Ontogeny of Additive and Maternal Genetic Effects

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increasing in sheep) result from declining maternal and environ- mental components rather ...... wild populations does not clearly support the first of these predictions ..... Vargas, C. A., M. A. Elzo, C. C. Chase Jr., and T. A. Olson. 2000. Genetic ...
vol. 167, no. 1

the american naturalist

january 2006

E-Article

Ontogeny of Additive and Maternal Genetic Effects: Lessons from Domestic Mammals

Alastair J. Wilson1,* and Denis Re´ale2,†

1. Institute of Evolutionary Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, United Kingdom; 2. Groupe de Recherche en E´cologie Comportementale et Animale, De´partement des Sciences Biologiques, Universite´ du Que´bec a` Montre´al, Montre´al, Que´bec H3C 3P8, Canada Submitted May 9, 2005; Accepted July 19, 2005; Electronically published November 29, 2005

abstract: Evolution of size and growth depends on heritable variation arising from additive and maternal genetic effects. Levels of heritable (and nonheritable) variation might change over ontogeny, increasing through “variance compounding” or decreasing through “compensatory growth.” We test for these processes using a metaanalysis of age-specific weight traits in domestic ungulates. Generally, mean standardized variance components decrease with age, consistent with compensatory growth. Phenotypic convergence among adult sheep occurs through decreasing environmental and maternal genetic variation. Maternal variation similarly declines in cattle. Maternal genetic effects are thus reduced with age (both in absolute and relative terms). Significant trends in heritability (decreasing in cattle, increasing in sheep) result from declining maternal and environmental components rather than from changing additive variation. There was no evidence for increasing standardized variance components. Any compounding must therefore be masked by more important compensatory processes. While extrapolation of these patterns to processes in natural population is difficult, our results highlight the inadequacy of assuming constancy in genetic parameters over ontogeny. Negative covariance between direct and maternal genetic effects was common. Negative correlations with additive and maternal genetic variances indicate that antagonistic pleiotropy (between additive and maternal genetic effects) may maintain genetic variance and limit responses to selection. Keywords: ontogeny, genetic variance, maternal effect, heritability, meta-analysis.

* Corresponding author; e-mail: [email protected]. †

E-mail: [email protected].

Am. Nat. 2006. Vol. 167, pp. E23–E38. 䉷 2006 by The University of Chicago. 0003-0147/2006/16701-41064$15.00. All rights reserved.

The starting point for any quantitative genetic analysis is that phenotypic evolution can be modeled using an explicit function of parameters describing selection and the heritable basis of phenotype variation (Falconer and Mackay 1996).While quantitative genetic studies typically consider traits measured at a single point in time, these parameters used to describe trait evolution might more generally be expected to change over ontogeny. It has long been argued that phenotypic variation must actually arise through interindividual differences in developmental processes during ontogeny (e.g., Cheverud et al. 1983; Atchley 1987). Failure to incorporate the developmental processes shaping variation in trait ontogenies has therefore been identified as a major omission of the modern evolutionary synthesis (Schlichting and Pigliucci 1998; West-Eberhard 2004). For example, while empirical studies have shown that selection on a trait may change in strength or direction at different ontogenetic stages (Milner et al. 1999; Wilson et al. 2003), less attention has been given to elucidating ontogenetic patterns in the genetic (co)variance components that will determine any evolutionary response. Despite this, some theoretical predictions do exist, and the primary aim of this study is to test the generality of these. To do this, we perform a meta-analysis of quantitative genetic parameters drawn from the literature, focusing on estimated parameters for weight traits in domestic populations of cattle (Bos spp.) and sheep (Ovis aries). The evolutionary response of any trait to selection is classically determined by its additive genetic variance (VA). Generally, heritability (h2), the ratio of VA to total phenotypic variance (VP), is used as a measure of potential response (Falconer and Mackay 1996), although standardizing VA by the phenotypic mean may be more appropriate for comparing levels of genetic variance among traits (Houle 1992). Selection on body weight, measured as the covariance between phenotype and fitness, often changes with age. In part, this is because weight is not a static component of phenotype (usually tending to increase with time as a consequence of growth). However, weight may also covary with age-specific components of fitness such as early viability (Schluter and Nychka 1994; Festa-

E24 The American Naturalist Table 1: Putative mechanisms of ontogenetic change in components of phenotypic variance Mechanism

Predicted change over ontogeny

Variance compounding of additive effects (“timing hypothesis”)

Increasing additive variance, increasing h 2, decreasing m 2 Variance compounding of environmental effects Increasing residual variance, decreasing h 2, decreasing m 2 Variance compounding of maternal effects Increasing maternal variance until the end of maternal care, followed by stabilization, increasing m 2, decreasing h 2 Compensatory growth Decreasing phenotypic variance, decreasing additive variance, decreasing maternal variance, decreasing residual variance

