The peak of the likelihood curve in linkage testing

It is often suggested that when z-scores are used for linkage estimation, a maximum z-score of 3 (or maximum antilod score, M = 1000) is good evidence for the presence of linkage. It is pointed out that a better formula, applicable if nothing more is known about the loci concerned, would be that the probability that linkage is present is roughly 1--4/Msigma, whereas sigma is the standard error, i.e. square root(2-3 X downward curvature of z curve at peak). A consideration of typical cases suggests that a value M = 1000 would imply something like a 90% chance of linkage. It would seem simpler to use the formula, probability of linkage approximately to 1--H/20, where H is the average height of the antilod curve.