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Recombination often concentrates in small regions called recombination hotspots where recombination is much higher than the genome's 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 where they are found. 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 allelic frequencies oscillate leading to stable limit cycles. From a biological perspective this means that when fertility selection is weaker than gene conversion, it cannot stop individual hotspots from dying but can save them from extinction by driving their re-activation (resuscitation). In our model, mutation balances death and resuscitation of hotspots, thus maintaining their number over evolutionary time. Interestingly, we find that multiple alleles result in oscillations that are chaotic and multiple targets in oscillations that are asynchronous between targets thus helping to maintain the average genomic recombination probability constant. Furthermore, we find that the level of expression of PRDM9 should control for the fraction of targets that are hotspots and the overall temperature of the genome. Therefore, our co-evolutionary model improves our understanding of how hotspots may be replaced, thus contributing to solve the Recombination Hotspot Paradox. From a more applied perspective our work provides testable predictions regarding the relation between mutation probability and fertility selection with life expectancy of hotspots.
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