Bianchet et al. 1997) or adult reproductive success (Coltman et al. 1999). While selection regimes will therefore be age specific, phenotypic responses also depend on the presence of additive genetic variance, levels of which may also vary over ontogeny. Furthermore, it is being increasingly recognized that indirect genetic effects may also play an important role in determining phenotypic responses to selection (Wolf et al. 1998). In particular, maternal genetic variance (VM), which arises when an individual’s phenotype is influenced by the maternal genotype (independently of the direct effects of genes inherited), represents an additional source of heritable phenotypic variance (Mousseau and Fox 1998). In mammals, the importance of both additive and maternal genetic effects on weight traits has been extensively documented (for examples, see references in the appendix), and covariance may also occur between additive and maternal genetic components of variance. In the presence of maternal effects, the response to selection will therefore be determined by the “total heritability” (h 2T), which can be estimated as h 2T p (VA ⫹ 1.5CovAM ⫹ 0.5VM)/VP (Willham 1972). From this equation, it is apparent that increased VM and positive direct-maternal genetic covariance (CovAM) will accelerate a response to selection, while negative values of CovAM can have a damping effect (Cheverud 1984; Kirkpatrick and Lande 1989; Wolf et al. 1998). Antagonistic pleiotropy has long been considered a probable mechanism for the maintenance of genetic variance (Roff 2002), and in this context, it is notable that strong negative CovAM would arise from genes having antagonistic pleiotropic effects on maternal performance and offspring trait. Thus, by limiting an evolutionary response, negative direct-maternal genetic covariance may act to maintain genetic variance (both VA and VM) in a trait under selection. For these reasons, and because they are more often estimated than other components of variance (i.e., dominance, epistasis), we focus here on the ontogeny of additive and maternal components of variance. As individual weight changes over an animal’s lifetime,

it is likely that phenotypic variance (and its constituent components) measured in the population will also show ontogenetic variation. Several processes may influence the ontogeny of variance components in antagonistic ways (table 1). Among these, it has been suggested that cumulative effects of allelic variants will lead to variance compounding over ontogeny. Thus, a trait expressed later in life will inherit variation from earlier stages, as well as being influenced by any new episodes of genetic expression (Atchley and Zhu 1997), and will show greater additive genetic variance than the same trait expressed earlier (e.g., the timing hypothesis; Houle 1998). Variance compounding may also occur for environmental effects. Typically, the partitioning of VP yields a residual component of variance (VR) that is interpreted as resulting from environmental effects on phenotype (although it may include important nonadditive genetic sources; Merila¨ and Sheldon 1999). Because additional sources of environmental variance may occur throughout ontogeny (individual animals experiencing differing age-specific environments), residual variance VR might also increase with the age at which phenotype is measured. Under the variance compounding hypothesis, maternal variance should also increase until weaning (after which direct maternal influence on the growth of an individual will decline). Despite these predicted increases, phenotypic variance for size traits is often found to be lower for older animals compared with earlier ontogenetic stages. While variance can be reduced by episodes of directional or stabilizing selection through differential viability of young animals, declining variance is frequently reported in artificial populations where early mortality is effectively zero, ruling out selection as the causative mechanism. Here, decreasing variance is often attributed to compensatory (or targeted) growth (Monteiro and Falconer 1966; Riska et al. 1984; Cheverud et al. 1996). Compensatory growth can be defined as the tendency of growth trajectories to converge on a reduced range of phenotypes (Monteiro and Falconer 1966), with individ-

Ontogeny of Genetic Variance Components uals that grow fast early in their ontogeny being characterized by slow late growth and vice versa (Cheverud et al. 1996). It is an important mechanism of canalization, buffering the adult phenotype against any types of effects (genetic or environmental) experienced earlier in life, that is commonly reported in fish (e.g., Ali et al. 2003), birds (e.g., Badyaev and Martin 2000), and mammals (e.g., Re´ale and Bousse`s 1999; Solberg et al. 2004). It is frequently detected as an increase in growth following an environmentally induced period of reduced growth (e.g., temporary starvation). Phenotypic convergence among adults requires a decrease in phenotypic variance such that the presence of compensatory growth can be inferred from reductions in one or more variance components over ontogeny (Riska et al. 1984; Atchley 1987). Therefore, we use the term “compensation” herein to describe any reduction in variance with increasing age. Analyzing patterns of change with age in VP and its constituent components should allow us to examine which of these processes is the most important. If variance compounding plays the major role in structuring ontogenetic patterns, we expect an increase in VP, VA, and VR with age (while VM will increase until weaning before stabilizing). In contrast, with compensatory growth, we should expect a decrease in VP, VA, VM, and VR with increasing age. Conflicting predictions therefore exist with respect to expected changes in components of phenotypic variance across ontogeny (table 1). It is important to note that the processes and mechanisms outlined here need not be mutually exclusive, and an absence of change in variance with age may suggest a balance between both processes. Selection by differential mortality may also cause a decrease in VA (and subsequently in h2) within a cohort. However, because of low mortality in the domestic species considered herein, we believe this probably has a negligible role. Expectations regarding variance components standardized by VP are less straightforward. All else being equal, with the variance compounding hypothesis, increasing VA will result in increased heritability. However, if variance compounding over ontogeny occurs for both additive and environmental processes, then the direction and magnitude of any change in h2 would depend on the relative rates of increase for VA and VR. It is generally argued that the relative importance of maternal genotype will decline with offspring age, such that the maternal effect (denoted m2, the ratio of VM to VP) will normally be undetectable in adult traits. This idea is supported by empirical studies (e.g., Fox et al. 2003), although maternal effects on adult traits are sometimes detected (e.g., Kruuk et al. 2000; Fox et al. 2004). While it is rarely stated explicitly, the most intuitive explanation for declining m2 is that the maternal genotype can contribute no additional variance after the cessation of maternal care, while additive and environ-

