1965), allowing rapid expansion into novel environments but whose architecture i s resistant to change by founder effects (Carson and Templeton 1984). These non- mutable genomes are thought to belong to highly inbred or haploid species, yet very old species with t i g h t l y coadapted gene complexes may also be non-mutable (Carson and Templeton 1984). Speciating lineages are thought to arise from less t i g h t l y integrated complexes which are broken by a founder event and reorganized under selection, resulting in a s h i f t to a new adaptive peak. Incipient "isolation may result as a consequence of the movement between peaks (Templeton 1981). What type of genetic architecture has f a c i l i t a t e d the evolution of morphological divergence between freshwater stickleback populations? I believe the estimation of the genetic covariance between characters suggests two al t e r n a t i v e s . In reconstructing the pattern of interpopulation morphological divergence, I have assumed constancy of the pooled 63 variance/covariance matrix. If t h i s measure of 'G' has been made without error i t may indicate that Gasterosteus should be viewed as a weed species. The matrix i s characterized by weak correlations between characters, which may f a c i l i t a t e s h i f t s in mean phenotype under antagonistic selection (Lande 1979). This selection operates to change the mean phenotype of two correlated characters against the sign of the c o r r e l a t i o n . By this d e f i n i t i o n then, antagonistic selection includes two subsets of s e l e c t i v e forces: the f i r s t a r i s i n g from selection for d i r e c t i o n a l change in one of two p o s i t i v e l y correlated t r a i t s ; the second a r i s i n g from selection on one of two negatively correlated t r a i t s . Shape change and/or change in other characters associated with s h i f t s in trophic resource use (e.g. GRN) w i l l be promoted by these weaker correl a t i o n s , allowing a more rapid response to a novel s e l e c t i v e regime. Could i t be that the extensive freshwater d i v e r s i t y of Gasterosteus r e s u l t s from a generalist genome, characterized by 'loosely' correlated complexes of coadapted genes? The s i m i l a r i t y in structure of the Bear and Grant Lake dendrograms would seem to support the hypothesis of a generalist genome. These populations appear to be responding to d i f f e r e n t environmental constraints with the same architecture. However their organization contrasts with that of Caycuse which shows a much d i f f e r e n t pattern of character c l u s t e r s . If the Caycuse structure i s r e a l ( i . e . does not a r i s e from error in the measurements of Va) then the Caycuse population must be considered g e n e t i c a l l y d i s t i n c t from Bear Lake (the 64 geographically proximate population) and may be reorganized in comparison to i t and Grant Lake (or conversely, they are reorganized with respect to Caycuse). Reorganization would imply a more t i g h t l y integrated ancestral architecture which was broken during the founder episode, or possibly altered by selecti o n . Unfortunately, we know l i t t l e about the types or intensity of selec t i v e pressures that would be required to a l t e r character c o r r e l a t i o n s . Short term and long term selection experiments have demonstrated considerable constancy of the variance/covariance matrix over time (Cheung and Parker 1974 ; Leamy and Atchley 1984). In the face of the resu l t s , the second strategy (genomic reorganization) seems somewhat unlikely compared to the f i r s t (colonizer genome). If genetic reorganization of the ancestral population has occurred i t i s unlikely that the pattern of character c o r r e l a t i o n s within Grant and Bear lakes would be so si m i l a r . Rather, the results suggest a generalist genome responding to a variety of selective regimes, with weak correlations f a c i l i t a t i n g s h i f t s in trophic phenotype. The significance of these s h i f t s i s examined in the following chapter. 65 CHAPTER 3 Introduction Reproductive i s o l a t i o n a r i s i n g through adaptive divergence of subpopulations, i s s t i l l thought to be a primary mode of speciation (review in Templeton 1981). Those studies which focus on the h i s t o r i c a l patterns of population divergence t y p i c a l l y attempt to correlate morphological or genetic v a r i a b i l i t y with one or more selective constraints (e.g. Mitter and Futuyma 1979; Findley and Black 1983; Felley 1984); that i s , evolutionary h i s t o r i e s are reconstructed primarily from inference (Mayr 1983). Such 1 adaptationist programs' have been c r i t i c i z e d for their i n a b i l i t y to properly define the targets of natural selection (Gould and Lewontin 1979) leading to the erection of erroneous h i s t o r i e s (Chapter 2). However the explanatory power derived from i n f e r e n t i a l studies may be increased both by an investigation of the organism's ecology (Clarke 1978) and some knowledge of a pa r t i c u l a r t r a i t ' s functional significance (Bock 1980). Recently t h i s approach has allowed the direct measurement of natural selection in populations of Darwin's finches (Boag and Grant 1981). This study and others (e.g. Miles and Ric k l e f s 1984; Mittlebach 1984; Schluter and Grant 1984) have concentrated on selection for divergence in trophic morphology (e.g. beak size) and i t s corr e l a t i o n with food type and a v a i l a b i l i t y . In studies of teleost evolution, modifications of trophic morphology are thought to be a common mechanism promoting such 66 evolutionary phenomena as the explosive radiation of the African Great Lakes c i c h l i d s (Greenwood 1984). Almost a l l occurrences of these "species flocks" involve some a l t e r a t i o n of the feeding apparatus (review in Eshelle and Kornfield 1984). Divergence in teleost trophic morphology