Estimation,variance and optimal sampling of gene diversity

An extension of Nei's analysis of diversity in a subdivided population is proposed for a haploid locus. The differentiation G _STbecomes a natural extension of Wright's F _STand generalizes Weir and Cockerham's parameter of co-ancestry by relaxing the assumption of identical correlation for all the alleles. Inter- and intrapopulation variances of the estimated diversities and differentiation are derived. Finally, the optimal sampling strategy for measuring G _STwhen a fixed number of individuals can be analysed is considered. It is shown that, at a given locus, there is a unique sample size per population which yields the smallest variance of G _ST,regardless of the number of populations studied. These theoretical developments are illustrated with an analysis of chloroplast DNA diversity in a forest tree. The results emphasize the necessity of sampling many populations, rather than many individuals per population, for an accurate measurement of the subdivision of gene diversity at a single locus.     

Does GST underestimate genetic differentiation from marker data?

The widely applied genetic differentiation statistics F_ST and G_ST have recently been criticized for underestimating differentiation when applied to highly polymorphic markers such as microsatellites. New statistics claimed to be unaffected by marker polymorphisms have been proposed and advocated to replace the traditional F_ST and G_ST. This study shows that G_ST gives accurate estimates and underestimates of differentiation when demographic factors are more and less important than mutations, respectively. In the former case, all markers, regardless of diversity (H_S), have the same G_ST value in expectation and thus give replicated estimates of differentiation. In the latter case, markers of higher H_S have lower G_ST values, resulting in a negative, roughly linear correlation between G_ST and H_S across loci. I propose that the correlation coefficient between G_ST and H_S across loci, r_GH, can be used to distinguish the two cases and to detect mutational effects on G_ST. A highly negative and significant r_GH, when coupled with highly variable G_ST values among loci, would reveal that marker G_ST values are affected substantially by mutations and marker diversity, underestimate population differentiation, and are not comparable among studies, species and markers. Simulated and empirical data sets are used to check the power and statistical behaviour, and to demonstrate the usefulness of the correlation analysis.     

Isolated in an ocean of grass: low levels of gene flow between termite subpopulations

Habitat fragmentation is one of the most important causes of biodiversity loss, but many species are distributed in naturally patchy habitats. Such species are often organized in highly dynamic metapopulations or in patchy populations with high gene flow between subpopulations. Yet, there are also species that exist in stable patchy habitats with small subpopulations and presumably low dispersal rates. Here, we present population genetic data for the ‘magnetic’ termite Amitermes meridionalis, which show that short distances between subpopulations do not hinder exceptionally strong genetic differentiation (F_ST: 0.339; R_ST: 0.636). Despite the strong genetic differentiation between subpopulations, we did not find evidence for genetic impoverishment. We propose that loss of genetic diversity might be counteracted by a long colony life with low colony turnover. Indeed, we found evidence for the inheritance of colonies by so‐called ‘replacement reproductives’. Inhabiting a mound for several generations might result in loss of gene diversity within a colony but maintenance of gene diversity at the subpopulation level.     

What is genetic differentiation,and how should we measure it—GST,D, neither or both?

Estimates of the fixation index, F_ST, have been used as measures of population differentiation for many decades. However, there have been persistent voices in the literature suggesting that these statistics do not measure true differentiation. In particular, the statistics Nei's G_ST and Wier and Cockerham's θ have been criticized for being ‘constrained’ to not equal one in some situations that seem to represent maximal differentiation. Here, we address the issue of how to evaluate exactly how much information a particular statistic contains about the process of differentiation. This criterion can be used to counter most concerns about the performance of G_ST (and related statistics), while also being reconciled with the insights of those who have proposed alternative measures of differentiation. In particular, the likelihood‐based framework that we put forward can justify the use of G_ST as an effective measure of differentiation, but also shows that in some situations G_ST is insufficient on its own and needs supplementing by another measure such as Jost's D or Hedrick's G′_ST. This approach will become increasingly important in the future, as greater emphasis is placed on analysing large data sets.     

Calculations of population differentiation based on GST and D: forget GST but not all of statistics!

