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.     

Demystifying the age of old olive trees

Iconic to the Mediterranean landscape, the age of monumental olive trees with large trunks and unique silhouettes is often considered several centuries to millennia. Here we combine tree-ring and radiocarbon dating to show that most monumental olive trees may have maximum ages between 300 and 500 years. Our example helps disentangling the tree size-longevity conundrum in a major Mediterranean cultivated tree species and important cultural heritage.     

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)].     

Investigating the relationship between climate,stand age,and temporal trends in masting behavior of European forest trees

Masting—temporally variable seed production with high spatial synchrony—is a pervasive strategy in wind‐pollinated trees that is hypothesized to be vulnerable to climate change due to its correlation with variability in abiotic conditions. Recent work suggests that aging may also have strong effects on seed production patterns of trees, but this potential confounding factor has not been considered in previous times series analysis of climate change effects. Using a 54 year dataset for seven dominant species in 17 forests across Poland, we used the proportion of seed‐producing trees (PST) to contrast the predictions of the climate change and aging hypotheses in Abies alba, Fagus sylvatica, Larix decidua, Picea abies, Pinus sylvestris, Quercus petraea, and Quercus robur. Our results show that in all species, PST increased over time and that this change correlated most strongly with stand age, while the standardized precipitation–evapotranspiration index, a measure of drought, contributed to temporal trends in PST of F. sylvatica and Q. robur. Temporal variability of PST also increased over time in all species except P. sylvestris, while trends in temporal autocorrelation and among‐stand synchrony reflect species‐specific masting strategies. Our results suggest a pivotal role of plant ontogeny in driving not only the extent but also variability and synchrony of reproduction in temperate forest trees. In a time of increasing forest regrowth in Europe, we therefore call for increased attention to demographic effects such as aging on plant reproductive behavior, particularly in studies examining global change effects using long‐term time series data.     

Tissue age,orchard location and disease management influence the composition of fungal and bacterial communities present on the bark of apple trees

Plants host microbial communities that can be affected by environmental conditions and agronomic practices. Despite the role of bark as a reservoir of plant pathogens and beneficial microorganisms, no information is available on the effects of disease management on the taxonomic composition of the bark-associated communities of apple trees. We assessed the impact of disease management strategies on fungal and bacterial communities on the bark of a scab-resistant apple cultivar in two orchard locations and for two consecutive seasons. The amplicon sequencing revealed that bark age and orchard location strongly affected fungal and bacterial diversity. Microbiota dissimilarity between orchards evolved during the growing season and showed specific temporal series for fungal and bacterial populations in old and young bark. Disease management did not induce global changes in the microbial populations across locations and seasons, but specifically affected the abundance of some taxa according to bark age, orchard location and sampling time. Therefore, the disease management applied to scab-resistant cultivars, which is based on a limited use of fungicides, partially changed the taxonomic composition of bark-associated fungal and bacterial communities, suggesting the need for a more accurate risk assessment regarding possible pathogen outbreaks.     

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.     

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.     

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.     

Comparisons of arthropod assemblages on an invasive and native trees: abundance,diversity and damage

The success of exotic plants may be due to lower herbivore loads than those on native plants (Enemies Release Hypothesis). Predictions of this hypothesis include lower herbivore abundances, diversity, and damage on introduced plant species compared to native ones. Greater density or diversity of predators and parasitoids on exotic versus native plants may also reduce regulation of exotic plants by herbivores. To test these predictions, we measured arthropod abundance, arthropod diversity, and foliar damage on invasive Chinese tallow tree (Triadica sebifera) and three native tree species: silver maple (Acer saccharinum), sycamore (Platanus occidentalis), and sweetgum (Liquidambar styraciflua). Arthropod samples were collected with canopy sweep nets from six 20 year old monoculture plots of each species at a southeast Texas site. A total of 2,700 individuals and 285 species of arthropods were caught. Overall, the species richness and abundance of arthropods on tallow tree were similar to the natives. But, ordination (NMS) showed community composition differed on tallow tree compared to all three native trees. It supported an arthropod community that had relatively lower herbivore abundance but relatively more predator species compared to the native species examined. Leaves were collected to determine damage. Tallow tree experienced less mining damage than native trees. The results of this study supported the Enemies Release Hypothesis predictions that tallow tree would have low herbivore loads which may contribute to its invasive success. Moreover, a shift in the arthropod community to fewer herbivores without a reduction in predators may further limit regulation of this exotic species by herbivores in its introduced range.     

Microsatellite allele frequencies in humans and chimpanzees, with implications for constraints on allele size

The distributions of allele sizes at eight simple-sequence repeat (SSR) or microsatellite loci in chimpanzees are found and compared with the distributions previously obtained from several human populations. At several loci, the differences in average allele size between chimpanzees and humans are sufficiently small that there might be a constraint on the evolution of average allele size. Furthermore, a model that allows for a bias in the mutation process shows that for some loci a weak bias can account for the observations. Several alleles at one of the loci (Mfd 59) were sequenced. Differences between alleles of different lengths were found to be more complex than previously assumed. An 8-base-pair deletion was present in the nonvariable region of the chimpanzee locus. This locus contains a previously unrecognized repeated region, which is imperfect in humans and perfect in chimpanzees. The apparently greater opportunity for mutation conferred by the two perfect repeat regions in chimpanzees is reflected in the higher variance in repeat number at Mfd 59 in chimpanzees than in humans. These data indicate that interspecific differences in allele length are not always attributable to simple changes in the number of repeats.      

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.