Patchy reaction-diffusion and population abundance: the relative importance of habitat amount and arrangement

A discrete reaction-diffusion model was used to estimate long-term equilibrium populations of a hypothetical species inhabiting patchy landscapes to examine the relative importance of habitat amount and arrangement in explaining population size. When examined over a broad range of habitat amounts and arrangements, population size was largely determined by a pure amount effect (proportion of habitat in the landscape accounted for >96% of the total variation compared to <1% for the arrangement main effect). However, population response deviated from a pure amount effect as coverage was reduced below 30%-50%. That deviation coincided with a persistence threshold as indicated by a rapid decline in the probability of landscapes supporting viable populations. When we partitioned experimental landscapes into sets of "above" and "below" persistence threshold, habitat arrangement became an important factor in explaining population size below threshold conditions. Regression analysis on below-threshold landscapes using explicit measures of landscape structure (after removing the covariation with habitat amount) indicated that arrangement variables accounted for 33%-39% of the variation in population size, compared to 27%-49% for habitat amount. Thus, habitat arrangement effects became important when species persistence became uncertain due to dispersal mortality.