STATISTICAL ANALYSIS OF HETEROZYGOSITY DATA: INDEPENDENT SAMPLE COMPARISONS

The distribution of mean heterozygosities under an infinite allele model with constant mutation rate was examined through simulation studies. It was found that, although the variance of the distribution decreases with increasing numbers of loci examined as expected, the shape of the distribution may remain skewed or bimodal. The distribution becomes symmetrical for increasing mean heterozygosity levels and numbers of loci. As a result, parametric statistical tests may not be valid for making comparisons among populations or species. Independent sample t-tests were examined in detail to determine the frequency of rejection of the null hypothesis when pairs of samples are drawn from populations with the same mean heterozygosity. Differing numbers of loci and levels of mean heterozygosity were examined. For mean heterozygosity levels above 7.5%, t-tests provide the proper rejection rate, with as few as five loci. When mean heterozygosity is as low as 2.5%, the t-test is conservative even when 40 loci are examined in each population. Independent sample t-tests were then examined for their power to detect true differences between populations as the degree of difference and number of loci vary. Although large differences can be found with high certainty, differences on the order of 5% heterozygosity may require that large numbers of loci (>40) be examined in order to be 80% or more certain of detecting them. In addition, it is emphasized that, for small numbers of loci (<25), the statistical detection of differences of interesting magnitude requires that relatively rare sampling events occur and that much larger differences be observed among the samples than exist for the population means. Two reasons exist for the lack of sensitivity of the test procedures. First, when mean heterozygosity levels are low, the non-normality of the sample means is perhaps most important. Second, even when mean heterozygosity levels are high or when sample sizes are large enough so sample means are approximately normally distributed, the intrinsically high interlocus variance of heterozygosity estimates makes the tests insensitive to the presence of heterozygosity differences that might be biologically meaningful. Finally, the implications of the results of this study are discussed with regard to observed low levels of correlation between heterozygosity and other explanatory variables.     

Moderately and Highly Polymorphic Microsatellites Provide Discordant Estimates of Population Divergence in Sockeye Salmon, Oncorhynchus nerka

Mutation rate can vary widely among microsatellite loci. This variation may cause discordant single-locus and multi-locus estimates of F_ST, the commonly used measure of population divergence. We use 16 microsatellite and five allozyme loci from 14 sockeye salmon populations to address two questions about the affect of mutation rate on estimates of F_ST: (1) does mutation rate influence F_ST estimates from all microsatellites to a similar degree relative to allozymes?; (2) does the influence of mutation rate on F_ST estimates from microsatellites vary with geographic scale in spatially structured populations? For question one we find that discordant estimates of F_ST among microsatellites as well as between the two marker classes are correlated with mean within-population heterozygosity (H_S) and thus are likely due to differences in mutation rate. Highly polymorphic microsatellites (H_S > 0.84) provide significantly lower estimates of F_ST than moderately polymorphic microsatellites and allozymes (H_S < 0.60). Estimates of F_ST from binned allele frequency data and R_ST provide more accurate measures of population divergence for highly polymorphic but not for moderately polymorphic microsatellites. We conclude it is more important to pool loci of like H_S rather than marker class when estimating F_ST. For question two we find the F_ST values for moderately and highly polymorphic loci, while significantly different, are positively correlated for geographically proximate but not geographically distant population pairs. These results are consistent with expectations from the equilibrium approximation of Wright's infinite island model and confirm that the influence of mutation on estimates of F_ST can vary in spatially structured populations presumably because the rate of migration varies inversely with geographic scale.     

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

Effects of ascertainment bias on recovering human demographic history.

In recent years multilocus data sets have been used to study the demographic history of human populations. In this paper (1) analyses previously done on 60 short tandem repeat (STR) loci are repeated on 30 restriction site polymorphism (RSP) markers; (2) relative population weights are estimated from the RSP data set and compared to previously published estimates from STR and craniometric data sets; and (3) computer simulations are performed to show the effects of ascertainment bias on relative population weight estimates. Not surprisingly, given that the RSP markers were originally identified in a small panel of Caucasians, estimates of relative population weights are biased and the European population weight is artificially inflated. However, the effects of ascertainment bias are not apparent in a principal components plot or estimates of FST. Ascertainment bias can have a large effect in other genetic systems with inherently low heterozygosity such as Alus or single nucleotide polymorphisms (SNPs), and care must be taken to have prior knowledge of how polymorphic markers in a given data set were originally identified. Otherwise, results can be skewed and interpretations faulty.     

