Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Estimation of mating system parameters in plant populations using marker loci with null alleles

Summary An Expectation-Maximization (EM)-algorithm procedure is presented that extends Cheliak et al. (1983) method of maximum-likelihood estimation of mating system parameters of mixed mating system models. The extension permits the estimation of the rate of self-fertilization (s) and allele frequencies (Pi) at loci in outcrossing pollen, at marker loci having recessive null alleles. The algorithm makes use of maternal and filial genotypic arrays obtained by the electrophoretic analysis of cohorts of progeny. The genotypes of maternal plants must be known. Explicit equations are given for cases when the genotype of the maternal gamete inherited by a seed can (gymnosperms) or cannot (angiosperms) be determined. The procedure can accommodate any number of codominant alleles, but only one recessive null allele at each locus. An example, using actual data from Pinus banksiana, is presented to illustrate the application of this EM algorithm to the estimation of mating system parameters using marker loci having both codominant and recessive alleles.Issued as AECL-8745     

Mating patterns and gene flow in the neotropical epiphytic orchid, Laelia rubescens

Understanding mating patterns and gene movement in plant populations occupying highly disturbed landscapes is essential for insights into their long-term survival. We used allozyme genetic markers to examine mating patterns and to directly measure pollen flow in the Central American epiphytic orchid, Laelia rubescens. Study populations were located in disturbed, seasonally dry tropical forest in Costa Rica. Every flowering individual within 15 populations and 12-18 seedlings from each maternal individual were genotyped over two reproductive seasons. Strict correlated mating by orchids produces full-sib progeny arrays from which the multilocus diploid genotype of the pollen parent can be inferred. These paternity analyses produced detailed quantitative estimates of pollen movement within and among populations of this species. Although our data illustrate that mating patterns vary spatially and temporally among trees, among pastures, and between years, overall patterns were surprisingly consistent. Thirty-four per cent of the capsules produced in both years resulted from gene flow events. Where pollen parents were identified, pollen moved mean distances of 279 m and 519 m in 1999 and 2000 respectively and a maximum documented distance of 1034 m. A substantially larger floral display in 2000 corresponded to a marked increase in pollen dispersal distances. Smaller populations, which more closely resembled those in undisturbed forest, had higher rates of gene flow than the large populations that characterize disturbed sites. We predict the occurrence of greater gene flow between low-density populations occupying undisturbed habitats.     

Genetic relatedness in open-pollinated families of two leguminous tree species,Robinia pseudoacacia L. and Gleditsia triacanthos L.

Summary When conducting tree breeding experiments, geneticists often assume that individuals from open-pollinated families are halfsibs. The reliability of this assumption was tested using data from enzyme electrophoresis to estimate the genetic relatedness among progeny within 22 open-pollinated families of Robinia pseudoacacia L. (black locust) and 34 open-pollinated families of Gleditsia triacanthos L. (honey locust) from natural stands. An algorithm employing population estimates of fixation indices, pollen allele frequencies, and selfing rates was used to calculate the mean expected number of alleles in common across loci under assumptions of either full-sib (i.e., a single pollen parent) or half-sib (i.e., random mating) relationships. For each open-pollinated family, the average coefficient of relationship among progeny was calculated by linear interpolation from the observed number of alleles in common. For most families of both species, coefficients were significantly higher than 0.25 (half-sib relation), but were significantly lower than 0.50 (full-sib relation). These results suggest that the assumption of a half-sib relationship among progeny of open-pollinated families is violated for these tree species. More critical to the estimation of heritabilities and the prediction of genetic gains was the observation that estimates of the coefficient of relationship varied widely among open-pollinated families (for R. pseudoacacia r ₀=0.20–0.43, mean=0.34; for G. triacanthos r ₀=0.29–0.55, mean=0.36).     

植物种群交配系统、亲本分析以及基因流动研究

 在过去的二十年中,有关植物种群交配与散布过程的研究与日俱增,重点集中在利用母本子代系列(Maternal progeny arrays)来估计种群间自交与异交的相对比例,种群的花粉散布与雄性育性变异的模式。早期的研究主要依靠排除法来确定亲本,但几乎同时也意识到基因流动事件几乎是检测不到的。在大多数估计中,难以做到为大多数非迁移子代确定唯一的亲本。因此,基因流动与雄性育性的最大似然性方法得以引入该领域的研究。本文介绍了用单位点和多位点模型来估计家系与种群自交与异交的相对频率,着重阐述了目前可用于亲本分析与基因流的估计方法。最后介绍了我们对木根麦冬交配系统与亲本分析的研究以及亲本分析将来的研究方向。     

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.     

