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The Kolmogorov model addresses a limitation of the Volterra equations by imposing self-limiting growth in prey populations, preventing unrealistic exponential growth scenarios. It also provides a predictive model for the qualitative behavior of predator-prey systems without requiring explicit functional forms for the interaction terms. [5]
The optimal diet model also predicts that different types of animals should adopt different diets based on variations in search time. This idea is an extension of the model of prey choice that was discussed above. The equation, E 2 /h 2 > E 1 /(h 1 +S 1), can be rearranged to give: S 1 > [(E 1 h 2)/E 2] – h 1.
The prey are assumed to have an unlimited food supply and to reproduce exponentially, unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation on the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy.
Prey switching is frequency-dependent predation, where the predator preferentially consumes the most common type of prey. The phenomenon has also been described as apostatic selection , however the two terms are generally used to describe different parts of the same phenomenon.
The match/mismatch hypothesis (MMH) was first described by David Cushing. [1] [2] The MMH "seeks to explain recruitment variation in a population by means of the relation between its phenology—the timing of seasonal activities such as flowering or breeding—and that of species at the immediate lower level". [3]
Aggressive mimicry compared to a defensive form, Batesian mimicry.The mechanism is often called "Wolf in sheep's clothing".The model for an aggressive mimic can be a harmless species, in which case the 3 roles are separate, or the model can be the prey itself, in which case there are only 2 species involved.
The marginal value theorem (MVT) is an optimality model that usually describes the behavior of an optimally foraging individual in a system where resources (often food) are located in discrete patches separated by areas with no resources. Due to the resource-free space, animals must spend time traveling between patches.
Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differential equations to model behaviour. Population dynamics is also closely related to other mathematical biology fields such as epidemiology, and also uses techniques from evolutionary game theory in its modelling.