Population structure and evolutionary progress

Wright's shifting-balance theory is discussed as an example of a process that can cause species to evolve combinations of characters that could not evolve under natural selection alone. A review of the existing theory of peak shifts indicates that the conditions of extreme isolation that are necessary to permit genetic drift to alter the outcome of natural selection in local populations would make gene flow too weak to spread a new combination of genes to other populations in a reasonable time. Instead, it seems likely that major demographic changes must occur in a species for the shifting-balance process to work. A discussion of direct and indirect studies of gene flow in natural populations suggests that the current genetic structure of many species is likely to reflect past demographic events rather than ongoing gene flow. It is possible then that demographic processes could be responsible for spreading new traits in a species, but that would be true whether those new traits evolved only owing to natural selection or owing in addition to genetic drift and other forces.     

The Projection of a Test Genome onto a Reference Population and Applications to Humans and Archaic Hominins

We introduce a method for comparing a test genome with numerous genomes from a reference population. Sites in the test genome are given a weight, w, that depends on the allele frequency, x, in the reference population. The projection of the test genome onto the reference population is the average weight for each x, w¯(x). The weight is assigned in such a way that, if the test genome is a random sample from the reference population, then w¯(x)=1. Using analytic theory, numerical analysis, and simulations, we show how the projection depends on the time of population splitting, the history of admixture, and changes in past population size. The projection is sensitive to small amounts of past admixture, the direction of admixture, and admixture from a population not sampled (a ghost population). We compute the projections of several human and two archaic genomes onto three reference populations from the 1000 Genomes project—Europeans, Han Chinese, and Yoruba—and discuss the consistency of our analysis with previously published results for European and Yoruba demographic history. Including higher amounts of admixture between Europeans and Yoruba soon after their separation and low amounts of admixture more recently can resolve discrepancies between the projections and demographic inferences from some previous studies.     

DETECTING RANGE EXPANSIONS FROM GENETIC DATA

We propose a method that uses genetic data to test for the occurrence of a recent range expansion and to infer the location of the origin of the expansion. We introduce a statistic ψ (the directionality index) that detects asymmetries in the 2D allele frequency spectrum of pairs of population. These asymmetries are caused by the series of founder events that happen during an expansion and they arise because low frequency alleles tend to be lost during founder events, thus creating clines in the frequencies of surviving low‐frequency alleles. Using simulations, we show that ψ is more powerful for detecting range expansions than both and clines in heterozygosity. We also show how we can adapt our approach to more complicated scenarios such as expansions with multiple origins or barriers to migration and we illustrate the utility of ψ by applying it to a data set from modern humans.     

QUANTITATIVE GENETICS OF HETEROCHRONY

A model of quantitative-genetic variation in developmental processes is introduced and analyzed. The model is of a bifurcating sequence of events in which traits develop from the same tissue until a transition occurs, after which they develop partially independently. Genetic and environmental variation in both the rates of tissue growth and in the timing of transitions is considered. The model shows how genetic variation in developmental parameters governs variation and covariation in phenotypic traits and how selection on the phenotype alters the distributions of developmental parameters. Particular attention is paid to the conditions under which selection will lead to changes in the average times of developmental events.     

Epigenetic Inheritance and the Missing Heritability Problem

Epigenetic phenomena, and in particular heritable epigenetic changes, or transgenerational effects, are the subject of much discussion in the current literature. This article presents a model of transgenerational epigenetic inheritance and explores the effect of epigenetic inheritance on the risk and recurrence risk of a complex disease. The model assumes that epigenetic modifications of the genome are gained and lost at specified rates and that each modification contributes multiplicatively to disease risk. The potentially high rate of loss of epigenetic modifications causes the probability of identity in state in close relatives to be smaller than is implied by their relatedness. As a consequence, the recurrence risk to close relatives is reduced. Although epigenetic modifications may contribute substantially to average risk, they will not contribute much to recurrence risk and heritability unless they persist on average for many generations. If they do persist for long times, they are equivalent to mutations and hence are likely to be in linkage disequilibrium with SNPs surveyed in genomewide association studies. Thus epigenetic modifications are a potential solution to the problem of missing causality of complex diseases but not to the problem of missing heritability. The model highlights the need for empirical estimates of the persistence times of heritable epialleles.THE modern definition of epigenetics is the study of heritable changes in gene expression that are not caused by changes in DNA sequence (Richards 2006; Bird 2007; Bossdorf et al. 2008). Epigenetic effects include methylation of the cytosine residue in DNA and the modification of chromatin proteins that package DNA (Youngson and Whitelaw 2008). Although this definition of epigenetics includes inheritance during both mitosis and meiosis, I am concerned in this article only with epigenetic changes that are transmitted to offspring, what has been called “transgenerational epigenetic inheritance” (Morgan and Whitelaw 2008; Youngson and Whitelaw 2008). The modern definition of epigenetics arose from the original definition of Waddington (1957; Holliday and Pugh 1975).The possibility of nongenetic inherited effects on phenotype has excited great interest among both evolutionary biologists and human geneticists because it provides an additional mechanism of inherited variability and one that is not detectable in genomic surveys of sequence variation. Inherited epigenetic changes have been proposed as an explanation for the “missing heritability,” meaning inherited causes of risk of complex genetic diseases that have not yet been identified in genomewide association studies (GWAS) (Maher 2008; McCarthy and Hirschhorn 2008). Inherited epigenetic changes that contribute to disease risk would not be detectable in GWAS but may contribute to average risk and to similarities among relatives.In this article, I present a simple model of the inheritance of epigenetic changes. The goal is to quantify the potential contribution they can make to average risk and recurrence risk. The model is developed in a standard population genetics framework and can be regarded as a generalization of previous multilocus models of complex diseases, particularly that of Risch (1990).I assume that epigenetic effects are caused by the presence or the absence of epigenetic modifications of specific chromosomal locations. Bird (2007), Haig (2007), Richards (2008), and others have emphasized that, although epigenetic changes differ in many ways from mutations, their transmission to offspring is the same as the transmission of mutations, except for the possibility that they might be spontaneously lost. If the gain and loss of epigenetic changes are controlled by a locus elsewhere in the genome, as modeled by Bjornsson et al. (2004), then the resulting phenotypic effects are attributable to variation at that locus (Richards 2006; Johannes et al. 2008). The epigenetic changes are simply the mechanism by which that locus affects phenotype. If, however, the appearance of an epigenetic change at a location in the genome is not attributable to any particular locus or loci, then the phenotypic effects of the presence or the absence of an epigenetic change are attributable to the genomic location itself. That is the case I am concerned with here.I begin by introducing the basic model of a randomly mating population and extend standard genetic theory to the case of epigenetic inheritance. Then I consider nonequilibrium populations in which environmental changes cause an increase in the rate of gain of epigenetic changes.     

