Alastair J. Wilson, Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JT, UK. Tel.: 0131 6507287; fax: 0131 6506564; e-mail: firstname.lastname@example.org
Heritable maternal effects have important consequences for the evolutionary dynamics of phenotypic traits under selection, but have only rarely been tested for or quantified in evolutionary studies. Here we estimate maternal effects on early-life traits in a feral population of Soay sheep (Ovis aries) from St Kilda, Scotland. We then partition the maternal effects into genetic and environmental components to obtain the first direct estimates of maternal genetic effects in a free-living population, and furthermore test for covariance between direct and maternal genetic effects. Using an animal model approach, direct heritabilities (h2) were low but maternal genetic effects (m2) represented a relatively large proportion of the total phenotypic variance for each trait (birth weight m2 = 0.119, birth date m2 = 0.197, natal litter size m2 = 0.211). A negative correlation between direct and maternal genetic effects was estimated for each trait, but was only statistically significant for natal litter size (ram = −0.714). Total heritabilities (incorporating variance from heritable maternal effects and the direct-maternal genetic covariance) were significant for birth weight and birth date but not for natal litter size. Inadequately specified models greatly overestimated additive genetic variance and hence direct h2 (by a factor of up to 6.45 in the case of birth date). We conclude that failure to model heritable maternal variance can result in over- or under-estimation of the potential for traits to respond to selection, and advocate an increased effort to explicitly measure maternal genetic effects in evolutionary studies.
Maternal effects occur when an offspring's phenotype is influenced by that of its mother independently of the direct effects of the genes that it inherits. These effects have long been acknowledged and are particularly prevalent in taxa that provide an extended period of parental care (Reinhold, 2002). However, maternal effects have largely been treated as an environmental source of phenotypic variance, and only recently has there been an increasing realization of their potential to shape the evolutionary responses of phenotypic traits under selection (e.g. Mousseau & Fox, 1998; Wolf et al., 1998; Wolf, 2003). In particular, maternal effects may be caused by genes that a mother is carrying as well as by the environment she experiences. In the former case, such maternal genetic effects will represent a heritable source of phenotypic variance. Effectively modelling and predicting evolutionary responses to selection is therefore likely to require the estimation of maternal genetic effects, although few evolutionary studies have done this to date. Here we characterize the genetic basis of maternal effects on a suite of early life traits in a feral population of Soay sheep, Ovis aries.
In addition to the presence of maternal genetic variance for offspring phenotype, covariance can also exist between direct additive genetic effects (of genes carried by an individual) and maternal genetic effects. Quantitative genetic models have shown that, as a result, phenotypic responses to selection may be accelerated by maternal genetic effects, but can also be dampened (or even occur in counterintuitive directions) if there is negative covariance between direct and maternal genetic effects (Kirkpatrick & Lande, 1989; Wolf et al., 1998). At a mechanistic level such negative covariance might occur through pleiotropy, for example if a gene has a positive effect on an offspring trait but a negative effect on maternal performance for that trait.
It has therefore been argued that in the presence of maternal effects, heritability (h2), the ratio of additive genetic variance () to total phenotypic variance (), will not necessarily provide a useful measure of a trait's potential to evolve. A more appropriate measure is total heritability h which is defined by the equation:
where is the maternal genetic variance and σam is the covariance between direct additive and maternal genetic effects (Willham, 1972). Total heritability has the intuitive interpretation of describing the potential response to selection, replacing direct heritability in the classical breeders equation (R = h2S) when maternal genetic effects are present.
The estimation of maternal genetic effects has a long history in animal breeding, where studies of cattle and sheep have demonstrated the importance of heritable maternal variance for many commercially important traits. Furthermore, these studies have commonly reported the presence of strong correlations between direct and maternal genetic effects on traits (e.g. Meyer, 1992; Tosh & Kemp, 1994). In contrast, the estimation of maternal genetic effects in evolutionary biology is a relatively recent development, and has largely been restricted to laboratory-based studies (e.g. Hunt & Simmons, 2002). In general, quantitative genetic analysis of natural (or free-living) populations has been problematic because of the inherent difficulty of obtaining accurate pedigree information, as well as the typically unbalanced nature of data available. Although mother–offspring relationships can be determined by observation in many taxa, this is less effective for paternity assignment. It should be noted that the estimation of maternal effects is conceptually based on determining the difference between father–offspring and mother–offspring phenotypic covariances, such that paternal links in the pedigree are a requirement. Recently, the use of molecular markers (notably microsatellites) for pedigree inference, and the development of restricted maximum likelihood (REML) approaches to estimate variance components have facilitated an increase in quantitative genetic analyses of natural populations (e.g. Réale et al., 1999; Kruuk et al., 2002; Coltman et al., 2003; Wilson et al., 2003a).
