Multiple mutations, covert mutations,
and false exclusions in paternity casework
CH Brenner, Consulting in forensic mathematics, Oakland, California
The universal practice, up to now, is to make the judgement "paternity
excluded" whenever there are more than some established number - such
as two - of loci in which the genetic pattern, barring mutation, is
inconsistent with paternity. Such a rule is founded on the implicit
assumption that the probability of two mutations is vanishingly small.
However the ideal procedure would of course be to evaluate the
over all loci, taking possible mutation into account.
With STR's, unlike with RFLP's, a reasonably
accurate mathematical model of mutation
exists and hence the ideal procedure is finally
possible. What happens when it is applied is somewhat surprising.
Notwithstanding two or even three inconsistent loci, the posterior
probability of paternity (assuming 50% prior probability) can easily
be 20%. Unless the inconsistencies are particularly implausible as
mutations (i.e. multiple repeat units) the posterior probability is
not vanishingly small. The old rule causes bad decisions; it excludes
fathers. Instead, we should compute the proper paternity index across
all loci, considering the possibility of multiple mutations, and
evaluate the result. The computing part is easy. The evaluation part
brings a new difficulty, for it forces us to confront a question that
the inaccurate policy of the past hid from view: How unlikely must
paternity be in order to justify the decision "paternity
An incidental discovery is the heretofore overlooked implication
that the existence of "covert mutations" imply that most STR mutation
estimates from paternity studies are wrong.
Keywords: mutation, covert mutation, stepwise, paternity index, exclusion
Dealing with possible mutations in paternity casework has always been awkward. In recent years the use of STR
systems have nearly supplanted RFLP's. It is time to reconsider the outmoded policies as well.
|Table 1. Paternity inference based on counting inconsistencies|
||rate among false trios
||rate among true trios
||LR supporting paternity|
||1/61 000 000
||1/1 300 000|
mutation inconsistency rate for true trios at STR loci
appears to average about 1/400
[AABB, Brinkmann, Kayser,
unpublished data]. Assuming a 13 marker paternity test
and binomial model, the expectations are shown in Table 1
[corrected August 2010 — thanks to Giuseppe Cardillo, Naples.]
Clearly, two inconsistencies is the critical case. Prima facie it
supports non-paternity by a likelihood ratio of 2.4, which is
inconclusive. This paper examines more closely the case of two
- Materials and methods
Four hundred paternity trios, half true and half false trios but all
with two inconsistent loci were generated by an accelerated Monte
Carlo method. The simulations were allowed to continue generating
Monte Carlo genotypes of trios until the desired number of trios of
each type with exactly two inconsistences had been produced.
Mutations are generated according to a modified stepwise mutation model, which assumes that most mutations are
by plus or minus one repeat unit and are paternal.
The model parameters [5, 6] are:
- μ = rate of one-step paternal mutations (locus-dependent)
- i = proportion of mutations that increase size. i=½ for this study.
- rs = factor by which |s+1| step mutations are rarer
than |s| step mutations. (r=20±)
- ma = factor by which maternal mutations are rarer than paternal ones.
Next, a likelihood ratio was computed for each of the 400 cases using the above model.
|common case||another possibility
The incidence of covert mutations might be quite large. It will vary by
locus, and by preliminary calculations the rate is 18%±9%.
- Covert mutations
Analyzing the results of the true-trio simulations revealed an obvious in retrospect phenomenon, which we might call "covert
mutations" whose significance, so far as I know, has not been previously noted.
The figures illustrates ways that a mutation may go unnoticed.
|Table 2. Distribution of PI's among simulated 2-inconsistency cases|
||% false trios with PI>x
||% true trios with PI>x|
As table 1 shows, if one merely counts
inconsistencies without regard to the particulars, a finding of two
inconsistencies is modest evidence favoring non-paternity. Table 2 shows that taking into account the rarity of
shared alleles and the plausibility as mutations of inconsistencies
i.e. computing the paternity index (PI) somewhat
distinguishes true from false trios.
- Covert mutations
The significance of covert mutations is that since all published
estimates of mutation rates are derived from paternity studies, all of
the ones for autosomal loci are too low by a possibly significant
amount. The rate of apparent mutations is the right number to use to
calculate table 1, but for case calculations
table 2 the covert-adjusted must be
used. For example, in CSF1PO apparent μ=3/1000 but the true μ=4/1000.
Failure to account for covert mutations thus inflates paternity
indices, so is anti-conservative. There may also be an implication in
evolutionary studies when a mutational clock is considered.
- Telling true from false
Considering that true trios predominate over false ones in paternity
laboratories, cases with two inconsistencies are false trios by a
margin of only 2:1. "Paternity excluded" based on two inconsistencies
is a very poor policy. Computing a likelihood ratio is the proper
course. Interpreting it, though, can be a problematic when it is small.
The 19% of true trios with PI>100 notwithstanding the two
mutations, can possibly be reported (with so-called "paternity
probability" > 99%) and the burden of interpretation left to the
judge. A majority of the true trios will have 1/10 < PI < 100
and are obviously inconclusive. Possibly further testing will help;
nothing else will.
- What to do?
Once the untenable policy of the past pretending in effect that PI=0
whenever some target number of inconsistencies are observed is
abandoned, one is confronted with making a policy based on interpreting
the true PI. For example, if PI=1/10000 reporting "paternity excluded"
may be acceptable (notwithstanding the paradox that in the symmetrically
opposite case that PI=10000, no one would report "paternity certain").
But what of the less extreme cases with a smaller PI, such as 1/10 or 1/100?
Science and justice collide; there is no obvious and acceptable answer.
Assuming, as is customary, a 50% prior probability, the posterior
probability of paternity W is 10% or 1%. It is well established social
policy that the laboratory doesn't claim "definitely paternity" when
W=99%, so how can it be right for the laboratory to claim "excluded
from paternity" when W=1% - or 0.1% for that matter? The
mathematically honest solution of reporting the small PI whatever it
is after testing resources are exhausted to a judge who, up to now,
is not prepared for such evidence, is also not very satisfactory.
Fortunately, the situation is infrequent (see table 1). And part of
the solution is clear: compute the paternity index correctly,
including inconsistent loci. It that is done, it will be seen that
occasionally even in some cases with three inconstencies, paternity
cannot be excluded. And conversely, there are probably cases that have
only one inconsistency but it is of such a nature that it alone
effectively rules out paternity.
- AABB. Apparent Mutations Observed at the 13 CODIS STR Loci in the Course of Paternity Testing.
- Brinkmann B, Klintschar M, Neuhuber F, Huhne J, Rolf B. Mutation rate in human microsatellites:
influence of the structure and length of the tandem repeat. Am J Hum Genet. 1999 May;64(5):1473-4
- Kayser M, Sajantila A. Mutations at Y-STR loci: implications for paternity testing and forensic analysis.
For Sci International 118(2001) 116-121
- unpublished data of 400 mutations
- May 2005 re so far as I know I may be wrong. A while ago I saw a paper
published maybe in 1992, authors including Chakraborty
that seemed to consider the covert mutation concept with respect to VNTR loci.
July 2005. Thanks to Jiri Drabek for the reference below. It makes theoretical predictions of
the proportion of covert mutations based on a random rather than stepwise
mutation model, which probably explains why my estimate of the incidence of covert mutations
is a bit smaller than theirs.
Chakraborty R, Stivers D, Zhong Y. Estimation of mutation rates from parentage exclusion data:
applications to STR and VNTR loci. Mutation Research 354 (1996) 41-48
- Brenner CH. http://dna-view.com/mudisc.htm
- Brenner CH. http://dna-view.com/mufeatur.htm
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