THE EVOLUTION OF TRADE-OFFS: EFFECTS OF INBREEDING ON FECUNDITY RELATIONSHIPS IN THE CRICKET GRYLLUS FIRMUS

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1 Evolution, (),, pp. THE EVOLUTION OF TRADE-OFFS: EFFECTS OF INBREEDING ON FECUNDITY RELATIONSHIPS IN THE CRICKET GRYLLUS FIRMUS DEREK A. ROFF AND MARC A. DEROSE Department of Biology, McGill University, Dr. Penfield Avenue, Montreal Quebec, HA B, Canada Abstract. The evolution of traits is modulated by their interrelationships with each other, particularly when those relationships result in a fitness trade-off. In this paper we explore the consequences of genetic architecture on functional relationships between traits. Specifically, we address the consequences of inbreeding on these relationships. We show that the linear regression between two traits will not be affected if there is no dominance genetic variance in either trait, whereas the intercept but not the slope of the regression will change if there is dominance genetic variance in one trait only. We test the latter hypothesis using fecundity relationships in the cricket Gryllus firmus. Data from pedigree analysis and an inbreeding experiment show that there is significant dominance genetic variance in fecundity, but not head width (an index of body size) or dorsal longitudinal muscle (DLM) mass. Fecundity increases with head width, but decreases with DLM mass. As predicted, the intercepts of the regressions of fecundity on these two morphological traits decrease with inbreeding, but there is little or no change in slope. Gryllus firmus is wing dimorphic, with the macropterous (LW) morph having a lower fecundity than the micropterous (SW) morph. We hypothesize that the difference in fecundity arises primarily because of a competition for resources in the LW females between DLM maintenance (i.e., mass) and egg production. As a consequence, we predict that the fecundity within each morph should decline linearly with the inbreeding coefficient at the same rate in both morphs. The result of this will be a change in the relative fitness of the two morphs, that of the SW morph increasing with inbreeding. This prediction is supported. These results indicate that trade-offs will evolve and such changes will affect evolutionary trajectories by altering the pattern of relationships among fitness components. Key words. Antagonistic pleiotropy, fecundity, inbreeding depression, trade-offs, wing dimorphism. The Society for the Study of Evolution. All rights reserved. Received December,. Accepted August,. Trade-offs are an essential component of life-history theory, because without them there would be little constraint on the evolution of traits (Charlesworth, ; Roff ; Stearns ; Charnov ; Bjorklund ). A second reason for their importance in life-history theory is that under the appropriate conditions antagonistic pleiotropy can play a significant role in the maintenance of genetic variation (Curtsinger et al. ). Thus, trade-offs are potentially important because they determine, at least in part, the direction and rate of evolutionary change. In a more general sense, relationships between two traits even if positive can have important evolutionary implications because they favor evolution in a particular direction. For example, fecundity typically increases with body size (Roff, ) and therefore, with respect to this relationship alone, selection will favor an increased body size: Changes in body size may be opposed by other factors such as increased development time (Roff ). Both additive and nonadditive genetic variation are relevant in the direction of evolutionary change, the additive genetic variance and covariances modulating the evolutionary trajectory (Lande ; Via and Lande 8; Arnold ), whereas the nonadditive genetic component, in the form of dominance variance, is a necessary requirement for antagonistic pleiotropy to maintain additive genetic variation (Curtsinger et al. ). For antagonistic pleiotropy to preserve significant amounts of genetic variation the ratio of dominance to additive variance in simple models must exceed. (Curtsinger et al. ). Empirical studies have shown that these levels do not appear to be generally found in morphological traits (Mousseau and Roff 8; Crnokrak and Roff ), but are common in life-history traits (see Roff, table.). Thus, additive genetic variance in two life-history traits that comprise a trade-off (e.g., early and late fecundity) could plausibly be maintained by antagonistic pleiotropy. However, a trade-off between two morphological traits probably requires another explanation. But what about a trade-off between a life-history trait and a morphological trait? If the genetic variance in the morphological trait is almost all additive while there is a large dominance component in the life-history trait, then the loci that act pleiotropically must generate primarily additive genetic covariation. Therefore, the genetic variance in the two traits is unlikely to be maintained by antagonistic pleiotropy. However, as shown below, this does not mean that the relationship between the two variables will be independent of the nonadditive component of the genetic variation in the life-history trait. Functions relating two traits (positive or negative) can take any shape, but to determine the phenotypic and genetic correlations between the component traits the function must be transformed so that it is linear. The phenotypic linear regression between a life-history trait and a morphological trait can be written as y y p x x y r (x ), () where y is the life-history trait, x is the morphological trait, r p is the phenotypic correlation between traits, and x and y are the phenotypic standard deviations. Assuming no environmental covariance between the two traits, the equation can be written as Cov a(x, y) y (x ), () y x where Cov a (x, y) is the additive genetic covariance between x

