1 October 2009 Empirical Comparison of G Matrix Test Statistics: Finding Biologically Relevant Change
Brittny Calsbeek, Charles J. Goodnight
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A central assumption of quantitative genetic theory is that the breeder's equation (R = GP-1 S) accurately predicts the evolutionary response to selection. Recent studies highlight the fact that the additive genetic variance-covariance matrix (G) may change over time, rendering the breeder's equation incapable of predicting evolutionary change over more than a few generations. Although some consensus on whether G changes over time has been reached, multiple, often-incompatible methods for comparing G matrices are currently used. A major challenge of G matrix comparison is determining the biological relevance of observed change. Here, we develop a “selection skewers” G matrix comparison statistic that uses the breeder's equation to compare the response to selection given two G matrices while holding selection intensity constant. We present a bootstrap algorithm that determines the significance of G matrix differences using the selection skewers method, random skewers. Mantel's and Bartlett's tests, and eigenanalysis. We then compare these methods by applying the bootstrap to a dataset of laboratory populations of Tribolium castaneum. We find that the results of matrix comparison statistics are inconsistent based on differing a priori goals of each test, and that the selection skewers method is useful for identifying biologically relevant G matrix differences.

© 2009 The Society for the Study of Evolution.
Brittny Calsbeek and Charles J. Goodnight "Empirical Comparison of G Matrix Test Statistics: Finding Biologically Relevant Change," Evolution 63(10), 2627-2635, (1 October 2009). https://doi.org/10.1111/j.1558-5646.2009.00735.x
Received: 16 December 2008; Accepted: 1 May 2009; Published: 1 October 2009

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Breeder's equation
G matrix evolution
matrix comparison
selection skewers
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