Alternatives to the Wright-Fisher model: the robustness of mitochondrial Eve dating

Coalescence in the diffusion limit of a Bienaymé-Galton-Watson branching process

We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienaymé-Galton-Watson branching process. More specifically, we are interested in the diffusion limit appropriate to a supercritical process in the near-critical limit evolving over a large number of time steps. Our approach differs from earlier analyses in that we assume the only known information is the mean and variance of the number of offspring per parent, the observed total population size at the time of sampling, and the size of the sample. We obtain a formula for the probability that a finite random sample of the population is descended from a single ancestor in the initial population, and derive a confidence interval for the initial population size in terms of the final population size and the time since initiating the process. We also determine a joint likelihood surface from which confidence regions can be determined for simultaneously estimating two parameters, (1) the population size at the time of the most recent common ancestor, and (2) the time elapsed since the existence of the most recent common ancestor.

Mutation in populations governed by a Galton-Watson branching process

A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is presented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral mutations. The asymptotic stationary solution is obtained and has the property that the extant population partitions into subpopulations whose relative sizes are determined by mutation rates. An approximate time-dependent solution is obtained in the limit of low mutation rates. This solution has the property that the system undergoes a rapid transition from a drift-dominated phase to a mutation-dominated phase in which the distribution collapses onto the asymptotic stationary distribution. The changeover point of the transition is determined by the per-generation growth factor and mutation rate. The approximate solution is confirmed using numerical simulations.

Genetic drift in populations governed by a Galton-Watson branching process

Most population genetics studies have their origins in a Wright-Fisher or some closely related fixed-population model in which each individual randomly chooses its ancestor. Populations which vary in size with time are typically modelled via a coalescent derived from Wright-Fisher, but use a nonlinear time-scaling driven by a deterministically imposed population growth. An alternate, arguably more realistic approach, and one which we take here, is to allow the population size to vary stochastically via a Galton-Watson branching process. We study genetic drift in a population consisting of a number of distinct allele types in which each allele type evolves as an independent Galton-Watson branching process. We find the dynamics of the population is determined by a single parameter κ0=(2m0/σ(2))logλ, where m0 is the initial population size, λ is the mean number of offspring per individual; and σ(2) is the variance of the number of offspring. For 0≲κ0≪1, the dynamics are close to those of Wright-Fisher, with the added property that the population is prone to extinction. For κ0≫1 allele frequencies and ancestral lineages are stable and individual alleles do not fix throughout the population. The existence of a rapid changeover regime at κ0≈1 enables estimates to be made, together with confidence intervals, of the time and population size of the era of mitochondrial Eve.

Stochastic Hypothesis of Transition from Inborn Neutropenia to AML: Interactions of Cell Population Dynamics and Population Genetics

We present a stochastic model of driver mutations in the transition from severe congenital neutropenia to myelodysplastic syndrome to acute myeloid leukemia (AML). The model has the form of a multitype branching process. We derive equations for the distributions of the times to consecutive driver mutations and set up simulations involving a range of hypotheses regarding acceleration of the mutation rates in successive mutant clones. Our model reproduces the clinical distribution of times at diagnosis of secondary AML. Surprisingly, within the framework of our assumptions, stochasticity of the mutation process is incapable of explaining the spread of times at diagnosis of AML in this case; it is necessary to additionally assume a wide spread of proliferative parameters among disease cases. This finding is unexpected but generally consistent with the wide heterogeneity of characteristics of human cancers.

Expectation-maximization algorithm for determining natural selection of Y-linked genes through two-sex branching processes

A two-dimensional bisexual branching process has recently been presented for the analysis of the generation-to-generation evolution of the number of carriers of a Y-linked gene. In this model, preference of females for males with a specific genetic characteristic is assumed to be determined by an allele of the gene. It has been shown that the behavior of this kind of Y-linked gene is strongly related to the reproduction law of each genotype. In practice, the corresponding offspring distributions are usually unknown, and it is necessary to develop their estimation theory in order to determine the natural selection of the gene. Here we deal with the estimation problem for the offspring distribution of each genotype of a Y-linked gene when the only observable data are each generation's total numbers of males of each genotype and of females. We set out the problem in a non parametric framework and obtain the maximum likelihood estimators of the offspring distributions using an expectation-maximization algorithm. From these estimators, we also derive the estimators for the reproduction mean of each genotype and forecast the distribution of the future population sizes. Finally, we check the accuracy of the algorithm by means of a simulation study.

Man the fat hunter: the demise of Homo erectus and the emergence of a new hominin lineage in the Middle Pleistocene (ca. 400 kyr) Levant

The worldwide association of H. erectus with elephants is well documented and so is the preference of humans for fat as a source of energy. We show that rather than a matter of preference, H. erectus in the Levant was dependent on both elephants and fat for his survival. The disappearance of elephants from the Levant some 400 kyr ago coincides with the appearance of a new and innovative local cultural complex--the Levantine Acheulo-Yabrudian and, as is evident from teeth recently found in the Acheulo-Yabrudian 400-200 kyr site of Qesem Cave, the replacement of H. erectus by a new hominin. We employ a bio-energetic model to present a hypothesis that the disappearance of the elephants, which created a need to hunt an increased number of smaller and faster animals while maintaining an adequate fat content in the diet, was the evolutionary drive behind the emergence of the lighter, more agile, and cognitively capable hominins. Qesem Cave thus provides a rare opportunity to study the mechanisms that underlie the emergence of our post-erectus ancestors, the fat hunters.