Species coexistence in a lattice-structured habitat: Effects of species dispersal and interactions

•We explore the role of spatial structure in species coexistence.•The spatial pattern does not affect coexistence if two species have the same traits.•The spatial pattern may alter coexistence if the effective birth rate is altered.•The different combination of the local interactions and dispersal modes leads to different spatial patterns.

Opinions differ on how the spatial distribution of species over space affects species coexistence. Here, we constructed both mean-field and pair approximation (PA) models to explore the effects of interspecific and intraspecific interactions and dispersal modes on species coexistence. We found that spatial structure resulting from species dispersal traits and neighboring interactions in PA model did not promote coexistence if two species had the same traits, though it might intensify the contact frequency of intraspecific competition. If two species adopt different dispersal modes, the spatial structure in PA would make the coexistence or founder control less likely since it alters the species effective birth rate. This suggests that the spatial distribution caused by neighboring interactions and local dispersal does not affect species coexistence unless it adequately alters the effective birth rate for two species. Besides, we modeled how the initial densities and patterns affected population dynamics and revealed how the final spatial pattern was generated.