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Polyploids are traditionally classified into allopolyploids and autopolyploids, based on their evolutionary origin and their disomic or multisomic mode of inheritance. Over the past decade it has become increasingly clear that there is a continuum between disomic and multisomic inheritance, with the rate of tetrasomy differing among species and among chromosomes within species. Here, we use a simple population genetic model to study the impact of the mode of inheritance on the genetic diversity and population divergence of tetraploids. We found that under almost strict disomic inheritance the tetraploid genome is divided into two separate subgenomes, such as found in classical allopolyploids. In those cases, assuming full tetrasomy in the analysis of polyploid genetic data will lead to an important bias in estimates of genetic diversity and population divergence. However, we found that even a low rate of allele exchange between the two subgenomes, at about one event per generation, is sufficient to homogenise the allele frequencies over the subgenomes, and the estimates become essentially unbiased. The inbreeding coefficient F(IS) can then be used to detect whether the estimates of diversity and divergence will be biased when full multisomy is assumed. Finally, we found that different summary statistics for measuring the strength of population differentiation are differentially affected by a deviation from full tetrasomy. Our model results provide several useful guidelines for the analysis of polyploid data, helping researchers to determine when their inferences are biased and which summary statistics to use.

Introgression is the permanent incorporation of genes from the genome of one population into another. This can have severe consequences, such as extinction of endemic species, or the spread of transgenes. Quantification of the risk of introgression is an important component of genetically modified crop regulation. Most theoretical introgression studies aimed at such quantification disregard one or more of the most important factors concerning introgression: realistic genetical mechanisms, repeated invasions and stochasticity. In addition, the use of linkage as a risk mitigation strategy has not been studied properly yet with genetic introgression models. Current genetic introgression studies fail to take repeated invasions and demographic stochasticity into account properly, and use incorrect measures of introgression risk that can be manipulated by arbitrary choices. In this study, we present proper methods for risk quantification that overcome these difficulties. We generalize a probabilistic risk measure, the so-called hazard rate of introgression, for application to introgression models with complex genetics and small natural population sizes. We illustrate the method by studying the effects of linkage and recombination on transgene introgression risk at different population sizes.

Comparison of population structure between studies can be difficult, because the value of the often-used FST-statistic depends on the amount of genetic variation within populations. Recently, a standardized measure of genetic differentiation was developed based on GST, which addressed this problem, though no method was provided to estimate this standardized measure without bias. Here I present a method to estimate a standardized measure of population differentiation based on the analysis of molecular variance framework. One advantage of the method is that it can be readily expanded to include different hierarchical levels in the tested population structure.