COMPARISON OF VARIANCE COMPONENTS BETWEEN TWO POPULATIONS OF HOLCUS LANATUS: A REANALYSIS.

Abstract

In a recent paper, Billington, et al. (1988) examined differences between two populations of the grass Holcus lanatus. The two populations, designated respectively traditional field and improved field, have long been subject to distinct management regimes (see details in the original paper). To examine the nature and magnitude of genetic differences that may exist between these populations, the authors grew samples of the two populations in a common greenhouse environment. They documented significant differences in means and phenotypic variances of several vegetative and reproductive characters (their Table 1). They further carried out two series of genetic crosses to examine the genetic structure of the phenotypic variation in the two populations (estimates and tests of the genetic components of variance are given in their Tables 2 and 3). Finally, for each of the traits, the magnitudes of the quantitative genetic components of variance were compared between populations. Unfortunately, due to misunderstanding between the present authors, the analyses comparing the populations (the last two columns of their Tables 2 and 3) are erroneous. Here, we rectify the error, suspected by Barton and Turelli (1989). We amend the previous conclusion that significant differences in genetic components of variance and covariance of many traits exist between the two populations. From our present analysis of a subset of the original traits, we conclude that the differences between the populations in the magnitude of the additive genetic variance are not sufficiently large to be detected as statistically significant, given the size of the experiment. Further analysis of one of the traits, flowering time, provides some, albeit equivocal, support for the previous conclusion that the populations differ significantly in their additive genetic variance for flowering time. We here provide an overview of the method of likelihood for comparing genetic components of variance between populations. The method is presented more fully in Shaw (1 991). Using standard methods in quantitative genetics (Falconer, 1989), it is a relatively straightforward matter to partition the phenotypic variance of a single population into its genetic and environmental components. For example, with data comprising groups of full and half-sibs in a nested or crossed, approximately balanced, design, this partitioning can be accomplished using either the analysis of variance (ANOVA) or likelihood (Shaw, 1987). ANOVA provides no method for testing the null hypothesis that the components of variance are the same in the two populations. Such a test, comparing, for instance, the estimates of additive genetic variance, can be carried out using likelihood methods. In the following, we define VA, as the additive genetic variance of a particular trait within the ith population. Under the null hypothesis,