Gene Genealogies within Mutant Allelic Classes

A coalescent theory of the gene genealogy within an allelic class that arises by a unique mutational event is developed and analyzed. To interpret this theory it was necessary to expand on existing theory for populations of varying size. Two features of the gene genealogy--the average pairwise distance and the total tree length--within the mutant class and within the nonmutant class are found. An index, I, is proposed that describes the extent to which a genealogy is similar to one from a population of constant size (for which I = 0) or to a star genealogy (for which I = 1). The value of I is positive in growing populations and is generally positive for the gene genealogy for the mutant class. The value of I is negative for a population decreasing in size and for the nonmutant class, if the mutant arose recently. The results are discussed in the context of the infinite sites model of mutation, which is appropriate for nucleotide sequence data, and the generalized stepwise mutation model, which is appropriate for microsatellite loci. The same genealogical methods are used to find the probability of at least one recombination event between a nucleotide that defines an allelic class and a marker at a nearby linked site.     

Estimating the number of founder lineages from haplotypes of closely linked SNPs

We consider an isolated population founded by a small number of individuals randomly chosen from a source population of known genetic composition at a known time in the past. We develop a Monte-Carlo maximum-likelihood method for estimating the number of founding individuals from the haplotype frequencies at several SNP (single nucleotide polymorphism) loci in a sample. We assume the isolated population was founded recently enough that that mutation can be ignored and that haplotype frequencies in the source population have not changed. We apply the method to simulated data and show that it is unbiased. With a reasonable number of individuals sampled, it is possible to estimate the number of founders within a factor of 2. We show that the performance of the method is not degraded substantially if the frequencies of the rare haplotypes in the source are not known precisely and if there is some recombination. We illustrate the use of our method by applying it to a previously published data set from a recently founded population of wolves (Canis lupus) in Scandinavia.     

Non-equilibrium theory of the allele frequency spectrum

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.     

Exploring variation in the d(N)/d(S) ratio among sites and lineages using mutational mappings: applications to the influenza virus

We use a likelihood-based method for mapping mutations on a phylogeny in a way that allows for both site-specific and lineage-specific variation in selection intensity. The method accounts for many of the potential sources of bias encountered in mapping of mutations on trees while still being computationally efficient. We apply the method to a previously published influenza data set to investigate hypotheses about changes in selection intensity in influenza strains. Influenza virus is sometimes propagated in chicken cells for several generations before sequencing, a process that has been hypothesized to induce mutations adapting the virus to the lab medium. Our analysis suggests that there are approximately twice as many replacement substitutions in lineages propagated in chicken eggs as in lineages that are not. Previous studies have attempted to predict which viral strains future epidemics may arise from using inferences regarding positive selection. The assumption is that future epidemics are more likely to arise from the strains in which positive selection on the so-called “trunk lineages” of the evolutionary tree is most pervasive. However, we find no difference in the strength of selection in the trunk lineages versus other evolutionary lineages. Our results suggest that it may be more difficult to use inferences regarding the strength of selection on mutations to make predictions regarding viral epidemics than previously thought. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Reviewing Editor: Dr. Willie Swanson     

The number of segregating sites in expanding human populations, with implications for estimates of demographic parameters

The frequency distribution of pairwise differences between sequences of mtDNA has recently been used to estimate the size of human populations before and after a hypothetical episode of rapid population growth and the time at which the population grew. To test the internal consistency of this method, we used three different sets of human mtDNA data and the corresponding demographic parameters estimated from the distribution of pairwise differences to determine by simulation the expected number of segregating sites, S, and its empirical distribution. The results indicate that the observed values of S are significantly lower than expected in two of three cases under the assumption of the infinite-sites model. Further simulations in which mutations were allowed to occur more than once at the same site and in which there was variation in mutation rate among sites show that the expected number of segregating sites can be much lower than under the infinite-site assumption. Nevertheless, the observed value of S is still significantly different from the value expected under the expansion hypothesis in two of three cases.      

Detecting Small Amounts of Gene Flow from Phylogenies of Alleles

The method of coalescents is used to find the probability that none of the ancestors of alleles sampled from a population are immigrants. If that is the case for samples from two or more populations, then there would be concordance between the phylogenies of those alleles and the geographic locations from which they are drawn. This type of concordance has been found in several studies of mitochondrial DNA from natural populations. It is shown that if the number of sequences sampled from each population is reasonably large (10 or more), then this type of concordance suggests that the average number of individuals migrating between populations is likely to be relatively small (Nm less than 1) but the possibility of occasional migrants cannot be excluded. The method is applied to the data of E. Bermingham and J. C. Avise on mtDNA from the bowfin, Amia calva.     

Research at the European Synchrotron Radiation Facility medical beamline.

The application of synchrotron radiation in medical research has become a mature field of research at synchrotron facilities worldwide. In the relatively short time that synchrotrons have been available to the scientific community, their characteristic beams of UV and X-ray radiation have been applied to virtually all areas of medical science which use ionizing radiation. The ability to tune intense monochromatic beams over wide energy ranges differentiates these sources from standard clinical and research tools. At the European Synchrotron Radiation Facility (Grenoble, France), a major research facility is operational on an advanced wiggler radiation beamport, ID17. The beamport is designed to carry out a broad range of research ranging from cell radiation biology to in vivo human studies. Medical imaging programs at ID17 include transvenous coronary angiography, computed tomography, mammography and bronchography. In addition, a major research program on microbeam radiation therapy is progressing. This paper will present a very brief overview of the beamline and the imaging and therapy programs.     

Using maximum likelihood to estimate population size from temporal changes in allele frequencies.

We develop a maximum-likelihood framework for using temporal changes in allele frequencies to estimate the number of breeding individuals in a population. We use simulations to compare the performance of this estimator to an F-statistic estimator of variance effective population size. The maximum-likelihood estimator had a lower variance and smaller bias. Taking advantage of the likelihood framework, we extend the model to include exponential growth and show that temporal allele frequency data from three or more sampling events can be used to test for population growth.