A general model for sample size determination for collecting germplasm

The paper develops a general model for determining the minimum sample size for collecting germplasm for genetic conservation with an overall objective of retaining at least one copy of each allele with preassigned probability. It considers sampling from a large heterogeneous 2k-ploid population under a broad range of mating systems leading to a general formula applicable to a fairly large number of populations. It is found that the sample size decreases as ploidy levels increase, but increases with the increase in inbreeding. Under exclusive selfing the sample size is the same, irrespective of the ploidy level, when other parameters are held constant. Minimum sample sizes obtained for diploids by this general formula agree with those already reported by earlier workers. The model confirms the conservative characteristics of genetic variability of polysomic inheritance under chromosomal segregation.     

Inference of individual ploidy level using codominant markers

A significant portion of plant species are polyploids, with ploidy levels sometimes varying among individuals and/or populations. Current techniques to determine the individual ploidy, e.g., flow cytometry, chromosome counting or genotyping‐by‐sequencing, are often cumbersome. Based on the genotypic probabilities for polysomic inheritance under double‐reduction, we developed a model to estimate allele frequency and infer the ploidy status of individuals from the allelic phenotypes of codominant genetic markers. The allele frequencies are estimated by an expectation‐maximization algorithm in the presence of null alleles, false alleles, negative amplifications and self‐fertilization, and the posterior probabilities are used to assign individuals into different levels of ploidy. The accuracy of this method under different conditions is evaluated. Our methods are freely available in a new software package, ploidyinfer , for use by other researchers which can be downloaded from http://github.com/huangkang1987/ploidyinfer .     

Insights into population genetics and evolution of polyploids and their ancestors

We have developed the first comprehensive simulator for polyploid genomes (PolySim) and demonstrated its value by performing large‐scale simulations to examine the effect of different population parameters on the evolution of polyploids. PolySim is unlimited in terms of ploidy, population size or number of simulated loci. Our process considered the evolution of polyploids from diploid ancestors, polysomic inheritance, inbreeding, recombination rate change in polyploids and gene flow from lower to higher ploidies. We compared the number of segregating single nucleotide polymorphisms, minor allele frequency, heterozygosity, R² and average kinship relatedness between different simulated scenarios, and to real data from polyploid species. As expected, allotetraploid populations showed no difference from their ancestral diploids when population size remained constant and there was no gene flow or multivalent (MV) pairing between subgenomes. Autotetraploid populations showed significant differences from their ancestors for most parameters and diverged from their ancestral populations faster than allotetraploids. Autotetraploids can have significantly higher heterozygosity, relatedness and extended linkage disequilibrium compared with allotetraploids. Interestingly, autotetraploids were more sensitive to increasing selfing rate and decreasing population size. MV formation can homogenize allotetraploid subgenomes, but this homogenization requires a higher MV rate than previously proposed. Our results can be considered as the first building block to understand polyploid population evolutionary dynamics. PolySim can be used to simulate a wide variety of polyploid organisms that mimic empirical populations, which, in combination with quantitative genetics tools, can be used to investigate the power of genomewide association, genomic selection or breeding programme designs in these species.     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

A comparison of single‐sample estimators of effective population sizes from genetic marker data

In molecular ecology and conservation genetics studies, the important parameter of effective population size (N_e) is increasingly estimated from a single sample of individuals taken at random from a population and genotyped at a number of marker loci. Several estimators are developed, based on the information of linkage disequilibrium (LD), heterozygote excess (HE), molecular coancestry (MC) and sibship frequency (SF) in marker data. The most popular is the LD estimator, because it is more accurate than HE and MC estimators and is simpler to calculate than SF estimator. However, little is known about the accuracy of LD estimator relative to that of SF and about the robustness of all single‐sample estimators when some simplifying assumptions (e.g. random mating, no linkage, no genotyping errors) are violated. This study fills the gaps and uses extensive simulations to compare the biases and accuracies of the four estimators for different population properties (e.g. bottlenecks, nonrandom mating, haplodiploid), marker properties (e.g. linkage, polymorphisms) and sample properties (e.g. numbers of individuals and markers) and to compare the robustness of the four estimators when marker data are imperfect (with allelic dropouts). Extensive simulations show that SF estimator is more accurate, has a much wider application scope (e.g. suitable to nonrandom mating such as selfing, haplodiploid species, dominant markers) and is more robust (e.g. to the presence of linkage and genotyping errors of markers) than the other estimators. An empirical data set from a Yellowstone grizzly bear population was analysed to demonstrate the use of the SF estimator in practice.     