A number of studies have estimated the magnitude of maternal effects on particular aspects of phenotype in natural populations (e.g. Milner et al., 1999; Kruuk et al., 2000; Coltman et al., 2001). However, effective separation of maternal effects into genetic and environmental components requires large amounts of data, as well as a pedigree structure spanning multiple generations. As a result, the variance associated with maternal identity has been treated as a completely environmental effect in all but one study of vertebrate populations in natural environments. Using a cross-fostering approach, McAdam et al. (2002) indirectly inferred the presence of large heritable maternal effects on size and growth traits in red squirrels (Tamiasciurus hudsonicus), as well as a large positive covariance between direct and maternal genetic effects. Their results suggest that the potential response to selection on body mass is over three times greater than indicated by direct heritability alone. This finding highlights the importance of determining maternal genetic effects for predicting evolutionary trajectories. However, to our knowledge, no study of a wild population has used the analytical approach adopted in animal breeding for partitioning maternal genetic and environmental components of variance.
Here we estimate quantitative genetic parameters for three early life traits (birth weight, birth date and natal litter size) in Soay sheep, on the Island of Hirta, St Kilda, Scotland. This population has been the subject of long-term study (see Clutton-Brock & Pemberton, 2004), and previous work has shown these traits to be under selection operating through differential viability and breeding success. In particular there is directional selection favouring larger lambs (e.g. Coltman et al., 1999a; Milner et al., 1999), whereas individuals born as twins also have higher lifetime fitness after correcting for size differences (A.J. Wilson, unpublished data). Directional selection for later birth date also occurs through differential first year survival (Clutton-Brock et al., 1992), although there is no evidence for a significant association between birth date and lifetime fitness (A.J. Wilson, unpublished data). An influence of maternal identity on offspring phenotype and fitness has also been demonstrated (Clutton-Brock et al., 1996), suggesting that maternal effects are likely to be important in this system. In addition, these traits are known to be correlated, with later born lambs tending to be heavier, and twins being typically lighter at birth than singletons (Clutton-Brock et al., 1992, 1996). The contribution of specific genetic and environmental sources of covariance to the observed phenotypic correlations is not known.
The aim of this work is therefore to determine the quantitative genetic architecture of early life traits in this population of Soay sheep. To do this we employ a REML ‘Animal Model’ approach that readily allows partitioning of phenotypic variance into its constituent components, and is well suited to the analysis of natural populations (see Kruuk, 2004 for a review). In particular the Animal Model allows use of unbalanced data, and can also accommodate multiple classes of relationship from multi-generational pedigrees. We test for heritable variation in phenotype, and obtain the first directly made estimates of maternal genetic variance, and direct-maternal genetic covariance for phenotypic traits in a free-living population. In this way we determine the importance of maternal effects and also assess their consequences for expected responses to phenotypic selection. Finally, given the known phenotypic correlations, we extend our analysis to a multivariate framework in order to determine sources of covariance between these traits.
Materials and methods
Data and pedigree structure
The Village Bay population of Soay sheep are resident on the Scottish island of Hirta, in the St Kilda archipelago in the North Atlantic (57°49′N, 08°34′W). Since 1985 the sheep have been the subject of individual level study, with animals tagged and monitored throughout their lifetime (see Clutton-Brock & Pemberton, 2004 for extensive details). The population has been censused 30 times annually, with a round up of animals each August, and systematic searches for corpses were made early each spring. In this way, individual level data relating to birth, death, reproduction and phenotype have been collected for the tagged animals. The current analysis is based on phenotypic records for individuals born between 1985 and 2003. Birth date, treated as a characteristic of the lamb, was measured as the number of days from 1 January, and natal litter size was scored as a binary trait having values 1 (singleton) or 2 (twin). As many lambs could not be weighed for several days after birth, we defined birth weight operationally as the residuals from a linear regression of capture weight on capture age (in days). Although weight at capture had a mean value of 2.14 Kg, our analysis used a metric that is corrected for differences in capture age and had zero mean. Summary statistics for the three traits are: birth weight n = 2696, = 0.000, SD = 0.639; birth date n = 3247, = 110.0, SD = 7.71; natal litter size n =3345, = 1.226, SD = 0.419).
