Modelling population dynamics is of paramount importance in many fields of applications. In ecology, it is a matter to understand the dynamics and life history of various species across different environments. Indeed, environmental changes can generate rapid changes on the composition of a given population, its length, its phenotypic trait or also its genotype distribution. In demography, we are generally interested in predicting human life-span as well as the population structure with critical implication in pension systems and public policy decision making. However, these dynamics raise a number of problems to which historical experience offers no answers. This research proposal considers in some integrated way the modelling of populations growth and biodiversity prediction using cutting edge stochastic models with a specific focus on ecological problems. First, we will consider applications of Taylor's law. We will comprehensively introduce a new variant related to self-normalisation issue based on weak dependence conditions. This will consider some of the stylised facts encountered when working with real-world datasets.
Besides, we will investigate challenges facing marine ecology, especially those related to changing environment and its impact on the marine species. We will introduce new modelling frameworks for populations dynamics incorporating, for instance, covariates and we will investigate their statistical properties. These problems involve isotonic models parsimony in the presence of non-linearity and non-stationarity. Causality relationships will be important too for the synthetic approach of data streams.
To model the expansion of pandemics is also a highly challenging problem. Finally, applications will be devoted, among others, to the effects of climate change on coral reefs, the modelling of abundances in ecology and the prediction of marine ecosystems.