Private alleles in a partially isolated population. II. Distribution of persistence time and probability of emigration

Two diffusion limits were derived from a discrete Wright-Fisher model of migration, mutation, and selection with an arbitrary degree of dominance. Instantaneous killing of the process due to emigration of a mutant leads to one of two diffusion processes with a killing term. One (weak gene flow) is the boundary case of the other (strong gene flow), which can cover a wide range of gene flow. The diffusion process subject to strong gene flow is similar to that studied by S. Karlin and S. Tavaré (1983, SIAM J. Appl. Math. 43, 31-41). The spectral decomposition of the transition probability density of "private" allele frequencies is presented in the case of strong gene flow. The fate of mutant in a deme is discussed in terms of the probabilities of survival and emigration.     

SEARCHING FOR EVOLUTIONARY PATTERNS IN THE SHAPE OF A PHYLOGENETIC TREE

If all species in a clade are equally likely to speciate or become extinct, then highly symmetric and highly asymmetric phylogenetic trees are unlikely to result. Variation between species in speciation and extinction rates can cause excessive asymmetry. We developed six non-parametric statistical tests that test for nonrandom patterns of branching in any bifurcating tree. The tests are demonstrated by applying them to two published phylogenies for genera of beetles. Comparison of the power of the six statistics under a simple model of biased speciation suggests which of them may be most useful for detecting nonrandom tree shapes.     

PEAK SHIFTS PRODUCED BY CORRELATED RESPONSE TO SELECTION

Traits may evolve both as a consequence of direct selection and also as a correlated response to selection on other traits. While correlated response may be important for both the production of evolutionary novelty and in the build-up of complex characters, its potential role in peak shifts has been neglected empirically and theoretically. We use a quantitative genetic model to investigate the conditions under which a character, Y, which has two alternative optima, can be dragged from one optimum to the other as a correlated response to selection on a second character, X. High genetic correlations between the two characters make the transition, or peak shift, easier, as does weak selection tending to restore Y to the optimum from which it is being dragged. When selection on Y is very weak, the conditions for a peak shift depend only on the location of the new optimum for X and are independent of the strength of selection moving it there. Thus, if the “adaptive valley” for Y is very shallow, little reduction in mean fitness is needed to produce a shift. If the selection acts strongly to keep Y at its current optimum, very intense directional selection on X, associated with a dramatic drop in mean fitness, is required for a peak shift. When strong selection is required, the conditions for peak shifts driven by correlated response might occur rarely, but still with sufficient frequency on a geological timescale to be evolutionarily important.     

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.      

F(st) in a Hierarchical Island Model

It is shown that in a hierarchical island model, in which demes within a neighborhood exchange migrants at a much higher rate than do demes in different neighborhoods, hierarchical F statistics introduced by S. Wright can indicate the extent of gene flow within and between neighborhoods. At equilibrium, the within-neighborhood inbreeding coefficient, FSN, is approximately 1/(1 + 4Nm1) where N is the deme size and m1 is the migration rate among demes in the same neighborhood. The between-neighborhood inbreeding coefficient, FNT, is approximately 1/(1 + 4Ndm2) where d is the number of demes in a neighborhood and m2 is the migration rate among demes in different neighborhoods.     

Likelihood analysis of disequilibrium mapping, and related problems.

In this paper a theory is developed that provides the sampling distribution of alleles at a diallelic marker locus closely linked to a low-frequency allele that arose as a single mutant. The sampling distribution provides a basis for maximum-likelihood estimation of either the recombination rate, the mutation rate, or the age of the allele, provided that the two other parameters are known. This theory is applied to (1) the data of Hästbacka et al., to estimate the recombination rate between a locus associated with diastrophic dysplasia and a linked RFLP marker; (2) the data of Risch et al., to estimate the age of a presumptive allele causing idiopathic distortion dystonia in Ashkenazi jews; and (3) the data of Tishkoff et al., to estimate the date at which, at the CD4 locus, non-African lineages diverged from African lineages. We conclude that the extent of linkage disequilibrium can lead to relatively accurate estimates of recombination and mutation rates and that those estimates are not very sensitive to parameters, such as the population age, whose values are not known with certainty. In contrast, we also conclude that, in many cases, linkage disequilibrium may not lead to useful estimates of allele age, because of the relatively large degree of uncertainly in those estimates.     

Gene Flow and Selection in a Two-Locus System

A model of gene flow and selection in two linked loci is analyzed. The problems considered are the effects of linkage on the clines in frequencies at the two loci and the role of gene flow in producing linkage disequilibrium between the loci. Also, the possible significance of linkage as a mechanism for permitting a population of "track" spatial changes in the environment is considered. The results are that when the recombination fraction between the loci is of the same order of magnitude as the selection coefficients or smaller, then linkage is important in determining the gene frequencies and a substantial amount of linkage disequilibrium is present in the cline. Depending on the spatial pattern of selection on the two loci, linkage can either decrease or increase a population's response to local selection.     

On Treating the Chromosome as the Unit of Selection

A simple method is presented for approximating the behavior of a multiple genetic system under the action of selection and linkage. The effects of genetic drift and mutation are left out. It is found that the results are close to those obtained from a computer simulation of the same problem by Franklin and Lewontin (1970). It is possible to describe the system in terms of a correlation length on the chromosome which measures the degree to which the different parts are bound by linkage. There is also a brief discussion about the higher order correlation coefficients as a measure of the interaction effects.     

Trapline foraging by bumble bees: II. Definition and detection from sequence data

Trapline foraging—repeated sequential visits to a seriesof feeding locations—presents interesting problems seldomtreated in foraging models. Work on traplining is hampered bythe lack of statistical, operational approaches for detectingits existence and measuring its strength. We propose severalstatistical procedures, illustrating them with records of interplantflight sequences by bumble bees visiting penstemon flowers.An asymmetry test detects deviations from binomial expectationin the directionality of visits between pairs of plants. Severaltests compare data from one bee to another frequencies of visitsto plants and frequencies of departures to particular destinationsare compared using contingency tables; similarities of repeatedsequences within bees are compared to those between bees bymeans of sequence alignment and Mantel tests. We also comparedobserved movement patterns to those generated by null modelsdesigned to represent realistic foraging by non-traplining bees,examining: temporal patterns of the bee's spatial displacementfrom its starting point using spectral analysis; the varianceof return times to particular plants; and the sequence alignmentof repeated cycles within sequences. We discuss the differentindications and the relative strengths of these approaches     

Estimating the age of alleles by use of intraallelic variability.

A method is presented for estimating the age of an allele by use of its frequency and the extent of variation among different copies. The method uses the joint distribution of the number of copies in a population sample and the coalescence times of the intraallelic gene genealogy conditioned on the number of copies. The linear birth-death process is used to approximate the dynamics of a rare allele in a finite population. A maximum-likelihood estimate of the age of the allele is obtained by Monte Carlo integration over the coalescence times. The method is applied to two alleles at the cystic fibrosis (CFTR) locus, deltaF508 and G542X, for which intraallelic variability at three intronic microsatellite loci has been examined. Our results indicate that G542X is somewhat older than deltaF508. Although absolute estimates depend on the mutation rates at the microsatellite loci, our results support the hypothesis that deltaF508 arose < 500 generations (approximately 10,000 years) ago.