Revealing Evolutionarily Optimal Strategies in Self-Reproducing Systems via a New Computational Approach

Abstract

Modelling the evolution of complex life history traits and behavioural patterns observed in the natural world is a challenging task. Here, we develop a novel computational method to obtain evolutionarily optimal life history traits/behavioural patterns in population models with a strong inheritance. The new method is based on the reconstruction of evolutionary fitness using underlying equations for population dynamics and it can be applied to self-reproducing systems (including complicated age-structured models), where fitness does not depend on initial conditions, however, it can be extended to some frequency-dependent cases. The technique provides us with a tool to efficiently explore both scalar-valued and function-valued traits with any required accuracy. Moreover, the method 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 herbivorous zooplankton in the vertical water column which is a widespread phenomenon in both oceans and lakes, generally considered to be the largest synchronised movement of biomass on Earth. We reveal optimal trajectories of daily vertical motion of zooplankton grazers in the water column depending on the presence of food and predators. Unlike previous studies, we explore both scenarios of DVM with static and dynamic predators. We find that the optimal pattern of DVM drastically changes in the presence of dynamic predation. Namely, with an increase in the amount of food available for zooplankton grazers, the amplitude of DVM progressively increases, whereas for static predators DVM would abruptly cease. Electronic supplementary materialThe online version of this article (10.1007/s11538-019-00663-4) contains supplementary material, which is available to authorized users.

Mathematical modelling evolutionarily stable behavior of zooplankton with state constraints

“…The article continues the series of author's works devoted to modeling zooplankton behavioral strategies and creating a package of applied programs to support such research [2][3][4][5][6]. An essential feature of this work is the inclusion in the mathematical model of state constraints on the strategy of behavior, which represent the most difficult case for the solution of the optimal control problem used to analyze the model.…”

Modelling Biological Evolution: Developing Novel Approaches

“…Kuzenkov and Morozov (2019) then obtain expressions for evolutionary fitness for various models including those with age structuring and delay, which was previously a challenge. The related study by Sandhu et al (2019) extends the theoretical ideas of Kuzenkov and Morozov (2019) and proposes a novel computational method to determine evolutionarily optimal life-history traits in selfreplicating systems with strong inheritance. The need for an efficient computational method comes from the fact that in many cases it is hard to obtain an analytical expression for evolutionary fitness for an arbitrary model (Morozov and Kuzenkov 2016).…”

“…The next contributions to the issue, by Kuzenkov and Morozov (2019) and Sandhu et al (2019), aim to revisit mathematical approaches to modelling natural selection in generic self-replicating systems with strong inheritance. The theoretical study by Kuzenkov and Morozov (2019) suggests a novel framework to model evolution in an arbitrary function space of inherited strategies (applicable to model both scalarvalued and function-valued traits).…”

“…The need for an efficient computational method comes from the fact that in many cases it is hard to obtain an analytical expression for evolutionary fitness for an arbitrary model (Morozov and Kuzenkov 2016). The main idea of the method of Sandhu et al (2019) is the reconstruction of evolutionary fitness using the underlying model equations of population dynamics. Interestingly, under some assumptions, the computational method can be used even in the case where we only have population dynamics time series, i.e.…”

“…without the underlying model. As an insightful biological example, Sandhu et al (2019) explore optimal patterns of diel vertical migration (DVM) of zooplankton in the water column, which is generally considered to be the largest synchronised movement of biomass on Earth (Hays 2003). Unlike some previous studies on the topic, the authors consider both scenarios of DVM with static and dynamic predators.…”