i s not limited to cases involving multiple radiations. In systems containing only a single species pair, i n t e r s p e c i f i c differences in trophic morphology appear to be correlated with resource p a r t i t i o n i n g (e.g. Lindsey 1981). In the threespine stickleback species complex,, interpopulation morphological v a r i a b i l i t y i s evidenced in many characters (review in B e l l 1984). In Enos Lake on Vancouver Island, b i o l o g i c a l speciation (Mayr 1963) i s associated with extreme divergence in trophic morphology and thi s divergence has resulted in almost complete separation of food type exploited by the two species (Bentzen and McPhail 1984). In thi s chapter I wish to examine the functional significance of divergence in trophic morphology between lake-dwelling populations of Gasterosteus within the Cowichan drainage. Having described the s i t e - s p e c i f i c morphological v a r i a b i l i t y of each population within each lake, and proposed three morphotypes, i t i s my intent to demonstrate that each morphotype i s indeed an ecotype (sensu Turesson 1922). 67 Materials and Methods Trophic Morphology In a l l the feeding experiments described below I have again used animals representing each of the proposed morphotypes. The representative populations chosen were the same as those used in the genetic study ( i . e . the limnetic from Caycuse, the benthic from Grant Lake, and the intermediate from Bear Lake). Hereafter the three populations w i l l be referred to as 'limnetic', 'benthic' and 'intermediate' respectively. Three trophic variables were chosen for studies of functional s i g n i f i c a n c e : upper jaw length - length of the premaxilla (UPJL), g i l l raker number(GRN) and g i l l raker length (GRL). Upper jaw length is thought to be a surrogate measure of mouth gape and hence should be correlated with p a r t i c l e size in gape- limited predators (Aleev 1969). UPJL i s a representative of the head shape cluster defined in Chapter 2, and selection appears to have operated strongly on i t , in t r a n s i t i o n s between population phenotypes. G i l l raker architecture, was the second character cluster defined and l i k e UPJL, GRN appears to have been strongly altered by sele c t i o n . Variation in g i l l r a k e r morphology has been studied extensively and has been shown to be related to planktivory (Magnuson and Heitz 1971; Wright et a l . 1983). G i l l raker spacing i s thought to be the mechanism a f f e c t i n g p a r t i c l e retention in planktivores. For t h i s reason I sought to ident i f y interpopulation differences in spacing; however due to the small size of these animals, d i f f e r e n t i a l 68 spacing i s confounded by measurement error. Consequently g i l l raker density was estimated as a surrogate measure of spacing. G i l l raker number and length were determined for individuals from each " population from rakers on the f i r s t g i l l arch (Hubbs and Lagler 1958). The arch was then excised from the opercular cavity and an enlarged tracing made of the outline using a Wild- M5 dissecting scope and camera lucida. Area occupied by the g i l l rakers was determined by d i g i t i z i n g the tracings. Sheffe's test was used to compare differences in r e l a t i v e area. G i l l raker density was expressed as the number of rakers occupying one square millimeter. The results were then plotted against standard length and analyzed by ANCOVA. Diet of each population was broadly characterized by gut contents of samples taken from each lake in la t e spring. Prey organisms were c l a s s i f i e d as benthic or limnetic following Kliewer (1970) and a chi-square contingency test performed for diet and population. Feeding patterns may change with dispersal to d i f f e r e n t lake areas af t e r breeding but thi s should accentuate dietary differences between the limnetic and benthic morphs. Sticklebacks taken from Cowichan Lake in midwater trawls during winter seem to be e n t i r e l y dependent on plankton (Carl 1953). Gape Experiments The functional r e l a t i o n s h i p between upper jaw length and maximum gape, was determined by presenting brackishwater amphipods (Eogammarus confervicolus) to each of the three 6 9 populations. Several workers have used amphipods in determinations of maximum gape for Gasterosteus (Burko 1973, Larson 1976, Bentzen 1982) thus results from the present experiments are readily comparable to previous studies. Individual f i s h were held in 20 l i t r e aquaria for 3 days prior to each test and fed amphipods. The bottom of each aquarium was painted a uniform brown and aquaria were separated by beige- coloured p a r t i t i o n s . Fish were starved for 24 hours preceding each test in order to standardize hunger. Periods of starvation longer than 24 hours have been shown to influence feeding behaviour in Gasterosteus (Beukema 1968). Amphipods were anaesthetized with carbonated water and measured with an ocular micrometer. Each amphipod was assigned to a size category based on body length. Body length was defined as the distance from the base of the antennae to the base of the uropods with the body flexed (Bentzen 1982). Sixteen size classes were tested ranging from 1.55mm to 13.17mm; size- c l a s s d i v i s i o n s were 0.77mm. Amphipods were allowed to recover f u l l y before introduction to the aquaria. Three amphipods, one from each of three size-classes, were presented to .each f i s h . P i l o t studies revealed an appropriate amphipod size range with which to begin each t r i a l . Fish were allowed one hour in which to ingest the prey; after one hour the amphipods were removed, reaneasthetized and remeasured. Fish were fed to sati a t i o n with chopped l i v e r after each t r i a l . Following a further 24 hour period of starvation, the test was rerun and each size-class presented was increased by one 70 d i v i s i o n . This sequence was continued