Breeders equation - 5 practice problems

The response to selection ( R ) can be calculated using the breeder’s
equation:

2
R=H ∙ S
Where:

R = Response to selection

(Change in the mean trait value from one generation to the next due to
selection)
2
H = Narrow-sense heritability
(The proportion of phenotypic variance that is due to additive genetic
variance)
S = Selection differential

(The difference between the mean trait value of the selected parents and
the mean trait value of the original population)



To calculate R , you need to determine heritability H 2 and the selection
differential S

2
H is obtained from estimates using parent-offspring regression, twin
studies, variance component analysis and more

S is obtained by subtracting the mean trait value of the original population
from the mean trait value of the selected parents



Example:

Suppose:


- The heritability of a trait is 0.4
- The mean trait value in the original population is 50
- The mean trait value in the selected parents is 60



To calculate R , we need H 2 and S
2
H is given, 0.4

, S = mean trait value in the selected parents – mean trait value of the
original population

S = 60 – 50 = 10

And then to calculate R:

2
R=H ∙ S
R=0 .4 ∙10=4



Now we can predict the mean trait value in the next generation F1 by
adding R to the mean trait value of the original population:


50 + 4 = 54

2
H , the narrow-sense heritability, can be calculated by dividing the
additive genetic variance with the phenotypic variance

Va
H 2=
Vp

Where:

2
H = Narrow-sense heritability
Va = Additive genetic variance: The genetic contribution to the trait that
can be passed on from parent to offspring
V p = Phenotypic variance: The total variation observed in the trait,
including both genetic and environmental effects.



Example

Suppose:


- The additive genetic variance is 15
- The total phenotypic variance is 25

To calculate H 2, we need Va and Vp