The pedigree structure of the Village Bay population of Soay sheep has been resolved using observational and molecular methodologies to determine maternal and paternal links respectively (Coltman et al., 1999b; Pemberton et al., 1999). Maternity is assigned based on field observations which are known to be reliable. Paternity assignment was carried out using available microsatellite data and the maximum-likelihood method implemented in CERVUS (Marshall & J.M. Pemberton, 1998). Full details of this microsatellite methodology are presented elsewhere (see A.D.J. Overall & J.M. Pemberton, unpublished data). For the current study, paternal identities were accepted if they were assigned with a confidence level of 80% or higher, and provided that there was no more than one locus showing an allelic incompatibility between the offspring and assigned sire. On this basis, the pedigree structure used herein contains 5720 individual records with 3050 maternal links, and 1668 paternal links (from 709 distinct dams and 527 distinct sires respectively), and has a maximum depth of nine generations. This structure is comprised of all individually identified sheep, including animals born prior to 1984. These sheep are included as the animal model is able to utilise all available pedigree information (including links to individuals with unmeasured phenotype).
Determination of fixed effects
Nongenetic variation associated with known environmental effects can be removed by fitting fixed effects in an animal model. Based on previous analyses of this population, it is known that environmental variables including climate, population density and maternal age can have important influences on the traits studied here (Clutton-Brock & Pemberton, 2004 and references therein). We therefore used a general linear modelling (GLM) framework, implemented in SPLUS 6 Professional Edition (Insightful Corporation, Seattle, WA, USA), to determine an appropriate fixed effects structure to fit in subsequent animal models. Maternal age was fitted as an 11 level factor with levels corresponding to ages 1 through to 10 or older, and an additional level for unknown age. Sex was fitted as a two level factor and birth year fitted as a multilevel factor. This latter term is expected to account for variance contributed by annual variation in density and climate effects, as well as by other potential unknown or unmeasured variables. Separate analyses were performed for each trait, assuming a normal error structure for birth weight and birth date, and a binomial error structure for natal litter size. The importance of each term was assessed from the change in deviance explained when dropped from the full model, and statistical significance was determined using χ2 tests against the appropriate degrees of freedom. Both maternal age and birth year explained significant amounts of deviance in all three traits (results not shown), whereas sex was also significant for birth weight and birth date, with males tending to be born heavier and later. On this basis all three effects were fitted in the subsequent animal models. Although not statistically significant in the GLM analysis, we elected to also include sex in the univariate animal model of natal litter size for consistency with the other traits and with the multivariate models.
Estimation of (co)variance components
Univariate animal models were fitted for each trait, including the important fixed effects as determined from the GLM analyses. Following the approach widely used in the animal breeding literature, we fitted a hierarchical set of animal models with increasingly complex random effects structures. Four different univariate models were fitted in order to model genetic and environmental sources of phenotypic variance. In Model 1 only a direct additive genetic effect was fitted corresponding to the additive influence of genes carried by the offspring. In Model 2 a maternal permanent environment effect was also fitted, allowing partitioning of phenotypic variance associated with maternal effects with the assumption that these effects are completely environmental in nature. In Models 3 and 4, a maternal genetic effect was also fitted to separate any maternal effects into permanent environment and genetic components. Models 3 and 4 differed in that the direct-maternal genetic covariance (σam) was assumed to be zero in the former whereas it was estimated as an additional parameter in the latter. In matrix notation these models were specified as follows:
Where y is the vector of phenotypic observations for all individuals and b is the vector of fixed effects to be fitted. The random effects are related to individual records with the corresponding incidence matrices X, Z1, Z2 and Z3, which are used to relate random effects to the individual phenotypic records.
