Breakdown of self-incompatibility due to genetic interaction between a specific S-allele and an unlinked modifier.

Breakdown of self-incompatibility has frequently been attributed to loss-of-function mutations of alleles at the locus responsible for recognition of self-pollen (i.e. the S-locus). However, other potential causes have rarely been tested. Here, we show that self-compatibility of S1S1-homozygotes in selfing populations of the otherwise self-incompatible Arabidopsis lyrata is not due to S-locus mutation. Between-breeding-system cross-progeny are self-compatible if they combine S1 from the self-compatible cross-partner with recessive S1 from the self-incompatible cross-partner, but self-incompatible with dominant S-alleles. Because S1S1 homozygotes in outcrossing populations are self-incompatible, mutation of S1 cannot explain self-compatibility in S1S1 cross-progeny. This supports the hypothesis that an S1-specific modifier unlinked to the S-locus causes self-compatibility by functionally disrupting S1. Self-compatibility in S19S19 homozygotes may also be caused by an S19-specific modifier, but we cannot rule out a loss-of-function mutation of S19. Taken together, our findings indicate that breakdown of self-incompatibility is possible without disruptive mutations at the S-locus.

Differences in mating system and predicted parental conflict affect post-pollination reproductive isolation in a flowering plant.

Mating system shifts from outcrossing to selfing are frequent in plant evolution. Relative to outcrossing, selfing is associated with reduced parental conflict over seed provisioning, which may result in postzygotic, asymmetric, reproductive isolation in crosses between populations of different mating systems. To test the hypothesis that post-pollination reproductive isolation between populations increases with increasing differences in mating system and predicted parental conflict, we performed a crossing experiment involving all combinations of three self-compatible populations (with low outcrossing rates), and three self-incompatible populations (with high outcrossing rates) of the arctic-alpine herb Arabis alpina, assessing fitness-related seed and plant traits of the progeny. Predicted levels of parental conflict ("genome strength") were quantified based on strength of self-incompatibility and estimates of outcrossing rates. Crosses between self-compatible and self-incompatible populations yielded very small seeds of low viability, resulting in strong reproductive isolation. In 14 of 15 reciprocal between-population crosses, seeds were heavier when the paternal plant had the stronger genome, and seed mass differences between cross directions increased with an increased difference in parental conflict. Overall, our results suggest that, when sufficiently large, differences in mating system and hence in expected parental conflict may result in strong post-pollination reproductive barriers contributing to speciation.

Outcrossing rates in an experimentally admixed population of self-compatible and self-incompatible Arabidopsis lyrata.

The transition to self-compatibility from self-incompatibility is often associated with high rates of self-fertilization, which can restrict gene flow among populations and cause reproductive isolation of self-compatible (SC) lineages. Secondary contact between SC and self-incompatible (SI) lineages might re-establish gene flow if SC lineages remain capable of outcrossing. By contrast, intrinsic features of SC plants that reinforce high rates of self-fertilization could maintain evolutionary divergence between lineages. Arabidopsis lyrata subsp. lyrata is characterized by multiple origins of self-compatibility and high rates of self-fertilization in SC-dominated populations. It is unclear whether these high rates of selfing by SC plants have intrinsic or extrinsic causes. We estimated outcrossing rates and examined patterns of pollinator movement for 38 SC and 40 SI maternal parents sampled from an admixed array of 1509 plants sourced from six SC and six SI populations grown under uniform density. Although plants from SI populations had higher outcrossing rates (mean tm = 0.78 ± 0.05 SE) than plants from SC populations (mean tm = 0.56 ± 0.06 SE), outcrossing rates among SC plants were substantially higher than previous estimates from natural populations. Patterns of pollinator movement appeared to contribute to lower outcrossing rates for SC plants; we estimated that 40% of floral visits were geitonogamous (between flowers of the same plant). The relatively high rates of outcrossing for SC plants under standardized conditions indicate that selfing rates in natural SC populations of A. lyrata are facultative and driven by extrinsic features of A. lyrata, including patterns of pollinator movement.

No evidence for incipient speciation by selfing in North American Arabidopsis lyrata.

