Unifying selection acts on competitive ability and relative growth rate in Scabiosa columbaria

Q_ST vs. F_ST comparisons can reveal diversifying or unifying selection pressures among populations for specific traits. In this study we performed Q_ST–F_ST analyses on eleven populations of Scabiosa columbaria from the Swiss Jura to reveal genetic differentiation in two quantitative traits (above-ground biomass and relative growth rate of leaf lengths) and in neutral molecular markers. Above-ground biomass of plants under competition has been shown to correlate with their competitive ability, which is an important fitness-related trait. We hypothesized that strong unifying selection acts on above-ground biomass, since underperformance would result in decreased fitness and overperformance is unlikely due to trade-offs with other plant functions.Overall G_ST (an F_ST analogue) was 0.12. Analysis of variance revealed that above-ground biomass and relative growth rate did not differ among populations, but both traits differed among seed families and were heritable (h² = 0.31 and h² = 0.35, respectively). Q_ST was close to zero for above-ground biomass and zero for relative growth rate of leaf lengths, and thus Q_ST was much lower than G_ST, indicating unifying selection on these traits.This conclusion is restricted by the limits of the used methodology. Q_ST < F_ST cannot always be considered as a proof for unifying selection, because in complex traits the assumption of purely additive effects of underlying genes may be violated. However, given the large differences between Q_ST and G_ST, together with substantial heritabilities of the traits under study, we conclude that our findings are not in contradiction with the hypothesis of unifying selection.     

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.     

A New Method to Scan Genomes for Introgression in a Secondary Contact Model

Secondary contact between divergent populations or incipient species may result in the exchange and introgression of genomic material. We develop a simple DNA sequence measure, called G _min, which is designed to identify genomic regions experiencing introgression in a secondary contact model. G _min is defined as the ratio of the minimum between-population number of nucleotide differences in a genomic window to the average number of between-population differences. Although it is conceptually simple, one advantage of G _min is that it is computationally inexpensive relative to model-based methods for detecting gene flow and it scales easily to the level of whole-genome analysis. We compare the sensitivity and specificity of G _min to those of the widely used index of population differentiation, F _ST, and suggest a simple statistical test for identifying genomic outliers. Extensive computer simulations demonstrate that G _min has both greater sensitivity and specificity for detecting recent introgression than does F _ST. Furthermore, we find that the sensitivity of G _min is robust with respect to both the population mutation and recombination rates. Finally, a scan of G _min across the X chromosome of Drosophila melanogaster identifies candidate regions of introgression between sub-Saharan African and cosmopolitan populations that were previously missed by other methods. These results show that G _min is a biologically straightforward, yet powerful, alternative to F _ST, as well as to more computationally intensive model-based methods for detecting gene flow.     

The effect of parental divergence on F2 heterosis in winter wheat crosses

Summary In winter wheat (Triticum aestivum L.), the development of a methodology to estimate genetic divergence between parental lines, when combined with knowledge of parental performance, could be beneficial in the prediction of bulk progeny performance. The objective of this study was to relate F₂ heterosis for grain yield and its components in 116 crosses to two independent estimates of genetic divergence among 28 parental genotypes of diverse origins. Genetic divergence between parents was estimated from (a) pedigree relationships (coefficients of kinship) determined without experimentation, and (b) quantitative traits measured in two years of field experimentation in Kansas and North Carolina, USA. These distances, designated (1 -r) and G, respectively, provided ample differentiation among the parents. The 116 F₂ bulks were evaluated at four locations in Kansas and North Carolina in one year. Significant rank correlations of 0.46 (P = 0.01) and 0.44 (P = 0.01) were observed between G and grain yield and kernel number heterosis, respectively. Although (1 -r) was poorly associated with grain yield heterosis, G and midparent performance combined to account for 50% of the variation in F₂ yields among crosses when (1 -r) was above the median value, whereas they accounted for only 9% of the variation among crosses when (1-r) was below the median. Midparent and (1 -r) had equal effects on F₂ grain yield (R ²= 0.40) when G was greater than the median value. A breeding strategy is proposed whereby parents are first selected on the basis of performance per se and, subsequently, crosses are made between genetically divergent parents that have both large quantitative (G) and pedigree divergence (1 -r).Paper No. 12162 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27695-7643, and Contribution No. 89-396-J of the Kansas Agricultural Experiment Station, Manhattan, KS 66506     

