Likelihood Ratio (LR) calculations in Parentage Assessments

The likelihood ratio (LR) compares two competing hypotheses:

• H1: The stated parents are the biological parents.
• H2: The stated parents are not the biological parents. The offspring's alleles originate from random, unrelated animals of the same population.

For each of the two hypotheses, the probability of the observed DNA findings is calculated, assuming the hypothesis is true. The LR is the ratio of these two probabilities:

LR = probability of the findings under H1 / probability of the findings under H2

• LR greater than 1: the findings support the stated parents.
• LR less than 1: the findings speak against the stated parents.
• LR equal to 1: the findings are not informative.

Important: The LR describes the weight of the DNA evidence. It is not itself the probability that the stated parents are the true parents.

For high values, the LR is given as a logarithm to base 10 (log10). A log10 value of 6 means an LR of 1,000,000 : 1. The findings are then one million times more probable if the stated parents are the biological parents than if they are not. If the log10 value is negative (LR less than 1), the findings speak against the stated parents.

To turn the LR into a probability of parentage, an assumption is needed about how probable the stated parentage was before the analysis (prior probability, see Bayes Theorem). A neutral assumption of 50 % is customary. Then:

Probability of parentage = LR / (LR + 1)

Example: an LR of 1,000,000 results in a probability of parentage of 99.9999 %.

To evaluate the two hypotheses, all animals involved are analysed for a defined set of DNA markers. Their overall number and information content must be sufficient to allow an evaluation to be made with an acceptable degree of certainty.

The respective allele findings of the markers of the offspring are checked to see whether they can originate from the two parent animals. If no exclusion situations are found, the LR is calculated for each marker:

• H1: the probability that the stated parents pass on exactly the alleles found in the offspring. It follows Mendel's rules and depends on the genotypes of the parents: a homozygous parent always passes on its allele (probability 1), a heterozygous parent passes on each of its two alleles with a probability of only 1/2.
• H2: the probability that random animals of the population pass on the same alleles. It results from the frequency of the alleles in the population (allele frequency). The rarer an allele, the less likely a chance match and the higher the LR.

Example for one marker (father without taking the mother into account): the offspring carries the alleles A and B, the stated father is homozygous A/A. Allele A has a frequency of 10 % in the population. The LR for this marker is then 1 / (2 × 0.1) = 5. If the father were heterozygous A/C, he would pass on allele A in only half of the cases; the LR halves to 2.5.

The LRs of the individual markers are multiplied with each other and result in the overall LR. This requires that the markers are inherited independently of each other. With a sufficient number of informative markers, very high values are reached in this way.

• Related animals as the alternative: H2 assumes an unrelated animal. In animal breeding, however, the true parent is often related to the stated one, for example a full brother or a son of the stated sire. Related animals share many alleles, so the weight of the LR drops considerably. If related animals come into question as a parent, they should be tested as well.
• Single mismatches: If a single marker does not match a parent, this may also be due to a new mutation or a genotyping error. A reliable exclusion is therefore based on several independent mismatches.
• Suitable reference data: The allele frequencies must come from a suitable reference population, for example the same breed. Otherwise the LR is over- or underestimated.

At Generatio, we consider 3 different starting situations that allow us to recognise the individual contribution of each parent and to evaluate cases where only one parent is present:

1. Both parents are evaluated together. The value is referred to as the co-parentage index (in the literature also combined parentage index or trio parentage index).
2. LR of the mother without taking the father into account / Fatherless maternity index
3. LR of the father without taking the mother into account / Motherless paternity index

Lexicon:

• Bayes Theorem
• STR marker
• Genetic Proof of Origin

Literature:

• Evett, I.W., Weir, B.S.: Interpreting DNA Evidence: Statistical Genetics for Forensic Scientists. Sinauer Associates, Sunderland (1998).