Co-evolution between PRDM9 and target sites and the Recombination Hotspot Paradox

Recombination often concentrates in small regions called recombination hotspots where recombination is much higher than the genomes average. In many vertebrates, including humans, gene PRDM9 specifies which DNA motifs will be the target for breaks that initiate recombination ultimately determining the location of recombination hotspots. Because the sequence that breaks (allowing recombination) is converted into the sequence that does not break (preventing recombination), the latter sequence is over-transmitted to future generations and recombination hotspots are self-destructive. Given their self-destructive nature, recombination hotspots should eventually become extinct in genomes they are observed. While empirical evidence shows that individual hotspots do become inactive over time (die), hotspots are abundant in many vertebrates: a contradiction called the Recombination Hotspot Paradox. What saves recombination hotspots from their foretold extinction? Here we formulate a co-evolutionary model of the interaction among sequence specific gene conversion, fertility selection and recurrent mutation. We find that when fertility selection is weaker than gene conversion, fertility selection cannot stop individual hotspots from dying but can save them from extinction by driving their re-activation (resuscitation). It can also save them from extinction by driving the birth of new hotspots in target sites with small allelic variation. The amount of allelic variation that can result in the birth of a hotspot depends on the strength of fertility selection and the mutation rate. In our model mutations balance death and resuscitation of hotspots maintaining their numbers over time. Interestingly we find that mutations are responsible for the oscillation of individual hotspots being asynchronous across the genome such that the average recombination across the genome remains constant. Our model thus contributes to better understanding how new hotspots may be formed thus explaining the Recombination Hotspots Paradox. From a more applied perspective our work provides testable predictions regarding the relation between mutation and fertility with life expectancy of hotspots.