Reliability assessment of null allele detection: inconsistencies between and within different methods

Microsatellite loci are widely used in population genetic studies, but the presence of null alleles may lead to biased results. Here, we assessed five methods that indirectly detect null alleles and found large inconsistencies among them. Our analysis was based on 20 microsatellite loci genotyped in a natural population of Microtus oeconomus sampled during 8 years, together with 1200 simulated populations without null alleles, but experiencing bottlenecks of varying duration and intensity, and 120 simulated populations with known null alleles. In the natural population, 29% of positive results were consistent between the methods in pairwise comparisons, and in the simulated data set, this proportion was 14%. The positive results were also inconsistent between different years in the natural population. In the null‐allele‐free simulated data set, the number of false positives increased with increased bottleneck intensity and duration. We also found a low concordance in null allele detection between the original simulated populations and their 20% random subsets. In the populations simulated to include null alleles, between 22% and 42% of true null alleles remained undetected, which highlighted that detection errors are not restricted to false positives. None of the evaluated methods clearly outperformed the others when both false‐positive and false‐negative rates were considered. Accepting only the positive results consistent between at least two methods should considerably reduce the false‐positive rate, but this approach may increase the false‐negative rate. Our study demonstrates the need for novel null allele detection methods that could be reliably applied to natural populations.     

Gene flow's effect on the genetic architecture of a local adaptation and its consequences for QTL analyses

This paper uses computer simulations to determine how gene flow between populations affects (1) the genetic architecture of a local adaptation and (2) properties of alleles segregating in quantitative trait locus (QTL) mapping populations. Results suggest that the average magnitude of an allele that causes a phenotypic difference between populations declines as the migration rate increases, but with an increase in migration, alleles of larger magnitude cause proportionally more of the phenotypic difference between populations. Gene flow between populations that are used in a QTL study tends to cause the average magnitude and percent variance explained (PVE) of an allele in a mapping population to increase. Thus, although the average magnitude of an allele causing a difference declines with migration the average magnitude or PVE of an allele in a QTL mapping population may increase. The reason is that the probability an allele is sampled for a QTL mapping population is in direct proportion to its frequency and alleles of larger magnitude tend to segregate at relatively higher frequencies than alleles of smaller effect with an increased migration. As the rate of gene flow between populations increases, the proportion of the phenotypic difference explained by alleles that are segregating in a QTL mapping population (and therefore potentially detected) decreases. Lastly, results suggest QTL alleles of large effect (>20% PVE) should be commonly found, provided the divergence time between populations is not too long or optima of populations are not too far apart.     

Inference of population structure under a Dirichlet process model

Inferring population structure from genetic data sampled from some number of individuals is a formidable statistical problem. One widely used approach considers the number of populations to be fixed and calculates the posterior probability of assigning individuals to each population. More recently, the assignment of individuals to populations and the number of populations have both been considered random variables that follow a Dirichlet process prior. We examined the statistical behavior of assignment of individuals to populations under a Dirichlet process prior. First, we examined a best-case scenario, in which all of the assumptions of the Dirichlet process prior were satisfied, by generating data under a Dirichlet process prior. Second, we examined the performance of the method when the genetic data were generated under a population genetics model with symmetric migration between populations. We examined the accuracy of population assignment using a distance on partitions. The method can be quite accurate with a moderate number of loci. As expected, inferences on the number of populations are more accurate when theta = 4N(e)u is large and when the migration rate (4N(e)m) is low. We also examined the sensitivity of inferences of population structure to choice of the parameter of the Dirichlet process model. Although inferences could be sensitive to the choice of the prior on the number of populations, this sensitivity occurred when the number of loci sampled was small; inferences are more robust to the prior on the number of populations when the number of sampled loci is large. Finally, we discuss several methods for summarizing the results of a Bayesian Markov chain Monte Carlo (MCMC) analysis of population structure. We develop the notion of the mean population partition, which is the partition of individuals to populations that minimizes the squared partition distance to the partitions sampled by the MCMC algorithm.     

