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In this study, spatial stochastic and logistic model (SSLM) describingdynamics of a population of a certain species was analysed. The behaviour ofthe extinction threshold as a function of model parameters was studied. Morespecifically, we studied how the critical values for the model parameters thatseparate the cases of extinction and persistence depend on the spatial scalesof the competition and dispersal kernels. We compared the simulations andanalytical results to examine if and how the mathematical approximations breakdown at the vicinity of the extinction threshold, and found a functional formof the naive approximation for which higher-order term of analyticalapproximation converges.

Extinction threshold of a population in spatial and stochastic model