A MULTIVARIATE ANALYSIS OF GENETIC VARIATION IN THE ADVERTISEMENT CALL OF THE GRAY TREEFROG, HYLA VERSICOLOR

Authors


Abstract

Genetic variation in sexual displays is crucial for an evolutionary response to sexual selection, but can be eroded by strong selection. Identifying the magnitude and sources of additive genetic variance underlying sexually selected traits is thus an important issue in evolutionary biology. We conducted a quantitative genetics experiment with gray treefrogs (Hyla versicolor) to investigate genetic variances and covariances among features of the male advertisement call. Two energetically expensive traits showed significant genetic variation: call duration, expressed as number of pulses per call, and call rate, represented by its inverse, call period. These two properties also showed significant genetic covariance, consistent with an energetic constraint to call production. Combining the genetic variance–covariance matrix with previous estimates of directional sexual selection imposed by female preferences predicts a limited increase in call duration but no change in call rate despite significant selection on both traits. In addition to constraints imposed by the genetic covariance structure, an evolutionary response to sexual selection may also be limited by high energetic costs of long-duration calls and by preferences that act most strongly against very short-duration calls. Meanwhile, the persistence of these preferences could be explained by costs of mating with males with especially unattractive calls.

Patterns of genetic variation underlying secondary sexual traits are central to our understanding of sexual selection. Genetic variation is required for traits to show an evolutionary change in response to selection (Falconer and Mackay 1996; Roff 1997) and can be important for the evolution and maintenance of mating preferences (Pomiankowski et al. 1991). However, sustained sexual selection is predicted to erode additive genetic variance in sexually preferred traits, thereby halting the evolution of these traits and neutralizing the benefits of preferring them (the “paradox of the lek”: Borgia 1979; Taylor and Williams 1982; Kirkpatrick and Ryan 1991). Additive genetic variation has nonetheless been documented in a variety of traits under sexual selection (Pomiankowski and Møller 1995; Chenoweth and McGuigan 2010). Several mechanisms have been proposed to explain this apparent contradiction (reviewed in Radwan 2008). We focus on the effect of genetic covariances among a suite of traits on the potential for a response to sexual selection. Even if individual traits show significant heritability, genetic covariances can limit genetic variation for the combination of trait values favored by multivariate sexual selection (Blows and Hoffmann 2005; Walsh and Blows 2009).

Although the structure of genetic variation within and among traits can influence the rate and direction of evolution (Lande 1979), these effects cannot be predicted solely from genetic correlations or covariances (Conner 2012). Rather, it is necessary to examine the genetic variance–covariance matrix, G, with respect to multivariate selection (Lande 1979; Hansen and Houle 2008; Agrawal and Stinchcombe 2009). Moreover, our understanding of the extent to which G matrix structure may hamper, facilitate, or shape sexual selection is limited because relatively few studies have combined estimates of G with measures of multivariate sexual selection to investigate the potential for evolution (e.g., Brooks and Endler 2001; Blows et al. 2004). Here, we estimate the genetic (co)variance matrix for the energetically costly, sexually selected display of an anuran amphibian and investigate its effect on the potential for evolution under multivariate sexual selection via female choice.

Anurans have been popular model organisms for studies of sexual selection, and eastern gray treefrogs, Hyla versicolor, are a particularly well-studied system (Gerhardt and Huber 2002). The advertisement calls of male H. versicolor consist of a simple pulse train (trill), with considerable variation among males in call duration, call rate, and dominant frequency (Gerhardt 1991; Runkle et al. 1994; Gerhardt et al. 1996). Repeatability has been reported in each of these call parameters (Gerhardt 1991; Gerhardt et al. 1996), suggesting that male call traits can provide a consistent target for sexual selection. Dominant frequency depends strongly on male body size (Gerhardt 2005), although temporal call properties show little relationship with size (Hausfater et al. 1990). Some variation in call duration and call rate reflects plasticity in response to social environment, as male gray treefrogs typically increase call duration and decrease call rate in response to increases in chorus density and playback of conspecific calls (Wells and Taigen 1986; Schwartz et al. 2002) and increase call duration without necessarily changing call rate in response to intense, close-range vocal competition (Reichert and Gerhardt 2012). Nonetheless, repeatable variation, particularly in call duration, has been documented in samples of calling males across nights (Sullivan and Hinshaw 1992; Gerhardt et al. 1996) and across a range of chorus densities (Schwartz et al. 2002).

