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Problem Set #7: Quantitative Genetics, Complex Traits KEY
1).
A horse breeder wants to develop a breed of small horses for children to ride.
From a
heterogenous population of 100 horses with a mean height of 60 inches, a subpopulation of horses
with a mean height of 45 inches was chosen and interbred.
The progeny of these matings had a
mean height of 55 inches.
a. What is the narrow sense heritability (h
2
) of height in this population of horses?
f8e5
y
= 60, y
p
= 45, y
o
= 55
h
2
= (y
o
– y) /(y
p
– y) = 5/15 = 0.33
b.
From the progeny of the first round of selective matings, a subpopulation of horses is again
chosen with a mean height of 45 inches and interbred.
What do you expect to be the mean height
of the progeny of this second round of matings?
y = 55, y
p
= 45, h
2
= 0.33
y
o
=
f8e5
y +
h
2
(y
p
– y) = 55 +
0.33 (45 – 55) = 51.7
2.)
Two inbred lines of Drosophila are crossed together – one with a high density of abdominal
bristles and another with a low density. F
1
flies have a mean of 20 abdominal bristles with a
standard deviation of 2. F1s are crossed to produce an F
2
generation, in which the flies also have
a mean of 20 abdominal bristles but with a standard deviation of 3. Calculate the genotypic
variance, environmental variance, and broad sense heritability (H
2
).
Variance = standard deviation
2
so variance for F
1
population is 4 and for F
2
population is 9.
For a genetically uniform population such as this F
1
population produced by crossing two
inbred lines together, all the variance is environmental so V
e
= 4
.
In the genetically heterogeneous F
2
population, V
t
= V
g
+ V
e
so V
g
= V
t
– V
e
= 9 – 4 = 5
.
H
2
= V
g
/V
t
= 5/9 = 0.556
Broad sense heritability is measure of how much of the phenotypic variation (variance)
observed in a population is due to genetic factors (as opposed to environmental factors)
3).
Wild relatives of cultivated crop plants often provide a valuable source of alleles for crop
improvement.
An inbred strain of cultivated strawberries, whose fruit is sweet and juicy but
highly susceptible to mold (mean mold susceptibility score of 100) was crossed to an inbred
strain of wild strawberries whose fruit is relatively hard and not as sweet, but more resistant to
mold (mean susceptibility score 20).
The F
1
hybrids had a mean susceptibility score of 60 with a
variance of 26.
Selfpollination of the F
1
s produced a heterogeneous F
2
population with a mean
susceptibility score of 60 and a variance of 225.
a. What is the broad sense heritability for mold susceptibility in strawberries?
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 Fall '08
 Nehring
 Genetics

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