Diffusion approximation of a multilocus model with assortative mating

To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population evolves according to a Moran model with weak assortative mating, strong recombination and low mutation rates. With an appropriate rescaling of time, we obtain that the evolution of the genotypic frequencies in a large population can be approximated by the evolution of the product of the allelic frequencies at each locus, and the vector of the allelic frequencies is approximately governed by a diffusion. We present some features of the limiting diffusions (in particular their boundary behaviour and conditions under which the allelic frequencies at different loci evolve independently). If mutation rates are strictly positive then the limiting diffusion is reversible and, under some assumptions, the critical points of the stationary density can be characterised.Comment: 56 pages, 8 figures ; corrected typo

Genealogical constructions of population models

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on $[0,\lambda ]$, whereas in the infinite intensity limit $\lambda\rightarrow\infty$, at each time $t$, the joint distribution of types and levels is conditionally Poisson, with mean measure $\Xi (t)\times \ell$ where $\ell$ denotes Lebesgue measure and $\Xi (t)$ is a measure-valued population process. The time-evolution of the levels captures the genealogies of the particles in the population. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, one-for-one replacement, immigration, independent `thinning' and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend on type, they also include natural selection. The primary goal of the paper is to present particle-with-level or lookdown constructions for each of these elements of a population model. Then the elements can be combined to specify the desired model. In particular, a non-trivial extension of the spatial $\Lambda$-Fleming-Viot process is constructed

A new model for evolution in a spatial continuum

We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans(1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of side L as L tends to infinity. Under appropriate conditions (and on a suitable timescale), we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).Comment: 63 pages, version accepted to Electron. J. Proba

Coalescent simulation in continuous space:Algorithms for large neighbourhood size

Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail

LANDSAT/MMS propulsion module design. Volume 1: Task 4.3, trade studies

Evaluations are presented of alternative LANDSAT follow-on launch configurations to derive the propulsion requirements for the multimission modular spacecraft (MMS). Two basic types were analyzed including use of conventional launch vehicles and shuttle-supported missions. It was concluded that two sizes of modular hydrazine propulsion modules would provide the most cost-effective combination for future missions of this spacecraft. Conceptual designs of the selected propulsion modules were performed to the depth permitting determination of mass properties and estimated costs

Compact interface property for symbiotic branching

A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment equations are still available in this generalized context. As an application, we show that in the setting of the one-dimensional continuum the compact interface property holds: starting from complementary Heaviside states, the interface is finite at all times almost surely

The infinitesimal model with dominance

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and a non-genetic (environmental) component and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the trait values of the parents. In previous work, Barton et al.(2017), we showed that when trait values are determined by the sum of a large number of Mendelian factors, each of small effect, one can justify the infinitesimal model as limit of Mendelian inheritance. In this paper, we show that the robustness of the infinitesimal model extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and identities determined by the pedigree. In this setting, it is natural to decompose trait values, not just into the additive and dominance components, but into a component that is shared by all individuals within the family and an independent `residual' for each offspring, which captures the randomness of Mendelian inheritance. We show that, even if we condition on parental trait values, both the shared component and the residuals within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/\sqrt{M}. We illustrate our results with some numerical examples.Comment: 62 pages, 8 figure

Comparison of reproducibility, accuracy, sensitivity, and specificity of miRNA quantification platforms

Given the increasing interest in their use as disease biomarkers, the establishment of reproducible, accurate, sensitive, and specific platforms for microRNA (miRNA) quantification in biofluids is of high priority. We compare four platforms for these characteristics: small RNA sequencing (RNA-seq), FirePlex, EdgeSeq, and nCounter. For a pool of synthetic miRNAs, coefficients of variation for technical replicates are lower for EdgeSeq (6.9%) and RNA-seq (8.2%) than for FirePlex (22.4%); nCounter replicates are not performed. Receiver operating characteristic analysis for distinguishing present versus absent miRNAs shows small RNA-seq (area under curve 0.99) is superior to EdgeSeq (0.97), nCounter (0.94), and FirePlex (0.81). Expected differences in expression of placenta-associated miRNAs in plasma from pregnant and non-pregnant women are observed with RNA-seq and EdgeSeq, but not FirePlex or nCounter. These results indicate that differences in performance among miRNA profiling platforms impact ability to detect biological differences among samples and thus their relative utility for research and clinical use