*** h2, heritability

http://content.csbs.utah.edu/~rogers/ant5221/lecture/QTs2.pdf

See also 

https://en.wikipedia.org/wiki/Coefficient_of_determination

https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient

http://hongqinlab.blogspot.com/2013/11/how-to-generated-correlated-random.html

http://hongqinlab.blogspot.com/2014/03/simulated-correlated-data-points-with.html

My R code on h2

set.seed(2015)

N=1E3

genotype_elements = c(-1,0,1)

#genotype_elements = rnorm(N)

error = rnorm(N)

tb = data.frame(error)

tb$g1 = sample(genotype_elements, N, replace=T)

h2 = 0.5

tb$phynotype = sqrt(h2)*tb$g1 + sqrt(1-h2)*tb$error

summary(lm(tb$phynotype ~ tb$g1))

tb$g2 = sample(genotype_elements, N, replace=T)

h2 = 1/10

tb$phynotype = sqrt(h2)*tb$g1 + sqrt(h2)*tb$g2+ sqrt(1-2*h2)*tb$error

summary(lm(tb$phynotype ~ tb$g1 + tb$g2))

h2 = 1/10

tb$g3 = sample(genotype_elements, N, replace=T)

tb$phynotype = sqrt(h2)*tb$g1 + sqrt(h2)*tb$g2 + sqrt(h2)*tb$g3 + sqrt(1-2*h2)*tb$error

summary(lm(tb$phynotype ~ tb$g1 + tb$g2 + tb$g3))

summary(lm(tb$phynotype ~ tb$g1 ))

summary(lm(tb$phynotype ~ tb$g2 ))

summary(lm(tb$phynotype ~ tb$g3 ))