G _ST‐values and its relatives (F_ST) belong to the most used parameters to define genetic differences between populations. Originally, they were developed for allozymes with very low number of alleles. Using highly polymorphic microsatellite markers it was often puzzling that G_ST‐values were very low but statistically significant. In their papers, Jost (2008) and Hedrick (2005) explained that G_ST‐values do not show genetic differentiation, and Jost suggested calculating D‐values instead. Theoretical mathematical considerations are often difficult to follow; therefore, we chose an applied approach comparing two artificial populations with different number of alleles at equal frequencies and known genetic divergence. Our results show that even for more than one allele per population G_ST‐values do not calculate population differentiation correctly; in contrast, D‐values do reflect the genetic differentiation indicating that data based on G_ST‐values need to be re‐evaluated. In our approach, statistical evaluations remained similar. We provide information about the impact of different sample sizes on D‐values in relation to number of alleles and genetic divergence.     

Heterozygote deficiency,population substructure and their implications in DNA fingerprinting

Summary Substructured populations exhibit an overall deficiency of heterozygosity whose proportional magnitude depends on the nature of substructuring, i.e., the number of subpopulations (s), their time of divergence (t) from the ancestral population, and the rate of gene flow amongst them (m). Since apparent heterozygote deficiency could be caused by many factors other than population substructuring, one must examine the nature of substructuring that could produce the observed extent of heterozygote deficiency, in order to infer the substructuring from an observed heterozygote deficiency. Using the equivalence of proportional heterozygote deficiency and the coefficient of gene differentiation (G _ST), we can generate isolines of G _ST as functions of s, t (in units of 2N _e generations, N _e being the effective population size) and m. Analytical results suggest that large G _ST values cannot be reached by substructuring alone, unless the number of subpopulations are large and they remain isolated over a long period of time. Application of the theory to population data on six variable number of tandem repeats (VNTR) loci in US Caucasians and US Blacks demonstrates that the observed heterozygote deficiencies at these loci cannot be explained by substructuring within these populations alone. This is so because such large values of G _ST (3%–10%) would require an absence of gene exchange between the subpopulations and a divergence time from each other of at least 25000 years ago, neither of which is compatible with the demography and ethnohistory of US Caucasians and Blacks. In contrast, the inability to detect extreme-sized alleles and/or incomplete resolution of nearly similar-sized alleles following Southern gel electrophoresis could easily explain the observed heterozygote deficiencies. The implications of these results are discussed in the context of the forensic use of DNA-typing data, and justify the employment of population genetic principles in forensic genetics.     

Contributions of subpopulations to total gene diversity

 The concept of the partitioning of genetic diversity into a component within and a component among populations (F _ST - or G _ST -statistics) can be easily expanded to compute the contribution of single subpopulations to total gene diversity. A subpopulation contributes to total gene diversity with its single-population gene diversity plus the (weighted) mean of Nei’s minimum genetic distances to all subpopulations. The suggested method allows one to unambiguously rank subpopulations according to the amount they contribute to the total gene diversity. Genetic polymorphisms at four isozyme gene loci of Alnus acuminata in Costa Rica are used to illustrate the procedure and its biological interpretation. Received: 15 August 1998 / Accepted: 8 September 1998     

mmod: an R library for the calculation of population differentiation statistics

mmod is a library for the R programming language that allows the calculation of the population differentiation measures D_est, G″_ST and φ′_ST. R provides a powerful environment in which to conduct and record population genetic analyses but, at present, no R libraries provide functions for the calculation of these statistics from standard population genetic files. In addition to the calculation of differentiation measures, mmod can produce parametric bootstrap and jackknife samples of data sets for further analysis. By integrating with and complimenting the existing libraries adegenet and pegas , mmod extends the power of R as a population genetic platform.     

Relative performance of Bayesian clustering software for inferring population substructure and individual assignment at low levels of population differentiation

Traditional methods for characterizing genetic differentiation among populations rely on a priori grouping of individuals. Bayesian clustering methods avoid this limitation by using linkage and Hardy–Weinberg disequilibrium to decompose a sample of individuals into genetically distinct groups. There are several software programs available for Bayesian clustering analyses, all of which describe a decrease in the ability to detect distinct clusters as levels of genetic differentiation among populations decrease. However, no study has yet compared the performance of such methods at low levels of population differentiation, which may be common in species where populations have experienced recent separation or high levels of gene flow. We used simulated data to evaluate the performance of three Bayesian clustering software programs, PARTITION, STRUCTURE, and BAPS, at levels of population differentiation below F _ST=0.1. PARTITION was unable to correctly identify the number of subpopulations until levels of F _ST reached around 0.09. Both STRUCTURE and BAPS performed very well at low levels of population differentiation, and were able to correctly identify the number of subpopulations at F _ST around 0.03. The average proportion of an individual’s genome assigned to its true population of origin increased with increasing F _ST for both programs, reaching over 92% at an F _ST of 0.05. The average number of misassignments (assignments to the incorrect subpopulation) continued to decrease as F _ST increased, and when F _ST was 0.05, fewer than 3% of individuals were misassigned using either program. Both STRUCTURE and BAPS worked extremely well for inferring the number of clusters when clusters were not well-differentiated (F _ST=0.02–0.03), but our results suggest that F _ST must be at least 0.05 to reach an assignment accuracy of greater than 97%.     

