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Equation 3 · Part 8 · Comparing the Main Approaches to Evolutionary Biology and Ecology

Numerator: p_t (1 + s)

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

ptp_t (1 + s) occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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