Allelic genealogies in sporophytic self-incompatibility systems in plants.

Expectations for the time scale and structure of allelic genealogies in finite populations are formed under three models of sporophytic self-incompatibility. The models differ in the dominance interactions among the alleles that determine the self-incompatibility phenotype: In the SSIcod model, alleles act codominantly in both pollen and style, in the SSIdom model, alleles form a dominance hierarchy, and in SSIdomcod, alleles are codominant in the style and show a dominance hierarchy in the pollen. Coalescence times of alleles rarely differ more than threefold from those under gametophytic self-incompatibility, and transspecific polymorphism is therefore expected to be equally common. The previously reported directional turnover process of alleles in the SSIdomcod model results in coalescence times lower and substitution rates higher than those in the other models. The SSIdom model assumes strong asymmetries in allelic action, and the most recessive extant allele is likely to be the most recent common ancestor. Despite these asymmetries, the expected shape of the allele genealogies does not deviate markedly from the shape of a neutral gene genealogy. The application of the results to sequence surveys of alleles, including interspecific comparisons, is discussed.     

Conditional gene genealogies under strong purifying selection

The ancestral selection graph, conditioned on the allelic types in the sample, is used to obtain a limiting gene genealogical process under strong selection. In an equilibrium, two-allele system with strong selection, neutral gene genealogies are predicted for random samples and for samples containing at most one unfavorable allele. Samples containing more than one unfavorable allele have gene genealogies that differ greatly from neutral predictions. However, they are related to neutral gene genealogies via the well-known Ewens sampling formula. Simulations show rapid convergence to limiting analytical predictions as the strength of selection increases. These results extend the idea of a soft selective sweep to deleterious alleles and have implications for the interpretation of polymorphism among disease-causing alleles in humans.     

Rapid recent radiation of S-RNase lineages in Witheringia solanacea (Solanaceae)

Strong frequency-dependent selection as found in the self-incompatibility loci of flowering plants maintains allelic lineages for extremely long time scales, such that allelic genealogies can shed insight into long-term demographic patterns of species. Effective mutation rate, as well as demographic change such as population bottlenecks, can influence genealogical structure. In addition, loss of functionality at the self-incompatibility locus is likely to affect radiation rates. Partial sequences for 21 S-RNase alleles of the mid-elevation tropical species Witheringia solanacea were obtained in order to compare their substitution rates and genealogy with those of Witheringia maculata and two species in the closely related genus Physalis. Sequences for W. solanacea fell into the three clades within the Solanaceae already identified for the genus. Terminal branch lengths for W. solanacea, scaled to the total depth of its phylogeny, were intermediate between the unusually short terminal branches of W. maculata and those of the two Physalis species. In contrast to the Physalis species, where interspecific dN/dS for closely related alleles exceeded 1.0 to the same degree as did intraspecific dN/dS, in Witheringia only intraspecific comparisons showed an excess of nonsynonymous substitutions, suggesting postspeciation radiation of alleles. Alleles associated with lowered S-RNase production and self-compatibility showed extremely short terminal branches. In summary, it appears that rapid recent diversification of alleles characterizes the Witheringia lineages. In some cases, this rapid diversification can be attributed to relaxed constraints due to breakdown of self-incompatibility.     

Genealogical Structure among Alleles Regulating Self-Incompatibility in Natural Populations of Flowering Plants

A method is proposed for characterizing the structure of genealogies among alleles that regulate selfincompatibility in flowering plants. Expected distributions of ratios of divergence times among alleles, scaled by functions of allele number, were generated by numerical simulation. These distributions appeared relatively insensitive to the particular parameter values assigned in the simulations over a fourfold range in effective population size and a 100-fold range in mutation rate. Generalized leastsquares estimates of the scaled indices were obtained from genealogies reconstructed from nucleotide sequences of self-incompatibility alleles from natural populations of two solanaceous species. Comparison of the observed indices to the expected distributions generated by numerical simulation indicated that the allelic genealogy of one species appeared consistent with the symmetric balancing selection generated by self-incompatibility. However, the allelic genealogy of the second species showed unusually long terminal branches, suggesting the operation of additional evolutionary processes.     

Estimating effective population size from samples of sequences: inefficiency of pairwise and segregating sites as compared to phylogenetic estimates.

