CONSTRAINT ON THE EVOLUTION OF CHARACTER DISPLACEMENT
In a previous investigation (Smith and Rausher 2008), we found that there was selection for reproductive character displacement in I. hederacea when this species co-occurs with congener I. purpurea. Specifically, selection favored a decrease in anther separation by favoring a decrease in the height of the tallest anther, and an increase in the height of the shortest anther. Reduction of anther separation increases clustering of anthers around the stigma, which in turn reduces the susceptibility of plants to deleterious heterospecific pollen flow from I. purpurea (Smith and Rausher 2007, 2008). Reduced anther separation was not favored in the absence of I. purpurea.
In this study, we investigated the extent to which selection for character displacement in I. hederacea is constrained by the genetic architecture of floral traits in this species. The genetic variance–covariance structure among the six traits examined suggests that character displacement is constrained in this system. All traits are pairwise positively genetically correlated. However, for some characters, selection for character displacement favors an increase in size or height, whereas for other characters, selection favors a decrease in size or height. In particular, although the heights of the tallest and shortest anthers are strongly positively correlated (r= 0.93), selection favors a decrease in the height of the tallest anther, but an increase in the height of the shortest anther. In the face of the overall positive correlation structure for floral traits in this species, this antagonist selection is likely to result in constrained responses in many of the characters.
Analysis using method 2 indicates that genetic constraints in the form of both unequal genetic variances and nonzero genetic correlations are expected to affect the evolution of the floral traits we examined. Unequal genetic covariances cause the direction of the predicted selection response to deviate by more than 73° from the direction favored by selection. In addition, nonzero genetic covariances cause the expected response to deviate in direction from the response with all covariances equal to zero by 49°. These effects are not strictly additive, but they are also not completely compensatory: their combined effects cause the predicted response with both types of constraint to deviate by 99° from the direction of change favored by selection.
Analysis by method 1 confirms the conclusions that nonzero genetic covariances constrain the evolution of floral characters in I. hederacea; in addition it permits determination of the degree to which individual characters are constrained. By comparing the predicted response to selection with and without constraint due to genetic covariances between traits (Vc and Vnc), we found that for all but one character, the predicted response in the presence of constraint was less than half that expected in the absence of constraint; for two characters the predicted response is actually in the direction opposite to that favored by selection. For anther separation, the predicted response with constraint is only about 10% of the predicted response without constraint. Thus, the rate of evolution of increased reproductive character displacement in I. hederacea is expected to be markedly reduced from the rate one would expect based only on the magnitude of selection and the amount of genetic variation in floral traits alone. This result illustrates the principle that constraint is determined jointly by the pattern of genetic correlations and the direction of the selection gradient vector.
The pattern of constraint due to character correlations is similar to that found in other plant species. Contrary to the expectations of sex allocation theory, which predicts trade-offs in investment in male and female structures, positive genetic correlations between male and female floral traits are quite common in hermaphroditic plant species (Ashman and Majetic 2006). Genetic correlations among other floral traits (e.g., corolla and petal dimensions) are also typically quite high and positive (e.g., Connner and Via 1993; Campbell 1996; Elle 1998; Conner 2002), presumably because these traits share a common underlying developmental pathway (e.g., Hill and Lord 1989). By contrast, these floral characters are generally less strongly correlated with nonfloral traits such as leaf and stem dimensions (Meagher 1992; Conner and Via 1993; Mitchell et al. 1998; Ashman and Majetic 2006). The positive genetic correlations among floral morphological features has led several authors to suggest that these correlations are likely to constrain responses to selection that favor changes in relative shape, that is, selection for increasing some of these characters while decreasing others (Conner and Via 1993; Elle 1998). Our results provide some of the first evidence supporting this expectation. We know of only one other study to examine this question. Caruso (2004) reports that the expected response to selection in opposite directions on corolla and floral tube dimensions in Lobelia siphilitica is substantially reduced by the positive genetic correlations among these traits.
The highly constrained predicted response to selection for decreased anther separation in I. hederacea implies that despite the relatively high levels of genetic variation for short and tall anther heights individually, there is little genetic variation in the direction associated with decreasing separation. Although this may be an inherent property of these traits due to highly correlated development, it is also possible that genetic variation in this direction was higher in the past and has been reduced by selection for clustering. Anther clustering in I. hederacea appears to be a derived trait, with only I. hederacea exhibiting clustering among the six species in the clade to which it belongs (Smith and Rausher 2008). It is thus possible that in the past, before clustering evolved, that there was additional variation in this direction that was depleted as clustering evolved. If this hypothesis is true, it would predict that the genetic correlation between tall and short anther heights would be lower in the other species in this clade, a prediction that is open to experimental testing.
STATISTICAL ANALYSIS OF CONSTRAINT
We have presented two methods for assessing the effects of genetic constraints on the expected response to selection. These methods provide different information, and each has advantages and disadvantages. The primary advantage of method 2 is that it permits the partitioning of the overall genetic constraint into a component due just to nonequal genetic variances and a component due to nonzero genetic covariances, whereas method 1 only permits examining the effect of nonzero genetic covariances. This limitation occurs because although the selection gradient vector provides a direction for comparing the expected response vector in the absence of genetic covariances, it does not specify a magnitude for comparison. The magnitude of the unconstrained response (i.e., in the absence of unequal genetic variances and nonzero covariances) depends on the assumed common genetic variance of the characters, which cannot be specified nonarbitrarily.
