Estimating recombination rates from population genetic data.

We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationally intensive statistical procedure (importance sampling) to calculate the likelihood under a coalescent-based model. Detailed comparisons of the new algorithm with two existing methods (the importance sampling method of Griffiths and Marjoram and the MCMC method of Kuhner and colleagues) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum-likelihood estimator of the recombination rate and its robustness to misspecification of the demographic model.     

Estimating recombination rates from population-genetic data

Obtaining an accurate measure of how recombination rates vary across the genome has implications for understanding the molecular basis of recombination, its evolutionary significance and the distribution of linkage disequilibrium in natural populations. Although measuring the recombination rate is experimentally challenging, good estimates can be obtained by applying population-genetic methods to DNA sequences taken from natural populations. Statistical methods are now providing insights into the nature and scale of variation in the recombination rate, particularly in humans. Such knowledge will become increasingly important owing to the growing use of population-genetic methods in biomedical research.     

Estimating hypermutation rates from clonal tree data

To understand the mechanisms underlying the varying patterns of mutations that occur during immune and autoimmune responses, estimates of the somatic hypermutation rate are critical. However, despite its significance, precise estimates of the mutation rate do not currently exist. Microdissection studies of mutating B cell clones provide an opportunity to measure this rate more accurately than previously possible. Each microdissection provides a number of clonally related sequences that, through the analysis of shared mutations, can be genealogically related to each other. The shape of these clonal trees is influenced by many processes, including the hypermutation rate. We have developed two different methods to estimate the mutation rate based on these data. These methods are applied to two sets of experimental data, one from an autoimmune response and one from the antihapten response to (4-hydroxy-3-nitrophenyl)acetyl (NP). Comparable mutation rates are estimated for both responses, 0.7-0.9 x 10(-3) and 0.9-1.1 x 10(-3) bp(-1) division(-1) for the autoimmune and NP responses, respectively. In addition to comparing the results of the two procedures, we investigate the effect on our estimate of assumptions, such as the fraction of lethal mutations.     

Estimating effective population size and migration rates from genetic samples over space and time

In the past, moment and likelihood methods have been developed to estimate the effective population size (N(e)) on the basis of the observed changes of marker allele frequencies over time, and these have been applied to a large variety of species and populations. Such methods invariably make the critical assumption of a single isolated population receiving no immigrants over the study interval. For most populations in the real world, however, migration is not negligible and can substantially bias estimates of N(e) if it is not accounted for. Here we extend previous moment and maximum-likelihood methods to allow the joint estimation of N(e) and migration rate (m) using genetic samples over space and time. It is shown that, compared to genetic drift acting alone, migration results in changes in allele frequency that are greater in the short term and smaller in the long term, leading to under- and overestimation of N(e), respectively, if it is ignored. Extensive simulations are run to evaluate the newly developed moment and likelihood methods, which yield generally satisfactory estimates of both N(e) and m for populations with widely different effective sizes and migration rates and patterns, given a reasonably large sample size and number of markers.     

Estimating population growth rates from stochastic Leslie matrices

Stochastic versions of exponential growth models predict that even when r or λ values calculated from mean vital statistics indicate exponential growth, most of the individual populations may become extinct. Several recent papers have considered this problem and some misunderstanding has arisen due to the difference between mathematical expectation of population size and most likely course of population growth. We replicated Boyce's (1977, 1979) simulations of population growth with age structure and a single randomly varying vital statistic, and reconciled some of these differences. Mean number can be projected using the dominant eigenvalue of the mean Leslie matrix, but the modal number may be considerably lower. We compared several measures of the rate of growth of the geometric mean or median of numbers and conclude that Tuljapurkar's α is an acceptable measure.     

Estimating growth and mortality rates from size data

Summary A method is presented for estimating rates of individual growth and population mortality utilizing average individual size at two times during a year. The model assumes a constant rate of mortality, Brody-Bertalanffy growth, a stationary age distribution, and recruitment confined to one month each year. A hypothetical example is presented to show the interrelationships of the growth and mortality constants, size at recruitment, asymptotic size and average individual size. Three examples are presented using data from the literature: Flathead sole (Hippoglossoides elassodon), a sea urchin(Echinus esculentus), and the crown-of-thorns starfish(Acanthaster planci). The method appears to be a means of obtaining reasonable approximations of growth and mortality rates for a variety of organisms.     

