When Mendel first figured out the basic rules that govern inheritance by carefully controlled breeding experiments with peas in the garden of the monastery is Brno, all of the seven traits that he was interested in followed the same set of rules that he summarized by The Law of Segregation and The Law of Independent Assortment. I outlined the first of these laws previously in another essay (link), the second simply states that there is a 50/50 chance for which of the two alleles an individual has for each trait will go into any given gamete. Further, there is no relationship between the inheritance of alleles of different traits. That is, if we are examining a monohybrid cross (one trait) and an individual has the genotype of Aa, then there is an equal chance that any given gamete will get either A or a. That also suggests that ½ of that individual’s gametes have A and one half have a.
This idea appears simplistic in a monohybrid cross, but it takes on greater significance in a dihybrid cross. In these crosses we are following the inheritance of two traits simultaneously, e.g. Aa and Bb. The Law of Segregation says that any given gamete will get either A or a and that the distribution of B and b is also perfectly random – and in no way influenced by the A/a distribution.
That’s a lot of words. What does it mean?
It means that in a monohybrid cross…
50% of gametes have A
50% have a
in a dihybrid cross…
25% have AB
25% have Ab
25% have aB
25% have ab
This should be borne out by the proportion of offspring had by these individuals. If this AaBb organism is crossed with an aabb, then we should get the following:
Much of the time this is exactly what we see and it is in perfect accord with Mendel’s Law of Independent Assortment. But, from time to time these predictions are not borne out. Instead, we see something else, skewing toward two of the four possible genotypes at the expense of the other two.
The reason for this is because these alleles are not just concepts floating around in space, but physical entities that are
carried on chromosomes. More specifically, each allele has a very specific place (locus) on the chromosome and the distance between these chromosomes has an inverse relationship with the probability that two alleles will be inherited together. That is, the smaller the distance they are apart, the greater the likelihood that the two genes will travel together. This relationship was first untangled by a professor at Columbia University named Thomas Hunt Morgan, who speculated that degree that inheritance is skewed away from random was related to a physical distance.
He reasoned that if alleles were completely linked, then in the situation above(AaBb x aabb, where the first animal is an F1 from two homozygous parents), the result would be:
The outcome of this is presented graphically in the accompanying figure:
Instead, he often found middling results where two types of offspring were favored at the expense of the other two, and that the two that were favored were the same two he thought would result from a situation with complete linkage.
He measured the distance between the alleles by the frequency of recombinations that occurred between the loci (in this case 10% + 10% = 20%, or 20 centiMorgans).
Now that we measure in basepairs rather than centiMorgans, we know that 1 centiMorgan = 1% chance of recombination between the loci = ~1Million bps.
One of Morgan’s students is credited for having the breakthrough epiphany that if these distances were meaningful as a measure of the frequencies of crossover events that they should be additive with one another. To demonstrate this, the student, Alfred Sturtevent, used extant data from the lab to demonstrate it. (I can imagine this as being one hell of a triumphant lab meeting presentation)
The importance of this work was not just that these positions could be mapped using recombination frequencies, but also that it helped to verify that genes were physical entities that existed in real space and many are linked to one another physically.
Considering this method of measurement, what is the maximum distance one could conceivably measure between two loci without intervening points?
What happens when two crossover events occurs between the genes of interest?