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The Ricker model is a mathematical model used in population dynamics to describe the relationship between the number of offspring produced by a population and the size of the parent population. It is a type of density-dependent model, meaning that the growth rate of the population is influenced by its own density.

The core of the Ricker model is a recurrence relation: Nt+1 = Nt * exp(r * (1 - Nt/K)). Here, Nt is the population size at time t, Nt+1 is the population size at the next time step, r is the intrinsic rate of increase, and K is the carrying capacity of the environment. The exponential term represents the reproductive rate, which is reduced as the population size approaches the carrying capacity.

One of the key features of the Ricker model is its ability to exhibit complex dynamics, including stable equilibrium, periodic oscillations, and chaotic behavior, depending on the values of r and K. This makes it a valuable tool for studying population fluctuations and the conditions that can lead to population collapse or boom-bust cycles. The model is widely used in fisheries management, wildlife conservation, and ecological research to predict population trends and assess the impact of various factors on population viability. Its simplicity and ability to generate realistic population dynamics have made it a cornerstone of theoretical ecology.