Rescaling limits of the spatial Lambda-Fleming-Viot process with selection

We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the model is well-defined and provide a measure-valued dual process encoding the locations of the `potential ancestors' of a sample taken from such a population. We then consider two cases, one in which the dynamics of the process are driven by events of bounded radii and one incorporating large-scale events whose radii have a polynomial tail distribution. In both cases, we consider a sequence of spatial Lambda-Fleming-Viot processes indexed by n, and we assume that the fraction of individuals replaced during a reproduction event and the relative frequency of events during which natural selection acts tend to 0 as n tends to infinity. We choose the decay of these parameters in such a way that when reproduction is only local, the measure-valued process describing the local frequencies of the less favoured type converges in distribution to a (measure-valued) solution to the stochastic Fisher-KPP equation in one dimension, and to a (measure-valued) solution to the deterministic Fisher-KPP equation in more than one dimension. When large-scale extinction-recolonisation events occur, the sequence of processes converges instead to the solution to the analogous equation in which the Laplacian is replaced by a fractional Laplacian. We also consider the process of `potential ancestors' of a sample of individuals taken from these populations, which we see as a system of branching and coalescing symmetric jump processes. We show their convergence in distribution towards a system of Brownian or stable motions which branch at some finite rate. In one dimension, in the limit, pairs of particles also coalesce at a rate proportional to their collision local time.Comment: 97 page

Conditioning the logistic branching process on non-extinction

We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as a model for numbers of individuals in populations competing for some resource, or for numbers of species. However, because of the quadratic death rate, even if the intrinsic growth rate is positive, the population will, with probability one, die out in finite time. There is considerable interest in understanding the process conditioned on non-extinction. In this paper, we exploit a connection with the ancestral selection graph of population genetics to find expressions for the transition rates in the logistic branching process conditioned on survival until some fixed time $T$, in terms of the distribution of a certain one-dimensional diffusion process at time $T$. We also find the probability generating function of the Yaglom distribution of the process and rather explicit expressions for the transition rates for the so-called Q-process, that is the logistic branching process conditioned to stay alive into the indefinite future. For this process, one can write down the joint generator of the (time-reversed) total population size and what in population genetics would be called the `genealogy' and in phylogenetics would be called the `reconstructed tree' of a sample from the population. We explore some ramifications of these calculations numerically

Fixation Probability for Competing Selective Sweeps

We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the population. Previous work has dealt with the case where the second mutation to arise confers a smaller benefit than the first. In that case population size plays almost no role. Here we consider the opposite case and observe that, by contrast, the probability of both mutations fixing can be heavily dependent on population size. Indeed the key parameter is $\rho N$, the product of the population size and the recombination rate between the two selected loci. If $\rho N$ is small, the probability that both mutations fix can be reduced through interference to almost zero while for large $\rho N$ the mutations barely influence one another. The main rigorous result is a method for calculating the fixation probability of a double mutant in the large population limit.Comment: 33 pages, 3 figure

Assessment of selected soil parameters in a long-term Western Canadian organic field experiment

A long-term field study was used to compare soil nitrogen and phosphorous status, and soil aggregate stability in organic and conventional cropping systems. Two rotations were tested: a grain only and a grain-alfalfa hay rotation. The organic systems had a lower nitrate leaching potential than the same rotations under conventional management. After 13 years, one organic system (the grain-alfalfa; no manure return) is suffering serious soil P depletion. However, the grain only and the grain-alfalfa with manure return to land systems had soil P levels similar to the prairie grass control treatment and showed no signs of P deficiency. Despite having lower levels of organic carbon, the organic soils had higher levels of wet aggregate stability than conventionally managed soils

Design for Service Innovation & Development. Final Report

This is an AHRC research report exploring design's contribution to Service Innovation and New Service Development

Genomic and biologic comparisons of cyprinid herpesvirus 3 strains

Cyprinid herpesvirus 3 (CyHV-3) is the archetypal fish alloherpesvirus and the etiologic agent of a lethal disease in common and koi carp. To date, the genome sequences of only four CyHV-3 isolates have been published, but no comparisons of the biologic properties of these strains have been reported. We have sequenced the genomes of a further seven strains from various geographical sources, and have compared their growth in vitro and virulence in vivo. The major findings were: (i) the existence of the two genetic lineages previously described as European and Asian was confirmed, but inconsistencies between the geographic origin and genotype of some strains were revealed; (ii) potential inter-lineage recombination was detected in one strain, which also suggested the existence of a third, as yet unidentified lineage; (iii) analysis of genetic disruptions led to the identification of non-essential genes and their potential role in virulence; (iv) comparison of the in vitro and in vivo properties of strains belonging to the two lineages revealed that inter-lineage polymorphisms do not contribute to the differences in viral fitness observed; and (v) a negative correlation was observed among strains between viral growth in vitro and virulence in vivo. This study illustrates the importance of coupling genomic and biologic comparisons of viral strains in order to enhance understanding of viral evolution and pathogenesis

Associations between maternal depressive symptoms and child feeding practices in a cross-sectional study of low-income mothers and their young children

Background: Maternal depression may influence feeding practices important in determining child eating behaviors and weight. However, the association between maternal depressive symptoms and feeding practices has been inconsistent, and most prior studies used self-report questionnaires alone to characterize feeding. The purpose of this study was to identify feeding practices associated with maternal depressive symptoms using multiple methodologies, and to test the hypothesis that maternal depressive symptoms are associated with less responsive feeding practices. Methods: In this cross-sectional, observational study, participants (n = 295) included low-income mothers and their 4- to 8-year-old children. Maternal feeding practices were assessed via interviewer-administered questionnaires, semi-structured narrative interviews, and videotaped observations in home and laboratory settings. Maternal depressive symptoms were measured using the Center for Epidemiologic Studies-Depression scale (CES-D). Regression analyses examined associations between elevated depressive symptoms (CES-D score ≥16) and measures of maternal feeding practices, adjusting for: child sex, food fussiness, number of older siblings; and maternal age, body mass index (BMI), education, race/ethnicity, single parent status, perceived child weight, and concern about child weight. Results: Thirty-one percent of mothers reported depressive symptoms above the screening cutoff. Mothers with elevated depressive symptoms reported more pressuring of children to eat (β = 0.29; 95% Confidence Interval (CI): 0.03, 0.54) and more overall demandingness (β = 0.16; 95% CI: 0.03, 0.29), and expressed lower authority in child feeding during semi-structured narrative interview (Odds Ratio (OR) for low authority: 2.82; 95% CI: 1.55, 5.12). In homes of mothers with elevated depressive symptoms, the television was more likely audible during meals (OR: 1.91; 95% CI: 1.05, 3.48) and mothers were less likely to eat with children (OR: 0.48; 95% CI: 0.27, 0.85). There were no associations between maternal depressive symptoms and encouragement or discouragement of food in laboratory eating interactions. Conclusions: Mothers with elevated depressive symptoms demonstrated less responsive feeding practices than mothers with lower levels of depressive symptoms. These results suggest that screening for maternal depressive symptoms may be useful when counseling on healthy child feeding practices. Given inconsistencies across methodologies, future research should include multiple methods of characterizing feeding practices and direct comparisons of different methodologies