Despite the importance of polyploidy and the increasing availability of new genomic data, there remain important gaps in our knowledge of polyploid population genetics. These gaps arise from the complex nature of polyploid data (e.g. multiple alleles and loci, mixed inheritance patterns, association between ploidy and mating system variation). Furthermore, many of the standard tools for population genetics that have been developed for diploids are often not feasible for polyploids. This review aims to provide an overview of the state-of-the-art in polyploid population genetics and to identify the main areas where further development of molecular techniques and statistical theory is required. We review commonly used molecular tools (amplified fragment length polymorphism, microsatellites, Sanger sequencing, next-generation sequencing and derived technologies) and their challenges associated with their use in polyploid populations: that is, allele dosage determination, null alleles, difficulty of distinguishing orthologues from paralogues and copy number variation. In addition, we review the approaches that have been used for population genetic analysis in polyploids and their specific problems. These problems are in most cases directly associated with dosage uncertainty and the problem of inferring allele frequencies and assumptions regarding inheritance. This leads us to conclude that for advancing the field of polyploid population genetics, most priority should be given to development of new molecular approaches that allow efficient dosage determination, and to further development of analytical approaches to circumvent dosage uncertainty and to accommodate 'flexible' modes of inheritance. In addition, there is a need for more simulation-based studies that test what kinds of biases could result from both existing and novel approaches.

Whole genome duplication (leading to polyploidy) is widely accepted as an important evolutionary force in plants, but it is less recognized as a driver of animal diversification. Nevertheless, it occurs across a wide range of animals; this review investigates why it is particularly common in fish and amphibians, while rare among other vertebrates. We review the current geographic, ecological and phylogenetic distributions of sexually reproducing polyploid taxa before focusing more specifically on what factors drive polyploid formation and establishment. In summary, (1) polyploidy is phylogenetically restricted in both amphibians and fishes, although entire fish, but not amphibian, lineages are derived from polyploid ancestors. (2) Although mechanisms such as polyspermy are feasible, polyploid formation appears to occur principally through unreduced gamete formation, which can be experimentally induced by temperature or pressure shock in both groups. (3) External reproduction and fertilization in primarily temperate freshwater environments potentially exposes zygotes to temperature stress, which can promote increased production of unreduced gametes. (4) Large numbers of gametes and group breeding in relatively confined areas could increase the probability of compatible gamete combinations in both groups. (5) Both fish and amphibians have a propensity to form reproductively successful hybrids; although the relative frequency of autopolyploidy versus allopolyploidy is difficult to ascertain, multiple origins involving hybridization have been confirmed for a number of species in both groups. (6) Problems with establishment of polyploid lineages associated with minority cytotype exclusion could be overcome in amphibians via assortative mating by acoustic recognition of the same ploidy level, but less attention has been given to chemical or acoustic mechanisms that might operate in fish. (7) There is no strong evidence that polyploid fish or amphibians currently exist in more extreme environments than their diploid progenitors or have broader ecological ranges. (8) Although pathogens could play a role in the relative fitness of polyploid species, particularly given duplication of genes involved in immunity, this remains an understudied field in both fish and amphibians. (9) As in plants, many duplicate copies of genes are retained for long periods of time, indicative of selective maintenance of the duplicate copies, but we find no physiological or other reasons that could explain an advantage for allelic or genetic complexity. (10) Extant polyploid species do not appear to be more or less prone to extinction than related diploids in either group. We conclude that, while polyploid fish and amphibians share a number of attributes facilitating polyploidy, clear drivers of genome duplication do not emerge from the comparison. The lack of a clear association of sexually reproducing polyploids with range expansion, harsh environments, or risk of extinction could suggest that stronger correlations in plants may be driven by s...

Although polyploidy has been involved in speciation in both animals and plants, the general perception is often that it is too rare to have been a significant factor in animal evolution and its role in plant diversification has been questioned. These views have resulted in a bias towards explanations for what deters polyploidy, rather than the somewhat more interesting question of the mechanisms by which polyploidy arises and becomes established in both plants and animals. The evidence for and against some of the traditional views on polyploidy is reviewed, with an attempt to synthesize factors promoting evolution through genome duplication in both groups. It is predicted that polyploidy should be more common in temperate than in tropical breeders because environmental fluctuations may promote unreduced gamete formation, it should be most common in organisms with sufficient numbers of gametes that random meiotic problems can be overcome, and it should be more frequent when mechanisms to promote assortative mating are a direct byproduct of genome duplication.

Theoretical and empirical comparisons of molecular diversity in selfing and outcrossing plants have primarily focused on long-term consequences of differences in mating system (between species). However, improving our understanding of the causes of mating system evolution requires ecological and genetic studies of the early stages of mating system transition. Here, we examine nuclear and chloroplast DNA sequences and microsatellite variation in a large sample of populations of Arabidopsis lyrata from the Great Lakes region of Eastern North American that show intra-and interpopulation variation in the degree of self-incompatibility and realized outcrossing rates. Populations show strong geographic clustering irrespective of mating system, suggesting that selfing either evolved multiple times or has spread to multiple genetic backgrounds. Diversity is reduced in selfing populations, but not to the extent of the severe loss of variation expected if selfing evolved due to selection for reproductive assurance in connection with strong founder events. The spread of self-compatibility in this region may have been favored as colonization bottlenecks following glaciation or migration from Europe reduced standing levels of inbreeding depression. However, our results do not suggest a single transition to selfing in this system, as has been suggested for some other species in the Brassicaceae.Arabidopsis, bottlenecks, breakdown of self-incompatibility, demography, effective population size, inbreeding depression, mating system evolution, population genetics.

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