THE EVOLUTION OF TRADE-OFFS UNDER DIRECTIONAL AND CORRELATIONAL SELECTION

Authors


Abstract

Using quantitative genetic theory, we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sibling experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.

Evolutionary biological thought is firmly grounded upon the assumption that trait evolution is constrained by trade-offs (Stephens and Krebs 1986; Charnov 1989; Roff 1992, 2002; Stearns 1992; Futyuma 1998; Houston and McNamara 1999; Reznick et al. 2000; Roff and Fairbairn 2007a). From the perspective of life-history theory, a trade-off occurs when an increase in fitness due to a change in one trait is opposed by a decrease in fitness due to a concomitant change in the second trait. Trade-offs between life-history traits, such as between fecundity and survival, have been demonstrated in a large number of studies and numerous taxa in laboratory, seminatural and natural populations (e.g., Reznick 1985; Partridge and Sibley 1991; Roff 1992, 2002; Stearns 1992; Gustafsson et al. 1994; Ots and Horak 1996; Sinervo and DeNardo 1996; Zuk 1996; Preziosi and Fairbairn 1997). While neither the existence of trade-offs nor their central place in driving and constraining evolution are in doubt, there is still little understanding, from either a theoretical or empirical perspective, of how trade-offs evolve (Houle 1991; Chippindale et al. 1996; Fry 1996; Reznick et al. 2000; Roff 2002).

Phenotypic models of trait evolution typically focus upon models in which trade-offs and other bivariate relationships are represented by deterministic equations that describe the consequences of changes in one trait upon other traits and thus the overall trait means (Maynard Smith 1982; Roff 1992, 2002, 2010; Stearns 1992; Charnov 1993; Houston and McNamara 1999; Clark and Mangel 2001; Kokko 2007). In contrast, quantitative genetic theory focuses upon the population variances and covariances and uses the breeder's equation or its multivariate equivalent consisting of the product of the genetic variance–covariance matrix, G, and the vector of selection gradients, β to predict the change in trait means (inline image: Bulmer 1985; Falconer 1989; Lynch and Walsh 1997; Roff 1997, 2010). While the phenotypic models use the functional form of the trade-off, quantitative genetic models subsume this in the assumed multivariate normal distribution of traits. An important difference between these two approaches is that the quantitative genetic model does not presume the functional form to be fixed but by virtue of its formulation actually predicts that it will evolve (Roff et al. 2002, 2003). However, while this prediction is a feature of quantitative genetic theory, its importance in directing research on the evolution of trade-offs has not been generally recognized nor appreciated. To date empirical tests of the response of traits involved in trade-offs to selection on one or two of these traits have considered changes in trait means but not changes in the bivariate relationships (e.g., Falconer 1954; Sen and Robertson 1964; Bell and Burris 1973; Rutledge et al. 1973; Sheridan and Barker 1974; Nordskog 1977; Palmer and Dingle 1986; Grant and Grant 1995).

Comparisons among taxa (e.g., Tinkle et al. 1970; Roff 1982; Harvey and Read 1988), and even among populations within species (Roff et al. 2002, 2003) provide clear evidence that trade-off functions do evolve. However, these studies do not allow us to view the process or trajectory of trade-off evolution. In the present experiment we use artificial selection to quantitatively evaluate the evolution of a trade-off in response to directional and bivariate correlational selection (i.e., nonlinear selection in which two traits have an interactive effect on fitness [Gray and McKinnon 2007]). Specifically, we test a prediction of quantitative genetic theory developed by Roff et al. (2002), that trade-offs will generally evolve via changes in their intercept but not their slope. Previous analyses of selection on single traits that are negatively correlated with other traits have limited themselves to measuring changes in mean trait values rather than changes in the actual trade-off function (e.g., Nordskog and Festing 1962; Dawson 1966; Bell and Burris 1973; Dingle et al. 1988; Hoffmann and Parsons 1993; Prasad et al. 2001; Cortese et al. 2002). In the experiment reported herein, we examine the response of trait means and the trade-off functions under directional selection on a single trait and a combination of directional and correlational selection on both traits in the trade-off.

