Likelihood Models for Forensic Genealogy

TL;DR

This paper develops a probabilistic model for shared DNA distributions in forensic genealogy, improving accuracy over previous methods by using a Monte Carlo simulation and a novel normal approximation in the square-root of shared fraction.

Contribution

It introduces a new multivariate normal model based on the square-root of shared DNA fraction, enhancing the accuracy of forensic relationship inference.

Findings

A functional form with one parameter fits shared DNA distributions well.

Shared DNA distribution approximates a normal distribution in the square-root of shared fraction.

The model improves practical forensic genealogy tasks.

Abstract

In the idealized Morgan model of crossover, we study the probability distributions of shared DNA (identical by descent) between individuals having a wide range of relationships (not just lineal descendants), especially cases for which previous work produces inaccurate results. Using Monte Carlo simulation, we show that a particular, complicated functional form with just one continuous fitted parameter accurately approximates the distributions in all cases tried. Analysis of that functional form shows that it is close to a normal distribution, not in shared fraction f, but in the square-root of f. We describe a multivariate normal model in this variable for use as a practical framework for several general tasks in forensic genealogy that are currently done by less-accurate and less well-founded methods.