# Two-Parameter Characterization of Chromosome-Scale Recombination Rate

## TL;DR

This study introduces a two-parameter model to better understand chromosome-scale recombination rates across species, revealing a consistent excess of recombination on smaller chromosomes and variability in the rate of increase with physical length.

## Contribution

It proposes a two-parameter linear regression model for chromosome recombination rates, improving upon the traditional single-parameter approach and highlighting the role of smaller chromosomes in recombination.

## Key findings

- A two-parameter model fits recombination data better than a one-parameter model.
- Smaller chromosomes show a consistent excess of recombination events.
- The parameter k varies widely among species, indicating diverse recombination dynamics.

## Abstract

The genome-wide recombination rate ($RR$) of a species is often described by one parameter, the ratio between total genetic map length ($G$) and physical map length ($P$), measured in centiMorgans per Megabase (cM/Mb). The value of this parameter varies greatly between species, but the cause for these differences is not entirely clear. A constraining factor of overall $RR$ in a species, which may cause increased $RR$ for smaller chromosomes, is the requirement of at least one chiasma per chromosome (or chromosome-arm) per meiosis. In the present study, we quantify the relative excess of recombination events on smaller chromosomes by a linear regression model, which relates the genetic length of chromosomes to their physical length. We find for several species that the two-parameter regression, $G= G_0 + k \cdot P$ provides a better characterization of the relationship between genetic and physical map length than the one-parameter regression that runs through the origin. A non-zero intercept ($G_0$) indicates a relative excess of recombination on smaller chromosomes in a genome. Given $G_0$, the parameter $k$ predicts the increase of genetic map length over the increase of physical map length. The observed values of $G_0$ have a similar magnitude for diverse species, whereas $k$ varies by two orders of magnitude. The implications of this strategy for the genetic maps of human, mouse, rat, chicken, honeybee, worm and yeast are discussed.