A map of local adaptation in Arabidopsis thaliana

Local adaptation is critical for species persistence in the face of rapid environmental change, but its genetic basis is not well understood. Growing the model plant Arabidopsis thaliana in field experiments in four sites across the species' native range, we identified candidate loci for local adaptation from a genome-wide association study of lifetime fitness in geographically diverse accessions. Fitness-associated loci exhibited both geographic and climatic signatures of local adaptation. Relative to genomic controls, high-fitness alleles were generally distributed closer to the site where they increased fitness, occupying specific and distinct climate spaces. Independent loci with different molecular functions contributed most strongly to fitness variation in each site. Independent local adaptation by distinct genetic mechanisms may facilitate a flexible evolutionary response to changing environment across a species range.

Distribution of genetic variation within and among local populations of Arabidopsis thaliana over its species range

A detailed description of local population structure in Arabidopsis thaliana is presented, including an assessment of the genetic relatedness of individuals collected from the same field. A hierarchical sample of four individuals from 37 local populations, including North America, England, Eastern and Western Europe, and Asia, and a selection of ecotypes, were analysed for variation in Adh, ChiA, FAH1, F3H, Rpm1, Rps5, and five microsatellite loci. Twenty-eight of the 37 population samples contained individuals with identical multilocus haplotypes, 12 of which were fixed for a single haplotype. These monomorphic populations were evenly distributed over the species range. Only in North America did we find a single multilocus haplotype shared among different populations, perhaps indicating a continental founder event. Despite the occurrence of local inbreeding, a considerable amount of genetic variation was found segregating within and among local populations. A novel analysis of haplotype differences reveals that genetic differentiation occurs at every geographic scale in A. thaliana, where we find a surprising under-representation of recent migrants between local populations. This leads us to hypothesize that most dispersal between A. thaliana populations is by pollen rather than seed. Based on the structure of A. thaliana populations, it appears that regional groups of local populations may provide the most appropriate genetic material for linkage disequilibrium mapping of adaptive traits.

On the meaning and existence of an effective population size

We investigate conditions under which a model with stochastic demography or population structure converges to the coalescent with a linear change in timescale. We argue that this is a necessary condition for the existence of a meaningful effective population size. We find that such a linear timescale change is obtained when demographic fluctuations and coalescence events occur on different timescales. Simple models of population structure and randomly fluctuating population size are used to exemplify the ideas and provide an intuitive feel for the meaning of the conditions.

Likelihoods and simulation methods for a class of nonneutral population genetics models

Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.

Linkage disequilibrium, gene trees and selfing: an ancestral recombination graph with partial self-fertilization

It is shown that partial self-fertilization can be introduced into neutral population genetic models with recombination as a simple change in the scaling of the parameters. This means that statistical and computational methods that have been developed under the assumption of random mating can be used without modification, provided the appropriate parameter changes are made. An important prediction is that all forms of linkage disequilibrium will be more extensive in selfing species. The implications of this are discussed.

The effect of seed and rosette cold treatment on germination and flowering time in some Arabidopsis thaliana (Brassicaceae) ecotypes

The germination and flowering responses to cold treatment were investigated in 32 ecotypes of Arabidopsis thaliana. A month-long cold treatment at the seed stage decreased the time until flowering in all but one strain, whereas a 3-d cold treatment had little, or the opposing effect. A month-long cold treatment at the rosette stage also decreased the time until flowering, but was less effective than seed cold treatment. Seed and rosette cold treatments did not have an additive effect on time until flowering. Cold treatment usually increased the speed of germination, however no clear response patterns for the probability of germination were detected. These findings are discussed in relation to the life cycle of the plant.

The effects of local selection, balanced polymorphism and background selection on equilibrium patterns of genetic diversity in subdivided populations

Levels of neutral genetic diversity in populations subdivided into two demes were studied by multilocus stochastic simulations. The model includes deleterious mutations at loci throughout the genome, causing 'background selection', as well as a single locus at which a polymorphism is maintained, either by frequency-dependent selection or by local selective differences. These balanced polymorphisms induce long coalescence times at linked neutral loci, so that sequence diversity at these loci is enhanced at statistical equilibrium. We study how equilibrium neutral diversity levels are affected by the degree of population subdivision, the presence or absence of background selection, and the level of inbreeding of the population. The simulation results are compared with approximate analytical formulae, assuming the infinite sites neutral model. We discuss how balancing selection can be distinguished from local selection, by determining whether peaks of diversity in the region of the polymorphic locus are seen within or between demes. The width of such diversity peaks is shown to depend on the total species population size, rather than local deme sizes. We show that, with population subdivision, local selection enhances between-deme diversity even at neutral sites distant from the polymorphic locus, producing higher FST values than with no selection; very high values can be generated at sites close to a selected locus. Background selection also increases FST, mainly because of decreased diversity within populations, which implies that its effects may be distinguishable from those of local selection. Both effects are stronger in selfing than outcrossing populations. Linkage disequilibrium between neutral sites is generated by both balancing and local selection, especially in selfing populations, because of linkage disequilibrium between the neutral sites and the selectively maintained alleles. We discuss how these theoretical results can be related to data on genetic diversity within and between local populations of a species.