Female gray treefrogs prefer long-duration advertisement calls to short-duration calls as well as calls delivered at faster rates (Gerhardt et al. 1996; Gerhardt et al. 2000; Gerhardt and Brooks 2009), resulting in an overall preference for higher calling effort. Preferences for long calls and high calling effort have been demonstrated in laboratory phonotaxis tests (e.g., Gerhardt et al. 1996, 2000) as well as in an investigation of female choices among males in a seminatural chorus (Schwartz et al. 2001). For a given calling effort, females also prefer long-duration calls produced at a slower rate to short-duration calls at faster rate (Klump and Gerhardt 1987; Gerhardt et al. 1996). However, the directional preferences for calls of long duration and high call rate weaken at higher values, suggesting diminishing benefits of further elaboration of these properties (Gerhardt et al. 1996; Gerhardt and Brooks 2009). Genetic benefits may help to explain the female preference for long-duration calls: larval offspring of males with long-duration calls showed higher growth and viability relative to offspring of males with short-duration calls (Welch et al. 1998; Welch 2003). Female preferences appear to exert primarily stabilizing selection on dominant frequency (Gerhardt 2005; Gerhardt and Brooks 2009).

To investigate the relationship between sexual selection and multivariate genetic variation in H. versicolor, we examined the genetic variance and covariance of three features of the advertisement call. We used a full-sib/half-sib breeding design and recorded the advertisement calls of males in the parental generation and their offspring, which were reared in the laboratory under controlled acoustic conditions. We then combined our quantitative genetic results with published estimates of directional selection gradients to estimate the potential for a multivariate response to sexual selection and to test the degree to which a response to selection may be influenced by the genetic covariance structure.

Methods

ADVERTISEMENT CALL PROPERTIES AND RECORDINGS

In gray treefrogs, the duration of the advertisement call depends on the number of pulses (hereafter, pulse number) and repetition rate of pulses (Fig. 1A). Because pulse repetition is highly dependent on temperature (Gerhardt 1978), we analyzed pulse number as a correlate of call duration that shows much less influence of temperature. We assessed the rate at which calls are produced by measuring call period, which is the time from the beginning of one call to the beginning of the next (Fig. 1B). We analyzed call period rather than its inverse, call rate, both to facilitate comparison with previous work (Gerhardt and Brooks 2009) and because call period shows a more linear relationship with pulse number. Gray treefrog calls include two main spectral peaks—the fundamental frequency and dominant frequency (i.e., which contains the greatest acoustic energy), which is invariably the second harmonic of the fundamental frequency (Gerhardt 2005).

Figure 1.

Acoustic properties of advertisement calls of Hyla versicolor. (A) Oscillogram (amplitude vs. time display) of a single typical advertisement call. We assessed the number of pulses per call (21 in this example) as a correlate of call duration that is less dependent on temperature (see text). (B) Oscillogram of two successive advertisement calls. The line below indicates the call period, which we measured in seconds. The reciprocal of call period is the call rate, usually expressed as calls per minute.

Because male gray treefrogs adjust temporal properties of their calls in response to male spacing and chorus size (Wells and Taigen 1986) as well as individual call properties of neighbors (A. M. Welch and M. S. Reichert, unpubl. ms.), we controlled these features of the social environment to record each male under conditions that were as similar as possible. We accomplished this in two stages. First, males were stimulated to call in a seminatural chorus within a large, screen-enclosed artificial pond. Once a frog was calling consistently in the artificial pond, he was moved to a semianechoic chamber located a few meters away for recording. Within the chamber, an array of six speakers played synthetic H. versicolor calls (see Table S1 for stimulus properties), providing a simulated social environment under which we recorded each male's calls. These procedures are detailed in Supporting Information: Methods.

Calls produced in the semianechoic chamber were digitally recorded (Marantz PMD670, PMD671, or PMD660; Mahwah, NJ) remotely via a microphone (Sennheiser, ME67 with K6 powering module; Wedemark, Germany) suspended approximately 1 m above the frog. The frog was then returned to the artificial pond and allowed to continue calling. We attempted to record at least 25 calls per male in a single session, and we did not analyze recordings with fewer than 10 calls. When fewer than 25 calls were recorded, the frog was recorded again later if possible. We measured pulse number, call period, and dominant frequency of each call (Raven Pro 1.2.1, Cornell Lab of Ornithology). Occasionally, a frog stopped calling during a recording but resumed within 10 min. To exclude these extended pauses, we excluded from analysis calls for which call period exceeded seven times the average call period for the other calls in the recording. This threshold was optimized to remove large breaks in calling activity while retaining typical variation in call period.

