Fractional paternity assignment: theoretical development and comparison to other methods

A 2b-RAD parentage analysis pipeline for complex and mixed DNA samples

Next-generation sequencing technology has revolutionized genotyping in many fields of study, yet parentage analysis often still relies on microsatellite markers that are costly to generate and are currently available only for a limited number of species. 2b-RAD sequencing (2b-RAD) is a DNA sequencing technique developed for ecological population genomics that utilizes type IIB restriction enzymes to generate consistent, uniform fragments across samples. This technology is inexpensive, effective with low DNA inputs, and robust to DNA degradation. Here, we developed a probabilistic genotyping-by-sequencing genetic testing pipeline for parentage analysis by using 2b-RAD for inferring familial relationships from mixed DNA samples and populations. Our approach to partial paternity assignment utilizes a novel weighted outlier paternity index (WOPI) adapted for next-generation sequencing data and an identity-by-state (IBS) matrix-based clustering method for pedigree reconstruction. The combination of these two parentage assignment methods overcomes two major obstacles faced by other genetic testing methods: 1) It allows detection of parentage when closely related or inbred individuals are in the alleged parent population (e.g., in laboratory strains); and 2) it resolves mixed DNA samples. We successfully demonstrate this novel approach by correctly inferring paternity for samples pooled from multiple offspring (i.e., entire clutches) in a highly inbred population of an East African cichlid fish. The unique advantages of 2b-RAD in combination with our bioinformatics pipeline enable straightforward and cost-effective parentage analysis in any species regardless of genomic resources available.

The future of parentage analysis: From microsatellites to SNPs and beyond

Parentage analysis is a cornerstone of molecular ecology that has delivered fundamental insights into behaviour, ecology and evolution. Microsatellite markers have long been the king of parentage, their hypervariable nature conferring sufficient power to correctly assign offspring to parents. However, microsatellite markers have seen a sharp decline in use with the rise of next-generation sequencing technologies, especially in the study of population genetics and local adaptation. The time is ripe to review the current state of parentage analysis and see how it stands to be affected by the emergence of next-generation sequencing approaches. We find that single nucleotide polymorphisms (SNPs), the typical next-generation sequencing marker, remain underutilized in parentage analysis but are gaining momentum, with 58 SNP-based parentage analyses published thus far. Many of these papers, particularly the earlier ones, compare the power of SNPs and microsatellites in a parentage context. In virtually every case, SNPs are at least as powerful as microsatellite markers. As few as 100-500 SNPs are sufficient to resolve parentage completely in most situations. We also provide an overview of the analytical programs that are commonly used and compatible with SNP data. As the next-generation parentage enterprise grows, a reliance on likelihood and Bayesian approaches, as opposed to strict exclusion, will become increasingly important. We discuss some of the caveats surrounding the use of next-generation sequencing data for parentage analysis and conclude that the future is bright for this important realm of molecular ecology.

Efficient inference of paternity and sibship inference given known maternity via hierarchical clustering

Pedigree and sibship reconstruction are important methods in quantifying relationships and fitness of individuals in natural populations. Current methods employ a Markov chain-based algorithm to explore plausible possible pedigrees iteratively. This provides accurate results, but is time-consuming. Here, we develop a method to infer sibship and paternity relationships from half-sibling arrays of known maternity using hierarchical clustering. Given 50 or more unlinked SNP markers and empirically derived error rates, the method performs as well as the widely used package Colony, but is faster by two orders of magnitude. Using simulations, we show that the method performs well across contrasting mating scenarios, even when samples are large. We then apply the method to open-pollinated arrays of the snapdragon Antirrhinum majus and find evidence for a high degree of multiple mating. Although we focus on diploid SNP data, the method does not depend on marker type and as such has broad applications in nonmodel systems.

BREEDING STRUCTURE OF A YUCCA FILAMENTOSA (AGAVACEAE) POPULATION

Yucca filamentosa and its species-specific pollinator, the yucca moth, Tegeticula yuccasella (Lepidoptera: Prodoxidae), form a relationship that is often cited as a classic example of a coevolved plant-pollinator mutualism. Observations of the moth's behavior have led to predictions that moth dispersal is relatively limited and that, as a consequence, the self-compatible Y. filamentosa should experience relatively high rates of self-fertilization. In contrast, analyses of its mating system indicated that Y. filamentosa was predominantly outcrossed. To better understand effective breeding patterns in Y. filamentosa populations, 10 polymorphic allozyme loci were investigated to analyze the breeding structure of a natural Y. filamentosa population. Analyses revealed that Y. filamentosa is predominantly outcrossed, has multiply sired fruits, and that each fruit was sired by a different set of pollen donors. The effective number of pollen donors per fruit ranged from 1.56 to 3.13, indicating that some correlated mating exists within fruits. Paternity analyses revealed that pollen moved from 6 m to 293 m (mean = 118 m) within the study population and that a minimum of 10% of the progeny were sired by pollen originating outside of the population. These results are discussed in the context of the yucca-yucca moth mutualism.