Life history changes in Trogoderma variabile and T. inclusum due to mating delay with implications for mating disruption as a management tactic

Controlling postharvest pest species is a costly process with insecticide resistance and species‐specific control requiring multiple tactics. Mating disruption (MD) can be used to both decrease a female's access to males and delay timing of mating and decreases overall mating success in a population and population growth rate. Development of new commercially available MD products requires an understanding of life history parameters associated with mating delay. These can provide information for targeting proportions of reproducing individuals using MD. After delaying mating for females of two closely related beetle species, Trogoderma variabile and T. inclusum, we surveyed survivorship, number of eggs laid, and number of progeny emerged. With increases in mating age, total number of eggs laid and total number of progeny emerged significantly declined over time. T. inclusum typically had greater numbers of eggs laid and progeny emerged compared to T. variabile as female age at mating increased, suggesting that T. inclusum may be more resistant to long‐term delays in mating. Life span showed an increase as mating age increased but life span significantly decreased almost immediately following mating. Simulations depicting multiple distributions of mating within a population suggest that in a closed population, high levels of mating delay significantly reduced reproductive growth rates. Although reproductive growth rates were decreased with increased mating age, they are still large enough to maintain populations. This study highlights the differences in life history between two closely related species, suggesting that T. inclusum outperforms T. variabile over the course of a life span, but T. variabile has better reproductive capabilities early in life. MD may also be a viable component of a pest management system for these two species as it significantly decreased overall reproductive output and population growth.     

Conservation implications of the mating system of the Pampa Hermosa landrace of peach palm analyzed with microsatellite markers

Peach palm (Bactris gasipaes) is cultivated by many indigenous and traditional communities from Amazonia to Central America for its edible fruits, and is currently important for its heart-of-palm. The objective of this study was to investigate the mating system of peach palm, as this is important for conservation and breeding. Eight microsatellite loci were used to genotype 24 open-pollinated progenies from three populations of the Pampa Hermosa landrace maintained in a progeny trial for genetic improvement. Both the multi-locus outcrossing rates (0.95 to 0.99) and the progeny level multi-locus outcrossing rates (0.9 to 1.0) were high, indicating that peach palm is predominantly allogamous. The outcrossing rates among relatives were significantly different from zero (0.101 to 0.202), providing evidence for considerable biparental inbreeding within populations, probably due to farmers planting seeds of a small number of open-pollinated progenies in the same plot. The correlations of paternity estimates were low (0.051 to 0.112), suggesting a large number of pollen sources (9 to 20) participating in pollination of individual fruit bunches. Effective population size estimates suggest that current germplasm collections are insufficient for long-term ex situ conservation. As with most underutilized crops, on farm conservation is the most important component of an integrated conservation strategy.     

Extensive pollen immigration and no evidence of disrupted mating patterns or reproduction in a highly fragmented holm oak stand

Aims Forest fragmentation and reduced tree population densities can potentially have negative impacts on mating patterns, offspring genetic diversity and reproductive performance. The aim of the present study is to test these hypotheses comparing an extremely fragmented, low tree density (~0.02 trees/ha) holm oak (Quercus ilex L.) stand from Central Spain with a nearby high tree density stand (~50 trees/ha).Methods We genotyped adult trees and seeds from the low-density stand (436 seeds from 15 families) and the high-density stand (404 seeds from 11 families) using nine microsatellite markers. With these data, we performed paternity analyses, determined pollen flow, mating patterns and pollen pool structure, and estimated progeny genetic diversity in both stands. We also studied seed set and production and performed a pollen supplementation experiment to determine whether reduced tree density has limited foreign pollen availability.Important findings We have found extensive pollen immigration (>75%) into the low tree density stand and Monte Carlo simulations revealed that pollen moves larger distances than expected from null models of random dispersal. Mating patterns and differentiation of pollen pools were similar in the high-density stand and the low-density stand but we found higher inter-annual differentiation of pollen pools in the former. Progeny genetic diversity and self-fertilization rates did not differ between the low-density stand and the high-density stand. Seed set rates were significantly lower in the low-density stand than in the high-density stand and experimental cross-pollen supplementation evidenced that foreign pollen availability is indeed a limiting factor in the former. However, seed crops did not differ between the low-density stand and the high-density stand, indicating that limitation of foreign pollen is not likely to be of great concern in terms of reduced seed production and potential recruitment. Poor forest regeneration due to other ecological and human factors is probably a more important threat for the persistence of fragmented and low tree density stands than reduced pollen flow and only extremely small and isolated tree populations would be expected to suffer severe loss of genetic diversity in the long term.     

