Multivariate Qst - Fst comparisons: a neutrality test for the evolution of the G matrix in structured populations
Guillaume Martin 1*, Elodie Chapuis 2 and Jerome Goudet 3
1 GEMI CNRS, Montpellier
2 ISEM CNRS, Montpellier
3 Université de Lausanne
* To whom correspondence should be addressed. E-mail: guillaume.martin{at}mpl.ird.fr.
Submitted on August 20, 2007
Revised on October 8, 2007
Accepted on 18 November 2007
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Abstract |
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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 (Qst - Fst) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this paper, 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 = 2Fst / (1 - Fst)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 (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 (2Fst / (1 - Fst)) 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 Qst - Fst 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.
Key Words:
G matrix evolution, Qst - Fst comparisons, coalescent theory, neutrality test, quantitative trait divergence