ESTIMATION OF GENE FLOW FROM F-STATISTICS

We present theory clarifying the general behavior of F_ST-based and G_ST-based estimators of gene flow, and confirm these predictions with simulations. In particular, we use the correlation of genes within groups within populations to define an estimator. The theoretical value of the correlation doe not depend on the number of groups in a population, and properties of the estimated correlation do not depend on the number of groups sampled or the number of individuals sampled per group. This invariance is in contrast to properties of G_ST. For a complete census of a population, bias and variance considerations would suggest the use of the G_ST-based estimator of gene flow, but lack of knowledge of population size or group number in practice suggests preference be given to the correlation-based estimator. We acknowledge that these estimators require that several conditions of a population-genetic model be met, since they do not make use of direct observations on the flow of genes. Our results differ from some of those based on simulation in a series of recent papers by M. Slatkin.     

The empirical Bayes estimators of fine‐scale population structure in high gene flow species

An empirical Bayes (EB) pairwise F_ST estimator was previously introduced and evaluated for its performance by numerical simulation. In this study, we conducted coalescent simulations and generated genetic population structure mechanistically, and compared the performance of the EBF_ST with Nei's G_ST, Nei and Chesser's bias‐corrected G_ST (G_{ST_NC}), Weir and Cockerham's θ (θ_WC) and θ with finite sample correction (θ_{WC_F}). We also introduced EB estimators for Hedrick’ G’_ST and Jost’ D. We applied these estimators to publicly available SNP genotypes of Atlantic herring. We also examined the power to detect the environmental factors causing the population structure. Our coalescent simulations revealed that the finite sample correction of θ_WC is necessary to assess population structure using pairwise F_ST values. For microsatellite markers, EBF_ST performed the best among the present estimators regarding both bias and precision under high gene flow scenarios (). For 300 SNPs, EBF_ST had the highest precision in all cases, but the bias was negative and greater than those for G_{ST_NC} and θ_{WC_F} in all cases. G_{ST_NC} and θ_{WC_F} performed very similarly at all levels of F_ST. As the number of loci increased up to 10 000, the precision of G_{ST_NC} and θ_{WC_F} became slightly better than for EBF_ST for cases with , even though the size of the bias remained constant. The EB estimators described the fine‐scale population structure of the herring and revealed that ~56% of the genetic differentiation was caused by sea surface temperature and salinity. The R package finepop for implementing all estimators used here is available on CRAN.     

The use and abuse of genetic marker‐based estimates of relatedness and inbreeding

Genetic marker‐based estimators remain a popular tool for measuring relatedness (r_xy) and inbreeding (F) coefficients at both the population and individual level. The performance of these estimators fluctuates with the number and variability of markers available, and the relatedness composition and demographic history of a population. Several methods are available to evaluate the reliability of the estimates of r_xy and F, some of which are implemented in the program COANCESTRY. I used the simulation module in COANCESTRY since assess the performance of marker‐based estimators of r_xy and F in a species with very low genetic diversity, New Zealand's little spotted kiwi (Apteryx owenii). I also conducted a review of published papers that have used COANCESTRY as its release to assess whether and how the reliability of the estimates of r_xy and F produced by genetic markers are being measured and reported in published studies. My simulation results show that even when the correlation between true (simulated) and estimated r_xy or F is relatively high (Pearson's r = 0.66–0.72 and 0.81–0.85, respectively) the imprecision of the estimates renders them highly unreliable on an individual basis. The literature review demonstrates that the majority of studies do not report the reliability of marker‐based estimates of r_xy and F. There is currently no standard practice for selecting the best estimator for a given data set or reporting an estimator's performance. This could lead to experimental results being interpreted out of context and render the robustness of conclusions based on measures of r_xy and F debatable.     