The primary drawback of method 2 is that it does not permit a clear interpretation of how individual characters contribute to the observed directional deviations of the response vectors. For example, in the comparison of the selection gradient vector with the expected response under full constraint (i.e., the comparison represented by 1θdiff), the fifth component of 1θdiff is substantially larger than the other components (See Table 3A). This component represents the difference between two angles: (1) the angle between the axis corresponding to corolla tube length (which was used as the reference axis) and the projection of the selection gradient vector onto the plane represented by the axes corresponding to corolla tube length and height of the shortest anther; and (2) the corresponding angle for the response vector with full constraint. Because this difference could be caused by a constraint that affects either tube length or anther height or both, it is not clear which of these characters is constrained, and thus which character contributes more to the value of the fifth component of 1θdiff. Method 1 does not suffer from this limitation because it directly evaluates and compares the magnitudes of change in each character for different responses, although this comparison is limited to assessing the effect of genetic covariances. Moreover, method 1 allows comparisons of linear combinations of characters, as illustrated by the predicted responses of anther separation, which is the difference between the heights of the shortest and tallest anthers.
With method 1, deviation from equality of predicted response vectors with and without genetic covariances may be caused by facilitation as well as constraint. For example, in the two-character case in which the characters are positively correlated and selection acts to increase the value of each character, the multivariate response vector will be longer, and each character will increase to a greater extent, than if the characters were not correlated. In general, whether a deviation from the null hypothesis is due to constraint or facilitation can be determined by comparison of the response vectors. In the case reported here, none of the predicted responses with genetic covariances were greater than the predicted response without the covariances, so there was obviously no facilitation. In other cases, some characters may be constrained and others facilitated, depending on both the variance–covariance structure and the signs of the components of the selection gradient vector.
Our approaches to assessing genetic constraint differs in important ways from previous attempts. Notably, with method 1 we compare the predicted univariate response to a given pattern of selection with the predicted multivariate response using a statistical approach that takes into account uncertainty in the measurement of the variance–covariance structure. Etterson and Shaw (2001) also used this approach in examining constraints on response to selection caused by global warming in Chamaecrista fasciculata, although they do not compare the two responses statistically. Caruso (2004) also reported the relative magnitudes of both the univariate and multivariate responses to selection, although her statistical analysis compared the predicted multivariate response to the selection gradient (β) rather than to the predicted univariate response. Similarly, Mitchell et al. (1998) compared the predicted multivariate response to h2s, where h2 is the heritability of the character and s is the selection differential for that character. We believe that these latter two approaches are inappropriate for assessing the magnitude of constraint. Comparison of the multivariate response to β is equivalent to our approach only if all traits are standardized to have genetic variances equal to 1 (because then VAβ=β). However, it is not obvious how such standardization can be achieved. Standardizing the traits to have a phenotypic variance of 1 does not accomplish this objective, and failure to standardize VA to 1 means that β is not a prediction of response to selection. Similarly, the predicted univariate response h2s is not free from the influence of genetic correlations, and hence is not appropriate for comparison with the multivariate prediction to estimate constraint. In particular, the selection differential for a trait, s, is the phenotypic covariance of fitness and the trait (Lande 1979; Lande and Arnold 1983). This covariance is a composite of the effects of the covariances between each trait and fitness and between all traits and the focal trait, as reflected in the relationship s=Σ (covp)iβi, where (covp)i is the phenotypic covariance between the focal trait and trait i (for i= focal trait, covp= phenotypic variance). Because covp is partially determined by the additive genetic covariance, it is clear that s is not free from the influence of genetic covariances. Thus, h2s is not an appropriate predictor of the response to selection in the absence of genetic covariances.
Our method 2 shares features with the approach taken by Blows and colleagues (Blows and Higgie 2003; Blows et al. 2004; Blows and Hoffmann 2005) in that it focuses on the angular deviation between the selection gradient vector and the expected response vector. In their case, a constraint is inferred if the selection gradient vector is at a large angle relative to the principal axes of the G-matrix accounting for most of the character variation. In this situation, the selection gradient is essentially pointing in a direction in which there is little genetic variation to allow a response. In our analysis, we calculate the expected response vector with constraints present and determine the angle between the selection gradient and response vectors. If the angle is large, we infer constraint. One advantage of our approach is that it allows the effects of unequal genetic variances and nonzero genetic covariances to be distinguished.
Our results suggest that with reasonable sample sizes, G-matrix estimation error is small enough to allow detection of the effects of genetic constraints on the expected response to selection. One caveat to our analyses, however, is that because we are primarily interested in understanding how uncertainty associated with estimation of the G-matrix influences conclusions about constraints, we have not explicitly considered the effects of errors associated with estimating the selection gradient. One possibility for incorporating this uncertainty would be to bootstrap the selection gradient as well as the genetic variances and covariances. In our case, this does not seem to be a promising approach because the bootstrap error is much greater than the errors associated with parametric estimates of the selection gradient, and thus would lead to an overly conservative test. Other approaches will thus need to be developed. In spite of this caveat, our results do indicate that with our best estimate of the selection gradient, responses to selection on anther separation in I. hederacea are substantially constrained.