Reversibility and the age of an allele II. Two-allele models,with selection and mutation

A Markov process with absorbing boundaries may be made recurrent by returning the process to the interior whenever a boundary is reached. The age of such a process may be defined as the length of time since the last return event. Examples drawn from two-allele genetic models are discussed, in which reversibility of the return process means that the age of an allele, whose present frequency in the population is known, has the same probability distribution as its future extinction time. Some discrete models are not reversible, yet if approximated by diffusion processes, the (approximate) age distribution is the same as the future extinction time distribution. Various results in the literature are unified by this viewpoint.     

Extinction time and age of an allele in a large finite population

For a single locus with two alleles we study the expected extinction and fixation times of the alleles under the influence of selection and genetic drift. Using a diffusion model we derive asymptotic approximations for these expected exit times for large populations. We consider the case where the fitness of the heterozygote is in between the fitnesses of the homozygotes (incomplete dominance). The asymptotic analysis not only yields new quantitative results but also reveals interesting features that remain hidden in the exact solution. Some of the outcomes are extensions of results known in the literature. The asymptotic approximations also apply to the expected first arrival time of an allele at a specified frequency and to the expected age of an allele.     

The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele

The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to be polymorphic. This distribution is widely used in population genetic inferences, including statistical tests of neutrality in which a skew in the observed frequency spectrum across independent sites is taken as a signature of departure from neutral evolution. Theoretical aspects of the frequency spectrum have been well studied and several interesting results are available, but they are usually under the assumption that a site has undergone at most one mutation event in the history of the sample. Here, we extend previous theoretical results by allowing for at most two mutation events per site, under a general finite allele model in which the mutation rate is independent of current allelic state but the transition matrix is otherwise completely arbitrary. Our results apply to both nested and nonnested mutations. Only the former has been addressed previously, whereas here we show it is the latter that is more likely to be observed except for very small sample sizes. Further, for any mutation transition matrix, we obtain the joint sample frequency spectrum of the two mutant alleles at a triallelic site, and derive a closed-form formula for the expected age of the younger of the two mutations given their frequencies in the population. Several large-scale resequencing projects for various species are presently under way and the resulting data will include some triallelic polymorphisms. The theoretical results described in this paper should prove useful in population genomic analyses of such data.     

Reversibility and the age of an allele. I. Moran's infinitely many neutral alleles model

A population of constant size is subjected to mutation, such that each mutant is of a new allelic type. For the particular population model studied in this paper, the age of an allele, whose present frequency is known, is a random variable with distribution independent of the frequencies of other alleles. As a consequence of reversibility of the population process, the age of an allele, from the past to the present, has the same distribution as its time to extinction, from the present into the future. This verifies, and re-interprets, certain diffusion approximations found by Kimura and Ohta [Genetics 75, 199–212 (1973)] and Maruyama [Genet. Res. Cambridge 23, 137–143 (1974)].     

Directional positive selection on an allele of arbitrary dominance

Most models of positive directional selection assume codominance of the beneficial allele. We examine the importance of this assumption by implementing a coalescent model of positive directional selection with arbitrary dominance. We find that, for a given mean fixation time, a beneficial allele has a much weaker effect on diversity at linked neutral sites when the allele is recessive.     

Microspatial heterogeneity of allele frequencies at allozyme loci in the bivalveMytilus trossulus: Dependence on age and depth

Allozyme variability was investigated at 18 polymorphic loci in 9 samples of the bivalveMytilus trossulus (Gould, 1850) from Vostok Bay, Sea of Japan. Significant differences in allele frequencies at some loci were found between samples from different age cohorts and different depths. Genetic distances between samples were as great as (and often exceeded) those typically found between geographically separate populations in Peter the Great Bay. Some practical recommendations for experimental researchers are proposed.     

A Bayesian method for jointly estimating allele age and selection intensity.

