|Animal Trait Correlation Database|
Frequently Asked Questions
Correlation Coefficient (r) is a statistical parameter that describes the degree as how closely the pairs of variables are related.
R-square: The square of the coefficient (, also known as "coefficient of determination") is equal to the percent of the variation in one variable that is related to the variation in the other,While correlation coefficients () are normally reported as a value between -1 and +1, r-square is always between 0 and 100%. E.g. After squaring r, ignore the decimal point. An r of .5 means 25% of the variation is related (.5 squared =.25). An r value of .7 means 49% of the variance is related (.7 squared = .49).
For genetic analysis, the geneticists partition the correlation into phenotypic correlations and genetic correlations. The phenotypic correlation is the correlation between records of two traits on the same animal and is usually estimated by the product-moment correlation statistic (or Pearson correlation coefficient, for short).
Variance Components of a Quantitative Trait in the eyes of geneticists:Phenotypic variance is simply the observed, measured variance in a trait. Its estimates is the sum of total genetic variance, non-genetic variance, and possibily the interactions of the two factors.
VP = VG + VE + VGE
where VP = total phenotypic variation
VG = total genetic factor variation
VE = total environmental factor variation
VGE = genetic X environmental factor interaction variation
Genetic variance = additive genetic variance
+ dominant genetic variance
+ epestatic genetic variance
+ interaction between/among all previous genetic variances
Non-genetic variance = variances due to environmental factors + Error.
Sources of Genetic Variations:Genetic variations may come from Additive Genetic Variations (VA), Dominance Variations (VD), and Epistatic Variations, or Interaction Genetic Variations (VI). VD and VI are called Non-Additive Genetic Variations. Thus:
VG = VA + VD + VI
∴ VP = VA + VD + VI + VE + VGE
Variance Components of a Quantitative Trait in the eyes of statisticians:
In classical genetic analysis, the residual variance is often conveniently used to represent environmental variations, referring to "everything else" after the explained variations.
It is worth to note that, in a more resent study, Huang and Mackay (2016) showed evidences to indicate that variance component analysis should not be used to infer genetic architecture of quantitative traits.
H2 = VG / VPThis is called heritability in the broad sense because it is a rather crude measure that includes reasons for the genetic variation that are not necessarily passed on to the next generation.
Narrow sense heritability gives the ratio of additive genetic variance/ phenotypic variance:
h2 = VA / VP
The reason why the additive genetic variance matters here is because what's passed on to the next generation are only the alleles (NOT the dominance interaction NOR the epistatic interaction). The allele sets to be passed on are formed newly at each generation. For example, at generation one, some offspring may have alleles A1/A3 and B2/B4. They are new combinations not seen in either parent, therefore the dominance and epistatic interactions will be new. In general, greater the additive genetic variability VA in a population, greater the diversity it, thus greater selection potentials (greater the narrow-sense heritability);
There could have been a confusion between "environmental veriance" and "residual variance" as they both serve as "the other", or "everything else", less important variance component when study focus is mostly on genetic variances. Although "environmental veriance" and "residual variance" may pretty much overlap, they are not the same. The "environmental veriance" is a genetic concept (or method for variance partitions), whereas the "residual variance" is a statistical concept (or method for variance partitions).
It is not uncommon to see in publications that some only report "genetic + environment", and some others report "genetic + residual" variances. When they are curated into the CorrDB, we record they as they are (i.e. "residual" variance into a "residual" field and "environment" variance into a "environment" field. It will be up to users how these data will be looked at.
Genomic heritability: the proportion of variance of a trait that can be explained (in the population) by a linear regression on a set of markers. Depending on the types of marker used, there can be SNP-based, Indel based, on methods there can be GCTA based heritability estimates. (GCTA - Genome-wide Complex Trait Analysis.)
SNP-based heritability (or SNP) was initially defined as the proportion of phenotypic variance explained by all SNPs on a genotyping array and is therefore dependent of the number of SNPs on a SNP array, and later expanded to refer to the variance explained by any set of SNPs (Yang et al., 2017).
One can estimate the relationships between individuals based on their genotypes and use a linear mixed model to estimate the variance explained by the genetic markers. This gives a genomic heritability estimate based on the variance captured by common genetic variants. Other types of estimates include using GCTA approch (GCTA), among others.
First draft: January 9, 2018
Last update: December 31 2019 09:25:37.
By Zhiliang Hu|
Dept of Animal Science
Iowa State University
Douglas S. Falconer, Trudy F.C. Mackay (1996), Introduction to Quantitative Genetics. Published by Pearson, Edinburgh Gate, Harlowm Essex CM20 2JE, England.
Wen Huang and Trudy F.C.Mackay (2016), "The Genetic Architecture of Quantitative Traits Cannot Be Inferred from Variance Component Analysis". PLoS Genet. 12(11).
Peter M. Visscher, William G. Hill and Naomi R. Wray, (2008), "Heritability in the genomics era — concepts and misconceptions". Nat Rev Genet. 9(4):255-66.
Jian Yang, Jian Zeng, Michael E Goddard, Naomi R Wray & Peter M Visscher (2017), "Concepts, estimation and interpretation of SNP-based heritability". Nature Genetics, 49:1304–1310.
John Stanton-Geddes, Jeremy B. Yoder, Roman Briskine, Nevin D. Young, and Peter Tiffin (2013), "Estimating heritability using genomic data". Methods in Ecology and Evolution, 4:1151–1158.
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