Understanding population growth at the local scale is essential for understanding ecological dynamics and guiding conservation actions. In this work, we present a methodological approach to predict the variation of abundance at a small scale.

We model population evolution as a spatial marked point process governed by birth and death functions, incorporating interactions between individuals and with environmental factors (climatic, landscape, etc.). A central challenge in this framework lies in the spatial dependence of these interactions and the  fact that the observations are sometimes the result of a random process. We introduce estimators of the birth and death kernels and, by leveraging stabilization theory — which assumes interactions occur at a variable but local scale — we aim to demonstrate convergence and asymptotic normality properties of these estimators, ensuring robust local prediction of abundance variations.

This method is then applied to the analysis of data from the French Common Birds Monitoring Program (STOC).