A pairwise relatedness estimator for polyploids

Studies in genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. Many diploid estimators have been developed using either method‐of‐moments or maximum‐likelihood estimates. However, there are no relatedness estimators for polyploids. The development of a moment estimator for polyploids with polysomic inheritance, which simultaneously incorporates the two‐gene relatedness coefficient and various ‘higher‐order’ coefficients, is described here. The performance of the estimator is compared to other estimators under a variety of conditions. When using a small number of loci, the estimator is biased because of an increase in ill‐conditioned matrices. However, the estimator becomes asymptotically unbiased with large numbers of loci. The ambiguity of polyploid heterozygotes (when balanced heterozygotes cannot be distinguished from unbalanced heterozygotes) is also considered; as with low numbers of loci, genotype ambiguity leads to bias. A software, PolyRelatedness , implementing this method and supporting a maximum ploidy of 8 is provided.     

Effect of recurrent selfing on inbreeding depression and mating system evolution in an autopolyploid plant

Genome duplication resulting in polyploidy can have significant consequences for the evolution of mating systems. Most theory predicts that self‐fertilization will be selectively favored in polyploids; however, many autopolyploids are outcrossing or mixed‐mating. Here, we examine the hypothesis that the evolution of selfing is restricted in autopolyploids because the genetic cost of selfing (i.e., inbreeding depression) increases monotonically with successive generations of inbreeding. Using the herbaceous, autotetraploid plant Chamerion angustifolium, we generated populations with different inbreeding coefficients (F= 0, 0.17 and 0.36) through three consecutive generations of selfing and compared their magnitudes of inbreeding depression in a common environment. Mating system estimates for four natural populations confirmed that tetraploid selfing rates (s_m= 0.25, SE = 0.02) are similar to those of diploids (s_m= 0.12, SE = 0.12; F_1,2= 1.34, P= 0.37) indicating that both cytotypes are predominantly outcrossing. Compared to an outbred control line, mean inbreeding depression for seed production, survival, and height (vegetative and total) in the inbred line differed among generations (inbreeding coefficients). Across all stages, inbreeding depression (relative to control) was positively related to generation (inbreeding coefficient). Although the initial costs of inbreeding in extant and newly synthesized polyploids may be low compared to diploids, the monotonic increase in inbreeding depression with repeated inbreeding may limit the extent to which selfing variants are favored.     

Polymorphic microsatellite DNA markers in black grouse (Tetrao tetrix)

Ten GATA microsatellite DNA markers were isolated and characterized from black grouse (Tetrao tetrix) using an enrichment cloning procedure. High levels of heterozygosity (mean H_O = 0.74 ± 0.026), and a large number of alleles (range = 5–16) were resolved in 70 individuals, indicating these markers will be useful for examining parentage, inbreeding and population structure in black grouse. No evidence for linkage disequilibrium or the presence of null alleles was found.     

Inbreeding depression is high in a self‐incompatible perennial herb population but absent in a self‐compatible population showing mixed mating

High inbreeding depression is thought to be one of the major factors preventing evolutionary transitions in hermaphroditic plants from self‐incompatibility (SI) and outcrossing toward self‐compatibility (SC) and selfing. However, when selfing does evolve, inbreeding depression can be quickly purged, allowing the evolution of complete self‐fertilization. In contrast, populations that show intermediate selfing rates (a mixed‐mating system) typically show levels of inbreeding depression similar to those in outcrossing species, suggesting that selection against inbreeding might be responsible for preventing the transition toward complete self‐fertilization. By implication, crosses among populations should reveal patterns of heterosis for mixed‐mating populations that are similar to those expected for outcrossing populations. Using hand‐pollination crosses, we compared levels of inbreeding depression and heterosis between populations of Linaria cavanillesii (Plantaginaceae), a perennial herb showing contrasting mating systems. The SI population showed high inbreeding depression, whereas the SC population displaying mixed mating showed no inbreeding depression. In contrast, we found that heterosis based on between‐population crosses was similar for SI and SC populations. Our results are consistent with the rapid purging of inbreeding depression in the derived SC population, despite the persistence of mixed mating. However, the maintenance of outcrossing after a transition to SC is inconsistent with the prediction that populations that have purged their inbreeding depression should evolve toward complete selfing, suggesting that the transition to SC in L. cavanillesii has been recent. SC in L. cavanillesii thus exemplifies a situation in which the mating system is likely not at an equilibrium with inbreeding depression.     