ATTERNS AND LEVELS OF POLLEN-MEDIATED GENE FLOW IN LATHYRUS LATIFOLIUS

While gene flow can be an important force in evolution, few direct measures are available in the plant literature. Descriptions of gene movement within populations are more common, but have primarily involved crop species and artificially constructed populations. In this study, fractional paternity procedures were used to examine patterns of pollen movement over two years within two sites of Lathyrus latifolius, a bumblebee-pollinated, self-compatible perennial legume. Study sites consisted of 15 to 23 semi-discrete flowering patches that contained 1 to 29 distinct genotypes. Distributions of gene movement distances within the study sites differed significantly from that expected under random mating. Mean gene movement was 14 m. On average, 17.6% (range = 0-52%) of matings occurred within a flowering patch. Outcrossing rates, estimated from paternity analysis, ranged from 0.87 to 0.90 across sites and years. Significant heterogeneity occurred among maternal individuals with respect to outcrossing and immigration rates, indicating that mating patterns were idiosyncratic to each plant. Apparent rates of pollen flow into the sites ranged from 5 to 15%, while estimates of total pollen flow into sites ranged from 16 to 46%. Significant increases in immigration rates between years were associated with decreases in the density of flowering plants.

CONSEQUENCES OF FLORAL VARIATION FOR MALE AND FEMALE REPRODUCTION IN EXPERIMENTAL POPULATIONS OF WILD RADISH, RAPHANUS SATIVUS L

We documented effects of floral variation on seed paternity and maternal fecundity in a series of small experimental populations of wild radish, R. sativus. Each population was composed of two competing pollen donor groups with contrasting floral morphologies and several designated maternal plants. Progeny testing with electrophoretic markers allowed us to measure paternal success. Realized fecundity by each maternal plant and the fraction of those seeds attributable to each pollen donor group were used as outcome variables in path analysis to explore relationships between floral characters (petal size, pollen grain number per flower, and modal pollen grain size), pollinator visitation patterns, and reproductive success. A wide range of pollinator taxa visited the experimental populations, and patterns of discrimination appeared to vary among them. The impact of visitation on male and female reproduction also varied among taxa; visits of small native bees significantly increased paternal success, while those of honey bees reduced male fitness. Only visits by large native bees had discernible effects on recipient fecundity, and, overall, fecundity was not limited by visitation. Maternal plants bearing large-petalled flowers produced fewer flowers during the experiment, reducing their total seed production. In these small populations, postpollination processes (at least in part, compatibility) significantly influenced male and female reproductive success. Variation in pollinator pools occurring on both spatial and temporal scales may act to preserve genetic variation for floral traits in this species.

Gene flow and natural selection shape spatial patterns of genes in tree populations: implications for evolutionary processes and applications

A central question in evolutionary biology is how gene flow and natural selection shape geographic patterns of genotypic and phenotypic variation. My overall research program has pursued this question in tree populations through complementary lines of inquiry. First, through studies of contemporary pollen and seed movement, I have studied how limited gene movement creates fine-scale genetic structure, while long-distance gene flow promotes connectivity. My collaborators and I have provided new tools to study these processes at a landscape scale as well as statistical tests to determine whether changes in landscape conditions or dispersal vectors affect gene movement. Second, my research on spatial patterns of genetic variation has investigated the interacting impacts of geography and climate on gene flow and selection. Third, using next-generation genomic tools, I am now studying genetic variation on the landscape to find initial evidence of climate-associated local adaptation and epigenetic variation to explore its role in plant response to the climate. By integrating these separate lines of inquiry, this research provides specific insight into real-world mechanisms shaping evolution in tree populations and potential impacts of landscape transformation and climate change on these populations, with the prospective goal of contributing to their management and conservation.

The causes of selection on flowering time through male fitness in a hermaphroditic annual plant

Flowering is a key life-history event whose timing almost certainly affects both male and female fitness, but tests of selection on flowering time through male fitness are few. Such selection may arise from direct effects of flowering time, and indirect effects through covariance between flowering time and the environment experienced during reproduction. To isolate these intrinsically correlated associations, we staggered planting dates of Brassica rapa families with known flowering times, creating populations in which age at flowering (i.e., flowering time genotype) and Julian date of flowering (i.e., flowering time environment) were positively, negatively, or uncorrelated. Genetic paternity analysis revealed that male fitness was not strongly influenced by seasonal environmental changes. Instead, when age and date were uncorrelated, selection through male fitness strongly favored young age at flowering. Strategic sampling offspring for paternity analysis rejected covariance between sire age at flowering and dam quality as the cause of this selection. Results instead suggest a negative association between age at flowering and pollen competitive ability. The manipulation also revealed that, at least in B. rapa, the often-observed correlation between flowering time and flowering duration is environmental, not genetic, in origin.

orchard: Paternity program for autotetraploid species

Advances in molecular marker technology have provided new opportunities to study the population genetics of polyploid taxa. Paternity analysis using microsatellite markers can be used in detection of gene flow between individuals and populations, in mating system analysis, to identify factors that influence fecundity and fertility, to identify behaviour of parent-offspring relationships and in the analysis of the reproductive success of different ecological groups. As there is no specific program for carrying out paternity analysis in tetraploid species, specialized software was designed for the assignment of paternity for autotetraploid species. orchard is a novel implementation of exclusion and likelihood statistics for carrying out paternity analysis of autotetraploids. First, the program performs an exclusion method, and then, a likelihood statistic is used with nonexcluded candidate fathers. Optional features include estimation of allele dosage of known mother trees and the estimation of pollen flow distances. orchard was tested using a data set of microsatellite data of Dipteryx odorata, a tetraploid Amazonian tree species.