Population structure at the S-locus of Sorbus aucuparia L. (Rosaceae: Maloideae)

Low sequence divergence within functional alleles is predicted for the self-incompatibility locus because of strong negative frequency-dependent selection. Nevertheless, sequence variation within functional alleles is essential for current models of the evolution of new mating types. We genotyped the stylar self-incompatibility RNase of 20 Sorbus aucuparia from a population in the Pyrenees mountains of France in order to compare alleles found there to those previously sampled in a Belgian population. Both populations returned 20 different alleles from samples of 20 individuals, providing maximum-likelihood estimates of 24.4 (95% CI 20-34) alleles in each. Ten alleles occurred in both samples. The maximum likelihood (ML) estimate of the overlap in the alleles present in both populations was 16, meaning that an estimated eight alleles are private to each population, and a total of 32 alleles occur across the two populations examined. We used Fisher's (1961) missing plot method to estimate that 40 alleles occur in the species. In accord with population genetics theory, we observed at most one synonymous sequence difference between copies of alleles sampled from the different populations and no variation within populations. Phylogenetic analysis shows that nearly every allele in S. aucuparia arose prior to divergence of this species from members of three different genera of the Rosaceae subfamily, Maloideae. Lack of observable sequence variation within alleles, coupled with the slow pace of allelic relative to taxonomic diversification, implies that finding intermediate stages in the process of new allele creation will be difficult in this group.     

Estimation of the number of individuals founding colonized populations

A method for estimating the number of founding chromosomes in an isolated population is introduced. The method assumes that n/2 diploid individuals are sampled from a population and that alleles are identified at L unlinked loci. The population is assumed to have been founded T generations in the past by individuals carrying c chromosomes drawn randomly from a known source population, which has also been sampled. If c is small and the population grew rapidly after it was founded, accurate estimates of c can be obtained and those estimates are not sensitive to details of the history of population sizes. If c is larger or the population remained small after it was founded, then estimates of c depend on the history of population sizes. We test the performance of our method on simulated data and demonstrate its use on data from a rainbow trout (Oncorhynchus mykiss) population.     

Comparative analysis of genetic diversity in the mangrove species Avicennia marina (Forsk.) Vierh. (Avicenniaceae) detected by AFLPs and SSRs

Avicennia marina is an important mangrove species with a wide geographical and climatic distribution which suggests that large amounts of genetic diversity are available for conservation and breeding programs. In this study we compare the informativeness of AFLPs and SSRs for assessing genetic diversity within and among individuals, populations and subspecies of A. marina in Australia. Our comparison utilized three SSR loci and three AFLP primer sets that were known to be polymorphic, and could be run in a single analysis on a capillary electrophoresis system, using different- colored fluorescent dyes. A total of 120 individuals representing six populations and three subspecies were sampled. At the locus level, SSRs were considerably more variable than AFLPs, with a total of 52 alleles and an average heterozygosity of 0.78. Average heterozygosity for AFLPs was 0.193, but all of the 918 bands scored were polymorphic. Thus, AFLPs were considerably more efficient at revealing polymorphic loci than SSRs despite lower average heterozygosities. SSRs detected more genetic differentiation between populations (19 vs 9%) and subspecies (35 vs 11%) than AFLPs. Principal co-ordinate analysis revealed congruent patterns of genetic relationships at the individual, population and subspecific levels for both data sets. Mantel testing confirmed congruence between AFLP and SSR genetic distances among, but not within, population comparisons, indicating that the markers were segregating independently but that evolutionary groups (populations and subspecies) were similar. Three genetic criteria of importance for defining priorities for ex situ collections or in situ conservation programs (number of alleles, number of locally common alleles and number of private alleles) were correlated between the AFLP and SSR data sets. The congruence between AFLP and SSR data sets suggest that either method, or a combination, is applicable to expanded genetic studies of mangroves. The codominant nature of SSRs makes them ideal for further population-based investigations, such as mating-system analyses, for which the dominant AFLP markers are less well suited. AFLPs may be particularly useful for monitoring propagation programs and identifying duplicates within collections, since a single PCR assay can reveal many loci at once. Received: 3 October 2000 / Accepted: 19 February 2001     

The structure of common genetic variation in United States populations

The common-variant/common-disease model predicts that most risk alleles underlying complex health-related traits are common and, therefore, old and found in multiple populations, rather than being rare or population specific. Accordingly, there is widespread interest in assessing the population structure of common alleles. However, such assessments have been confounded by analysis of data sets with bias toward ascertainment of common alleles (e.g., HapMap and Perlegen) or in which a relatively small number of genes and/or populations were sampled. The aim of this study was to examine the structure of common variation ascertained in major U.S. populations, by resequencing the exons and flanking regions of 3,873 genes in 154 chromosomes from European, Latino/Hispanic, Asian, and African Americans generated by the Genaissance Resequencing Project. The frequency distributions of private and common single-nucleotide polymorphisms (SNPs) were measured, and the extent to which common SNPs were shared across populations was analyzed using several different estimators of population structure. Most SNPs that were common in one population were present in multiple populations, but SNPs common in one population were frequently not common in other populations. Moreover, SNPs that were common in two or more populations often differed significantly in frequency from one population to another, particularly in comparisons of African Americans versus other U.S. populations. These findings indicate that, even if the bulk of alleles underlying complex health-related traits are common SNPs, geographic ancestry might well be an important predictor of whether a person carries a risk allele.     