PARENTAL GENERATION MALES AND ARTIFICIAL FERTILIZATIONS

We collected adult male H. versicolor from a natural population at the Baskett Wildlife Area, Boone County, Missouri, between April 18 and June 7, 2005 and between May 9 and June 15, 2006. Males judged to have produced relatively long- or short-duration calls, in comparison with their neighbors, were collected and returned to the laboratory for further testing. On subsequent nights, we recorded each male's calls under consistent acoustic conditions to control for the effects of social environment on call properties (described above and in Supporting Information: Methods). The distribution of pulse number among the 121 males that were recorded (Fig. S1) approximated the distribution in the source population (Gerhardt and Brooks 2009). Based on these recordings, 24 males were selected for breeding each year, 12 of which produced longer than average (high pulse number) calls and 12 that produced shorter than average (low pulse number) calls, for a total of 48 sires across two cohorts. Call properties of selected and unselected parental generation males are summarized in Table S2.

We generated maternal half-sibships, in which males selected as long-callers and those selected as short-callers were crossed with the same female, thus controlling for maternal genetic and nongenetic contributions to offspring. Gravid females were collected from the same population as the males on June 6 and 14, 2005 and June 13 and 29, 2006 (three females per night with the exception of two females on the final date). Artificial fertilizations, which allow unambiguous assignment of paternity, were performed following procedures described previously (Doty and Welch 2001; Welch 2003), except that testes were crushed in 10% modified Holtfreter's solution (Armstrong et al. 1989) rather than pond water. On the night of collection, we fertilized the ova of each female in four separate dishes with sperm from four different males, two with long calls and two with short calls, except on June 29, 2006, when six males (three with long and three with short calls) were assigned to each female. We assigned a different set of males to each female to generate 48 full-sibships nested within 11 maternal half-sibships between two years. Within 12 h of fertilization, embryos from each full-sibship were distributed among two to six separate dishes (hexagonal polystyrene weigh dishes, 13.2 cm diameter × 3.2 cm high) to keep embryo densities similar among sibships and to reduce the effects of sharing a common environment within sibships. Embryos were maintained in 10% modified Holtfreter's solution.

REARING AND RECORDING CALLS OF OFFSPRING

Offspring resulting from artificial crosses were reared individually to maturity under controlled laboratory conditions. Approximately six months after metamorphosis, we sorted juveniles within each family by body mass and then assigned them alternately to two diet treatments such that equal numbers from each family were assigned to each treatment while keeping body mass similar between the two treatment groups. At each feeding, food type and amount were held constant across treatments, but frogs in the low-diet treatment received fewer feedings per week than did those in the high-diet treatment. Details of the rearing procedures are provided in Supporting Information: Methods.

Advertisement calls were recorded from reproductively mature male offspring at approximately two years of age under consistent acoustic conditions as described above and in Supporting Information: Methods. We recorded 178 offspring from the 2005 cohort between May 4 and July 15, 2007 and 158 offspring from the 2006 cohort between May 13 and July 30, 2008. We recorded at least 25 consecutive calls from all but six of these frogs. All procedures, from rearing tadpoles through recording and analyzing sons’ calls, were performed blind with respect to frogs’ parentage.

QUANTITATIVE GENETIC ANALYSIS

Genetic variances and covariances for three call features—pulse number, call period, and dominant frequency—were estimated using a multivariate mixed effects model. We used an animal model approach (Lynch and Walsh 1998) by fitting breeding values for individuals in both generations, including selected and unselected males in the parental generation, dams (also in the parental generation), and offspring. For offspring, maternal identity was fitted as an additional random effect and dietary treatment was included as a fixed effect. Mixed effects models that make use of data from all individuals available for selection have been shown to be unbiased by selection (e.g., Sorenson and Kennedy 1984; Gianola and Fernando 1986; Gianola et al. 1989; van der Werf and de Boer 1990; Schenkel and Schaeffer 2000), including stabilizing and disruptive selection (Gianola et al. 1988). Thus, to help avoid bias due to selection of sires (Robertson 1977), our analysis included all males from the parental generation for which we have phenotype data (i.e., selected as well as unselected males; see Table S2). The distribution of call phenotypes from the parental generation appears to reflect an unbiased sample of the source population (Fig. S1). Because our breeding design nested sires within dams, variance associated with dominance or other nonadditive genetic effects is not partitioned with the maternal effect and may inflate our estimates of additive genetic variances and covariances. The values we report should thus be regarded as upper estimates (Falconer and Mackay 1996; Wilson et al. 2009).