The role of population origin and microenvironment in seedling emergence and early survival in Mediterranean maritime pine (Pinus pinaster Aiton)

Understanding tree recruitment is needed to forecast future forest distribution. Many studies have reported the relevant ecological factors that affect recruitment success in trees, but the potential for genetic-based differences in recruitment has often been neglected. In this study, we established a semi-natural reciprocal sowing experiment to test for local adaptation and microenvironment effects (evaluated here by canopy cover) in the emergence and early survival of maritime pine (Pinus pinaster Aiton), an emblematic Mediterranean forest tree. A novel application of molecular markers was also developed to test for family selection and, thus, for potential genetic change over generations. Overall, we did not find evidence to support local adaptation at the recruitment stage in our semi-natural experiment. Moreover, only weak family selection (if any) was found, suggesting that in stressful environments with low survival, stochastic processes and among-year climate variability may drive recruitment. Nevertheless, our study revealed that, at early stages of recruitment, microenvironments may favor the population with the best adapted life strategy, irrespectively of its (local or non-local) origin. We also found that emergence time is a key factor for seedling survival in stressful Mediterranean environments. Our study highlights the complexity of the factors influencing the early stages of establishment of maritime pine and provides insights into possible management actions aimed at environmental change impact mitigation. In particular, we found that the high stochasticity of the recruitment process in stressful environments and the differences in population-specific adaptive strategies may difficult assisted migration schemes.

Environment-dependent microevolution in a Mediterranean pine (Pinus pinaster Aiton)

Background

A central question for understanding the evolutionary responses of plant species to rapidly changing environments is the assessment of their potential for short-term (in one or a few generations) genetic change. In our study, we consider the case of Pinus pinaster Aiton (maritime pine), a widespread Mediterranean tree, and (i) test, under different experimental conditions (growth chamber and semi-natural), whether higher recruitment in the wild from the most successful mothers is due to better performance of their offspring; and (ii) evaluate genetic change in quantitative traits across generations at two different life stages (mature trees and seedlings) that are known to be under strong selection pressure in forest trees.

Results

Genetic control was high for most traits (h² = 0.137-0.876) under the milder conditions of the growth chamber, but only for ontogenetic change (0.276), total height (0.415) and survival (0.719) under the more stressful semi-natural conditions. Significant phenotypic selection gradients were found in mature trees for traits related to seed quality (germination rate and number of empty seeds). Moreover, female relative reproductive success was significantly correlated with offspring performance for specific leaf area (SLA) in the growth chamber experiment, and stem mass fraction (SMF) in the experiment under semi-natural conditions, two adaptive traits related to abiotic stress-response in pines. Selection gradients based on genetic covariance of seedling traits and responses to selection at this stage involved traits related to biomass allocation (SMF) and growth (as decomposed by a Gompertz model) or delayed ontogenetic change, depending also on the testing environment.

Conclusions

Despite the evidence of microevolutionary change in adaptive traits in maritime pine, directional or disruptive changes are difficult to predict due to variable selection at different life stages and environments. At mature-tree stages, higher female effective reproductive success can be explained by differences in their production of offspring (due to seed quality) and, to a lesser extent, by seemingly better adapted seedlings. Selection gradients and responses to selection for seedlings also differed across experimental conditions. The distinct processes involved at the two life stages (mature trees or seedlings) together with environment-specific responses advice caution when predicting likely evolutionary responses to environmental change in Mediterranean forest trees.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-014-0200-5) contains supplementary material, which is available to authorized users.

Quantitative analysis of low-density SNP data for parentage assignment and estimation of family contributions to pooled samples

Background

While much attention has focused on the development of high-density single nucleotide polymorphism (SNP) assays, the costs of developing and running low-density assays have fallen dramatically. This makes it feasible to develop and apply SNP assays for agricultural species beyond the major livestock species. Although low-cost low-density assays may not have the accuracy of the high-density assays widely used in human and livestock species, we show that when combined with statistical analysis approaches that use quantitative instead of discrete genotypes, their utility may be improved. The data used in this study are from a 63-SNP marker Sequenom® iPLEX Platinum panel for the Black Tiger shrimp, for which high-density SNP assays are not currently available.

Results

For quantitative genotypes that could be estimated, in 5% of cases the most likely genotype for an individual at a SNP had a probability of less than 0.99. Matrix formulations of maximum likelihood equations for parentage assignment were developed for the quantitative genotypes and also for discrete genotypes perturbed by an assumed error term. Assignment rates that were based on maximum likelihood with quantitative genotypes were similar to those based on maximum likelihood with perturbed genotypes but, for more than 50% of cases, the two methods resulted in individuals being assigned to different families. Treating genotypes as quantitative values allows the same analysis framework to be used for pooled samples of DNA from multiple individuals. Resulting correlations between allele frequency estimates from pooled DNA and individual samples were consistently greater than 0.90, and as high as 0.97 for some pools. Estimates of family contributions to the pools based on quantitative genotypes in pooled DNA had a correlation of 0.85 with estimates of contributions from DNA-derived pedigree.

