@article{7736, abstract = {We develop a novel approach to identify regions of the genome underlying population genetic differentiation in any genetic data where the underlying population structure is unknown, or where the interest is assessing divergence along a gradient. By combining the statistical framework for genome-wide association studies (GWASs) with eigenvector decomposition (EigenGWAS), which is commonly used in population genetics to characterize the structure of genetic data, loci under selection can be identified without a requirement for discrete populations. We show through theory and simulation that our approach can identify regions under selection along gradients of ancestry, and in real data we confirm this by demonstrating LCT to be under selection between HapMap CEU–TSI cohorts, and we then validate this selection signal across European countries in the POPRES samples. HERC2 was also found to be differentiated between both the CEU–TSI cohort and within the POPRES sample, reflecting the likely anthropological differences in skin and hair colour between northern and southern European populations. Controlling for population stratification is of great importance in any quantitative genetic study and our approach also provides a simple, fast and accurate way of predicting principal components in independent samples. With ever increasing sample sizes across many fields, this approach is likely to be greatly utilized to gain individual-level eigenvectors avoiding the computational challenges associated with conducting singular value decomposition in large data sets. We have developed freely available software, Genetic Analysis Repository (GEAR), to facilitate the application of the methods.}, author = {Chen, G-B and Lee, S H and Zhu, Z-X and Benyamin, B and Robinson, Matthew Richard}, issn = {0018-067X}, journal = {Heredity}, pages = {51--61}, publisher = {Springer Nature}, title = {{EigenGWAS: Finding loci under selection through genome-wide association studies of eigenvectors in structured populations}}, doi = {10.1038/hdy.2016.25}, volume = {117}, year = {2016}, } @article{3624, abstract = {The state of a diploid population segregating for two alleles at each of n loci is described by 22(n) genotype frequencies, or equivalently, by allele frequencies and by multilocus moments or cumulants of various orders. These measures of linkage disequilibrium cannot usually be determined, both because one cannot tell whether a gene came from the maternal or paternal gamete, and because such a large number of parameters cannot be estimated even from large samples. Simplifying assumptions must therefore be made. This paper sets out methods for estimating multilocus genotype frequencies which are appropriate for unlinked neutral loci, and for populations that are ultimately derived by mixing of two source populations. In such a hybrid population, all multilocus associations depend primarily on the number of loci involved that derive from the maternal genome, and the number derived from the paternal genome Allele frequencies may differ across loci, and the contribution of each locus to multilocus associations may be scaled by the difference in allele frequency between source populations for that locus (δp ≤ 1). For example, the cumulant describing the association between genes i, j, k from the maternal genome, and genes i, l from the paternal genome is K(tJ,k,iλ*), = δp(i)/2 δp(J) δp(k) δp(l) κ3,2. The state of the population is described by n allele frequencies; n divergences, δp; and by a symmetric matrix of cumulants, κ(J,K) (J = 0 ,..., n, K = 0 ,..., n). Expressions for these cumulants under short- and long-range migration are given. Two methods for estimating the cumulants are described: a simple method based on multivariate moments, and a maximum likelihood procedure, which uses the Metropolis algorithm. Both methods perform well when tested against simulations with two or four loci.}, author = {Barton, Nicholas H}, issn = {0018-067X}, journal = {Heredity}, number = {3}, pages = {373 -- 389}, publisher = {Nature Publishing Group}, title = {{Estimating multilocus linkage disequilibria}}, doi = {10.1046/j.1365-2540.2000.00683.x}, volume = {84}, year = {2000}, } @article{3658, abstract = {Females of the grasshopper Podisima pedestris were collected from the middle of a hybrid zone between two chromosomal races in the Alpes Maritimes. They had already mated in the field, and could therefore lay fertilised eggs in the laboratory. The embryos were karyotyped, and found to contain an excess of chromosomal homozygotes. No evidence of assortative mating was found from copulating pairs taken in the field. The excess appears to have been caused by a combination of multiple insemination and assortative fertilisation. The genetics of the assortment, and the implications for the evolution of reproductive isolation are discussed.}, author = {Hewitt, Godfrey and Nichols, R. and Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {457 -- 466}, publisher = {Nature Publishing Group}, title = {{Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.156}, volume = {59}, year = {1987}, } @article{4319, abstract = {The grasshopper Podisma pedestris contains two chromosomal races, which differ by a Robertsonian fusion between the sex chromosome and an autosome, and which meet in a narrow hybrid zone in the Alpes Maritimes. DNA content variation across this hybrid zone was investigated by optical densitometry of Feulgen stained spermatids. Spermatids from males with the unfused sex chromosome stain more strongly than those from males with the fused chromosome. The difference between the karyotypes is greater in the centre of the hybrid zone, suggesting that it is not a pleiotropic effect of the fusion itself, but is due instead to differences at closely linked loci.