2 D. A. ROFF AND M. A. DEROSE x and y. Now, under inbreeding the mean of the life-history trait, y, will be decreased as a linear function of the inbreeding coefficient, F, but the mean value of the morphological trait, x, because it has little or no dominance variance, will remain the same (Crow and Kimura, p. 8). Inbreeding reduces the additive genetic covariance between y and x and the additive genetic variance of x by a proportion F (Crow and Kimura, p. ) and thus the slope of the above function, Cov a (x, y)/ x, will show little or no change. Therefore, inbreeding should shift the function by a change in the intercept, but not the slope. If both traits have significant dominance variance, then both y and x will decrease with inbreeding, but the effect of inbreeding on the slope will depend on how inbreeding affects x, which contains both additive and dominance variance (Crow and Kimura, p. ). These conclusions apply to any pairwise relationship between traits, not only to traits showing antagonistic pleiotropy, although the latter will typically be of the greatest evolutionary importance. The above analysis shows that changes in means and variances brought about by inbreeding can produce shifts in a function provided the genetic variance of at least one of the components of the function consists of both additive and dominance genetic variance. Thus, the evolution of trait functions, particularly trade-offs, can be sensitive to inbreeding effects. In the present paper we test the above hypothesis by examining two sets of relationships between traits in outbred and inbred lines of the sand cricket, Gryllus firmus: () fecundity as a function of body size and dorsal longitudinal muscle (DLM) histolysis; and () fecundity in macropterous (LW) versus micropterous (SW) morphs. The rationale for choosing these components is detailed below. MATERIALS AND METHODS Rationale for the Relationships Examined Fecundity, body size, and dorsal longitudinal muscle histolysis As with many organisms, in G. firmus there is a positive correlation between fecundity and adult body size (Roff 8, unpubl. data). Both pedigree analysis and a comparison of outbred females with offspring from brother-sister matings indicate that the genetic variance in fecundity has a large dominance component, whereas there is little dominance in the genetic variance of body size (Roff 8). There is also a significant genetic correlation between fecundity and body size (.; D. A. Roff, unpubl. data). This relationship fulfills the conditions outlined above; thus, we predict that in the absence of other confounding factors the linear relationship between fecundity and body size will be maintained under inbreeding but the intercept will decline. Gryllus firmus is wing dimorphic, consisting of a macropterous (LW) morph that is capable of flight, possessing fully functional flight apparatus (e.g., dorsal longitudinal muscles, long wings) and a micropterous (SW) morph that is flightless (reduced dorsal longitudinal muscles, short wings). Roff (8) showed that there was a positive, phenotypic correlation between the rate of dorsal longitudinal muscle (DLM) histolysis and fecundity in macropterous females, suggesting a trade-off between the maintenance of the flight apparatus and fecundity. The heritability of muscle histolysis estimated from full sibs is. and the genetic correlation between fecundity and histolysis from the same experiment is. (Roff a). A significant genetic correlation was also established by examining the correlated response of muscle histolysis to selection on wing morph (Fairbairn and Roff ). Although the full-sib analysis cannot separate additive and dominance components of variance, the predicted correlated response of muscle histolysis very closely matched the observed response (r.8, n, P.; see Roff a for details), which suggests that the genetic variance in muscle histolysis is primarily additive. Thus, we predict, as with the former relationship, that inbreeding should alter only the intercept of the fecundity on flight muscle histolysis function. In wing dimorphic species in general, and in G. firmus in particular, SW females have a significantly higher fecundity than LW females (Roff 8; Roff and Fairbairn ). The difference in fecundity is due in part to a trade-off between resources devoted to fecundity versus resources devoted to flight muscle construction and/or maintenance (Roff 8, 8, 8; Tanaka ; Mole and Zera ; Zera and Denno ; Zera et al. ; Roff and Fairbairn ). Because the flight muscles in the SW morph are vestigial relative to those in the LW morph, we predict that there will be a difference in the relationship between fecundity and muscle histolysis in the two morphs, with a shallower slope in the SW morph relative to the LW morph. The simple linear regression relationships described above assume that there are not confounding influences such as a correlation between the two traits. If body size and muscle histolysis are uncorrelated traits, then the relationship should remain additive and the intercept alone will change under inbreeding. Fecundity in the LW females versus fecundity in the SW females Because of the significant dominance genetic variance, the mean fecundity of each morph