A new method for the partition of allelic diversity within and between subpopulations

A method is proposed for the analysis of allelic diversity in the context of subdivided populations. The definition of an allelic distance between subpopulations allows for the partition of total allelic diversity into within- and between-subpopulation components, in a way analogous to the classical partition of gene diversity. A new definition of allelic differentiation, A _ST , between subpopulations results from this partition, and is contrasted with the concept of allelic richness differentiation. The partition of allelic diversity makes it possible to establish the relative contribution of each subpopulation to within and between-subpopulation components of diversity with implications in priorisation for conservation. A comparison between this partition and that corresponding to allelic richness is illustrated with an example. Computer simulations are used to investigate the behaviour of the new statistic A _ST in comparison with F _ST for a finite island model under a range of mutation and migration rates. A _ST has less dependence on migration rate than F _ST for large values of migration rate, but the opposite occurs for low migration rates. In addition, the variance in the estimates of A _ST is higher than that of F _ST for low mutation rates, but the opposite for high mutation rates.     

Indicators to assess temporal genetic diversity in the French Catalogue: no losses for maize and peas

The aim of this study, led by the GEVES (Research and Control Group for Varieties and Seeds), was to suggest indicators to assess the diversity available to farmers since the French Official Catalogue for Plant Varieties and Species was initiated. The largest datasets of 1990 inbred maize lines and 578 pea lines from the last 50 years were analysed using morphological and enzymatic parameters. Lines were grouped into three to five periods. Genetic diversity was estimated in each period from morphological and enzymatic markers by computing numerous indices, such as the number of classes of scores for each characteristic, allelic richness or genetic diversity index (H _e ). Population differentiation parameters (G_ST, G_ST′, F_ST, Q_ST) were also estimated between periods. While genetic diversity computed from distinction, uniformity, stability traits was more marked for maize (0.66) than for garden peas (0.35) or feed peas (0.29), the opposite trend was observed with enzymes, resulting in a genetic diversity of 0.43, 0.35 and 0.22 for garden peas, feed peas and maize, respectively. However, no significant changes in genetic diversity were observed over time, and genetic differentiation was slight between periods. All our results demonstrated that no significant reduction in the diversity available to farmers had been observed since initiation of the French Catalogue. The H _e was a good indicator providing a quantitative estimate of genetic diversity, but it should be interpreted alongside a more precise indicator such as allelic richness or the number of classes for morphological characteristics.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

General <Emphasis Type="Italic">G</Emphasis><Subscript>ST</Subscript> and <Emphasis Type="Italic">θ</Emphasis> inflation due to biased intra-population sampling,and its consequences for the conservation of the Canarian Flora

While knowledge of the degree of inter-population genetic differentiation underlies the understanding of microevolutionary processes in any organism, its calculation through G _ST, F _ST, or θ (which, unlike the previous two, was designed to correct for unequal and small sample sizes) is often based in severely restricted intra-population samples, which are nonetheless tacitly assumed adequate to their accurate estimation. Empirical assessment of the influence of the number and intra-population distribution of samples on the values of G _ST and θ for several Canarian endemic plants compellingly suggests that (1) contrary to expectations based on simulated datasets, θ does not account for empirical sampling bias better than G _ST; (2) sample sizes being equal, collections scattered across each population’s occupancy area entail significantly lower over-estimates of G _ST and θ than if they only consider one of the population extremes, especially in narrow allogamous taxa with small populations; (3) in small samples, a scattered sampling strategy is significantly less sensitive to G _ST inflation than sampling in one of the population extremes; and (4) a software-related component of bias should be considered when pooling values of G _ST from different studies to calculate averages. Thus, unlike the sampling methods used for many plant endemics from the Canaries and other regions, collections for a reliable estimation of inter-population differentiation using molecular markers should encompass the whole occupancy area of each population, and include a higher proportion of individuals respect to the total size in narrow endemics than in widespread congeners. Critically, the high average allozyme inter-population differentiation reported for the Canarian endemic Flora is possibly an over-estimate, and could be explained predominantly by the generally biased intra-population sampling associated with G _ST estimates, rather than by specific factors of insularity that restrict gene flow radically, as it has been hitherto assumed.     