Structured coalescent processes on different time scales

It is demonstrated that the structured coalescent model can readily be extended to include phenomena such as partial selfing and background selection through the use of an approximation based on separation of time scales. A model that includes these phenomena, as well as geographic subdivision and linkage to a polymorphism maintained either by local adaptation or by balancing selection, is derived, and the expected coalescence time for a pair of genes is calculated. It is found that background selection reduces coalescence times within subpopulations and allelic classes, leading to a high degree of apparent differentiation. Extremely high levels of subpopulation differentiation are also expected for regions of the genome surrounding loci important in local adaptation. These regions will be wider the stronger the local selection, and the higher the selfing rate.

The coalescent process with selfing

A method of estimating the selfing rate using DNA sequence data was recently proposed by Milligan. Unfortunately, a number of errors make interpretation of his results problematic. In the present paper we first show how the usual coalescent process can be adapted to models that include selfing, and then use this result to find moment estimators as well as the likelihood surface for the selfing rate, s, and the scaled mutation rate, theta. We conclude that, regardless of the method used, large sample sizes are necessary to estimate s with any degree of certainty, and that the estimate is always highly sensitive to recent changes in the true value.

The effect of recombination on background selection

An approximate equation is derived, which predicts the effect on variability at a neutral locus of background selection due to a set of partly linked deleterious mutations. Random mating, multiplicative fitnesses, and sufficiently large population size that the selected loci are in mutation/selection equilibrium are assumed. Given these assumptions, the equation is valid for an arbitrary genetic map, and for an arbitrary distribution of selection coefficients across loci. Monte Carlo computer simulations show that the formula performs well for small population sizes under a wide range of conditions, and even seems to apply when there are epistatic fitness interactions among the selected loci. Failure occurred only with very weak selection and tight linkage. The formula is shown to imply that weakly selected mutations are more likely than strongly selected mutations to produce regional patterning of variability along a chromosome in response to local variation in recombination rates. Loci at the extreme tip of a chromosome experience a smaller effect of background selection than loci closer to the centre. It is shown that background selection can produce a considerable overall reduction in variation in organisms with small numbers of chromosomes and short maps, such as Drosophila. Large overall effects are less likely in species with higher levels of genetic recombination, such as mammals, although local reductions in regions of reduced recombination might be detectable.

Effects of cis-trans viability selection on some two-locus models

Most analyses of two-locus viability models have assumed that the fitness of double heterozygotes are the same whether in the cis or trans configuration. This assumption is unlikely to hold for polymorphic sites within the same locus. We examine the quantitative and qualitative effects of incorporating cis-trans viability differences into a number of deterministic two-locus models. A new result is the finding that two asymmetric equilibria with similar levels of linkage disequilibrium, but different gene frequencies, may arise in quite realistic biological models. The general, and most important, conclusion is that high levels of linkage disequilibrium may be generated by very small selective differences in cis and trans. Polymorphic sites that interact selectively are expected to show high levels of linkage disequilibrium. Conversely, if two polymorphic sites within a gene are found to be in linkage equilibrium, it is likely that one or both are selectively neutral.

Estimating allelic diversity generated by excision of different transposon types

Methods are presented for calculating the number and type of different DNA sequences generated by base excision and insertion events at a given site in a known DNA sequence. We calculate, for example, that excision of the Mu1 transposon from the bz1::Mu1 allele of maize should generate more than 500,000 unique alleles given the extent of base deletion (up to 34 bases removed) and base insertion (0-5 bases) observed thus far in sequenced excision alleles. Analysis of this universe of potential alleles can, for example, be used to predict the frequency of creation of stop codons or repair-generated duplications. In general, knowledge of the distribution of alleles can be used to evaluate models of both excision and repair by determining whether particular events occur more frequently than expected. Such quantitative analysis complements the qualitative description provided by the DNA sequence of individual events. Similar methods can be used to evaluate the outcome of other cases of DNA breakage and repair such as programmed V(D)J recombination in immunoglobin genes.

A model of gender modification in gynodioecious plants

The conditions under which hermaphrodites in gynodioecious populations might evolve increased allocation to male function are important for understanding the evolution of plant mating systems. A model is presented here that investigates these conditions under the assumptions that sex determination is nucleo-cytoplasmic and polymorphism is maintained by population subdivision. It is found that modifiers affecting the sex allocation in gynodioecious populations can invade under restrictive conditions, and that under these conditions hermaphroditism no longer is an evolutionary stable strategy. The reasons for the differences between this and related models are discussed.

Female infanticide and human sex ratio evolution

The possible effect on the evolution of the human sex ratio of a preference for male children is examined in a genetic model. It is shown that the killing of infant daughters can lead to either a female- or a male-biased sex ratio, the outcome depending on the decision rule used to determine the fate of a child. This reconciles long-standing contradictory results.