Inferring recent migration rates from individual genotypes

We present a novel and straightforward method for estimating recent migration rates between discrete populations using multilocus genotype data. The approach builds upon a two-step sampling design, where individual genotypes are sampled before and after dispersal. We develop a model that estimates all pairwise backwards migration rates ( m_ij , the probability that an individual sampled in population i is a migrant from population j ) between a set of populations. The method is validated with simulated data and compared with the methods of BayesAss and Structure. First, we use data for an island model and then we consider more realistic data simulations for a metapopulation of the greater white-toothed shrew ( Crocidura russula ). We show that the precision and bias of estimates primarily depend upon the proportion of individuals sampled in each population. Weak sampling designs may particularly affect the quality of the coverage provided by 95% highest posterior density intervals. We further show that it is relatively insensitive to the number of loci sampled and the overall strength of genetic structure. The method can easily be extended and makes fewer assumptions about the underlying demographic and genetic processes than currently available methods. It allows backwards migration rates to be estimated across a wide range of realistic conditions.     

Genetic and demographic dynamics of small populations of Silene latifolia

Small local populations of Silene alba, a short-lived herbaceous plant, were sampled in 1994 and again in 1999. Sampling included estimates of population size and genetic diversity, as measured at six polymorphic allozyme loci. When averaged across populations, there was very little change between samples (about three generations) in population size, measures of within-population genetic diversity such as number of alleles or expected heterozygosity, or in the apportionment of genetic diversity within and among populations as measured by F(st). However, individual populations changed considerably, both in terms of numbers of individuals and genetic composition. Some populations doubled in size between samples, while others shrank by more than 75%. Similarly, expected heterozygosity and allele number increased by more than two-fold in individual populations and decreased by more than three-fold in others. When population-specific change in number and change in measures of genetic diversity were considered together, significant positive correlations were found between the demographic and genetic variables. It is speculated that some populations were released from the demographic consequences of inbreeding depression by gene flow.     

RARE ALLELES AS INDICATORS OF GENE FLOW

A. method for estimating the average level of gene flow in a subdivided population, as measured by the average number of migrants exchanged between local populations, Nm, is presented. The results from a computer simulation model show that the logarithm of Nm is approximately linearly related to the logarithm of the average frequency of private alleles, p?(1), in a sample of alleles from the population. It is shown that this result is relatively insensitive to changes in parameters of the model other than Nm and the number of individuals sampled per population. The dependence of the value of p?(1) on the numbers of individuals sampled provides a rough way to correct for differences in sample size. This method was applied to data from 16 species, showing that estimated values of Nm range from much greater than 1 to less than 0.1. These results confirm the qualitative analysis of Slatkin (1981). This method was also applied to subsamples from a population to show how to measure the extent of isolation of local populations.     

Mathematical consequences of the genealogical species concept

A genealogical species is defined as a basal group of organisms whose members are all more closely related to each other than they are to any organisms outside the group ("exclusivity"), and which contains no exclusive group within it. In practice, a pair of species is so defined when phylogenies of alleles from a sample of loci shows them to be reciprocally monophyletic at all or some specified fraction of the loci. We investigate the length of time it takes to attain this status when an ancestral population divides into two descendant populations of equal size with no gene exchange, and when genetic drift and mutation are the only evolutionary forces operating. The number of loci used has a substantial effect on the probability of observing reciprocal monophyly at different times after population separation, with very long times needed to observe complete reciprocal monophyly for a large number of loci. In contrast, the number of alleles sampled per locus has a relatively small effect on the probability of reciprocal monophyly. Because a single mitochondrial or chloroplast locus becomes reciprocally monophyletic much faster than does a single nuclear locus, it is not advisable to use mitochondrial and chloroplast DNA to recognize genealogical species for long periods after population divergence. Using a weaker criterion of assigning genealogical species status when more than 50% of sampled nuclear loci show reciprocal monophyly, genealogical species status depends much less on the number of sampled loci, and is attained at roughly 4-7 N generations after populations are isolated, where N is the historically effective population size of each descendant. If genealogical species status is defined as more than 95% of sampled nuclear loci showing reciprocal monophyly, this status is attained after roughly 9-12 N generations.     

