Recombination parameterization

[Hanbin Lee]

Dear slim-discuss group members

In a simple WF-based simulation with recombination rate `REC_RATE`, is it correct that the probability of two loci of distance `d` (in bp) has a recombination probability per generation per haplosome of exp(-REC_RATE * d) ? I'm trying to figure out a simple simulation to confirm a theoretical result.

Best,

Hanbin

[Hanbin Lee]

Oh, I'm sorry. I mean \exp(-1 / (REC_RATE * d)). 

[Peter Ralph]

Good question.  The recombination rate is the per-base and per-meiosis probability of a crossover; in other words, if the recombination rate is REC_RATE, then when generating a new recombinant haplosome, between each adjacent pair of positions there is a crossover with probability REC_RATE, independent of all other pairs of adjacent positions.

So, the number of crossovers in a segment is Binomial, and so the chance of there being at least one crossover between positions x and x+d is 1 - (1 - REC_RATE)^d, approximately 1 - exp(-d * REC_RATE).  However, the chance that the two positions are inherited together is the probability that the Binomial(d, REC_RATE) is even, which is another expression (that'd be a "mapping function"); see https://math.stackexchange.com/questions/1149270/probability-that-binomial-random-variable-is-even for instance.

Happy recombining,

--peter

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From: slim-d...@googlegroups.com <slim-d...@googlegroups.com> on behalf of Hanbin Lee <hb...@umich.edu>
Sent: Friday, March 13, 2026 10:53 AM
To: slim-discuss <slim-d...@googlegroups.com>
Subject: Re: Recombination parameterization

 

Oh, I'm sorry. I mean \exp(-1 / (REC_RATE * d)). On Friday, March 13, 2026 at 1: 52: 25 PM UTC-4 Hanbin Lee wrote: Dear slim-discuss group members In a simple WF-based simulation with recombination rate `REC_RATE`, is it correct that the probability

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SLiM forward genetic simulation: http://messerlab.org/slim/
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