Mating system parameters in species of genus Prosopis (Leguminosae)

The section Algarobia of genus Prosopis involves important natural resources in arid and semiarid regions of the world. Their rationale use requires a better knowledge of their biology, genetics and mating system. There are contradictory information about their mating system. Some authors claim they are protogynous and obligate outcrosser. However, some evidence have been shown indicating that they might not be protogynous and that they might be somewhat self-fertile. The current paper analyses genetic structure and mating system parameters in populations of seven species of this section from South and North America based on isozyme data. In all species a significant homozygote excess was found in the offspring population but not in mother plant genotypes. Multilocus and mean single locus outcrossing rates (tm, ts) indicated that about 15% selfing can occur in the studied populations. The heterogeneity between pollen and ovule allele frequencies was low suggesting population structuration, in agreement with the estimates of correlation of tm within progeny (rt) and correlation of outcrossed paternity (rp). The difference of FIS estimates between offspring and mother plants suggest some selection favouring heterozygotes between seedling and adult stages.     

Surprising similarity of sneaking rates and genetic mating patterns in two populations of sand goby experiencing disparate sexual selection regimes

Molecular markers have proved extremely useful in resolving mating patterns within individual populations of a number of species, but little is known about how genetic mating systems might vary geographically within a species. Here we use microsatellite markers to compare patterns of sneaked fertilization and mating success in two populations of sand goby (Pomatoschistus minutus) that differ dramatically with respect to nest‐site density and the documented nature and intensity of sexual selection. At the Tvärminne site in the Baltic Sea, the microsatellite genotypes of 17 nest‐tending males and mean samples of more than 50 progeny per nest indicated that approximately 35% of the nests contained eggs that had been fertilized by sneaker males. Successful nest holders mated with an average of 3.0 females, and the distribution of mate numbers for these males did not differ significantly from the Poisson expectation. These genetically deduced mating‐system parameters in the Tvärminne population are remarkably similar to those in sand gobies at a distant site adjoining the North Sea. Thus, pronounced differences in the ecological setting and sexual selection regimes in these two populations have not translated into evident differences in cuckoldry rates or other monitored patterns of male mating success. In this case, the ecological setting appears not to be predictive of alternative male mating strategies, a finding of relevance to sexual selection theory.     

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.     

Linkage analysis in unconventional mating designs in line crosses

Linkage estimation and genetic map construction with genotyped DNA markers in plants preferentially employ a few maximally informative early-generation or recombinant-inbred mating designs. Fitting their recombination models to unconventional designs adapted to cultivar development (series of backcrossing, selfing, haploid-doubling, random-intercrossing, and sib-mating steps) distorts single- and multipoint linkage estimates even with dense marker coverage. Two methods are provided for correct linkage estimation in unconventional designs: fitting a correct multigeneration model, or correcting the estimates produced by fitting a one-generation model with any conventional software. These methods also support calculation of multilocus genotype frequencies and QTL-genotype distributions and are available in software.     

Sexual antagonism in the pistil varies among populations of a hermaphroditic mixed‐mating plant

