1. Introduction
Both genetic gains from artificial selection in breeding populations and the genetic responses to selection in natural populations have long been studied since the publication of Darwin’s [1] On the Origin of Species. How best to predict genetic gain from selection in a trait remains crucial in breeding. Lush [2] first proposed the classical breeder’s equation (BE) to predict the genetic response (R) as the product of selection differential (
S
) and the narrow-sense heritability (
h
N
2
), i.e.,
R
=
h
N
2
S
. Lush’s BE was initially applied to predict the genetic response to artificial selection in animal breeding. This BE is now frequently expressed as
Δ
G
=
h
N
2
S
, where
G
is the mean of a trait in the population and
Δ
G
is the change in the mean over one complete cycle of artificial selection, which is commonly termed as genetic gain in plant and animal breeding. The selection differential (
S
) is the difference between the mean of a trait of the selected parents and the mean of the whole parental population.
It is well known that artificial selection is a method of selecting individuals or populations according to the objectives that meet human demands (e.g., yields and quality), with the aim of producing genetically improved populations. It differs from natural selection in objective, the intensity of selection, and the rate of genetically changing populations. The target traits for genetic improvement often refer to those of economical values, although they infrequently refer to the fitness. The selection intensity (or selection differential) is artificially controlled according to the genetic variation in a candidate population. Usually, a strong strength of selection is set to rapidly increase the frequencies of target genes. Analogous to natural selection, artificial selection may be conducted using different ways to change gene frequencies, such as directional, stable, or disruptive selection, depending on the breeding objectives. Multiple cycles of artificial selection are frequently needed to fulfil the breeding objectives.
Most traits studied in plant and animal breeding are quantitative in nature and controlled by many genes. The beauty of this BE is that …