As an initial test of the quantitative genetic model of trade-off evolution (Roff et al. 2002) quantified the trade-off between dispersal capability and fecundity in the wing dimorphic cricket Gryllus firmus and compared the trade-off functions among geographically separated populations. This trade-off has been particularly well documented in G. firmus. Previous studies have revealed that: (1) micropterous (short-winged, SW) females have greatly reduced dorsolongitudinal muscles (the major flight muscles, abbreviated as DLM) relative to macropterous (long-winged, LW) females (Roff 1989; Zera et al. 1997); (2) the majority of LW females histolyse their DLM sometime during the first two weeks after their molt into the adult form (Fairbairn and Roff 1990; Stirling et al. 2001); (3) SW females show an earlier onset of reproduction and a greater reproductive output than LW females (Roff 1984, 1989, 1994); (4) The fecundity of LW females is itself negatively correlated with the condition of the DLM measured in terms of degree (complete, partial, or none) of histolysis (Roff 1989, 1994; Stirling et al. 1999), muscle mass (Roff and DeRose 2001; Roff and Gelinas 2003), and muscle color (Stirling et al. 2001); (5) Both pedigree analysis (Roff 1994; 1997; Roff and Fairbairn 2011) and selection experiments (Roff et al. 1999; Stirling et al. 2001) have demonstrated significant negative phenotypic and genetic correlations between fecundity and the condition of the DLM. Selection for increased proportion LW has also shown a correlated decrease in histolysis of the DLM and increase in the flight propensity of individuals with functional DLM (Fairbairn and Roff 1990).

Roff et al. (2002) compared three newly collected populations from Florida, South Carolina, and Bermuda, and a population that had been maintained in the laboratory for 19 years (approximately 80 generations). Assuming that the differences in proportion LW (assayed both in the field and in common laboratory conditions) reflected differences in the local selection regimes, they predicted among-population variation in the intercept of the trade-off function. In addition, because of the likelihood that natural selection in the laboratory environment had caused changes in the variances and covariances of fecundity and mass of the DLM (Roff and DeRose 2001; Roff et al. 2002), they predicted that the laboratory population might also differ with respect to the slope of the trade-off function. Both predictions were confirmed: the three field populations differed only with respect to the intercept of the trade-off function, whereas the laboratory population differed in both intercept and slope (Roff et al. 2002).

Roff et al. (2002) were only able to compare the contemporary states of divergent evolutionary trajectories and hence their results provide only indirect, qualitative support for the quantitative genetic model of trade-off evolution. Here we report an experiment designed to test the model directly and quantitatively. In this experiment we imposed positive, directional selection separately on mass of the DLM, fecundity, and an index that combined the two traits. In the latter case, directional selection on the index was predicted to result in both directional and correlational selection on the two traits making up the index. To quantitatively test the model, we measured the resulting evolutionary changes in the regression parameters of the trade-off function and compared these observed responses to a priori predictions generated from the model, as described below. Further, using estimates of genetic correlations, we predicted the direction of evolution of trait means with particular focus on the changes in trait means when selection acts on an index formed from the two traits (index selection) rather than on the traits individually.

Theory for the Changes in a Trade-Off under Directional Selection on One of the Component Traits

We have previously developed the quantitative genetic framework for trade-off evolution (Roff et al. 2002) and here present a brief summary, developing the theory as it applies to directional selection on a single trait or two traits. It should be noted here that the theory applies equally to any pairwise association, either negative (e.g., trade-offs) or positive (e.g., allometric relationships). In general, trade-off functions are described by the simple linear regression between the two traits, which can be written as

image(1)

where inline imageare the means of traits x1 and x2, respectively; rP is the phenotypic correlation between the two traits, which will be negative if the trade-off is phenotypically manifest; inline image are the standard deviations of traits x1 and x2, respectively; and ɛ is a normally distributed error term (Roff et al. 2002). The first terms in parentheses define the intercept of the regression line and the terms in the second set of parentheses define the slope. With respect to response under selection, the designation of which trait is the dependent or independent variable is governed by the trait under selection: if selection is on trait x1 then the appropriate regression is x1 on x2 whereas if selection is on trait x2 then the appropriate regression is x2 on x1 (Roff and Fairbairn 2009). When selection acts on both traits the selection of the dependent or independent variable is more arbitrary: we recommend that two sets of analyses be done in this case, one using x1 on x2 and the other using x2 on x1.

In principle, selection will change the variances and covariances (Bohren et al. 1966; Falconer 1989; Roff 1997), which would thereby change both the intercept and the slope of the trade-off function. However, artificial selection experiments over 10–15 generations generally have little effect on heritabilities and genetic correlations (Roff 1997), suggesting at least short-term stability of genetic variances and covariances even under strong selection. The slope of the trade-off function under short term selection is, therefore, expected to remain constant, except under very restrictive conditions (Roff et al. 2002), whereas the intercept will change due to changes in inline image and inline image Suppose there is directional selection for increased values of trait x1: the direct response of trait x1 is

image(2)

where inline imageis the mean of trait x1 at generation t, inline image is the heritability of trait x1, and S1 is the selection differential. The correlated response of trait x2 is

image(3)

where rA is the genetic correlation between x1 and x2. Substituting equations (2) and (3) into the intercept value from equation (1) gives

image(4)

where at+1 is the intercept at generation t+1. The signs of rP and rA are both negative and hence the intercept is increased by the direct response but decreased by the correlated responses. Thus, it is possible for selection to increase the value of the trait under selection, decrease the correlated trait but either increase or decrease the intercept.

