<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0187-5779</journal-id>
<journal-title><![CDATA[Terra Latinoamericana]]></journal-title>
<abbrev-journal-title><![CDATA[Terra Latinoam]]></abbrev-journal-title>
<issn>0187-5779</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de la Ciencia del Suelo A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0187-57792019000400479</article-id>
<article-id pub-id-type="doi">10.28940/terra.v37i4.545</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[General inbreeding coefficient of maize synthetics derived from three-way line hybrids]]></article-title>
<article-title xml:lang="es"><![CDATA[Coeficiente de endogamia general de sintéticos de maíz formados con híbridos trilineales]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ibarra-Sánchez]]></surname>
<given-names><![CDATA[Alejandro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez-Pérez]]></surname>
<given-names><![CDATA[Juan Enrique]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sahagún-Castellanos]]></surname>
<given-names><![CDATA[Jaime]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma Chapingo Departamento de Fitotecnia ]]></institution>
<addr-line><![CDATA[ Edo. de México]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>37</volume>
<numero>4</numero>
<fpage>479</fpage>
<lpage>485</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0187-57792019000400479&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0187-57792019000400479&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0187-57792019000400479&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[SUMMARY: The scarcity of pure and unrelated maize inbred lines that possess high combining ability in Mexico has led breeders wishing to form single crosses to develop double-cross or three-way line hybrids (TWLHs) instead. However, some of the farmers who grow these hybrids cultivate their advanced generations later on. Although the resulting populations can be viewed as the synthetics that the random mating of the parental lines (Syn  L ) of these hybrids would produce, there may be differences. The synthetic variety whose parents are t TWLHs (Syn  T ) is interesting because the contributed gene frequencies of the three lines that are parents of a TWLH are not balanced and this may generate a difference between the inbreeding coefficients (ICs) of the Syn  L and Syn  T . Since an unbiased and general inbreeding coefficient of the Syn  T and a prediction formula for the Syn  T genotypic mean (GM) are not yet known, the objective of this study was to derive formulae for these two important parameters of Syn  T . To form the t TWLHs, it was assumed that 3t unrelated lines whose IC was F (0 &#8804; F &#8804; 1) were used. Unbiased and general formulae for FSyn  T and GM were derived for the first time. In particular, it was found that FSyn  T = [3(1 + F)]/(16t). Since the inbreeding coefficient of the Syn  L derived from the same 3t lines is (1 + F)/(6t), then FSyn  T &gt; FSyn  L . These findings suggest that the genotypic mean of the Syn  L grain yield is larger than the Syn  T &#8217;s.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN: La escasez de líneas puras no emparentadas y de aptitud combinatoria alta, en México, ha orientado a los mejoradores que desean formar cruzas simples al desarrollo de variedades híbridas trilineales (CTs) o de cruza doble. Sin embargo, de los agricultores que llegan a cultivar estos híbridos, algunos siembran las generaciones avanzadas de éstos en ciclos posteriores. Aunque las poblaciones resultantes pueden ser visualizadas como los sintéticos que produciría el apareamiento aleatorio de las líneas progenitoras de dichos híbridos, puede haber diferencias. El caso de la variedad sintética cuyos progenitores son t CTs (Sin  T ) es interesante porque las frecuencias de los genes que aportan las tres líneas de cada progenitor no son balanceadas. Esto puede hacer que el coeficiente de endogamia (CE) del Sin  T difiera al del Sin  L . Como se desconocen fórmulas para predecir el CE insesgado y generalizado del Sin  T (FSin  T ) y de su media genotípica (MG), el objetivo principal de este trabajo fue derivar fórmulas para estos dos importantes parámetros del Sin  T . Para la formación de las t CTs se supuso el uso de 3t líneas no emparentadas cuyo CE fue F (0 &#8804; F &#8804; 1). Se derivó fórmulas generales (0 &#8804; F &#8804; 1) e insesgadas para el FSin  T y la MG. En particular, se encontró que FSin  T = 3(1 + F)/(16t). Por otra parte, como el coeficiente de endogamia de la VS cuyos progenitores son las 3t líneas (FSin  L ) es (1 + F)/(6t), FSin  T &gt; FSin  L . Estas diferencias implican que deba esperarse que el Sin  L tenga una media de rendimiento de grano mayor que la del Sin  T .]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[coancestry]]></kwd>
<kwd lng="en"><![CDATA[genotypic mean]]></kwd>
<kwd lng="en"><![CDATA[identity by descent]]></kwd>
<kwd lng="en"><![CDATA[Zea mays L.]]></kwd>
<kwd lng="es"><![CDATA[coancestría]]></kwd>
<kwd lng="es"><![CDATA[media genotípica]]></kwd>
<kwd lng="es"><![CDATA[identidad por descendencia]]></kwd>
<kwd lng="es"><![CDATA[Zea mays L.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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