The vector a contains the additive genetic effects for each individual (ai) having mean of zero and a variance of , the additive genetic variance. This is estimated from the variance–covariance matrix of additive genetic effects which is equal to A where A is the additive numerator relationship matrix containing the individual elements Aij = 2Θij, and Θij is the coefficient of coancestry between individuals i and j obtained from the pedigree structure. Similarly maternal permanent environment variance () and maternal genetic variance () were estimated by including c and m, the vectors of maternal permanent environment and maternal genetic effects respectively. In all models e was fitted as the vector of residual errors (corresponding to temporary environment effects) with variance of . Maternal permanent environment effects and residual errors were assumed to be normally distributed with means of 0 and variance covariance matrices of I and I, where and are the maternal permanent environment variance and residual (temporary environmental) variances. I is an identity matrix with order equal to the number of maternal individuals or number of individual records as appropriate. We are therefore assuming that all environmental errors are uncorrelated across individuals. The variance–covariance matrix of maternal genetic effects is specified as A such that estimating uses the relationship matrix (i.e. the pedigree structure) in the same way as the additive genetic effect (Lynch & Walsh, 1998).
For each model, variance components (and the direct-maternal genetic covariance σam in Model 4) were estimated using REML implemented in the program ASReml (Gilmour et al., 2002). For Models 2 to 4, only those individuals with known maternal identity could be included (a total of 3050 individuals), and for consistency we similarly restricted the data when fitting Model 1. This restriction resulted in the numbers of phenotypically informative records for each trait being; birth weight n =2427, birth date n = 2845, and natal litter size n = 2978. Total phenotypic variance () was estimated as the sum of all (co)variance components. Estimates of the direct heritability (h2), maternal permanent environment effect (c2), and maternal genetic effect (m2) were calculated (as appropriate to each model) as the ratio of the relevant variance component to the total phenotypic variance. Under Model 4 the direct-maternal genetic correlation (ram) was calculated as σam/(σa.σm). Finally, total heritability was calculated according to the formula of Willham (1972). For each trait, the statistical significance of random effects was determined using likelihood ratio tests (Meyer, 1992) to compare models, with −2 times the difference in log-likelihood scores being distributed as χ2 with 1 d.f. for each additional (co)variance component in the more complex model.
Subsequently three-trait versions of the univariate models were used to estimate covariances between each pair of traits. Multivariate models were again compared using likelihood ratio tests and the appropriate degrees of freedom determined from the number of additional covariance components in the more complex model. Covariance components were summed to estimate the total phenotypic covariance between each pair of traits, and used to estimate additive genetic, maternal permanent environment, and maternal genetic correlations between traits.
Estimates of variance components and their associated ratios to total phenotypic variance differed across models for each trait (Table 1, Fig. 1). In particular use of Model 1 resulted in high estimates of additive genetic variance and direct heritability (h2 ± SE of 0.349 ± 0.042 for birth weight, 0.355 ± 0.036 for birth date, 0.382 ± 0.036 for natal litter size). Inclusion of maternal effects (Models 2–4) resulted in much smaller estimates of h2 (Fig. 1). Comparing models with likelihood ratio tests showed that Model 3 performed significantly better than Models 1 and 2 for all three traits (e.g. comparing Model 3 with 2: birth weight = 9.8, P < 0.05; birth date = 38, P < 0.001; natal litter size = 12.6, P < 0.001). However, Model 4 performed significantly better than Model 3 for natal litter size only (birth weight = 1.2, ns; birth date = 0.6, ns; natal litter size = 5.6, P < 0.05). Therefore Model 3 was deemed the most appropriate model of the random effect structure for birth weight and birth date whereas Model 4 was deemed more appropriate for natal litter size (Table 1). These findings support the presence of significant maternal effects on all three traits, and furthermore provide evidence for maternal genetic, as well as permanent environment, effects.
Table 1. Estimates of variance components and their associated ratios showing; total phenotypic variance (), additive genetic variance (), maternal permanent environment variance (), maternal genetic variance (), direct additive-maternal genetic covariance (σam) and correlation (ram), direct heritability (h2), maternal permanent environment effect (c2) and maternal genetic effect (m2).
Parameter estimate (SE)
*Values significantly different from zero at P < 0.05 based on estimated standard errors.
†Most appropriate univariate model for each trait.
