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.     

Genealogy of neutral genes in two partially isolated populations

Gene genealogy in two partially isolated populations which diverged at a given time t in the past and have since been exchanging individuals at a constant rate m is studied based upon an analytic method for large t and a simulation method for any t. Particular attention is paid to the conditions under which neutral genes sampled from populations are mono-, para-, and polyphyletic in terms of coalescence (divergence) times of genes. It is shown tha the probability of monophyly is high if M = 2Nm less than 0.5 and T = t/(2N) greater than 1, where N is the size of ancestral and descendant haploid populations, in which case most gene genealogies are likely to be concordant with the population relatedness. This probbility decreases as the sample size of genes increases. On the other hand, the case where the probability of monophyly is low will be either that of M greater than 1 and any T or that of M less than 1 and T less than 1, but the clear distinction between these conditions appears very difficult to make. These results are also examined if the gene genealogy is reconstructed from nucleotide differences. It is then shown that the results based upon coalescence times remain valid if the number of nucleotide differences between any pair of genes is not much smaller than 10. To observe such large nucleotide differences in small populations and therefore infer a reliable gene genealogy, we must examine a fairly long stretch of DNA sequences.     

Trans-specific Mhc polymorphism and the origin of species in primates

The major histocompatibility complex (Mhc) is a cluster of loci controlling the specific immune response in vertebrates. Mhc alleles often differ by a large number of nucleotide substitutions, some of which began to accumulate before the emergence of extant species. We have applied the theory of allelic genealogy to the primate Mhc genes with the aim of estimating the size of the founding populations. The calculations indicate that the long-term effective population size of the studied species was between 10⁴ and 10⁵ individuals and that it most likely never dropped below 10³ individuals.     

Estimating mutation parameters,population history and genealogy simultaneously from temporally spaced sequence data

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.     

The nucleotide sequence of the murine I-E beta b immune response gene: evidence for gene conversion events in class II genes of the major histocompatibility complex.

We have determined the DNA sequence of the murine I-E beta b immune response gene of the major histocompatibility complex (MHC) of the C57BL/10 mouse and compared it with the sequence of allelic I-E and non-allelic I-A genes from the d and k haplotypes. The polymorphic exon sequences which encode the first extracellular globular domain of the E beta domain show approximately 8% nucleotide substitutions between the E beta b and E beta d alleles compared with only approximately 2% substitutions for the intron sequences. This suggests that an active mechanism such as micro gene conversion events drive the accumulation of these mutations in the polymorphic exons. The fact that several of the nucleotide changes are clustered supports this hypothesis. The E beta b and E beta k genes show approximately 2-fold fewer nucleotide substitutions than the E beta d/E beta b pair. The A beta bm12, a mutant I-A beta b gene from the C57BL/6 mouse, has been shown to result from three nucleotide changes clustered in a short region of the beta 1 domain, which suggests that a micro gene conversion event caused this mutation. We show here that the E beta b gene is identical to the non-allelic A beta bm12 DNA sequence in the mutated region and suggest, therefore, that the E beta b gene was the donor sequence for this intergenic transfer of genetic information. Diversity in class II MHC genes appears therefore to be generated, at least in part, by the same mechanism proposed for class I genes: intergenic transfer of short DNA regions between non-allelic genes.     

Conditional genealogies and the age of a neutral mutant.

This paper is concerned with the structure of the genealogy of a sample in which it is observed that some subset of chromosomes carries a particular mutation, assumed to have arisen uniquely in the history of the population. A rigorous theoretical study of this conditional genealogy is given using coalescent methods. Particular results include the mean, variance, and density of the age of the mutation conditional on its frequency in the sample. Most of the development relates to populations of constant size, but we discuss the extension to populations which have grown exponentially to their present size.     

Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

MNU-induced mutant pools and high performance TILLING enable finding of any gene mutation in rice

Mutant populations are indispensable genetic resources for functional genomics in all organisms. However, suitable rice mutant populations, induced either by chemicals or irradiation still have been rarely developed to date. To produce mutant pools and to launch a search system for rice gene mutations, we developed mutant populations of Oryza sativa japonica cv. Taichung 65, by treating single zygotic cells with N-methyl-N-nitrosourea (MNU). Mutagenesis in single zygotes can create mutations at a high frequency and rarely forms chimeric plants. A modified TILLING system using non-labeled primers and fast capillary gel electrophoresis was applied for high-throughput detection of single nucleotide substitution mutations. The mutation rate of an M₂ mutant population was calculated as 7.4 × 10⁻⁶ per nucleotide representing one mutation in every 135 kb genome sequence. One can expect 7.4 single nucleotide substitution mutations in every 1 kb of gene region when using 1,000 M₂ mutant lines. The mutations were very evenly distributed over the regions examined. These results indicate that our rice mutant population generated by MNU-mutagenesis could be a promising resource for identifying mutations in any gene of rice. The modified TILLING method also proved very efficient and convenient in screening the mutant population. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Rapid evolution of the MH class I locus results in different allelic compositions in recently diverged populations of Atlantic salmon

