#Choosing a dataset

STRidER publishes frequencies per country, per continent and for the whole database. They give different numbers, so a match probability belongs to a profile and a chosen reference population together. One export carries all of them; pick by name after the parse:

def t as strider.Table init strider.parse($xml);

def at as forensics.FrequencyDb init strider.toFrequencyDb($t, "AUSTRIA", "STRidER AT");
def eu as forensics.FrequencyDb init strider.toFrequencyDb($t, "Europe", "STRidER Europe");
def all as forensics.FrequencyDb init strider.toFrequencyDb($t, "Entire Database", "");

strider.populations($t) lists what an export offers. The label becomes FrequencyDb.name, so a result can say which dataset produced it. One parse serves every population.

#Two or more populations

If the donor could be German or Austrian, there are two operations. They give different answers, and only one answers that question.

#Pooling: one merged population

forensics.combineFrequencies sums observed allele counts across tables, weighted by sample size:

def pooled as forensics.FrequencyDb init forensics.combineFrequencies(
    [$de, $at], "DE+AT");

Only loci that every input carries are pooled. The result describes one merged population; use it for a genuinely admixed reference group.

#Uncertain donor: the law of total probability

For "German or Austrian":

def p as float init forensics.randomMatchProbabilityAcross(
    [$de, $at], [0.5, 0.5], $suspect, forensics.THETA_GENERAL);
def lr as float init forensics.matchLikelihoodRatioAcross(
    [$de, $at], [0.5, 0.5], $suspect, forensics.THETA_GENERAL);

This computes the match probability within each population and averages the results, weighted by the prior probability that the donor comes from each. The weights must sum to 1; equal weights say only "one of these, no reason to prefer either".

#Why pooling is the dangerous one

Pooling averages allele frequencies; the across form averages genotype probabilities. The gap between them is the Wahlund effect: merging populations whose frequencies differ leaves the pool short of heterozygotes relative to Hardy-Weinberg. The match probability assumes Hardy-Weinberg, so a pooled table biases it downwards and overstates the evidence, in the direction that favours the prosecution.

A case from the forensicgenetics test suite: two populations, one locus, equal sample sizes.

For a 6,6 homozygote, with no theta correction:

The pooled likelihood ratio (4.0) is about a third higher than the correct one (2.9). Over a multi-locus profile the error compounds at every locus.

#The conservative alternative

Compute the match probability in each candidate population and report the largest:

for (def db in [$de, $at, $europe]) {
    io.printf("%s: %f\n", $db.name,
        forensics.randomMatchProbability($db, $suspect, forensics.THETA_GENERAL));
}

If the conclusion holds in every plausible population, the choice of population stops being a point of dispute. If it does not, that is itself the finding.

#Theta

The NRC II theta correction covers sub-population structure within a reference population, and randomMatchProbabilityAcross applies it inside each one. It does not replace choosing the right population, and the right population does not replace it.