# An evaluation of allowing for mismatches as a way to manage genotyping errors in parentage assignment by exclusion

M. Vandeputte, S. Mauger, M. Dupont-Nivet

► To cite this version:

M. Vandeputte, S. Mauger, M. Dupont-Nivet. An evaluation of allowing for mismatches as a way to manage genotyping errors in parentage assignment by exclusion. Molecular Ecology Notes, 2005, 6 (1), pp.265-267. 10.1111/j.1471-8286.2005.01167.x. hal-04297870

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# An evaluation of allowing for mismatches as a way to manage

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## genotyping errors in parentage assignment by exclusion

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M. VANDEPUTTE, S. MAUGER and M. DUPONT-NIVET

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INRA Génétique des Poissons, Domaine de Vilvert, 78352 Jouy en Josas cedex, France

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Correspondence: Marc Vandeputte, Fax: +33 1 34 65 23 90; E-mail: Marc.Vandeputte@jouy.inra.fr

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## Abstract

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In parentage assignment by exclusion, using multiple and very polymorphic loci, genotyping errors are a major cause of non-assignment. Using stochastic simulations, we tested the possibility to allow for mismatches at one or more allele as a way to recover assignment power. This was very efficient provided the set of loci used had a high assignment power (> 99%) and the error rate was not too high (below 3-4%). In these cases, most of the theoretical assignment power could be recovered. We also showed the efficiency of the method in a practical experiment with rainbow trout

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**Keywords:** exclusion, microsatellites, parentage assignment.

Using multilocus genotypes to ascertain parentage for genetic studies is a widely used method in natural populations (Milner et al. 2000; Garant & Kruuk 2005) or in experimental populations for which matings are not fully controlled or individuals cannot be tagged (e.g., fish, Vandeputte et al. 2004). Exclusion is a simple and efficient method for assigning parents to an offspring that uses incompatibilities (regarding Mendelian inheritance rules) between parents and offspring. A major drawback of exclusion is that a single mismatch between parent and offspring genotypes is enough to exclude a potential parent, thus making this technique extremely sensitive to genotyping errors or mutations (Jones & Ardren 2003). There is a wide range of variation for genotyping errors, often 1% or less (Hoffman & Amos 2005), but up to 17–29% in some cases (Maudet et al. 2004). For the management of such errors, several programs give the possibility to allow for a given number of mismatches between the offspring and its parents. Probmax allows for mismatches in a stepwise mutation/error approach (Danzmann 1997), whereas
newpat (Worthington Wilmer et al. 1999) and parente (Cercueil et al. 2002) only allow the user to define
the number of mismatches authorized. In addition, parente calculates a probability for each triplet with
mismatches, taking into account the genotype, but also the error rate and the sampling rate in the
population. However, no evaluation is done of the global efficiency of allowing for mismatches for
managing typing errors or mutations.

Here, we use stochastic simulations to study (i) the impact of genotyping errors, and (ii) the effect of
allowing for a small number of mismatches on the efficiency of parentage assignment by exclusion.

We simulated loci with five equally distributed alleles, corresponding to an individual offspring
exclusion probability of 0.77 (0.60 for paternity or maternity exclusion probability, Doddset al. 1996),
which is the usual range of exclusion probabilities for microsatellites (e.g., Lemes et al. 2002; Bessert
& Orti 2003; Castro et al. 2004).

For each combination of parameters (number of loci: 6–12; number of parents: 20–200; genotyping error
rate: 0–10%), we generated 30 parental sets, and 1000 offspring/ parental set. For each offspring, the
sire and the dam, as well as the alleles they transmitted, were randomly chosen. Genotyping errors were
simulated by substituting one or more parental allele by another randomly drawn allele (error frequency
= error rate per allele). We assigned offspring to their parents using an exclusion program running in
Visual Basic for Excel ( vitassign, available on request to Marc.Vandeputte@jouy.inra.fr), and the
different types of assignment (single correct, single incorrect, multiple, unassigned) were recorded.

Single correct (SC) assignments are offspring assigned to the right parental couple, single incorrect (SI)
are those assigned to an incorrect single parental pair, multiple are assigned to several possible parental
pairs, and unassigned are not assigned to any parental pair. Assignment power is defined as the
proportion of SC assignments when the error rate is set to zero. The unassigned offspring were then
tested allowing for one mismatch (one incompatible allele allowed), and the remaining unassigned were
tested allowing for two mismatches.

We also applied this procedure to the assignment of 390 rainbow trout offspring from a 45 males * 2
females factorial cross, genotyped for five loci (estimated single assignment power in this cross: 81.7%).

