Genetic resources of common ash (Fraxinus excelsior L.) in Poland.

BACKGROUND: Knowledge of genetic structure and the factors that shape it has an impact on forest management practices. European ash (Fraxinus excelsior L.) has declined dramatically throughout its range as a result of a disease caused by the fungus Hymenoscyphus fraxineus. Despite the need for conservation and restoration of the species, genetic data required to guide these efforts at the country level are scarce. Thereofore, we studied the chloroplast and nuclear genetic diversity of 26 natural common ash populations (1269 trees) in Poland. RESULTS: Chloroplast polymorphisms grouped the populations into two geographically structured phylogenetic lineages ascribed to different glacial refugia (the Balkans and the Eastern Alps). However, the populations demonstrated high genetic diversity (mean AR = 12.35; mean Ho = 0.769; mean He = 0.542) but low differentiation based on nuclear microsatellites (FST = 0.045). Significant spatial genetic structure, consistent with models of isolation by distance, was detected in 14 out of 23 populations. Estimated effective population size was moderate-to-high, with a harmonic mean of 57.5 individuals per population. CONCLUSIONS: Genetic diversity was not homogeneously distributed among populations within phylogenetic gene pools, indicating that ash populations are not equal as potential sources of reproductive material. Genetic differences among populations could be related to their histories, including founder effects or gene flow between evolutionary lineages (admixture). Our results suggest that ash stands across Poland could be treated as two main management units (seed zones). Therefore, despite the homogenizing effect of pollen gene flow known for this species, the genetic structure should be taken into account in the management of the genetic resources of the common ash. Although ash dieback poses an additional challenge for the management of genetic resources, efforts should be directed towards protecting populations with high genetic diversity within defined phylogenetic units, as they may be an important source of adaptive variation for future stands.

NMπ 2.0: Software update to minimize the risk of false positives among determinants of reproductive success.

In plant populations, parentage analysis helps understand factors shaping individual reproductive success. However, estimating reproductive success determinants based on parentage counts requires decoupling the effects of individual fecundity and propagule dispersal. The neighbourhood model implemented in the NMπ software provides a standard solution for this problem based on the fixed-effects regression-like approach. Nonetheless, it has been recently shown that the method is prone to false discoveries when important fecundity determinants are omitted. To account for the unexplained variance in fecundity, the Bayesian approach was developed based on the new model (the hierarchical neighbourhood model; HNM). Here, I present the NMπ software update that allows the HNM approach to be used in the framework of a friendly interface. More importantly, the HNM approach is now made available for both dispersed (seedlings) and nondispersed (seeds with known mothers) progeny data. The Bayesian approach, among others, selects significant fecundity determinants, estimates the proportion of variance in reproductive potential explained by selected determinants (R2 ), and provides individual female and male fecundity values. Although the software was designed to handle microsatellite marker data, a solution is proposed for large sets of single nucleotide polymorphisms. The program can be run on Windows (using either a terminal or a graphical interface) as well as (using a terminal) on Linux, or macOS platforms. In any case, NMπ can utilize multicore processors to speed up the analysis. The updated package containing the code, the executable file, the user manual, and example data is available at https://www.ukw.edu.pl/pracownicy/plik/igor_chybicki/3694/.

Identification of determinants of pollen donor fecundity using the hierarchical neighborhood model.

Individual differences in male reproductive success drive genetic drift and natural selection, altering genetic variation and phenotypic trait distributions in future generations. Therefore, identifying the determinants of reproductive success is important for understanding the ecology and evolution of plants. Here, based on the spatially explicit mating model (the neighborhood model), we develop a hierarchical probability model that links co-dominant genotypes of offspring and candidate parents with phenotypic determinants of male reproductive success. The model accounts for pollen dispersal, genotyping errors as well as individual variation in selfing, pollen immigration, and differentiation of immigrant pollen pools. Unlike the classic neighborhood model approach, our approach is specially designed to account for excessive variation (overdispersion) in male fecundity. We implemented a Bayesian estimation method (the Windows computer program available at: https://www.ukw.edu.pl/pracownicy/plik/igor_chybicki/1806/) that, among others, allows for selecting phenotypic variables important for male fecundity and assessing the fraction of variance in fecundity (R2 ) explained by selected variables. Simulations showed that our method outperforms both the classic neighborhood model and the two-step approach, where fecundities and the effects of phenotypic variables are estimated separately. The analysis of two data examples showed that in wind-pollinated trees, male fecundity depends on both the amount of produced pollen and the ability to pollen spread. However, despite that the tree size was positively correlated with male fecundity, it explained only a fraction of the total variance in fecundity, indicating the presence of additional factors. Finally, case studies highlighted the importance of accounting for pollen dispersal in the estimation of fecundity determinants.

Bayesian quantification of ecological determinants of outcrossing in natural plant populations: Computer simulations and the case study of biparental inbreeding in English yew.

