Why is it more likely that exactly 1 crossover will take place?

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Hello. I'm studying genetic linkage and the recombination frequency calculation (that is assumed to be directly proportional to allele distance) considers that only one cross over will take place. I know this is an estimation, but I want to know what the biological mechanism is that justify the probability that EXACTLY ONE crossover will take place.
In other words, what is the probability of no cross overs taking place, or a double cross over, or a triple cross over, and why are these probabilities lower than for a single crossover? And also, it is considered that all regions in the chromosome have the same chance to suffer a cross over, is this correct? If not, what are the most probable and the least probable sites and why?
 
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Ygggdrasil
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Introductory genetics courses consider only the possiblility of one crossover between locations in order to simplify the math, but real calculations of genetic linkage do consider the possibility of multiple crossover events between loci: https://en.wikipedia.org/wiki/Centimorgan#Relation_to_the_probability_of_recombination

These calculations do make the assumption that all regions of the chromosome have the same chance to crossover, which may not be correct. I have not followed this area much, but this is an area of active research (e.g. see this paper published last week in Science http://science.sciencemag.org/content/363/6433/eaau8861)
 
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Thanks @Ygggdrasil, I actually found a very interesting paper that shows the relationship between locus of female vs male autosomal chromosomes and the probability density of cross over in mouses. The females have low probability densities at the extremes, but constant probability density in almost 60% orf the chromosome. However the male has low probability densities at the left extreme and non-constant probability densities at the rest (the highest probability occurs in a place that correspond approximately to 90% of the chromosome). See the graph below:

Commentaries:
Asymmetric spatial distribution of crossovers in male meiosis in singly vs.multiply recombinant chromosomes. Shown are kernel density estimates of crossover frequency across single-recombinant (left) and double-recombinant (right) autosomes in female (pink lines) and male (blue lines) meioses. The sharp peak in crossover density observed at the distal end of autosomes in males is present in both single- and double-recombinant autosomes. An additional broader peak is present in the proximal region of double-recombinant chromosomes. This effect is independent of the distribution of double-strand breaks (DSBs) in male meiosis reported by Brick et al. (2012), plotted in gray.

Link of the paper:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4012503/#!po=50.0000

This shows that the probabilities varies drastically depending on the distance, speially in males.
 

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