Moment equations for simplifying dynamic spatial point processes work for models with locally linear interactions and movement rates. That is a major limitation to the applicability of moment equations, because most ecological interactions of interest involve nonlinear functional forms to local densities. Several authors suggested that Taylor expansions around expected densities might be useful to overcome these limitations, and we report on a few advances in that direction. We describe how Taylor expansions transform the equations, show numerical results, and highlight key areas where progress could be made.

moment equations; point process; Taylor expansion; nonlinearities; ecology;