Conclusions

Even with low numbers of SNPs of variable quality, parentage testing and family assignment from pooled samples are sufficiently accurate to provide useful information for a breeding program. Treating genotypes as quantitative values is an alternative to perturbing genotypes using an assumed error distribution, but can produce very different results. An understanding of the distribution of the error is required for SNP genotyping platforms.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0051-y) contains supplementary material, which is available to authorized users.

Fractional parentage analysis and a scale-free reproductive network of brown trout

In this study, we developed a method of fractional parentage analysis using microsatellite markers. We propose a method for calculating parentage probability, which considers missing data and genotyping errors due to null alleles and other causes, by regarding observed alleles as realizations of random variables which take values in the set of alleles at the locus and developing a method for simultaneously estimating the true and null allele frequencies of all alleles at each locus. We then applied our proposed method to a large sample collected from a wild population of brown trout (Salmo trutta). On analyzing the data using our method, we found that the reproductive success of brown trout obeyed a power law, indicating that when the parent-offspring relationship is regarded as a link, the reproductive system of brown trout is a scale-free network. Characteristics of the reproductive network of brown trout include individuals with large bodies as hubs in the network and different power exponents of degree distributions between males and females.

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.

Effects of male fecundity, interindividual distance and anisotropic pollen dispersal on mating success in a Scots pine (Pinus sylvestris) seed orchard

Quantifying the effect of pollen dispersal and flowering traits on mating success is essential for understanding evolutionary responses to changing environments and establishing strategies for forest tree breeding. This study examined, quantitatively, the effects of male fecundity, interindividual distance and anisotropic pollen dispersal on the mating success of Scots pine (Pinus sylvestris), utilizing a well-mapped Scots pine seed orchard. Paternity analysis of 1021 seeds sampled from 87 trees representing 28 clones showed that 53% of the seeds had at least one potential pollen parent within the orchard. Pronounced variation in paternal contribution was observed among clones. Variations in pollen production explained up to 78% of the variation in mating success, which was 11.2 times greater for clones producing the largest amount of pollen than for clones producing the least pollen. Mating success also varied with intertree distance and direction, which explained up to 28% of the variance. Fertilization between neighboring trees 2.3 m apart was 2.4 times more frequent than between trees 4.6 m apart, and up to 12.4 times higher for trees downwind of the presumed prevailing wind direction than for upwind trees. The effective number of pollen donors recorded in the seed orchard (12.2) was smaller than the theoretical expectation (19.7). Based on the empirical observations, a mating model that best describes the gene dispersal pattern in clonal seed orchards was constructed.

A new version of PRT software for sibling groups reconstruction with comments regarding several issues in the sibling reconstruction problem

Pedigree reconstruction using genotypic markers has become an important tool for the study of natural populations. The nonstandard nature of the underlying statistical problems has led to the necessity of developing specialized statistical and computational methods. In this article, a new version of pedigree reconstruction tools (PRT 2.0) is presented. The software implements algorithms proposed in Almudevar & Field (Journal of Agricultural Biological and Environmental Statistics, 4, 1999, 136) and Almudevar (Biometrics, 57, 2001a, 757) for the reconstruction of single generation sibling groups (SG). A wider range of enumeration algorithms is included, permitting improved computational performance. In particular, an iterative version of the algorithm designed for larger samples is included in a fully automated form. The new version also includes expanded simulation utilities, as well as extensive reporting, including half-sibling compatibility, parental genotype estimates and flagging of potential genotype errors. A number of alternative algorithms are described and demonstrated. A comparative discussion of the underlying methodologies is presented. Although important aspects of this problem remain open, we argue that a number of methodologies including maximum likelihood estimation (COLONY 1.2 and 2.0) and the set cover formulation (KINALYZER) exhibit undesirable properties in the sibling reconstruction problem. There is considerable evidence that large sets of individuals not genetically excluded as siblings can be inferred to be a true sibling group, but it is also true that unrelated individuals may be genetically compatible with a true sibling group by chance. Such individuals may be identified on a statistical basis. PRT 2.0, based on these sound statistical principles, is able to efficiently match or exceed the highest reported accuracy rates, particularly for larger SG. The new version is available at http://www.urmc.rochester.edu/biostat/people/faculty/almudevar.cfm.

The aunt and uncle effect revisited--the effect of biased parentage assignment on fitness estimation in a supplemented salmon population

We investigated differences in the statistical power to assign parentage between an artificially propagated and wild salmon population. The propagated fish were derived from the wild population and are used to supplement its abundance. Levels of genetic variation were similar between the propagated and wild groups at 11 microsatellite loci, and exclusion probabilities were >0.999999 for both groups. The ability to unambiguously identify a pair of parents for each sampled progeny was much lower than expected, however. Simulations demonstrated that the proportion of cases in which the most likely pair of parents were the true parents was lower for propagated parents than for wild parents. There was a clear relationship between parentage assignment ability and the estimated effective number of grandparents of the progeny to be assigned. If a stringent threshold for parentage assignment was used, estimates of relative fitness were biased downward for the propagated fish. The bias appeared to be largely eliminated by either fractionally assigning progeny among parents in proportion to their likelihood of parentage or by assigning progeny to the most likely set of parents without using a statistical threshold.