Evolution in populations of Swedish sand lizards: genetic differentiation and loss of variability revealed by multilocus DNA fingerprinting

The Swedish sand lizard (Lacerta agilis) is a relict species from the period of warmth following the last glacial episode and has a fragmented distribution in central Sweden and a more continuous distribution in the southern part of the country. We used this model system of colonization–extinction for a study of genetic variability within and among Swedish populations from different parts of the distribution range using multilocus DNA fingerprinting. The results from the Swedish populations are then contrasted with those from a large Hungarian population in the centre of the species geographical distribution range, which is likely to closely resemble the ancestral founding population of Sweden. Swedish populations have a low level of genetic variability compared with the Hungarian reference population, which showed a genetic variability within the range described for outbred populations. Within the Swedish populations, the average bandsharing was 0.61, the mean heterozygosity 0.45 and the estimated number of alleles 2.7. The figures for the Hungarian population were a bandsharing of 0.19, a heterozygosity of 0.89 and an estimated number of alleles of 9.8. A population bottleneck, common to all Swedish sand lizards, is indicated by less than 20% of the alleles in the Hungarian population being retained in the Swedish populations, and higher bandsharing similarity between different Swedish populations (0.33) as opposed to the Hungarian population (0.19). The limited variability found in Swedish sand lizards is strongly subdivided between populations, with an average F_ST of 0.32, indicating a very limited gene flow between the isolated populations, as well as between populations in the region where the sand lizard has a more or less continuous distribution (F_ST = 0.41).     

An instantaneous coalescent method insensitive to population structure

Conventional coalescent inferences of population history make the critical assumption that the population under examination is panmictic. However, most populations are structured. This complicates the prevailing coalescent analyses and sometimes leads to inaccurate estimates. To develop a coalescent method unhampered by population structure, we perform two analyses. First, we demonstrate that the coalescent probability of two randomly sampled alleles from the immediate preceding generation(one generation back)is independent of population structure. Second, motivated by this finding, we propose a new coalescent method: i-coalescent analysis. The i-coalescent analysis computes the instantaneous coalescent rate by using a phylogenetic tree of sampled alleles. Using simulated data, we broadly demonstrate the capability of i-coalescent analysis to accurately reconstruct population size dynamics of highly structured populations, although we find this method often requires larger sample sizes for structured populations than for panmictic populations. Overall, our results indicate i-coalescent analysis to be a useful tool, especially for the inference of population histories with intractable structure such as the developmental history of cell populations in the organs of complex organisms.     

A spatial statistical model for landscape genetics

Landscape genetics is a new discipline that aims to provide information on how landscape and environmental features influence population genetic structure. The first key step of landscape genetics is the spatial detection and location of genetic discontinuities between populations. However, efficient methods for achieving this task are lacking. In this article, we first clarify what is conceptually involved in the spatial modeling of genetic data. Then we describe a Bayesian model implemented in a Markov chain Monte Carlo scheme that allows inference of the location of such genetic discontinuities from individual geo-referenced multilocus genotypes, without a priori knowledge on populational units and limits. In this method, the global set of sampled individuals is modeled as a spatial mixture of panmictic populations, and the spatial organization of populations is modeled through the colored Voronoi tessellation. In addition to spatially locating genetic discontinuities, the method quantifies the amount of spatial dependence in the data set, estimates the number of populations in the studied area, assigns individuals to their population of origin, and detects individual migrants between populations, while taking into account uncertainty on the location of sampled individuals. The performance of the method is evaluated through the analysis of simulated data sets. Results show good performances for standard data sets (e.g., 100 individuals genotyped at 10 loci with 10 alleles per locus), with high but also low levels of population differentiation (e.g., F_ST < 0.05). The method is then applied to a set of 88 individuals of wolverines (Gulo gulo) sampled in the northwestern United States and genotyped at 10 microsatellites.     

High inbreeding and low connectivity among Ambystoma texanum populations in fragmented Ohio forests

Habitat loss and fragmentation negatively impact the size and diversity of many natural populations. Woodland amphibians require connected aquatic and terrestrial habitats to complete their life cycle, and often rely on metapopulation structure for long‐term persistence. Wetland loss and deforestation fragment amphibian populations, which may result in population isolation and its negative effects. The aim of this research was to analyze the population genetic structure of small‐mouthed salamanders (Ambystoma texanum) in western Ohio, where agriculture is now the dominant land use. Salamander tail tissue was collected from eight breeding pools. Three pools occur in the same forest; the other five are in forest patches at distances ranging from 250 m to 20 km from one another. Eight microsatellite loci were amplified by PCR and genotyped for allele size. Observed heterozygosities were lower than expected in all sampled populations; the two most isolated sites (Ha1, Ha2) had the highest inbreeding coefficients. Ha2 also had the lowest mean number of alleles and was found to be genetically differentiated from populations to which our data analysis indicates it was historically connected by gene flow. The most distant site (Ha1) had the highest number of private alleles and showed genetic differentiation from other populations both historically and currently. Geographic distance between pools was strongly correlated with the number of private alleles in a population. The results suggest that population isolation results in decreased genetic diversity and that a breakdown of metapopulation structure due to landscape change may contribute to differentiation between once‐connected populations.     