Comparing the van Oosterhout and Chybicki‐Burczyk methods of estimating null allele frequencies for inbred populations

In spite of the usefulness of codominant markers in population genetics, the existence of null alleles raises challenging estimation issues in natural populations that are characterized by positive inbreeding coefficients (F > 0). Disregarding the possibility of F > 0 in a population will generally lead to overestimates of null allele frequencies. Conversely, estimates of inbreeding coefficients (F) may be strongly biased upwards (excess homozygotes), in the presence of nontrivial frequencies of null alleles. An algorithm has been presented for the estimation of null allele frequencies in inbred populations (van Oosterhout method), using external estimates of the F‐statistics. The goal of this study is to introduce a modification of this method and to provide a formal comparison with an alternative likelihood‐based method (Chybicki‐Burczyk). Using simulated data, we illustrate the strengths and limitations of these competing methods. Under most circumstances, the likelihood method is preferable, but for highly inbred organisms, a modified van Oosterhout method offers some advantages.     

Effect of partial selfing and polygenic selection on establishment in a new habitat

This article analyzes how partial selfing in a large source population influences its ability to colonize a new habitat via the introduction of a few founder individuals. Founders experience inbreeding depression due to partially recessive deleterious alleles as well as maladaptation to the new environment due to selection on a large number of additive loci. I first introduce a simplified version of the inbreeding history model to characterize mutation‐selection balance in a large, partially selfing source population under selection involving multiple nonidentical loci. I then use individual‐based simulations to study the eco‐evolutionary dynamics of founders establishing in the new habitat under a model of hard selection. The study explores how selfing rate shapes establishment probabilities of founders via effects on both inbreeding depression and adaptability to the new environment, and also distinguishes the effects of selfing on the initial fitness of founders from its effects on the long‐term adaptive response of the populations they found. A high rate of (but not complete) selfing is found to aid establishment over a wide range of parameters, even in the absence of mate limitation. The sensitivity of the results to assumptions about the nature of polygenic selection is discussed.     

Detecting and mapping repulsion-phase linkage in polyploids with polysomic inheritance

It has been suggested that ratios of coupling- to repulsion-phase linked markers can be used to distinguish between allopolyploids and autopolyploids, because repulsion-phase linkages are much more difficult to detect in autopolyploids with polysomic inheritance than allopolyploids with disomic inheritance. In this report, we analyze the segregation pattern of repulsion-phase linked markers in polyploids without complete preferential pairing. The observed repulsion-phase recombination fraction (R) in such polyploids is composed of a fraction due to crossing-over (R_c) and another fraction due to independent assortment (R_i). R_i is the minimum distance that can be detected between repulsion-phase linked markers. Because R_i is high in autopolyploids (0.3373, 0.4000, 0.4286 and 0.4444) for autopolyploids of 2n=4x, 6x, 8x and 10x), large population sizes are required to reliably detect repulsion linkages. In addition, the default linkage used in mapping-programs must be greater than the corresponding R_i to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the R_is have been used in recent polyploid studies to determine polyploid type, and markers have been incorporated into polyploid maps based on the R values. Herein, we describe how mapping repulsion linkages can result in spurious results, and present methods to accurately detect the degree of preferential pairing in polyploids using repulsion linkage analysis. Received: 29 February 2000 / Accepted: 17 July 2000     