should decline linearly with the inbreeding coefficient. If as suggested above, flight muscle histolysis is determined primarily by additive genetic variance and this is the principle factor determining the tradeoff between fecundity and wing morphology, then the actual decline in fecundity will be determined only by the inbreeding coefficient and will be the same for each morph. In contrast, if other components are also involved in the trade-off and these have dominance genetic variance, then it is possible for the two morphs to have different rates of decline with inbreeding. From an evolutionary perspective, an important question is whether the relative fecundities, and thus relative fitnesses, change under inbreeding. Therefore, we consider three statistical models: one in which the absolute decline is the same in both morphs (the additive model), one in which the rate of decline differs between morphs without specific reference to the relative rate (the full model), and one in which the rate of decline is such that the relative fecundities remain constant (the constant ratio model).

3 EVOLUTION OF TRADE-OFFS TABLE. Number of individuals taken from each of the inbred and outbred lines per generations. The numbering of lines is arbitrary. Line 8 Total 8 8 Inbred lines generation Total Outbred lines generation Total Experimental Design The crickets used in this experiment were taken from a laboratory stock population originating from approximately individuals (equal sex ratio) collected from northern Florida in 8. To reduce the likelihood of genetic drift or inbreeding, the stock population is maintained at breeding individuals. We have no direct estimates of the effective population size and therefore it is possible that the present laboratory stock is inbred relative to the wild population. If there are no epistatic effects, the relationship between trait means and F will be linear (Crow and Kimura ) and, therefore, if no purging had occurred, the present results can still be referred to the original population by converting the results into decrease per fraction of inbreeding. If there had been purging of deleterious alleles, the present estimates of inbreeding depression would be underestimates. In 8 the stock produced approximately % LW females at 8 C (Roff :. and. in two separate experiments) and in, at the start of the present experiment, the percentage was %, suggesting that no major changes had occurred in the stock during this period. A detailed description of the initial construction of the inbred and outbred lines is given in Roff (8). Here we present only an overview. Containers of moist earth were placed in the stock cage to provide the females with a place for oviposition. Our initial generation was derived from eggs retrieved from these containers. Nymphs were raised in groups of in -L buckets (approximately cm in diameter cm in height) with ad libitum food (crushed Purina rabbit chow) and water. All individuals were reared at 8 C with a photoperiod of : L:D. At final ecdysis, adults were removed from the -L buckets and male-female breeding pairs set up. The offspring were raised as described above. Lines were formed from the offspring of each breeding pair. Upon eclosion as adults, full siblings were mated to form inbred lines. Outbred lines were made by mating females within each line with males randomly chosen from the stock population. Eggs, nymphs, and adults were reared as before. Thus, at each generation, each line, including outbreds, were formed from a single pair. This procedure ensured that genetic drift, which would confound the analysis of the effects of inbreeding, was present equally in both control (outbred) and inbred lines. Some lines were lost, generally due to failure of the females to produce offspring (there was no difference between inbred and outbred lines; D. A. Roff, unpubl. data), but the number of inbred and outbred; lines available for the present analysis was very similar ( inbred, outbred; Table ), thus ensuring, as noted before, that effects of genetic drift should be equally represented in the two treatments. At final eclosion, adult males and females were removed from the -L buckets and placed in individual containers. One-week posteclosion males and females were sacrificed and their dorsal longitudinal muscles were removed and weighed. There are high correlations between the three variables wing muscle histolysis; wing muscle status (functional or nonfunctional); and the mass of the main flight muscles, the DLMs (Crnokrak 8; G. Stirling, unpubl. data); because DLM mass is a continuous variable, we used this as an index of flight muscle status. A low DLM mass indicates either a lack of muscle development (as in the SW morph) or histolysis of the muscles (as in the LW morph). In either case it is potentially indicative of a commitment to reproduction rather than flight capability. In addition to DLM mass, we also measured the mass of the two ovaries in the females. The mass of the ovaries (hereafter ovary mass ) is proportional to total egg production in the first week after final eclosion in both mated and virgin females (Roff a), and is thus an index of early fecundity. Adult head width was measured as an index of adult body size. Measurements of ovary mass, DLM mass, and adult head width were taken at generations,,, and for both inbred and outbred lines, corresponding to inbreeding coefficients of. (outbred),.,.,., and.8 (except in the cases of DLM mass and adult head width, where there were no measurements taken at F. and F., respectively).

