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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 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 Lotka–Volterra predator-prey model makes a number of assumptions about the environment and biology of the predator and prey populations: [5] The prey population finds ample food at all times. The food supply of the predator population depends entirely on the size of the prey population.
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.
Anti-predator adaptation in action: the kitefin shark (a–c) and the Atlantic wreckfish (d–f) attempt to prey on hagfishes. First, the predators approach their potential prey. Predators bite or try to swallow the hagfishes, but the hagfishes have already projected jets of slime (arrows) into the predators' mouths.
In the 1930s Alexander Nicholson and Victor Bailey developed a model to describe the population dynamics of a coupled predator–prey system. The model assumes that predators search for prey at random, and that both predators and prey are assumed to be distributed in a non-contiguous ("clumped") fashion in the environment. [30]
The theory behind choice modelling was developed independently by economists and mathematical psychologists. The origins of choice modelling can be traced to Thurstone's research into food preferences in the 1920s and to random utility theory. [4]
The model is defined in discrete time. It is usually expressed as [1] [2] + = + = with H the population size of the host, P the population size of the parasitoid, k the reproductive rate of the host, a the searching efficiency of the parasitoid, and c the average number of viable eggs that a parasitoid lays on a single host.