Theory for the Changes in a Trade-Off under Directional Selection on Both of the Component Traits

If selection acts on both traits simultaneously, as in our index selection, the change in the intercept of x1 on x2 is given by the correlated responses in both traits

image(5)

where the subscript I indicates index and rA,I1, rA,I2 are the genetic correlations between the index and the two traits, x1, x2, respectively. As in the previous case, the change in the intercept is contingent on the relative values of the genetic parameters.

In the present experiment, we followed the recommendation of Baker (1974) and used a variant of Elston's weight-free selection index, I (an algorithm for independent culling levels):

image(6)

where Ii is the index value for the ith family, inline image are the trait means for this family, inline image are the grand means of all families, and inline image are the respective standard deviations among family means. Subtracting the minimum of the standardized values (which is equivalent to adding the absolute value of the minimum) sets the lower limit to zero and ensures that high index values cannot be formed by multiplying two negative values together, which would result in selecting combinations of the smallest trait values. This index produced selected families whose DLM and ovary masses, the two traits under selection (see below), were above and roughly parallel to the mean trade-off function (Fig. 1). It is clear that in this case, we would predict selection to increase the intercept.

Figure 1.

An example of index selection (generation 1 of replicate 1). ×= unselected families.

Changes in the intercepts are predicted to occur as a result of changes in the mean masses of the ovaries and DLMs. Because the genetic and phenotypic correlations between ovary and DLM mass are negative, the correlated response of the trait not under selection will be opposite in direction to the direct response of the selected trait. The responses of the ovary and DLM masses when index selection is applied depend on the genetic correlation between the index and the two component traits. These can be determined as follows. Let x1 be trait 1 distributed normally with mean μ1 and variance inline image and trait x2 a linear function of x1, inline image, where a, b are constants and ɛ is distributed normally with zero mean and variance inline image. First, we standardize trait values to give

image(7)

As in the present experiment, the index value is defined as

image(8)

where for simplicity of expression, inline image. The values of X01 and X02 are chosen such that there is a negligible probability of negative values of X1+X01 and X2+X02 (equivalent to inline image in eq. 6). After some tedious algebra the covariances between the index and the original trait values can be shown to be

image(9)

All parameters except b are positive. If the bivariate function is positive, as in an allometric function, then the covariances between the index and trait values will necessarily be positive. On the other hand, if the bivariate function represents a trade-off, the slope b will be negative and one of the covariances could be negative (it is logically impossible for both to be negative). Thus, it is possible for selection favoring an increase in the index to cause a correlated increase in both ovary mass and DLM mass, or to cause an increase in one and a decrease in the other.

To predict the directional change in the intercepts and trait means for our selection experiment, we estimated the required parameters using data from a half-sibling experiment reported in Roff and Fairbairn (2011). To match our selection protocol we estimated the genetic parameters for the wing morphs combined, rather than separately or as a fixed effect as previously reported.

The direction of change in the intercepts under single trait selection is specified by the bracketed components in equation (4), inline image, where the numeral 1 specifies the trait under selection and 2 the correlated trait. Substituting the heritabilities and correlations estimated from the half-sibling data (HS in Table 1) gives values of 0.12 and 0.14 if selection is on DLM or fecundity, respectively. Thus, we predict that in both cases the intercepts will increase under positive directional selection.

Table 1.  Heritabilities (diagonal), genetic correlations (above diagonal), and phenotypic correlations (below diagonal) from the analysis of half-sibling data from Roff and Fairbairn (2011) and full-sibling data from present experiment.
 DLMOvaryIndex
Half sibling
 DLM0.40  (0.05)−0.46  (0.08)0.94  (0.02)
 Ovary−0.53  (0.02)0.43  (0.05)−0.25  (0.10)
 Index0.88  (0.01)−0.29  (0.02)0.29  (0.04)
Replicate 1
 DLM0.37  (0.03)−0.64  (0.05)0.73  (0.08)
 Ovary−0.64  (0.03)0.42  (0.02)−0.14  (0.12)
 Index0.74  (0.02)−0.13  (0.03)0.29  (0.03)
Replicate 2
 DLM0.31  (0.03)−0.48  (0.05)0.87  (0.10)
 Ovary−0.54  (0.04)0.45  (0.04)−0.27  (0.04)
 Index0.82  (0.01)−0.23  (0.03)0.23  (0.03)

As described above, we predict that selection on the index will increase the intercept. In addition, because the genetic and phenotypic correlations between the index and DLM mass are positive while those between the index and ovary mass are negative (Table 1), positive directional selection on the index is predicted to increase the mean of DLM mass but decrease the mean ovary mass.