Using parentage analysis to examine gene flow and spatial genetic structure

Numerous approaches have been developed to examine recent and historical gene flow between populations, but few studies have used empirical data sets to compare different approaches. Some methods are expected to perform better under particular scenarios, such as high or low gene flow, but this, too, has rarely been tested. In this issue of Molecular Ecology, Saenz-Agudelo et al. (2009) apply assignment tests and parentage analysis to microsatellite data from five geographically proximal (2-6 km) and one much more distant (1500 km) panda clownfish populations, showing that parentage analysis performed better in situations of high gene flow, while their assignment tests did better with low gene flow. This unusually complete data set is comprised of multiple exhaustively sampled populations, including nearly all adults and large numbers of juveniles, enabling the authors to ask questions that in many systems would be impossible to answer. Their results emphasize the importance of selecting the right analysis to use, based on the underlying model and how well its assumptions are met by the populations to be analysed.

FRANz: reconstruction of wild multi-generation pedigrees

SUMMARY

We present a software package for pedigree reconstruction in natural populations using co-dominant genomic markers such as microsatellites and single nucleotide polymorphisms (SNPs). If available, the algorithm makes use of prior information such as known relationships (sub-pedigrees) or the age and sex of individuals. Statistical confidence is estimated by Markov Chain Monte Carlo (MCMC) sampling. The accuracy of the algorithm is demonstrated for simulated data as well as an empirical dataset with known pedigree. The parentage inference is robust even in the presence of genotyping errors.

AVAILABILITY

The C source code of FRANz can be obtained under the GPL from http://www.bioinf.uni-leipzig.de/Software/FRANz/.

Powers of discerning: challenges to understanding dispersal processes in natural populations

In this issue of Molecular Ecology, authors Robledo-Arnuncio & Garcia present a compelling approach for quantifying seed dispersal in plant populations. Building upon methods previously used for quantification of pollen dispersal, the authors not only examine the behaviour of the model with respect to sample sizes, dispersal distance, and the kurtosis of the dispersal function but also provide an empirical example using Prunus mahaleb.

Long distance pollen-mediated gene flow at a landscape level: the weed beet as a case study

Gene flow is a crucial parameter that can affect the organization of genetic diversity in plant species. It has important implications in terms of conservation of genetic resources and of gene exchanges between crop to wild relatives and within crop species complex. In the Beta vulgaris complex, hybridization between crop and wild beets in seed production areas is well documented and the role of the ensuing hybrids, weed beets, as bridges towards wild forms in sugar beet production areas have been shown. Indeed, in contrast to cultivated beets that are bi-annual, weed beets can bolt, flower and reproduce in the same crop season. Nonetheless, the extent of pollen gene dispersal through weedy lineages remains unknown. In this study, the focus is directed towards weed-to-weed gene flow, and we report the results of a pollen-dispersal analysis within an agricultural landscape composed of five sugar beet fields with different levels of infestation by weed beets. Our results, based on paternity analysis of 3240 progenies from 135 maternal plants using 10 microsatellite loci, clearly demonstrate that even if weedy plants are mostly pollinated by individuals from the same field, some mating events occur between weed beets situated several kilometres apart (up to 9.6 km), with rates of interfield-detected paternities ranging from 11.3% to 17.5%. Moreover, we show that pollen flow appears to be more restricted when individuals are aggregated as most mating events occurred only for short-distance classes. The best-fit dispersal curves were fat-tailed geometric functions for populations exhibiting low densities of weed beets and thin-tailed Weibull function for fields with weed beet high densities. Thus, weed beet populations characterized by low density with geographically isolated individuals may be difficult to detect but are likely to act as pollen traps for pollen emitted by close and remote fields. Hence, it appears evident that interfield pollen-mediated gene flow between weed beets is almost unavoidable and could contribute to the diffusion of (trans)genes in the agricultural landscape.

A graphical approach to relatedness inference

The estimation of relatedness structure in natural populations using molecular marker data has become an important tool in population biology, resulting in a variety of estimation procedures for specific sampling scenarios. In this article a general approach is proposed, in which the detailed relationship structure, typically a pedigree graph or partition, is considered to be the object of inference. This makes available tools used in complex model selection theory which have demonstrated effectiveness. An important advantage of this approach is that it permits a fully Bayesian approach to the problem, providing a principled and accessible way to measure statistical error. The approach is demonstrated by applying the minimum description length principle. This technique is used in model selection to provide a rational way of comparing models of varying complexity. We show how the resulting score may be interpreted and applied as a Bayesian posterior density.

Pollen Dispersal in Spatially Aggregated Populations

We perform a theoretical study of effective pollen dispersal within plant populations exhibiting intraspecific spatial aggregation. We simulate nonuniform distributions of individuals by means of a Poisson cluster process and use an individual-based spatially explicit model of pollen dispersal to assess the effects of different aggregation patterns on the effective pollen pool size (N(ep)) and the axial variance of pollen dispersal (sigma (p)). Results show clear interactions between clumping and both N(ep) and sigma (p), whose precise form and intensity depend on the relative spatial scale of aggregation to pollen dispersal range. If clump size is small relative to dispersal range, clumping results in lower N(ep) and sigma (p) than in randomly distributed populations. Interestingly, by contrast, aggregation may actually enlarge N(ep) and has minimum impact on sigma (p) if clump size is near or above the scale of dispersal. High intraclump to global density ratios enhance the sensitivity of both N(ep) and sigma (p) to clumping, while leptokurtic pollen dispersal generates sharper reductions of both N(ep) and sigma (p) for small clump sizes and stronger increments of N(ep) for larger clump sizes. Overall, our results indicate that isolation-by-distance models in plants should not ignore the effects of intraspecific spatial aggregation on effective dispersal.