Pulse number and call period were log-transformed, which improved the equality of error variances and the linearity of relationships among variables; dominant frequency was already normally distributed, so was not transformed. Variables were then standardized to mean of 0 and SD of 1. To account for differences in trait means and variances between generations and cohorts, data from each of the two cohorts within each generation were standardized separately. Thus, the analysis provides estimates of genetic variances and covariances for trait values considered relative to other individuals tested in the same year (years 1 and 2: field-collected parental generation; years 3 and 4: laboratory-reared offspring generation).

We analyzed our multivariate animal model within a Bayesian framework (building from the univariate example in Waldmann 2009; see also Damgaard 2007 and Gorjanc 2010). Bayesian inference of quantitative genetic parameters can be particularly appropriate for relatively small datasets, providing more accurate information about the uncertainty surrounding parameter estimates (O'Hara et al. 2008). The model was conducted using OpenBUGS software (version 3.2.2; Lunn et al. 2009) run within the R statistical package using the R2WinBUGS package (Sturtz et al. 2005). We used an inverse Wishart distribution for the prior for the error covariance matrix and scaled inverse Wishart priors for the additive and maternal covariance matrices (Gelman and Hill 2007). Parameter estimates were relatively insensitive to variation in priors across a realistic range of values. Three chains were run for 150,000 iterations; the first 50,000 iterations discarded and every 200th iteration thereafter sampled, resulting in 1500 sampled iterations (500 from each of three chains) from which parameters were estimated (see Supporting Information for code for the Bayesian model and subsequent analyses).

Heritabilities and genetic correlations were calculated from the matrix of genetic variances and covariances, G, and phenotypic correlations were calculated from the phenotypic (co)variance matrix, P (Lynch and Walsh 1998). Correlations were considered to be significant if their 95% credible intervals did not include zero. Because the posterior estimates of the variance components, and hence heritability, are constrained to be positive, they cannot be used to assess statistical significance. Instead, for each of the three call parameters, the statistical support for the sire variance component was tested by comparing deviance information criterion (DIC) values between univariate models with and without the additive variance component (Burnham and Anderson 1998; Spiegelhalter et al. 2002). Univariate models included maternal identity as a random effect but did not include the fixed effect of diet due to poor convergence of the model; we note that diet had no discernable effect on any of the call parameters in the multivariate analysis (see Results) or in preliminary univariate analyses. We also estimated heritability from parent–offspring regression as twice the slope of the regression of mean trait values of the sons of each sire against sires’ trait values (Falconer and Mackay 1996). These heritability estimates are unbiased by maternal and nonadditive genetic effects (Falconer and Mackay 1996; Lynch and Walsh 1998) and thus offer an important comparison with our animal model results. Coefficients of phenotypic and additive genetic variation (math formula and math formula, respectively; Houle 1992; Garcia-Gonzalez et al. 2012) were calculated using untransformed phenotypic data from the offspring generation and, for CVA, estimates of h2 from parent–offspring regressions.

ESTIMATING RESPONSE TO SELECTION

To investigate the influence of the genetic covariance structure on the predicted response to sexual selection imposed by female mating preferences, we combined our data with existing estimates of directional selection on advertisement calls in gray treefrogs from the same natural population that was used in the present study. Gerhardt and Brooks (2009) tested preferences of female H. versicolor using synthetically generated stimuli representing the range of variation in each of five call parameters; trait correlations were decoupled by randomly selecting the value for each call parameter used for each stimulus. This experimental design allowed estimation of selection gradients uninfluenced by correlations among call parameters. Because we measured only three of the five call parameters used in the previous study, we have disregarded the selection gradients for the other two traits (pulse rate and relative amplitude of the two frequency peaks), which were not significantly different from zero and were smaller than the selection gradients for our focal traits (Gerhardt and Brooks 2009). Disregarding these selection gradients is equivalent to assuming that the two disregarded traits show zero genetic covariance with the three focal traits. In support of this assumption, relative amplitude of the two frequency peaks is phenotypically uncorrelated with any of the focal traits (H. C. Gerhardt, unpubl. ms.); pulse rate is weakly correlated with pulse number and call period, reflecting the effects of temperature on each trait (Gayou 1984). More importantly, the low magnitude of the selection gradients on the disregarded call parameters (Table 2 in Gerhardt and Brooks 2009) indicates minimal selection on these parameters. Including them would thus have little effect on the multivariate response to selection, even if the genetic covariances were appreciable.