Materials and Methods

EXPERIMENTAL PROTOCOL

The source populationz of G. firmus was derived from 100 male and 100 female crickets collected in Florida (Gainesville) in 1998. Since that time, it has been maintained in the laboratory at a standing adult population of 100–300 individuals (20–25 generations). We tested the predictions developed in the previous sections using three positive selection regimes: selection for increased fecundity (hereafter, fecundity line), selection for increased mass of the DLM (hereafter, DLM line), and simultaneous selection for increased fecundity and mass of the DLM (hereafter, index line). Selection for increased mass of the DLM is predicted to cause a reduction in fecundity and vice versa, because of the negative genetic and phenotypic correlation between the two traits. The third selection regime combined these two directions of selection and is representative of the extreme “conflict” that a trade-off can generate, because response to this selection requires a change not only in allocation between the two focal traits but also a reallocation of resources from other traits and/or a change in acquisition (King et al. 2011a,b). Our experimental design included the three selected lines plus a control line derived from the same source populations and reared under identical conditions but with random mating. The entire experiment was replicated resulting in two sets of four lines for hypothesis testing.

Fecundity was measured by the mass of the ovaries in virgin females at 7 days after the final molt. Virgin female G. firmus produce eggs but do not lay them and ovary mass is highly correlated (r= 0.98, n= 46) with the sum of the number of eggs laid and still within the body of mated females (Roff 1994). Ovaries and DLM were dissected out of the females on the seventh day following the adult molt, dried for 24 h at 60°C and weighed to an accuracy of 0.0001 g.

Because dissection of the ovaries and DLM required sacrificing the crickets, the measured animals could not be used as parents for subsequent generations. We therefore used the variant of family selection known as sibling selection. In this method whole siblingships are selected based on the value of measured siblings that do not themselves contribute as parents (Falconer 1989). All dissections had to be accomplished before families could be selected, which took approximately 2 weeks. To ensure that we had adults of a suitable age each family consisted of two sets of cages initiated 2 weeks apart, the second set providing the parents for the subsequent generation. Each cage contained approximately 40 nymphs. To ensure synchrony within a generation, the first set of cages had to be started within a 1-week period. These requirements severely constrained the number of families that could be used: in the first replicate the mean number of families per line was 63 (range 40–93, SE = 2.6) and in the second replicate the mean number of families per line was 77 (range 57–99, SE = 2.3). In total, during the course of the experiment we dissected 14,664 crickets, which provide the basic data for this analysis.

We measured five females from each family and to minimize drift we selected the top 25 families in each generation. Five virgin males and five virgin females were taken at random from the selected families and pairs set up at random, imposing the condition that no pairs were siblings. The resulting 125 pairs were kept individually and eggs were collected from them to form the next generation. Each replicate was run for six generations (thus five rounds of selection).

For logistical reasons the two replicate experiments were run sequentially. In both replicates the three selection lines and control line were created from the same set of families.

STATISTICAL METHODS

All trait values were initially converted to standardized units by subtracting the mean of the first generation trait values and dividing by their standard deviations. In any selection experiment the first question to be answered is whether there has been a significant response to selection. Following the suggestion of Muir (1986, see also Hoffman and Parsons 1989) we used covariance to estimate the response to selection and the realized heritability, as this takes into account both correlated and uncorrelated sources of variability.

Because selection was practiced on the mean family values, we measured all responses in these units (i.e., these are our experimental units of replication) and used the grand means to estimate realized heritability. To allow the possibility of an interaction we compared the saturated model,

image(10)

where x is the response in the control line and b is the realized heritability, with the additive model,

image(11)

With one exception (fecundity line of replicate 1) the additive model gave a significantly better fit and was used to estimate the realized heritability. The standard error of b was used as an approximate estimate of the standard error of the realized heritability.

In addition to the initial estimates from the half-sibling experiment, we were also able to estimate the genetic parameters for each generation/line/replicate of the selection experiment itself using the data from our full-sibling families. This gave us a second method of predicting the direction of response of the intercepts and trait means. Previous analyses have shown that neither cage nor dam effects are significant (Roff and Fairbairn 2011) and hence these full-sibling estimates are valid estimates of the additive genetic effects. Estimates were calculated for each generation/line/replicate combination and these were used to calculate the means and standard errors of the heritabilities and correlations for each replicate.

