Spatiotemporal population distributions and their implications for species coexistence in a variable environment

A population experiences environmental variation both directly, through effects on life history parameters such as fecundity, and indirectly, through effects on the population distributions of competitors and thus on the distribution of competition. Which spatial and temporal scales of environmental variation most influence the coexistence of two species thus depends in part on the degree to which the resident population responds to different scales of variation. In this paper, I calculate an approximation for a spatiotemporal population distribution as the result of a filter function convolved with the environmental variation. I find that there is no straightforward connection between spatial or temporal scales inherent to an organism's life history, such as mean lifetime or dispersal distance, and the population's sensitivity to variation at different scales. Rather, life history traits interact sensitively with the way environmental variation affects the organism. I comment on the implications for variation-mediated coexistence.