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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>
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| : <math>a_{t+1} = a_t e^{r\left(1-\frac{a_t}{k}\right)}.\,</math>
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| 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]].
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| 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
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| : <math>a_{t+1} = k_1 \frac{a_t}{ \left(1+k_2 a_t\right)^c}. </math>
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| When ''c'' = 1, the Hassell model is simply the [[Beverton–Holt model]].
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| ==See also==
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| * [[Population dynamics of fisheries]]
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| ==Notes==
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| {{reflist}}
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| ==References==
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| * 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.
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| * 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.
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| * 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.
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| * 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}}
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| * 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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| {{Use dmy dates|date=September 2010}}
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| {{DEFAULTSORT:Ricker Model}}
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| [[Category:Demography]]
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