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mental effects may continue to contribute to VP. Based on this explanation we predict that m2 will show a declining trend with age caused by increasing VA or VR (or both) rather than by decreasing levels of maternal variance (table 1). In contrast, the compensation hypothesis predicts that m2 will decline as a result of a decrease in maternal variance. The primary objective of this study is therefore to examine ontogenetic patterns in additive, maternal genetic, and environmental components of phenotypic variance and hence test the generality of these predictions. A secondary objective is to examine the relationships among VA, VM, and CovAM in order to test the hypothesis that strong negative covariance between direct and maternal genetic effects can act to maintain genetic variance for a fitness-related trait. To meet these objectives, we perform a meta-analysis of quantitative genetic parameter estimates derived from studies of domestic cattle and sheep. Although evolutionary biologists are normally more interested in processes of natural populations, domestic species have previously been used for evolutionary studies, and this approach has a number of advantages. While quantitative genetic analysis of natural populations is a growing field (see Kruuk 2004; Garant and Kruuk 2005), comparatively few studies have considered traits at multiple points in ontogeny (but see, e.g., Re´ale et al. 1999; Badyaev and Martin 2000; Kunz and Ekman 2000; Wilson et al. 2003). Furthermore, while field-based studies have considered maternal effects, the genetic component of these effects has rarely been estimated (but see, e.g., McAdam et al. 2002; Wilson et al. 2005a). In contrast to the paucity of estimates from natural populations, studies of commercially important traits in domestic animals provide abundant, simultaneous estimates of VA, VM, and CovAM at different stages of ontogeny. Here we focus on cattle and sheep, and we additionally restrict our attention to analyses of weight. In doing so, we are able to collect a large number of parameter estimates made on the same (or similar) traits within each species, limiting the difficulties associated with scale effects that can be problematic for meta-analyses of multiple trait types (Lynch and Walsh 1998). A further advantage is that analyses of domestic species typically are based on very large sample sizes and extensive pedigree information (in comparison with studies in natural populations). As such, parameter estimates are probably characterized by higher accuracy and precision. Our aim in this work is therefore to address the following two questions. First, how do variance components change with age, and second, what are the functional relationships between both additive and maternal genetic variances and the direct-maternal genetic covariance CovAM?

E26 The American Naturalist Methods Data Compilation A review of the literature was performed to obtain estimated genetic parameters from quantitative genetic analyses of weight traits (live and carcass) measured at different ages in domestic cattle and sheep. For the purposes of this study, we used only parameters that were estimated using restricted maximum likelihood under an animal model (Lynch and Walsh 1998). For each trait, parameters of interest were the total phenotypic variance (VP) and its components: additive genetic variance (VA), maternal genetic variance (VM), direct-maternal genetic covariance (CovAM), and residual variance (VR; including maternal environmental variance). Where not explicitly stated, VR was calculated as VR p VP ⫺ (VA ⫹ VM ⫹ CovAM). Additionally, the ratios of these (co)variance components to phenotypic variance were obtained (or calculated). These are the narrow-sense heritability (h2), the maternal genetic effect (m2), the ratio of CovAM to VP (denoted am2), and the residual effect (r 2). Because failure to explicitly model maternal effects can result in overestimation of additive variance (and hence h2; e.g., Meyer 1992), we excluded any studies that had not explicitly modeled VM and CovAM in addition to the additive genetic variance. Age (days from birth) at which phenotype was measured was used to test for ontogenetic variation in quantitative genetic parameters. Where measurements of a single trait were made on animals of slightly varying age, the mean number of days from birth was used. Additionally, each trait was assigned to a categorical age class with four levels denoted: 0 (birth), 1 (weaning), 2 (yearling), and 3 (adult). In total, genetic parameters for 195 weight traits were obtained from 47 peer-reviewed studies published between 1993 and 2004 (appendix). Of these, 131 traits were analyzed in domestic cattle Bos taurus (n p 126) and Bos indicus (n p 5), comprising studies of 27 different breeds and composite breeds. A further 64 traits were analyzed in domestic sheep (21 different breeds and composite breeds). Parameter estimates from all studies were based on analysis of phenotypic data from a large numbers of animals (with a mean of 8,407 over all included traits). Data Analysis Linear models were used to test for ontogenetic changes in quantitative genetic parameters. Scatterplots were first used to visually assess the relationship between each (co)variance component and age in Bos and Ovis separately, with lines of best fit determined from linear regressions. However, as variance often increases with the square of the mean, scale effects may limit the utility of directly comparing the magnitudes of (co)variance com-

ponents across ages. This is particularly true for weight because the phenotypic mean increases over ontogeny as a consequence of growth. For such comparisons, coefficients of variation are therefore more appropriate than are the nonstandardized variance components (Houle 1992). The coefficient of variation (CV) is given by