4 D. A. ROFF AND M. A. DEROSE TABLE. Means and estimated inbreeding depression (%) at each generation for Gryllus firmus. DLM, dorsal longitudinal muscle; SW, micropterous; LW, macropterous. Generation Head width (mm) DLM mass (g ) Ovary weight (g) Outbred Inbred Outbred Inbred Outbred Inbred *.8* SW morph... LW morph If the mean of the inbreds exceeds that of the outbreds ( [ inbred/outbred]) is set to zero. * At least one sample size is less than. *.* * * Statistical Analysis of Fecundity Changes with F We analyzed the data in two ways. First we initially tested for a difference using the model Y c cmorph cf c (morph)(f), () where Y is ovary mass, morph is a dummy variable designating wing morph, F is the inbreeding coefficient, and c i - values are fitted constants. Because it is possible that the slope of the relationship between fecundity and morph could change in a nonlinear manner with F, we entered F as a categorical variable. This model cannot address the question of a constant ratio of fecundity with F. For this purpose, we used the following approach, in this case using F as a continuous variable (it will be shown that this is justified by the results of the preceding analysis). Under the null hypothesis of no change in relative fitness as a consequence of inbreeding depression, we have, YSW a bf and (a) Y c (a bf), (b) LW where Y SW and Y LW are the fecundities of the SW and LW females, respectively; F is the coefficient of inbreeding; and a, b, c are the intercept, the slope, and a constant of proportionality, respectively. We shall refer to this model as the constant fitness model. This model was compared to the two models given above by separately fitting the additive and full (saturated) ANCOVA functions. The ANCOVA additive model is YSW a bf and (a) Y c bf, (b) LW where a and c are the intercepts and b is the common slope. The ANCOVA full model is YSW a bf and (a) Y c df, (b) LW where a and c are the intercepts and b and d are the slopes. Assuming normally distributed errors, the maximum-likelihood estimates of the parameters for the three models can be obtained by minimization of the error sums of squares. Because they contain the same number of parameters, the first two models cannot be easily compared statistically, but both can be compared to the full model by the F-statistic (Dobson 8, p. ): SSO SSA F,df A, () SS A df A where SS O is the error sums of squares for either the constant fitness or additive models, SS A is the error sums of squares for the full model, and df A is the degrees of freedom for the full model (n ). Note that the above statistical comparison between the additive and full models is the same as that for the standard ANCOVA analysis. RESULTS General Overview of the Data Previous analysis of the first-generation data showed that the same quantitative answers were obtained using either line means or the entire dataset (Roff 8). Because of sample size restrictions, we combined all lines in the present analysis. LW adults histolyse their flight muscles, and therefore, there exists the possibility that at some age the distribution of DLM mass will be bimodal. Inspection of the distributions of DLM masses did not show any obvious bimodality in any generation. Generation means for the three traits are presented in Table. There appears to be considerable inbreeding depression in ovary mass ( %, excluding estimates based on sample sizes less than ), but little in head width ( %). Because it is not obvious how DLM mass relates to fitness it is not clear what a depressed value would be, but there is no evident decrease in DLM mass and, in fact, the mean inbred value appears to be slightly larger than the outbred mean (Table ). To obtain a more quantitative assessment, we analyzed the data using a three-way ANOVA with morph, generation, and status (inbred or outbred) as categorical variables. For ovary mass, there were highly significant effects due to each of the separate factors (P. in all cases) and a sig-

5 EVOLUTION OF TRADE-OFFS nificant interaction between morph and generation (F,8., P.8). In the case of head width, there were significant effects due to morph (F,., P.), status (F,., P.), morph generation (F,., P.), and status generation (F,., P.). For DLM mass, significant effects were found for morph (F,8., P.), generation (F,8., P.), morph generation (F,8., P.), status generation (F,8.8, P.), and morph status generation (F,8 8., P.). Thus, in all three traits inbreeding produced a change in trait value. Analysis using only the outbred individuals showed that there was significant variation among generations; therefore, we conducted further analyses using the residuals obtained by subtracting the generation means of the outbred individuals. For simplicity, we shall refer to theses residuals as X (ovary mass, DLM mass, or head width) rather than residuals of X. Is Fecundity a Function of Adult Head Width and Dorsal Longitudinal Muscle Mass? For these analyses, we considered only the outbred females and used stepwise linear regression to find the best model, with the full model including head width (HW), DLM mass, wing morph, and all possible interactions. We did the analysis using both the raw data and the residuals. The results were qualitatively the same; for consistency with the later analyses, we present here the analysis using residuals. The final model obtained was highly significant (F,., P.; R.; SEs in parentheses after the coefficients): Y. (.) [.8 (.) HW] [. (.8) DLM] [. (.) HW DLM]. (8) Although the final model included an interaction term (HW DLM) the contribution to the overall explained variance was very low, contributing only an additional.