Fidelity of meiotic gene conversion in yeast

Summary Gene conversion was studied in a sample of 3869 unselected meiotic tetrads obtained from three diploids, respectively; heterozygous for a single ochre mutant, heteroallelic for a pair of ochre alleles, and heterozygous for an ochre specific suppressor. Although the genetic system were sufficiently sensitive to detect single base changes at the mutant codon level, none were found among 36 conversions (1+:3m) of the ochre mutants and 153 conversions (3S:1+) of the suppressor locus. These findings lead to the conclusion that the informational transfer in gene conversion occurred with complete fidelity. Gene conversion conserved and did not generate new genetic information. The error level of conversion was estimated as less than 10^-2/N.P.     

Estimating selfing rates from reconstructed pedigrees using multilocus genotype data

Several methods have been developed to estimate the selfing rate of a population from a sample of individuals genotyped for several marker loci. These methods can be based on homozygosity excess (or inbreeding), identity disequilibrium, progeny array (PA) segregation or population assignment incorporating partial selfing. Progeny array-based method is generally the best because it is not subject to some assumptions made by other methods (such as lack of misgenotyping, absence of biparental inbreeding and presence of inbreeding equilibrium), and it can reveal other facets of a mixed-mating system such as patterns of shared paternity. However, in practice, it is often difficult to obtain PAs, especially for animal species. In this study, we propose a method to reconstruct the pedigree of a sample of individuals taken from a monoecious diploid population practicing mixed mating, using multilocus genotypic data. Selfing and outcrossing events are then detected when an individual derives from identical parents and from two distinct parents, respectively. Selfing rate is estimated by the proportion of selfed offspring in the reconstructed pedigree of a sample of individuals. The method enjoys many advantages of the PA method, but without the need of a priori family structure, although such information, if available, can be utilized to improve the inference. Furthermore, the new method accommodates genotyping errors, estimates allele frequencies jointly and is robust to the presence of biparental inbreeding and inbreeding disequilibrium. Both simulated and empirical data were analysed by the new and previous methods to compare their statistical properties and accuracies.     

Estimating quantitative genetic parameters using sibships reconstructed from marker data

Previous techniques for estimating quantitative genetic parameters, such as heritability in populations where exact relationships are unknown but are instead inferred from marker genotypes, have used data from individuals on a pairwise level only. At this level, families are weighted according to the number of pairs within which each family appears, hence by size rather than information content, and information from multiple relationships is lost. Estimates of parameters are therefore not the most efficient achievable. Here, Markov chain Monte Carlo techniques have been used to partition the population into complete sibships, including, if known, prior knowledge of the distribution of family sizes. These pedigrees have then been used with restricted maximum likelihood under an animal model to estimate quantitative genetic parameters. Simulations to compare the properties of parameter estimates with those of existing techniques indicate that the use of sibship reconstruction is superior to earlier methods, having lower mean square errors and showing nonsignificant downward bias. In addition, sibship reconstruction allows the estimation of population allele frequencies that account for the relationships within the sample, so prior knowledge of allele frequencies need not be assumed. Extensions to these techniques allow reconstruction of half sibships when some or all of the maternal genotypes are known.     

Maximum likelihood estimation of recombination rates from population data

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.     

Estimating developmental and mortality rates and stage recruitment from insect stage-frequency data

A model for the analysis of insect stage-frequency data is developed which includes stage-specific variable developmental periods and stage-specific daily survival rates. The model can predict the development of an insect population through its developmental stages and consequently may form the basis for a simulation model of the population.     

Estimating the strength of selective sweeps from deep population diversity data

Selective sweeps are typically associated with a local reduction of genetic diversity around the adaptive site. However, selective sweeps can also quickly carry neutral mutations to observable population frequencies if they arise early in a sweep and hitchhike with the adaptive allele. We show that the interplay between mutation and exponential amplification through hitchhiking results in a characteristic frequency spectrum of the resulting novel haplotype variation that depends only on the ratio of the mutation rate and the selection coefficient of the sweep. On the basis of this result, we develop an estimator for the selection coefficient driving a sweep. Since this estimator utilizes the novel variation arising from mutations during a sweep, it does not rely on preexisting variation and can also be applied to loci that lack recombination. Compared with standard approaches that infer selection coefficients from the size of dips in genetic diversity around the adaptive site, our estimator requires much shorter sequences but sampled at high population depth to capture low-frequency variants; given such data, it consistently outperforms standard approaches. We investigate analytically and numerically how the accuracy of our estimator is affected by the decay of the sweep pattern over time as a consequence of random genetic drift and discuss potential effects of recombination, soft sweeps, and demography. As an example for its use, we apply our estimator to deep sequencing data from human immunodeficiency virus populations.     