The problem of jointly estimating the intensity of past selection affecting an allele and the allele's age is formulated in a Bayesian framework. The prior distribution of allele age given its frequency is obtained from existing population genetics theory. The prior distribution of selection intensity is assumed to reflect the fact that positive selection on a new mutant is more likely to be weak than strong. The general approach is illustrated by the development of an importance sampling method applicable to low-frequency alleles. This method can be used either when the haplotypes of closely linked marker loci are known or when the lengths of linked ancestral chromosomal segments can be inferred. The method is illustrated with an application to the A-allele of G6PD in Africa. Because changes in allele frequency and recombination are both intrinsically stochastic, there are limits to the accuracy achievable with any method.     

Leaf age and the timing of leaf abscission in two tropical dry forest trees

We used experimental defoliations to examine the effect of leaf age on the timing of leaf shedding in two tropical dry forest trees. Trees of the deciduous Bombacopsis quinata (bombacaceae, a.k.a. Pachira quinata) and the brevi-deciduous Astronium graveolens (anacardiaceae) were manually defoliated for three times during the rainy season. All trees started to produce a new crown of leaves 2 weeks after defoliation, and continued expanding leaves throughout the rainy season. At the transition to the dry season, the experimental groups consisted of trees with known differences in maximum leaf age. Defoliations resulted in declines in stem growth but did not affect the mineral content or water relations of the leaves subsequently produced. There was no effect of leaf age on the timing of leaf abscission in B. quinata. In A. graveolens, the initiation of leaf shedding followed in rank order, the maximum leaf age of the four treatments, but there was substantial coherence among treatments in the major period of leaf abscission such that trees completed leaf shedding at the same time. In the two species, leaf water potential (Ψ_L) and stomatal conducantce (g _S) declined with the onset of the dry season, reaching minimum values of –0.9 MPa in P. quinata and <–2.0 MPa in A. graveolens. Within each species, leaves of different age exhibited similar Ψ_L and g _S at the onset of drought, and then decreased at a similar rate as the dry season progressed. Overall, our study suggests that the environmental factors were more important than leaf age in controlling the timing of leaf shedding.     

Association between the APOE*4 allele and atherosclerosis is age dependent among Argentine males

Several studies have shown evidence of an association between the *4 allele of apolipoprotein E (APOE) and coronary heart disease (CHD) in different populations. We determined the APOE genotype and total cholesterol (TC), triglycerides (TG), and high-density lipoprotein cholesterol (HDLC) values in 189 patients with angiographically evaluated atherosclerosis. The APOE*4 allele was found to be statistically significantly more frequent (odds ratio, 1.93; 95% confidence interval, 1.12-3.32) among male patients than in a randomly chosen population-based sample. No significant difference was found when female patients were compared to the general population. The APOE*4 allele was found primarily among young (30-45-year-old) male patients (p < 0.04). Despite the ascending linear tendency of the mean TC values for genotypes APOE*2/*3, APOE*3/*3, and APOE*3/ *4 reported in our case population, no differences were observed among our patients. We conclude that the APOE*4 allele is associated with an increased risk for atherosclerotic vascular disease, that this association has an age-dependent effect, and that it acts as a genetic factor that increases susceptibility to developing the disease in young to middle-aged male adults in our population.     

A method for detecting recent selection in the human genome from allele age estimates

Mutations that have recently increased in frequency by positive natural selection are an important component of naturally occurring variation that affects fitness. To identify such variants, we developed a method to test for recent selection by estimating the age of an allele from the extent of haplotype sharing at linked sites. Neutral coalescent simulations are then used to determine the likelihood of this age given the allele's observed frequency. We applied this method to a common disease allele, the hemochromatosis-associated HFE C282Y mutation. Our results allow us to reject neutral models incorporating plausible human demographic histories for HFE C282Y and one other young but common allele, indicating positive selection at HFE or a linked locus. This method will be useful for scanning the human genome for alleles under selection using the haplotype map now being constructed.     