The mating system is a central parameter of plant biology because it shapes their ecological and evolutionary properties. Therefore, determining ecological variables that influence the mating system is important for a deeper understanding of the functioning of plant populations. Here, using old concepts and recent statistical developments, we propose a new statistical tool to make inferences about ecological determinants of outcrossing in natural plant populations. The method requires codominant genotypes of seeds collected from maternal plants within different locations. Using extensive computer simulations, we demonstrated that the method is robust to the issues expected for real-world data, including the Wahlund effect, inbreeding and genotyping errors such as allele dropout and allele misclassification. Furthermore, we showed that the estimates of ecological effects and outcrossing rates can be severely biased if genotyping errors and genetic differentiation are not treated explicitly. Application of the new method to the case study of a dioecious tree (Taxus baccata) allowed revealing that female trees that grow in lower local densities have a greater tendency towards mating with relatives. Moreover, we also demonstrated that biparental inbreeding is higher in populations that are characterized by a longer mean distance between trees and a smaller mean trunk perimeter. We found these results to agree with both the theoretical predictions and the history of English yew.

Seed and pollen gene dispersal in Taxus baccata, a dioecious conifer in the face of strong population fragmentation.

Background and Aims: Dispersal is crucial due to its direct impact on dynamics of a species' distribution as well as having a role in shaping adaptive potential through gene flow. In plants forming scarce and small populations, knowledge about the dispersal process is required to assess the potential for colonizing new habitats and connectivity of present and future populations. This study aimed to assess dispersal potential in Taxus baccata, a dioecious gymnosperm tree with a wide but highly fragmented distribution. Methods: Seed and pollen dispersal kernels were estimated directly in the framework of the spatially explicit mating model, where genealogies of naturally established seedlings were reconstructed with the help of microsatellite markers. In this way, six differently shaped dispersal functions were compared. Key Results: Seed dispersal followed a leptokurtic distribution, with the Exponential-Power, the Power-law and Weibull being almost equally best-fitting models. The pollen dispersal kernel appeared to be more fat-tailed than the seed dispersal kernel, and the Lognormal and the Exponential-Power function showed the best fit. The rate of seed immigration from the background sources was not significantly different from the rate of pollen immigration (13.1 % vs. 19.7 %) and immigration rates were in agreement with or below maximum predictions based on the estimated dispersal kernels. Based on the multimodel approach, 95 % of seeds travel <109 m, while 95 % of pollen travels <704 m from the source. Conclusions: The results showed that, at a local spatial scale, yew seeds travel shorter distances than pollen, facilitating a rapid development of a kinship structure. At the landscape level, however, although yew exhibits some potential to colonize new habitats through seed dispersal, genetic connectivity between different yew remnants is strongly limited. Taking into account strong population fragmentation, the study suggests that gene dispersal may be a limiting factor of the adaptability of the species.

NMπ-improved re-implementation of NM+, a software for estimating gene dispersal and mating patterns.

This study introduces the NMπ computer program designed for estimation of plant mating system and seed and pollen dispersal kernels. NMπ is a re-implementation of the NM+ program and provides new features such as support for multicore processors, explicit treatment of dioecy, the possibility of incorporating uniparentally cytoplasmic markers, the possibility of assessing assortative mating due to phenotypic similarity and inference about offspring genealogies. The probability model of parentage (the neighbourhood model) accounts for missing data and genotyping errors, which can be estimated along with regular parameters of the mating system. The program has virtually no restrictions with respect to a number of individuals, markers or phenotypic characters. A console version of NMπ can be run under a wide variety of operating systems, including Windows, Linux or Mac OS. For Windows users, a graphical user interface is provided to facilitate operating the software. The program, user manual and example data are available on http://www.ukw.edu.pl/pracownicy/plik/igor_chybicki/3694/.

Seeing the forest through the trees: comprehensive inference on individual mating patterns in a mixed stand of Quercus robur and Q. petraea.

BACKGROUND AND AIMS: Sexual reproduction is one of the most important moments in a life cycle, determining the genetic composition of individual offspring. Controlled pollination experiments often show high variation in the mating system at the individual level, suggesting a persistence of individual variation in natural populations. Individual variation in mating patterns may have significant adaptive implications for a population and for the entire species. Nevertheless, field data rarely address individual differences in mating patterns, focusing rather on averages. This study aimed to quantify individual variation in the different components of mating patterns. METHODS: Microsatellite data were used from 421 adult trees and 1911 seeds, structured in 72 half-sib families collected in a single mixed stand of Quercus robur and Q. petraea in northern Poland. Using a Bayesian approach, mating patterns were investigated, taking into account pollen dispersal, male fecundity, possible hybridization and heterogeneity in immigrant pollen pools. KEY RESULTS: Pollen dispersal followed a heavy-tailed distribution (283 m on average). In spite of high pollen mobility, immigrant pollen pools showed strong genetic structuring among mothers. At the individual level, immigrant pollen pools showed highly variable divergence rates, revealing that sources of immigrant pollen can vary greatly among particular trees. Within the stand, the distribution of male fecundity appeared highly skewed, with a small number of dominant males, resulting in a ratio of census to effective density of pollen donors of 5·3. Male fecundity was not correlated with tree diameter but showed strong cline-like spatial variation. This pattern can be attributed to environmental variation. Quercus petraea revealed a greater preference (74 %) towards intraspecific mating than Q. robur (36 %), although mating preferences varied among trees. CONCLUSIONS: Mating patterns can reveal great variation among individuals, even within a single even-age stand. The results show that trees can mate assortatively, with little respect for spatial proximity. Such selective mating may be a result of variable combining compatibility among trees due to genetic and/or environmental factors.

