During meiosis I, each pair of homologous chromosomes lines up and can exchange segments at random points — crossing over. Two genes far apart on the same chromosome are more likely to have a crossover land between them than two genes close together, so the chance a gamete carries a new (recombinant) combination of alleles grows with the physical distance between the loci. This is the basis of genetic mapping: 1 centiMorgan (cM) is defined as the distance that gives roughly a 1% recombination frequency, for short distances.
This simulator models crossovers along the chromosome as a Poisson process with an average of 1 crossover per 100 cM (1 Morgan) — the standard "no interference" (Haldane) model. For two loci a genetic distance d Morgans apart, the number of crossover points landing strictly between them is Poisson-distributed with mean d, and the gamete is recombinant exactly when that count is odd (an even number, including zero, restores the original combination).
d = map distance in Morgans (cM / 100)
crossovers between loci ~ Poisson(d)
recombinant ⇔ odd number of crossovers between the loci
Haldane mapping function:
r = ½(1 − e^(−2d)) (recombination frequency from distance)
d = −½ ln(1 − 2r) (distance from observed frequency)
- Distance slider — sets how far apart, in cM, the two marked loci A and B sit on the chromosome ribbon shown.
- Run 1 Meiosis — draws a fresh set of crossover points and animates the chiasmata resolving on the ribbon; the colour at each locus shows which parental chromatid (blue or red) that segment ended up on.
- Run 200 Trials — repeats the same random process instantly at the current distance and accumulates the empirical recombination frequency for that distance.
- Auto Map-Distance Sweep — runs a batch of trials at many distances from 1 to 160 cM in one pass and plots every point on the recombination-frequency-vs-map-distance chart below, so the Haldane curve emerges without manually dragging the slider.
- At small d, r ≈ d (roughly 1% per cM); at large distances r saturates at 0.5 because loci far enough apart assort as if unlinked — exactly what real linkage maps show, and exactly the flattening visible on the chart.
Simplification: real bivalents have four chromatids (two sister chromatids per homolog) and only two participate in any one chiasma; this sim tracks the two homologs directly, which reproduces the same Poisson/Haldane mapping statistics used to build real genetic maps.