The joint effects of selection and dominance on the QST - FST contrast

Q_ST measures the differentiation of quantitative traits between populations. It is often compared to F_ST, which measures population differentiation at neutral marker loci due to drift, migration, and mutation. When Q_ST is different from F_ST, it is usually taken as evidence that selection has either restrained or accelerated the differentiation of the quantitative trait relative to neutral markers. However, a number of other factors such as inbreeding, dominance, and epistasis may also affect the Q_ST − F_ST contrast. In this study, we examine the effects of dominance, selection, and inbreeding on Q_ST − F_ST. We compare Q_ST with F_ST at selected and neutral loci for populations at equilibrium between selection, drift, mutation, and migration using both analytic and simulation approaches. Interestingly, when divergent selection is acting on a locus, inbreeding and dominance generally inflate Q_ST relative to F_ST when they are both measured at the quantitative locus at equilibrium. As a consequence, dominance is unlikely to hide the signature of divergent selection on the Q_ST − F_ST contrast. However, although in theory dominance and inbreeding affect the expectation for Q_ST − F_ST, of most concern is the very large variance in both Q_ST and F_ST, suggesting that we should be cautious in attributing small differences between Q_ST and F_ST to selection.     

Estimation and adjustment of microsatellite null alleles in nonequilibrium populations

Nonamplified (null) alleles are a common feature of microsatellite genotyping and can bias estimates of allele and genotype frequencies, thereby hindering population genetic analyses. The frequency of microsatellite null alleles in diploid populations can be estimated for populations that are in Hardy–Weinberg equilibrium. However, many microsatellite data sets are from nonequilibrium populations, often with known inbreeding coefficients (F) or fixation indices (F_IS or F_ST). Here, we propose a novel null allele estimator that can be used to estimate the null allele frequency and adjust visible allele frequencies in populations for which independent estimates of F, F_IS or F_ST are available. The algorithm is currently available as an Excel macro that can be downloaded at no cost from http://www.microchecker.hull.ac.uk/ and will be incorporated into the software micro ‐checker .     

A comparison of approaches to estimate the inbreeding coefficient and pairwise relatedness using genomic and pedigree data in a sheep population

Genome-wide SNP data provide a powerful tool to estimate pairwise relatedness among individuals and individual inbreeding coefficient. The aim of this study was to compare methods for estimating the two parameters in a Finnsheep population based on genome-wide SNPs and genealogies, separately. This study included ninety-nine Finnsheep in Finland that differed in coat colours (white, black, brown, grey, and black/white spotted) and were from a large pedigree comprising 319 119 animals. All the individuals were genotyped with the Illumina Ovine SNP50K BeadChip by the International Sheep Genomics Consortium. We identified three genetic subpopulations that corresponded approximately with the coat colours (grey, white, and black and brown) of the sheep. We detected a significant subdivision among the colour types (F _ST = 5.4%, P<0.05). We applied robust algorithms for the genomic estimation of individual inbreeding (F _SNP) and pairwise relatedness (Φ _SNP) as implemented in the programs KING and PLINK, respectively. Estimates of the two parameters from pedigrees (F _PED and Φ _PED) were computed using the RelaX2 program. Values of the two parameters estimated from genomic and genealogical data were mostly consistent, in particular for the highly inbred animals (e.g. inbreeding coefficient F>0.0625) and pairs of closely related animals (e.g. the full- or half-sibs). Nevertheless, we also detected differences in the two parameters between the approaches, particularly with respect to the grey Finnsheep. This could be due to the smaller sample size and relative incompleteness of the pedigree for them.We conclude that the genome-wide genomic data will provide useful information on a per sample or pairwise-samples basis in cases of complex genealogies or in the absence of genealogical data.     

