Effective Population Size

Effective population size asks how a real population behaves rather than how many individuals it contains. Formally it is the size of an idealised population — equal sex ratio, random mating, no selection — that would lose genetic variation at the same rate as the one in front of you. It is almost always smaller than the census count, sometimes dramatically.

The sex-ratio version makes the point sharply. Ten pollen parents and ninety seed parents is a hundred plants, but $N_e = 4 \times 10 \times 90 / 100 = 36$. The rarer sex dominates the result, and adding more of the commoner one barely helps: raising the females to nine hundred with ten males still gives only 39.6. The ceiling is four times the rarer sex, whatever you do with the other.

The consequence is inbreeding at a rate of $1/(2N_e)$ per generation, accumulating whether anyone intends it or not. Conservation and germplasm guidance generally wants $N_e$ above 50 to keep short-term inbreeding tolerable and above 500 to retain enough variation for long-term adaptation. Seed regeneration protocols for genebanks are written around exactly this arithmetic, because regenerating an accession from too few plants quietly destroys the diversity the genebank exists to hold.

Sex ratio is only one of several ways $N_e$ collapses. Unequal family contributions, fluctuating population size across generations — where the harmonic mean dominates, so one bad year outweighs several good ones — and overlapping generations all push it down further. A breeding nursery that keeps a hundred plants but takes most of its seed from a handful of favourites has a far smaller effective size than its head count suggests.