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Equation 3 · Part 9 · Comparing the Main Approaches to Evolutionary Biology and Ecology

Denominator: 1 + s p_t

pt+1=pt(1+s)1+s ptp_{t+1} = \frac{p_t (1 + s)}{1 + s\, p_t}
1+s pt1 + s\, p_t

What this part means

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

Its job in the formula

1 + s ptp_t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.