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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2025-01-01
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| author | Juan Enrique Rodríguez-Pérez Jaime Sahagún-Castellanos Aureliano Peña-Lomelí Clemente Villanueva-Verduzco Denise Arellano-Suarez |
| author_facet | Juan Enrique Rodríguez-Pérez Jaime Sahagún-Castellanos Aureliano Peña-Lomelí Clemente Villanueva-Verduzco Denise Arellano-Suarez |
| author_sort | Juan Enrique Rodríguez-Pérez |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-351be6a3bb0849299e97efcbca6ce48e |
| institution | Kabale University |
| issn | 2223-7747 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Plants |
| spelling | doaj-art-351be6a3bb0849299e97efcbca6ce48e2025-01-24T13:46:38ZengMDPI AGPlants2223-77472025-01-0114218210.3390/plants14020182Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite ModelJuan Enrique Rodríguez-Pérez0Jaime Sahagún-Castellanos1Aureliano Peña-Lomelí2Clemente Villanueva-Verduzco3Denise Arellano-Suarez4Departamento de Fitotecnia, Instituto de Horticultura, Universidad Autónoma Chapingo, km 38.5 Carretera México-Texcoco, Chapingo 56230, Estado de México, MexicoDepartamento de Fitotecnia, Instituto de Horticultura, Universidad Autónoma Chapingo, km 38.5 Carretera México-Texcoco, Chapingo 56230, Estado de México, MexicoDepartamento de Fitotecnia, Instituto de Horticultura, Universidad Autónoma Chapingo, km 38.5 Carretera México-Texcoco, Chapingo 56230, Estado de México, MexicoDepartamento de Fitotecnia, Instituto de Horticultura, Universidad Autónoma Chapingo, km 38.5 Carretera México-Texcoco, Chapingo 56230, Estado de México, MexicoDepartamento de Fitotecnia, Instituto de Horticultura, Universidad Autónoma Chapingo, km 38.5 Carretera México-Texcoco, Chapingo 56230, Estado de México, MexicoA 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.https://www.mdpi.com/2223-7747/14/2/182identity by descentdifferent permutationsnestingsample size |
| spellingShingle | Juan Enrique Rodríguez-Pérez Jaime Sahagún-Castellanos Aureliano Peña-Lomelí Clemente Villanueva-Verduzco Denise Arellano-Suarez Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model Plants identity by descent different permutations nesting sample size |
| title | Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model |
| title_full | Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model |
| title_fullStr | Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model |
| title_full_unstemmed | Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model |
| title_short | Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model |
| title_sort | genetic stability and inbreeding in a synthetic maize variety based on a finite model |
| topic | identity by descent different permutations nesting sample size |
| url | https://www.mdpi.com/2223-7747/14/2/182 |
| work_keys_str_mv | AT juanenriquerodriguezperez geneticstabilityandinbreedinginasyntheticmaizevarietybasedonafinitemodel AT jaimesahaguncastellanos geneticstabilityandinbreedinginasyntheticmaizevarietybasedonafinitemodel AT aurelianopenalomeli geneticstabilityandinbreedinginasyntheticmaizevarietybasedonafinitemodel AT clementevillanuevaverduzco geneticstabilityandinbreedinginasyntheticmaizevarietybasedonafinitemodel AT denisearellanosuarez geneticstabilityandinbreedinginasyntheticmaizevarietybasedonafinitemodel |