Research in population dynamics has a long history dating back to almost one thousand year ago with Fibonacci modeling of rabbits population. Nevertheless there are still several open issues in the research of ecological population dynamics and the current loss of earth biodiversity makes this research field still relevant today more than ever.
From a theoretical point of view, an emerging alternative approach to niche-based multi-species deterministic modelling is the Neutral Theory (NT) of Biodiversity. The NT is an ecological theory within which organisms of a community have identical per-capita probabilities of giving birth, dying, migrating, and speciating, regardless of the species they belong to. An important example of neutral model is the Voter model, a non-equlibrium spin model originally used describe opinion spreading dynamics. The common interpretation in Ecology, is that the values of the spins represent different species competing for space and resources. However, an important limitation of Voter model in ecology is that it does not consider explicitly species interactions (e.g. mutualism).
We will present a theoretical framework where, starting from a Voter model-like microscopic stochastic modelling, we add cooperative interactions among species. Reconciling apparently contrasting observations and results of previous studies, we show that in our model ecosystem cooperation promotes biodiversity and system complexity increases its stability.