#### Comparisons of methods

Given the flexibility, the power and the robustness of its method, the animal model provides a true benchmark to which other estimates can be compared to assess their efficiency in obtaining quantitative genetics estimates. However, only a few published studies have explicitly compared the quantitative genetic results obtained with either the regression approach, the likelihood method or the reconstructed sibships, to the estimates obtained from a pedigree or from known relationships (see Thomas *et al*. 2002; Wilson *et al*. 2003b). Here we briefly summarize the main conclusions of these studies (see also Table 1).

Thomas *et al*. (2002) compared estimates of heritability for body weight in a feral population of Soay sheep (*Ovis aries*) obtained from the pedigree-free approaches (regression and likelihood methods) to pedigree-based method (from reconstructed sibships alone, from a combination of known maternities and molecular-based paternities, and from a combination of both). Using 12 microsatellite loci on a subset of the 759 measurements obtained from the Soay sheep database (see Milner *et al*. 2000), they found that the regression approach gave unreliable results that were highly sensitive to the fixed effects included in the analysis of body weight (see Fig. 2). In general, low amounts of marker data and low numbers of relatives in the sample resulted in poor estimates of the actual variance of the relatedness, which were greatly underestimated. As well, the likelihood approach gave negative estimates of the heritability and so estimates were fixed at the boundary of the parameter space (Table 1). Again this was because of insufficient amounts of marker data available to generate useful relationship information, and low numbers of relatives in the sample with which to partition the phenotypic variance. Interestingly, the MCMC approach using only reconstructed sibships also failed for similar reasons. Thomas *et al*. (2002) thus suggested that for these techniques to be successful in a natural situation, a greater number of relatives are required in the sample as well as a greater amount of marker information. Finally, they also clearly showed that the incorporation of known relationship information (such as maternal identities) into the likelihood, combined with the MCMC approach, allowed more reliable estimates of the genetic variance to be determined. They concluded that in their situation, reconstructing the most complete pedigree possible and then using an animal model was preferable to the ‘pedigree-free’ approaches.

In another comparative study, Wilson *et al*. (2003b) used rainbow trout (*Oncorhynchus mykiss*) strains to estimate heritability and genetic correlations of weight and spawning time. They used 71 parental fish to obtain a progeny generation containing 595 individuals originating from both intra- and interstrain crosses that were genotyped with at least eight microsatellite loci. They compared the regression approach and the MCMC sibship reconstruction procedure to values obtained from their true pedigree obtained from full parentage analysis (parentage exclusion approach, where 97% of offspring were assigned to a single parental pair). They found that both the regression and MCMC methods were able to detect significant components of genetic variance and covariance for the traits analysed. However, while the genetic correlations were fairly close to the values estimated with the pedigree, the regression model provided estimates of heritability that were quantitatively unreliable (Table 1, Fig. 2). Indeed, the regression method had both a significant bias and a low precision, apparently due to the poor performance of the estimator of pairwise relatedness. In fact, estimates of heritability were mostly outside the true parameter space (0 > *h*^{2} > 1). In contrast, genetic parameters estimated from the reconstructed pedigree showed close agreement with ideal values obtained from the true pedigree (Table 1). However, the parameters based on the reconstructed pedigree were underestimated due to the complex structure of the true pedigree. The true pedigree consisted of a high number of half-sibling relationships, causing the partitioning of full-sibships to be inaccurate and reducing the recognition of relatedness between families (see Wilson *et al*. 2003b).

Finally, using data from a population of Capricorn silvereyes (*Zosterops lateralis chlorocephalus*), Frentiu (2004) presented a comparison of genetic variances and covariances (and corresponding heritabilities and correlations), for six morphological traits estimated from an analysis of variance amongst full-siblings vs. estimates from regressions using the Ritland method. The data set included 214 individuals genotyped at 11 microsatellite loci, cross-fostered as chicks so as to minimize common environment effects. Several conclusions arise from the comparison. Figure 2 shows the estimates of heritability for the only three traits for which values could be estimated (remaining traits had negative additive variance). First, there is little similarity between the estimates of heritability from the two methods (see Fig. 2). Similarly, estimates of the 15 additive genetic covariances between the six traits, showed little obvious correspondence between the two methods, in either relative or absolute magnitude (not shown). This is notable given that the estimates of genetic covariances or correlations do not incorporate estimates of the variance in relatedness (see Box 2), so the apparent lack of accuracy is not due simply to problems with the latter. Thus, it seems that the results here differ from those of Wilson *et al*. (2003b), where genetic correlations were fairly accurate.

However, Frentiu also reports a comparison of the structure of the G-matrix, using Krzanowski's (1979) method based on the alignment of the principal components of the subspaces defined by the two variance–covariance matrices. This approach indicated significantly greater similarity between the two subspaces than would be expected by chance, implying a high similarity between the principal components of the two matrix subspaces. This result is more difficult to interpret, given the apparent lack of similarity of the explicit values, but it suggests that estimates made using the Ritland approach can detect similar patterns in the genetic architecture, as can those from the conventional analyses.

Thus, it seems that estimates of variance components based on pedigree reconstruction are consistently more accurate than the pedigree-free methods. In some cases, such as the Capricorn silvereye study (Frentiu 2004), estimates from the two methods differ by an order of magnitude (Fig. 2). However, despite the scarcity of comparative evidence, there are some indications that pedigree-free methods could still provide useful indications of the genetic architecture underlying multiple phenotypic traits (see also unpublished data from D. W. Coltman in Table 1 and Fig. 2). These few studies also suggest that the regression method could still be used to some extent for comparison of relative amounts of additive variance/*h*^{2} for different traits within a population (see Fig. 2).