u n t i l the f i s h could no longer ingest the maximum class presented for three consecutive days. Data were analyzed by ANCOVA. In the i n i t i a l > a n a l y s i s , standard length was treated as the covariate to determine the eff e c t s of re l a t i v e upper jaw length on gape, across populations. This analysis was repeated s u b s t i t u t i n g upper jaw length as the covariate. In thi s instance s i g n i f i c a n t interpopulation differences in mean amphipod siz e attained must indicate the contribution of some effect other than upper jaw length. Amphipod Manipulation Experiments Since wild f i s h had been used in the gape experiment I was interested in examining the contribution of behaviour to differences in foraging success. In thi s series of experiments amphipods from a single s i z e - c l a s s were presented to individual f i s h in a 218 l i t r e aquarium for twenty minutes while the observer scored behaviour through a hole in a black p a r t i t i o n . The prey size-class chosen was 4.65mm. This s i z e - c l a s s had been ingested by f i s h as small as 30mm from a l l populations. Fifteen prey were presented to each f i s h , as some in d i v i d u a l s had been observed to take as many as ten prey items during a twenty minute feeding bout. Fish were held i n d i v i d u a l l y in 20 l i t r e aquaria and starved for 24 hours. Individuals were placed in the experimental tank for 15 minutes preceding each run to allow time for acclimation. After 15 minutes the prey were introduced from the top of the tank and recording of the t r i a l began after 71 the f i r s t o rientation. Five behaviours were scored: 1. Orientation to a prey item 2. Strike on a prey item 3. End of a successful manipulation 4. End of an unsuccessful manipulation 5. A break in orientation with no s t r i k e at the prey. Each t r i a l lasted twenty minutes and f i s h never consumed a l l the prey. A l l data were c o l l e c t e d using an OS-3 event recorder (Observational Systems Inc.). A two way fixed e f f e c t s ANOVA was performed on the proportion of foraging success. The proportion of foraging success was defined as the number of successful strikes ( i . e . those followed by prey ingestion) divided by the number of s t r i k e s . Probability plots (cumulative percent of the d i s t r i b u t i o n vs raw data) indicated that these proportional data had a s i g n i f i c a n t l y non-normal d i s t r i b u t i o n . Consequently the data were transformed using the arcsine square-root transform (Sokal and Rohlf 1981). The two factors in the ANOVA were population and upper jaw length. As a l l the f i s h in t h i s experiment were capable of taking the siz e - c l a s s of prey presented, I predicted no difference in foraging success between populations, given that the behavioural components to foraging success were approximately constant between populations. A s i g n i f i c a n t effect of population or a s i g n i f i c a n t interaction term would implicate some e f f e c t , apart from morphology, in benthic foraging success. I n i t i a l l y upper jaw length was divided into three levels 72 based on the following standard lengths: 30-40mm, 40-50mm and 50-60mm. Regression equations obtained from previously c o l l e c t e d samples were used to determine upper jaw length. Ten f i s h were to be run in each c e l l of the ANOVA, however I was unable to at t a i n complete c e l l s for two size-classes which resulted in an unbalanced, and badly weighted design; therefore the data were analyzed as a two way but with only two levels of upper jaw length. The ANOVA was performed using UBC:GENLIN. Interpopulation behavioural differences in foraging were examined for two behavioural variables which were thought to be r e l a t i v e l y independent of morphology: average successful manipulation time and st r i k e p r o b a b i l i t y . Average successful manipulation time was defined as the t o t a l time spent handling prey, which were eventually ingested, divided by the t o t a l number of prey ingested. Strike p r o b a b i l i t y was expressed as a proportion of the number of orientations which were followed by a s t r i k e . A Kruskall-Wallis one way ANOVA was performed on each variable across populations. This non-parametric test was used as i t is less sensitive to o u t l i e r s than i t s parametric' equivalents. To investigate the r e l a t i v e contributions of these behaviours to foraging success, in addition to the effect of upper jaw length, each behaviour was entered simultaneously into a multiple regression. The proportion of foraging success was the dependent variable in the model; upper jaw length, average successful manipulation time, and st r i k e p r o b a b i l i t y were treated as the predictor variables. The d i s t r i b u t i o n s of 73 foraging success and s t r i k e p r o b a b i l i t y were s i g n i f i c a n t l y non- normal; consequently these data were again arcsine square-root transformed. This transformation was successful in normalizing the data for multiple regression. Limnetic Foraging T r i a l s Foraging a b i l i t y on limnetic prey was tested in the laboratory using Artemia s a l i n i i as the experimental prey. Particulate feeding teleosts tend to be s i z e - s e l e c t i v e and behaviour is a s i g n i f i c a n t component of s e l e c t i v i t y (O'Brien 1979). Size-selective predation would tend to obscure the significance of morphology, for t h i s reason only a single size class of Artemia was used. In addition nauplii colour appears to be approximately constant at t h i s stage. Differences in prey colour have been shown to mediate d i f f e r e n t i a l attack responses for a variety of teleosts (review in Hyatt, 1979). Lab-reared f i s h were used in t h i s series of experiments in an attempt to standardize any learned component of interpopulation behavioural differences in