%. Because of the requirement that both DLM and HW measurements must be available for a data point to be entered, the sample size for the multiple regression model comprised observations compared to and 8 for the simple linear regressions using DLM or HW, respectively. The multiple and simple linear regression models gave qualitatively the same result: Fecundity decreased with increased DLM mass and increased with head width (Fig. ). The lack of significance due to wing morph can be explained by the very high collinearity between DLM mass and wing morph (r., n 8, P.; for the SW morph x., SD.; LW morph x.8, SD.8). As found previously (Roff 8, 8), the mean ovary mass was larger in outbred, SW females than in outbred, LW females (.8. g vs... g, respectively, when averaged over all generations). Does Inbreeding Affect Dorsal Longitudinal Muscle Mass or Head Width? For DLM mass and head width, we analyzed the data using the ANCOVA model, Y c c F c morph c sex (interactions involving F, morph, and sex), where Y was either DLM mass or head width, F the inbreeding coefficient, morph a dummy variable designating wing morph, and sex a dummy variable designating sex. In the case of DLM mass, there was a significant morph sex interaction (F,8., P.), but neither F nor interactions involving F were significant (P. in all cases). An extra sums of squares test showed that all terms involving F could be dropped from the regression (F,88., P.). These results are in accord with the generation averages presented in Table, and we conclude that there is no detectable relationship between inbreeding and DLM mass. Head width also showed a significant morph sex interaction (F, 8.8, P.) and a marginally significant effect of F (F,.8, P.8). To quantitatively assess the impact of inbreeding we found the best predictive model using stepwise regression: HW..8F.8sex.(morph)(F).(morph)(sex), () where morph for LW females and for SW females, and sex for females and for males. For F. (e.g., brother-sister mating) the predicted inbreeding depressions range from % to.%. Even at complete inbreeding (F ) the predicted inbreeding depression values only range from % to.8%, respectively. Thus, as suggested by the mean values given in Table, although there is inbreeding depression in head width, it is small. Does Inbreeding Influence the Joint or Single Relationships between Fecundity and the Two Traits Head Width and Dorsal Longitudinal Muscle Mass? Although the first three predictions presented above were made by moving from two simple linear regressions to a multiple regression, to minimize the problem of multiple testing, we begin the analysis with the multiple regression model and then consider the simple regressions to explain the results of the multiple regression analysis and test the two singlefactor predictions. We conducted the analyses using the inbreeding coefficient, F, as a continuous variable and as a categorical variable, the latter to examine the possibility that any relationship was not linear. Comparison of the explained variance for the two models showed little difference, indicating that the linearity assumption was justified. Therefore, for simplicity, we present only the results of the analysis with F as a continuous variable. Stepwise linear regression using DLM, F, wing morph, HW, and all possible interactions produced a highly significant multiple regression (F,., P.) with the variables shown in Table. The failure of wing morph to enter into the model can be explained as before by the high collinearity between wing morph and DLM mass. Individual tests on the simple additive components HW, DLM, and F all produced significant results, whereas the tests of the interactions involving F were nonsignificant (Table ). Taken as a group, the three interaction terms with F do not contribute significantly to the explained variance (F,., P.8), the model shown in Table accounting for.% of the variance, whereas the model excluding the