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

Genetic influences on anxiety disorders are well documented; however, the specific genes underlying these disorders remain largely unknown. To identify quantitative trait loci (QTL) for conditioned fear and open field behavior, we used an F₂ intercross (n = 490) and a 34th-generation advanced intercross line (AIL) (n = 687) from the LG/J and SM/J inbred mouse strains. The F₂ provided strong support for several QTL, but within wide chromosomal regions. The AIL yielded much narrower QTL, but the results were less statistically significant, despite the larger number of mice. Simultaneous analysis of the F₂ and AIL provided strong support for QTL and within much narrower regions. We used a linear mixed-model approach, implemented in the program QTLRel, to correct for possible confounding due to familial relatedness. Because we recorded the full pedigree, we were able to empirically compare two ways of accounting for relatedness: using the pedigree to estimate kinship coefficients and using genetic marker estimates of “realized relatedness.” QTL mapping using the marker-based estimates yielded more support for QTL, but only when we excluded the chromosome being scanned from the marker-based relatedness estimates. We used a forward model selection procedure to assess evidence for multiple QTL on the same chromosome. Overall, we identified 12 significant loci for behaviors in the open field and 12 significant loci for conditioned fear behaviors. Our approach implements multiple advances to integrated analysis of F₂ and AILs that provide both power and precision, while maintaining the advantages of using only two inbred strains to map QTL.     

Estimating FST and kinship for arbitrary population structures

F_ST and kinship are key parameters often estimated in modern population genetics studies in order to quantitatively characterize structure and relatedness. Kinship matrices have also become a fundamental quantity used in genome-wide association studies and heritability estimation. The most frequently-used estimators of F_ST and kinship are method-of-moments estimators whose accuracies depend strongly on the existence of simple underlying forms of structure, such as the independent subpopulations model of non-overlapping, independently evolving subpopulations. However, modern data sets have revealed that these simple models of structure likely do not hold in many populations, including humans. In this work, we analyze the behavior of these estimators in the presence of arbitrarily-complex population structures, which results in an improved estimation framework specifically designed for arbitrary population structures. After generalizing the definition of F_ST to arbitrary population structures and establishing a framework for assessing bias and consistency of genome-wide estimators, we calculate the accuracy of existing F_ST and kinship estimators under arbitrary population structures, characterizing biases and estimation challenges unobserved under their originally-assumed models of structure. We then present our new approach, which consistently estimates kinship and F_ST when the minimum kinship value in the dataset is estimated consistently. We illustrate our results using simulated genotypes from an admixture model, constructing a one-dimensional geographic scenario that departs nontrivially from the independent subpopulations model. Our simulations reveal the potential for severe biases in estimates of existing approaches that are overcome by our new framework. This work may significantly improve future analyses that rely on accurate kinship and F_ST estimates.     