limnetic feeding. A l l f i s h were i n i t i a l l y reared on l i v e Artemia nauplii before switching to a mixture of l i v e r and frozen Artemia ; consequently individual representatives of the three morphotypes were exposed to l i v e shrimp for similar lengths of time. Test f i s h were chosen at random from the tanks in which they had been raised. Each test was run in the same 20 l i t r e aquaria as used in the maximum gape experiments. Tanks were scrubbed and r e f i l l e d with dechlorinated water between each t r i a l to minimize 74 suspended p a r t i c u l a t e s which might a l t e r foraging success. Fish were held i n d i v i d u a l l y for two days prior to each test and fed l i v e Artemia to s a t i a t i o n . Tank temperature was 10 + 1.0 °C. At t h i s temperature t o t a l gut evacuation time i s more than 16 hours (Tugendhat 1960). Immediately preceding each test, individuals were starved for 24 hours to standardize hunger. At the beginning of each t r i a l 100 Artemia ( 5 / l i t r e ) were presented to each i n d i v i d u a l . Fish were allowed to feed for one hour after which they were removed and s a c r i f i c e d . Preservation was in 10% buffered formalin. After the f i s h had fixed for approximately one week the i r stomachs were excised between the upper and lower sphincters (Wootton 1976), opened, and the contents flushed out with water, using a micropipette. The number of Artemia per stomach was scored with the aid of a dissecting microscope. Nine morphological measures were made on each f i s h : STDLEN, HEAL, SNOL, EYED, UPJL, HEAD, INOW, GRN and GRL. G i l l r a k e r density was determined from regression of g i l l r a k e r area on standard length. Foraging success was expressed as a proportion of the 100 prey taken by each f i s h . P r o b a b i l i t y plots indicated these data had a non-normal d i s t r i b u t i o n for each population, hence the data were arcsine square-root transformed (Sokal and Rohlf 1980). This transform was successful in normalizing the data. Interpopulation differences in the proportion of foraging success were examined using a one-way ANOVA. Univariate c o r r e l a t i o n s were made within and among populations for each morphological variable scored, against foraging success. A l l 75 morphological variables were log (base e) transformed for a l l analyses. Results Trophic Morphology Sheffe's test on the adjusted mean areas indicated no differences in g i l l raker area, thus the benthic and intermediate populations appear to be packing fewer rakers into the same r e l a t i v e space as the limnetic f i s h . ANCOVA for g i l l raker density on standard length suggests t h i s i s probably the case. Slopes of population regressions were not s i g n i f i c a n t l y Table 14. Summary of ANCOVA results for g i l l r a k e r density on standard length. Population Bear Caycuse Mean raker 13.49 11.26 density Adjusted mean 14.16 12.03 raker density (Std. Error) 0.42 0.48 Note: pr o b a b i l i t y of equal adjusted means = 0.000. d i f f e r e n t ; however there were s i g n i f i c a n t differences between adjusted mean g i l l raker density (Table 14). For any given standard length, the intermediate and limnetic individuals have more c l o s e l y spaced rakers then the benthic type (p < 0.0001). However, the intermediate sample also had s i g n i f i c a n t l y more Grant 1 1 .02 9.42 0.49 76 rakers than the limnetic morph (p < 0.001). Table 15 summarizes the gut content data for samples recovered by pole-seine in May. Diets of the intermediate and benthic morphs were dominated by chironomids and ostracods. A small number of copepods were found in the stomachs of the intermediate morph, but no planktonic Crustacea were found in the stomachs of the benthic form. Diet of the limnetic morph was numerically dominated by limnetic and surface prey, although chironomids and ostracods again contributed to diet composition. The chi-square contingency test showed diet type (limnetic or benthic) to depend s i g n i f i c a n t l y on morph (p < 0.001). Maximum Gape The results of the gape experiments are summarized in Table 16. For both covariates, standard length and upper jaw length, the relationship with maximum amphipod length was c u r v i l i n e a r therefore a l l data were log (base e) transformed. The slopes of a l l regressions of amphipod length on standard length proved to be s i g n i f i c a n t l y d i f f e r e n t from zero (p < 0.05), but the slopes did not d i f f e r among populations. The adjusted mean lengths of ingested amphipods were s i g n i f i c a n t l y heterogeneous between populations, after the effect of the covariate had been removed. Pair-wise t-tests indicated no difference between the lengths of amphipods ingested by the intermediate and limnetic morphs (p > 0.05); however, both of these mean lengths were s i g n i f i c a n t l y less than that achieved by the benthic morph. The strongly linear r e l a t i o n between amphipod size and standard length 77 Table 15. Gut content data from wild population samples. 