6 D. A. ROFF AND M. A. DEROSE FIG.. Ovary mass as a function of dorsal longitudinal muscle (DLM) mass and head width separately (top panels) and jointly (bottom panel; the fitted equation did not include the interaction term). Wing morphs indicated by L (macropterous, or LW) and S (micropterous, or SW). last three interaction terms accounted for.88% of the variance. As in the multiple regression model using only the outbred females, the final model here included the interaction HW DLM (Table ), but as before this component accounts for only a very small proportion of the total variance (.%). Thus, a model that accounts for the vast majority of the variance includes only the three separate components HW, DLM, and F (F,.8, P., R.): Y. (.8) [. (.) HW] [8.8 (.) DLM] [. (.) F]. () As predicted, the relationship between fecundity and the two traits HW and DLM changes only with respect to the intercept under inbreeding. Further, if HW and DLM are uncorrelated or one is kept fixed, then the relationship between fecundity and HW or DLM stays constant under inbreeding except for a change in intercept. HW and DLM mass are significantly correlated (r., n, P., outbred females only). Stepwise regression using either HW or DLM, but not both, gave rise to equations that included wing morph: For HW the final model included HW, F, and wing morph, whereas for DLM the terms retained were DLM, F, wing morph, DLM F and DLM wing morph (Table ). Thus, if variation in both traits (HW, DLM) is not taken into consideration, the relationship between fecundity and either trait differs between wing morphs. For head width, the intercept of the regression of fecundity on HW declines with F, with SW females having a consistently higher fecundity than LW females (Table, Fig. ). The equation for fecundity on DLM is more complex. There is a marginally significant interaction between DLM and F (Table ), which leads to the surfaces being tilted so that for low DLM fecundity declines with F, whereas for high DLM the slope is reversed (Fig. ). This result is contrary to our prediction, but the marginal value of the result suggests caution. We predicted that for the simple regression between fecundity and DLM mass, the slope of the regression for the

7 EVOLUTION OF TRADE-OFFS TABLE. Final model obtained by stepwise linear regression of ovary mass as a function of head width (HW), dorsal longitudinal muscle (DLM) mass, and F, wing morph. Variables Coefficient SE t P Intercept HW DLM F HW DLM HW F DLM F DLM HW F SW females would be shallower than for the LW females. This prediction is substantiated (Fig. ), the fitted slopes being-. for the LW females and.8 (. 8., Table ) for the SW females. Is There an Effect of Inbreeding on Relative Fitness between the Two Wing Morphs? The preceding analysis suggested that the relationship between fecundity and other traits (HW, DLM) is sensitive to inbreeding and changes brought about by inbreeding may differ between the wing morphs. This raises the possibility that the relative fitness may change between the two morphs. In this section, we test the three models predicting the functional relationship between ovary mass and F. First, we consider the two-way ANOVA model with morph and inbreeding coefficient (here introduced as a categorical variable). There was no significant interaction between morph and F (F,88.8, P.), but there were highly significant additive effects of the coefficient of inbreeding, F (F,88., P.), and wing morph (F,88.8, P.) on ovary mass (Fig. ). The variance accounted for by the additive model in which F was a categorical variable was 8.% compared to.% for the model in which F was continuous, confirming that declines were in fact linear. Ovary mass decreased with increased inbreeding coefficient and was lower in LW females than in SW females. As would be expected from the above analysis, there was no statistical difference between the additive and full models (F,.8, P.), indicating that the interaction term in the full model accounted for a nonsignificant amount of variance. However, there was a highly significant difference between the constant ratio model and the full model (F,., P.), indicating that the full model was a superior fit than the constant ratio model. Because the full model itself was not better than the additive model, we conclude that the best of the three models is the additive model. The decline in ovary mass residuals with inbreeding is best described by the equations Y SW..F and Y LW..F. Taking the grand means of the ovary masses as a reference point, the ratio of the fitnesses (LW/ SW) are. at F. and. at F.8 (the maximal inbreeding coefficient in the present experiment). Thus, the above analysis supports the prediction that the decline in ovary mass is the same in both morphs and, as a consequence, the relative fitness changes with inbreeding with the SW morph having relatively greater fitness. DISCUSSION Trade-offs play central role in evolutionary theory (Roff, ; Stearns ). There have been some theoretical explorations of how trade-offs may be determined by genetic architecture (e.g., James ; Riska 8; Pease and Bull 88; Charlesworth ; Houle ; Laguerie et al. ), but most of these analyses have focused on the problem of how positive genetic correlations could arise when negative correlations might be expected. In the present paper we have taken as our starting point the presence of a functional relationship between two traits, including both positive and negative trade-offs, and asked how that relationship will be modified by a particular change in the genetic architecture, TABLE. Final models obtained by stepwise linear regression of ovary mass as a function of F, wing morph (, macropterous;, micropterous), and head width (HW) or dorsal longitudinal muscle (DLM) mass. Variables Coefficient SE t P Intercept HW F Wing Intercept DLM F Wing DLM wing DLM F Head width...8. Dorsal longitudinal muscle mass