冑V CV p 100 #



,

where V is the sample variance and x¯ is the sample mean. For a number of cattle studies, phenotypic means were not provided in the literature source, and these were therefore excluded from the linear model analyses of coefficients of variation. For all others, we calculated CVP, CVA, CVM, and CVR as the standardized coefficients of phenotypic, additive genetic, maternal genetic, and residual variance, respectively. The distributions of the four coefficients exhibited positive skew in both genera (distributions not shown) and were therefore log10 transformed for use as dependent variables in the models. The direct-maternal genetic correlation (ram) was used as a standardized measure of CovAM, and additional models were fitted for the ratios of each (co)variance component to VP. Thus, for each of nine response variables (log CVP, log CVA, log CVM, log CVR, ram, h2, m2, r 2, and am2), age (in days) was fitted as the explanatory variable to test for linear changes over ontogeny. Additionally, a parallel set of models was fitted, including age class, the categorical variable (as described above). The significance of age (or age class) was assessed from the sums of squares under an assumed normal error structure, and separate analyses were performed for each genus. It is common practice in metaanalyses to weight results of particular studies according to some measure of their precision. However, standard errors were not available for all parameter estimates, and sample size probably represents a very crude indicator of expected precision. Not only were sample sizes that were used in individual studies high by comparison with those typical of evolutionary and ecological studies, but sample size may also be less relevant than other features of the data (notably pedigree depth and structure) in determining precision for quantitative genetic parameter estimates. Nevertheless, for comparison, we fitted equivalent age and age class models with data weighted by study sample size. Additionally, to ensure that the inclusion of different breeds did not influence our assessment of ontogenetic patterns, we fitted corresponding generalized linear mixed models, with breed included as a random effect. All models were fitted using SPLUS 6 Professional Edition (2001; Insightful). To facilitate visual interpretation of ontogenetic patterns, we plotted mean values of each parameter by age

Ontogeny of Genetic Variance Components class in both Bos and Ovis. We controlled for false discovery rates associated with multiple dependent tests using Benjamini and Liu’s method (Benjamini et al. 2001). Correlation analyses were performed to test the hypothesis that direct-maternal genetic covariance is associated with higher genetic variance (both additive and maternal). Scatterplots of VA and VM against CovAM were first used to visually assess the data and to identify any extreme outliers that may unduly effect correlations. All else being equal, (co)variance components are expected to increase with total phenotypic variance; to account for this probable source of positive covariance, we thus considered the relationships of VA, VM, and CovAM to VP as well as to each other. Both full (Pearson’s coefficient r) and partial correlations were estimated between VP, VA, VM, and CovAM. Pearson’s correlation coefficients were also estimated between the ratios h2, m2, and am2. Each genus was separately analyzed. Results Ontogeny of Quantitative Genetic Parameters Scatterplots show that phenotypic variance for weight increases with age in both Bos and Ovis (fig. 1). Positive gradients for lines of best fit show the same is true for additive, maternal genetic, and residual variance components. Gradients are significantly greater than 0 in all cases (results not shown), a finding consistent with the expected dependence of variance on the phenotypic mean (which increases with age). The order of the relative magnitudes of variance components remains constant across ontogeny, with phenotypic variance dominated by the residual component VR and the additive genetic variance being greater than the maternal genetic variance at all ages in both genera (fig. 1). The regression line for direct-maternal genetic covariance (CovAM) on age has a negative gradient in Bos and is positive in Ovis. However, only in Bos does this gradient differ significantly from 0 (gradient p ⫺0.156, P ! .001). While the unstandardized variance components therefore increase with age, this pattern is not reflected in the coefficients of variation and may therefore be attributed to scale effects. Nevertheless, linear models did show evidence for ontogenetic changes in many of the standardized response parameters tested in both genera (table 2). Results were qualitatively similar using the simple linear models and when analyses were weighted by sample size. Furthermore, analyses using generalized linear mixed models showed that inclusion of breed as a random effect caused little qualitative or quantitative change to the results. Consequently, we present only the results of the unweighted linear models. In Bos, there was no significant ontogenetic trend in the

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total phenotypic variance as measured by log CVP, although maternal variance was found to decline with age (indicated by the significant negative coefficient for log CVM; table 2). Heritability, h2, also declined significantly across ontogeny, while the opposite was true for r 2. Fitting age as a categorical rather than continuous variable explained more of the variance in all models (table 2), and significant differences across the age classes were found for log CVM, ram, h2, m2, and r 2. Plots of parameter means by age class confirm that log CVM drops from birth to adulthood in Bos, with a major decline from age class 2 to 3 (fig. 2). Associated with this reduction in maternal genetic variance is a similar trend in the ratio m2, which declines (from 0.12 at age 0 to 0.04 at age 3, the latter value not being significantly greater than 0 at a p 0.05). Mean m2 is actually slightly higher for weaning weights than for birth weights. This is caused by a slight decrease in additive variance and hence total phenotypic variance between birth and weaning (seen in the plots of mean log CVA by age class; fig. 2) rather than any increase in maternal genetic variance. Although the decreased additive variance at age 1 is not itself significant (based on the linear model of log CVA; table 2), the resultant decrease in mean heritability (h2) and concomitant increase in the residual effect (r 2) are. Thus, mean h2 declines from 0.40 at birth to 0.27 at weaning, after which it changes little (with a mean h2 of 0.26 for adult weight traits). In contrast, the plot of mean r 2 shows that residual variance accounts for more than half of VP in all age classes but also shows a general pattern of increasing with age class (with mean trait-corrected r 2 rising from 0.51 at age 0 to 0.74 at age 3; fig. 2). Mean additive-maternal genetic correlation (ram) is negative in all age classes. The significant effect of age class on this correlation is a consequence of increased magnitude in age class 2 (with a mean traitcorrected ram of ⫺0.43; fig. 2). Despite the stronger genetic correlations found for yearling weight traits, age class was not significant in the model of the ratio am2 (table 2). In Ovis, fitting age as a continuous variable provided evidence for a significant decline in total phenotypic variance, maternal genetic variance, and residual variance (as measured by log CVP, log CVM, and log CVR, respectively; table 2). The log CVA shows a nonsignificant negative association with age (⫺3.30 # 10⫺5, P p .738). As a consequence of maternal variance decreasing more rapidly with age than phenotypic variance, m2 shows a significant decrease over ontogeny (table 2). In contrast, h2 shows a significant increase with age because additive variance declines more slowly than the total phenotypic variance. This is reflected by the greater magnitude of the coefficient associated with age in the model of log CVP as compared with the model of log CVA (these being ⫺2.47 # 10⫺4 and ⫺3.30 # 10⫺5, respectively; table 2).

