Dispersal in a metapopulation neighbourhood model of an annual plant with a seedbank

1 A metapopulation neighbourhood model of an annual plant species in a harsh environment is derived. It includes the effects of seed survival, dormancy, competition, dispersal, spatial and temporal heterogeneity, and stochastic local extinctions. 2 The model contained the following assumptions: (i) the time step is 1 year; (ii) competition is density-dependent via a Hassell-type submodel; (iii) each local population is regulated separately within a hexagonal cell, 1 m across, and the cells form a tessellated array; (iv) dispersal is from a parent cell to its neighbours and declines exponentially with distance; (v) the harshness of the environment is a value set for each cell; spatial and temporal heterogeneity are introduced by altering this value; (vi) each local population is rounded to give an integer number of individuals at the end of each generation so that those with density below unity may become extinct, with a probability inversely proportional to density. 3 In spatially homogeneous and heterogeneous harsh environments with moderate levels of density-dependent competition, all populations persisted and dispersal aided metapopulation growth when the population growth rate was sufficiently large. When the population growth rate was smaller, dispersal increased the risk of, and speeded up the time to, metapopulation extinction. Metapopulation growth was faster when the heterogeneity was at a larger-scale spatial pattern. 4 Temporal heterogeneity had an adverse effect when added to the existing spatial heterogeneity; strongly dispersing metapopulations were affected only slightly, while those with only moderate or no dispersal became extinct. The more frequently the environment changed, the greater was the probability of extinction. 5 The model simulations in 2-4 were repeated for more-severe density-dependence. In the spatially homogeneous environment dispersal prevented metapopulation extinction, while lack of dispersal encouraged it. Dispersal aided metapopulation growth in the spatially heterogeneous unchanging environment. The addition of temporal heterogeneity had little effect on populations with strong dispersal but the effect on the other metapopulations was catastrophic.