Simulating genealogies of selected alleles in a population of variable size

An importance-sampling method is presented that allows the simulation of the history of a selected allele in a population of variable size. A sample path describing the number of copies of an allele that arose as a single mutant is generated by simulating backwards from the current frequency until the allele is lost. The mathematical expectation of a quantity or statistic is then estimated by taking averages over replicate simulations, weighting each replicate by the ratio of its probabilities under the Markov chains for the forward and backwards processes. This method was used to find the average age of a selected allele in an exponentially growing population. In terms of the effect on average allele age, selection in favour of an allele is not equivalent to exponential growth. To generate gene genealogies of a sample of copies of a selected allele, the neutral coalescent model is simulated for the subpopulation containing only the selected allele. From the resulting intra-allelic genealogy, it is possible to calculate the likelihood of the selection intensity as a function of the observed level of variability at marker loci closely linked to the selected allele. This method was used to estimate the intensity of selection affecting the delta 32 allele at the CCR5 locus in Europeans and a mutant at the MLH1 locus associated with colorectal cancer in the Finnish population.     

Boron neutron capture therapy of a murine mammary carcinoma using a lipophilic carboranyltetraphenylporphyrin

The first control of a malignant tumor in vivo by porphyrin- mediated boron neutron capture therapy (BNCT) is described. In mice bearing implanted EMT-6 mammary carcinomas, boron uptake using a single injection of either p-boronophenylalanine (BPA) or mercaptoundecahydrododecaborane (BSH) was compared with either a single injection or multiple injections of the carboranylporphyrin CuTCPH. The BSH and BPA doses used were comparable to the highest doses of these compounds previously administered in a single injection to rodents. For BNCT, boron concentrations averaged 85 microg (10)B/g in the tumor and 4 microg (10)B/g in blood 2 days after the last of six injections (over 32 h) that delivered a total of 190 microg CuTCPH/g body weight. During a single 15, 20, 25 or 30 MW-min exposure to the thermalized neutron beam of the Brookhaven Medical Research Reactor, a tumor received average absorbed doses of approximately 39, 52, 66 or 79 Gy, respectively. A long-term (>200 days) tumor control rate of 71% was achieved at a dose of 66 Gy with minimal damage to the leg. Equivalent long-term tumor control by a single exposure to 42 Gy X rays was achieved, but with greater damage to the irradiated leg.     

Likelihood-based disequilibrium mapping for two-marker haplotype data

We report a theory that gives the sampling distribution of two-marker haplotypes that are linked to a rare disease mutation. The sampling distribution is generated with successive Monte Carlo realizations of the coalescence of the disease mutation having recombination and marker mutation events placed along the lineage. Given a sample of mutation-bearing, two-marker haplotypes, the maximum likelihood estimate of the location of the disease mutation can be calculated from the generated sampling distribution, provided that one knows enough about the population history in order to model it. The two-marker likelihood method is compared to a single-marker likelihood and a composite likelihood. The two-marker maximum likelihood gives smaller confidence intervals for the location of the disease locus than a comparable single-marker maximum likelihood. The composite likelihood can give biased results and the bias increases as the extent of linkage disequilibrium on mutation-bearing chromosomes decreases. Haplotype configurations exist for which the composite likelihood will fail to place the disease locus in the correct marker interval.     

A vectorized method of importance sampling with applications to models of mutation and migration

An importance-sampling method is presented for computing the likelihood of the configuration of population genetic data under general assumptions about population history and transitions among states. The configuration of the data is the number of chromosomes sampled that are in each of a finite set of states. Transitions among states are governed by a Markov chain with transition probabilities dependent on one or more parameters. The method assumes that the joint distribution of coalescence times of the underlying gene genealogy is independent of the genetic state of each lineage. Given a set of coalescence times, the probability that a pair of lineages is chosen to coalesce in each replicate is proportional to the contribution that the coalescence event makes to the probability of the data. This method can be applied to gene genealogies generated by the neutral coalescent process and to genealogies generated by other processes, such as a linear birth-death process which provides a good approximation to the dynamics of low-frequency alleles. Two applications are described. In the first, the fit of allele frequencies at two microsatellite loci sampled in a Sardinian population to the one-step mutation model is tested. The one-step model is rejected for one locus but not for the other. The second application is to low-frequency alleles in a geographically subdivided population. The geographic location is the allelic state, and the alleles are assumed to be sufficiently rare that their dynamics can be approximated by a linear birth-death process in which the birth and death rates are independent of geographic location. The analysis of eight low-frequency allozyme alleles found in the glaucous-winged gull, Larus glaucescens, illustrates how geographically restricted dispersal can be detected.