Sexual conflicts and their evolutionary outcomes may be influenced by population‐specific features such as mating system and ecological context; however, very few studies have investigated the link between sexual conflict and mating system. The self‐compatible, mixed‐mating hermaphrodite Collinsia heterophylla (Plantaginaceae) is thought to exhibit a sexual conflict over timing of stigma receptivity. This conflict involves (i) delayed stigma receptivity, which intensifies pollen competition, and (ii) early fertilization forced by pollen, which reduces seed set. We investigated the potential for the conflict to occur under field conditions and performed glasshouse crosses within eight populations to assess its consistency across populations. Flowers were visited, and produced seeds after pollination, at all developmental stages, suggesting that the conflict can be of significance under natural conditions. In the glasshouse, early pollination imposed costs in all populations. Overall, the timing of first seed set was most strongly affected by the maternal parent, denoting stronger female than male ability to influence the onset of stigma receptivity. Crosses also revealed a negative relationship between donor‐ and recipient‐related onset of receptivity within individuals, a novel result hinting at trade‐offs in sex allocation or a history of antagonistic selection. Neither timing of stigma receptivity, timing of first seed set, nor pollen competitive ability covaried with population outcrossing rate. In conclusion, these results indicate that sexually antagonistic selection may be present in varying degrees in different populations of C. heterophylla, but this variation does not appear to be directly related to mating system variation.     

Estimating the impact of divergent mating phenology between residents and migrants on the potential for gene flow

Gene flow between populations can allow the spread of beneficial alleles and genetic diversity between populations, with importance to conservation, invasion biology, and agriculture. Levels of gene flow between populations vary not only with distance, but also with divergence in reproductive phenology. Since phenology is often locally adapted, arriving migrants may be reproductively out of synch with residents, which can depress realized gene flow. In flowering plants, the potential impact of phenological divergence on hybridization between populations can be predicted from overlap in flowering schedules—the daily count of flowers capable of pollen exchange—between a resident and migrant population. The accuracy of this prospective hybridization estimate, based on parental phenotypes, rests upon the assumptions of unbiased pollen transfer between resident and migrant active flowers. We tested the impact of phenological divergence on resident–migrant mating frequencies in experiments that mimicked a single large gene flow event. We first prospectively estimated mating frequencies two lines of Brassica rapaselected or early and late flowering. We then estimated realized mating frequencies retrospectively through progeny testing. The two estimates strongly agreed in a greenhouse experiment, where procedures ensured saturating, unbiased pollination. Under natural pollination in the field, the rate of resident–migrant mating, was lower than estimated by phenological divergence alone, although prospective and retrospective estimates were correlated. In both experiments, differences between residents and migrants in flowering schedule shape led to asymmetric hybridization. Results suggest that a prospective estimate of hybridization based on mating schedules can be a useful, although imperfect, tool for evaluating potential gene flow. They also illustrate the impact of mating phenology on the magnitude and symmetry of reproductive isolation.     

Ecology and evolution of plant mating

Plants exhibit complex mating patterns because of their immobility, hermaphroditism and reliance on vectors for pollen transfer. Research on plant mating attempts to determine who mates with whom in plant populations and how and why mating patterns become evolutionarily modified. Most theoretical models of mating-system evolution have focused on the fitness consequences of selling and outcrossing, stimulating considerable empirical work on the ecology and genetics of inbreeding depression. Less attention has been given to how the mechanics of pollen dispersal influence the transmission of self and outcross gametes. Recent work on the relation between pollen dispersal and mating suggests that many features of floral design traditionally interpreted as anti-selling mechanisms may function to reduce the mating costs associated with large floral displays.     

batemanater: a computer program to estimate and bootstrap mating system variables based on Bateman's principles

Bateman's principles continue to play a major role in the characterization of genetic mating systems in natural populations. The modern manifestations of Bateman's ideas include the opportunity for sexual selection (i.e. I_s – the variance in relative mating success), the opportunity for selection (i.e. I – the variance in relative reproductive success) and the Bateman gradient (i.e. β_ss – the slope of the least‐squares regression of reproductive success on mating success). These variables serve as the foundation for one convenient approach for the quantification of mating systems. However, their estimation presents at least two challenges, which I address here with a new Windows‐based computer software package called batemanater . The first challenge is that confidence intervals for these variables are not easy to calculate. batemanater solves this problem using a bootstrapping approach. The second, more serious, problem is that direct estimates of mating system variables from open populations will typically be biased if some potential progeny or adults are missing from the analysed sample. batemanater addresses this problem using a maximum‐likelihood approach to estimate mating system variables from incompletely sampled breeding populations. The current version of batemanater addresses the problem for systems in which progeny can be collected in groups of half‐ or full‐siblings, as would occur when eggs are laid in discrete masses or offspring occur in pregnant females. batemanater has a user‐friendly graphical interface and thus represents a new, convenient tool for the characterization and comparison of genetic mating systems.     

