Equation 1 · Darwin's Finches: The Beak the Grants Measured for Forty Years
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol R
the response: the amount the population’s mean should shift in the next generation, if the difference between survivors and non-survivors was genetic rather than purely environmental.
Symbol S
the selection differential actually measured on the population in one generation, is the trait’s heritability.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Heritability is what turns a measured selection differential into a testable prediction, through the simplest quantitative-genetics identity in the field, the breeder’s equation: . where S is the selection differential actually measured on the population in one generation, is the trait’s heritability, and R is the response: the amount the population’s mean should shift in the next generation, if the difference between survivors and non-survivors was genetic rather than purely environmental. Grant and Grant ran exactly this check on their own data, comparing the mean of a trait before a selection episode with the mean of the same trait in the following generation. The…
Read the full surrounding passage
Heritability is what turns a measured selection differential into a testable prediction, through the simplest quantitative-genetics identity in the field, the breeder’s equation: . where S is the selection differential actually measured on the population in one generation, is the trait’s heritability, and R is the response: the amount the population’s mean should shift in the next generation, if the difference between survivors and non-survivors was genetic rather than purely environmental. Grant and Grant ran exactly this check on their own data, comparing the mean of a trait before a selection episode with the mean of the same trait in the following generation. The two independent beak traits, size and shape, evolved in the direction and close to the magnitude the equation predicted, with predicted and observed responses correlated at r = 0.832 across ten such episodes [ 2 ] . The equation is not a metaphor for what happened on Daphne Major. It is the arithmetic the team ran, in real time, against birds they had already caught and released.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to Darwin's Finches: The Beak the Grants Measured for Forty Years