The Ricker model, named after
Bill Ricker William Edwin Ricker, (August 11, 1908 – September 8, 2001) 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 t ...
, is a classic discrete
population model A population model is a type of mathematical model that is applied to the study of population dynamics.
Rationale
Models allow a better understanding of how complex interactions and processes work. Modeling of dynamic interactions in nature can ...
which gives the expected number ''N''
''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
The carrying capacity of an environment is the maximum population size of a biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available. The carrying capacity is defined as t ...
of the environment. The Ricker model was introduced in 1954 by Ricker in the context of
stock
In finance, stock (also capital stock) consists of all the shares by which ownership of a corporation or company is divided.Longman Business English Dictionary: "stock - ''especially AmE'' one of the shares into which ownership of a company ...
and recruitment in
fisheries
Fishery can mean either the enterprise of raising or harvesting fish and other aquatic life; or more commonly, the site where such enterprise takes place ( a.k.a. fishing ground). Commercial fisheries include wild fisheries and fish farms, both ...
.
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
In ecology, scramble competition (or complete symmetric competition or exploitation competition) refers to a situation in which a resource is accessible to all competitors (that is, it is not monopolizable by an individual or group). However, sinc ...
,
[Brännström and Sumpter(2005)] within-year resource limited competition
or even as the outcome of source-sink Malthusian patches linked by density-dependent dispersal.
[Bravo de la Parra et al (2013)] The Ricker model is a
limiting case of the Hassell model
[Geritz and Kisdi (2004)] which takes the form
:
When ''c'' = 1, the Hassell model is simply the
Beverton–Holt model
The Beverton–Holt model is a classic discrete-time population model which gives the expected number ''n'' ''t''+1 (or density) of individuals in generation ''t'' + 1 as a function of the number of individuals in the previous gen ...
.
See also
*
Population dynamics of fisheries
A fishery is an area with an associated fish or aquatic population which is harvested for its commercial or recreational value. Fisheries can be wild or farmed. Population dynamics describes the ways in which a given population grows and shrinks o ...
Notes
References
* Brännström A and Sumpter DJ (2005
"The role of competition and clustering in population dynamics"''Proc Biol Sci.'', 272(1576): 2065–72.
* Bravo de la Parra, R., Marvá, M., Sánchez, E. and Sanz, L. (2013
Reduction of discrete dynamical systems with applications to dynamics population models ''Math Model Nat Phenom''. 8(6). pp 107–129
* 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.
* Noakes, David L. G. (Ed.) (2006
''Bill Ricker: an appreciation''シュプリンガー・ジャパン株式会社, .
* Ricker, W. E. (1954
Stock and Recruitment''Journal of the Fisheries Research Board of Canada'', 11(5): 559–623.
* Ricker, W. E. (1975) Computation and Interpretation of Biological Statistics of Fish Populations. Bulletin of the Fisheries Research Board of Canada, No 119. Ottawa.
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Demography
Stochastic models