Estimating heritabilities and genetic correlations: comparing the 'animal model' with parent-offspring regression using data from a natural population

Quantitative genetic parameters are nowadays more frequently estimated with restricted maximum likelihood using the 'animal model' than with traditional methods such as parent-offspring regressions. These methods have however rarely been evaluated using equivalent data sets. We compare heritabilities and genetic correlations from animal model and parent-offspring analyses, respectively, using data on eight morphological traits in the great reed warbler (Acrocephalus arundinaceus). Animal models were run using either mean trait values or individual repeated measurements to be able to separate between effects of including more extended pedigree information and effects of replicated sampling from the same individuals. We show that the inclusion of more pedigree information by the use of mean traits animal models had limited effect on the standard error and magnitude of heritabilities. In contrast, the use of repeated measures animal model generally had a positive effect on the sampling accuracy and resulted in lower heritabilities; the latter due to lower additive variance and higher phenotypic variance. For most trait combinations, both animal model methods gave genetic correlations that were lower than the parent-offspring estimates, whereas the standard errors were lower only for the mean traits animal model. We conclude that differences in heritabilities between the animal model and parent-offspring regressions were mostly due to the inclusion of individual replicates to the animal model rather than the inclusion of more extended pedigree information. Genetic correlations were, on the other hand, primarily affected by the inclusion of more pedigree information. This study is to our knowledge the most comprehensive empirical evaluation of the performance of the animal model in relation to parent-offspring regressions in a wild population. Our conclusions should be valuable for reconciliation of data obtained in earlier studies as well as for future meta-analyses utilizing estimates from both traditional methods and the animal model.     

The relative importance of meiotic gene conversion,selection and mutation pressure,in population genetics and evolution

Disparity in the direction of meiotic gene conversion can change allele frequencies, favouring one allele of a pair in heterozygotes. Equilibrium allele frequencies for large diploid populations are examined by means of equations relating them to meiotic gene conversion, selection and mutation for deleterious recessives, deleterious dominants, and deleterious alleles with no dominance. Using observed conversion parameters from various fungi,Zea mays andDrosophila, it is shown that conversion is generally much more important than mutation pressure and may be of greater or lesser importance than selection, depending on dominance and the strength of selection and conversion forces for the alleles involved.     

Estimating death rates from transect counts

Abstract.

• 1 The time course of abundance of adult insects emerging in discrete generations is modelled, assuming the absence of net migration and a constant death rate. The time till emergence is assumed to be logistically distributed.
• 2 The qualitative features of the model depend on one dimensionless parameter only, namely the product of the death rate and a dispersion measure for the symmetric emergence distribution.
• 3 The model is fitted to data on the abundance of five butterfly species. The tit is excellent; moreover, the estimated death rates are well within the range given in the literature (mostly 0.1–0.2 day^-1). Death rates are generally obtained by mark-recapture methods. The present model gives the opportunity to evaluate some assumptions of these methods.

     

Estimating diversification rates from phylogenetic information

Patterns of species richness reflect the balance between speciation and extinction over the evolutionary history of life. These processes are influenced by the size and geographical complexity of regions, conditions of the environment, and attributes of individuals and species. Diversity within clades also depends on age and thus the time available for accumulating species. Estimating rates of diversification is key to understanding how these factors have shaped patterns of species richness. Several approaches to calculating both relative and absolute rates of speciation and extinction within clades are based on phylogenetic reconstructions of evolutionary relationships. As the size and quality of phylogenies increases, these approaches will find broader application. However, phylogeny reconstruction fosters a perceptual bias of continual increase in species richness, and the analysis of primarily large clades produces a data selection bias. Recognizing these biases will encourage the development of more realistic models of diversification and the regulation of species richness.     

Estimation of effective population sizes from data on genetic markers

The effective population size (Ne) is an important parameter in ecology, evolutionary biology and conservation biology. It is, however, notoriously difficult to estimate, mainly because of the highly stochastic nature of the processes of inbreeding and genetic drift for which Ne is usually defined and measured, and because of the many factors (such as time and spatial scales, systematic forces) confounding such processes. Many methods have been developed in the past three decades to estimate the current, past and ancient effective population sizes using different information extracted from some genetic markers in a sample of individuals. This paper reviews the methodologies proposed for estimating Ne from genetic data using information on heterozygosity excess, linkage disequilibrium, temporal changes in allele frequency, and pattern and amount of genetic variation within and between populations. For each methodology, I describe mainly the logic and genetic model on which it is based, the data required and information used, the interpretation of the estimate obtained, some results from applications to simulated or empirical datasets and future developments that are needed.