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Understanding complex behavioural patterns of organisms observed in nature can be facilitated using mathematical modelling. The conventional paradigm in animal behavior modelling consists of maximisation of some evolutionary fitness function. However, the definition of fitness of an organism or population is generally subjective, and using different criteria can lead us to contradictory model predictions regarding optimal behaviour. Moreover, structuring of natural populations in terms of individual size or developmental stage creates an extra challenge for theoretical modelling. Here we revisit and formalise the definition of evolutionary fitness to describe long-term selection of strategies in deterministic self-replicating systems for generic modelling settings which involve an arbitrary function space of inherited strategies. Then we show how optimal behavioural strategies can be obtained for different developmental stages in a generic von-Foerster stage-structured population model with an arbitrary mortality term. We implement our theoretical framework to explore patterns of optimal diel vertical migration (DVM) of two dominant zooplankton species in the north-eastern Black Sea. We parameterise the model using 7 years of empirical data from 2007-2014 and show that the observed DVM can be explained as the result of a trade-off between depth-dependent metabolic costs for grazers, anoxia zones, available food, and visual predation.

Self-regulation of population dynamics in nutrient-rich (eutrophic) ecosystems has been a fascinating topic for decades in ecological literature. Simple theoretical models predict population oscillations of large amplitudes in such systems, those predictions often being at odds with reality. Plankton communities possess a particular combination of two important properties, making them unique among ecosystems with eutrophication. These are: (i) the existence of a pronounced spatial gradient of the prey growth rate (through light attenuation with depth) and (ii) the presence of fast-moving predator (zooplankton) capable of quick adjustment of grazing load in vertical direction throughout the whole habitat. Surprisingly, the interplay of those factors is rarely taken into account while analysing stability of nutrient-rich plankton communities. In this paper, we construct generic plankton models (based on integro-differential equations) incorporating the light attenuation in the water column as well as food-searching behaviour of zooplankton. We found that the interplay between the two factors would stabilize a system at low species densities even for an 'unlimited' nutrient stock (infinite system's carrying capacity). Different possible scenarios of stabilization have been found. Since both the vertical gradient of light and the active food search by zooplankton in the column are common characteristics of real plankton communities, we suggest that the obtained mechanism of self-regulation is rather generic in nature. We argue that taking into account this mechanism would be important for understanding the dynamics of nutrient-rich low-chlorophyll ocean systems as well as major causes of non-seasonal plankton blooms.