Animal Trait Correlation Database |
Frequently Asked Questions
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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,
= Explained variation / Total variation
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). The genetic correlation is the correlation between an animal's genetic value for one trait and the same animal's genetic value for the other trait.
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.
V_{P} = V_{G} + V_{E} + V_{GE}
where V_{P} = total phenotypic variation
V_{G} = total genetic factor variation
V_{E} = total environmental factor variation
V_{GE} = 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 (V_{A}),
Dominance Variations (V_{D}), and Epistatic Variations, or
Interaction Genetic Variations (V_{I}). V_{D} and V_{I}
are called Non-Additive Genetic Variations. Thus:
V_{G} = V_{A} + V_{D} + V_{I}
∴ V_{P} = V_{A} + V_{D} + V_{I} + V_{E} + V_{GE}
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.
H^{2} = V_{G} / V_{P}
This 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:
h^{2} = V_{A} / V_{P}
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 V_{A} 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.
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First draft: January 9, 2018 Last update: February 15 2019 11:57:50. |
By Zhiliang Hu Associate Scientist Dept of Animal Science Iowa State University | ||||||||||||
Reference
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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