Small Numbers, Large Consequences

Eight identical populations, one hundred generations, nothing selecting

Every population below starts at the same allele frequency and faces no selection at all. Each generation, the alleles that make it into the next one are drawn at random from the ones present. That sampling is the whole mechanism — and it is enough.

Average of all 200 populations—

How far a population typically strays—

Fixed or lost by generation 100—

Variation still left—

The same four sizes, side by side

Population size	Average final frequency	Spread of outcomes	Fixed or lost	Variation left

What genetic drift is, and what it is not

The first column of the table is the point most often missed. Drift is not a weak version of selection and it does not push an allele anywhere: averaged over two hundred populations the frequency has not moved at any size. What changes with population size is not where a population ends up but how far it can get — and in a small population it can get all the way.

Checking the simulation against the standard prediction

Population genetics predicts that the variation held by a population under drift should fall by a factor of (1 − 1/2N) every generation. The simulation was never given that formula — it draws alleles at random and counts what it gets.

Population size	Variation left, simulated	Variation left, predicted

A population with four alleles, and something that goes badly wrong

The source population holds four alleles at this locus, one of them rare. A crash leaves a handful of survivors, chosen entirely at random — nothing about any allele makes its carriers more or less likely to survive. The left-hand bars are the source population; the right-hand ones are what a single crash of that severity actually left behind.

Survivors—

Alleles still present, on average—

Crashes that lost the rare allele—

Crashes that lost the commonest—

The same sampling, told as a founding

Now nothing goes wrong at all. A dozen individuals leave the source population and settle somewhere new. Their allele frequencies — whatever they happen to be — become the frequencies of everyone descended from them.

Outcome for the rare allele	Share of foundings

Bottleneck and founder effect, side by side

Why this is the answer to “why is that disorder so common here?”

A rare recessive disorder found in one in four thousand people worldwide can be found in one in fifty on a small island, and nothing about the island needs to favor it. If one of the original settlers happened to carry the allele, its frequency in that founding group was set by chance at a value it could never have reached by selection — and with little immigration since, that frequency has simply stayed.

Forty populations, one process, no labels

Each line is one population, all starting at the same frequency, all run for sixty generations. One of drift, selection and gene flow is acting. Look at a single line and then at all forty.

Average endpoint—

Spread of endpoints—

Populations that rose—

Range of endpoints—

Gene flow, on its own

Two populations, one at 0.90 and one at 0.10, exchanging some fraction of their members each generation. This is the only process on this page that makes populations more alike rather than less.

Migration rate	Difference after 60 generations	Fraction of the original difference left

Why one population cannot tell you which process acted

The one process that changes no allele frequencies at all

Non-random mating — here, individuals preferring partners of their own type. Watch the allele frequency column and the genotype columns separately.

Generation	Allele frequency p	AA	Aa	aa	Aa if mating were random

All five processes, and what each one does

Process	Changes allele frequencies?	Creates new variation?	Direction

How slow mutation actually is

Population size	New copies expected each generation

The last row is the reason mutation is not negligible in the way the first row makes it look. A single population of a thousand waits fifty generations for one new copy at this locus; a species of ten million gets two hundred every generation. Mutation is slow per individual and relentless per species.