Subject: Genetic Algorithms
Presenter: Jérémy Barbay
Abstract Hot Spot Paradox

When diploids organisms product gametes, a cell reproducts and divides itself into 4 haploids gametes.

During this division the aparried chromosomes can recombine their genes: it happens that the structure of one of the chromosomes breaks in some specific points called ``hotspots''. The structure is then repaired by copying the corresponding allele from the aparried chromosome, which results eventually in the exchange of whole sections of the chromosomes, called ``crossover''.

The analysis of this phenomenon reveals a paradox of evolution: the hotspots can be inactivated by mutation, which change them so that they don't break anymore, and don't initiate a crossover any more.

If a recombination is still initiated by the aparried chromosome, its hotspot is repaired using the mutated allele: the inactivated hotspots can propagate to the entire population. Such a mechanism should lead to the disappearance of the active hotspots, but in nature they didn't and each diploid species have several of them on each chromosome: this is the paradox.

The recombination of the chromosomes helps the migration of those during the cell division, which permits an equilibrated distribution of chromosomes in the gametes. Without recombination, two aparried chromosomes could end in the same gamete, sterilizing it and the gamete missing this chromosome. Boulton, Myers et Redfield tried to solve the hotspot paradox by taking into account this negative effect, but it doesn't seem to be strong enough to explain the proportion of active hotspots measured in practice [Boulton Myers Redfield].

The other contribution of hotspots is to the evolution of the species. This factor is only feebly taken into account in the simulations of Boulton et al., where the population is initially optimal. In collaboration with Mario Pineda, a post-doctoral student from the department of Zoology, I defined a simple model neglecting the effect of hotspots on the chromosome separation, but taking into account the effect on the evolution of the species. I try to analyze this model with techniques similar to the ones used for genetic algorithms, on which I have been working for my master's thesis, and I implemented this model for simulations.

(This is a sequel to Mario's talk in october)