Self-fertilization inherently restricts gene flow by reducing the fraction of offspring that can be produced by inter-population matings. Therefore, mating system transitions from outcrossing to selfing could result in reproductive isolation between selfing and outcrossing lineages and provide a starting point for speciation. In newly diverged lineages, for example after a transition to selfing, further reproductive isolation can be caused by a variety of prezygotic and post-zygotic mechanisms that operate before, during and after pollination. In animals, prezygotic barriers tend to evolve faster than post-zygotic ones. This is not necessarily the case for plants, for which the relative importance of post-mating, post-fertilization and early-acting post-zygotic barriers has been investigated far less. To test whether post-pollination isolation exists between populations of North American Arabidopsis lyrata that differ in breeding (self-incompatible versus self-compatible) and mating system (outcrossing versus selfing), we compared patterns of seed set after crosses made within populations, between populations of the same mating system and between populations with different mating systems. We found no evidence for post-pollination isolation between plants from selfing populations (self-compatible, low outcrossing rates) and outcrossing populations (self-incompatible, high outcrossing rates) via either prezygotic or early-acting post-zygotic mechanisms. Together with the results of other studies indicating the absence of reproductive barriers acting before and during pollination, we conclude that the transition to selfing in this study system has not led to the formation of reproductive barriers between selfing and outcrossing populations of North American A. lyrata.

Declines in occurrence of plants characteristic for a nutrient-poor meadow habitat are partly explained by their responses to nutrient addition and competition.

Species losses and local extinctions are alarmingly common, frequently as a consequence of habitat destruction. Nevertheless, many intact habitats also face species losses, most likely due to environmental changes. However, the exact drivers, and why they affect some species more than others in apparently intact habitats, are still poorly understood. Addressing these questions requires data on changes in occurrence frequency of many species, and comparisons of the responses of those species to experimental manipulations of the environment. Here, we use historic (1911) and contemporary (2017) data on the presence-absence of 42 plant species in 14 seemingly intact Molinia meadows around Lower Lake Constance to quantify changes in occurrence frequency. Then, we performed a common-garden experiment to test whether occurrence frequencies in 1911 and changes therein by 2017 could be explained by responses of the 42 species to nutrient addition and competition with the acquisitive generalist grass Poa pratensis. Within the 14 still intact Molinia meadows, 36 of the 42 species had declined since 1911. As expected, nutrient addition generally led to increased biomass production of the 42 target species, and competition with P. pratensis had a negative effect. The latter was stronger at high nutrient availability. The more frequent species were in 1911 and the more they declined in frequency between 1911 and 2017, the less above-ground biomass they produced in our experiment. Competition with P. pratensis magnified this effect. Our work highlights that environmental change can contribute to local extinction of species in otherwise intact habitat remnants. Specifically, we showed that increased nutrient availability negatively affected formerly widespread Molinia-meadow species in competition with P. pratensis. Our study thus identified a likely mechanism for the decline in occurrence frequency of species in the remaining Molinia meadows.

Manipulation of cytosine methylation does not remove latitudinal clines in two invasive goldenrod species in Central Europe.

Invasive species frequently differentiate phenotypically in novel environments within a few generations, often even with limited genetic variation. For the invasive plants Solidago canadensis and S. gigantea, we tested whether such differentiation might have occurred through heritable epigenetic changes in cytosine methylation. In a 2-year common-garden experiment, we grew plants from seeds collected along a latitudinal gradient in their non-native Central European range to test for trait differentiation and whether differentiation disappeared when seeds were treated with the demethylation agent zebularine. Microsatellite markers revealed no population structure along the latitudinal gradient in S. canadensis, but three genetic clusters in S. gigantea. Solidago canadensis showed latitudinal clines in flowering phenology and growth. In S. gigantea, the number of clonal offspring decreased with latitude. Although zebularine had a significant effect on early growth, probably through effects on cytosine methylation, latitudinal clines remained (or even got stronger) in plants raised from seeds treated with zebularine. Thus, our experiment provides no evidence that epigenetic mechanisms by selective cytosine methylation contribute to the observed phenotypic differentiation in invasive goldenrods in Central Europe.

Limited phenological and pollinator-mediated isolation among selfing and outcrossing Arabidopsis lyrata populations.