Little to no inbreeding depression in a tapeworm with mixed mating

Meta‐studies on hermaphrodites have found a negative relationship between primary selfing rates and levels of inbreeding depression (ID) and, thus, generally support purging in inbred systems. However, in plants, high among‐taxa variance in ID results in no difference in the mean ID between outcrossing and mixed‐mating taxa. Selective interference likely explains high ID among mixed‐mating taxa, whereas low levels of ID among mixed‐mating taxa are not as stressed. Among animal hermaphrodites, primarily molluscs, there are little data on mixed‐mating systems. To fill a taxonomic and mating system gap, we tested for ID in a mixed‐mating tapeworm, Oochoristica javaensis. We provide a direct estimate of ID across infection of an intermediate host by comparing selfing rates at two life history stages. We found little to no evidence for ID, and the level of ID falls in line with what is reported for highly selfing species even though O. javaensis has mixed mating. We discuss this result within the context of kin mating in O. javaensis. Our results emphasize that primary selfing rates alone may be insufficient to classify the inbreeding history in all species when testing for a relationship to ID. Mixed‐mating taxa, and possibly some outcrossing taxa, may exhibit low levels of ID if biparental inbreeding is also driving purging. We advocate that ID studies report estimates of inbreeding history (e.g. F_IS or identity disequilibrium) from nature‐derived adult samples to provide context rather than relying on primary selfing rates alone.     

Microsatellites and the Genetics of Highly Selfing Populations in the Freshwater Snail Bulinus Truncatus

Hermaphrodite tropical freshwater snails provide a good opportunity to study the effects of mating system and genetic drift on population genetic structure because they are self-fertile and they occupy transient patchily distributed habitats (ponds). Up to now the lack of detectable allozyme polymorphism prevented any intrapopulation studies. In this paper, we examine the consequences of selfing and bottlenecks on genetic polymorphism using microsatellite markers in 14 natural populations (under a hierarchical sampling design) of the hermaphrodite freshwater snail Bulinus truncatus. These population genetics data allowed us to discuss the currently available mutation models for microsatellite sequences. Microsatellite markers revealed an unexpectedly high levels of genetic variation with <=41 alleles for one locus and gene diversity of 0.20-0.75 among populations. The values of any estimator of F(is) indicate high selfing rates in all populations. Linkage disequilibria observed at all loci for some populations may also indicate high levels of inbreeding. The large extent of genetic differentiation measured by F(st), R(st) or by a test for homogeneity between genic distributions is explained by both selfing and bottlenecks. Despite a limited gene flow, migration events could be detected when comparing different populations within ponds.     

Microsatellite DNA markers for assessing phylogeographic and population structure in Preble's meadow jumping mice (Zapus hudsonius preblei) and cross‐amplification among neighbouring taxa

We document the isolation and characterization of 14 tetranucleotide microsatellite DNA markers in Preble's meadow jumping mouse (Zapus hudsonius preblei). The identified markers displayed moderate levels of allelic diversity (averaging 4.9 alleles per locus) and heterozygosity (averaging 55.1%). Genotypic and allelic frequencies in a collection of 30 individuals conformed to Hardy–Weinberg equilibrium expectations and indicated no linkage disequilibrium. High levels of cross‐amplification (95% overall) among neighbouring subspecies and two congeners (Zapus princeps and Zapus trinotatus) were observed. Multilocus genotypes resulting from these markers appear to provide ample genetic diversity for studies assessing individual‐ and population–level ecological interactions within Z. h. preblei and evolutionary relationships among neighbouring subspecies (Z. h. campestris, Z. h. intermedius, Z. h. pallidus and Z. h. luteus).     

The divergence history of the perennial plant Linaria cavanillesii confirms a recent loss of self‐incompatibility

Many angiosperms prevent inbreeding through a self‐incompatibility (SI) system, but the loss of SI has been frequent in their evolutionary history. The loss of SI may often lead to an increase in the selfing rate, with the purging of inbreeding depression and the ultimate evolution of a selfing syndrome, where plants have smaller flowers with reduced pollen and nectar production. In this study, we used approximate Bayesian computation (ABC) to estimate the timing of divergence between populations of the plant Linaria cavanillesii that differ in SI status and in which SI is associated with low inbreeding depression but not with a transition to full selfing or a selfing syndrome. Our analysis suggests that the mixed‐mating self‐compatible (SC) population may have begun to diverge from the SI populations around 2810 generation ago, a period perhaps too short for the evolution of a selfing syndrome. We conjecture that the SC population of L. cavanillesii is at an intermediate stage of transition between outcrossing and selfing.     