78 Table 15. Summary of gut content data from samples recovered with pole-seines in May 1983. Tabulated values are the pooled number of prey items/stomach for each sample Population Bear Caycuse Grant I tern (N = 30) (N = 20) (N = 30) Chi ronomids 103 1 2 1 28 Chaoborus 1 Megaloptera(larvae) 1 Megaloptera(adult) 1 Ephemeroptera 4 5 Simulidae(adult) 2 — " ~' 8 Tipulidae(adult) 1 Unidentified insect 2 6 3 (adult) Unidentified insect 4 4 (larvae) Gasterosteus eggs 6 28 99 Unidentified eggs 1 0 Ostracods 312 20 433 Hydracarina 1 Nematodes 1 5' Gammaridae 2 Cladocera 26 Cyclopoid copepods 2 Calanoid copepods 2 68 79 Table 16. ANCOVA results for amphipod size on standard length and upper jaw length. Table 16. Summary of ANCOVA results for amphipod size on: (a) standard length (b) upper jaw length. (A) Standard length. Populat ion Bear Caycuse Grant Mean amphipod 1.6527 1.6205 1.8745 size Adjusted mean 1.6292 1.5577 1.9437 amphipod size (Std.Error) 0.0575 0.0694 0.0596 Note: pro b a b i l i t y of equal adjusted means = 0.0007 (B) Upper jaw length. Populat ion Bear Caycuse Grant Mean amphipod 0.7177 0.7037 0.8140 size Adjusted mean 0.7278 0.7081 0.8008 amphipod size (Std.Error) 0.0243 0.0285 0.0244 Note: pro b a b i l i t y of equal adjusted means = 0.04 81 suggests that the difference in mean size-class attained, arises through increases in mouth gape (upper jaw length) with increased standard length. This conclusion was tested using upper jaw length as the covariate in the ANCOVA. Amphipod size is plotted against upper jaw length in Figure 7. Clearly increased upper jaw length confers an increased maximum gape for a l l populations. ANCOVA indicated that the slopes of individual population regressions were not s i g n i f i c a n t l y d i f f e r e n t from one another (p > 0.05) but the adjusted population means were s i g n i f i c a n t l y heterogeneous (p < 0.05). Benthic individuals are able to ingest larger prey items than individuals of either the limnetic or intermediate morphs. One should note however that although there i s a clear r e l a t i o n between prey size and upper jaw length there are differences between populations that must arise by some mechanism other than differences in upper jaw length. For wild-caught f i s h , behavioural v a r i a b i l i t y between populations, seems the most obvious source of variable foraging success; therefore I sought to address general behavioural modifications between populations. Amphipod Manipulation Experiments The ANOVA indicated no heterogeneity in foraging success among populations (p > 0.05) however there were s i g n i f i c a n t differences in variance among the two levels of upper jaw length (p = 0.0005). The interaction term (population * upper jaw length) was not significant.. B a r t l e t t ' s test indicated that a l l c e l l variances were homogeneous. This result confirms the 82 Figure 7. Plot of amphipod size vs UPJL for each morph. 0.8 0.9 1.1 1.2 1.3 1.4 UPPER JAW LENGTH (In mm) 1.5 1.6 — i 1.7 Legend BEAR O CAYCUSE • GRANT 84 effe c t of upper jaw length on foraging success demonstrated in the gape experiments. It remains possible however that Table 17. C e l l means and standard deviations for ANOVA on the proportion of benthic foraging success. UPJL Population Bear Caycuse Grant Level 1 0.2099(0.2819) 0.1344(0.2328) 0.2591(0.3127) Level 2 0.4824(0.2672) 0.5360(0.3191) 0.5372(0.2199) individual variance in foraging success obscures any extant differences between morph types in foraging behaviour. The within population component of variance i s probably i n f l a t e d by o u t l i e r s . Standard deviations of mean foraging success were high (Table 17) suggesting individual v a r i a t i o n in behaviour does indeed influence foraging success. Aside from th i s random va r i a t i o n there may be more general differences in foraging behaviour between populations which enhance the effect of upper jaw length in the gape experiments. I therefore attempted to id e n t i f y patterns of behaviour which might contribute to interpopulation foraging success. The Kruskall-Wallis ANOVA indicated no differences among populations in pr o b a b i l i t y of s t r i k e , but there was s i g n i f i c a n t heterogeneity among populations for average successful manipulation time. The benthic morph appeared to spend less time manipulating the prey before ingestion than the other two morphs. Both of the behavioural variables and upper jaw length were entered into a multiple regression. The independent 85 variables in the regression are of mixed mode, therefore the data were standardized and the c o e f f i c i e n t s of regression become Beta weights which are d i r e c t l y comparable (Sokal and Rohlf 1981). The results of t h i s analysis are summarized in Table 18. The o v e r a l l regression was highly s i g n i f i c a n t (p = 0.0000); however only upper jaw length and average successful manipulation time had p a r t i a l regression c o e f f i c i e n t s that contributed s i g n i f i c a n t l y to the model (p = 0.0001). The Beta Table 18. Summary arcsine success of multiple regression analysis using transformed proportions of foraging as the dependent variable. Var iable Beta-weight Std.Error Significance Strike p r o b a b i l i t y Upper jaw length Average successful manipulation time 0.0829 0.0986 0.3939 0.0986 0.4106 0.0980 0.4008 0.0001 0.0002 Note: multiple R = 0.6117 weights for these variables are very nearly i d e n t i c a l . Therefore I suspected that upper jaw length and average successful manipulation time might be strongly correlated; c e r t a i n l y some proportion of manipulation time i s expected to result from morphology. This prediction was tested by c o r r e l a t i o n for upper jaw length and average successful manipulation time, both within and between populations. In a l l instances the cor r e l a t i o n was negative (Table 19). Pearson's 'r' for data pooled across populations was s i g n i f i c a n t within populations only, the 86 c o e f f i c i e n t attained for the limnetic morph was s t a t i s t i c a l l y s i g n i f i c a n t . These results suggest that the contribution of Table 19. Correlation c o e f f i c i e n t s for average successful manipulation time and upper jaw length. Treatment N Co e f f i c i e n t Pooled Populations 70 -0.2981* Within Populations Bear 31 -0.4556 Caycuse 21 -0.5234* Grant 18 -0.4227 * Si g n i f i c a n t at p < 0.05. manipulation time to foraging success i s largely attributable to jaw morphology. Thus I was unable to i d e n t i f y any general behavioural processes, independent of morphology, that might have produced the differences observed in the gape experiments. Limnetic Foraging T r i a l s A summary of limnetic foraging i s given for each population in Table 