A simple derivation of the partitioning of genetic differentiation within subdivided populations

The genetic differentiation within a subdivided population can be partitioned into two proportions, one due to differentiation within sub-populations and the other due to differentiation among subpopulations. A simple mathematical derivation of this procedure, known as Nei's G _ST -statistics, is presented. The significance of considering the differing relative sizes of subpopulations is stressed. Possible fields of applications for breeders and conservationists who are concerned with the establishment of genetically diverse populations are mentioned.     

Genetic Diversity and Population Structure of Alnus hirsuta (Betulaceae) in Korea

Alnus hirsuta in Korea was measured to estimate the amount and pattern of genetic diversity and population structure. The mean genetic diversity within populations was 0.166. Korean alder populations have slightly high levels of genetic diversity compared to those of two Canadian alder species. The genetic differentiation among populations accounted for 9% of the total variation. The rate of gene flow was estimated high (Nm=2.63). Analysis of inbreeding coefficient, calculated for all polymorphic loci in each population, showed a substantial heterozygote deficiency relative to Hardy-Weinberg expectations. The mean G _ST value of A. hirsuta in Korea was 0.087. The low value of G _ST in this species, reflecting little spatial genetic differentiation, may indicate extensive gene flow. A relationship between the mean heterozygosity and annual rainfall showed a positive relationship (r ²=0.54, F=4.67). Received 8 August 1998/ Accepted in revised form 7 July 1999     

Distribution of variation over populations

Understanding the significance of the distribution of genetic or phenotypic variation over populations is one of the central concerns of population genetic and ecological research. The import of the research decisively depends on the measures that are applied to assess the amount of variation residing within and between populations. Common approaches can be classified under two perspectives: differentiation and apportionment. While the former focuses on differences (distances) in trait distribution between populations, the latter considers the division of the overall trait variation among populations. Particularly when multiple populations are studied, the apportionment perspective is usually given preference (via F _ST/G _ST indices), even though the other perspective is also relevant. The differences between the two perspectives as well as their joint conceptual basis can be exposed by referring them to the association between trait states and population affiliations. It is demonstrated that the two directions, association of population affiliation with trait state and of trait state with population affiliation, reflect the differentiation and the apportionment perspective, respectively. When combining both perspectives and applying the suggested measure of association, new and efficient methods of analysis result, as is outlined for population genetic processes. In conclusion, the association approach to an analysis of the distribution of trait variation over populations resolves problems that are frequently encountered with the apportionment perspective and its commonly applied measures in both population genetics and ecology, suggesting new and more comprehensive methods of analysis that include patterns of differentiation and apportionment.     

Genetic Diversity in Monilinia laxa Populations in Peach Orchards in Spain

One‐hundred and forty‐four random amplified polymorphic DNA markers, of which 59 were polymorphic and 85 monomorphic, were used to assess the genetic diversity and to study the structure of Monilinia laxa populations in Spain. Twenty‐one isolates collected from several orchards (subpopulations), in various years and in various hosts, were used. The analysis of population structure revealed that genetic diversity within orchards (H_S) accounted for 97% of the total genetic diversity (H_T), while genetic diversity among the orchards represented only 3%. The relative magnitude of gene differentiation between subpopulations (G_ST) and the estimate of the number of migrants per generation (N_m) averaged 0.032 and 15.1 respectively. The results obtained in dendrograms were in accordance with the gene diversity analysis. Grouping of isolates in the dendrogram was independent of whether they came from the same or different orchards. There was no relationship between clustering among isolates from distinct years and hosts. The relative importance of several evolutionary forces in populations of M. laxa is discussed, together with implications for the management of brown rot.     