Transitions from outcrossing to selfing have been a frequent evolutionary shift in plants and clearly play a role in species divergence. However, many questions remain about the initial mechanistic basis of reproductive isolation during the evolution of selfing. For instance, how important are pre-zygotic pre-pollination mechanisms (e.g. changes in phenology and pollinator visitation) in maintaining reproductive isolation between newly arisen selfing populations and their outcrossing ancestors? To test whether changes in phenology and pollinator visitation isolate selfing populations of Arabidopsis lyrata from outcrossing populations, we conducted a common garden experiment with plants from selfing and outcrossing populations as well as their between-population hybrids. Specifically, we asked whether there was isolation between outcrossing and selfing plants and their between-population hybrids through differences in (1) the timing or intensity of flowering; and/or (2) pollinator visitation. We found that phenology largely overlapped between plants from outcrossing and selfing populations. There were also no differences in pollinator preference related to mating system. Additionally, pollinators preferred to visit flowers on the same plant rather than exploring nearby plants, creating a large opportunity for self-fertilization. Overall, this suggests that pre-zygotic pre-pollination mechanisms do not strongly reproductively isolate plants from selfing and outcrossing populations of Arabidopsis lyrata.

Differential Contribution of P5CS Isoforms to Stress Tolerance in Arabidopsis.

Proline accumulation is a widespread response of plants to salt stress as well as drought and cold stress. In most plant species, two isoforms of pyrroline-5-carboxylate synthetase (P5CS) catalyze the first step in proline biosynthesis from glutamate. In Arabidopsis, these isoforms differ in their spatial and temporal expression patterns, suggesting sub-functionalization. P5CS1 has been identified as the major contributor to stress-induced proline accumulation, whereas P5CS2 has been considered important for embryo development and growth. In contrast to previous results, our analysis of P5CS1- and P5CS2-GFP fusion proteins indicates that both enzymes were exclusively localized in the cytosol. The comparison of the susceptibility of p5cs1 and p5cs2 mutants to infection with Pseudomonas syringae and salt stress provided novel information on the contribution of the two P5CS isoforms to proline accumulation and stress tolerance. In agreement with previous studies, salt-stressed p5cs1 mutants accumulated very little proline, indicating that P5CS1 contributed more to stress-induced proline accumulation, whereas its impact on stress tolerance was rather weak. Germination and establishment of p5cs2 mutants were impaired under ambient conditions, further supporting that P5CS2 is most important for growth and development, whereas its contribution to stress-induced proline accumulation was smaller than that of P5CS1. In contrast to p5cs1 mutants or wildtype plants, p5cs2 mutants were only weakly affected by sudden exposure to a high NaCl concentration. These findings show that proline content, which was intermediate in leaves of p5cs2 mutants, was not directly correlated with stress tolerance in our experiments. In rosettes of NaCl-exposed p5cs2 mutants, nearly no accumulation of Na+ was observed, and the plants showed neither chlorosis nor reduction of photosynthesis. Based on these data, we suggest a function of P5CS2 or P5CS2-mediated proline synthesis in regulating Na+ accumulation in leaves and thereby salt stress tolerance.

A shift towards the annual habit in selfing Arabidopsis lyrata.

An annual life history is often associated with the ability to self-fertilize. However, it is unknown whether the evolution of selfing commonly precedes the evolution of annuality, or vice versa. Using a 2-year common garden experiment, we asked if the evolution of selfing in the normally perennial Arabidopsis lyrata was accompanied by a shift towards the annual habit. Despite their very recent divergence from obligately outcrossing populations, selfing plants exhibited a 39% decrease in over-winter survival after the first year compared with outcrossing plants. Our data ruled out the most obvious underlying mechanism: differences in reproductive investment in the first year did not explain differences in survival. We conclude that transitions to selfing in perennial A. lyrata may be accompanied by a shift towards annuality, but drivers of the process require further investigation.

Allelopathic effects of native and invasive Brassica nigra do not support the novel-weapons hypothesis.