The messenger matters: Pollinator functional group influences mating system dynamics

The incredible diversity of plant mating systems has fuelled research in evolutionary biology for over a century. Currently, there is broad concern about the impact of rapidly changing pollinator communities on plant populations. Very few studies, however, examine patterns and mechanisms associated with multiple paternity from cross‐pollen loads. Often, foraging pollinators collect a mixed pollen load that may result in the deposition of pollen from different sires to receptive stigmas. Coincident deposition of self‐ and cross‐pollen leads to interesting mating system dynamics and has been investigated in numerous species. But, mixed pollen loads often consist of a diversity of cross‐pollen and result in multiple sires of seeds within a fruit. In this issue of Molecular Ecology, Rhodes, Fant, and Skogen ( 2017 ) examine how pollinator identity and spatial isolation influence multiple paternity within fruits of a self‐incompatible evening primrose. The authors demonstrate that pollen pool diversity varies between two pollinator types, hawkmoths and diurnal solitary bees. Further, progeny from more isolated plants were less likely to have multiple sires regardless of the pollinator type. Moving forward, studies of mating system dynamics should consider the implications of multiple paternity and move beyond the self‐ and cross‐pollination paradigm. Rhodes et al. ( 2017 ) demonstrate the importance of understanding the roles that functionally diverse pollinators play in mating system dynamics.     

The fitness effects of outcrossing in Calylophus serrulatus, a permanent translocation heterozygote

Small and relatively isolated populations that occupy fragmented habitat are at risk of local extinction. However, fitness consequences of fragmentation related to mating distance, such as inbreeding depression following increased self- and near-neighbor mating, may not follow standard expectations in species with specialized genetic systems. We investigated the effect of mating distance on progeny fitness in Calylophus serrulatus, a primarily autogamous, permanent translocation heterozygote that is restricted to prairie fragments in the North American tallgrass prairie region. We pollinated flowers by hand in the field with pollen sampled at various distances from the maternal parent within and between three populations in southeastern Minnesota. We raised the progeny in a greenhouse and measured fitness-related characters. Because their genetic system prevents loss of heterozygosity throughout much of the genome, regardless of inbreeding, permanent translocation heterozygotes are not expected to exhibit inbreeding depression. Consistent with this expectation, in no case did progeny of self matings suffer significantly reduced mean fitness compared to progeny from crosses between plants. Crosses between plants in the two closely situated (2 km) populations yielded progeny with fitness intermediate to their parents, but crosses between each of those populations and the more distant (20 km) population yielded progeny with reduced fitness, suggesting outbreeding depression at this largest spatial scale. Similarly, fitness of self-pollinated progeny and progeny from "near" crosses (<2 m) within populations tended to be higher than "mid" (10-25 m) and "far" (>35 m) cross-progeny fitness. Under the current conditions of fragmentation, it seems likely that the distant matings that produce outbreeding depression are rare. It appears that mean fitness in this species is maintained in the context of severe fragmentation of its populations, largely because of its genetic system.     

Genetic and environmental factors affecting mating type frequency in natural isolates of Tetrahymena thermophila

In Tetrahymena thermophila mating type alleles specify temperature sensitive frequency distributions of multiple mating types. A-like alleles specify mating types I, II, III, V and VI, whereas B-like alleles specify mating types II through VII. We have characterized the mating type distributions specified by several A- and B-like genotypes segregated by genomic exclusion from cells isolated from a pond in northwestern Pennsylvania. The B-like genotypes are alike in specifying very low frequencies of mating type III, but differ with respect to the frequencies of other mating types, particularly II and VII. An A-like genotype specifies a high frequency of mating type III and is unstable in successive generations for the expression of mating type II, suggesting a possible modifier. Inter se crosses performed at 18 degrees C, 28 degrees C and 34 degrees C showed that each genotype specifies a frequency distribution that is uniquely affected by temperature. No mating type was affected the same way by temperature in all genotypes. In A/B heterozygotes, the B-like genotype exhibited partial dominance. The genotypes described here differ significantly from previously described genotypes from the same pond, indicating that there are numerous mating type alleles. For frequency-dependent selection to equalize mating type frequencies, it must act not only on complex multiple alleles but also on the response of mating type alleles to temperature.