Figure 1: Relationships of phenotypic variance and its constituent (co)variance components to age for weight traits in Bos and Ovis. Lines indicate best linear fit.

Ontogeny of Genetic Variance Components These patterns are also apparent from the plots of agespecific parameter means (fig. 2) and the models with age class fitted (table 2). A notable exception is that r 2 shows a significant increase with age (table 2), while mean r 2 is actually lowest for age class 3 (mean r 2 p 0.56; fig. 2). However, it should be noted that in Ovis, age class 3 is represented by a sample size of just three traits. Hence, confidence intervals around parameter means are very wide, and inferences regarding adult traits, including the suggested reduction in r 2 should be made cautiously. The additive-maternal genetic correlation shows a significant increase with age in Ovis (table 2), and mean ram increases consistently across age classes (fig. 2), starting from a mean ram p ⫺0.28 for birth weights to become positive for yearling and adult traits. The same pattern is reflected by the ratio am2, although the effect of age is marginally nonsignificant (R 2 p 0.0511, P p .072; table 2). Associations between VA, VM, and CovAM Lines of best linear fit through the scatter plots show negative relationships between VA and CovAM and between VM and CovAM in both genera (fig. 3), and correlation analyses supported the hypothesis of significant associations between (co)variance components (table 3). Thus, in Bos, CovAM shows significant negative correlations with VA and VM, while these latter variables are positively associated with each other (table 3). Significant partial correlations confirm that CovAM has negative associations with both additive and maternal genetic variance independently of other variance components. In contrast, the positive correlation between additive and maternal genetic components of variance is due to a shared dependence on phenotypic variance (because the partial correlation between them is negative, though not significant; table 3). Since VA, VM, and CovAM are all components of VP, the significant positive partial correlations between VP and the other variables seen in table 3 are expected. VA shows the highest partial correlation with VP (rVAVP7VMCovAM p ⫹0.737, P ! .001), indicating that additive variance is a more important determinant of total variance that either VM or CovAM. Additionally, because this partial correlation is positive, the negative value of Pearson’s r between CovAM and VP (rVPCovAM p ⫺0.518, P ! .001) must result from the negative effect of CovAM on additive and maternal genetic components of variance. In Ovis, the signs of all full and partial correlations are the same as in Bos (table 3), and there is thus some support for the hypothesized relationships between covariance components. Significant positive values of r were again found between VA, VM, and VP, while partial correlations showed that VP was again most strongly correlated with VA (rVAVP7VMCovAM p ⫹0.847, P ! .001). How-

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Table 2: Linear model analyses of log-transformed coefficients of variation, direct-maternal genetic correlations, and ratios of (co)variance components to phenotypic variance in Bos and Ovis Genus/ response Bos: log CVP log CVA log CVM log CVR r am h2 m2 r2 am 2 Ovis: log CVP log CVA log CVM log CVR r am h2 m2 r2 am 2

Age class model

Mean age model b (SE)

R2

P

R2

P

⫺.092 ⫺.141 ⫺.519 ⫹.004 ⫺.126 ⫺.315 ⫺.132 ⫹.427 ⫺.088

(.107) (.107) (.092) (.108) (.088) (.084) (.088) (.080) (.088)

.0085 .0199 .2693 .00002 .0159 .0993 .0174 .1839 .0078

.392 .190 !.001 .969 .155 !.001 .136 !.001 .332

.0105 .0345 .4269 .0072 .0678 .1722 .1158 .1984 .0357

.827 .397 !.001 .895 .032 !.001 .001 !.001 .210

⫺.446 ⫺.043 ⫺.455 ⫺.484 ⫹.279 ⫹.296 ⫺.259 ⫺.229 ⫹.225

(.114) (.127) (.112) (.111) (.122) (.121) (.123) (.124) (.124)

.1991 .0018 .2175 .2339 .0780 .0874 .0668 .0526 .0511

!.001

.2817 .0258 .4007 .2759 .4029 .0610 .3129 .2272 .0789

!.001

.738 !.001 !.001 .025 .012 .039 .068 .072

.664 !.001 !.001

.142 .283 !.001 .001 .174

Note: P denotes significance of age as an explanatory variable when fitted as a continuous variable (mean age model) or using categorical age classes (age class model). Bold denotes significance at the nominal .05 level after a false discovery rate analysis for multiple dependent tests (following Benjamini and Liu’s method; P limit p .0062 for Bos and .0074 for Ovis, respectively).

ever, while full and partial correlations between CovAM and both VA and VM were negative, they were of lower magnitude than in Bos and were not significantly different than 0 (table 3). However, the scatterplot of CovAM against VM in Ovis suggests the presence of two putative outliers that may affect the correlations (fig. 3). Removal of these outliers results in full and partial correlations that are highly significant (rVMCovAM p ⫺0.415, P p .001; rVMCovAM7VAVP p ⫺0.465, P ! .001). Analysis of the ratios of the (co)variance components to VP also supported our a priori hypotheses. Negative correlations between am2 and both h2 and m2 were significant or marginally nonsignificant in Bos (rh 2am2 p ⫺0.167, P p .06; rm2am2 p ⫺0.370, P ! .001) and Ovis (rh 2am2 p ⫺0.506, P ! .001; rm2am2 p ⫺0.615, P ! .001). In the absence of an association between VA and VM, a positive autocorrelation between h2 and m2 is expected (since both are calculated by dividing by VP). It is therefore notable that significant positive correlations between h2 and m2 were not found in Bos (rh 2m2 p ⫺0.153, P p .08) or Ovis (rh 2m2 p ⫹0.124, P p .329).

