Estimating recombination fraction via Pearson correlation

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:math> populations, which can be computationally intensive. While most existing methods focus on recombination fractions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:math> , recombination fractions in later generations ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mi>t</mml:mi></mml:msub> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mi>t</mml:mi></mml:msub> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mn>3</mml:mn></mml:msub> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi> <mml:mn>4</mml:mn></mml:msub> </mml:math> 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.