8 8 D. A. ROFF AND M. A. DEROSE FIG.. Effect of inbreeding on ovary weight in micropterous (SW) and macropterous (LW) Gryllus firmus. FIG.. Predicted relationships between ovary mass and the independent variables F, wing morph, and head width (top graph) or dorsal longitudinal muscle (DLM) mass (lower graph). In both graphs, the surface for the micropterous (SW) females lies above that of the macropterous (LW) females. namely a change in the relative amount of dominance variance. There are three broad categories of relationships: () a relationship between two traits in which dominance variance is significant in both (e.g., two life-history traits); () a relationship between a trait with a large dominance variance and a trait with an insignificant component (e.g., a life-history trait and a morphological trait); and () a relationship between two traits in which neither exhibits a significant dominance variance (e.g., two morphological traits). From the theory outlined in the introduction, the last relationship will not be affected by inbreeding, that between a life-history and morphological trait will be altered by a change only in the intercept, and that between two life-history traits will be changed both in the intercept and slope. To test the above hypothesis, we examined the consequences of inbreeding in the cricket G. firmus on the four relationships fecundity versus body size, fecundity versus flight muscle size, fecundity versus both body size and flight muscle size, and fecundity versus wing morphology. Fecundity is obviously a component of fitness and the relationship between fecundity and body size is a very common observation (Roff ), although the proposition that this represents a trade-off comes from a presumed correlation between body size and another fitness trait such as development time (e.g., McLaren ; Roff 8, 8; Stearns and Crandall 8; Kachi and Hirose 8; Abrams et al. ). The important aspect of the fecundity body size relationship in the present context is not whether in this particular species the relationship represents a trade-off, but rather that it represents a relationship between a life-history trait and a morphological trait. Flight muscle size is a morphological trait, but is related to fitness because there is an apparent competition for resources between the flight muscles and fecundity (see introduction). Gryllus firmus is wing dimorphic, with the dimorphism being hypothesized to be maintained as a consequence of a trade-off resulting from the dispersal advantages accruing to the LW morph versus the increased fecundity of the SW morph (Southwood ; Dingle 8; Harrison 8; Roff 8,, b; Denno et al. ; Roff and Fairbairn ). A previous study demonstrated that the genetic variance in fecundity, but not body size, consisted of a significant fraction of dominance variance (Roff 8). An indirect argument was made that flight muscle mass is like a typical morphological trait in that its genetic variance is primarily additive (see Materials and Methods). Given these conditions, we predict that the linear regression between fecundity and either body size or muscle mass will show a decline in the intercept under inbreeding. If the trade-off in fecundity between the two wing morphs is largely a result of the tradeoff between the allocation to flight muscle versus fecundity, we predict that the fecundity of each morph should decline linearly with F but remain parallel to each other (i.e., have the same slope). The result of such a relationship is that the relative fitness of the two morphs will not stay constant. As in the previous study we found that fecundity showed considerable inbreeding depression, whereas body size did

9 EVOLUTION OF TRADE-OFFS not (Table, Roff 8). DLM mass also showed little change with inbreeding, supporting our hypothesis that DLM mass resembles a typical morphological trait. Fecundity increased with head width and decreased with DLM mass, with wing morph not being a significant component (Fig. ). The lack of an effect of wing morph was attributed to the very high collinearity between wing morph and DLM mass (Fig. ). Macropterous females can commit to reproduction either by failing to produce large flight muscles or by histolysing them, the latter response enabling them to partially reduce the cost of dispersal capability (Roff a; Zera and Denno ; Zera et al. ; Stirling et al. ). A high correlation between DLM mass and histolysis condition suggests that DLM mass probably reflects variation in histolysis more than simply variation in muscle mass per se (Crnokrak 8; G. Stirling, unpubl. data). As we predicted, the above relationships were affected by inbreeding primarily by a change in the intercept. These results also support the hypothesis that the fecundities of the