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Three-locus ordering.

We turn now to our first truly multilocus analyses, that is, not only there are more than two loci under discussion, but they are considered in the same experiment. Three-locus (also called three-point) and higher order analyses almost certainly began with the Drosophila group under Morgan, but I am unable to document this precisely.

Example. Consider the cross: (female) wmf/+++ wmf/ Y (male), where the loci w (white eyes), m (miniature wings) and f (forked thoracic bristles) are all X-linked. The following data comes from one of Morgan's experiments, and refers to both male and female progeny. Note that recombination only occurs in the mother flies, and that we can identify when it occurs because the traits are recessive. (Our cross is essentially a backcross.)

We can put these data in a table, rows indicating whether there is recombination or not across w-m and columns the same across m-f.

If recombination was independent across the two intervals w-m and m-f, then we would expect doubles; instead we see 6. This is known as positive interference: exchanges in one of the intervals are negatively associated with exchanges in the adjacent interval. The term positive presumably comes from interpreting this negative association causally as positive discouragement. The magnitude of such interference is greatest for adjacent intervals, and decreases as the intervals separate. (To see it for disjoint intervals, we'd need data on the 4 endpoints of the intervals.)

What interests me just now is how we learn which of the markers is in the middle. One simple answer goes back to the two-point data: simply declare the flanking markers to be the pair with the largest recombination fraction. Clearly that is the pair w-f, so m is in the middle. However, this two-point answer is not making the most efficient of the data, and it is a nice exercise to obtain the MLE of locus order.



next up previous
Next: ML estimation of Up: Stat 260: Statistics Previous: Fisher's use of



Simon Cawley
Mon Apr 20 19:52:17 PDT 1998