Towards unbiased parentage assignment: combining genetic, behavioural and spatial data in a Bayesian framework

Inferring the parentage of a sample of individuals is often a prerequisite for many types of analysis in molecular ecology, evolutionary biology and quantitative genetics. In all but a few cases, the method of parentage assignment is divorced from the methods used to estimate the parameters of primary interest, such as mate choice or heritability. Here we present a Bayesian approach that simultaneously estimates the parentage of a sample of individuals and a wide range of population-level parameters in which we are interested. We show that joint estimation of parentage and population-level parameters increases the power of parentage assignment, reduces bias in parameter estimation, and accurately evaluates uncertainty in both. We illustrate the method by analysing a number of simulated test data sets, and through a re-analysis of parentage in the Seychelles warbler, Acrocephalus sechellensis. A combination of behavioural, spatial and genetic data are used in the analyses and, importantly, the method does not require strong prior information about the relationship between nongenetic data and parentage.

A new method of estimating the pollen dispersal curve independently of effective density

We introduce a novel indirect method of estimating the pollen dispersal curve from mother-offspring genotypic data. Unlike an earlier indirect approach (TwoGener), this method is based on a normalized measure of correlated paternity between female pairs whose expectation does not explicitly depend on the unknown effective male population density (d(e)). We investigate the statistical properties of the new method, by comparison with those of TwoGener, considering the sensitivity to reductions of d(e), relative to census density, resulting from unequal male fecundity and asynchronous flowering. Our main results are: (i) it is possible to obtain reliable estimates of the average distance of pollen dispersal, delta, from indirect methods, even under nonuniform male fecundity and variable flowering phenology; (ii) the new method yields more accurate and more precise delta-estimates than TwoGener under a wide range of sampling and flowering scenarios; and (iii) TwoGener can be used to obtain approximate d(e) estimates, if needed for other purposes. Our results also show that accurately estimating the shape of the tail of the pollen dispersal function by means of indirect methods remains a very difficult challenge.

Pollen‐mediated gene dispersal within continuous and fragmented populations of a forest understorey species,Trillium cuneatum

Pollen movement plays a critical role in the distribution of genetic variation within and among plant populations. Direct measures of pollen movement in the large, continuous populations that characterize many herbaceous plant species are often technically difficult and biologically unreliable. Here, we studied contemporary pollen movement in four large populations of Trillium cuneatum. Three populations, located in the Georgia Piedmont, are exposed to strong anthropogenic disturbances, while the fourth population, located in the Southern Appalachian Mountains, is relatively undisturbed. Using the recently developed TwoGener analysis, we extracted estimates of the effective number of pollen donors (N(ep)), effective mating neighbourhood size (A(ep)) and the average distance of pollen movement (delta) for each population. We extended the TwoGener method by developing inference on the paternal gametic contribution to the embryo in situations where offspring genotypes are inferred from seeds and elaiosomes of species with bisporic megagametogenesis. Our estimates indicate that maternal plants do not sample pollen randomly from a global pool; rather, pollen movement in all four populations is highly restricted. Although the effective number of pollen donors per maternal plant is low (1.22-1.66) and pollen movement is highly localized in all populations, N(ep) in the disturbed Piedmont populations is higher and there is more pollen movement than in the mountains. The distance pollen moves is greater in disturbed sites and fragmented populations, possibly due to edge effects in Trillium habitats.

Using genetic markers to directly estimate gene flow and reproductive success parameters in plants on the basis of naturally regenerated seedlings

Estimating seed and pollen gene flow in plants on the basis of samples of naturally regenerated seedlings can provide much needed information about "realized gene flow," but seems to be one of the greatest challenges in plant population biology. Traditional parentage methods, because of their inability to discriminate between male and female parentage of seedlings, unless supported by uniparentally inherited markers, are not capable of precisely describing seed and pollen aspects of gene flow realized in seedlings. Here, we describe a maximum-likelihood method for modeling female and male parentage in a local plant population on the basis of genotypic data from naturally established seedlings and when the location and genotypes of all potential parents within the population are known. The method models female and male reproductive success of individuals as a function of factors likely to influence reproductive success (e.g., distance of seed dispersal, distance between mates, and relative fecundity--i.e., female and male selection gradients). The method is designed to account for levels of seed and pollen gene flow into the local population from unsampled adults; therefore, it is well suited to isolated, but also wide-spread natural populations, where extensive seed and pollen dispersal complicates traditional parentage analyses. Computer simulations were performed to evaluate the utility and robustness of the model and estimation procedure and to assess how the exclusion power of genetic markers (isozymes or microsatellites) affects the accuracy of the parameter estimation. In addition, the method was applied to genotypic data collected in Scots pine (isozymes) and oak (microsatellites) populations to obtain preliminary estimates of long-distance seed and pollen gene flow and the patterns of local seed and pollen dispersal in these species.