Note on the applicability of the F-model in analysis of pollen pool heterogeneity.

Measuring genetic structure of pollen gametes has become the standard approach in studies on plant mating system and pollen flow. However, the popular statistical procedure, TwoGener, provides the point estimate of the pollen pool heterogeneity based on AMOVA, implying any statistical tests regarding pollen pool structure to be based on permutation procedures. In this article, the Bayesian approach was developed based on the Dirichlet-multinomial model (the so-called F-model). Computer simulations revealed the applicability of the Bayesian method in the analysis of pollen pool heterogeneity. Compared with TwoGener, the Bayesian method appeared to have better statistical properties when estimating the inverse of heterogeneity index, mostly due to the relatively high accuracy of the Bayesian estimate when the actual heterogeneity is low. Hence, the Bayesian approach may be preferred, for example, when the effective number of pollen parents is to be assessed. Other applications and potential further developments of the Bayesian method are also briefly discussed.

NM+: software implementing parentage-based models for estimating gene dispersal and mating patterns in plants.

NM+ is computer software designed for making inferences on plant gene dispersal and mating patterns by modelling parentage probabilities of offspring based on the spatially explicit neighbourhood model. NM+ requires a sample of mapped and genotyped candidate parents and offspring; however, offspring may optionally be assigned to single maternal parents (forming so-called half-sib progeny arrays). Using maximum likelihood, NM+ estimates a number of parameters, including proportions of offspring due to self-fertilization, pollen immigration from outside of a defined study site, parameters of pollen (and/or seed) dispersal kernels (exponential-power, Weibull, geometric or 2Dt) and selection gradients relating covariates (phenotypic traits) with male (and/or female) reproductive success. NM+ allows for missing data both in parents and in offspring. It accounts for null alleles and their frequencies can optionally be considered as estimable parameters. Data files are formatted in a table-like structure so they can be easily prepared in a spreadsheet software. By default NM+ is for studying plant populations, however, it can be used for any organism as long as data requirements and model assumptions are met. NM+ runs under Windows, but it can be launched under Linux using WINE emulator. NM+ can be downloaded free of charge from http://www.genetyka.ukw.edu.pl/index_pliki/software.htm.

Simultaneous estimation of null alleles and inbreeding coefficients.

Although microsatellites are a very efficient tool for many population genetics applications, they may occasionally produce "null" alleles, which, when present in high proportion, may affect estimates of key parameters such as inbreeding and relatedness coefficients or measures of genetic differentiation. In order to account for the presence of null alleles, it is first necessary to estimate their frequency within studied populations. However, the commonly used null allele frequency estimators are not of general applicability because they can produce upwardly biased estimates when a population under study experiences some inbreeding. In such a case, 2 formerly described approaches, population inbreeding model and individual inbreeding model, can be applied for simultaneous estimation of null allele frequencies and of the inbreeding coefficient. In this study, we demonstrate the properties and utility of these 2 methods and show that they outperform the commonly used approaches in the estimation of null allele frequencies based on genotypic data. The methods are applied to empirical data from a natural population of European beech (Fagus sylvatica L.), and results are briefly discussed. The methods presented in this paper are implemented in the Windows-based user-friendly INEST computer program (available free of charge at http://genetyka.ukw.edu.pl/INEst10_setup.exe).

Cautions on direct gene flow estimation in plant populations.

Through simulations we have investigated the statistical properties of two of the main approaches for directly estimating pollen gene flow (m) in plant populations: genotypic exclusion and mating models. When the assumptions about accurately known background pollen pool allelic frequencies are met, both methods provide unbiased results with comparable variances across a range of true m values. However, when presumed allelic frequencies differ from actual ones, which is more likely in research practice, both estimators are biased. We demonstrate that the extent and direction of bias largely depend on the difference (measured as genetic distance) between the presumed and actual pollen pools, and on the degree of genetic differentiation between the local population and the actual background pollen sources. However, one feature of the mating model is its ability to estimate pollen gene flow simultaneously with background pollen pool allelic frequencies. We have found that this approach gives nearly unbiased pollen gene flow estimates, and is practical because it eliminates the necessity of providing independent estimates of background pollen pool allelic frequencies. Violations of the mating model assumptions of random mating within local population affect the precision of the estimates only to a limited degree.