It is known that under neutral mutation at a known mutation rate a sample of nucleotide sequences, within which there is assumed to be no recombination, allows estimation of the effective size of an isolated population. This paper investigates the case of very long sequences, where each pair of sequences allows a precise estimate of the divergence time of those two gene copies. The average divergence time of all pairs of copies estimates twice the effective population number and an estimate can also be derived from the number of segregating sites. One can alternatively estimate the genealogy of the copies. This paper shows how a maximum likelihood estimate of the effective population number can be derived from such a genealogical tree. The pairwise and the segregating sites estimates are shown to be much less efficient than this maximum likelihood estimate, and this is verified by computer simulation. The result implies that there is much to gain by explicitly taking the tree structure of these genealogies into account.     

Mapping trait loci by use of inferred ancestral recombination graphs

Large-scale association studies are being undertaken with the hope of uncovering the genetic determinants of complex disease. We describe a computationally efficient method for inferring genealogies from population genotype data and show how these genealogies can be used to fine map disease loci and interpret association signals. These genealogies take the form of the ancestral recombination graph (ARG). The ARG defines a genealogical tree for each locus, and, as one moves along the chromosome, the topologies of consecutive trees shift according to the impact of historical recombination events. There are two stages to our analysis. First, we infer plausible ARGs, using a heuristic algorithm, which can handle unphased and missing data and is fast enough to be applied to large-scale studies. Second, we test the genealogical tree at each locus for a clustering of the disease cases beneath a branch, suggesting that a causative mutation occurred on that branch. Since the true ARG is unknown, we average this analysis over an ensemble of inferred ARGs. We have characterized the performance of our method across a wide range of simulated disease models. Compared with simpler tests, our method gives increased accuracy in positioning untyped causative loci and can also be used to estimate the frequencies of untyped causative alleles. We have applied our method to Ueda et al.'s association study of CTLA4 and Graves disease, showing how it can be used to dissect the association signal, giving potentially interesting results of allelic heterogeneity and interaction. Similar approaches analyzing an ensemble of ARGs inferred using our method may be applicable to many other problems of inference from population genotype data.     

The effect of subdivision on variation at multi-allelic loci under balancing selection

Simulations are used to investigate the expected pattern of variation at loci under different forms of multi-allelic balancing selection in a finite island model of a subdivided population. The objective is to evaluate the effect of restricted migration among demes on the distribution of polymorphism at the selected loci at equilibrium, and to compare the results with those expected for a neutral locus. The results show that the expected number of alleles maintained, and numbers of nucleotide differences between alleles, are relatively insensitive to the migration rate, and differentiation remains low even under very restricted migration. However, nucleotide divergence between copies of functionally identical alleles increases sharply when migration decreases. These results are discussed in relation to published surveys of allelic diversity in MHC and plant self-incompatibility systems, and to the possibility of inferring ancient population genetic events and processes. In addition, it is shown that, for sporophytic self-incompatibility systems, it is not necessarily true in a subdivided population that recessive alleles are more frequent than dominant ones.     

A vectorized method of importance sampling with applications to models of mutation and migration

An importance-sampling method is presented for computing the likelihood of the configuration of population genetic data under general assumptions about population history and transitions among states. The configuration of the data is the number of chromosomes sampled that are in each of a finite set of states. Transitions among states are governed by a Markov chain with transition probabilities dependent on one or more parameters. The method assumes that the joint distribution of coalescence times of the underlying gene genealogy is independent of the genetic state of each lineage. Given a set of coalescence times, the probability that a pair of lineages is chosen to coalesce in each replicate is proportional to the contribution that the coalescence event makes to the probability of the data. This method can be applied to gene genealogies generated by the neutral coalescent process and to genealogies generated by other processes, such as a linear birth-death process which provides a good approximation to the dynamics of low-frequency alleles. Two applications are described. In the first, the fit of allele frequencies at two microsatellite loci sampled in a Sardinian population to the one-step mutation model is tested. The one-step model is rejected for one locus but not for the other. The second application is to low-frequency alleles in a geographically subdivided population. The geographic location is the allelic state, and the alleles are assumed to be sufficiently rare that their dynamics can be approximated by a linear birth-death process in which the birth and death rates are independent of geographic location. The analysis of eight low-frequency allozyme alleles found in the glaucous-winged gull, Larus glaucescens, illustrates how geographically restricted dispersal can be detected.     

