A note on the bias of genetic distances in linkage maps based on small samples for backcrosses and intercrosses with complete dominance.

This paper investigates the bias (the difference between the expectation (mean) of an estimator and its true value) of genetic distances for small samples. Exact results on this bias have not received much attention in genetic mapping literature. We show that bias drops quickly with increasing sample size for both a backcross population and an F2 in coupling. By contrast, bias may be substantial even for larger sample size for an F2 when markers are in repulsion. It is concluded that Karlin's map function should be used with care when mapping is done using an F2 population. The same note of caution applies to other map functions such as Haldane's and Kosambi's. Finite-sample bias of these latter functions cannot be assessed because of the nonexistence of an expected value, but their median bias is similar to that of Karlin's function.