Abstract
Autopolyploids present several challenges to researchers studying population genetics, since almost all population genetics theory, and the expectations derived from this theory, has been developed for haploids and diploids. Also many statistical tools for the analysis of genetic data, such as AMOVA and genome scans, are available only for haploids and diploids. In this paper, we show how the Analysis of Molecular Variance (AMOVA) framework can be extended to include autopolyploid data, which will allow calculating several genetic summary statistics for estimating the strength of genetic differentiation among autopolyploid populations (FST, φST, or RST.). We show how this can be done by adjusting the equations for calculating the Sums of Squares, degrees of freedom and covariance components. The method can be applied to a dataset containing a single ploidy level, but also to datasets with a mixture of ploidy levels. In addition, we show how AMOVA can be used to estimate the summary statistic ρ, which was developed especially for polyploid data, but unfortunately has seen very little use. The ρ-statistic can be calculated in an AMOVA by first calculating a matrix of squared Euclidean distances for all pairs of individuals, based on the within-individual allele frequencies. The ρ-statistic is well suited for polyploid data since its expected value is independent of the ploidy level, the rate of double reduction, the frequency of polysomic inheritance, and the mating system. We tested the method using data simulated under a hierarchical island model: the results of the analyses of the simulated data closely matched the values derived from theoretical expectations. The problem of missing dosage information cannot be taken into account directly into the analysis, but can be remedied effectively by imputation of the allele frequencies. We hope that the development of AMOVA for autopolyploids will help to narrow the gap in availability of statistical tools for diploids and polyploids. We also hope that this research will increase the adoption of the ploidy-independent ρ-statistic, which has many qualities that makes it better suited for comparisons among species than the standard FST, both for diploids and for polyploids.
Highlights
Autopolyploidy is an important, but often overlooked, aspect of the evolution of all major groups of Eukaryotes-plants, animals, and fungi- and may constitute an underappreciated source of biodiversity (Hardy, 2015)
We show how the ploidy-independent ρ-statistic can be calculated in Analysis of Molecular Variance (AMOVA) by using a matrix of squared Euclidean distances between individuals, calculated from the within-individual allele frequencies
This is the first study—as far as we are aware—that has compared the theoretical expectations for the hierarchical island model with simulated data; even though hierarchical F-statistics are widely used in analyses of genetic marker data, the theoretical derivations have received very little attention, for autopolyploids as well as for diploids
Summary
Autopolyploidy is an important, but often overlooked, aspect of the evolution of all major groups of Eukaryotes-plants, animals, and fungi- and may constitute an underappreciated source of biodiversity (Hardy, 2015). In a species with different ploidy levels, the different cytotypes often show intricate geographical patterns in their distribution, which may be the result of historical, demographic, ecological, or genetic processes (Glennon et al, 2014; Kolár et al, 2017). The analysis of population genetic structure of autopolyploids may reveal a lot about these processes. Polyploids present several challenges to the researchers studying their population genetics (Dufresne et al, 2014). This is because population genetic theory, the expectations derived from this theory, and the statistical tools for data analysis were developed mostly for haploids and diploids and require translation for polyploids (Meirmans et al, 2018)
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