Recombination and bitsets

TL;DR

This paper explores the mathematical theory of recombination using bitsets, deriving fundamental results on gamete frequencies and disequilibrium, with an emphasis on accessibility for students.

Contribution

It introduces a comprehensive, accessible mathematical framework for understanding recombination and gamete evolution using bitsets, including derivations with and without migration.

Findings

Derived fundamental results on gamete frequencies

Analyzed disequilibrium measures

Included derivations with migration effects

Abstract

A bitset is a set that encodes for a binary number. Bitsets are at the basis of a beautiful theory of recombination with n-loci and here we begin from scratch and advance to include the derivation of the fundamental results about the evolution of gamete frequencies and of disequilibrium measures with and without migration. All techniques have been illustrated and we have invested moreover a great effort to make the mathematics of this work accessible even for students in their first year at the university.