Spatial Representations of Habitat in Competition‐Colonization Models

Ecological models with species differentiated by competition and colonization traits have shown that some extant species in remnants of habitat go extinct after a lag. These models have, however, analyzed landscape patterns in two phases: habitat and nonhabitat. Here, the consequences of representing landscape patterns as a continuous surface of habitat quality versus as two categories are examined. With a continuous representation, the amount of habitat is constant at 100 percent, but its quality can vary from 0 to 1; with a binary representation the amount of habitat varies. Continuous landscapes with mean habitat qualities of .8, .5, and .2 are compared to binary landscapes with the proportion of habitat at .8, .5, and .2. The model projections of the abundances of species differ substantially between the two‐phase and continuous representations. The effects of decreased habitat quality with no decrease in abundance exceed the effects of decreased habitat abundance. Differences between the projections for the two representations increase as the proportion of habitat and habitat quality decrease. Increases in the variance of habitat quality within the continuous representations decrease extinctions. The basic insight of earlier models, that superior competitors are at a long‐term disadvantage in remnant habitat, is magnified with a continuous representation. As in the binary models, the disadvantage is lessened if the spatial variation in habitat quality is smoother, but pattern matters less in continuous landscapes. The continuous representation shows that lagged extinction is relevant to cases of habitat deterioration.