Pair and triplet approximation of a spatial lattice population model with multiscale dispersal using Markov chains for estimating spatial autocorrelation
| Autor: | David E. Hiebeler, Nicholas E. Millett |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
Spatial correlation State variable Population Population Dynamics Markov process Models Biological General Biochemistry Genetics and Molecular Biology symbols.namesake Statistics Humans Statistical physics education Spatial analysis Mathematics education.field_of_study General Immunology and Microbiology Markov chain Applied Mathematics General Medicine Emigration and Immigration Markov Chains Population model Modeling and Simulation symbols Biological dispersal General Agricultural and Biological Sciences |
| Zdroj: | Journal of theoretical biology. 279(1) |
| ISSN: | 1095-8541 |
| Popis: | We investigate a spatial lattice model of a population employing dispersal to nearest and second-nearest neighbors, as well as long-distance dispersal across the landscape. The model is studied via stochastic spatial simulations, ordinary pair approximation, and triplet approximation. The latter method, which uses the probabilities of state configurations of contiguous blocks of three sites as its state variables, is demonstrated to be greatly superior to pair approximations for estimating spatial correlation information at various scales. Correlations between pairs of sites separated by arbitrary distances are estimated by constructing spatial Markov processes using the information from both approximations. These correlations demonstrate why pair approximation misses basic qualitative features of the model, such as decreasing population density as a large proportion of offspring are dropped on second-nearest neighbors, and why triplet approximation is able to include them. Analytical and numerical results show that, excluding long-distance dispersal, the initial growth rate of an invading population is maximized and the equilibrium population density is also roughly maximized when the population spreads its offspring evenly over nearest and second-nearest neighboring sites. |
| Databáze: | OpenAIRE |
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