The results using the very first reading of five loci allowing or not for mismatches were compared to the
‘true’ results where litigious genotypes had been verified, and where up to five additional markers (total
assignment power: 98.7%) were genotyped when needed. We used these first readings because we knew
58 they had a high genotyping error rate, for testing in a real condition, the efficiency of allowing for mismatches. These results were compared with those of a simulation with 45 sires, 2 dams and 5 loci with 6 equally distributed alleles (giving a global exclusion probability similar to that of the true set of loci), with error rates from 0 to 15%. 59 60

61 The impact of genotyping errors on assignment rates was very high, and was highest when the 62 assignment power of the set of loci used was high, which may lead to less assigned offspring with more 63 powerful sets of loci (e.g. in the case of 20 parents and 1% error rate, 87.9% correct assignment is 64 observed with eight 5-allele loci, vs. 84.0% with twelve 5-allele loci). In Fig. 1, we show the case of 50 65 parents, which is a good illustration of the general picture. With the most powerful set of loci (ten 66 67 allele loci, 99.5% assignment power), allowing for one mismatch allows to assign correctly (SC) 81.0% 68 of the offspring with 5% genotyping error rate, vs. 46.9% only with perfect exclusion. Allowing for two 69 mismatches yields further improvement, with 90.2% of the offspring correctly assigned. Similarly, the 70 proportion of offspring assigned to an incorrect single parental pair (SI) raises from 0.2% with perfect 71 exclusion to 0.7% with one mismatch allowed and to 1.2% with two mismatches allowed. However, the 72 total rate of false assignment remains very low. The picture is quite different with a less powerful set of 73 loci (seven 5-allele loci, 90.9% assignment without genotyping error). In this case, using one mismatch 74 allows to assign correctly only 67.8% of the offspring (with 5% error rate) vs. 53.5% with perfect 75 exclusion, but allowing for one mismatch more yields no improvement (68.2% reassignment). The false 76 assignment rate is also much higher (2.2% for perfect exclusion, 4.3% with one mismatch), but not 77 modified (4.4%) by allowing for two mismatches. 78

79 The differences seem to lie essentially in the assignment power of the set of loci in a given size of 80 crossing design with a given error rate. For the same assignment power, the number of parents and/or 81 the number of loci have no visible impact neither on the loss of power caused by genotyping errors nor 82 on the efficiency of mismatches to recover assignment power. For example, in all combinations tested 83 with 1% error rate, it appears that an assignment power over 99% guarantees the correct assignment of 84 more than 98% of the offspring using one mismatch, whereas only 83–88% would be correctly assigned 85 using perfect exclusion. It also appears that the rate of false assignment with one mismatch is low in all 86 these cases, and in most cases hardly higher than the rate of false assignment with perfect exclusion. 87
(90%), but very high error rates (Fig. 1), where as much as 12% of the offspring may be assigned to a false single couple.

In the 'real life' example with rainbow trout (Table 1), allowing for two mismatches on the first run of genotypes raised the number of correct unique assignments from 137 (35.1%) to 223 (57.1%), with only 10 (2.6%) false unique assignments. Multiple assignments remain high due to the limited assignment power of the markers set used (87.1% without genotyping error). The simulated values with 12.5% error rate gave comparable results (35.0% unique assignments with 0 mismatches, 53.9% with 1 mismatch and 56.3% with 2 mismatches). However, the simulation results point out theoretical values of 5.4, 10.1 and 10.9% false assignments with 0, 1 and 2 mismatches, respectively, which is much higher than what is seen here. Probably, some assignments considered as exact are false (offspring that matched one single couple with five loci were not regenotyped, and among those some 5% should be false assignments).
Using one mismatch should have generated 4.7% more false assignments, and we find 2.6%, which is quite close given the sample size. Therefore, the predictions fit well with real life, in this example with voluntary huge genotyping error.

Genotyping errors or mutations have been identified as a major cause of reduced assignment power with exclusion methods, although other causes exist (e.g., null alleles, missing parental samples). It has been shown previously that maximum-likelihood assignment methods could manage genotyping errors (SanCristobal & Chevalet 1997). Here, we have evaluated a simple and efficient alternative using exclusion methodology. Provided the assignment power of the set of loci is high (> 99%, which is anyway a necessity for parentage assignment) and the error rate is reasonable (below 3–4%), allowing for mismatches allows to recover most of the assignment power without generating more than 1% of false assignments, which should not be harmful in subsequent analyses, especially in quantitative genetics where 95% confidence in the pedigree seems appropriate (Milner et al. 2000).

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<figure><img src="image_2.png" /><figcaption>**Fig. 1** Correct (a) and incorrect (b) unique parentage assignment rates in simulated offspring from 25 sires and 25 dams for different genotyping error rates using 7 loci with 5 alleles (90% assignment power) or 8 alleles (99% assignment power), allowing for 0, 1 or 2 mismatches (ms).</figcaption></figure>

<table><thead><tr><th rowspan="2">Kind of assignments observed</th><th colspan="4">Maximum number of mismatches authorized</th></tr><tr><th>0</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Single correct</td><td>137</td><td>212</td><td>223</td><td>223</td></tr><tr><td>Single incorrect</td><td>0</td><td>9</td><td>10</td><td>10</td></tr><tr><td>Multiple</td><td>26</td><td>114</td><td>150</td><td>157</td></tr><tr><td>Unassigned</td><td>227</td><td>55</td><td>7</td><td>0</td></tr></tbody></table>

<caption>**Table 1** Numbers and accuracy of parental pairs identified with five microsatellites when allowing mismatches or not in 390 fish from a 45 males*2 females factorial cross in rainbow trout</caption>