Effect of balancing selection on spatial genetic structure within populations: theoretical investigations on the self-incompatibility locus and empirical studies in Arabidopsis halleri

The effect of selection on patterns of genetic structure within and between populations may be studied by contrasting observed patterns at the genes targeted by selection with those of unlinked neutral marker loci. Local directional selection on target genes will produce stronger population genetic structure than at neutral loci, whereas the reverse is expected for balancing selection. However, theoretical predictions on the intensity of this signal under precise models of balancing selection are still lacking. Using negative frequency-dependent selection acting on self-incompatibility systems in plants as a model of balancing selection, we investigated the effect of such selection on patterns of spatial genetic structure within a continuous population. Using numerical simulations, we tested the effect of the type of self-incompatibility system, the number of alleles at the self-incompatibility locus and the dominance interactions among them, the extent of gene dispersal, and the immigration rate on spatial genetic structure at the selected locus and at unlinked neutral loci. We confirm that frequency-dependent selection is expected to reduce the extent of spatial genetic structure as compared to neutral loci, particularly in situations with low number of alleles at the self-incompatibility locus, high frequency of codominant interactions among alleles, restricted gene dispersal and restricted immigration from outside populations. Hence the signature of selection on spatial genetic structure is expected to vary across species and populations, and we show that empirical data from the literature as well as data reported here on three natural populations of the herb Arabidopsis halleri confirm these theoretical results.     

Genetic identity between populations when mutation rates vary within and across loci

A formula is derived for the probability that two genes taken at random from the same locus in two populations isolated at time t ago are of the same allelic type. The model assumed is a neutral one where there are possibly different mutation rates between different alleles. Inequalities are derived for this probability. A particular result is that for a fixed overall mutation rate, the probability is least for the infinite alleles model. Inequalities and approximations are found for Nei's genetic identity at one locus when mutation rates vary, and also for the identity across loci when the overall mutation rates per locus vary. Genetic identity at the molecular level is considered and a probability generating function found for the number of segregating sites between two randomly chosen gametes from two divergent populations, under various models.     

Gametophytic self-incompatibility in Lycium parishii (Solanaceae): allelic diversity, genealogical structure, and patterns of molecular evolution at the S-RNase locus

We characterized allelic diversity at the locus controlling self-incompatibility (SI) for a population of Lycium parishii (Solanaceae) from Organ Pipe National Monument, Arizona. Twenty-four partial sequences of S-RNase alleles were recovered from 25 individuals. Estimates of allelic diversity range from 23 to 27 alleles and, consistent with expectations for SI, individuals are heterozygous. We compare S-RNase diversity, patterns of molecular evolution, and the genealogical structure of alleles from L. parishii to a previously studied population of its congener L. andersonii. Gametophytic SI is well characterized for Solanaceae and although balancing selection is hypothesized to be responsible for high levels of allelic divergence, the pattern of selection varies depending on the portion of the gene considered. Site-specific models investigating patterns of selection for L. parishii and L. andersonii indicate that positive selection occurs in those regions of the S-RNase gene hypothesized as important to the recognition response, whereas positive selection was not detected for any position within regions previously characterized as conserved. A 10-species genealogy including S-RNases from a pair of congeners from each of five genera in Solanaceae reveals extensive transgeneric evolution of L. parishii S-RNases. Further, within Lycium, the Dn/Ds ratios for pairs of closely related alleles for intraspecific versus interspecific comparisons were not significantly different, suggesting that the S-RNase diversity recovered in these two species was present prior to the speciation event separating them. Despite this, two S-RNases from L. parishii are identical to two previously reported alleles for L. andersonii, suggesting gene flow between these species.     

Mathematical consequences of the genealogical species concept

A genealogical species is defined as a basal group of organisms whose members are all more closely related to each other than they are to any organisms outside the group ("exclusivity"), and which contains no exclusive group within it. In practice, a pair of species is so defined when phylogenies of alleles from a sample of loci shows them to be reciprocally monophyletic at all or some specified fraction of the loci. We investigate the length of time it takes to attain this status when an ancestral population divides into two descendant populations of equal size with no gene exchange, and when genetic drift and mutation are the only evolutionary forces operating. The number of loci used has a substantial effect on the probability of observing reciprocal monophyly at different times after population separation, with very long times needed to observe complete reciprocal monophyly for a large number of loci. In contrast, the number of alleles sampled per locus has a relatively small effect on the probability of reciprocal monophyly. Because a single mitochondrial or chloroplast locus becomes reciprocally monophyletic much faster than does a single nuclear locus, it is not advisable to use mitochondrial and chloroplast DNA to recognize genealogical species for long periods after population divergence. Using a weaker criterion of assigning genealogical species status when more than 50% of sampled nuclear loci show reciprocal monophyly, genealogical species status depends much less on the number of sampled loci, and is attained at roughly 4-7 N generations after populations are isolated, where N is the historically effective population size of each descendant. If genealogical species status is defined as more than 95% of sampled nuclear loci showing reciprocal monophyly, this status is attained after roughly 9-12 N generations.     