Seedling establishment of vascular epiphytes on isolated and enclosed forest trees in an Andean landscape, Ecuador

The impact of human disturbance on colonisation dynamics of vascular epiphytes is poorly known. We studied abundance, diversity and floristic composition of epiphyte seedling establishing on isolated and adjacent forest trees in a tropical montane landscape. All vascular epiphytes were removed from plots on the trunk bases of Piptocoma discolor. Newly established epiphyte seedlings were recorded after 2 years, and their survival after another year. Seedling density, total richness at family and genus level, and the number of families and genera per plot were significantly reduced on isolated trees relative to forest trees. Seedling assemblages on trunks of forest trees were dominated by hygrophytic understorey ferns, those on isolated trees by xerotolerant canopy taxa. Colonisation probability on isolated trees was significantly higher for plots closer to forest but not for plots with greater canopy or bryophyte cover. Seedling mortality on isolated trees was significantly higher for mesophytic than for xerotolerant taxa. Our results show that altered recruitment can explain the long-term impoverishment of post-juvenile epiphyte assemblages on isolated remnant trees. We attribute these changes to a combination of dispersal constraints and the harsher microclimate documented by measurements of temperature and humidity. Although isolated trees in anthropogenic landscapes are considered key structures for the maintenance of forest biodiversity in many aspects, our results show that their value for the conservation of epiphytes can be limited. We suggest that abiotic seedling requirements will increasingly constitute a bottleneck for the persistence of vascular epiphytes in the face of ongoing habitat alteration and atmospheric warming.     

Gene trees, species trees, and morphology converge on a similar phylogeny of living gars (Actinopterygii: Holostei: Lepisosteidae), an ancient clade of ray-finned fishes

Extant gars represent the remaining members of a formerly diverse assemblage of ancient ray-finned fishes and have been the subject of multiple phylogenetic analyses using morphological data. Here, we present the first hypothesis of phylogenetic relationships among living gar species based on molecular data, through the examination of gene tree heterogeneity and coalescent species tree analyses of a portion of one mitochondrial (COI) and seven nuclear (ENC1, myh6, plagl2, S7 ribosomal protein intron 1, sreb2, tbr1, and zic1) genes. Individual gene trees displayed varying degrees of resolution with regards to species-level relationships, and the gene trees inferred from COI and the S7 intron were the only two that were completely resolved. Coalescent species tree analyses of nuclear genes resulted in a well-resolved and strongly supported phylogenetic tree of living gar species, for which Bayesian posterior node support was further improved by the inclusion of the mitochondrial gene. Species-level relationships among gars inferred from our molecular data set were highly congruent with previously published morphological phylogenies, with the exception of the placement of two species, Lepisosteus osseus and L. platostomus. Re-examination of the character coding used by previous authors provided partial resolution of this topological discordance, resulting in broad concordance in the phylogenies inferred from individual genes, the coalescent species tree analysis, and morphology. The completely resolved phylogeny inferred from the molecular data set with strong Bayesian posterior support at all nodes provided insights into the potential for introgressive hybridization and patterns of allopatric speciation in the evolutionary history of living gars, as well as a solid foundation for future examinations of functional diversification and evolutionary stasis in a "living fossil" lineage.     

Characterization of an spm-controlled bronze-mutable allele in maize

The association of a receptor (Rs) of the Spm system with a Bz-1 allele has created a two-element Spm-controlled bz-mutable allele (bz-m13) of maize (Zea mays L.). In the absence of Spm, one copy of bz-m13 (bz/bz/bz-m13 ) conditions full anthocyanin production in the aleurone layer of the seed. In the presence of this Spm, bz-m13 produces a unique, coarsely variegated seed phenotype and has a high rate (50–83%) of gametic change to stable bz' or Bz' derivatives. Even one copy of a Bz' derivative allele conditions full anthocyanin production in the aleurone, but the enzyme (UFGT) level of the progenitor Bz-1 allele is not restored in most Bz' derivatives.