The Relationship Between FST and the Frequency of the Most Frequent Allele

F_ST is frequently used as a summary of genetic differentiation among groups. It has been suggested that F_ST depends on the allele frequencies at a locus, as it exhibits a variety of peculiar properties related to genetic diversity: higher values for biallelic single-nucleotide polymorphisms (SNPs) than for multiallelic microsatellites, low values among high-diversity populations viewed as substantially distinct, and low values for populations that differ primarily in their profiles of rare alleles. A full mathematical understanding of the dependence of F_ST on allele frequencies, however, has been elusive. Here, we examine the relationship between F_ST and the frequency of the most frequent allele, demonstrating that the range of values that F_ST can take is restricted considerably by the allele-frequency distribution. For a two-population model, we derive strict bounds on F_ST as a function of the frequency M of the allele with highest mean frequency between the pair of populations. Using these bounds, we show that for a value of M chosen uniformly between 0 and 1 at a multiallelic locus whose number of alleles is left unspecified, the mean maximum F_ST is ∼0.3585. Further, F_ST is restricted to values much less than 1 when M is low or high, and the contribution to the maximum F_ST made by the most frequent allele is on average ∼0.4485. Using bounds on homozygosity that we have previously derived as functions of M, we describe strict bounds on F_ST in terms of the homozygosity of the total population, finding that the mean maximum F_ST given this homozygosity is 1 − ln 2 ≈ 0.3069. Our results provide a conceptual basis for understanding the dependence of F_ST on allele frequencies and genetic diversity and for interpreting the roles of these quantities in computations of F_ST from population-genetic data. Further, our analysis suggests that many unusual observations of F_ST, including the relatively low F_ST values in high-diversity human populations from Africa and the relatively low estimates of F_ST for microsatellites compared to SNPs, can be understood not as biological phenomena associated with different groups of populations or classes of markers but rather as consequences of the intrinsic mathematical dependence of F_ST on the properties of allele-frequency distributions.DIFFERENTIATION among groups is one of the fundamental subjects of the field of population genetics. Comparisons of the level of variation among subpopulations with the level of variation in the total population have been employed frequently in population-genetic theory, in statistical methods for data analysis, and in empirical studies of distributions of genetic variation. Wright’s (Wright 1951) fixation indices, and F_ST in particular, have been central to this effort.Wright’s F_ST was originally defined as the correlation between two randomly sampled gametes from the same subpopulation when the correlation of two randomly sampled gametes from the total population is set to zero. Several definitions of F_ST or F_ST-like quantities are now available, relying on a variety of different conceptual formulations but all measuring some aspect of population differentiation (e.g., Charlesworth 1998; Holsinger and Weir 2009). Many authors have claimed that one or another formulation of F_ST is affected by levels of genetic diversity or by allele frequencies, either because the range of F_ST is restricted by these quantities or because these quantities affect the degree to which F_ST reflects population differentiation (e.g., Charlesworth 1998; Nagylaki 1998; Hedrick 1999, 2005; Long and Kittles 2003; Jost 2008; Ryman and Leimar 2008; Long 2009; Meirmans and Hedrick 2011). For example, Nagylaki (1998) and Hedrick (1999) argued that measures of F_ST may be poor measures of genetic differentiation when the level of diversity is high. Charlesworth (1998) suggested that F_ST can be inflated when diversity is low, arguing that F_ST might not be appropriate for comparing loci with substantially different levels of variation. In a provocative recent article, Jost (2008) used the diversity dependence of forms of F_ST to question their utility as differentiation measures at all.One definition that is convenient for mathematical assessment of the relationship of an F_ST-like quantity and allele frequencies is the quantity labeled G_ST by Nei (1973), which for a given locus measures the difference between the heterozygosity of the total (pooled) population, h_T, and the mean heterozygosity across subpopulations, h_S, divided by the heterozygosity of the total population:GST=hT−hShT.(1)In terms of the homozygosity of the total population, H_T = 1 − h_T, and the mean homozygosity across subpopulations, H_S = 1 − h_S, we can writeGST=HS−HT1−HT.(2)The Wahlund (1928) principle guarantees that H_S ≥ H_T and, therefore, because H_S ≤ 1 and for a polymorphic locus with finitely many alleles, 0 < H_T < 1, G_ST lies in the interval [0,1].Using G_ST for their definition of F_ST, Hedrick (1999, 2005) and Long and Kittles (2003) pointed out that because h_T < 1, F_ST cannot exceed the mean homozygosity across subpopulations, H_S:F_ST = 1 ? h_S/h_T < 1 ? h_S = H_S.(3)Hedrick (2005) obtained this result by considering a set of K equal-sized subpopulations, in which each allele is private to a single subpopulation. In the limit as K → ∞, a stronger upper bound on F_ST as a function of H_S and K reduces to Equation 3 (see also Jin and Chakraborty 1995 and Long and Kittles 2003).While Hedrick (1999, 2005) and Long and Kittles (2003) have clarified the relationship between F_ST and the mean homozygosity H_S across subpopulations, their approaches do not easily illuminate the connection between F_ST and allele frequencies themselves. A formal understanding of the relationship between F_ST and allele frequencies would make it possible to more fully understand the behavior of F_ST in situations where markers of interest differ substantially in allele frequencies or levels of genetic diversity. Our recent work on the relationship between homozygosity and the frequency of the most frequent allele (Rosenberg and Jakobsson 2008; Reddy and Rosenberg 2012) provides a mathematical approach for formal investigation of bounds on population-genetic statistics in terms of allele frequencies. In this article, we therefore seek to thoroughly examine the dependence of F_ST on allele frequencies by investigating the upper bound on F_ST in terms of the frequency M of the most frequent allele across a pair of populations. We derive bounds on F_ST given the frequency of the most frequent allele and bounds on the frequency of the most frequent allele given F_ST. We consider loci with arbitrarily many alleles in a pair of subpopulations. Using theory for the bounds on homozygosity given the frequency of the most frequent allele, we obtain strict bounds on F_ST given the homozygosity of the total population. Our analysis clarifies the relationships among F_ST, allele frequencies, and homozygosity, providing explanations for peculiar observations of F_ST that can be attributed to allele-frequency dependence.     

