A note on simulating null distributions for G matrix comparisons
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Genetic variances and covariances, summarised in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G . We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomising these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomised vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anticonservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.
Morrissey , M B , Hangartner , S & Monro , K 2019 , ' A note on simulating null distributions for G matrix comparisons ' , Evolution , vol. Early View . https://doi.org/10.1111/evo.13842
© 2019 The Author(s). Evolution © 2019 The Society for the Study of Evolution. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1111/evo.13842
DescriptionMBM is supported by a University Research Fellowship from the Royal Society (London). KM is supported by a Future Fellowship from the Australian Research Council.
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