Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is Next generation Re d P i n k W h i t e This generation Re d P i n k W h i t e .5 .5 0 .25 .5 .25 0 .5 .5 Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at 25 % red, 50 % pink, and 25 % white. (Find the stationary matrix.)
Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is Next generation Re d P i n k W h i t e This generation Re d P i n k W h i t e .5 .5 0 .25 .5 .25 0 .5 .5 Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at 25 % red, 50 % pink, and 25 % white. (Find the stationary matrix.)
Solution Summary: The author proves that regardless of the makeup of first generation, the genotype composition will eventually stabilize at 25% red,
Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is
Next generation
Re
d
P
i
n
k
W
h
i
t
e
This
generation
Re
d
P
i
n
k
W
h
i
t
e
.5
.5
0
.25
.5
.25
0
.5
.5
Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at
25
%
red,
50
%
pink, and
25
%
white. (Find the stationary matrix.)
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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