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March 2020 Modifying the Chi-square and the CMH test for population genetic inference: Adapting to overdispersion
Kerstin Spitzer, Marta Pelizzola, Andreas Futschik
Ann. Appl. Stat. 14(1): 202-220 (March 2020). DOI: 10.1214/19-AOAS1301


Evolve and resequence studies provide a popular approach to simulate evolution in the lab and explore its genetic basis. In this context, Pearson’s chi-square test, Fisher’s exact test as well as the Cochran–Mantel–Haenszel test are commonly used to infer genomic positions affected by selection from temporal changes in allele frequency. However, the null model associated with these tests does not match the null hypothesis of actual interest. Indeed, due to genetic drift and possibly other additional noise components such as pool sequencing, the null variance in the data can be substantially larger than accounted for by these common test statistics. This leads to $p$-values that are systematically too small and, therefore, a huge number of false positive results. Even, if the ranking rather than the actual $p$-values is of interest, a naive application of the mentioned tests will give misleading results, as the amount of overdispersion varies from locus to locus. We therefore propose adjusted statistics that take the overdispersion into account while keeping the formulas simple. This is particularly useful in genome-wide applications, where millions of SNPs can be handled with little computational effort. We then apply the adapted test statistics to real data from Drosophila and investigate how information from intermediate generations can be included when available. We also discuss further applications such as genome-wide association studies based on pool sequencing data and tests for local adaptation.


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Kerstin Spitzer. Marta Pelizzola. Andreas Futschik. "Modifying the Chi-square and the CMH test for population genetic inference: Adapting to overdispersion." Ann. Appl. Stat. 14 (1) 202 - 220, March 2020.


Received: 1 February 2019; Revised: 1 August 2019; Published: March 2020
First available in Project Euclid: 16 April 2020

zbMATH: 07200168
MathSciNet: MR4085090
Digital Object Identifier: 10.1214/19-AOAS1301

Keywords: Chi-square test , CMH test , evolve and resequence , experimental evolution , genetic drift , overdispersion , pool sequencing

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.14 • No. 1 • March 2020
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