Genetic Diversity and Structure of Two Prominent Zebu Cattle Breeds Adapted to the Arid Region of India Inferred from Microsatellite Polymorphism

This study aims to assess the genetic diversity and population structure of two major zebu dairy breeds (Tharparkar and Rathi) adapted to the arid region of Rajasthan state of India. Various variability estimates indicate the existence of sufficient within-breed genetic diversity. Mean estimates of F-statistics are significantly different from zero: F _IS = 0.112 ± 0.029, F _IT = 0.169 ± 0.033, F _ST = 0.065 ± 0.017. The overall positive value of F _IS (0.112) and an F _IT value (0.169) that is more than the F _ST (0.065) indicate departure from random mating. The drift-based estimates reflect a moderate yet significant level of breed differentiation between the Tharparkar and Rathi breeds. The evaluation of an exact test, showing that allele frequencies across all the loci differed significantly, supports the population differentiation. This is paralleled by the outcome of neighbor-joining clustering based on allele-sharing distance measures. The allocation of a high percentage of individuals (95.7%) to their population of origin and correspondence analysis further substantiates the existence of a cohesive genetic structure in both the breeds.     

Genetic diversity of Poa annua in western Oregon grass seed crops

The genetic diversity of Poa annua L.populations collected from western Oregon grass-seed fields was surveyed using 18 randomly amplified polymorphic DNA (RAPD) markers. Markers from 1357 individual plants from 47 populations collected at three sampling dates (fall, winter, and spring) for 16 sites were used to measure genetic diversity within and among populations. Site histories varied from low to high herbicide selection pressure, and some sites were subdivided by 3 years of differing post-harvest residue management. Gene diversity statistics, simple frequency of haplotype occurrence, and analysis of molecular variance (AMOVA) revealed the presence of significant variability in P. annua among sites, among collection dates within sites, and within collection dates. Nei gene-diversity statistics and population-differentiation parameters indicated that P. annua populations were highly diverse. Mean Nei gene diversity (h) for all 47 populations was 0.241 and total diversity (H_T) was 0.245. A greater proportion of this diversity, however, was within (H_S=0.209) rather than among (G_ST=0.146) populations. When populations were grouped by season of collection, within-group diversity was H_S=0.241, while among-group diversity was G_ST=0.017. When populations were grouped by site, within-group diversity was H_S=0.224, while among-group diversity was G_ST=0.087. The diversity among populations within season for fall, winter, and spring collections was G_ST=0.121, 0.142, and 0.133, respectively. Populations collected from fields with histories of high herbicide selection pressure showed low differentiation among collection dates, with G_ST as low as 0.016, whereas those collected from fields with low herbicide selection pressure showed greater differentiation among collection dates, with G_ST as high as 0.125. At high selection-pressure sites, populations were also lower in gene diversity (as low as h=0.155), while at low selection-pressure sites there was higher gene diversity (as high as h=0.286). The site to site variability was greater for the high selection-pressure sites (G_ST=0.107 or 69% of the total among-population variance), while the season of germination variability was greater at sites of low herbicide-selection pressure (G_ST=0.067, or 70% of the total among-population variance). High initial diversity coupled with a long-term re-supply of genotypes from the seed bank must have been factors in maintaining the genetic diversity of this weed despite the intensive use of herbicides. Knowledge of the genetic diversity of Willamette Valley P. annua should help in formulating more effective strategies for managing this weed. Received: 24 July 1999 / 11 November 1999     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

Unexpected cryptic species diversity in the widespread coral Seriatopora hystrix masks spatial‐genetic patterns of connectivity

Mounting evidence of cryptic species in a wide range of taxa highlights the need for careful analyses of population genetic data sets to unravel within‐species diversity from potential interspecies relationships. Here, we use microsatellite loci and hierarchical clustering analysis to investigate cryptic diversity in sympatric and allopatric (separated by 450 km) populations of the widespread coral Seriatopora hystrix on the Great Barrier Reef. Structure analyses delimited unique genetic clusters that were confirmed by phylogenetic and extensive population‐level analyses. Each of four sympatric yet distinct genetic clusters detected within S. hystrix demonstrated greater genetic cohesion across regional scales than between genetic clusters within regions (<10 km). Moreover, the magnitude of genetic differentiation between different clusters (>0.620 G”_ST) was similar to the difference between S. hystrix clusters and the congener S. caliendrum (mean G”_ST 0.720). Multiple lines of evidence, including differences in habitat specificity, mitochondrial identity, Symbiodinium associations and morphology, corroborate the nuclear genetic evidence that these distinct clusters constitute different species. Hierarchical clustering analysis combined with more traditional population genetic methods provides a powerful approach for delimiting species and should be regularly applied to ensure that ecological and evolutionary patterns interpreted for single species are not confounded by the presence of cryptic species.