page_title: Quantitative genetics
section_title: Meiosis determination – reproductive path analysis
hierarchical_section_title: Quantitative genetics / Selection / Background / Meiosis determination – reproductive path analysis
caption_attribution_description: English: Reproductive coefficients of determination and Inbreeding
context_page_description: Quantitative genetics deals with phenotypes that vary continuously —as opposed to discretely identifiable phenotypes and gene-products.
  Both branches use the frequencies of different alleles of a gene in breeding populations, and combine them with concepts from simple Mendelian inheritance to analyze inheritance patterns across generations and descendant lines. While population genetics can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes summaries only of the underlying genetics.
  Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods to link phenotypes to genotypes. Some phenotypes may be analyzed either as discrete categories or as continuous phenotypes, depending on the definition of cut-off points, or on the metric used to quantify them. Mendel himself had to discuss this matter in his famous paper, especially with respect to his peas attribute tall/dwarf, which actually was "length of stem".
context_section_description: The meiosis determination (b²) is the coefficient of determination of meiosis, which is the cell-division whereby parents generate gametes. Following the principles of standardized partial regression, of which path analysis is a pictorially oriented version, Sewall Wright analyzed the paths of gene-flow during sexual reproduction, and established the "strengths of contribution" (coefficients of determination) of various components to the overall result. Path analysis includes partial correlations as well as partial regression coefficients (the latter are the path coefficients). Lines with a single arrow-head are directional determinative paths, and lines with double arrow-heads are correlation connections. Tracing various routes according to path analysis rules emulates the algebra of standardized partial regression.
  The path diagram to the left represents this analysis of sexual reproduction. Of its interesting elements, the important one in the selection context is meiosis. That's where segregation and assortment occur—the processes that partially ameliorate the truncation of the phenotypic variance that arises from selection.  The path coefficients b are the meiosis paths. Those labeled a are the fertilization paths. The correlation between gametes from the same parent (g) is the meiotic correlation. That between parents within the same generation is rA. That between gametes from different parents (f) became known subsequently as the inbreeding coefficient.  The primes ( ' ) indicate generation (t-1), and the unprimed indicate generation t. Here, some important results of the present analysis are given. Sewall Wright interpreted many in terms of inbreeding coefficients.
  The meiosis determination (b²) is ½ (1+g) and equals ½ (1 + f₍ₜ₋₁₎) , implying that g = f₍ₜ₋₁₎. With non-dispersed random fertilization, f₍ₜ₋₁₎) = 0, giving b² = ½, as used in the selection section above. However, being aware of its background, other fertilization patterns can be used as required. Another determination also involves inbreeding—the fertilization determination (a²) equals 1 / [ 2 ( 1 + fₜ ) ] . Also another correlation is an inbreeding indicator—rA = 2 fₜ / ( 1 + f₍ₜ₋₁₎ ), also known as the coefficient of relationship. [Do not confuse this with the coefficient of kinship—an alternative name for the co-ancestry coefficient. See introduction to "Relationship" section.] This rA re-occurs in the sub-section on dispersion and selection.
  These links with inbreeding reveal interesting facets about sexual reproduction that are not immediately apparent. The graphs to the right plot the meiosis and syngamy (fertilization) coefficients of determination against the inbreeding coefficient. There it is revealed that as inbreeding increases, meiosis becomes more important (the coefficient increases), while syngamy becomes less important. The overall role of reproduction [the product of the previous two coefficients—r²] remains the same. This increase in b² is particularly relevant for selection because it means that the selection truncation of the Phenotypic variance is offset to a lesser extent during a sequence of selections when accompanied by inbreeding (which is frequently the case).
caption: Reproductive coefficients of determination and Inbreeding
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