Genetic evaluation using parentage information from genetic markers1

Genetic evaluation relies on pedigree information to account for the trait information on individuals and their relatives. Recording pedigrees may place unfavorable restrictions on the management of breeding populations, such as the use of single-sire mating groups and the observation of parturition. The use of DNA marker information is an alternative method to identify parents, but it is difficult to assign the parents unambiguously for all progeny in extensively farmed livestock without the use of very many markers. We present methods that use DNA information on parentage within a genetic evaluation system that allow for genotyping errors and for the parentage information to be incomplete, with probabilities assigned to possible parent pairs (i.e., fractional parentage assignment). Two of these methods use a computing strategy that circumvents the high memory requirements associated with the application of previous methods designed for use with fractional parentage assignment. This strategy has an additional advantage of allowing the same statistical models to be used in the evaluation as with recorded pedigrees. The use of DNA marker-based parentage for genetic evaluation is associated with lower genetic gain (at the same survival levels) than by using the true pedigree. This decrease in gain depends on a number of factors, including trait heritability and the DNA markers used. The methods we have described show how DNA marker information could be used to replace traditional pedigree recording.

High diversity of oilseed rape pollen clouds over an agro-ecosystem indicates long-distance dispersal

Abstract Estimating the frequency of long-distance pollination is important in cultivated species, particularly to assess the risk of gene transfer following the release of genetically modified crops. For this purpose, we estimated the diversity and origin of fertilizing pollen in a 10 x 10 km French oilseed rape production area. First, the cultivar grown in each field was identified through surveys to farmers and using microsatellite markers. Examination of the seed set in fields indicated high rates of seed contamination (8.7%) and pollination from other sources (5%). Then, male-sterile plants were scattered over the study area and their seed genotyped using the same markers. Most pollination was local: 65% of the seeds had a compatible sire in the closest field, i.e. at 50 or 300 m depending on site, but the nearest compatible field was found more than 1000 m away for 13% of the seeds. To assess the diversity of fertilizing pollen, each seed was assigned to the nearest putative siring cultivar. The observed diversity of pollen was then compared to that predicted by simulations using three empirical dispersal models with increasing proportion of long-distance pollination. The diversity was sensitive to the dispersal kernel used in the simulations, fatter-tailed functions predicting higher diversities. The dispersal kernel that was more consistent with our data predicted more long-distance dispersal than the exponential function.

Unbiased estimation of relative reproductive success of different groups: evaluation and correction of bias caused by parentage assignment errors

Parentage assignment is widely applied to studies on mating systems, population dynamics and natural selection. However, little is known about the consequence of assignment errors, especially when some parents are not sampled. We investigated the effects of two types of error in parentage assignment, failing to assign a true parent (type A) and assigning an untrue parent (type B), on an estimate of the relative reproductive success (RRS) of two groups of parents. Employing a mathematical approach, we found that (i) when all parents are sampled, minimizing either type A or type B error insures the minimum bias on RRS, and (ii) when a large number of parents is not sampled, type B error substantially biases the estimated RRS towards one. Interestingly, however, (iii) when all parents were sampled and both error rates were moderately high, type A error biased the estimated RRS even more than type B error. We propose new methods to obtain an unbiased estimate of RRS and the number of offspring whose parents are not sampled (zW(z)), by correcting the error effects. Applying them to genotypic data from steelhead trout (Oncorhynchus mykiss), we illustrated how to estimate and control the assignment errors. In the data, we observed up to a 30% assignment error and a strong trade-off between the two types of error, depending on the stringency of the assignment decision criterion. We show that our methods can efficiently estimate an unbiased RRS and zW(z) regardless of assignment method, and how to maximize the statistical power to detect a difference in reproductive success between groups.

Parentage versus two-generation analyses for estimating pollen-mediated gene flow in plant populations

Assessment of contemporary pollen-mediated gene flow in plants is important for various aspects of plant population biology, genetic conservation and breeding. Here, through simulations we compare the two alternative approaches for measuring pollen-mediated gene flow: (i) the NEIGHBORHOOD model--a representative of parentage analyses, and (ii) the recently developed TWOGENER analysis of pollen pool structure. We investigate their properties in estimating the effective number of pollen parents (N(ep)) and the mean pollen dispersal distance (delta). We demonstrate that both methods provide very congruent estimates of N(ep) and delta, when the methods' assumptions considering the shape of pollen dispersal curve and the mating system follow those used in data simulations, although the NEIGHBORHOOD model exhibits generally lower variances of the estimates. The violations of the assumptions, especially increased selfing or long-distance pollen dispersal, affect the two methods to a different degree; however, they are still capable to provide comparable estimates of N(ep). The NEIGHBORHOOD model inherently allows to estimate both self-fertilization and outcrossing due to the long-distance pollen dispersal; however, the TWOGENER method is particularly sensitive to inflated selfing levels, which in turn may confound and suppress the effects of distant pollen movement. As a solution we demonstrate that in case of TWOGENER it is possible to extract the fraction of intraclass correlation that results from outcrossing only, which seems to be very relevant for measuring pollen-mediated gene flow. The two approaches differ in estimation precision and experimental efforts but they seem to be complementary depending on the main research focus and type of a population studied.