A simple model of linkage disequilibrium and genetic drift in human genomic SNPs: importance of demography and SNP age

We propose a simple model of evolution at a pair of SNP loci, under mutation, genetic drift and recombination. The developed model allows to consider evolution of SNPs under different demographic scenarios. We applied it to SNP data containing polymorphisms spanning 19 gene regions. We initially matched the linkage disequilibrium (LD) data only, and then we reconciled both LD and heterozygosity data. The imbalance between LD and heterozygosity data, observed for some of the analyzed genomic regions, may be a signature of selection acting in these regions. However, assuming neutrality, we obtain estimates of the age of population expansion of modern humans, which are consistent with the consensus estimates. In addition, we are able to estimate the ages of the polymorphisms observed in different genomic regions and we find that they vary widely with respect to their age. Polymorphisms at loci implicated in human disease, seem to be younger than average. Our results supplement the conclusions originally obtained by Reich and co-workers for the same set of data.     

Deriving evolutionary relationships among populations using microsatellites and (deltamu)(2): all loci are equal,but some are more equal than others..

Numerous studies have relied on microsatellite DNA data to assess the relationships among populations in a phylogenetic framework, converting microsatellite allelic composition of populations into evolutionary distances. Among other coefficients, (deltamu)(2) and R(st) are often employed because they make use of the differences in allele sizes on the basis of the stepwise mutation model. While it has been recognized that some microsatellites can yield disproportionate interpopulation distance estimates, no formal investigation has been conducted to evaluate to what extent such loci could affect the topology of the corresponding dendrograms. Here we show that single loci, displaying extremely large among-population variance, can greatly bias the topology of the phylogenetic tree, using data from European grayling (Thymallus thymallus, Salmonidae) populations. Importantly, we also demonstrate that the inclusion of a single disproportionate locus will lead to an overestimation of the stability of trees assessed using bootstrapping. To avoid this bias, we introduce a simple statistical test for detecting loci with significantly disproportionate variance prior to phylogenetic analyses and further show that exclusion of offending loci eliminates the false increase in phylogram stability.     

The impact of homologous recombination on the generation of diversity in bacteria

The imprint of demographic and selective processes on bacterial population structure needs to be evaluated as deviation from the expectations of an appropriate null neutral model. We explore the impact of varying the population mutation and recombination rates theta and rho on ideal populations, using a recently developed model of neutral drift at multiple loci. This model may be fitted to experimental data to provide estimates of these parameters, and we do so for seven bacterial species (Neisseria meningitidis, Streptococcus pneumoniae, Streptococcus pyogenes, Staphylococcus aureus, Helicobacter pylori, Burkholderia pseudomallei and Bacillus cereus), illustrating that bacterial species vary extensively in these fundamental parameters. Historically, the influence of recombination has often been estimated through its influence on the Index of Association I(A). We show that this may be relatively insensitive to changes in either mutation or recombination rates. It is known that biased sampling can lead to artificially high estimates of I(A). We therefore provide a method of precisely separating the effects of such bias and true linkage between alleles. We also demonstrate that by fitting the neutral model to experimental data, more informative and precise estimates of the relative roles of recombination and mutation may be obtained.     

Precision and accuracy of divergence time estimates from STR and SNPSTR variation

Inference of intraspecific population divergence patterns typically requires genetic data for molecular markers with relatively high mutation rates. Microsatellites, or short tandem repeat (STR) polymorphisms, have proven informative in many such investigations. These markers are characterized, however, by high levels of homoplasy and varying mutational properties, often leading to inaccurate inference of population divergence. A SNPSTR is a genetic system that consists of an STR polymorphism closely linked (typically < 500 bp) to one or more single-nucleotide polymorphisms (SNPs). SNPSTR systems are characterized by lower levels of homoplasy than are STR loci. Divergence time estimates based on STR variation (on the derived SNP allele background) should, therefore, be more accurate and precise. We use coalescent-based simulations in the context of several models of demographic history to compare divergence time estimates based on SNPSTR haplotype frequencies and STR allele frequencies. We demonstrate that estimates of divergence time based on STR variation on the background of a derived SNP allele are more accurate (3% to 7% bias for SNPSTR versus 11% to 20% bias for STR) and more precise than STR-based estimates, conditional on a recent SNP mutation. These results hold even for models involving complex demographic scenarios with gene flow, population expansion, and population bottlenecks. Varying the timing of the mutation event generating the SNP revealed that estimates of divergence time are sensitive to SNP age, with more recent SNPs giving more accurate and precise estimates of divergence time. However, varying both mutational properties of STR loci and SNP age demonstrated that multiple independent SNPSTR systems provide less biased estimates of divergence time. Furthermore, the combination of estimates based separately on STR and SNPSTR variation provides insight into the age of the derived SNP alleles. In light of our simulations, we interpret estimates from data for human populations.     