E30 Figure 2: Plots of mean by age class for standardized measures of (co)variance components (upper panels) and ratios associated with variance components (lower panels) in Bos and Ovis. Bars indicate 95% confidence limits around means, and sample sizes are shown in parentheses. Significant differences among age classes are denoted with one asterisk (P ≤ .05 ) or three asterisks (P ≤ .001).

Figure 3: Relationships between the direct-maternal genetic covariance (CovAM ) and additive genetic variance (VA) and maternal genetic variance (VM) in Bos and Ovis. Lines indicate best linear fit.

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E32 The American Naturalist Table 3: Correlations between direct-maternal genetic covariance (CovAM), additive genetic variance (VA), maternal genetic covariance (VM), and phenotypic variance (VP) Genus (n) Bos (129): CovAM VA VM VP Ovis (64): CovAM VA VM VP

CovAM

VA

VM

VP

… ⫺.741*** ⫺.639*** ⫺.518***

⫺.617*** … ⫹.552*** ⫹.809***

⫺.464*** ⫺.117 … ⫹.532***

⫹.309*** ⫹.737*** ⫹.309*** …

… ⫺.078 ⫺.114 ⫺.027

⫺.133 … ⫹.550*** ⫹.893***

⫺.138 ⫺.101 … ⫹.648***

⫹.145 ⫹.847*** ⫹.429** …

Note: Pearson’s correlation coefficients (r) are shown below the diagonal and partial correlations are above. ** Significance for two-tailed tests at P ! .01, respectively. *** Significance for two-tailed tests at P ! .001, respectively.

Discussion Our meta-analysis of weight traits showed important changes in phenotypic variance and its constituent components occurring across ontogeny. Thus, age effects on the quantitative genetic parameters used to describe additive genetic, maternal genetic, and environmental effects were found in both genera. In the following discussion, we first address these patterns in the context of their support for the mechanistic processes outlined earlier (namely, variance compounding and compensatory growth). We then consider the implications of ontogenetic variation in heritability (and the proportional maternal effect m2) before focusing on the secondary objective of our study, that of scrutinizing the role of CovAM in maintaining genetic variance. Finally, we summarize our findings and the conclusions drawn from them. Variance Compounding In both genera, unstandardized phenotypic variance for weight increases with age, and the additive and residual components make significant contributions to this trend (fig. 1). This pattern in VA, found in other studies (Riska et al. 1984; Atchley and Zhu 1997), is consistent with the hypothesis of variance compounding for additive effects according to the timing hypothesis (Houle 1998). However, this conclusion is not supported by the standardized measure of additive variation (log CVA), which shows no significant increase across ontogeny. Similarly, VR increases across ontogeny in Bos and Ovis, but there is no concomitant increase in log CVR (the converse actually being true in sheep). It is therefore probable that changes in additive and residual variances are primarily an artifact of scale (caused by dependence of variance on the mean; see Riska

et al. 1984) rather than a biologically important phenomenon. Thus, variance compounding over ontogeny is not supported for either additive or environmental components of VP. An important caveat to this is that because the two processes need not be exclusive, variance compounding (the addition of new variance) may occur but be masked by compensatory processes having an equal or greater effect. Compensatory Growth Decreases in log-transformed coefficients of variation with age provided evidence for compensatory growth in both genera. In the absence of compensation, differential growth rates can only add to variance already present, such that measures of phenotypic variation (and its components) should never decrease (Riska et al. 1984). Declining log CVP in Ovis showed phenotypic convergence among older animals. Our results agree with the common assumption that compensatory growth occurs through a reduction of the environmental component of variance (LeBlanc et al. 2001; Bjorndal et al. 2003), and while experimental studies of rodent growth have shown that compensation may also act to reduce additive genetic variance (e.g., Riska et al. 1984), we found no evidence for this. Nevertheless, compensation was found in the maternal genetic variance as indicated by the decline of log CVM from birth to adulthood. It should be noted that while dominance variance (VD) is rarely estimated, it could cause overestimation of other components if present (Misztal et al. 1997). Both diallelcross studies (Atchley and Zhu 1997) and quantitative trait loci studies (Cheverud et al. 1996; Vaughn et al. 1999; Rocha et al. 2004) have shown the presence of strong directional dominance for early growth traits that subsequently declines with age. While the bias on VA is assumed to be negligible because of the low proportion of full sibs in livestock pedigrees, the residual (or “environmental”) variance could include nonadditive genetic sources (Misztal et al. 1997; Merila¨ and Sheldon 1999). We therefore cannot rule out the influence of dominance on the observed pattern of residual variation in this study. Evidence for compensatory growth at the phenotypic level was less conclusive in Bos. However, maternal genetic variation (log CVM) does decrease, notably between yearling and adult stages (which is somewhat later than in Ovis). Thus, in both genera, maternally induced variance for weight is reduced by accelerated growth of those individuals whose mothers have lower performance for offspring weight. This effect, documented in previous mammalian studies (e.g., Sikes 1998), is consistent with the assertion that compensatory growth occurs as a plastic response to environmentally induced depression of