}, author = {Westerman, Michael and Barton, Nicholas H and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, pages = {221 -- 228}, publisher = {Nature Publishing Group}, title = {{Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.36}, volume = {58}, year = {1987}, } @article{3663, abstract = {The conditional average frequency of rare alleles has been shown in simulations to provide a simple and robust estimator of the number of individuals exchanged between local populations in an island model (Nm). This statistic is defined as the average frequency of an allele in those samples in which the allele is present. Here, we show that the conditional average frequency can be calculated from the distribution of allele frequencies. It is a measure of the spread of this distribution, and so is analogous to the standardised variance, FST. Analytic predictions for the island model of migration agree well with the corresponding simulation results. These predictions are based on the assumption that the rare alleles found in samples have reached a "quasi-equilibrium" distribution. As well as relating the conditional average frequency to the underlying allele frequency distribution, our results provide a more accurate method of estimating Nm from the conditional average frequency of private alleles in samples of different sizes.}, author = {Barton, Nicholas H and Slatkin, Montgomery}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {409 -- 416}, publisher = {Nature Publishing Group}, title = {{A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population}}, doi = {10.1038/hdy.1986.63}, volume = {56}, year = {1986}, } @article{3664, abstract = {Suppose that selection acts at one or more loci to maintain genetic differences between hybridising populations. Then, the flow of alleles at a neutral marker locus which is linked to these selected loci will be impeded. We define and calculate measures of the barrier to gene flow between two distinct demes, and across a continuous habitat. In both cases, we find that in order for gene flow to be significantly reduced over much of the genome, hybrids must be substantially less fit, and the number of genes involved in building the barrier must be so large that the majority of other genes become closely linked to some locus which is under selection. This conclusion is not greatly affected by the pattern of epistasis, or the position of the marker locus along the chromosome.}, author = {Barton, Nicholas H and Bengtsson, Bengt}, issn = {1365-2540}, journal = {Heredity}, pages = {357 -- 376}, publisher = {Nature Publishing Group}, title = {{The barrier to genetic exchange between hybridising populations}}, volume = {57}, year = {1986}, } @article{3665, abstract = {The rate of gene flow across a hybrid zone may be reduced by the presence of a physical barrier, by a reduction of population density caused by reduced fitness of hybrids (the “hybrid sink” effect), and by linkage. If the reduction in hybrid fitness is not extreme, the strength of the barrier to gene flow caused by these effects is. Here, w is the width of the cline; ρ* is the carrying capacity; W̄* is the mean fitness of the population, excluding effects of density; R is the strength of density-dependent regulation; and r̄ is the harmonic mean recombination rate between the locus whose flow is being calculated, and loci under selection. +, 0 denote populations outside the hybrid zone, and at its centre, respectively. This relation is illustrated using data from hybrid ones in Bombina and Podisma, and its implications for interpretation of data from nature are discussed.}, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, pages = {415 -- 426}, publisher = {Nature Publishing Group}, title = {{The effects of linkage and density-dependent regulation on gene flow}}, volume = {57}, year = {1986}, } @article{3667, abstract = {Populations of the grasshopper Podisma pedestris were collected from two ends of a zone of hybridization between two chromosome races, at Seyne and Tende in southern France. 21 enzyme and protein loci were detected by gel electrophoresis. Six of these loci showed widespread polymorphism, and a further eleven had very little or no variation. Two loci (Idh, 6Pgd) had rare alleles in different frequencies in the two areas surveyed. The remaining two loci (Mdh-1, Mdh-2) showed a marked increase in the frequency of rare variants, from 1 per cent outside the hybrid zone, up to 5 per cent at its centre. This region of increased electrophoretic variation coincided with the chromosomal cline between the two races, and with a region of decreased viability. It was spread over about the same width as the chromosomal cline. Possible explanations for this extra variation include intragenic recombination and elevated mutation rates.}, author = {Barton, Nicholas H and Halliday, Bruce and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, number = {2}, pages = {139 -- 146}, publisher = {Nature Publishing Group}, title = {{Rare electrophoretic variants in a hybrid zone}}, doi = {10.1038/hdy.1983.15}, volume = {50}, year = {1983}, } @misc{4330, author = {Barton, Nicholas H}, booktitle = {Heredity}, issn = {1365-2540}, pages = {213 -- 213}, publisher = {Springer Nature}, title = {{Gene flow and speciation (abstract)}}, doi = {10.1038/hdy.1983.24}, volume = {50}, year = {1983}, } @article{3669, abstract = {The dispersal rate of the grasshopper Podisma pedestris has been measured, with the aim of interpreting the width of a chromosomal cline. 171 adults were marked individually, and released within the cline. 169 movements were seen over three subsequent scorings; the distribution of distances, after correction for the loss of long distance dispersants, was close to a normal curve, but there was an initial shift of ten metres, perhaps towards a better habitat. The linear variance increased at about 214 m2 day- 1, which corresponds to a standard deviation of 207 m gen- 1/2 over a 20 day life span. Statistical uncertainty in this estimate can be expressed using a distribution-free maximum likelihood method, which gives support limits of 186- 270 m gen- 1/2. However, the main errors come from extrapolating from this experiment to the cline as a whole.