The shape of a population
Plot the heights of ten thousand adults and a familiar shape emerges: a symmetric hump, fat in the middle, tapering on both sides. This is the normal distribution, or bell curve. It shows up again and again for quantitative traits for a deep reason — when a value is the sum of many small independent contributions, the totals naturally pile up near the average and become rare at the extremes.
Two numbers summarise the curve. The mean marks its centre — the typical value. The variance (and its square root, the standard deviation) measures its width — how spread out individuals are. A narrow curve means people are similar; a wide one means lots of variation. For quantitative genetics, that width is the star of the show, because variation is exactly what we want to explain.
Splitting the variance
The total spread of a trait in a population is its phenotypic variance, written V_P. The central move in quantitative genetics is to split that spread into the part caused by genetic differences (V_G) and the part caused by environmental differences (V_E). In its simplest form: V_P = V_G + V_E. Everything that follows — heritability, twin studies, breeding — is built on this one decomposition.
Phenotypic variance (the width of the bell curve):
V_P = V_G + V_E
| | |
total genetic environmental
spread spread spread
Example, height in a population:
V_P = 50 (cm^2)
V_G = 40
V_E = 10
-> genetic differences account for 40/50 = 80% of the spread.
Note: this is a property of the POPULATION + ENVIRONMENT,
not a fixed fact about the trait itself.Notice the subtlety: V_G and V_E describe differences within a particular population in a particular environment. Change the environment — say, fix everyone's nutrition — and V_E shrinks, so the same trait can have a different breakdown in a different setting. This dependence is why gene–environment interaction keeps reappearing later in this track, and why a single percentage never tells the whole story.