The directional selection gradients on pulse number, call period, and dominant frequency (β, Table 1) were used in combination with our estimate of G to investigate the potential for the genetic covariance structure to influence the response to multivariate sexual selection. The multivariate breeder's equation, Δz = (Lande 1979), was used to predict the response to sexual selection acting jointly on these three traits. For comparison, we also estimated the effect of sexual selection acting directly on each trait (i.e., in the absence of genetic correlations) as Δzi = Giiβi = VAiβi (Lande 1979; Arnold and Wade 1984; Conner and Via 1992; Agrawal and Stinchcombe 2009). The orientation of G relative to the direction of the sexual selection vector, β, was used to examine the extent to which multivariate genetic variation is available to selection (after Blows et al. 2004; Hine et al. 2004; see also Conner 2012). The angle between β and each eigenvector of G was calculated; the first eigenvector, gmax, represents the axis of G with the most variance. The axis of genetic variation most closely aligned with β was estimated by projecting β onto a subspace of G consisting of the first two eigenvectors (Blows et al. 2004); the angle between this axis and β was then calculated. Each parameter was estimated for each of the 1500 sampled iterations to generate 95% credible intervals for parameter estimates.

Table 1. Genetic variance–covariance matrix (G) and predicted response to selection (Δz) for three call parameters, pulse number (PN), call period (CP), and dominant frequency (DF). Data were log-transformed (except for dominant frequency) and then standardized to mean of 0 and SD of 1 within each cohort for each generation. Genetic variances and covariances are shown in bold; genetic correlations are below the diagonal and associated phenotypic correlations are shown in italics. Values reported are means from 1500 iterations, with 95% credible intervals in brackets. Predicted response to multivariate sexual selection (Δz) was estimated using a vector of selection gradients (β) for each call parameter imposed by female mating preferences (from Gerhardt and Brooks 2009), and indicates the expected change in phenotype in SDs. The predicted effects of sexual selection acting directly on each trait, with no influence from genetic covariances (Δzi = Giiβi), are included for comparison
 G   
 PNCPDFmath formulaΔzΔzi
PN0.37 [0.170.61]0.16 [0.010.33]0.05 [–0.050.19]0.0650.018 [0.006–0.031]0.024 [0.011–0.039]
CP0.52 [0.06–0.84] 0.25 [0.060.49]0.02 [–0.080.12]–0.047–0.001 [–0.012–0.008]–0.012 [–0.023 to –0.003]
0.51 [0.42–0.59]
DF0.28 [–0.57–0.85]0.11 [–0.66–0.76]0.10 [0.000.31]0.0220.005 [–0.001–0.014]0.002 [0.000–0.007]
0.17 [0.050.29]0.19 [0.080.30]

Results

GENETIC VARIANCE–COVARIANCE MATRIX

The genetic variance–covariance matrix indicates appreciable genetic variation for pulse number and call period (Table 1). Removing the additive component from the model led to a much poorer fit (ΔDIC > 60; Table S3), suggesting that heritable variation is an important source of multivariate variability in the advertisement call of H. versicolor. The multivariate animal model yielded moderate heritability estimates for pulse number and call period, with moderate credible intervals (Table 2). Comparison of similar univariate models with and without the additive variance component suggests that heritable variation is important for both pulse number and call period (ΔDIC = 61 and 28, respectively) but not for dominant frequency (ΔDIC = 3). Heritability estimates from the univariate animal model and parent–offspring regression were of similar magnitude to those from the multivariate animal model (Table 2).