Natal litter size
Based on use of the most appropriate model for each trait, the estimated ratios of variance components (±SE) were: birth weight, h2 = 0.075 ± 0.045, c2 = 0.111 ± 0.040, m2 = 0.119 ± 0.045; birth date, h2 = 0.055 ± 0.036, c2 = 0.069 ± 0.041, m2 = 0.283 ± 0.051; natal litter size, h2 = 0.109 ± 0.052 c2 = 0.142 ± 0.037, m2 = 0.211 ± 0.058. Thus for all three traits direct heritabilities were low and maternal genetic effects represented a larger source of phenotypic variance than direct additive effects.
Using Model 4, estimates of the direct-maternal genetic correlation were negative for all traits (estimates of ram ± SE, were: birth weight −0.410 ± 0.252, birth date −0.219 ± 0.232, natal litter size −0.714 ± 0.168). However, based on the estimated standard errors, ram was not significant for birth weight and birth date, and the likelihood ratio tests show that Model 4 does not perform significantly better than Model 3 for these traits. Our results therefore support the hypothesis of a statistically significant negative direct-maternal genetic correlation on natal litter size only.
The importance of the maternal effects was further shown by the total heritabilities (h) for traits (Table 2). Using the most appropriate model (Model 3), total heritabilities for birth weight and birth date were inflated relative to direct heritability by the contribution from (birth weight h = 0.135 ± 0.045, birth date h =0.197 ± 0.038). In contrast, under the most appropriate model of natal litter size (Model 4), including the negative direct-maternal genetic covariance (σam) as well as yielded a total heritability that was <h2 and, based on the standard errors, was not significantly >0 (h =0.052 ± 0.039).
Table 2. Estimates of total heritability  for birth weight, birth date and natal litter size from univariate Models 1–4.
Natal litter size
Standard errors are given in parentheses.
†Estimates based on the most appropriate model.
*Significantly different from zero at P < 0.05 based on estimated standard errors.
Difficulties were encountered when trying to fit multivariate formulations of Model 4 and model convergence did not occur. We therefore present estimates of between-trait covariance components based on the trivariate formulation of Model 3 (Table 3), which was found to perform significantly better than Models 1 and 2 (results not shown). Phenotypic covariances confirmed prior expectations, being positive between birth weight and birth date and negative between both of these traits and natal litter size. Between birth weight and birth date all covariance components were positive and there was evidence for a strong positive genetic correlation (ra =+0.962 ± 0.375). Estimates of the maternal correlations rc (permanent environment) and rm (maternal genetic) were positive though smaller and not significant based on their associated standard errors (Table 3). There was also evidence to support a significant negative genetic correlation underlying the phenotypic association of birth weight and litter size (ra = −0.677 ± 0.327) as well as an important maternal permanent environment correlation (rc = −0.579 ± 0.152). In both cases residual error covariances were significant, demonstrating an important contribution of temporary environmental effects to the observed phenotypic associations between traits. There was little evidence to support significant covariance components of correlations between birth date and litter size. Although the additive genetic correlation between these traits was strongly negative the associated standard error was very large, limiting the interpretation of this result (ra = −0.665 ± 0.618).
Table 3. Estimates of phenotypic (p), additive genetic (a), maternal permanent environment (c), maternal genetic (m), and residual error (e) correlations and covariances between traits.
Natal litter size
Correlations are shown above the diagonal, covariances below.
*Significant difference from zero at P < 0.05 based on estimated standard errors (shown in parentheses). Estimates are based on trivariate formulation of Model 3.
p +0.224* (0.024)
a +0.962* (0.375)
c +0.269 (0.299)
m +0.228 (0.186)
e +0.146* (0.038)
p +0.887* (0.103)
a +0.259* (0.115)
c +0.095 (0.115)
c +0.231 (0.280)
m +0.166 (0.147)
e +0.367* (0.102)
e +0.008 (0.036)
Natal litter size
c +0.066 (0.077)
e +0.014 (0.065)
Maternal effects clearly represent an important source of phenotypic variance in the early-life traits of birth weight, birth date and natal litter size in this population. This is consistent with previous studies of the Soay sheep (Clutton-Brock et al., 1996), and with the general expectation of large maternal effects in mammalian species (Reinhold, 2002). However, our results show that for all traits these effects have an important genetic basis. Maternal effects therefore include heritable components of phenotypic variance that will respond to selection. As a consequence it is expected that this suite of traits will evolve through changes in maternal performance, as well as through direct genetic effects.