Ontogeny of Genetic Variance Components growth. In this context, maternal genetic effects can be considered as a particular type of environmental effect, albeit one that is itself heritable (Wolf et al. 1998). Consequences for h2 and m2 Changes in genetic and environmental variance components have implications for the potential of age-specific weight traits to respond to selection. Heritability for weight changed significantly across ontogeny, although contrasting trends emerged in each genus. However, analysis by age class indicated h2 was actually comparatively stable over most of ontogeny, with the declining h2 in Bos resulting from a decrease between birth and weaning (caused by a concomitant reduction in additive variance). In Ovis, the contrasting trend of increasing h2 reflects compensation in maternal and residual variation between yearling and adult stages rather than any increase in additive variance. Traits closely associated with fitness often show lower heritabilities (Houle 1992; Stirling et al. 2002), and estimates for weight were generally more typical of values reported for life-history traits than for morphological traits (mean p 0.262 and 0.461, respectively; Mousseau and Roff 1987). Though normally considered a morphological trait, weight is frequently correlated with fitness components in natural populations, and it forms the basis of artificial selection in many animal breeding programs. Nevertheless, significant additive genetic variance was found at all ages, consistent with the increasingly prevalent view that low h2 for fitness-related traits reflects higher environmental or nonadditive components of variance rather than reduced additive variance (e.g., Price and Schluter 1991; Merila¨ and Sheldon 1999, 2000; McCleery et al. 2004). Both taxa have been subjected to long-term selection for increased weight, and the maintenance of additive variance therefore challenges the common interpretation of Fisher’s fundamental theorem, whereby strong selection is expected to rapidly fix or eliminate alleles regulating fitness. A common trend of declining maternal effect with age was found, such that mean m2 was not significantly greater than 0 for adult weight in cattle or sheep. While consistent with results from several empirical studies (e.g., Fox et al. 2003), it is also apparent that declining m2 results largely from decreasing maternal genetic variance rather than from increasing levels of additive or residual variance, as was initially hypothesized. Maternal effects on birth weight in Ovis were particularly high (representing an average 26% of VP), with sheep populations containing significantly more genetic variance for maternal performance than cattle. This may be a consequence of the less intensive livestock practices used in sheep farming (whereby selec-

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tion on both offspring trait and maternal performance is likely to be less intense than for cattle). However, given that strong selection has not removed additive variance for weight in cattle, such an interpretation should be made cautiously. Direct-Maternal Genetic Covariance (CovAM) Additive-maternal genetic covariances for weight traits were generally negative across all ages, indicating a pattern of antagonism between additive and maternal genetic effects on offspring weight. Furthermore, correlation analyses showed a clear association between strong negative covariance and higher levels of additive and maternal genetic variance. Although distributions of CovAM, VA, and VM exhibited some deviations from normality, removal of putative outliers had little effect (except with respect to the correlation between CovAM and VM in Ovis, as discussed above), and nonparametric tests produced qualitatively and quantitatively similar results (not shown). Similarly, the ratio am2 was negatively correlated with h2 and m2 in both genera (despite the fact that since all three parameters are dependent on VP, some degree of positive autocorrelation is expected here). Thus, for weight traits, our results are consistent with the hypothesis that negative covariance can act to limit the response to selection and hence with the idea that antagonistic pleiotropy may be an important mechanism for the maintenance of genetic variance (Roff 2002). However, it should be noted that strong negative values of the genetic correlation ram may sometimes be an artifact of the (co)variance estimation methodology. Estimates of ram may be biased by particular features of the data structure (Maniatis and Pollott 2003) or by failure to account for sire # herd or sire # year interactions (Robinson 1995; Lee and Pollak 1997), and further investigation of these issue is certainly warranted. Generalizing the results of this work to expected patterns in natural populations is certainly not without difficulty. In the only explicit estimate in a free-living population to date, ram for birth weight was estimated as ⫺0.71 in a feral population of Ovis aries (Wilson et al. 2005a), a value similar to those reported here. If selection is uniformly positive, antagonism between direct and maternal genetic effects is expected to limit the potential for genetic improvement (e.g., Hassen et al. 2003), but consequences may be less clear-cut under more complex selection regimes (e.g., if large size can incur fitness costs as well as benefits; Blanckenhorn 2000). Given the accumulation of evidence for maternal genetic effects in many taxa (Mousseau and Fox 1998) and of negative direct-maternal genetic correlations in some mammalian and insects species (e.g., Roff 1997), there is clearly a need for empirical estimates of CovAM in natural populations.

