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

Computer simulation of impurity diffusion in silicon, part 1

The elementary classical models for idealized diffusion conditions are described, and the principles are then used in developing more realistic models. The practical models require some type of numerical analysis. The numerical techniques are outlined and details concerning their implementation are given. Some results are presented which were obtained with the computer programs implementing the numerical techniques with implicit and explicit methods. Special problems of impurity-rich interlayers forming between an oxide and silicon are considered. A set of computed curves for sheet resistance, junction depth, and oxide thickness for different diffusion schedules is included

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

Branching Brownian Motion, mean curvature flow and the motion of hybrid zones

We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scaling limits of the spatial Λ-Fleming-Viot process with selection, in which the selection mechanism is chosen to model what are known in population genetics as hybrid zones. Our proofs will exploit a duality with a system of branching (and coalescing) random walkers which is of some interest in its own right

A comparison of CFD and full-scale measurement for analysis of natural ventilation

CFD modelling techniques have been used to simulate the coupled external and internal flow in a cubic building with two dominant openings. CFD predictions of the time-averaged cross ventilation flow rates have been validated against full-scale experimental data under various weather conditions in England. RANS model predictions proved reliable when wind directions were near normal to the vent openings. However, when the fluctuating ventilation rate exceeded the mean flow, RANS models were incapable of predicting the total ventilation rate. Improved results are expected by applying more sophisticated turbulence models, such as LES or weighted quasi-steady approximations

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

Extreme 13C depletion of CCl2F2 in firn air samples from NEEM, Greenland

A series of 12 high volume air samples collected from the S2 firn core during the North Greenland Eemian Ice Drilling (NEEM) 2009 campaign have been measured for mixing ratio and stable carbon isotope composition of the chlorofluorocarbon CFC-12 (CCl2F2). While the mixing ratio measurements compare favorably to other firn air studies, the isotope results show extreme 13C depletion at the deepest measurable depth (65 m), to values lower than d13C = -80‰ vs. VPDB (the international stable carbon isotope scale), compared to present day surface tropospheric measurements near -40‰. Firn air modeling was used to interpret these measurements. Reconstructed atmospheric time series indicate even larger depletions (to -120‰) near 1950 AD, with subsequent rapid enrichment of the atmospheric reservoir of the compound to the present day value. Mass-balance calculations show that this change is likely to have been caused by a large change in the isotopic composition of anthropogenic CFC-12 emissions, probably due to technological advances in the CFC production process over the last 80 yr, though direct evidence is lacking