Comparison of genetic differentiation at marker loci and quantitative traits

The comparison of the degree of differentiation in neutral marker loci and genes coding quantitative traits with standardized and equivalent measures of genetic differentiation (F_ST and Q_ST, respectively) can provide insights into two important but seldom explored questions in evolutionary genetics: (i) what is the relative importance of random genetic drift and directional natural selection as causes of population differentiation in quantitative traits, and (ii) does the degree of divergence in neutral marker loci predict the degree of divergence in genes coding quantitative traits? Examination of data from 18 independent studies of plants and animals using both standard statistical and meta‐analytical methods revealed a number of interesting points. First, the degree of differentiation in quantitative traits (Q_ST) typically exceeds that observed in neutral marker genes (F_ST), suggesting a prominent role for natural selection in accounting for patterns of quantitative trait differentiation among contemporary populations. Second, the F_ST – Q_ST difference is more pronounced for allozyme markers and morphological traits, than for other kinds of molecular markers and life‐history traits. Third, very few studies reveal situations were Q_ST < F_ST, suggesting that selection pressures, and hence optimal phenotypes, in different populations of the same species are unlikely to be often similar. Fourth, there is a strong correlation between Q_ST and F_ST indices across the different studies for allozyme (r=0.81), microsatellite (r=0.87) and combined (r=0.75) marker data, suggesting that the degree of genetic differentiation in neutral marker loci is closely predictive of the degree of differentiation in loci coding quantitative traits. However, these interpretations are subject to a number of assumptions about the data and methods used to derive the estimates of population differentiation in the two sets of traits.     

Measuring individual inbreeding in the age of genomics: marker-based measures are better than pedigrees

Inbreeding (mating between relatives) can dramatically reduce the fitness of offspring by causing parts of the genome to be identical by descent. Thus, measuring individual inbreeding is crucial for ecology, evolution and conservation biology. We used computer simulations to test whether the realized proportion of the genome that is identical by descent (IBD_G) is predicted better by the pedigree inbreeding coefficient (F_P) or by genomic (marker-based) measures of inbreeding. Genomic estimators of IBD_G included the increase in individual homozygosity relative to mean Hardy–Weinberg expected homozygosity (F_H), and two measures (F_ROH and F_E) that use mapped genetic markers to estimate IBD_G. IBD_G was more strongly correlated with F_H, F_E and F_ROH than with F_P across a broad range of simulated scenarios when thousands of SNPs were used. For example, IBD_G was more strongly correlated with F_ROH, F_H and F_E (estimated with ⩾10 000 SNPs) than with F_P (estimated with 20 generations of complete pedigree) in populations with a recent reduction in the effective populations size (from N_e=500 to N_e=75). F_ROH, F_H and F_E generally explained >90% of the variance in IBD_G (among individuals) when 35 K or more SNPs were used. F_P explained <80% of the variation in IBD_G on average in all simulated scenarios, even when pedigrees included 20 generations. Our results demonstrate that IBD_G can be more precisely estimated with large numbers of genetic markers than with pedigrees. We encourage researchers to adopt genomic marker-based measures of IBD_G as thousands of loci can now be genotyped in any species.     

