# Estimating recombination fraction via Pearson correlation

## TL;DR

This paper introduces a new method using Pearson correlation to estimate recombination fractions in advanced crop generations, offering a faster and accurate alternative to traditional methods.

## Contribution

The novel contribution is applying Pearson correlation to estimate recombination fractions in Ft populations (t ≥ 2), which is computationally efficient and reliable.

## Key findings

- The Pearson correlation method provides reliable and accurate recombination fraction estimates across F2, F3, and F4 rice populations.
- The method is computationally efficient compared to the expectation–maximization algorithm without sacrificing accuracy.
- Genetic maps constructed using this method show increased resolution and detection of recombination events in later generations.

## Abstract

Estimating recombination fractions is crucial for constructing genetic linkage maps and understanding the inheritance patterns of crop genome in breeding populations. Traditional methods, such as the maximum likelihood method, rely on iterative algorithms to estimate recombination fractions in \documentclass[12pt]{minimal}
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\begin{document}$$F_{2}$$\end{document}F2 populations, which can be computationally intensive. While most existing methods focus on recombination fractions in \documentclass[12pt]{minimal}
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\begin{document}$$F_{2}$$\end{document}F2, recombination fractions in later generations (\documentclass[12pt]{minimal}
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\begin{document}$$F_{t}$$\end{document}Ft for \documentclass[12pt]{minimal}
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\begin{document}$$t > 2$$\end{document}t>2) is also important for capturing the increasing resolution of genetic maps over generations. In this study, we introduced a Pearson correlation method for estimating recombination fractions in \documentclass[12pt]{minimal}
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\begin{document}$$F_{t}$$\end{document}Ft for \documentclass[12pt]{minimal}
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\begin{document}$$t \ge 2$$\end{document}t≥2. This is the first study to demonstrate that the Pearson correlation between marker alleles of different loci can be effectively used to estimate the recombination fractions between markers in advanced generations. This method is straightforward, allowing researchers to quickly and efficiently compute recombination fractions, offering a significant speed advantage without compromising estimating accuracy. We evaluated the performance of the new method by comparing it with the expectation–maximization (EM) algorithm across \documentclass[12pt]{minimal}
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\begin{document}$$F_{2}$$\end{document}F2, \documentclass[12pt]{minimal}
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\begin{document}$$F_{3}$$\end{document}F3, and \documentclass[12pt]{minimal}
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\begin{document}$$F_{4}$$\end{document}F4 populations using a rice dataset. The results show that the Pearson correlation method is both reliable and computationally efficient. In addition, we construct a genetic linkage map across generations utilizing the genetic distance calculated from the correlation converted recombination fractions. We observed map expansion, where the estimated genetic map length increases in later generations, reflecting improved resolution and detection of recombination events under finite marker density and sample size. This approach holds significant potential for broader applications in linkage mapping, quantitative trait loci (QTL) analysis, and design of breeding programs.

The online version contains supplementary material available at 10.1007/s00122-026-05178-w.