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A certain organism possesses a pair of each of 5 different
Chapter 3, Problem 69P(choose chapter or problem)
Problem 69P
A certain organism possesses a pair of each of 5 different genes (which we will designate by the first 5 letters of the English alphabet). Each gene appears in 2 forms (which we designate by lowercase and capital letters). The capital letter will be assumed to be the dominant gene, in the sense that if an organism possesses the gene pair xX, then it will outwardly have the appearance of the X gene. For instance, if X stands for brown eyes and x for blue eyes, then an individual having either gene pair XX or xX will have brown eyes, whereas one having gene pair xx will have blue eyes. The characteristic appearance of an organism is called its phenotype, whereas its genetic constitution is called its genotype. (Thus, 2 organisms with respective genotypes aA, bB, cc, dD, ee and AA, BB, cc, DD, ee would have different genotypes but the same phenotype.) In a mating between 2 organisms, each one contributes, at random, one of its gene pairs of each type. The 5 contributions of an organism (one of each of the 5 types) are assumed to be independent and are also independent of the contributions of the organism’s mate. In a mating between organisms having genotypes aA, bB, cC, dD, eE and aa, bB, cc, Dd, ee what is the probability that the progeny will (i) phenotypically and (ii) genotypically resemble
(a) the first parent?
(b) the second parent?
(c) either parent?
(d) neither parent?
Questions & Answers
QUESTION:
Problem 69P
A certain organism possesses a pair of each of 5 different genes (which we will designate by the first 5 letters of the English alphabet). Each gene appears in 2 forms (which we designate by lowercase and capital letters). The capital letter will be assumed to be the dominant gene, in the sense that if an organism possesses the gene pair xX, then it will outwardly have the appearance of the X gene. For instance, if X stands for brown eyes and x for blue eyes, then an individual having either gene pair XX or xX will have brown eyes, whereas one having gene pair xx will have blue eyes. The characteristic appearance of an organism is called its phenotype, whereas its genetic constitution is called its genotype. (Thus, 2 organisms with respective genotypes aA, bB, cc, dD, ee and AA, BB, cc, DD, ee would have different genotypes but the same phenotype.) In a mating between 2 organisms, each one contributes, at random, one of its gene pairs of each type. The 5 contributions of an organism (one of each of the 5 types) are assumed to be independent and are also independent of the contributions of the organism’s mate. In a mating between organisms having genotypes aA, bB, cC, dD, eE and aa, bB, cc, Dd, ee what is the probability that the progeny will (i) phenotypically and (ii) genotypically resemble
(a) the first parent?
(b) the second parent?
(c) either parent?
(d) neither parent?
ANSWER:
Step 1 of 4
(a)
We are asked to find the probability that the progeny will phenotypically and genotypically resemble the first parent.
The potential genotypes and phenotypes of the offspring produced by mating the first parent with an genotype and a second parent with an
genotype.
We can see that in 2 of 4 possible cases we get the gene pair and in 2 of 4 possible cases we get the gene pair
This gives the probability of for either genotype
and probabilities of
for the recessive phenotypes
and the dominant phenotypes
We can represent this in the table as,
Lets first compute the probability that a child receives various genotypes/phenotypes when crossing one single gene pair from each parent.
We can list this into the table that the probability of a child having genotypes that match the first parent and second parent.
These probabilities can be computed by considering the possible genes that a given parent can give to his/her offspring.
a,a |
a,a |
1 |
1 |
a,a |
a,A |
0.5 |
0.5 |
a,a |
A,A |
0 |
0 |
a,A |
a,a |
0.5 |
0.5 |
a,A |
a,A |
0.5 |
0.5 |
a,A |
A,A |
0.5 |
0.5 |
A,A |
a,a |
0 |
0 |
A,A |
a,A |
0.5 |
0.5 |
A,A |
A,A |
1 |
1 |
Table 1: The probability of various matching genotypes, for the child denoted by and the two parents
and
The notations
and
means that the child’s genotype matches that of the first and second parent respectively.
In the same way in Table 2 we list the probability of a child having phenotypes that match or not the two parents.
Each pair of genes is independent of the others.
a,a |
a,a |
1 |
1 |
a,a |
a,A |
0.5 |
0.5 |
a,a |
A,A |
0 |
1 |
a,A |
a,a |
0.5 |
0.5 |
a,A |
a,A |
0.75 |
0.75 |
a,A |
A,A |
1 |
1 |
A,A |
a,a |
1 |
0 |
A,A |
a,A |
1 |
1 |
A,A |
A,A |
1 |
1 |
Table 2: The probability of various matching phenotypes, for the child denoted by and the two parents
and
The notations
and
means that the child’s phenotype matches that of the first and second parent respectively.
Using Table 1 and independence of genes we can see that to get a child’s genotype that matches the first parent will happen with probability of
Using Table 2 and independence of genes we can see that to get a child’s genotype that matches the first parent will happen with probability of
Hence the probability that the progeny will phenotypically and genotypically resemble the first parent is and
respectively.