We compared major histocompatibility class I allelic diversity in two currently reproductively isolated Atlantic salmon (Salmo salar) populations (Irish and Norwegian) with a common postglacial origin in order to test for among-population differences in allelic composition and patterns of recombination and point mutation. We also examined the evidence for adaptive molecular divergence at this locus by analyzing the rate of amino acid replacement in relation to a neutral expectation. Contrary to our prediction, and in contrast to the situation for other genetic markers, the two populations have almost nonoverlapping sets of major histocompatibility class I alleles. Although there is a strong signal of point mutation that predates population divergence, recent recombination, acting in similar, but not identical, ways in both populations appears to be a significant force in creating new alleles. Moreover, selection acting on peptide-binding residues seems to favor new recombinant alleles and is likely to be responsible for the rapid divergence between populations.     

Relationship between DNA Polymorphism and Fixation Time

When there is no recombination among nucleotide sites in DNA sequences, DNA polymorphism and fixation of mutants at nucleotide sites are mutually related. Using the method of gene genealogy, the relationship between the DNA polymorphism and the fixation of mutant nucleotide was quantitatively investigated under the assumption that mutants are selectively neutral, that there is no recombination among nucleotide sites, and that the population is a random mating population with N diploid individuals. The results obtained indicate that the expected number of nucleotide differences between two DNA sequences randomly sampled from the population is 42% less when a mutant at a particular nucleotide site reaches fixation than at a random time, and that heterozygosity is also expected to be less when fixation takes place than at a random time, but the amount of reduction depends on the value of 4Nv in this case, where v is the mutation rate per DNA sequence per generation. The formula for obtaining the expected number of nucleotide differences between the two DNA sequences for a given fixation time is also derived, and indicates that, even when it takes a large number of generations for a mutant to reach fixation, this number is 33% less than at a random time. The computer simulation conducted suggests that the expected number of nucleotide differences between the two DNA sequences at the time when an advantageous mutant becomes fixed is essentially the same as that of neutral mutant if the fixation time is the same. The effect of recombination on the amount of DNA polymorphism was also investigated by using computer simulation.     

Population Bottlenecks and Nonequilibrium Models in Population Genetics. II. Number of Alleles in a Small Population That Was Formed by a Recent Bottleneck

A model is presented in which a large population in mutation/drift equilibrium undergoes a severe restriction in size and subsequently remains at the small size. The rate of loss of genetic variability has been studied. Allelic loss occurs more rapidly than loss of genic heterozygosity. Rare alleles are lost especially rapidly. The result is a transient deficiency in the total number of alleles observed in samples taken from the reduced population when compared with the number expected in a sample from a steady-state population having the same observed heterozygosity. Alternatively, the population can be considered to possess excess gene diversity if the number of alleles is used as the statistical estimator of mutation rate. The deficit in allele number arises principally from a lack of those alleles that are expected to appear only once or twice in the sample. The magnitude of the allelic deficiency is less, however, than the excess that an earlier study predicted to follow a rapid population expansion. This suggests that populations that have undergone a single bottleneck event, followed by rapid population growth, should have an apparent excess number of alleles, given the observed level of genic heterozygosity and provided that the bottleneck has not occurred very recently. Conversely, such populations will be deficient for observed heterozygosity if allele number is used as the sufficient statistic for the estimation of 4Nev. Populations that have undergone very recent restrictions in size should show the opposite tendencies.     

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.     

Unusual mutation clusters provide insight into class I gene conversion mechanisms.

Genetic diversity among the K and D alleles of the mouse major histocompatibility complex is generated by gene conversion among members of the class I multigene family. The majority of known class I mutants contain clusters of nucleotide changes that can be traced to linked family members. However, the details of the gene conversion mechanism are not known. The bm3 and bm23 mutations represent exceptions to the usual pattern and provide insight into intermediates generated during the gene conversion process. Both of these variants contain clusters of five nucleotide substitutions, but they differ from the classic conversion mutants in the important respect that no donor gene for either mutation could be identified in the parental genome. Nevertheless, both mutation clusters are composed of individual mutations that do exist within the parent. Therefore, they are not random and appear to be templated. Significantly, the bm3 and bm23 mutation clusters are divided into overlapping regions that match class I genes which have functioned as donor genes in other characterized gene conversion events. The unusual structure of the mutation clusters indicates an underlying gene conversion mechanism that can generate mutation clusters as a result of the interaction of three genes in a single genetic event. The unusual mutation clusters are consistent with a hypothetical gene conversion model involving extrachromosomal intermediates.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

