Speciation Snowball: Hybrid Incompatibility Simulator

Divergence

Divergence rate μ 12%

Incompatibility density p 18%

Live Readouts

Generation

Fixed loci A / B

0 / 0

Hybrid fitness (Dobzhansky-Muller incompatibilities: 0)

100%

Population A Population B F1 hybrids

How it works

After a founder split, two populations evolve independently. Each generation, an unfixed locus in lineage A (and, separately, in lineage B) fixes for a new "derived" allele with probability μ -- a stand-in for the combined action of drift and positive selection within that lineage. Because natural selection never has a chance to test allele i from A against allele j from B (they have never coexisted in one genome), some derived-allele pairs are silently incompatible when a hybrid finally brings them together -- a Dobzhansky-Muller incompatibility.

Loci fixed derived:   D_A (population A),  D_B (population B)
Incompatibility matrix: M[i][j] = 1 with prob. p, for i in D_A, j in D_B, i != j
Realized incompatibilities:  K = sum over i in D_A, j in D_B of M[i][j]
Hybrid fitness:        W = max(0, 1 - K * s)      (s = cost per incompatibility)

Because K counts pairs drawn from both growing sets, it grows roughly with the square of the number of substitutions (K ≈ p·|D_A|·|D_B|) even though each lineage accumulates changes at a constant linear rate μ -- the "snowball effect" predicted by H. Allen Orr's 1995 population-genetic model of speciation. Reproductive isolation therefore does not build up smoothly: it stays near zero for a while, then accelerates.

μ (divergence rate) -- how fast each lineage substitutes new derived alleles per generation.
p (incompatibility density) -- how often two independently-evolved derived alleles happen to clash; regenerates the genetic architecture immediately.
New Founder Split -- restarts the clock at generation 0 with a fresh incompatibility matrix, as if two new populations had just been isolated.

Real-world relevance: this is the accepted explanation for why post-zygotic reproductive isolation (hybrid inviability and sterility, e.g. horse×donkey mules) so often appears only after populations have been separated for a long time, and why isolation can appear to "switch on" abruptly rather than growing gradually.

Population A genome Population B genome F1 hybrid cloud

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.