AGB 121: Principles of Animal Genetics and Population Genetics (2+1)

ENVIRONMENTAL CORRELATION

• The Environmental correlation is the correlation of environmental deviations together with non-additive genetic deviations between two characters.

Where

• COV_E(XY) is the environmental covariance between X and Y traits and
• σ_E(X) and σ_E(Y) are the standard deviations of the environmental values of the traits X and Y.
• In practice, the environmental covariance and variance are obtained by subtracting additive genetic covariance and variance from the phenotypic covariance and variance. For example, the phenotypic correlation is

and the phenotypic covariance can be written as

• The phenotypic covariance is the sum of the genetic and environmental covariances i.e., COV_P = COV_A + COV_E
• Writing these covariances in terms of the correlations and standard deviations as above gives:

r_P σ_P(X) σ_P(Y) = r_A σ_A(X) σ_A(Y) + r_E σ_E(X) σ_E(Y)

Substituting σ_A = h σ_P and σ_E = e σ_P

r_P σ_P(X) σ_P(Y) = r_A h_X σ_P(X) h_Y σ_P(Y) + r_E e_X σ_P(X) e_Y σ_P(Y)

Dividing through by σ_P(X) σ_P(Y) on both sides leads to

r_P = r_A h_X h_Y + r_E e_X e_Y

• The above equation reveals how genetic and environmental causes of correlations combine together to give phenotypic correlation.
• If both characters have low heritability, the phenotypic correlation is chiefly determined by environmental correlation.
• If they have high heritability, then the r_P is almost entirely genetic.