Though polyploidy is an important aspect of the evolutionary genetics of both plants and animals, the development of population genetic theory of polyploids has seriously lagged behind that of diploids. This is unfortunate since the analysis of polyploid genetic data-and the interpretation of the results-requires even more scrutiny than with diploid data. This is because of several polyploidy-specific complications in segregation and genotyping such as tetrasomy, double reduction, and missing dosage information. Here, we review the theoretical and statistical aspects of the population genetics of polyploids. We discuss several widely used types of inferences, including genetic diversity, Hardy-Weinberg equilibrium, population differentiation, genetic distance, and detecting population structure. For each, we point out how the statistical approach, expected result, and interpretation differ between different ploidy levels. We also discuss for each type of inference what biases may arise from the polyploid-specific complications and how these biases can be overcome. From our overview, it is clear that the statistical toolbox that is available for the analysis of genetic data is flexible and still expanding. Modern sequencing techniques will soon be able to overcome some of the current limitations to the analysis of polyploid data, though the techniques are lagging behind those available for diploids. Furthermore, the availability of more data may aggravate the biases that can arise, and increase the risk of false inferences. Therefore, simulations such as we used throughout this review are an important tool to verify the results of analyses of polyploid genetic data.
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