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This question already has an answer here:

During the process of crossing over, Why is the maximum possible recombination frequency between two genes equal to 50% and not more than that?

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marked as duplicate by Remi.b genetics Apr 3 at 15:38

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Statistically, this is that the maximum mean recombination frequency is 50%.

Recombination defined this way means that Gene A and Gene B from one chromosome are not 'together' on the same chromosome after recombination. That means that the recombination frequency is the probability of an odd number of recombination events between the loci. If there is an even number of recombination events, Gene A and Gene B end up back together again (with some rearrangement between them).

Recombination events can be modeled by a Poisson distribution: that is, recombination events are discrete (you either get an event or you don't) and they don't depend on each other. The rate can be expressed in terms of base pairs, e.g. "mean number of recombinations per base pair" or "mean number of recombinations for 'distance' X."

The probability of getting an "odd" result from a Poisson distribution is always <0.5. See for example this Q&A from Math.SE.

Spoken in plain language, let's start from two loci that are very close where the recombination rate is very low. In most cases, then, we get 0 recombination events so the genes stay together. Now, as we increase the distance, we will get more cases where 1 event occurs. However, as we increase the distance further, we will also start to get cases where 2 events occur. 2 events has the same end result as 0 events: the genes stay together. It turns out mathematically that there is no rate that you can choose where the number of "1"s is more than the combined number of "0"s and "2"s; therefore, the frequency must be <0.5, but will approach 0.5 as the rate approaches infinity. If this doesn't seem intuitive, check the math from Math.SE!

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