This paper describes a set of stochastic processes that is useful for
modeling and analyzing a new genetic mapping method. Some of the proce
sses are Markov chains, and some are best described as functions of Ma
rkov chains. The central issue is boundary-crossing probabilities, whi
ch correspond to p-values for the existence of genes for particular tr
aits. The methods elaborated by Aldous (I 989) provide very accurate a
pproximate p-values, as spot-checked against simulations.