Towards constructing a mathematically rigorous framework for modelling evolutionary fitness

Research Centre: Department of Mathematics

Abstract:

Modelling evolution of complex life traits and behavioural patterns observed in natural world is a challenging task. Currently, there exist various modelling frameworks to reveal evolutionarily optimal behaviours. These involve optimisation of some pre-assigned criteria (e.g. the reproductive value of an individual), various game-theoretical approaches including adaptive dynamics, genetic algorithms of evolutionary modelling and some others. A particular challenge arises in the situation where we need to model a life trait or behavioural pattern which is described by a continuous function: this is known as function-valued trait. Here we introduce a novel theoretical approach of finding the evolutionarily optimal strategies in a generic population model with inheritance based on reconstruction of an underlying fitness function (which we refer to as the generalised fitness). The method uses the idea of ranking mutually competing strategies/behaviours according to their survival success in the presence of each other. We claim that for any system, where a generalised fitness exists, the method should provide us with a tool to efficiently explore both scalar-valued and function-valued traits with any required accuracy. In the talk, several examples will be provided of how we can analytically derive a generalised fitness for population models with age/stage structuring. Then a powerful computational method will be introduced to find the generalised fitness for an arbitrary population model with inheritance. Interestingly, the technique can be implemented even in the case where we ignore the underlying model equations and only have population dynamics time series. As a meaningful ecological case study, we explore optimal strategies of Diel Vertical Migration (DVM) of zooplankton in the vertical water column which is a widespread phenomenon in both oceans and lakes, and is generally considered to be the largest synchronized movement of biomass on Earth. We are interested in revealing the optimal trajectory of daily vertical motion of zooplankton grazers (a function-valued trait) depending on the presence of food and predators.