Stationary mutation models

Probability calculations for relationship inference based on DNA tests are often performed with computer packages such as Familias. When mutations are assumed to be a possibility, one may notice a curious and problematic effect of including untested parents: results tend to change slightly. In this paper, we trace this effect back to fundamental model-formulating issues which can only be resolved by using stationary mutation models. We present several methods for obtaining such stationary mutation matrices from original mutation matrices, and evaluate essential properties of these methods. Our conclusion is that typically, stationary mutation models can be obtained, but for many types of markers, it may be impossible to combine specific biologically reasonable requirements for a mutation matrix with the requirement of stationarity.