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pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t(1+s)}{1 + s\,p_t}

Why this formula appears here

A basic case illustrates the kind of prediction this apparatus makes possible. For a single locus with two alleles under simple directional selection with selection coefficient s favoring an allele at frequency p , one classical discrete-generation recursion is pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t(1+s)}{1 + s\,p_t}. This is a deliberately simplified model — haploid, one locus, constant s , no drift, no linkage — and real populations violate several of its assumptions routinely. Its value is not as a literal forecast of any specific population but as a baseline against which departures (frequency-dependent selection, epistasis, drift-dominated dynamics in small populations) can be identified and measured.

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1+s pt1 + s\,p_t

Denominator: 1 + sp_t

The complete quantity below the fraction bar; it must be nonzero for this division.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (2)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

pt+1=pt(1+s)1+s pt.p_{t+1} = \frac{p_t(1+s)}{1 + s\,p_t}.

Equation 6 · Biology

From Origins to Frontier: A History of Evolutionary Biology and Ecology

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A basic case illustrates the kind of prediction this apparatus makes possible. For a single locus with two alleles under simple directional selection with selection coefficient s favoring an allele at frequency p , one classical discrete-generation recursion is pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t(1+s)}{1 + s\,p_t}. This is a deliberately simplified model — haploid, one locus, constant s , no drift, no linkage — and real populations violate several of its assumptions routinely. Its value is not as a literal forecast of any specific population but as a baseline against which departures (frequency-dependent selection, epistasis, drift-dominated dynamics in small populations) can be identified and measured.

Meanings in this article

Equation guide → · Article →
pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t (1 + s)}{1 + s\, p_t}

Equation 3 · Biology

Comparing the Main Approaches to Evolutionary Biology and Ecology

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A basic model of directional selection acting on a single locus, of the kind both the field and laboratory results above are ultimately interpreted against, describes how an allele’s frequency changes by one generation under a constant selection coefficient s favoring the allele at frequency p : pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t (1 + s)}{1 + s\, p_t}. The equation exposes the model’s real content: selection is strongest while the favored allele is at intermediate frequency, where pt(1−pt)p_t(1-p_t) is largest, and weakens automatically as the allele nears fixation or loss, purely from the algebra of the denominator — a pattern of decelerating change that shows up empirically in both the Grants’ beak-size tracking and the LTEE’s…

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