E34 The American Naturalist Summary and Conclusions In summary, our analysis provided evidence of important age-related patterns in both genetic and environmental effects on weight. The analysis of scale-insensitive measures of the variance components provided no support for the variance compounding that has been hypothesized for additive and environmental effects. Conversely, we did find support for compensatory growth, particularly in Ovis, where phenotypic convergence at adulthood results from decreasing environmental and maternal components of variance. Evidence was less strong in Bos, though our results do show that early differences in weight attributable to maternal genetic effects are reduced over ontogeny. Thus, in both genera, declining m2 occurs through a reduction in maternal genetic variance, while tendencies toward decreasing (Bos) or increasing (Ovis) heritability of weight are also caused by these compensatory processes. An important caveat to these conclusions is that while we found no support for variance compounding, both compounding and compensatory processes could occur simultaneously, such that the signature of the former is masked by the latter. Reductions in components of variance over ontogeny could be attributed to increasing developmental canalization on body weight with age, a mechanism that buffers the expression of a phenotype despite environmental or genetic variation (Waddington 1942; Debat and David 2001). Genes responsible for genetic-canalizing effects are assumed to decrease visible additive genetic variance, whereas genes with environment-canalizing effects would decrease environmental variance (Debat and David 2001). Our results indicate environmental canalization on body weight (i.e., both log CVR and log CVM decline with age) but do not support genetic canalization (i.e., log CVA constant). Studies on the development of variance components could therefore provide some important insights on the mechanisms of canalization. A limitation of this meta-analysis is that we have considered only the univariate architecture of weight traits and have not given explicit consideration to sources of covariance that probably exist between weights measured at different ages. In this respect, it should be pointed out that genetic covariance will limit the potential of agespecific weights to respond independently to selection (Atchley 1987; Cowley and Atchley 1992). Furthermore, because compensatory growth is evidenced by negative phenotypic correlations between age-specific growth rates, estimation of environmental and genetic covariance structures would give further insight into mechanisms of canalization.

The extent to which the ontogenetic patterns found here are typical of weight (and other aspects of phenotype) in natural populations is largely unknown. Certainly domestic populations experience more stable environments, and this has led to the expectation that environmental variance components will be larger in natural populations, with heritabilities lower as a consequence (Riska et al. 1989). By similar reasoning, a greater potential for variance compounding of environmental effects in natural populations might also be expected. However, it is notable that previous comparison of h2 estimates from laboratory and wild populations does not clearly support the first of these predictions (Weigensberg and Roff 1996; but see also Hoffman 2000). More generally, the occurrence of compensatory growth has been documented at the phenotypic level in populations of various taxa (Metcalfe and Monaghan 2001), including organisms with indeterminate growth patterns (e.g., Carlson et al. 2004). Findings consistent with compensatory processes affecting weight and size traits have also been reported from quantitative genetic analyses of wild ungulates (Re´ale et al. 1999), birds (Badyaev and Martin 2000; Kunz and Ekman 2000), and wild-caught amphibians (Ragland and Carter 2004). However, there is clearly a need for further empirical studies of natural populations in which viability selection, particularly on early size traits (e.g., Wilson et al. 2005b), may be strong and will represent an additional mechanism for reducing phenotypic variance over ontogeny (i.e., within a generation). Since viability selection acting solely on environmentally induced phenotypic variation will not induce an evolutionary response, a comparison of environmental and genetic variance components across age classes may offer a useful strategy for assessing the evolutionary impact of selection episodes occurring at different ontogenetic stages. At a minimum, our results highlight the inadequacy of assuming constancy in quantitative genetic parameters with age. Thus, to understand and model the evolution of weight, it is necessary to examine the way in which genetic and environmental components of phenotypic variance change over ontogeny, as well as how selection may act at different ages. Acknowledgments We thank D. Coltman, L. Kruuk, B. Walsh, and an anonymous reviewer for discussion and comments on an earlier version of this manuscript. A.J.W. is supported by a Leverhulme Trust research project grant. This research was supported by a grant from the Natural Sciences and Engineering Council of Canada to D.R.

Ontogeny of Genetic Variance Components APPENDIX

Literature Cited

Literature Sources

Table A1: Literature sources for data set compiled in this study showing number of weight traits analyzed in cattle (Bos) and sheep (Ovis) Reference Bos: Bennett and Gregory 1996 Burrow 2001 Choi et al. 2000 Davis and Simmen 1997 de Mattos et al. 2000 Dodenhoff et al. 1998 Dodenhoff et al. 1999 Eler et al. 1995 Elzo et al. 1998 Ferreira et al. 1999 Gutierrez et al. 1997 Haile-Mariam and Kassa-Mersha 1995 Kaps et al. 1999 Keeton et al. 1996 Khombe et al. 1995 Lee et al. 1997 Lee et al. 2000 MacNeil et al. 1998 Meyer et al. 1994 Pariacote et al. 1998 Quintanilla et al. 1999 Robinson 1996 Shepard et al. 1996 Splan et al. 2002 Van Vleck et al. 1996 Vargas et al. 2000 Varona et al. 1999 van der Westhuizen et al. 1994 Ovis: Abegaz et al. 2002 Al-Shorepy 2001 Al-Shorepy and Notter 1996 Analla et al. 1995 El Fadili et al. 2000 Hanford et al. 2002 Hanford et al. 2003 Larsgard and Olesen 1998 Lewis and Beatson 1999 Ligda et al. 2000 Maniatis and Pollot 2003 Maria et al. 1993 Mousa et al. 1999 Nasholm 2004 Nasholm and Danell 1996 Neser et al. 2001 Notter 1998 Tosh and Kemp 1994 Yazdi et al. 1997 Yazdi et al. 1999

E35

Traits 24 4 3 3 3 8 12 3 4 3 2 3 1 1 1 1 3 2 2 2 1 4 1 1 27 1 1 8 4 1 3 2 3 2 2 3 2 2 1 3 4 4 5 3 7 9 3 1

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