On the Genealogy of a Rare Allele

The gene genealogy is derived for a rare allele that is descended from a mutant ancestor that arose at a fixed time in the past. Following Thompson (1976,Amer. J. Human Genet.28, 442–452), the fractional linear branching process is used as a model of the demography of a rare allele. The model does not require the total population size to be constant or the mutant class to be neutral; so long as individuals in the class are selectively equivalent, the class as a whole may have a selective advantage, or disadvantage, relative to other alleles in the population. An exact result is given for the joint probability distribution of the coalescence times among a sample of alleles descended from the mutant. A method is described for rapidly simulating these coalescence times. The relationship between the genealogical structure of a discrete generation branching process and a continuous generation birth–death process is elucidated. The theory may be applied to the problem of estimating the ages of rare nonrecurrent mutations.     

On the genealogy of a sample of neutral rare alleles

This paper concerns the genealogical structure of a sample of chromosomes sharing a neutral rare allele. We suppose that the mutation giving rise to the allele has only happened once in the history of the entire population, and that the allele is of known frequency q in the population. Within a coalescent framework C. Wiuf and P. Donnelly (1999, Theor. Popul. Biol. 56, 183-201) derived an exact analysis of the conditional genealogy but it is inconvenient for applications. Here, we develop an approximation to the exact distribution of the conditional genealogy, including an approximation to the distribution of the time at which the mutation arose. The approximations are accurate for frequencies q<5-10%. In addition, a simple and fast simulation scheme is constructed. We consider a demography parameterized by a d-dimensional vector alpha=(alpha(1), em leader, alpha(d)). It is shown that the conditional genealogy and the age of the mutation have distributions that depend on a=qalpha and q only, and that the effect of q is a linear scaling of times in the genealogy; if q is doubled, the lengths of all branches in the genealogy are doubled. The theory is exemplified in two different demographies of some interest in the study of human evolution: (1) a population of constant size and (2) a population of exponentially decreasing size (going backward in time).     

Times on trees, and the age of an allele

In this paper we consider the genealogy of a random sample of n chromosomes from a panmictic population which has evolved with constant size N over many generations. We address two related problems. First we describe how genealogical information may be usefully partitioned into information on the events (mutations and coalescences) which occur in the genealogy, and the times between these events. We show that the distribution of the times given information on the events is particularly simple and describe how this can considerably reduce the computational burden when performing inference for these times. Second we investigate the effect on the genealogy of conditioning on a single mutation having occurred during the ancestry of the sample. In particular we use results from the first part of the paper to derive explicit formulae for the density of the age of a mutant allele, conditional on its frequency in either a sample or the population.     

Phylogeography of Hemibarbus labeo (Cyprinidae): secondary contact of ancient lineages of mtDNA

Lin, C.-J., Lin, H.-D., Wang, J.-P., Chao, S.-C. & Chiang, T.-Y. (2007). Phylogeography of Hemibarbus labeo (Cyprinidae): secondary contact of ancient lineages of mtDNA. —Zoologica Scripta, 39, 23–35. Nucleotide sequences of the D-loop control region of mtDNA were used to assess the genetic structure and phylogeography of Hemibarbus labeo in Mainland China and Taiwan. A hierarchical analysis of molecular variance of populations in 11 major streams from three geographical regions revealed significant structuring among populations and geographical regions. High levels of nucleotide diversity (π = 1.88%) and haplotype diversity (h = 96 ± 0.009%) suggest a large effective population size. A maximum likelihood tree based on mtDNA variation identified two ancient mtDNA lineages, which split approximately 3.39 million years ago. Overlapping distribution of the major lineages displayed low correspondence with geographical regions and reflects a scenario of secondary mergence after long isolation. Gene genealogy further revealed a unidirectional migration. Nevertheless, there existed a phylogeographical structure that mostly agreed with a biogeographical hypothesis. That is, within each lineage, a close phylogeny between populations of the River-Campagna and East-Pacific regions was supported by the mtDNA gene genealogy, although monophyly of each geographical region was not supported. The degree of genetic differentiation was correlated with geographical distances between populations, displaying a pattern of ‘isolation by distance’. Gene genealogy of mtDNA revealed that Yangtzejiang population may act as a divergence centre of H. labeo. In addition, Taiwan population was colonized via a recent a founder event, likely from population Yangtzejiang River about 131 000 years before present. Low haplotype number and genetic variability also suggested possible bottleneck events in the Rongjiang and Dazhangjiang populations.