Group members involved: Stefan Geritz, Mats Gyllenberg, Eva Kisdi

Financial support: Finnish Academy of Sciences

Link to adaptive dynamics literature

Adaptive dynamics (AD) is a mathematical theory that explicitly links population dynamics to long-term evolution driven by mutation and natural selection. It provides methods of model formulation, methods of model analysis and mathematical theorems that relate phenomena on an evolutionary time scale to processes and structures defined in ecological and population dynamical terms. AD is a new but rapidly developing theory that poses various interesting and mathematically challenging problems. From an applications point of view, a great strength of adaptive dynamics is its capability to model evolution driven by complex ecological interactions. AD is being applied by a growing number of researchers to a wide variety of concrete ecological-evolutionary problems. (Click here for references to articles on the theory and applications of AD.)

AD is about the evolution of strategies. A strategy is a one- or multi-dimensional parameterization of an individual's ecologically relevant morphology or behavior that is inherited by the offspring. Now and then, however, a new strategy appears as a consequence of a mutation. A sequence of strategies generated by successive mutations in a line of direct descent we call a lineage of strategies.

AD incorporates processes on two different time scales: a fast ecological time scale and a slow evolutionary time scale. The ecological time scale concerns questions such as: Which are the positive attractors of a population of a given set of strategies? Which new mutant strategies could invade a given population at a given positive attractor? What would be the outcome of such an invasion event in terms of which strategies remain and which strategies are ousted as the population converges again to a population dynamical attractor?

On the evolutionary time scale adaptive dynamics addresses questions such as: How does the set of strategies present in a population change as a consequence of many successive invasion events and the possible subsequent elimination of strategies already present? What is the limiting behavior of such sequences of sets? Possible long-term patterns emerging in AD models include directional evolution within lineages of strategies, evolutionary cycles within lineages, extinction of individual lineages, evolutionary branching (i.e., the splitting of a given lineage into two or more different lineages and their subsequent gradual divergence) as well as combinations such as branching-extinction cycles. In particular, the discovery of evolutionary branching has renewed interest in the possibility of sympatric speciation and has stimulated many new publications on this topic.

AD integrates and extends various notions and techniques from the theory of dynamical systems, population dynamics and evolutionary game theory into a single mathematical framework. The application of AD to genetically explicit models is a more recent development. In the more typical applications, realism at the level of ecological interactions is “bought” at the cost of realism at the level of genetic detail. In population genetics, for example, the situation is reversed. In this sense, AD and population genetics are complementary. Most general results in adaptive dynamics so far concern the evolution of one-dimensional strategies in autonomous single-species systems of unstructured populations. Results for specific applications often reach much further, however. Present research revolves largely around generalizations to higher-dimensional strategies in multi-species system, structured populations and metapopulations.