PREMISE: The novel-weapons hypothesis predicts that some plants are successful invaders because they release allelopathic compounds that are highly suppressive to naïve competitors in invaded ranges but are relatively ineffective against competitors in the native range. For its part, the evolution of enhanced weaponry hypothesis predicts that invasive populations may evolve increased expression of the allelopathic compounds. However, these predictions have rarely been tested empirically. METHODS: Here, we made aqueous extracts of roots and shoots of invasive (North American) and native (European) Brassica nigra plants. Seeds of nine species from North America and nine species from Europe were exposed to these extracts. As control solutions, we used pure distilled water and distilled water with the osmotic potential adjusted with polyethylene glycol (PEG) to match that of root and shoot extracts of B. nigra. RESULTS: The extracts had a strong negative effect on germination rates and seedling root lengths of target species compared to the water-control. Compared to the osmolality-adjusted controls, the extracts had a negative effect on seedling root length. We found no differences between the effects of B. nigra plant extracts from the invasive vs. native populations on germination rates and seedling root growth of target plant species. Responses were largely independent of whether the target plant species were from the invaded or native range of B. nigra. CONCLUSIONS: The results show that B. nigra can interfere with other species through allelochemical interactions, but do not support predictions of the novel-weapons hypothesis and evolution of increased allelopathy.

Sibling competition does not magnify inbreeding depression in North American Arabidopsis lyrata.

About half of all angiosperms have some form of molecular self-incompatibility to promote outcrossing. If self-incompatibility breaks down, inbreeding depression (δ) is the main barrier to the evolution of self-fertilisation (selfing). If inbreeding depression is lower than 50% (δ < 0.5), the inherent transmission advantage of selfers should theoretically drive the evolution of selfing. However, this does not always happen in practice. For example, despite frequent breakdowns of self-incompatibility in North American Arabidopsis lyrata, selfing has only evolved in few populations. This is surprising given that previous inbreeding-depression estimates were well below the 0.5 threshold. Here, we test whether this could be due to underestimation of true inbreeding depression in competition-free environments. Specifically, we tested whether direct competition between crossed and selfed siblings magnified inbreeding-depression estimates in A. lyrata. We found that this was neither the case for belowground nor for aboveground biomass. For reproductive traits, there was hardly any significant inbreeding depression regardless of competition. Combined with previous findings that drought stress and inducing defence also did not magnify inbreeding depression, our results suggest that the relatively low estimates of inbreeding depression for biomass are indeed realistic estimates of the true inbreeding depression in North American A. lyrata.

No evidence for local adaptation and an epigenetic underpinning in native and non-native ruderal plant species in Germany.

Many invasive species have rapidly adapted to different environments in their new ranges. This is surprising, as colonization is usually associated with reduced genetic variation. Heritable phenotypic variation with an epigenetic basis may explain this paradox.Here, we assessed the contribution of DNA methylation to local adaptation in native and naturalized non-native ruderal plant species in Germany. We reciprocally transplanted offspring from natural populations of seven native and five non-native plant species between the Konstanz region in the south and the Potsdam region in the north of Germany. Before the transplant, half of the seeds were treated with the demethylation agent zebularine. We recorded survival, flowering probability, and biomass production as fitness estimates.Contrary to our expectations, we found little evidence for local adaptation, both among the native and among the non-native plant species. Zebularine treatment had mostly negative effects on overall plant performance, regardless of whether plants were local or not, and regardless of whether they were native or non-native. Synthesis. We conclude that local adaptation, at least at the scale of our study, plays no major role in the success of non-native and native ruderal plants. Consequently, we found no evidence yet for an epigenetic basis of local adaptation.

STRUCTURE is more robust than other clustering methods in simulated mixed-ploidy populations.

Analysis of population genetic structure has become a standard approach in population genetics. In polyploid complexes, clustering analyses can elucidate the origin of polyploid populations and patterns of admixture between different cytotypes. However, combining diploid and polyploid data can theoretically lead to biased inference with (artefactual) clustering by ploidy. We used simulated mixed-ploidy (diploid-autotetraploid) data to systematically compare the performance of k-means clustering and the model-based clustering methods implemented in STRUCTURE, ADMIXTURE, FASTSTRUCTURE and INSTRUCT under different scenarios of differentiation and with different marker types. Under scenarios of strong population differentiation, the tested applications performed equally well. However, when population differentiation was weak, STRUCTURE was the only method that allowed unbiased inference with markers with limited genotypic information (co-dominant markers with unknown dosage or dominant markers). Still, since STRUCTURE was comparatively slow, the much faster but less powerful FASTSTRUCTURE provides a reasonable alternative for large datasets. Finally, although bias makes k-means clustering unsuitable for markers with incomplete genotype information, for large numbers of loci (>1000) with known dosage k-means clustering was superior to FASTSTRUCTURE in terms of power and speed. We conclude that STRUCTURE is the most robust method for the analysis of genetic structure in mixed-ploidy populations, although alternative methods should be considered under some specific conditions.

