The study of spatiotemporal ecological point processes
Ecological spatial patterns are structured by a multiplicity of processes acting over a wide range of scales. The goal of spatial ecology is to disentangle the signature of processes that act at different and similar scales on observed spatial patterns. These processes may include dispersal, local interactions (conspecific and heterospecific), natural disturbances, habitat association and environmental filtering. To understand how some of these processes act on spatial patterns we need two fundamental tools. First we need to build spatial explicit models which are analytically tractable and able to reproduce expected patterns starting from basic ecological principles. Second we need robust statistics that can link the observed patterns to theoretical results.
We derive exact and approximate analytical solutions for the second order structures and they dynamic under different individual-based, spatially explicit models for sessile organisms (e.g., plants) using moment equations. We consider single species and multispecies models with local interactions, dispersal limitations, and natural enemy. We link these theoretical results to estimates of second order structure using wavelet transform.
The methods are demonstrated through numerical examples and case studies of several tropical tree species on Barro Colorado Island, Panama where multitemporal censuses were available.
We found that at small scales (2-30 m) most abundant species are less aggregated than less abundant, but at intermediate scales (30-100 m) most abundant species are more aggregated. The rate of dissipation of spatial structures was also strongly correlated with abundance and the ability to recruit in shade, with most abundant and shade tolerant being more spatial persistent.