Recombination, balancing selection and phylogenies in MHC and self-incompatibility genes.

Using a coalescent model of multiallelic balancing selection with recombination, the genealogical process as a function of recombinational distance from a site under selection is investigated. We find that the shape of the phylogenetic tree is independent of the distance to the site under selection. Only the timescale changes from the value predicted by Takahata's allelic genealogy at the site under selection, converging with increasing recombination to the timescale of the neutral coalescent. However, if nucleotide sequences are simulated over a recombining region containing a site under balancing selection, a phylogenetic tree constructed while ignoring such recombination is strongly affected. This is true even for small rates of recombination. Published studies of multiallelic balancing selection, i.e., the major histocompatibility complex (MHC) of vertebrates, gametophytic and sporophytic self-incompatibility of plants, and incompatibility of fungi, all observe allelic genealogies with unexpected shapes. We conclude that small absolute levels of recombination are compatible with these observed distortions of the shape of the allelic genealogy, suggesting a possible cause of these observations. Furthermore, we illustrate that the variance in the coalescent with recombination process makes it difficult to locate sites under selection and to estimate the selection coefficient from levels of variability.     

Unequal allelic frequencies at the self‐incompatibility locus within local populations of Prunus avium L.: an effect of population structure?

In this paper, we investigated the genetic structure and distribution of allelic frequencies at the gametophytic self-incompatibility locus in three populations of Prunus avium L. In line with theoretical predictions under balancing selection, genetic structure at the self-incompatibility locus was almost three times lower than at seven unlinked microsatellites. Furthermore, we found that S-allele frequencies in wild cherry populations departed significantly from the expected isoplethic distribution towards which balancing selection is expected to drive allelic frequencies (i.e. identical frequency equal to the inverse of the number of alleles in the population). To assess whether this departure could be caused either by drift alone or by population structure, we used numerical simulations to compare our observations with allelic frequency distributions expected : (1) within a single deme from a subdivided population with various levels of differentiation; and (2) within a finite panmictic population with identical allelic diversity. We also investigated the effects of sample size and degree of population structure on tests of departure from isoplethic equilibrium. Overall, our results showed that the observed allele frequency distributions were consistent with a model of subdivided population with demes linked by moderate migration rate.     

Historical events and allelic polymorphism at the gametophytic self-incompatibility locus in Solanaceae

The historical migration rate of a species is often difficult to estimate with neutral markers, because the relationship between the turnover time of the markers and the age of the species commonly remains unknown. Compared with neutral markers, the plant self-incompatibility locus (S) provides a much better source of data for migration-rate estimation due to its high allelic polymorphism and antiquity. Here, the results from extensive surveys of S alleles in two wild solanaceous species, Solanum carolinense and Physalis longifolia, indicate that historical migration rates have differed significantly between the species; the higher migration rate found in S. carolinense appears to have interacted with the balancing selection at the S locus to result in fewer S alleles being maintained in the species. Historical population growth rates estimated via a modified coalescent approach also suggest a faster growing population for S. carolinense than for P. longifolia, which would have further widened their interspecific difference in S-allelle polymorphism. These historical factors may have reduced the probability of new S alleles to prevailing in S. carolinense, leaving old ones segregating at the S locus with little signature of positive selection being currently detectable.     

Origin of allelic diversity in antirrhinum S locus RNases.

In many plant species, self-incompatibility (SI) is genetically controlled by a single multiallelic S locus. Previous analysis of S alleles in the Solanaceae, in which S locus ribonucleases (S RNases) are responsible for stylar expression of SI, has demonstrated that allelic diversity predated speciation within this family. To understand how allelic diversity has evolved, we investigated the molecular basis of gametophytic SI in Antirrhinum, a member of the Scrophulariaceae, which is closely related to the Solanaceae. We have characterized three Antirrhinum cDNAs encoding polypeptides homologous to S RNases and shown that they are encoded by genes at the S locus. RNA in situ hybridization revealed that the Antirrhinum S RNase are primarily expressed in the stylar transmitting tissue. This expression is consistent with their proposed role in arresting the growth of self-pollen tubes. S alleles from the Scrophulariaceae form a separate group from those of the Solanaceae, indicating that new S alleles have been generated since these families separated (approximately 40 million years). We propose that the recruitment of an ancestral RNase gene into SI occurred during an early stage of angiosperm evolution and that, since that time, new alleles subsequently have arisen at a low rate.     