DEG10 contributes to mitochondrial proteostasis, root growth, and seed yield in Arabidopsis.

Maintaining mitochondrial proteome integrity is especially important under stress conditions to ensure a continued ATP supply for protection and adaptation responses in plants. Deg/HtrA proteases are important factors in the cellular protein quality control system, but little is known about their function in mitochondria. Here we analyzed the expression pattern and physiological function of Arabidopsis thaliana DEG10, which has homologs in all photosynthetic eukaryotes. Both expression of DEG10:GFP fusion proteins and immunoblotting after cell fractionation showed an unambiguous subcellular localization exclusively in mitochondria. DEG10 promoter:GUS fusion constructs showed that DEG10 is expressed in trichomes but also in the vascular tissue of roots and aboveground organs. DEG10 loss-of-function mutants were impaired in root elongation, especially at elevated temperature. Quantitative proteome analysis revealed concomitant changes in the abundance of mitochondrial respiratory chain components and assembly factors, which partially appeared to depend on altered mitochondrial retrograde signaling. Under field conditions, lack of DEG10 caused a decrease in seed production. Taken together, our findings demonstrate that DEG10 affects mitochondrial proteostasis, is required for optimal root development and seed set under challenging environmental conditions, and thus contributes to stress tolerance of plants.

Preferential Homologous Chromosome Pairing in a Tetraploid Intergeneric Somatic Hybrid (Citrus reticulata + Poncirus trifoliata) Revealed by Molecular Marker Inheritance.

The creation of intergeneric somatic hybrids between Citrus and Poncirus is an efficient approach for citrus rootstock breeding, offering the possibility of combining beneficial traits from both genera into novel rootstock lineages. These somatic hybrids are also used as parents for further tetraploid sexual breeding. In order to optimize these latter breeding schemes, it is essential to develop knowledge on the mode of inheritance in the intergeneric tetraploid hybrids. We assessed the meiotic behavior of an intergeneric tetraploid somatic hybrid resulting from symmetric protoplast fusion of diploid Citrus reticulata and diploid Poncirus trifoliata. The analysis was based on the segregation patterns of 16 SSR markers and 9 newly developed centromeric/pericentromeric SNP markers, representing all nine linkage groups of the Citrus genetic map. We found strong but incomplete preferential pairing between homologues of the same ancestral genome. The proportion of gametes that can be explained by random meiotic chromosome associations (τ) varied significantly between chromosomes, from 0.09 ± 0.02 to 0.47 ± 0.09, respectively, in chromosome 2 and 1. This intermediate inheritance between strict disomy and tetrasomy, with global preferential disomic tendency, resulted in a high level of intergeneric heterozygosity of the diploid gametes. Although limited, intergeneric recombinations occurred, whose observed rates, ranging from 0.09 to 0.29, respectively, in chromosome 2 and 1, were significantly correlated with τ. Such inheritance is of particular interest for rootstock breeding because a large part of the multi-trait value selected at the teraploid parent level is transmitted to the progeny, while the potential for some intergeneric recombination offers opportunities for generating plants with novel allelic combinations that can be targeted by selection.

Small reductions in corolla size and pollen: ovule ratio, but no changes in flower shape in selfing populations of the North American Arabidopsis lyrata.

The shift from outcrossing to selfing is often accompanied by striking changes in floral morphology towards a "selfing syndrome", which is characterized by flowers with reduction in size, pollen: ovule (P/O) ratio, and herkogamy. This study aims to test whether such changes have occurred in the North American Arabidopsis lyrata, which is of particular interest because of the relatively recent transitions to selfing in this system. Flower size, flower shape, herkogamy levels, P/O ratio, and floral integration of six self-incompatible (outcrossing) and six self-compatible (selfing) populations of A. lyrata were measured in a common environment using conventional and geometric morphometrics methods. Although selfers had on average 9.2% smaller corollas, 8.4% longer pistils, and 21.5% lower P/O ratios than outcrossers, there were no differences in shape, floral integration, and herkogamy between outcrossing and selfing populations. Moreover, most variation in floral traits was explained by population genetic background rather than by mating system. We conclude that selfing populations in A. lyrata have not evolved a selfing syndrome.

