STOCHASTIC DYNAMICS OF ECOSYSTEMS

Although the study of an ecological system may appear very complex, recent studies have shown that, from a macroscopic point of view, the dynamics of systems such as tropical forests can be described by means of relatively simple models. Within Hubble’s neutral theory, the evolution of the species that populate a forest can be modeled with a stochastic linear birth-death process. This model provides the basis for probing the dynamical behavior of a forest and determining the parameters that characterize the system. However, obtaining analytical results starting from a stochastic model is not always easy. A possible approach involves the Doi-Peliti formalism: the birth and death of a tree are treated as the creation and annihilation of a bosonic particle. Within this formalism, which is reminiscent of second quantization one, it is possible to make use of methods of quantum physics to obtain analytical solutions and give a new interesting representation of the time evolution of the system. The aim of this thesis is to use the Doi-Peliti formalism in the study of a birth-death model in order to describe the dynamical evolution of tropical forests, highlighting the advantages and critical aspects of this approach.