The pivotal role of evolutionary theory in life sciences derives from its capability to provide causal explanations for phenomena that are highly improbable in the physicochemical sense. Yet, until recently, many facts in biology could not be accounted for in the light of evolution. Just as physicists for a long time ignored the presence of chaos, these phenomena were basically not perceived by biologists.
Evolution is due to the invasion and establishment of mutational innovations. This establishment changes the parameters and structure of the very population-dynamical systems the innovation took place in. Adaptive dynamics is a novel class of stochastic dynamical systems specially designed to describe such changes. The adaptive dynamic approach provides a rigorous and coherent mathematical framework that links the interactions of individuals through the dynamics of populations (made up of individuals) to the evolution of communities (made up of populations). To encompass the effects of evolutionary innovations, it allows, for the first time, for the simultaneous analysis of changes in population sizes and population traits. This approach captures the process of self-organization that enables complex systems to adapt to their environment.
The research team has as its primary objective the development and application of innovative mathematical tools for the analysis of biological adaptive systems, in close association with experimental testing.
While the basic theory of adaptive dynamics is in place, it will still benefit from rigorous mathematical advances. Increasingly sophisticated explorations of this theory's structure will be valuable, and additional mathematical tools that bridge the axiomatic theory to possible applications must be developed.
At present the theory allows for a number of general predictions, and provides various tools which can be applied to specific biological systems.