Estimates of maternal genetic effects are largely consistent with published results from studies of domestic sheep (e.g. Maria et al., 1993; Tosh & Kemp, 1994), and m2 for birth weight is also similar to that estimated indirectly for juvenile body mass in red squirrels (the only previous estimate in a free-living population; McAdam et al., 2002). It is also notable that for all three traits maternal genetic variance is greater than additive genetic variance. This is an intuitive result for natal litter size, there being no obvious mechanism by which the genotype of an offspring individual is expected to directly influence whether or not a sibling twin is conceived or carried to term. However, our results show that genes affecting maternal performance also have a greater influence on an individual's birth weight and birth date than do the genes carried by that individual.
A particularly striking result of the current study is the extent to which failing to adequately model the contribution of maternal effects may result in overestimation of additive genetic variance. This effect has been noted in other empirical and simulation based studies (e.g. Meyer, 1992; Clément et al., 2001), including work on the Soay sheep. For example, using a much reduced subset of the current data, Milner et al. (2000) found that inclusion of a maternal permanent environment effect led to significantly lower estimates of heritability for female body size traits. Here, comparisons of h2 between Model 1 and the most appropriate model for each trait show that the former overestimates direct heritability by a factor of 4.65 for birth weight, 6.45 for birth date, and 3.89 for natal litter size. A direct consequence of such parameter overestimation will be a similar upward bias in predicted responses to phenotypic selection measured. Although estimates of h2 also varied between the models with different maternal effects structures specified, these differences were minor in comparison. It is notable that the total proportion of variance attributed to maternal effects (maternal permanent environment effects plus maternal genetic effects) was relatively constant across Models 2–4. However, with no maternal effects specified in the model, a large amount of this variance was allocated as additive genetic variance, rather than being partitioned as residual variance associated with temporary environmental effects.
The presence of important relationships between direct and maternal genetic effects for birth weight and birth date was somewhat supported by our results. Although there are few comparable studies for the latter trait, many studies of domestic sheep have reported strong negative values of ram for birth weight (e.g. Tosh & Kemp, 1994; Al-Shorepy, 2001; Hassen et al., 2003), although significant correlations are not ubiquitous (e.g. Cloete et al., 2002). It has been suggested that this antagonism will limit the potential for genetic improvement of commercial flocks through artificial selection. The idea that an evolutionary response to selection on birth weight (or birth date) could be similarly constrained through this mechanism is supported by the negative values of ram estimated. However, the associated standard errors were large such that even the relatively strong correlation for birth weight was not significantly <0. This indicates that even with the large sample sizes and extensive pedigree structure available, statistical power for estimating ram may be limiting. For natal litter size, the strong negative direct-maternal genetic correlation was significant, and integrating the estimates of h2, m2 and ram yielded a total heritability that was close to zero. Nevertheless, the biological significance of the covariance will be limited as the true additive genetic variance for natal litter size will likely be negligible (as discussed above).
It should be noted that data structure can have a major influence on the estimation of genetic parameters using the animal model (Clément et al., 2001; Maniatis & Pollott, 2003). For example, by analysing subsets of a larger database, Maniatis & Pollott (2003) found stronger negative values of ram for early growth traits in sheep when fewer dams (10% of those in the pedigree structure) contributed phenotypically informative records, and when the average number of offspring per dam was low (1 or 2). Under these circumstances effective separation of maternal genetic and maternal environmental effects may be problematic, and estimates of ram may be affected. Although these are not particular features of the Soay sheep data set (the proportion of phenotypically informative dams is 66.2% with a mean number of 4.3 offspring per dam), such an effect cannot be entirely discounted.
Although estimates of the maternal genetic effect were high for all three traits, direct heritabilities were concomitantly low when the best models were used. Given that litter size, birth weight, and (to a lesser extent) birth date are known to be under directional selection (A.J. Wilson et al., unpublished data), this is consistent with the general assertion that traits closely related to fitness should have lower h2 (although not necessarily due to a lack of genetic variance; Merilä & Sheldon, 2000). Similarly, low estimates of heritability for birth weight and litter size have also been reported in captive populations of domestic sheep where these traits are of interest as targets of artificial selection (e.g. Altarriba et al., 1998; Al-Shorepy, 2001; El Fadili & Leroy, 2001). Despite these low values of h2, the strong maternal genetic effects influence total heritability such that any selection on birth weight and birth date might still be expected to elicit an evolutionary response. This may not be the case for natal litter size (as discussed above).