Table 2. Basic statistics and heritability estimates for traits examined in this study. Means, SDs, and coefficients of phenotypic and additive genetic variation (CVP and CVA, respectively) were calculated using untransformed phenotypic data from the offspring generation and, for CVA, estimates of h2 from parent–offspring regressions (see text for formulas). Heritability estimates calculated from the multivariate and univariate animal model (h2AM-M and h2AM-U, respectively) are shown with credible intervals in brackets, whereas those obtained from parent–offspring regressions (h2PO) are shown with SEs in parentheses and an asterisk to represent statistical significance (*P < 0.005)
VariableMean ± SDCVPCVah2AM-Mh2AM-Uh2PO
Pulse number16.5 ± 3.80.2310.1480.35 [0.16–0.54]0.35 [0.17–0.55]0.41 (0.14)*
Call period (sec)7.47 ± 5.970.8000.3650.23 [0.07–0.44]0.21 [0.03–0.42]0.21 (0.15)
Dominant frequency (kHz)2.25 ± 0.150.0670.0110.09 [0.00–0.29]0.06 [0.00–0.27]0.03 (0.20)

Pulse number and call period showed a significant positive genetic correlation of similar magnitude to their phenotypic correlation (Table 1; Fig. 2), indicating a genetic basis to the negative phenotypic relationship between call duration and calling rate. The genetic correlations of dominant frequency with call period and pulse number were not significant (Table 1; Fig. 2). The first eigenvector of the genetic variance–covariance matrix, gmax, accounted for the majority of the genetic variation and was heavily loaded by pulse number and call period, reflecting their positive genetic correlation (Table 3). This eigenvector is oriented well away from the vector of standardized directional selection gradients, β, with a relatively narrow credible interval (Table 3), suggesting that much of the multivariate genetic variance is largely unavailable to directional sexual selection. The estimates for the second and third eigenvectors lack precision as indicated by the wide credible intervals (Table 3). The axis of genetic variation most closely aligned with the direction of sexual selection, determined by projecting β onto gmax and g2 together, is estimated to be oriented 23.8° from β, with a wide 95% credible interval (1.0°–65.6°).

Table 3. Eigenanalysis of the genetic variance–covariance matrix (G). Eigenvectors of mean G, with factor loadings and eigenvalues. Traits are abbreviated as: pulse number (PN), call period (CP), and dominant frequency (DF). The orientation of each eigenvector from the vector of directional selection gradients, β, is also shown, with 95% credible interval (see text for details)
 gmaxg2g3
PN0.820.500.28
CP0.55–0.81–0.18
DF0.140.31–0.94
Eigenvalue0.680.200.12
Angle70.5°39.5°69.2°
 [40.2°–110.2°][9.7°–101.3°][24.4°–107.3°]
Figure 2.

Phenotypic and genetic correlations. Phenotypic correlations are shown between (A) the number of pulses per call and call period and (B) pulse number and dominant frequency. Each datapoint represents one individual from the offspring generation. Genetic correlations are illustrated by showing the relationship between mean phenotypes of the sons of each sire for (C) pulse number and call period and (D) pulse number and dominant frequency, with error bars indicating ± 1 SE. Untransformed data are shown, with pulse number and call period on a logarithmic scale and dominant frequency on a linear scale.

Dietary regimen did not have a significant effect on any of the call variables (Table S4). Removing diet from the analysis resulted in very similar estimates of all parameters in the model and an equivalent model fit.

ESTIMATED RESPONSE TO SELECTION

The predicted response to multivariate selection, Δz, indicates that pulse number is expected to increase by 1.8% of a phenotypic SD under directional sexual selection (Table 1). Among the three call parameters, only pulse number has a predicted response to selection significantly different from zero (i.e., credible interval not overlapping zero; Table 1). By contrast, the predicted response to selection acting directly on each trait, estimated apart from the influence of genetic covariances, was significantly different from zero for call period as well as pulse number (Δzi in Table 1). For both of these traits, the predicted response to direct selection, Δzi, was distinctly larger than the predicted multivariate response, Δz, indicating that genetic covariances considerably limit the expected response to sexual selection.

Discussion

Our investigation of multivariate genetic variation in three features of the advertisement call of male gray treefrogs, H. versicolor, revealed significant genetic variation in pulse number and call period as well as significant genetic covariance between these two traits. This genetic correlation is indicative of a negative genetic relationship between call duration, which is measured as pulse number, and call rate, which is the inverse of call period. Thus, although call duration and call rate are socially plastic traits (Schwartz et al. 2002), our results indicate that some genotypes produce longer, slower calls than others in a given social environment. Because the ratio of call duration to call period determines aerobic energetic expenditure (Wells and Taigen 1986), genotypes that produce long calls may be unable to sustain fast call rates and vice versa. Consequently, the genetic correlation between call duration and call period may reflect an energetic constraint on call production. The significant genetic covariance between pulse number and call period is reflected in gmax, the first eigenvector of G, indicating that the axis of multivariate variation most available to selection primarily represents variation in the allocation of calling effort to longer, slower calls versus shorter, faster calls.