20. Individuals from the benthic population were poor limnetic foragers compared to both the intermediate and limnetic morphs. Sample means were s i g n i f i c a n t l y heterogeneous by ANOVA (p < 0.05). Sheffe's contrasts indicated no s i g n i f i c a n t differences between the limnetic or intermediate morphs; however, both populations had s i g n i f i c a n t l y higher foraging success compared to the benthic population. Coefficients for a l l univariate correlations of foraging success with morphology are given in Table 21. None of these 87 Table 20. Summary of limnetic feeding experiments. Population N Mean Number of Mean Proportions of Artemia Taken Limnetic Foraging Bear 30 30.56(21.16) 0.55(0.26) Caycuse 31 31.93(22.15) 0.56(0.27) Grant 33 18.03(18.45) 0.36(0.28) Note: probability of equal means = 0.005. intrapopulation correlations were s i g n i f i c a n t (p > 0.05). Table 21. Intrapopulation c o r r e l a t i o n s for character and limnetic foraging success. Character Bear Caycuse Grant HEAL -0.1271 -0.1034 -0.0292 SNOL -0.1710 -0. 1826 -0.1445 EYED -0.1313 0.1362 -0.1980 UPJL -0.0286 -0.0010 -0.0918 GRL -0.0887 -0.1921 0.1336 HEAD -0.2641 -0.0268 0.1100 INOW -0.2345 -0.1277 0.2757 GRN -0.1229 -0.0005 -0.2251 GRDENS 0.0563 0.1441 -0.1004 Within each population functional r e l a t i o n s h i p s may be obscured by two factors: (a) the limited s i z e range tested for each population and (b) individual behavioural v a r i a t i o n . In each population a small number of f i s h appear to do extremely poorly or extremely well on Artemia. I was hesitant to label these as o u t l i e r s as they may be extensions of legitimate relationships. Interpopulation c o r r e l a t i o n c o e f f i c i e n t s are given in Table 22. Despite the fact there i s only one degree of freedom in thi s analysis two of the c o r r e l a t i o n s are s i g n i f i c a n t (p < 0.05). A chi-square test indicated the probability of finding 88 Table 22. Interpopulation c o r r e l a t i o n c o e f f i c i e n t s for transformed character and limnet ic foraging success. Character HEAL 0.999* SNOL 0.999* EYED 0.318 UPJL -0.454 GRL 0.356 HEAD -0.033 INOW -0.069 GRN 0.716 GRDENS 0.865 * S i g n i f i c a n t at p < 0.05. only two s i g n i f i c a n t c o r r e l a t i o n s , i f these a r i s e by chance, was low (0.05 < p < 0.1). The bivariate means are plotted for foraging success and adjusted character in Figure 8. In addition to HEAL and SNOL, GRN and GRDENS are strongly p o s i t i v e l y correlated with limnetic foraging success; the co r r e l a t i o n for GRL i s in the predicted d i r e c t i o n but much weaker. Bivariate means for GRL, GRN and GRDENS with the proportion of limnetic foraging are plotted in Figure 9. Discussion Previous investigations have examined the relationship between UPJL and maximum size of p a r t i c l e s eaten (Burko 1975; Larson 1976; Bentzen 1982), in a l l cases the maximum size ingested was a direct consequence of individual gape. Larson (1976) and Bentzen and McPhaiK1984) also demonstrated differences in maximum gape between limnetic and benthic 89 Figure 8.. Plots of bivariate means for the proportion of limnetic foraging and adjusted character. Glyphs indicate mean position for each population; black bars indicate one standard error on either side of the mean. • LIMNETIC • INTERMEDIATE • BENTHIC 8_ CD CD CD S- SNOL f i i 1 — 1 4.10 4.15 4.20 4.25 4.30 CD §-1 CD o CD E Y E D 3: I i 1 90 3.92 3.94 3.96 3.98 S CD § I CD H E A D 5 J l 1 — | 1 1 6 5.7 5.8 5.9 6 6.1 + INOW o CD ~ l r~ 1 1 2.3 2.4 2.5 2.6 2.7 4. 91 Figure 9. Plots of bivariate means for the proportion of limnetic foraging and GRL, GRN and GRDENS. Glyphs indicate mean position for each population; black bars indicate one standard error on either side of the mean. RAKER NUMBER • L IMNETIC • INTERMEDIATE • B E N T H I C 0 (0- 0 ti 8-. 0 LO ti 0 10 CO 0500.92 054 056 0.98 1 102 RAKER LBCIHN 9 10 H 12 13 14 15 RAKER DENSflY (numbers/sqmm) 93 Gasterosteus species p a i r s . The present study suggests that p a r t i c l e size i s a s i g n i f i c a n t selective force operating between populations and hence responsible for ecotypic v a r i a t i o n . The benthic with i t s increased gape i s permitted access to a wider range of prey sizes than i s the limnetic. In addition increased jaw length results in decreased handling time, which i s an energetic advantage and should i t s e l f be s e l e c t i v e l y favoured (Schoener 1971). The lack of an interpopulation behavioural component to benthic foraging i s somewhat surprising as behavioural modification has been shown to be associated with morphological differences in other groups of teleosts (Schultz and Northcote 1972). Bentzen and McPhail (1984) have shown that the limnetic species in Enos Lake, i s a poor forager on benthic substrate compared to the benthic species. Lab-reared male limnetics did poorly at sorting prey from the benthic substrate. In their study however, morphological divergence was far more extreme, than that found in the Cowichan drainage, and the limnetic and benthic forms behave as b i o l o g i c a l species (Ridgeway and McPhail 1984). The Enos Lake species pair is presumed to be the result of a double (or multiple) invasion(s) (McPhail 1984) therefore such behavioural differences may result from h i s t o r i c a l rather than s e l e c t i v e influences. If behaviour and morphology are t i g h t l y correlated i t may be unreasonable to attempt to separate their individual contributions to foraging. Indeed a genetic c o r r e l a t i o n between morphology and behaviour would result in a correlated response 94 to selection and the possible evolution of a 'trophic character', comprising aspects of both morphology and behaviour. The existence of such a character i s supported by the poorer handling a b i l i t y of F1 hybrids of Enos Lake limnetics and benthics, compared to either of the parental