One qualification to the finding of low heritabilities is that any errors in the paternity assignment procedure are expected to cause a downward bias in estimates of additive genetic variance. Errors may involve incorrect assignment of an unrelated male, or (more commonly) failure to assign the true sire leading to an assumed lack of relatedness between a father and offspring. These errors in the resulting relationship matrix will also cause downward bias in estimates of the maternal genetic variance (whereas potentially increasing estimates of the maternal permanent environment variance as a consequence). Estimation of genetic variance should therefore be viewed as inherently conservative when pedigree information is inferred, at least partially, from molecular markers (Wilson et al., 2003b). A similar caution also applies to pedigrees inferred from observation in systems such as passerine bird populations that often display some degree of extra pair paternity (Griffith et al., 2002). The likely magnitude of biases resulting from errors in pedigree information is unclear, and simulation studies would be useful for exploring this issue more fully.
Our analysis also highlights the importance of considering phenotypic traits in a multivariate framework. In particular, the finding of significant genetic correlations between birth weight and birth date, and between birth weight and natal litter size means that univariate predictions of responses to selection will be unreliable. These results demonstrate a genetic basis to the phenotypic correlations seen in the population, suggesting a potential trade-off and mechanism of evolutionary constraint as birth weight and natal litter size are both subject to positive directional selection (A.J. Wilson et al., unpublished data). It has been suggested that phenotypic correlations are often similar to genetic correlations, and might be used in their place where estimation of the latter is difficult or impossible (e.g. Cheverud, 1988; Roff, 1995). Here, although there is correspondence between the signs of these correlations for all trait pairs, the genetic correlations are of consistently greater magnitude (particularly so between birth weight and birth date, and between birth date and litter size).
One caveat to the results presented here is that all parameters were estimated on the observed scale for each trait using linear animal models. Although commonly employed, this method may not be entirely proper for binary traits (such as natal litter size) and it has been suggested that the use of nonlinear models may be more appropriate (Matos et al., 1997). As a simpler alternative, a threshold model of phenotypic expression can be assumed such that the heritability on the observed scale may be transformed to an underlying liability scale (Dempster & Lerner, 1950). For natal litter size this yields somewhat larger estimates of direct heritability (h2 ± SE on the liability scale of 0.726 ± 0.068, 0.146 ± 0.070, 0.082 ± 0.068 and 0.186 ± 0.084 from Models 1 to 4 respectively). However such a transformation results in only a small increase in total heritability under the most appropriate model of natal litter size (Model 4, h on the liability scale = 0.089 ± 0.067).
In conclusion, we find that there are important maternal genetic effects influencing birth weight, birth date and natal litter size in this population. Furthermore, these effects, together with the significant genetic associations detected between the early-life traits, will have profound implications for the expected response of phenotype to natural selection. More generally, it is notable that directional selection often fails to result in an evolutionary response, despite significant estimates of trait heritabilities (e.g. Milner et al., 1999; Kruuk et al., 2001). Although multiple hypotheses may explain this phenomenon (Meriläet al., 2001), it is certainly clear that inadequately specified models of phenotypic (co)variance can give misleading estimates of quantitative genetic parameters (including over-estimates of heritability). In this context it is important to consider trait evolution in a multivariate framework to facilitate detection of potential constraints acting through genetic correlations. However, given the widespread importance of maternal effects on phenotype, we also advocate that increased efforts should be made to explicitly test for maternal genetic effects wherever possible.
We thank the National Trust for Scotland and Scottish Natural Heritage for permission to work on St Kilda, the Royal Artillery Range (Hebrides) and Qinetiq and Eurest (and their predecessor organisations) for logistic support. The long-term data collection on St. Kilda has been supported by NERC, the Wellcome Trust, BBSRC and the Royal Society, and the work described here was funded by a Leverhulme Trust research project grant to LEBK and DWC. LEBK is supported the Royal Society. We thank Jill Pilkington, Tim Clutton-Brock, Mick Crawley and the many previous members of the project (including many volunteers) who have collected field data, and those who have contributed to the sheep genotyping in the past.