Estimation of effective population size and migration rate from one- and two-locus identity measures

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.     

A power analysis of microsatellite-based statistics for inferring past population growth

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.     

Evaluating SNP ascertainment bias and its impact on population assignment in Atlantic cod, Gadus morhua

The increasing use of single nucleotide polymorphisms (SNPs) in studies of nonmodel organisms accentuates the need to evaluate the influence of ascertainment bias on accurate ecological or evolutionary inference. Using a panel of 1641 expressed sequence tag-derived SNPs developed for northwest Atlantic cod (Gadus morhua), we examined the influence of ascertainment bias and its potential impact on assignment of individuals to populations ranging widely in origin. We hypothesized that reductions in assignment success would be associated with lower diversity in geographical regions outside the location of ascertainment. Individuals were genotyped from 13 locations spanning much of the contemporary range of Atlantic cod. Diversity, measured as average sample heterozygosity and number of polymorphic loci, declined (c. 30%) from the western (H(e) = 0.36) to eastern (H(e) = 0.25) Atlantic, consistent with a signal of ascertainment bias. Assignment success was examined separately for pools of loci representing differing degrees of reductions in diversity. SNPs displaying the largest declines in diversity produced the most accurate assignment in the ascertainment region (c. 83%) and the lowest levels of correct assignment outside the ascertainment region (c. 31%). Interestingly, several isolated locations showed no effect of assignment bias and consistently displayed 100% correct assignment. Contrary to expectations, estimates of accurate assignment range-wide using all loci displayed remarkable similarity despite reductions in diversity. Our results support the use of large SNP panels in assignment studies of high geneflow marine species. However, our evidence of significant reductions in assignment success using some pools of loci suggests that ascertainment bias may influence assignment results and should be evaluated in large-scale assignment studies.     

Effect of mutation on genetic differentiation among nonequilibrium populations

The usefulness of GST and similar measures of genetic differentiation has been questioned repeatedly because of their dependence on the amount of heterozygosity within populations, creating problems when comparing degrees of divergence at loci with different mutation rates. Although the effect of mutation on GST is expected to be small in the early phases of divergence, it is unclear for how long after separation from a common ancestral population that GST is largely unaffected by mutation and by the resulting effect on heterozygosity. We address this question through analysis of the recursion equations for gene identity under the infinite allele model of mutation, and derive conditions describing when the effect of mutation on GST can be ignored under mutation-migration-drift equilibrium conditions and during the preceding transition phase. An important result is that during the transition phase GST is not only affected by mutation, but also by the heterozygosity in the base population from which the subpopulations diverged. The effect of mutation on GST is significant from the very start of the divergence process when initial heterozygosity is low, whereas GST is only weakly affected by mutation in the early phases of differentiation when initial heterozygosity is high. Thus, differentiation following a severe bottleneck is strongly dependent on mutation. The standardized measure of differentiation, G'ST, suggested by Hedrick (2005), may be helpful when comparing amounts of divergence at loci with different mutation rates under steady-state conditions, provided that migration is very low. In many other situations the use of G'ST might be misleading, however, and its application should be exercised with caution.     

Selective sweeps and intercontinental migration in the cosmopolitan moss Ceratodon purpureus (Hedw.) Brid

The moss Ceratodon purpureus has long been used as a model system in plant development and physiology. However, the molecular population genetics of the species remains virtually unexplored. In this study, we used population genetic analyses of DNA sequence data from three unlinked loci (atpB-rbcL spacer, adk, and phy2) to examine biogeographical patterns in a global sample of this species. The three loci differed significantly in mutation frequency spectra and implied population structure. Pairs of haplotypes from single populations were frequently more divergent than haplotypes sampled from widely disjunct populations. In the atpB-rbcL spacer and adk samples, Australasian haplotypes were more closely related to Northern Hemisphere haplotypes than to haplotypes found in the equatorial regions. In contrast, the phy2 sample showed that the north and south temperate regions were genetically divergent, with the equatorial regions intermediate. Maximum-likelihood estimates (MLE) of the rates of migration between the two hemispheres were significantly different for the two nuclear genes. The frequency spectra of mutations indicated that differences in implied population structure among the three loci resulted from directional selection on the chloroplast genome and on the chromosomal segment containing adk. Collectively, these data suggest that long-distance migration within the Northern Hemisphere and Australasian regions is common (relative to the mutation rate) and that migration between these two regions, potentially via equatorial populations, is more frequent than migration among equatorial populations.     