Directional selection was imposed by truncation that should produce significant directional and quadratic selection in the single trait selected lines and both directional and correlational selection in the index lines. To verify this, we estimated the multivariate selection gradients for each generation with the models

image(12)

where w is relative fitness (0 or 1/proportion chosen to breed in each generation), X1, X2 are the standardized trait values (DLM and ovary mass, respectively), inline image are the directional selection gradients (the values from the top equation are reported here but the differences were slight), inline image are the quadratic (stabilizing or disruptive gradients), and inline image is the correlational selection gradient.

The theory developed above predicts that the intercept of the trade-off line will systematically change over the generations of selection but there will be no systematic change in the slope: thus the general statistical model is

image(13)

where x1 and x2 are the two traits, G is generation, ci are the fitted coefficients, and ɛ is the error term. We predict that for the selected lines c2 will differ significantly from zero whereas c3 will not, and neither will differ from zero in the control lines. For completeness we also considered the model

image(14)

where GF was set as a factor, allowing nonsystematic variation in the slope among generations.

The mean ovary and DLM masses are themselves made up of several components. The mean DLM mass for a family or population (when subscripts are suitably altered), inline image, is

image(15)

where PL1 is the proportion of females in the family or population with functional DLM and inline imageis the mean DLM of these females. The mean ovary mass, inline image, is given by

image(16)

where PS is the proportion of SW females in the family (population), inline imageis the mean ovary mass of these females, PL0 is the proportion of females that are LW and have nonfunctional DLM, inline image is the mean ovary mass of these females, PL1 is the proportion of females that are LW and have functional DLM, and inline image is the mean ovary mass of these females. There is a high genetic correlation between wing morph and DLM mass and between wing morph and ovary mass (Roff and Fairbairn 2011), which suggests that all components of the above equations will contribute to the net changes in DLM and ovary masses. To compare the relative contributions of the different components, we used the family data and first computed the variance accounted for by the “full” models

image(17)

where G is generation. We then computed the equations using only single components (e.g., inline image) and compared the variance accounted for by these “single component” models with the full models. Families that lacked estimates (e.g., no LW females in a family) were deleted.

Results

The phenotypic variances did not differ between starting populations for the two replicates, but the trait means did differ: the first replicate consisted of a higher proportion LW and a higher proportion of females with functional flight muscle but smaller ovaries than the second replicate (Table 2). This shift in trait combinations may have resulted from laboratory evolution between the initiation of the first and second replicates (Roff and Fairbairn 2007b)

Table 2.  Trait means in the initial generations of the two replicates.
Trait1Mean  (SE)nMean  (SE)n
  1. 1Ovary mass × 102 g; DLM mass × 10−3 g.

Ovary mass, LW9.13  (0.29)26313.93  (0.52)75
Ovary mass, SW12.10  (0.22)20214.54  (0.24)209
Ovary mass10.42  (0.20)46514.38  (0.22)284
DLM mass, LW3.37  (0.20)2631.91  (0.34)75
DLM mass, SW0.11  (0.04)2020.00  (0.00)209
DLM mass1.95  (0.14)4650.50  (0.10)284
Functional DLM, LW0.39   2630.19   75
Functional DLM0.22   4650.05   284
Proportion LW0.57   4650.26   284

All selected lines showed a significant increase over generations with the DLM masses in the DLM lines being increased by more than two standard deviations, ovary masses in the ovary lines by more than one standard deviation, and the index values in the index lines by approximately 0.4 standard deviations (Fig. 2). The control line in replicate 1 showed a small but significant increase in DLM mass and a significant decrease in the index value. However, changes in the control line were all small relative to those in the selected lines and, with the exception of the index line of replicate 2, these differences were highly statistically significant (Table 3).

Figure 2.

Changes in focal traits in replicate 1 (left column) and replicate 2 (right column). Trait selected given in panel heading. •, selected line: ○, control line. Error bars show ±1 SE.

Table 3.  Per generation response in standard deviation units of selected traits and the equivalent controls. Slopes in italics were not significantly different from zero.
TraitSlope  (SE)Diff.P1
SelectedControl
  1. 1Test for equality of slopes from ANCOVA.

