<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$F_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> populations, which can be computationally intensive. While most existing methods focus on recombination fractions in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$F_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, recombination fractions in later generations (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$F_{t}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$t > 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>></mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>) 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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$F_{t}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$t \ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. 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 <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$F_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$F_{3}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$F_{4}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

Estimating recombination fraction via Pearson correlation

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2026年2月14日

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Chin-Sheng Teng,
Shizhong Xu

摘要

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 $F_{2}$ $F_{2}$ populations, which can be computationally intensive. While most existing methods focus on recombination fractions in $F_{2}$ $F_{2}$ , recombination fractions in later generations ( $F_{t}$ $F_{t}$ for $t > 2$ $t > 2$ ) 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 $F_{t}$ $F_{t}$ for $t \ge 2$ $t \geq 2$ . 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 $F_{2}$ $F_{2}$ , $F_{3}$ $F_{3}$ , and $F_{4}$ $F_{4}$ 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.