Because anuran calling is energetically expensive (e.g., Wells and Taigen 1986; Prestwich 1994), increased resource availability could allow greater investment in calling, reflecting condition-dependent trait expression (e.g., Zahavi 1977; Iwasa et al. 1991; Rowe and Houle 1996). To the contrary, we found no effect of dietary treatments on the measured properties of the male advertisement call. The lack of a diet effect could be explained if none of the food levels was limiting. In support of this explanation, body size did not differ between the two dietary treatments for either male or female offspring (Welch et al., pers. obs.). Additional dietary resources may have been allocated not to growth or higher effort calls, but rather to investment in calling over longer time periods. In other acoustically signaling species, access to food can influence calling over a number of nights without necessarily altering call characteristics on a finer temporal scale (Murphy 1994; Holzer et al. 2003). Thus, although our study provides no evidence for condition-dependent signaling in H. versicolor, we cannot rule out the possibility that access to resources influences calling effort at more limiting food levels or on longer time scales.

GENETIC COVARIANCE AND PREDICTED RESPONSE TO SEXUAL SELECTION

The most important result of this study is that the genetic (co)variance structure of the advertisement call affects the potential response to selection more strongly for some call properties than for others, thereby influencing the predicted direction of evolution. Although sexual selection favors an increase in both call duration and call rate, the estimated response to multivariate selection (Δz = ) predicts a significant evolutionary change only for call duration. Contrasting this result with the responses predicted by selection acting on each trait in isolation reveals the effect of genetic covariances, which act to reduce the predicted response for pulse number by about 25% and to almost entirely oppose the predicted response for call period. Consequently, although selection directly favors shorter call periods, this response is offset by selection for longer call duration coupled with the positive genetic covariance between call duration and call period.

Thus, our results demonstrate how the trajectory of evolution among sexually selected traits may be constrained by genetic covariance structure. As in our study, the genetic (co)variance structure influenced both the magnitude and direction of predicted responses to multivariate sexual selection in a study of guppies, with some traits more greatly affected than others (Brooks and Endler 2001). Although several other studies documented genetic covariances among suites of sexually selected traits that resulted in limited genetic variation along the axis of selection and little potential for further evolution (e.g., Hine et al. 2004; von Homrigh et al. 2007; Hunt et al. 2007; Hall et al. 2010), our results indicate that even though the majority of genetic variation is oriented well away from the axis of selection, some variance remains and predicts a significant, though limited, response to multivariate selection. In keeping with this prediction, studies of artificial selection in opposition to the major axis of genetic variation have often revealed significant responsiveness to selection (reviewed in Conner 2012), yet these responses can be biased toward certain traits (e.g., Weber 1990; Frankino et al. 2005; Allen et al. 2008).

Although our analysis focused on directional selection, previous work has demonstrated that female gray treefrogs show nonlinear preferences for both call duration and call rate, showing less selectivity as calling effort increases. Gerhardt and Brooks (2009) found significant quadratic selection on call period in addition to directional selection, indicating that selection acts more strongly against low call rates than in favor of high rates. They also described an axis of significant multivariate stabilizing selection that indicated stronger selection at low levels of calling effort (i.e., short-duration calls with a low call rate). A similar nonlinear preference function has been documented for call duration with call rate held constant (Gerhardt et al. 1996, 2000; Bee 2008). Together, these findings indicate that preferences act most strongly in a purifying manner, resulting in sexual selection that is stronger at lower values of calling effort. In our sample of individuals, both call duration and call rate were shifted in the direction of lower calling effort relative to those used by Gerhardt and Brooks (2009) to estimate selection gradients. Consequently, we would expect the average call phenotype in our study to experience somewhat stronger selection on call period and pulse number than predicted from our analysis, which could potentially alter the multivariate response.