Genetic analysis of microsatellite polymorphism in the Elliot's Pheasant (Syrmaticus ellioti) in China

In this study, we reported the population genetic analyses in the Elliot's Pheasant(Syrnaticus ellioti) using seven polymorphism microsatellite loci based on 105 individuals from 4 geographical populations. Departures from Hardy-Weinberg equilibrium were found in four geographical populations. The average number of alleles was 8.86, with a total of 62 alleles across 7 loci; observed heterozygosity (HO) was generally low and the average number was 0.504. For the seven microsatellite loci, the polymorphism information content ranged from 0.549 to 0.860, with an average number 0.712. Population bottlenecks of the four geographical populations were tested by infinite allele mutation model, step-wise mutation model and two-phase mutation model, which found that each population had experienced bottleneck effect during the recent period. Fst analysis across all geographical populations indicated that the genetic differentiaton between the Guizhou geographical population and the Hunan geographical population was highly significant (P<0.001), a finding supported by the far genetic relationship showed by the neighbor-joining tree of four geographical populations based on Nei's unbiased genetic distances. Using hierarchical analysis of molecular variance (Guizhou geographical population relative to all others pooled), we found a low level of the genetic variation among geographical populations and that between groups. However, differences among populations relative to the total sample explained most of the genetic variance (92.84%), which was significant.     

Mitochondrial DNA variations in Russian and Belorussian populations

The sequence of the first hypervariable segment (HVS-I) of mitochondrial DNA (mtDNA) was determined in 251 individuals from three eastern Slavonic populations, two Russian and one Belorussian. Within HVS-I, 78 polymorphic positions were revealed. Within-population diversity of HVS-I varies slightly among three samples; its estimates do not differ strongly from those for European populations. Haplotype diversity for three populations calculated in this study is 0.949; mean pairwise differences estimate is 3.59. To assign mtDNA sequences to major phylogenetic clusters, haplogroup-specific restriction polymorphisms were selectively typed in most samples. The haplogroup distribution in the total Eastern Slavonic sample is similar to that reported for the European sample. However, the separate consideration of three Slavonic samples reveals the complicated structure of the mitochondrial gene pool in the Eastern European area. Data of this study support the proposed model of the origin of modern Eastern Slavs, which implies the admixture of ancient Slavonic tribes with pre-Slavonic populations of Eastern Europe. These data should contribute to general studies of mitochondrial DNA variations in Europe.     

Quantifying inbreeding in natural populations of hermaphroditic organisms

We review molecular methods for estimating selfing rates and inbreeding in populations. Two main approaches are available: the population structure approach (PSA) and progeny-array approach (PAA). The PSA approach relies on single-generation samples and produces estimates that integrate the inbreeding history over several generations, but is based on strong assumptions (for example, inbreeding equilibrium). The PSA has classically relied on single-locus inbreeding coefficients averaged over loci. Unfortunately PSA estimates are very sensitive to technical problems such as the occurrence of null alleles at one or more of the loci. Consequently inbreeding might be substantially overestimated, especially in outbred populations. However, the robustness of the PSA has recently been greatly improved by the development of multilocus methods free of such bias. The PAA, on the other hand, is based on the comparison between offspring and mother genotypes. As a consequence, PAA estimates do not reflect long-term inbreeding history but only recent mating events of the maternal individuals studied ('here and now' selfing). In addition to selfing rates, the PAA allows estimating other mating system parameters, including biparental inbreeding and the correlation of selfing among sibs. Although PAA estimates could also be biased by technical problems, incompatibilities between the mother's genotype and her offspring allow the identification and correction of such bias. For all methods, we provide guidelines on the required number of loci and sample sizes. We conclude that the PSA and PAA are equally robust, provided multilocus information is used. Although experimental constraints may make the PAA more demanding, especially in animals, the two methods provide complementary information, and can fruitfully be conducted together.     

