The founder effect
A few founders carry a random sample of the source gene pool, and each new colony then drifts from its own starting frequency.
Read first: The bottleneck effect
Founders are a sample
A founder event happens when a few individuals leave a large source population and start a new colony. The founders carry a sample of the source gene pool, not all of it. By chance alone, the frequency of allele A among them differs from the frequency in the source.
The module models one locus with alleles A and a. The source has N individuals in Hardy-Weinberg proportions for p. Each colony gets Nf founders, drawn at random from the source with replacement. The colony then grows by 10% per generation up to 500 individuals. Every generation its allele copies are a binomial sample of the previous generation, as in Pure Drift. Several colonies are founded independently from the same source, so the chart shows how much one source can give rise to.
The bottleneck module and this one are close relatives. In a bottleneck one population shrinks and then regrows. Here the sample leaves and starts a separate population, and the colonies do not interact. Each colony keeps the starting frequency of its founders and drifts away from it.
Five colonies from ten founders
Scatter at the start, divergence later
The founders hold 2Nf gene copies. Their frequency of A has mean p and variance p(1 − p)/2Nf. For Nf = 10 and p = 0.5 that is 0.25/20 = 0.0125, a standard deviation of 0.112. This is the scatter at generation 0 in the figure. The size of the source hardly matters, as long as it is much larger than Nf.
The colony then drifts. A colony of size n adds variance p(1 − p)/2n each generation, so drift is strongest while the colony is small. Its size is n = floor(Nf × 1.1^g), capped at 500. Ten founders take 42 generations to reach 500. Fifty founders take 25.
Drift is unbiased. Each colony is expected to stay at its starting frequency, and the mean over many colonies stays at the founders' mean. The colonies spread apart. Over 4,000 colonies with Nf = 10 the variance at the start is 0.013, and by generation 50 it is 0.106.
The page shows this in the comparison chart under the trajectories. It has three bars: the realised source frequency, the mean of the colonies' starting frequencies, and the mean of their final frequencies. Above them it prints the final variance. With at most 8 colonies these means are noisy, so press Colonize several times before you trust a pattern.
Eight colonies from fifty founders
Eight colonies from two founders
Exercise
Measure the scatter
Set Size (N) 500, Initial p 0.5, Founders 10, Trials 8 and Generations 50. Press Colonize and read the "Founders (mean)" and "Final variance" values in the comparison chart. Repeat with Founders 50.
What to expect. The starting frequencies spread with a standard deviation near 0.11 for 10 founders and near 0.05 for 50. The final variance is about 0.11 for 10 founders and about 0.03 for 50. A single run varies, so press Colonize a few times.
Open the walkthrough step →Exercise
Found with two
Set Founders 2, Trials 8 and Generations 50, and keep Size (N) 500 and Initial p 0.5. Press Colonize five times and count the lines that end at 0 or 1.
What to expect. Nearly every colony is fixed one way or the other, about 95% over many runs. About half of those have lost A and half have fixed it. Colonies stay at 2 individuals for the first 4 generations, which speeds up the drift.
Open the walkthrough step →Summary
- Founders are a random sample of 2Nf gene copies, so their allele frequency has variance p(1 − p)/2Nf.
- Ten founders give a starting standard deviation of 0.112 around p = 0.5, and 50 founders give 0.05.
- Each colony then drifts, most strongly while it is small, so independent colonies diverge from one source.
- Two founders push nearly all colonies to fixation or loss within 50 generations.
- A colony without allele A at founding never gets it back. The chance is (1 − p)^(2Nf).