  In this study, spatial stochastic and logistic model (SSLM) describing
dynamics of a population of a certain species was analysed. The behaviour of
the extinction threshold as a function of model parameters was studied. More
specifically, we studied how the critical values for the model parameters that
separate the cases of extinction and persistence depend on the spatial scales
of the competition and dispersal kernels. We compared the simulations and
analytical results to examine if and how the mathematical approximations break
down at the vicinity of the extinction threshold, and found a functional form
of the naive approximation for which higher-order term of analytical
approximation converges.