DLM0.51  (0.03) 0.12  (0.03)0.38<0.0001
Ovary0.30  (0.03)−0.06  (0.03)0.35<0.0001
Index0.12  (0.03)−0.08  (0.03)0.20<0.0001
DLM0.49  (0.6)−0.02  (0.03)0.51<0.0001
Ovary0.18  (0.03)0.03  (0.03)0.15  0.0002
Index0.07  (0.02)0.05  (0.02)0.02  0.4941

As predicted, directional selection on the single traits produced significant directional selection in all generations and in some generations significant quadratic selection on the focal trait (Table 4). Directional selection on the index produced directional selection on the two component traits and significant correlational selection in two generations of replicate 1 and in five generations of replicate 2 (Table 4).

Table 4.  Multivariate linear and nonlinear selection gradients  (SD) averaged over generations. Number of generations in which selection coefficient was significant  (P < 0.05) shown beneath estimates.
LineRepβ1 DLM massβ2 Ovary massγ1 DLM massγ2 Ovary massγ12 DLM×Ovary
  1. 10.00 means <0.005, −0.00 means <−0.005.

DLM10.95  (0.19)−0.09  (0.09)0.12  (0.24)0.11(0.09)0.11  (0.15)
  60210
DLM21.13  (0.24)0.00  (0.13)1−0.00  (0.14)−0.05  (0.14)0.08  (0.29)
  60300
Fecundity1−0.03  (0.19)0.93  (0.13)0.00  (0.09)0.02  (0.27)−0.30  (0.28)
  16011
Fecundity20.04  (0.15)1.02  (0.13)0.04  (0.06)0.23  (0.07)−0.03  (0.22)
  06050
Index11.27  (0.12)1.04  (0.18)−0.07  (0.29)−0.17  (0.25)0.28  (0.54)
  66102
Index21.30  (0.30)0.83  (0.45)0.09  (0.30)−0.03  (0.06)0.63  (0.35)
  66205

The full-sibling heritability estimates were very similar to those from the half-sibling analysis (Table 1). Genetic and phenotypic correlations were also similar and statistically significantly different from zero (inline image) with the exception of the genetic correlation between the index and ovary mass in the first replicate. The signs of the genetic correlations are the same as those from the half-sibling analysis and thus the same predictions follow. Some caution has to be attached to the uncertain value of the genetic correlation between the index and ovary mass in replicate 1. The large standard error attached to this estimate results from some individual values being positive and thus in some generations the direction of correlated response could be reversed with the final outcome dependent on the relative changes among generations.

Realized heritability estimates in the first replicate were very similar to those estimated from the half-sibling and full-sibling analyses but those in replicate 2 were substantially smaller (Table 5). This is particularly true for the index selection: in the second replicate there was a substantial shift after the first generation of selection but only modest gains thereafter.

Table 5.  Estimates of realized heritability.
Lineh2  (SE)
Replicate 1Replicate 2
DLM0.40  (0.12)0.21  (0.05)
Ovary0.30  (0.03)0.15  (0.09)
Index0.23  (0.06)0.02  (0.05)

As the statistical conclusions using equation (14) did not differ from those obtained using equation (13), we present only the results using equation (13). For lines selected for increased DLM mass we used the regression of DLM mass on ovary mass and for the lines selected for increased ovary mass we used the regression of ovary mass on DLM mass. In the case of the control and index lines we examined both regressions: as the statistical conclusions are the same, we present the results only for ovary mass on DLM mass.

In all cases, as predicted, the intercept of the trade-off regression increased relative to the base population in response to selection (Fig. 3, Table 5), with the intercepts increasing about twice as much in the first as compared to the second replicate. In contrast to the significant changes in intercepts of the selected lines, there were no significant changes in the control lines or in the slopes of the regressions, with the exception of the DLM line in the second replicate (Fig. 3, Table 6).

Figure 3.

Responses (in standard deviation units of the initial population) of the intercept (left column) and slope (right column) of the trade-off estimated using family mean values in replicates 1 (top row) and 2 (bottom row). • DLM line, ○ fecundity line, ▴ index line, x control line.

Table 6.  Probabilities for the tests of changes in intercepts and slopes over generations  (G) in the selected and control lines.
ReplicateLineG1G×Xn
  1. 1 G= Probability from test for additive effect of generation on intercept, G×X= probability from test for change of slope over generations, where X is the predictor variable.

  2. 2Probability not significant after correction for multiple tests  ( = 0.05/16).

