Pair-edge Approximation for Heterogeneous Lattice Population Models
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Date
2002-10-08
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Abstract
To increase the analytical tractability of lattice stochastic spatial population models, several approximations have been developed. The pair-edge approximation is a moment-closure method that is effective in predicting persistence criteria and invasion speeds on a homogeneous lattice. Here the effectiveness of the pair-edge approximation is evaluated on a spatially heterogeneous lattice in which some sites are unoccupiable, or 'dead'. This model has several possible interpretations, including a spatial SIS epidemic model, in which immobile host-species individuals occupy some sites while others are empty. As in the homogeneous model, the pair-edge approximation is found to be significantly more accurate than the ordinary pair approximation in determining conditions for persistence. However, habitat heterogeneity decreases invasion speed more than is predicted by the pair-edge approximation, and the discrepancy increases with greater clustering of dead sites. The accuracy of the approximation validates the underlying heuristic picture of population spread and therefore provides qualitative insight into the dynamics of lattice models. Conversely, the situations where the approximation is less accurate reveal limitations of pair approximation in the presence of spatial heterogeneity.
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invasion speed, critical birth rate, pair-edge approximation, lattice models, moment-closure
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Degree
MS
Discipline
Biomathematics