forms (Bentzen and McPhail 1984). For limnetic foraging, behaviour and morphology are almost c e r t a i n l y t i g h t l y correlated. Many features of head morphology contribute to behavioural variation in plankton feeders. Forward positioning of the eyes and increased eye diameter have been shown to increase reactive distance to limnetic prey in A r c t i c Grayling (Schmidt and O'Brien 1982). As a result of this apparent linkage, i t may prove d i f f i c u l t to d istinguish the contributions of individual characters. No behavioural component of limnetic feeding was examined in t h i s study and i t is possible that the observed differences result e n t i r e l y from interpopulation behavioural differences. If t h i s i s the case however, i t would suggest that limnetic behaviour i s under genetic control, since the lab-reared f i s h experienced similar feeding regimes. In t h i s instance, behaviour alone would be the target of selection and again the interpopulation responses are in the predicted d i r e c t i o n . The results however, indicate that interpopulation differences in g i l l r a k e r morphology probably contribute to the superior performance of the intermediate and limnetic morphs on Artemia. G i l l r a k e r morphology may set a lower l i m i t on the size of p a r t i c l e which i s retained (Hyatt 1979). The p r o b a b i l i t y that 95 an individual plankter w i l l escape, after passing into the buccal cavity, i s thought to be a function of g i l l r a k e r retention (Drenner 1977). Hence increased g i l l r a k e r density i s thought to permit a planktonic existence, and numerous studies have drawn a c o r r e l a t i o n between g i l l r a k e r architecture and planktivory (e.g. Kliewer 1970; Magnuson and Heitz 1971; Seghers 1975; Wright et a l . 1983). The mechanism of g i l l r a k e r action i s s t i l l imperfectly understood. In some teleosts, p a r t i c u l a r l y the so-called ' f i l t e r feeders' (e.g.Polyodon spathula), g i l l r a k e r s may act passively as a sieve. In these instances there may be a d i r e c t r e l a t i o n between spacing and p a r t i c l e s i z e . For Gasterosteus and other species of p a r t i c u l t e feeders however, the role of g i l l r a k e r s i s more complex. T y p i c a l l y p a r t i c l e size retained i s somewhat greater than minimum spacing might have allowed (Wright et a l . 1983); here again, behaviour seems to modify morphological constraints. By using only one size class of Artemia nauplii one should control for aspects of s i z e - s e l e c t i v i t y and be able to i d e n t i f y a 'step' in g i l l r a k e r composition at which many fewer plankton are retained. Some point must exist at which minimum spacing exceeds the maximum size dimension of the n a u p l i i . Intrapopulation v a r i a t i o n may not contain such a step, which would account for the lack of c o r r e l a t i o n within populations. Interpopulation contrasts however do contain s i g n i f i c a n t breaks in raker morphology and the benthic population with i t s reduced g i l l r a k e r density i s a s i g n i f i c a n t l y poorer planktonic forager than either the intermediate or limnetic populations. 96 I was unable to determine whether the intermediate morphology of f i s h from Bear Lake was translated into an intermediate foraging e f f i c i e n c y . This may in part result from the characters tested. Although, in terms of t o t a l morphological distance, the intermediate is more cl o s e l y linked to the benthic morph, UPJL was not s i g n i f i c a n t l y d i f f e r e n t from the limnetic sample. For UPJL then, the success of the intermediate is in the predicted d i r e c t i o n . This is also true for limnetic foraging success. E f f i c i e n c y on Artemia was associated with the higher g i l l r a k e r densities of the intermediate and limnetic. The g i l l r a k e r morphology of the intermediate may be a consequence of within generation fluctuating selective pressures. Populations of Gasterosteus move out of l i t t o r a l regions af t e r breeding, which i s often accompanied by a dietary switch to limnetic prey (Gross and Anderson 1983). Although Bear Lake contains an extensive l i t t o r a l zone, i t i s dominated by a large pelagic region in which f i s h no doubt contact plankton. In Bear Lake the breeding season does not last for more than a month and a half, hence the population spends the majority of i t s l i f e in a pelagic environment. In contrast, Grant Lake contains no appreciable pelagic zone and the population i s consistently subject to a benthic environment. The results of t h i s study indicate that marginal differences in population trophic morphology are s u f f i c i e n t to produce detectable differences in foraging success on a given prey type. The implications of t h i s result are two-fold. 97 F i r s t l y , the result supports the hypothesis that differences in population trophic morphology, within the Cowichan drainage, are adaptive responses to the primary resource consumed ( i . e . a small limnetic prey or a large benthic prey). Secondly, for such va r i a t i o n to be maintained each population must be genetically independent; each population must be considered a race (sensu Dobzhansky 1951). Given genetic independence and an adaptive significance to r a c i a l differences, interpopulation variation i s c l e a r l y ecotypic (Turesson 1922). Geographic distance alone may be responsible for the maintenance of population identity between the benthic and limnetic morphs; however the proximity of the intermediate and limnetic morphs precludes distance as an i s o l a t i n g mechanism. In t h i s instance some degree of habitat selection must be operating to maintain r a c i a l d i s t i n c t i o n , as the breeding seasons of the two forms are concurrent. Once two forms establish divergent habitat choice the framework is