Quantifying Darwin’s postulates • Individuals within species vary. • Some of these variations are heritable. • More offspring are produced than can survive. • Survival and reproduction are nonrandom. • The individuals that survive & reproduce the most are those • with variations that best suit their environment. Quantitative genetics allows us to measure the degree to which variation in a trait is heritable (and therefore can respond to selection). We can also measure the strength of selection. Combining heritability and strength of selection allows us to predict evolutionary change in response to selection.
VP = VG + VE phenotypic variance genetic variance environmental variance mean variance How can we study the genetic basis of quantitative variation? VP = Total variance in the trait (phenotype) VG = variance in the trait that’s due to variation in genes VE = variance in the trait that’s due to variation in the environment This is simply a mathematical way of saying that both genetic and environmental variation can contribute to phenotypic variation.
Requirements for evolution: Heritability Heritability – the degree to which variation in a quantitative trait can be passed from parent to offspring; how well parent’s trait predicts offspring’s trait NOT how much a trait is based on genes or environment, but how much the variation in a trait within a population is based on variation in genes or environment In other words, are the differences in the trait based on a genetic or environmental differences, or both NOT genes for milk production, but for variation in milk production
VP = VG + VE phenotypic variance genetic variance environmental variance mean variance Requirements for evolution: Heritability Broad-sense heritability H2 = VG / VP In words: broad-sense heritability is the fraction of the total variation that can be explained by variation in genes.
VP = VG + VD = VA + VE phenotypic variance dominance genetic variance genetic variance additive genetic variance environmental variance Requirements for evolution: Heritability Narrow-sense heritability h2 = VA / VP What does h2 = 1 mean? h2 = 0? h2 = 0.5?
Estimating narrow-sense heritability Slope ≈ ½ h2 Heritability means that offspring should resemble their parents and relatives offspring one parent midparent = average of trait in mom & dad
Slope ≈ h2 Slope ≈ h2 offspring offspring midparent midparent Slope ≈ ½ h2 Slope ≈ h2 offspring offspring midparent one parent
How can we make sure that the resemblance between relatives is due to shared genes and not due to shared environment? Why is this important to control? How can this be controlled? Common garden experiment: grow several families under the same controlled experiment. Everyone has the same environment. Therefore differences should be genetic.
Requirements for evolution: Selection Mean before selection Mean after selection number of individuals Selection differential body size (or other trait) 5 6 mean trait value of selected individuals mean trait value before selection S = - S = 6 – 5 = 1