A novel computational approach to reconstructing evolutionary fitness in self-replicating systems

Evolutionary fitness is a fundamental concept, widely utilised in modelling natural selection in self-replicating systems. This concept describes selective advantages of inherited elements in the underlying system. Maximisation of evolutionary fitness is traditionally used to predict the outcome of long-term evolution, in particular, to provide the best behavioural strategy or life-history trait. Deriving evolutionary fitness in theoretical models and in empirical systems has always been a challenge. Here we propose a novel computational approach to reconstructing fitness functions in biological systems, using empirical data under the scenario in which the result of competition and selection may depend on initial conditions. Such situations occur, for example, in systems with cyclic competition (e.g., rock–paper–scissors games), and modelling such scenarios has long been considered as a particularly complicated task. Our computational method combines the usage of empirical data with the implementation of a theoretical model of population dynamics in which each subpopulation uses a particular strategy. Firstly, we apply machine learning to empirical data to determine the relative ranking of competing strategies. Then we reconstruct fitness from data and estimate unknown model parameters by comparing the empirically determined fitness with its theoretical expression from the model. Unlike classical regression-based fitting, we quantify the goodness of fit based on the percentage of correctly reconstructed ranking orders of pairs of strategies. Finally, using the derived theoretical expression for fitness with the estimated parameters, we predict the evolutionarily optimal (winning) strategy. As an insightful biological case study, we derive evolutionarily stable diel vertical migration of zooplankton, when the predator (fish) density is a dynamic variable. Our methodology is generic, and can be applied to estimate fitness-like functions in non-biological systems, such as the optimisation of sales, Internet searches, or scientometrics.