two morphs change in parallel (the additive ANCOVA model, Fig. ). A direct examination of this hypothesis by comparing the relevant three models (additive ANCOVA model, full ANCOVA model, constant ratio model) also indicated that the best descriptive model was the additive model. As a consequence, the relative fitness of the SW morph is predicted to increase with inbreeding. Wing dimorphism is found in a wide range of insect taxa and is typically associated with species that inhabit ephemeral habitats (Roff, b). The sand or beach cricket, G. firmus, appears to be typical in this regard, being found on coastal beaches and sand dunes (Alexander 8; Harrison 8), which are likely to be ephemeral either because they are eventually overgrown or are storm swept (which would result in extermination of the local population). In an ephemeral environment, such as that of G. firmus, there will be constant selection for migratory capability. However, this will be offset within a particular patch by selection against the lower fecundity of the LW females. A consequence of this selection at two scales is that fitnesses are frequency dependent and both morphs can be maintained in the population (Roff c). Colonization is likely to be a result of just a few individuals; thus, in the initial phase of population expansion following colonization there is likely to be inbreeding (Howard, table.). The initial phase of inbreeding could significantly alter the evolutionary dynamics; specifically, because of the increased relative fitness of the SW morph, the rate at which this morph replaces the colonizing LW morph will be increased. There are no data on the rates of extinction of G. firmus populations or local population sizes. However, studies of other wing dimorphic insects and comparisons among volant and flightless species has shown that there is a positive correlation between flight capability and genetic variation among populations/species (Zera 8; Liebherr 8; Preziosi and Fairbairn ; Peterson and Denno, 8; but see Liebherr 88). In general, genetic variation among populations may be expected to be a function of dispersal capability (Waples 8; Govindaraju 88; Williams and Guries ; Doherty et al. ; Shulman and Bermingham ) and the frequency of local rates of extinction and recolonization (Wade and McCauley 88; Whitlock and McCauley ; Hastings and Harrison ). Increases in inbreeding due to the foregoing processes will lead to a change in all fitness relationships that involve traits in which genetic variation is partly due to dominance variance. Genetic variance in lifehistory traits appears to be commonly due to both additive and dominance effects (Crnokrak and Roff ) and thus it is possible that there will be a major shift in relative fitness components upon inbreeding. In accordance with the large dominance component in the genetic variance of life-history traits relative to morphological traits, life-history traits show significantly greater inbreeding depression than morphological traits (Falconer 8; DeRose and Roff ). Thus, in general, we expect that trade-offs between life-history and morphological traits will show changes in intercepts, whereas trade-offs involving two life-history traits will show more complex responses. Inbreeding occurs because of small population size, which might be caused by transient events as in the colonization episodes described above or be a general feature of the ecology of an organism. Estimates of effective population size in wild populations of a range of animal taxa, including both vertebrates and invertebrates, suggest that relatively small populations are common (Frankham ; Roff, table 8.). Another factor influencing rates of inbreeding is the mating system, particularly selfing rates, which are common in many species of plants (Charlesworth and Charlesworth 8; Husband and Schemske ; Husband and Barrett 8). Thus, colonization episodes are not the only scenario in which we might expect that trade-offs to fluctuate as a consequence of inbreeding. The above described changes in relationships between traits are a result of changes in mean trait values following inbreeding. Genetic architecture itself can change as a result of a population bottleneck, with the relative amounts of additive and nonadditive genetic variance either increasing or decreasing (reviewed in Roff, ch. 8). Such changes will quite possibly change covariances and therefore also change relationships between traits. Because evolutionary trajectories are governed in large part by trade-offs between traits, it is of considerable importance to understand how these relationships might change as a result of changes in genetic architecture, as might occur due to inbreeding, selection, or the coalescence of several populations. The present paper has examined one particular circumstance and shown that changes are predictable and potentially of consequence to the fitness of an organism. Additional theoretical and empirical work is necessary to judge the generality of these results. 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