Determination of Genetic Diversity of Vitis vinifera cv. Kabarcik Populations from the Coruh Valley Using SSR Markers

Northeastern Turkey is recognized as one of the most important germplasm centers for the grape in the world. In the present study, simple sequence repeat markers were used to investigate the genetic diversity between four Vitis vinifera cv. Kabarcik populations sampled from the Coruh Valley in Turkey, at altitudes of 800-1,150 m. The mean observed number of alleles per locus varied from 2 (loci VVMD7 and VVMD24) to 6 (VVS2) among populations. The population from the highest altitude showed the greatest average number of alleles, 4.5. With regard to the six loci examined in all populations, the mean observed heterozygosity was higher than the expected heterozygosity. Among the loci, VVS2 (probability of identity = 0.137) was found to be the most informative among populations. Genetic distances between populations ranged from 0.072 to 0.216. Genetic differentiation among populations was strongly related to geographic distances in all populations.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

A population genetic study of six VNTR loci in three ethnically defined populations.

To investigate the population genetic characteristics of VNTR polymorphisms in human populations, we have studied the allele frequency distribution of six VNTR loci (D1S57, RB1, D1S77, D1S61, alpha-globin 5'HVR, D1S76) in three well-defined populations (Kachari of Northeast India; Dogrib Indian of Canada; and New Guinea Highlander of Papua New Guinea). Even though the number of alleles sampled is limited, 48 to 92 alleles per locus per population, significant variation is noticed in the number of alleles per locus for all the populations. Using alternate summary measures, we have observed that genotype distributions at the six VNTR loci apparently conform to their respective Hardy-Weinberg predictions. Multilocus genotype profiles of the individuals in each of the three populations suggest that the VNTR alleles are independently segregating with the exception of the two linked loci D1S76 and D1S77. Lack of fit of all VNTR loci to one particular model of mutational change, either the Infinite Allele Model or the Stepwise Mutation Model, suggests more than one mechanism for production of new VNTR alleles. This study also indicates that increased heterozygosity at VNTR loci in comparison to protein and blood group loci may lead to more accurate estimates of genetic distance.     

Population estimators or progeny tests: what is the best method to assess null allele frequencies at SSR loci?

Nuclear SSRs are notorious for having relatively high frequencies of null alleles, i.e. alleles that fail to amplify and are thus recessive and undetected in heterozygotes. In this paper, we compare two kinds of approaches for estimating null allele frequencies at seven nuclear microsatellite markers in three French Fagus sylvatica populations: (1) maximum likelihood methods that compare observed and expected homozygote frequencies in the population under the assumption of Hardy-Weinberg equilibrium and (2) direct null allele frequency estimates from progeny where parent genotypes are known. We show that null allele frequencies are high in F. sylvatica (7.0% on average with the population method, 5.1% with the progeny method), and that estimates are consistent between the two approaches, especially when the number of sampled maternal half-sib progeny arrays is large. With null allele frequencies ranging between 5% and 8% on average across loci, population genetic parameters such as genetic differentiation (F _ST) may be mostly unbiased. However, using markers with such average prevalence of null alleles (up to 15% for some loci) can be seriously misleading in fine scale population studies and parentage analysis.     

On the size distribution of private microsatellite alleles

Private microsatellite alleles tend to be found in the tails rather than in the interior of the allele size distribution. To explain this phenomenon, we have investigated the size distribution of private alleles in a coalescent model of two populations, assuming the symmetric stepwise mutation model as the mode of microsatellite mutation. For the case in which four alleles are sampled, two from each population, we condition on the configuration in which three distinct allele sizes are present, one of which is common to both populations, one of which is private to one population, and the third of which is private to the other population. Conditional on this configuration, we calculate the probability that the two private alleles occupy the two tails of the size distribution. This probability, which increases as a function of mutation rate and divergence time between the two populations, is seen to be greater than the value that would be predicted if there was no relationship between privacy and location in the allele size distribution. In accordance with the prediction of the model, we find that in pairs of human populations, the frequency with which private microsatellite alleles occur in the tails of the allele size distribution increases as a function of genetic differentiation between populations.