  Heritability is a central parameter in quantitative genetics, both from an
evolutionary and a breeding perspective. For plant traits heritability is
traditionally estimated by comparing within and between genotype variability.
This approach estimates broad-sense heritability, and does not account for
different genetic relatedness. With the availability of high-density markers
there is growing interest in marker based estimates of narrow-sense
heritability, using mixed models in which genetic relatedness is estimated from
genetic markers. Such estimates have received much attention in human genetics
but are rarely reported for plant traits. A major obstacle is that current
methodology and software assume a single phenotypic value per genotype, hence
requiring genotypic means. An alternative that we propose here, is to use mixed
models at individual plant or plot level. Using statistical arguments,
simulations and real data we investigate the feasibility of both approaches,
and how these affect genomic prediction with G-BLUP and genome-wide association
studies. Heritability estimates obtained from genotypic means had very large
standard errors and were sometimes biologically unrealistic. Mixed models at
individual plant or plot level produced more realistic estimates, and for
simulated traits standard errors were up to 13 times smaller. Genomic
prediction was also improved by using these mixed models, with up to a 49%
increase in accuracy. For GWAS on simulated traits, the use of individual plant
data gave almost no increase in power. The new methodology is applicable to any
complex trait where multiple replicates of individual genotypes can be scored.
This includes important agronomic crops, as well as bacteria and fungi.