Mating patterns, pollen dispersal, and the ecological maternal neighbourhood in a Prunus mahaleb L. population

Gender polymorphism, plant-animal interactions, and environmental heterogeneity are the three important sources of variation in mating system and pollen dispersal patterns. We used progeny arrays and paternity analysis to assess the effects of gender type and density level on variation in mating patterns within a highly isolated population of Prunus mahaleb, a gynodioecious species. All the adult trees in the population were sampled and located. The direct estimate of long-distance insect-mediated pollination events was low (< 10%). Gender expression deeply influenced the mating system, decreasing the outcrossing rates (t(m)) and the pollen pool diversity in hermaphrodite trees. Long intermate distances (> 250 m) were significantly more frequent among female mother trees. Variation in local tree density also affected pollen pool diversity and intermate distance, with a higher effective number of fathers (k(e)) and longer intermate distances for female trees in low-density patches. A canonical correlation analysis showed significant correlations between mating variables and the maternal ecological neighbourhood. Only the first canonical variable was significant and explained 78% of variation. Outcrossing rates tended to decrease, and the relatedness among the fathers tended to increase, when mother trees grew in dense patches with high cover of other woody species and taller vegetation away from the pine forest edge. We highlight the relevance of considering maternal ecological neighbourhood effects on mating system and gene flow studies as maternal trees act simultaneously as receptors of pollen and as sources of the seeds to be dispersed.

How to use molecular marker data to measure evolutionary parameters in wild populations

Estimating the genetic basis of phenotypic traits and the selection pressures acting on them are central to our understanding of the evolution and conservation of wild populations. However, obtaining such evolutionary-related parameters is not an easy task as it requires accurate information on both relatedness among individuals and their breeding success. Polymorphic molecular markers are very useful in estimating relatedness between individuals and parentage analyses are now extensively used in most taxa. The next step in the application of molecular data to wild populations is to use them to derive estimates of evolutionary-related parameters for quantitative traits, such as quantitative genetic parameters (e.g. heritability, genetic correlations) and measures of selection (e.g. selection gradients). Despite their great appeal and potential, the optimal use of molecular tools is still debated and it remains unclear how they should best be used to obtain reliable estimates of evolutionary parameters in the wild. Here, we review the methods available for estimating quantitative genetic and selection parameters and discuss their merits and shortcomings, to provide a tool that summarizes the potential uses of molecular data to obtain such parameters in wild populations.

Contrasting genetic structure of adults and progeny in a Louisiana iris hybrid population

Studies of natural hybridization have suggested that it may be a creative stimulus for adaptive evolution and speciation. An important step in this process is the establishment of fit recombinant genotypes that are buffered from subsequent recombination with unlike genotypes. We used molecular markers and a two-generation sampling strategy to infer the extent of recombination in a Louisiana iris hybrid zone consisting predominantly of Iris fulva-type floral phenotypes. Genotypic diversity was fairly high, indicating that sexual reproduction is frequent relative to clonal reproduction. However, we observed strong spatial genetic structure even after controlling for clonality, which implies a low level of pollen and seed dispersal. We therefore used cluster analysis to explore the hypothesis that the fulva-type hybrids are an admixture of groups between which there has been limited recombination. Our results indicate that several such groups are present in the population and are strongly localized spatially. This spatial pattern is not attributable strictly to a lack of mating opportunities between dissimilar genotypes for two reasons: (1) relatedness of flowering pairs was uncorrelated with the degree of overlap in flowering, and (2) paternity analysis shows that pollen movement among the outcross fraction occurred over large distances, with roughly half of all paternity attributed to pollen flow from outside the population. We also found evidence of strong inbreeding depression, indicated by contrasting estimates of the rate of self-fertilization and the average inbreeding coefficient of fulva-type hybrids. We conclude that groups of similar hybrid genotypes can be buffered from recombination at small spatial scales relative to pollen flow, and selection against certain recombinant genotypes may be as important as or more important than clonal reproduction and inbreeding.

Long-distance pollen flow and tolerance to selfing in a neotropical tree species

Outcrossing rates, pollen dispersal and male mating success were assessed in Dicorynia guianensis Amshoff, a neotropical tree endemic to the Guiana shield. All adult trees within a continuous area of 40 ha (n = 157) were mapped, and were genotyped with six microsatellite loci. In addition, progenies were genotyped from 22 mature trees. At the population level, the species was mostly outcrossing (tm = 0.89) but there was marked variation among individuals. One tree exhibited mixed mating, confirming earlier results obtained with isozymes that D. guianensis can tolerate selfing. A Bayesian extension of the fractional paternity method was used for paternity analysis, and was compared with the neighbourhood method used widely for forest trees. Both methods indicated that pollen dispersal was only weakly related to distance between trees within the study area, and that the majority (62%) of pollen came from outside the study stand. Using maximum likelihood, male potential population size was estimated to be 1119, corresponding to a neighbourhood size of 560 hectares. Male mating success was, however, related to the diameter of the stem and to flowering intensity assessed visually. The mating behaviour of D. guianensis is a combination of long-distance pollen flow and occasional selfing. The species can still reproduce when it is extremely rare, either by selfing or by dispersing pollen at long distances. These results, together with the observation that male mating success was correlated with the size of the trees, could be implemented in management procedures aiming at regenerating the species.