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The '''Ricker model''', named after [[Bill Ricker]], is a classic discrete population model which gives the [[expected value|expected]] number ''a''<sub> ''t''+1</sub> (or density) of individuals in generation ''t'' + 1 as a function of the number of individuals in the previous generation,<ref>Ricker (1954)</ref> | |||
: <math>a_{t+1} = a_t e^{r\left(1-\frac{a_t}{k}\right)}.\,</math> | |||
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 [[Fish stock|stock]] and recruitment in [[fisheries]]. | |||
The model can be used to predict the number of fish that will be present in a fishery.<ref>de Vries et al.</ref><ref>Marland</ref> Subsequent work has derived the model under other assumptions such as [[scramble competition]]<ref>Brännström and Sumpter(2005)</ref> or within-year resource limited competition.<ref name=Geritz /> The Ricker model is a [[limiting case]] of the Hassell model<ref name=Geritz>Geritz and Kisdi (2004)</ref> which takes the form | |||
: <math>a_{t+1} = k_1 \frac{a_t}{ \left(1+k_2 a_t\right)^c}. </math> | |||
When ''c'' = 1, the Hassell model is simply the [[Beverton–Holt model]]. | |||
==See also== | |||
* [[Population dynamics of fisheries]] | |||
==Notes== | |||
{{reflist}} | |||
==References== | |||
* Brännström A and Sumpter DJ (2005) [http://www.math.uu.se/~david/web/BrannstromSumpter05a.pdf "The role of competition and clustering in population dynamics"] ''Proc Biol Sci.'', '''272'''(1576): 2065–72. | |||
* Geritz SA and Kisdi E (2004). [http://theory.bio.uu.nl/rdb/te/pdf/Geritz_jtb04.pdf "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) [http://books.google.co.nz/books?id=8aYNrPg5KhgC&pg=PA26&dq=Ricker+%22+Stock+and+recruitment.%22&hl=en&ei=CN8tTpPDEO-HmQXU-uTlBg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC0Q6AEwAQ#v=onepage&q=Ricker%20%22%20Stock%20and%20recruitment.%22&f=false ''Bill Ricker: an appreciation''] シュプリンガー・ジャパン株式会社, ISBN 978-1-4020-4707-7. | |||
* Ricker, W. E. (1954) [http://www.nrcresearchpress.com/doi/abs/10.1139/f54-039 Stock and Recruitment] ''Journal of the Fisheries Research Board of Canada'', '''11'''(5): 559–623. {{doi|10.1139/f54-039}} | |||
* Ricker, W E (1958) ''Handbook of computation for biological statistics of fish populations''. Bulletin 119 of the Fisheries Resource Board, Canada, Ottawa. | |||
{{Use dmy dates|date=September 2010}} | |||
{{DEFAULTSORT:Ricker Model}} | |||
[[Category:Demography]] | |||
Revision as of 20:55, 3 February 2014
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]
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
When c = 1, the Hassell model is simply the Beverton–Holt model.
See also
Notes
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References
- Brännström A and Sumpter DJ (2005) "The role of competition and clustering in population dynamics" Proc Biol Sci., 272(1576): 2065–72.
- 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, ISBN 978-1-4020-4707-7.
- Ricker, W. E. (1954) Stock and Recruitment Journal of the Fisheries Research Board of Canada, 11(5): 559–623. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- Ricker, W E (1958) Handbook of computation for biological statistics of fish populations. Bulletin 119 of the Fisheries Resource Board, Canada, Ottawa.
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