Ricker model

The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number a t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation,[1]

$a_{t+1} = a_t e^{r\left(1-\frac{a_t}{k}\right)}.\,$

Here r is interpreted as an intrinsic growth rate and k as the carrying capacity of the environment. The Ricker model was introduced in 1954 by Ricker in the context of stock and recruitment in fisheries.

The model can be used to predict the number of fish that will be present in a fishery.[2][3] Subsequent work has derived the model under other assumptions such as scramble competition[4] or within-year resource limited competition.[5] The Ricker model is a limiting case of the Hassell model[5] which takes the form

$a_{t+1} = k_1 \frac{a_t}{ \left(1+k_2 a_t\right)^c}.$

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