Queen execution increases relatedness among workers of the invasive Argentine ant,Linepithema humile

Polygyny in social insects can greatly reduce within‐nest genetic relatedness. In polygynous ant species, potential rival queens in colonies with multiple queens are often executed by other queens, workers, or both. The Argentine ant, Linepithema humile, native to South America, forms a “supercolony” that is composed of a large number of nests and is considered to contribute to the ant's invasion success. Currently, four mutually antagonistic supercolonies are contiguously distributed within a small area of Japan. Here, we analyzed the genetic structure and relatedness within and among the four supercolonies using microsatellite markers to clarify how L. humile maintains its supercoloniality. The results of AMOVA and BASP, the F_ST values, and the existence of several private alleles indicated that the L. humile population in the Kobe area had a characteristic genetic structure. Within a given supercolony, there was significant genetic differentiation (F_ST) among workers collected in May and those collected in September. The significant deviation from Hardy–Weinberg equilibrium increased, and the relatedness among workers significantly increased from May to September in all supercolonies. This result suggested that the supercolonies replaced old queens with new ones during the reproductive season, thus supporting the plausibility of queen execution. From the perspective of kin selection, workers collectively eliminate queens, thereby increasing their own inclusive fitness. Restricted gene flow among supercolonies, together with mating with sib and queen execution, could help to maintain the unique social structure of L. humile, the distribution of which is expanding worldwide.     

Individual increase in inbreeding allows estimating effective sizes from pedigrees

We present here a simple approach to obtain reliable estimates of the effective population size in real world populations via the computation of the increase in inbreeding for each individual (delta F_i) in a given population. The values of delta F_i are computed as t-root of 1 - (1 - F_i) where F_i is the inbreeding coefficient and t is the equivalent complete generations for each individual. The values of delta F computed for a pre-defined reference subset can be averaged and used to estimate effective size. A standard error of this estimate of N_e can be further computed from the standard deviation of the individual increase in inbreeding. The methodology is demonstrated by applying it to several simulated examples and to a real pedigree in which other methodologies fail when considering reference subpopulations. The main characteristics of the approach and its possible use are discussed both for predictive purposes and for analyzing genealogies.     

A spectral theory for Wright’s inbreeding coefficients and related quantities

Wright’s inbreeding coefficient, F_ST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright’s inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of F_ST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright’s F_ST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of F_ST approximates the proportion of genetic variation explained by the first (K − 1) principal components accurately. The new definition of F_ST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.     

Isozyme variation among teak (Tectona grandis L.f.) provenances

Fourteen enzyme systems were analysed in leaf parenchyma of nine native and introduced populations of teak. These enzyme systems were encoded by 20 putative loci of which 18 were polymorphic. Populations showed a general lack of heterozygosity (average F_IS = 0.11). On average over the 18 polymorphic loci, the genetic differentiation among provenances varied according to the estimator: 0.09 for G_ST, 0.12 for F_ST and 0.19 for . The cluster analysis showed two main gene pools, the first consisted of the Indian provenances and the second of African, Indonesian and Thai provenances. Genetic distances among populations of the same group were similar, and lower than the genetic distances between populations from different groups. The factorial analysis on genotypes of seedlings also showed the same geographic differentiation into two major groups. The possible natural distribution of teak in Java is discussed.