Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model
A synthetic variety (SV) of maize may not become stable if the sample size representing each parental line (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi></mrow></semantics...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Plants |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2223-7747/14/2/182 |
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| Summary: | A synthetic variety (SV) of maize may not become stable if the sample size representing each parental line (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi></mrow></semantics></math></inline-formula>) is small. This research aimed to evaluate the effect of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi></mrow></semantics></math></inline-formula> on the inbreeding coefficient (IC) of the SV (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>S</mi><mi>y</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula>) and on the stability of its genetic constitution. An SV formed by randomly mating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">l</mi></mrow></semantics></math></inline-formula> unrelated lines whose inbreeding coefficient is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi></mrow></semantics></math></inline-formula> was considered, and a random sample was taken from the genotypic array of the progeny produced by selfing a parental line <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo> </mo><mo>(</mo><mi>G</mi><mi>A</mi><mo>)</mo></mrow></semantics></math></inline-formula> This sample was visualized as a set of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi></mrow></semantics></math></inline-formula> groups of four plants whose genotypes are all four of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>A</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi></mrow></semantics></math></inline-formula> represented the number of plants that failed to form a group. The ICs of the selfings and those of the intragroup and intergroup crosses were calculated to derive the formula for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>S</mi><mi>y</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula> in terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi mathvariant="script">l</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi></mrow></semantics></math></inline-formula>. It was found that as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi></mrow></semantics></math></inline-formula> grows, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>S</mi><mi>y</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula> tends to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>F</mi><mo>)</mo><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>. With <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>=</mo><mn>15</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>S</mi><mi>y</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula> is practically stabilized and the probability of no genotype loss is 0.979. Moreover, the probability of losing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> is practically equal to zero from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>=</mo><mn>6</mn></mrow></semantics></math></inline-formula> onwards. However, the probability that their frequencies remain the same decreases as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi></mrow></semantics></math></inline-formula> gets larger. |
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| ISSN: | 2223-7747 |