established for incipient i s o l a t i o n (Mayr 1963). Hagen (1967) has demonstrated that the freshwater and anadromous forms of Gasterosteus separate during breeding by habitat choice, and Hay and McPhail (1975) have shown that these forms exhibit positive assortative mating, based in part on male choice (McPhail and Hay 1983). As yet there are no data on assortative mating between ecotypes in the Cowichan drainage, however the investigation of th i s p o s s i b i l i t y would be p a r t i c u l a r l y i n t e r e s t i n g as i t may provide insight into the ori g i n of reproductive i s o l a t i o n between the sympatric species pairs. It would be of great 98 interest to know whether selection maintains r a c i a l d i s t i n c t i o n a f t e r secondary contact, or whether habitat selection has led to i s o l a t i n g mechanisms as a byproduct of genetic change. Certainly many laboratory investigations have demonstrated that i s o l a t i o n may arise as a pl e i o t r o p i c response to morphological s h i f t s under contrasting selective regimes (e.g. Dobzhansky and Pavlovsky 1967; Dijken and Scharloo 1979 ). Gross changes in morphology however, need not result in reproductive i s o l a t i o n . Sage and Selander (1975) have shown that radiation of trophic morphs may be achieved through polymorphism rather than speciation. A similar conclusion was reached by Turner and Grosse (1980) for the d i f f e r e n t i a t i o n of Ilyodon. Clearly the next stage of the current research must be the investigation of assortative mating between trophic morphs at some zone of contact, in an attempt to identif y the mechanism(s) by which r a c i a l i n t e g r i t y in Gasterosteus i s maintained. 99 GENERAL DISCUSSION Heuts (1947) recognized that natural selection appears to favour d i s t i n c t complexes of genes c o n t r o l l i n g plate morphs, in di f f e r e n t ecological niches, and that t h i s selection would by d e f i n i t i o n give r i s e to adaptive divergence. In the present study I have attempted to demonstrate that selection on trophic morphology may also lead to population divergence. Unfortunately, with no knowledge of the founder population, the term 'divergence' in t h i s instance must describe only the re l a t i v e difference between population phenotypes (although each population has most l i k e l y diverged from a common marine ancestor). The response of trophic phenotype to differences in primary resource type consumed has been demonstrated previously in i n t e r s p e c i f i c comparisons (e.g. L i s t e r 1976; Bentzen and McPhail 1984; Schluter and Grant 1984). The sign i f i c a n c e of adaptive divergence to speciation in Gasterosteus remains to be demonstrated, c e r t a i n l y conditions appropriate to the establishment of reproductive i s o l a t i o n (e.g. r a c i a l i n t e g r i t y ) seem to be present in t h i s system. One can only speculate as to whether reproductive i s o l a t i o n would lead to mating b a r r i e r s , although the l a t t e r are thought to be fostered by sexual selection systems (Templeton 1981), some of which have been i d e n t i f i e d for Gasterosteus (Hagen 1967; Ridgeway and McPhail 1984). Interestingly, sexual selection may be based on trophic features alone ( R a t c l i f f e and Grant 1983). There are several questions that remain with respect to the v a r i a b i l i t y described in Chapter 1. For example, how 100 generalized i s the interpopulation response of trophic phenotype to primary resource? Within some species populations appear to show .multiple solutions to similar selective constraints (Schluter and Grant 1984), i t i s possible that in a separate r i v e r system, the response to selection might be en t i r e l y d i f f e r e n t . In addition the phenotypic response of trophic morphology may be modified by selection on linked character suit e s . The extensive intrapopulation v a r i a t i o n i d e n t i f i e d in this study also deserves inves t i g a t i o n . Is i t due simply to the recombination of the d i p l o i d genome each generation, or i s i t maintained by some selec t i v e force? Reimchen (1980b) has suggested that lake-dwelling populations of Gasterosteus may be subject to cryptic i n t r a l a c u s t r i n e environmental differences, which preserve polymorphisms within each population. Given the divergence of these populations and their apparent individual genetic i d e n t i t y , why has there not been the explosive radiation of freshwater b i o l o g i c a l species as evident in the c i c h l i d s (review in Greenwood 1974). B e l l (1976) has suggested that the genetic i d e n t i t y of freshwater populations may be largely independent of adaptive morphology. If thi s i s the case, there must be constraints acting on freshwater systems of Gasterosteus. One possible source of constraint i s history. C i c h l i d s are a very old group (Greenwood 1984) and are l i k e l y to have been subject to many more transient i s o l a t i o n events in the course of their evolution, p r i m a r i l y those associated with changes in lake l e v e l . Although Gasterosteus has experienced 101 geomorphological events, c i c h l i d populations were probably preserved in refugia and have undergone multiple recontacts. It is u n l i k e l y that there were any g l a c i a l refugia for freshwater populations of Gasterosteus in B r i t i s h Columbia during the pleistocene. The freshwater evolution of the stickleback therefore appears to be characterized by periods of extinction followed by rederivation from the marine form (Bell 1976). The second constraint on speciation may be i n t e r n a l . Wootton (1984) feels that the range of variation exhibited by Gasterosteus (including such anomalies as the loss of skeletal elements) represents an 'evolutionary p l a s t i c i t y ' under constraint. 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