Average heterozygosity revisited.

The estimate of heterozygosity and proportion of polymorphic loci for 33 red blood cell loci has been updated by the elimination of some loci of questionable status and the addition of data on 33 loci. The new figures for heterozygosity and proportion of polymorphic loci, .105 and .283, respectively, are based on 60 red blood cell loci of European origin populations. These values are less than those calculated by Lewontin in 1967, and furthermore they do not appear to be reaching an asymptote. At the present time, the red blood cell data and allozyme data for European populations have similar estimates of heterozygosity and proportion of polymorphic loci.     

Nineteen new microsatellite DNA polymorphisms in pigtailed macaques (Macaca nemestrina)

Microsatellite loci known to be polymorphic in baboons (Papio hamadryas) and/or humans were tested in pigtailed macaques (Macaca nemestrina) from the Washington Regional Primate Research Center. Nineteen polymorphisms were identified in the macaques, with an average of 9.2 alleles per locus and an average heterozygosity of 0.76. Seven loci were analyzed using radiolabelled PCR primers and standard gel electrophoresis. Twelve loci were studied using fluorescently labelled primers and the Perkin-Elmer ABI 377 genotyping system. Of these 19 pigtailed macaque polymorphisms, 12 were used to perform paternity testing among captive animals. In a set of 15 infants, this panel of 12 genetic polymorphisms was sufficient to establish paternity in all cases. The number of alleles per locus in pigtailed macaques was compared with the number of alleles in a sample of baboons, and no significant correlation was observed. This indicates that population genetic processes such as genetic drift and recurrent mutation act rapidly enough on these loci to eliminate any relationship in levels of polymorphism across those two species. These 19 loci will be valuable for a range of genetic studies in pigtailed macaques, including paternity testing, analysis of population structure and differentiation among wild populations, and genetic linkage mapping.     

High mitochondrial mutation rates estimated from deep-rooting Costa Rican pedigrees

Estimates of mutation rates for the noncoding hypervariable Region I (HVR-I) of mitochondrial DNA vary widely, depending on whether they are inferred from phylogenies (assuming that molecular evolution is clock-like) or directly from pedigrees. All pedigree-based studies so far were conducted on populations of European origin. In this article, we analyzed 19 deep-rooting pedigrees in a population of mixed origin in Costa Rica. We calculated two estimates of the HVR-I mutation rate, one considering all apparent mutations, and one disregarding changes at sites known to be mutational hot spots and eliminating genealogy branches which might be suspected to include errors, or unrecognized adoptions along the female lines. At the end of this procedure, we still observed a mutation rate equal to 1.24 × 10(-6) , per site per year, i.e., at least threefold as high as estimates derived from phylogenies. Our results confirm that mutation rates observed in pedigrees are much higher than estimated assuming a neutral model of long-term HVRI evolution. We argue that until the cause of these discrepancies will be fully understood, both lower estimates (i.e., those derived from phylogenetic comparisons) and higher, direct estimates such as those obtained in this study, should be considered when modeling evolutionary and demographic processes.     

Microsatellite polymorphism and population subdivision in natural populations of European sea bass Dicentrarchus labrax (Linnaeus, 1758)

Polymorphism of microsatellite markers was used to study the genetic variability and structure in natural populations of European sea bass Dicentrarchus labrax. The data consisted of six microsatellite loci analysed for 172 individuals from three samples collected in the Golfe-du-Lion (France) and one sample collected in the Golfo-de-Valencia (Spain). Our goals were (i) to assess the level of genetic variability as revealed by these markers, (ii) to estimate the genetic differentiation among natural populations within a restricted area, and (iii) to evaluate how microsatellite loci fit the predictions of the two most widely used mutation models (the infinite allele model and the stepwise mutation model). As expected, our results indicate that the genetic polymorphism is very high when compared with previously used genetic markers, the mean expected heterozygosity per locus ranging between 0.69 and 0.93. We also found that all loci but one fitted the infinite allele model better. Using this model as a lower limit, we could extrapolate from the observed diversity effective population sizes on the order of 35 000 individuals. Our results also suggest that there may be a slight genetic differentiation between the two gulfs (F_ST= 0.007, P < 0.05), indicating that the corresponding populations are likely to be dynamically independent. This finding for a species with high dispersal abilities, if confirmed, has important beatings on fish-stock assessment.