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,

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

Here r is interpreted as an intrinsic growth rate and k as the carrying capacity of the environment. The Ricker model was introduced in the context of the fisheries by Ricker (1954) (wrong reference - check the 1958 book). Subsequent work has derived the model under other assumptions such as scramble competition (e.g. Brännström & Sumpter 2005) or within-year resource limited competition (Geritz and Kisdi 2004). The Ricker model is a limiting case of the Hassell model (Brännström & Sumpter 2005) 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.

See also

• Population dynamics of fisheries

References

• Brännström A and Sumpter DJ (2005) The role of competition and clustering in population dynamics. Proc Biol Sci., Oct 7 272(1576):2065–72 [1]
• Geritz SA and Kisdi E (2004). On the mechanistic underpinning of discrete-time population models with complex dynamics. J Theor Biol., 21 May 2004;228(2):261–9.
• Ricker, WE (1954). Stock and recruitment. Journal of the Fisheries Research Board of Canada.

• Ricker, W E (1958) Handbook of computation for biological statistics of fish populations. Bulletin 119 of the Fisheries Resource Board, Canada, Ottawa.