In a paper in Investigative Genetics
, Ge, Budowle and Chakraborty [1
] consider DNA identification by pedigree likelihood ratio (LR). A mutation model 'to accommodate the possibility of false exclusion' is presented. The model is explained on page 5: 'The transmission probability of two identical allele (sic) is 1- μ. The probability of a mutation event with x
step (sic) (x
> 0) is
where α is the probability of being a one-step mutation and μ is the mutation rate of the locus. Equal probabilities for gaining or losing repeats are assumed.'
Apparently equation (8) does not define a probability distribution since summing over x
Below we interpret 'Equal probabilities for gaining or losing repeats are assumed' to mean that a scaling factor 1/2 should be inserted on the right hand side of equation (8) since this leads to a proper probability distribution summing to 1.
There are several problems with this model. Most importantly, it allows for alleles with zero or negative repeat numbers which is not meaningful. Furthermore, this may also be a practical problem. For instance, using the mutation model for marker THO1 having allele value of three repeats leads to an allele with a value less than or equal to zero with probability 1.25 × 10-6. While this probability, based on parameter values α = 0.95 and μ = 0.001 suggested in , is small, it is certainly not negligible. Unreasonable results will occur if the model is applied to a sufficiently large number of cases. The model is, therefore, inconsistent both from a biological and practical point of view. There are several ways of overcoming these inconsistencies. However, reasonable modifications may well lead to models that have already been published and implemented. One example of a consistent formulation is summarized by equation (1) in . This latter model is stationary and so population allele frequencies are not altered by the mutation process. The LR will be changed by including extra, irrelevant (untyped), persons if a non-stationary model is used. We refer to [3–6] for further information on mutation models and their implementation.
Ge et al. , when referring to the mutation model in  on page 6 of their paper, state that this model is 'not supportable' and criticize the fact that transmission probability is related to allele frequency. But are not allele frequencies merely the stationary distribution of a mutation process, given that selection can be assumed to have a negligible impact for forensic markers?
Ge et al.  dismiss several published models including those mentioned above. We are not convinced by the arguments presented by them and there appears to be no data in the paper or the referenced papers that can justify the claims. In the absence of convincing data and studies comparing models, forensic scientists will have to rely on biological understanding and their own judgment when it comes to choosing appropriate mutation models. It may also be reasonable to try different models and several have been documented and implemented. The model suggested in  is not an alternative as it violates basic principles.