We offer two additional caveats about the interpretation of our estimates of the response to multivariate selection. First, our analysis assumes that the laboratory rearing environment did not influence the genetic variances or covariances of call traits, so that our estimate of G may not be truly representative of a population in the wild. Second, because these selection gradients are based only on female mating preferences, the predicted response does not consider other possible sources of selection on male advertisement calls; in particular, natural selection could oppose sexual selection and limit further trait elaboration (e.g., Brooks 2000; Hine et al. 2011; Sharma et al. 2012). Nevertheless our results show that genetic covariances will almost certainly affect the pattern of evolutionary response to sexual selection in H. versicolor.

MAINTENANCE OF MULTIVARIATE GENETIC VARIATION

Although genetic covariances help to explain how individual traits can retain genetic variation in the face of sexual selection, an important question that remains is how genetic variation is maintained in the direction of multivariate selection (i.e., the multivariate lek paradox; Hine et al. 2004; Hall et al. 2010). One explanation that may be particularly applicable involves mutation–selection balance (e.g., Rowe and Houle 1996). For any complex trait near an adaptive peak or limit, mutations are expected to be predominately deleterious (Fisher 1930; Blows and Hoffmann 2005; McGuigan and Blows 2009; Walsh and Blows 2009). This form of biased mutation provides a crucial explanation for the maintenance of costly mating preferences that consequently serve to counteract the continual degradation of fitness by deleterious mutations (Iwasa and Pomiankowski 1991; Pomiankowski et al. 1991; Kokko et al. 2006; Radwan 2008). If most mutations are deleterious, then greater variance is expected in the direction of lower fitness (Frankham 1990; Blows and Hoffman 2005). This predicted asymmetry in genetic variance was recently demonstrated in tropical fruit flies, in which males preferred as mates had lower genetic variance than rejected males (McGuigan and Blows 2009; Sztepanacz and Rundle 2012). In our dataset, phenotypic variation in call period and pulse number revealed a long tail of low-effort signalers, suggesting that while most males produced calls near maximal effort, a few did not or could not. This asymmetrical variation in male call phenotypes is consistent with the hypothesis that biased mutation helps to maintain multivariate genetic variance and, by extension, mating preferences that favor high-effort signals.

One implication of this genetic asymmetry is that removing low-fitness individuals from a population should be more effective in improving mean fitness than is selection of high fitness individuals (Frankham 1990). Thus, among gray treefrogs, the nonlinear preferences discussed above, which strongly discriminate against low-effort calls, may be particularly effective in allowing females to avoid mates with deleterious alleles that would otherwise be inherited by their offspring (“absence of bad genes” selection; Tomkins et al. 2004). This benefit could explain the persistence of female preferences—particularly those that select against low-effort signals—even if further elaboration of the call phenotype is limited by physiological constraints, low genetic variation in the direction of selection, or opposing natural selection.

CONCLUSIONS

Overall, our work contributes to a growing body of evidence that genetic covariances involving sexual displays may not only impede the evolutionary response to sexual selection (e.g., Brooks 2000; Hall et al. 2004; McGuigan et al. 2008; Delcourt and Rundle 2011; Engqvist 2011) but also shape how evolution proceeds in response to sexual selection (Brooks and Endler 2001; Chenoweth et al. 2010; Hine et al. 2011). Understanding how sexual selection, standing genetic variation, and mutation interact remains an important goal in evolutionary biology, with implications for the evolution and maintenance of mating preferences and sexually selected displays (Rowe and Houle 1996) as well as the potential for evolutionary divergence via sexual selection (Chenoweth et al. 2010; Rodriguez et al. 2013).

ACKNOWLEDGMENTS

Assistance in raising frogs and recording and analyzing frog calls was provided by L. Watters, S. Humfeld, X. Sampablo, C. Hayes, S. Bisges, S. Yi, L. Riegel, B. Grunert, M. Tucker, J. Swingle, K. Vallowe, M. Stoltz, M. Forry, A. Davenport, and A. Williams. We thank M. Scroggie for his advice on the Bayesian modeling. We also thank K. Murphy and S. Arnold for helpful discussions of this work as well as R. Fuller, R. Shaw, and two anonymous reviewers for valuable suggestions on earlier versions of this manuscript. This work was supported by NSF IBN-0415972 to AMW, MJS, and HCG and by the Department of Biology and the Undergraduate Research and Creative Activities Program at the College of Charleston.

DATA ARCHIVING

The doi for our data is 10.5061/dryad.40sj6.

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