Functional gametophytic self-incompatibility in a peripheral population of Solanum peruvianum (Solanaceae)

The transition from self-incompatibility to self-compatibility is a common transition in angiosperms often reported in populations at the edge of species range limits. Geographically distinct populations of wild tomato species (Solanum section Lycopersicon (Solanaceae)) have been described as polymorphic for mating system with both self-incompatible and self-compatible populations. Using controlled pollinations and sequencing of the S-RNase mating system gene, we test the compatibility status of a population of S. peruvianum located near its southern range limit. Pollinations among plants of known genotypes revealed strong self-incompatibility; fruit set following compatible pollinations was significantly higher than following incompatible pollinations for all tested individuals. Sequencing of the S-RNase gene in parents and progeny arrays was also as predicted under self-incompatibility. Molecular variation at the S-RNase locus revealed a diverse set of alleles, and heterozygosity in over 500 genotyped individuals. We used controlled crosses to test the specificity of sequences recovered in this study; in all cases, results were consistent with a unique allelic specificity for each tested sequence, including two alleles sharing 92% amino-acid similarity. Site-specific patterns of selection at the S-RNase gene indicate positive selection in regions of the gene associated with allelic specificity determination and purifying selection in previously characterized conserved regions. Further, there is broad convergence between the present and previous studies in specific amino-acid positions inferred to be evolving under positive selection.     

Two patterns of variation among MHC class I loci in Tuatara (Sphenodon punctatus)

The genes of the major histocompatibility complex (MHC) are a central component of the immune system in vertebrates and have become important markers of functional, fitness-related genetic variation. We have investigated the evolutionary processes that generate diversity at MHC class I genes in a large population of an archaic reptile species, the tuatara (Sphenodon punctatus), found on Stephens Island, Cook Strait, New Zealand. We identified at least 2 highly polymorphic (UA type) loci and one locus (UZ) exhibiting low polymorphism. The UZ locus is characterized by low nucleotide diversity and weak balancing selection and may be either a nonclassical class I gene or a pseudogene. In contrast, the UA-type alleles have high nucleotide diversity and show evidence of balancing selection at putative peptide-binding sites. Twenty-one different UA-type genotypes were identified among 26 individuals, suggesting that the Stephens Island population has high levels of MHC class I variation. UA-type allelic diversity is generated by a mixture of point mutation and gene conversion. As has been found in birds and fish, gene conversion obscures the genealogical relationships among alleles and prevents the assignment of alleles to loci. Our results suggest that the molecular mechanisms that underpin MHC evolution in nonmammals make locus-specific amplification impossible in some species.     

Molecular Evolution at the Self-Incompatibility Locus of <Emphasis Type="BoldItalic">Physalis longifolia</Emphasis> (Solanaceae)

The simple codominant expression of the alleles at the self-incompatibility locus ( S) of Solanaceae and their extraordinary spectrum of sequence diversity present an ideal case for understanding the molecular forces that shape the sequence polymorphism of genes involved in recognition reactions. Here, with unprecedented conspecific sequences of 33 Physalis longifolia S alleles, including 27 of their single introns, the tempo-spatial nucleotide substitution patterns were first detailed for the S locus and analyzed in genealogical time scales. Three major genealogical clades of the 33 P. longifolia S alleles were used to divide the genealogical time into the within-clade and the between-clade periods. During the within-clade period, the average nonsynonymous substitution rate was 50% higher than the intron substitution rate but the opposite trend emerged for the between-clade period. A new and simple method developed here was utilized to estimate the selection intensity in the coding regions. The magnitudes and the distribution of these estimates, in conjunction with the spatial substitution pattern among closely related S sequences, revealed an initial short-term action of strong positive selection and a continuous but weaker action of negative selection brought by functional/structural constraints on the S alleles. The two modes of selection can significantly modify the branch lengths of an S genealogy and may be ubiquitous to recognition systems.