}, author = {Barton, Nicholas H and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, number = {2}, pages = {237 -- 249}, publisher = {Springer Nature}, title = {{A measurement of dispersal in the grasshopper Podisma pedestris (Orthoptera: Acrididae)}}, doi = {10.1038/hdy.1982.29}, volume = {48}, year = {1982}, } @article{3671, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, pages = {279 -- 282}, publisher = {Nature Publishing Group}, title = {{The width of the hybrid zone in Caledia captiva}}, doi = {10.1038/hdy.1981.86}, volume = {47}, year = {1981}, } @article{4333, abstract = {Samples were taken from five sites in a transect across the hybrid zone between two chromosomal races of the grasshopper Podisma pedestris. Crosses were set up between insects from the same population, and between populations spanning the zone, and the early viability of the offspring was measured. Hybrids between pure populations had reduced viability, and the viability of insects from the middle of the zone was still lower, showing that most (87 per cent) of the inviability was due to the breakup of coadapated gene complexes. Although the total selection acting was strong (log. fitness reduced by S25), it was spread over a region wider than the dispersal range (350 m vs. 20 m). Hence, the selection on each locus contributing towards the inviability is weak (3 per cent). Many (150) independent chromosome segments act cumulatively to produce inviability at this stage in the life history. The implications of these findings for models of divergence are discussed.}, author = {Barton, Nicholas H and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {367 -- 383}, publisher = {Springer Nature}, title = {{The genetic basis of hybrid inviability between two chromosomal races of the grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1981.98}, volume = {47}, year = {1981}, } @article{3672, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, pages = {277 -- 278}, publisher = {Springer Nature}, title = {{The hybrid sink effect}}, doi = {10.1038/hdy.1980.23}, volume = {44}, year = {1980}, } @article{4335, abstract = {Genetic incompatibilities between two races of the grasshopper Podisma pedestris, which differ by a Robertsonian fusion involving the sex chromosome, have been investigated. Crosses were made between four populations spanning the chromosomal cline; F1 hybrids between the races, though not between separated populations of the same race, showed markedly reduced hatching success. Observations of the fate of chromosomes transplanted across the cline supported this finding. Crosses between grasshoppers from a mixed population in the cline showed a lower average hatching success, but no correlation of this inviability with the chromosomal polymorphism. The karyotypes of pre-diapause embryos from both types of cross gave no evidence for non-disjunction of the sex chromosome trivalent in heterozygous females; an upper limit of 16 per cent can be set on the non-disjunction rate. These findings suggest that the karyotypic difference is only a weakly selected marker for more fundamental changes in genotype.}, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, pages = {47 -- 59}, publisher = {Springer Nature}, title = {{The fitness of hybrids between two chromosomal races of the grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1980.49}, volume = {45}, year = {1980}, } @article{3673, abstract = {The effect of a cline as a barrier to gene flow at closely linked, weakly selected loci is investigated using a continuous diffusion model. It is shown that a linked cline induces a step in the frequency of a neutral allele, which is proportional to the gradient in neutral allele frequency and to the inverse of the recombination rate. A barrier to dispersal or a local region of low abundance has a similar effect (Nagylaki, 1976). The cline will block the flow of neutral alleles over a region of chromosome roughly 2s/t map units long. However, a slightly advantageous allele will be little affected, and must be very tightly linked to be delayed for long.}, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {333 -- 339}, publisher = {Springer Nature}, title = {{Gene flow past a cline}}, doi = {10.1038/hdy.1979.86}, volume = {43}, year = {1979}, } @article{4336, abstract = {This paper investigates the dynamic behaviour of hybrid zones which are maintained by a balance between dispersal and selection against hybrids. In the first section it is shown that a hybrid zone involving a single locus can move in response to a selective imbalance between the two homozygotes, and also to variation in population density and dispersal rate. It can be trapped by natural barriers, and so an allele which is selected against when rare cannot advance, even if it is advantageous when common. The continuous model used in deriving these results is shown to be a good approximation to the stepping-stone model, provided that the cline contains several demes. The effect of stochastic forces on multi-locus hybrid zones is then considered. An expression giving the shift in position after an arbitrary perturbation in gamete frequency is derived. Using this formula, it is found that sampling drift is negligible unless the zone includes few organisms and involves few loci. Random variations in population structure are the dominant force, and could allow considerable movement in an even environment. However, natural barriers can still trap hybrid zones, and so it is likely that they will remain roughly where they first formed.}, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {341 -- 359}, publisher = {Springer Nature}, title = {{The dynamics of hybrid zones}}, doi = {10.1038/hdy.1979.87}, volume = {43}, year = {1979}, }