Academic journal article Genetics

Multivariate Q^sub St^-F^sub St^ Comparisons: A Neutrality Test for the Evolution of the G Matrix in Structured Populations

Academic journal article Genetics

Multivariate Q^sub St^-F^sub St^ Comparisons: A Neutrality Test for the Evolution of the G Matrix in Structured Populations

Article excerpt

ABSTRACT

Neutrality tests in quantitative genetics provide a statistical framework for the detection of selection on polygenic traits in wild populations. However, the existing method based on comparisons of divergence at neutral markers and quantitative traits (Q^sub st^-F^sub st^) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this article, we propose a multivariate extension of this neutrality test based on empirical estimates of the among-populations (D) and within-populations (G) covariance matrices by MANOVA. A simple pattern is expected under neutrality: D = 2F^sub st^/(1 - F^sub st^)G, so that neutrality implies both proportionality of the two matrices and a specific value of the proportionality coefficient. This pattern is tested using Flury's framework for matrix comparison [common principal-component (CPC) analysis], a well-known tool in G matrix evolution studies. We show the importance of using a Bartlett adjustment of the test for the small sample sizes typically found in empirical studies. We propose a dual test: (i) that the proportionality coefficient is not different from its neutral expectation [2F^sub st^/(1 - F^sub st^)] and (ii) that the MANOVA estimates of mean square matrices between and among populations are proportional. These two tests combined provide a more stringent test for neutrality than the classic Q^sub st^-F^sub st^ comparison and avoid several statistical problems. Extensive simulations of realistic empirical designs suggest that these tests correctly detect the expected pattern under neutrality and have enough power to efficiently detect mild to strong selection (homogeneous, heterogeneous, or mixed) when it is occurring on a set of traits. This method also provides a rigorous and quantitative framework for disentangling the effects of different selection regimes and of drift on the evolution of the G matrix. We discuss practical requirements for the proper application of our test in empirical studies and potential extensions.

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THE comparison of genetic differentiation at neutral markers and at quantitative traits is a commonly usedmethod to estimate the relative impacts of drift and selection on polygenic traits in the wild. Typically, a set of populations is sampled, from which the differentiation among populations is estimated for a set of molecular markers (F^sub st^) and is compared to the same measure of differentiation at a single or a set of quantitative traits (Q^sub st^).Under pure neutrality, and if the traits are additive, Q^sub st^=F^sub st^ for any trait (Spitze 1993).Departures from this neutral expectation are considered evidence of selection acting on the quantitative trait under study. Q^sub st^ , F^sub st^ is evidence of homogeneous selection for the trait among populations, i.e., selection for the same optimal value of the trait in all populations, while Q^sub st^ . F^sub st^ is evidence of heterogeneous selection for the trait, i.e., selection for different optima among populations (Merila and Crnokrak 2001).

However, proper empirical detection of selection requires being able to detect a statistically significant departure from the neutral expectation (Q^sub st^ = F^sub st^) and therefore depends on the confidence intervals (C.I.'s) of both Q^sub st^ and F^sub st^ estimates. When studying single traits, confidence intervals on Q^sub st^ are very large (Merila and Crnokrak 2001; Latta 2004;O'Hara andMerila 2005; Goudet and Buchi 2006), often spanning.50%of their total possible range [0, 1], even in themost recent studies with a large sampling effort (Porcher et al. 2006). Furthermore, the methods employed to estimate the C.I. are not always statistically efficient (O'Hara and Merila 2005). Overall, the power of the test with single traits Q^sub st^ is very low with the sampling designs typically possible inempirical studies (O'Hara andMerila 2005), so that rejection of the neutral expectation is unlikely, even when fairly strong selection is in fact occurring (Latta 2004). …

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