Abstract
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.
Highlights
As Wright noted (1978, p. 54), many species, such as the dominant plants in grasslands, have an essentially continuous and uniform distribution in space
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
A central goal of the spatial Λ-Fleming–Viot continuum model is to provide a means of incorporating events over different scales, ranging from the steady process of local reproduction to largescale demographic shifts
Summary
As Wright noted (1978, p. 54), many species, such as the dominant plants in grasslands, have an essentially continuous and uniform distribution in space. Assuming a single parent and a modest neighbourhood size of 100, we arrive at an impact of u = 1/100 These parameters present serious difficulties to a direct simulation of the coalescent process, in which we expect to generate 1/u events that intersect with a lineage before it jumps. In this case it is simple to calculate the exact distribution of the time that elapses between events in which a lineage jumps, allowing us to simulate only these events. A rigorous description of an algorithm allows us to analyse the properties of this algorithm using mathematical techniques, allowing us to improve performance without resorting to approximations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
