Ricker model
Encyclopedia
The Ricker model, named after Bill Ricker
Bill Ricker
William Edwin Ricker, OC, FRSC is an important founder of fisheries science. He is best known for the Ricker model, which he developed in his studies of stock and recruitment in fisheries. The model can be used to predict the number of fish that will be present in a fishery...

, is a classic discrete population model which gives the expected
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

 number a t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation,


Here r is interpreted as an intrinsic growth rate and k as the carrying capacity
Carrying capacity
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...

 of the environment. The Ricker model was introduced in 1954 by Ricker in the context of stock
Fish stock
Fish stocks are subpopulations of a particular species of fish, for which intrinsic parameters are the only significant factors in determining population dynamics, while extrinsic factors are considered to be insignificant.-The stock concept:All species have geographic limits to their...

 and recruitment in fisheries.

The model can be used to predict the number of fish that will be present in a fishery. Subsequent work has derived the model under other assumptions such as scramble competition
Scramble competition
In general terms, scramble competition is a type of competition in which equally rationed yet perpetually limited resources within an environment result in decreased survival rates for all competitors...

 or within-year resource limited competition. The Ricker model is a limiting case of the Hassell model which takes the form


When c = 1, the Hassell model is simply the Beverton–Holt model.
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