1DLM<10−160.2424400
1Ovary<10−160.1446390
1Index<10−160.4538443
2DLM2.2×10−70.0021452
2Ovary5.13×10−70.6184435
2Index1.02×10−50.9092462
1Control0.50650.03142369
2Control0.59010.2758440

As predicted from the genetic correlations (Table 1), directional selection on one trait produced a correlated negative response in the other trait (Fig. 4, Table S1). In the second replicate selection on the index resulted in an increase in DLM mass and a decrease in ovary mass, whereas in the first replicate both DLM mass and ovary mass increased (Fig. 4). With the exception of ovary mass in the index line of the second replicate, ovary and DLM masses in all selected lines differed significantly from the control lines in the last generation (all P < 0.01, using a t-test). In the fecundity lines the DLM masses decreased, whereas in the DLM lines the ovary masses decreased: thus the center of the trade-off line shifted upwards and to the left in the fecundity lines whereas in the DLM lines it shifted downwards and to the right (Fig. 4). Most of the shift in the index line was accomplished by a shift in DLM mass with a relatively small increase in ovary mass in replicate 1 and an approximately equivalent decrease in ovary mass in replicate 2 (Fig. 4). These opposite responses in ovary mass in the two index lines are consistent with the estimated genetic correlations between the index and ovary mass (Table 1).

Figure 4.

Bivariate plot of responses (in standard deviation units of initial population ±1 SE) of DLM and ovary masses in the selected and control lines. Left panel: replicate 1, right panel: replicate 2.

The relative contributions of the components making up the mean DLM and ovary masses varied with the type of selection and replicate (Table 7). Changes in mean DLM mass in all selected lines was accomplished by changes in the proportion of females with functional DLM (PL1). In the DLM and index lines there was also a relatively large contribution of the mean DLM of these females (inline image), whereas in the fecundity lines there was little contribution. Variation in ovary masses in all lines was strongly correlated with mean ovary masses in the three categories of females (inline image). The proportion of LW females with functional flight muscle (PL1) also contributed in all lines but the proportions in the other two categories (PS, PL0) varied between replicates, replicate 1 lines showing little contribution but replicate 2 lines a much higher effect (Table 7).

Table 7.  Comparison of contribution  (% variance explained) of traits to the mean DLM and ovary masses within families.
LineRepFullDLMOvary
PL1inline imagenFullPSinline imagePL0inline imagePL1inline imagen
  1. Full: inline image

  2. PL1: Proportion of females in a family with functional DLM.

  3. inline image: Mean DLM of above females.

  4. n: Number of families.

  5. PS: Proportion of SW females in a family, inline image: Mean ovary mass of above females.

  6. PL0: Proportion of females that are LW and have nonfunctional DLM.

  7. inline image: Mean ovary mass of above females.

  8. PL1: Proportion of females that are LW and have functional DLM.

  9. inline image: Mean ovary mass of above females.

DLM10.780.690.364821.000.050.400.070.510.250.38236
DLM20.930.790.221021.000.220.360.040.400.210.5653
Fecundity10.740.620.023601.000.080.410.060.520.220.44228
Fecundity20.660.590.05471.000.260.790.140.640.140.3832
Index10.760.660.274791.000.050.320.060.500.230.37277
Index20.890.660.18990.990.100.470.140.440.260.1754

Discussion

Quantitative genetic theory predicts that selection on a trade-off will usually change the intercept but not the slope of the relationship. The present experiment is the first to experimentally validate this prediction. As predicted, the intercept increased in all of our selected lines, whereas in the control lines no change was detected. Also as predicted, in five of the six selected lines, there was no significant change in slope in response to selection on the traits involved in the trade-off. These results support the general prediction that short-term evolutionary trajectories of trade-offs will be dominated by shifts up or down in the trade-off line, with little change in the slope.

While the prediction that the intercept but not the slope is a general prediction derived from quantitative genetic theory, how animals may actually accomplish this shift is not obvious. A general model for trade-offs is that they are the outcome of the allocation of a limiting resource. This model, typically referred to as the Y model, has received considerable theoretical attention (James 1974; Riska 1986; van Noordwijk and de Jong 1986; Houle 1991; Reznick et al. 2000; Angiletta 2003; Roff and Fairbairn 2007a) but little empirical study. Recent tests of this model using G. firmus and the same trade-off between flight capability and reproduction as in the present study, found general support for the predictions of the Y model (King et al. 2011a) and significant heritabilities for both acquisition and allocation (King et al. 2011b).

We surmise that the shifts in the intercept of the trade-off line are accomplished through evolutionary changes in patterns of acquisition and allocation. For example, selection on either ovary or DLM mass directly favors a change in the pattern of allocation from ovaries to flight muscles or the reverse. However, rather than just sliding along the original trade-off line, the selected populations jump to a new trade-off relationship with a higher intercept. The evolutionary response is an increase in ovary size for a given DLM mass, not simply larger ovaries and smaller DLM. This implies increased allocation to both the ovaries and the DLM, in other words, increased acquisition for both traits involved in the trade-off.

