Abstract
The dynamics of the metapopulation is described by a Markov chain with three possible states of each subpopulation: 0 (extinct), 1 (lower size), and 2 (carrying capacity). Migrations between subpopulations can depend both on the state of the source subpopulation (e.g., inversely) and the state of the target habitat. The strategies of conspecific attraction, when occupied patches receive a larger fraction of migrants, and conspecific repulsion, i.e., the preference for empty patches, are modelled. Emigration events affect the density of the source habitat. Immigration causes either a recolonisation of an empty patch or the transition from state 1 to state 2 of the target habitat. Application of queuing theory methods made it possible to obtain analytical formulas for extinction probability and persistence time. The effect of dispersal behaviour was investigated. The influence of random dispersal and of directional dispersal depends on population parameters. It is demonstrated that, while at high growth and mortality rates, conspecific repulsion provides better metapopulation viability, there exists a threshold value for the growth rate below which aggregation becomes favourable. Biological interpretation of these results is discussed and a classification of species is suggested associating population kinetic rates and dispersal strategy.
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