Characteristics of 13 polymorphic microsatellite markers in the corn earworm,Helicoverpa zea (Lepidoptera: Noctuidae)

Thirteen polymorphic microsatellite loci suitable for population genetic studies of Helicoverpa zea were discovered by screening partial genomic libraries enriched for microsatellite sequences. Insects collected (N = 96) in Stoneville, Mississippi were used to characterize these markers. The observed and effective number of alleles per locus ranged from two to nine (average 4.46) and from 1.07 to 2.45 (average 1.81), respectively. Fisher exact tests detected significant deviations from Hardy–Weinberg equilibrium at three loci, probably due to inbreeding, null alleles, or Wahlund's effect. Significant genotypic disequilibrium was not detected between any pair of loci.     

Mating system and ploidy influence levels of inbreeding depression in Clarkia (Onagraceae)

Inbreeding depression is the reduction in offspring fitness associated with inbreeding and is thought to be one of the primary forces selecting against the evolution of self-fertilization. Studies suggest that most inbreeding depression is caused by the expression of recessive deleterious alleles in homozygotes whose frequency increases as a result of self-fertilization or mating among relatives. This process leads to the selective elimination of deleterious alleles such that highly selfing species may show remarkably little inbreeding depression. Genome duplication (polyploidy) has also been hypothesized to influence levels of inbreeding depression, with polyploids expected to exhibit less inbreeding depression than diploids. We studied levels of inbreeding depression in allotetraploid and diploid species of Clarkia (Onagraceae) that vary in mating system (each cytotype was represented by an outcrossing and a selfing species). The outcrossing species exhibited more inbreeding depression than the selfing species for most fitness components and for two different measures of cumulative fitness. In contrast, though inbreeding depression was generally lower for the polyploid species than for the diploid species, the difference was statistically significant only for flower number and one of the two measures of cumulative fitness. Further, we detected no significant interaction between mating system and ploidy in determining inbreeding depression. In sum, our results suggest that a taxon's current mating system is more important than ploidy in influencing levels of inbreeding depression in natural populations of these annual plants.     

A new likelihood estimator and its comparison with moment estimators of individual genome-wide diversity

The inbreeding coefficient of an individual, F, is one of the central parameters in population genetics theory. It has found important applications in evolutionary biology, conservation and ecology, such as the study of inbreeding depression. In the absence of detailed and reliable pedigree records, researchers have developed quite a few estimators to estimate F or the genome-wide homozygosity from genetic marker data. The statistical properties and comparative performances of these metrics are rarely known, however, which impedes an informed choice of the most appropriate one in practical applications. In this investigation, I propose a new likelihood F estimator that makes efficient use of marker information and takes into account of allelic dropouts, null alleles and prior knowledge of inbreeding. I compare the likelihood estimator with three moment estimators of F and three metrics of genomic homozygosity (or heterozygosity) by analysing both simulated and empirical datasets. It is shown that the likelihood estimator invariably outperforms the other estimators and metrics across all datasets analysed. For a typical dataset in heterozygosity-fitness correlation studies involving 10-20 microsatellites and 50 individuals, the correlation between the likelihood estimator and F (the simulated true inbreeding coefficient) is about 8 ～ 35% higher than that between the moment estimators and F. A frequently applied metric, multilocus heterozygosity (MLH), and an F estimator based on the consideration of the proportion of alleles in homozygous conditions, [F R'), are shown to have particularly poor performances. The low correlation between MLH and fitness traits, which is widely observed in numerous empirical studies, might be partially caused by the adoption of this inefficient estimator of genomic inbreeding.     

THE EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION IN PLANTS. I. GENETIC MODELS

The amounts of inbreeding depression upon selfing and of heterosis upon outcrossing determine the strength of selection on the selfing rate in a population when this evolves polygenically by small steps. Genetic models are constructed which allow inbreeding depression to change with the mean selfing rate in a population by incorporating both mutation to recessive and partially dominant lethal and sublethal alleles at many loci and mutation in quantitative characters under stabilizing selection. The models help to explain observations of high inbreeding depression (> 50%) upon selfing in primarily outcrossing populations, as well as considerable heterosis upon outcrossing in primarily selfing populations. Predominant selfing and predominant outcrossing are found to be alternative stable states of the mating system in most plant populations. Which of these stable states a species approaches depends on the history of its population structure and the magnitude of effect of genes influencing the selfing rate.