Todd L. Parsons

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Historical patterns of species diversity inferred from phylogenies typically contradict the direct evidence found in the fossil record. According to the fossil record, species frequently go extinct, and many clades experience periods of dramatic diversity loss. However, most analyses of molecular phylogenies fail to identify any periods of declining(More)
Robustness seems to be the opposite of evolvability. If phenotypes are robust against mutation, we might expect that a population will have difficulty adapting to an environmental change, as several studies have suggested. However, other studies contend that robust organisms are more adaptable. A quantitative understanding of the relationship between(More)
We extend the one-locus two allele Moran model of fixation in a haploid population to the case where the total size of the population is not fixed. The model is defined as a two-dimensional birth-and-death process for allele number. Changes in allele number occur through density-independent death events and birth events whose per capita rate decreases(More)
We determine fixation probabilities in a model of two competing types with density dependence. The model is defined as a two-dimensional birth-and-death process with density-independent death rates, and birth rates that are a linearly decreasing function of total population density. We treat the 'quasi-neutral case' where both types have the same(More)
Much of population genetics is based on the diffusion limit of the Wright-Fisher model, which assumes a fixed population size. This assumption is violated in most natural populations, particularly for microbes. Here we study a more realistic model that decouples birth and death events and allows for a stochastically varying population size. Under this(More)
X iv :1 41 0. 40 38 v1 [ qbi o. PE ] 1 5 O ct 2 01 4 1 Linking statistical and ecological theory: Hubbell’s unified neutral theory of biodiversity as a hierarchical Dirichlet process Keith Harris, Todd L Parsons, Umer Z Ijaz, Leo Lahti, Ian Holmes, Christopher Quince6,∗ 1 School of Mathematics and Statistics, University of Sheffield, Sheffield, UK 2(More)
Kimura observed that the rate of neutral substitution should equal the neutral mutation rate. This classic result is central to our understanding of molecular evolution, and it continues to influence phylogenetics, genomics, and the interpretation of evolution experiments. By demonstrating that neutral mutations substitute at a rate independent of(More)
We study a generalisation of Moran's population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to(More)
Recent work has shown that genetic robustness can either facilitate or impede adaptation. But the impact of environmental robustness on adaptation remains unclear. Environmental robustness helps ensure that organisms consistently develop the same phenotype in the face of "environmental noise" during development. Under purifying selection, those genotypes(More)
∣ = 0 respectively. We also use Hardy notation: f(N) ≪ g(N) if f(N) = o(g(N)). • Throughout, I will use ∂i to indicate the partial derivative with respect to the i th cooordinate and D to denote the total derivative operator: if F : R → R, (DF) = (∂jFi)ij • R+ = {x ∈ R K : xi ≥ 0, i = 1, . . . ,K}. • If x,y ∈ R , we write x ≤ y if xi ≤ yi for all i, x < y(More)