Index selection favors simultaneous increases in both ovary and DLM mass, and so favors an increase in total acquisition for the trade-off without any selection for moving along the original trade-off line. The heritability of the index was lower than either component trait and thus the response to selection was correspondingly smaller. Further, the genetic correlation between the index and the component traits dictated that while both showed correlated responses their direction of response was, in one case, in opposite directions. Despite the reduced response to selection, both index lines showed significant increases in the intercepts, signifying significant increases in trade-off acquisition.

Because of the dimorphic variation in wing morph, changes in allocation within the trade-off can occur via shifts in the proportions of LW and SW morphs, or through changes in the mean ovary or DLM masses within each wing morph. For example, allocation to flight capability could increase through an increase in proportion LW, an increase in mean DLM mass within LW individuals, or both. Similarly, allocation to reproduction could increase by in increase in the proportion SW, an increase in mean ovary mass within SW and LW individuals, or both. High genetic correlations between the liability of wing morph, DLM mass, and ovary mass indicate that changes in both proportion LW and the mean trait values within wing morphs are to be expected (Fairbairn and Roff 1990; Roff et al. 1999; Roff and Fairbairn 2011). The observed shifts were consistent with previously measured genetic correlations (Roff and Fairbairn 2011) and those estimated from the full siblings of the present experiment: selection produced changes in both the proportion LW and the mean values of the traits within the three morph categories (SW, LW with nonfunctional DLM, LW with functional DLM), but which of these components contributed most to the direct or correlated response varied with replicate and type of selection.

The index selection practiced in the present experiment favored the product of the trait values and our estimates of the selection gradients confirmed significant correlational selection in the index lines. Because neither directional nor correlational selection would be expected to alter the phenotypic variances and covariances of the two component traits within the time frame of the experiment, no change in slope of the trade-off function was expected. While the correlational selection did produce an elevation of the trade-off line, importantly, this does not mean that selection will necessarily favor a simultaneous increase in the mean masses of both ovaries and DLMs. The population response depends on the genetic correlation between the index and the two component traits. As demonstrated by equation (9) one of the covariances between the index and a component trait could be negative. The empirical estimates indicate that the covariance between the index and DLM mass is positive and, as predicted, in both replicates mean DLM mass increased in response to selection on the index. In contrast, the covariance between the index and ovary mass was negative in replicate 2, and ovary mass decreased in response to selection on the index. In replicate 1 the covariance between the index and ovary mass varied from generation to generation, but the net effect was a positive response of ovary mass to selection on the Index. These results illustrate that response to correlational selection is not intuitively obvious: selection for correlated evolution of two traits may produce counterproductive responses if the underlying covariances are not aligned with the direction of selection.

While there is abundant evidence that the G matrix can evolve (Roff 1997; Arnold et al. 2008), results from artificial selection experiments have shown that the assumption of a constant G matrix is reasonable over 10–15 generations (Roff 1997). Theoretical studies suggest that in the longer term selection can alter the G matrix, causing it to become aligned in the direction of selection (Lande 1980; Arnold and Wade 1984; Cheverud 1984, 1996; Wagner 1996; Jones et al. 2003, 2004; Blows et al. 2004; Jones 2004; Blows and Hoffman 2005; McGlothlin et al. 2005). In this regard, nonadditive effects may play an important role in increasing additive genetic variance (Pavlicev et al. 2008, 2010).

An understanding of the evolution of trade-offs is fundamental to a general understanding of the evolution of suites of correlated traits. The results presented in this article demonstrate that quantitative genetic theory can predict how trade-offs will evolve in the short term when one or both traits are subject to directional and correlational selection. The latter is likely to be particularly relevant in natural populations were selection is unlikely to act on single traits in isolation. Fitness traits are inherently multiplicative and composed of trade-offs (e.g., the trade-off between egg size and egg number contributes to the multiplicative fitness trait, clutch mass, or reproductive effort). Allometric relationships among morphological, behavioral, and physiological traits also imply correlational selection and trade-offs between different components influencing function (e.g., Peters 1983; Calder 1984; Lawler et al. 2005; Calsbeek and Irschick 2007). Our experiment has demonstrated that the response of correlated traits to selection can be counterintuitive, but is ultimately predicable, given a priori knowledge of the quantitative genetic architecture of the component traits.


Associate Editor: G. Marroig

ACKNOWLEDGMENTS

We are grateful for the technical assistance of M. Walsh, E. King, and I. Saglam in the collection of data used in the present analysis, and for the constructive comments of two anonymous reviewers. This research was supported by National Science Foundation grant DEB044510 to DJF and DAR.

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