Probability that a chromosome is lost without trace under the neutral Wright-Fisher model with recombination

TL;DR

This paper introduces an analytical approximation and bounds for the short-term probability of chromosome loss in a neutral Wright-Fisher model with recombination, aiding efficient simulations of genetic populations.

Contribution

It provides a novel analytical approximation and bounds for chromosome loss probability under the Wright-Fisher model with recombination, improving computational efficiency.

Findings

Approximate probabilities are accurate for small number of generations.

Bounds provide useful limits for loss probability.

Approximation is computationally efficient compared to exact calculations.

Abstract

I describe an analytical approximation for calculating the short-term probability of loss of a chromosome under the neutral Wright-Fisher model with recombination. I also present an upper and lower bound for this probability. Exact analytical calculation of this quantity is difficult and computationally expensive because the number of different ways in which a chromosome can be lost, grows very large in the presence of recombination. Simulations indicate that the probabilities obtained using my approximate formula are always comparable to the true expectations provided that the number of generations remains small. These results are useful in the context of an algorithm that we recently developed for simulating Wright-Fisher populations forward in time. C++ programs that can efficiently calculate these formulas are available on request.