The Interaction between Root Herbivory and Competitive Ability of Native and Invasive-Range Populations of Brassica nigra.

The evolution of increased competitive ability (EICA) hypothesis predicts that escape from intense herbivore damage may enable invasive plants to evolve higher competitive ability in the invasive range. Below-ground root herbivory can have a strong impact on plant performance, and invasive plants often compete with multiple species simultaneously, but experimental approaches in which EICA predictions are tested with root herbivores and in a community setting are rare. Here, we used Brassica nigra plants from eight invasive- and seven native-range populations to test whether the invasive-range plants have evolved increased competitive ability when competing with Achillea millefolium and with a community (both with and without A. millefolium). Further, we tested whether competitive interactions depend on root herbivory on B. nigra by the specialist Delia radicum. Without the community, competition with A. millefolium reduced biomass of invasive- but not of native-range B. nigra. With the community, invasive-range B. nigra suffered less than native-range B. nigra. Although the overall effect of root herbivory was not significant, it reduced the negative effect of the presence of the community. The community produced significantly less biomass when competing with B. nigra, irrespective of the range of origin, and independent of the presence of A. millefolium. Taken together, these results offer no clear support for the EICA hypothesis. While native-range B. nigra plants appear to be better in dealing with a single competitor, the invasive-range plants appear to be better in dealing with a more realistic multi-species community. Possibly, this ability of tolerating multiple competitors simultaneously has contributed to the invasion success of B. nigra in North America.

Admixture between native and invasive populations may increase invasiveness of Mimulus guttatus.

Self-fertilization and admixture of genotypes from different populations can have major fitness consequences in native species. However, few studies have addressed their potential roles in invasive species. Here, we used plants of Mimulus guttatus from seven native North American, three invasive Scottish and four invasive New Zealand populations to address this. We created seeds from self-fertilization, within-population outcrossing, between-population outcrossing within the same range, and outcrossing between the native and invasive ranges. A greenhouse experiment showed that native and invasive plants of M. guttatus suffered to similar degrees from inbreeding depression, in terms of asexual reproduction and biomass production. After outcrossing with plants from other populations, M. guttatus benefited from heterosis, in terms of asexual and sexual reproduction, and biomass production, particularly when plants from native and invasive populations were crossed. This suggests that, when novel genotypes of M. guttatus from the native North American range will be introduced to the invasive ranges, subsequent outcrossing with M. guttatus plants that are already there might further boost invasiveness of this species.

Evolution of the Selfing Syndrome in Arabis alpina (Brassicaceae).

INTRODUCTION: The transition from cross-fertilisation (outcrossing) to self-fertilisation (selfing) frequently coincides with changes towards a floral morphology that optimises self-pollination, the selfing syndrome. Population genetic studies have reported the existence of both outcrossing and selfing populations in Arabis alpina (Brassicaceae), which is an emerging model species for studying the molecular basis of perenniality and local adaptation. It is unknown whether its selfing populations have evolved a selfing syndrome. METHODS: Using macro-photography, microscopy and automated cell counting, we compared floral syndromes (size, herkogamy, pollen and ovule numbers) between three outcrossing populations from the Apuan Alps and three selfing populations from the Western and Central Alps (Maritime Alps and Dolomites). In addition, we genotyped the plants for 12 microsatellite loci to confirm previous measures of diversity and inbreeding coefficients based on allozymes, and performed Bayesian clustering. RESULTS AND DISCUSSION: Plants from the three selfing populations had markedly smaller flowers, less herkogamy and lower pollen production than plants from the three outcrossing populations, whereas pistil length and ovule number have remained constant. Compared to allozymes, microsatellite variation was higher, but revealed similar patterns of low diversity and high Fis in selfing populations. Bayesian clustering revealed two clusters. The first cluster contained the three outcrossing populations from the Apuan Alps, the second contained the three selfing populations from the Maritime Alps and Dolomites. CONCLUSION: We conclude that in comparison to three outcrossing populations, three populations with high selfing rates are characterised by a flower morphology that is closer to the selfing syndrome. The presence of outcrossing and selfing floral syndromes within a single species will facilitate unravelling the genetic basis of the selfing syndrome, and addressing which selective forces drive its evolution.

Recent progress and challenges in population genetics of polyploid organisms: an overview of current state-of-the-art molecular and statistical tools.

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.