Several recent mapping efforts have used so-called ''directed'' approa
ches to construct their maps. However, most, but not all, published me
thods for modeling the progress in physical mapping projects have been
focused on random approaches, such as bottom-up fingerprinting and ST
S-content mapping. In addition, those few efforts that did model direc
ted approaches used methods that required assuming that all insert len
gths were the same. This assumption is unnecessary. Using properties o
f stationary processes, one can derive simple asymptotic formulas that
apply equally to constant and variable clone lengths. Also, in the ca
se of constant clone lengths, these results are equivalent to, and ext
end, those published results for directed mapping derived by other met
hods. Simulations show that these methods provide estimates well withi
n the limits of uncertainty inherent in any mapping project. (C) 1994
Academic Press, Inc.