Answer:
The distribution of the genotypes in the next generation will be 25% homozygous recessive, 50% heterozygous and 25% homozygous dominant
Step-by-step explanation:
We have a population of butterflies which can have two possible phenotypes, blue and red, depending on a single gene that exhibits mendelian behaviour.
Let's call the recessive allele "b" and the dominant one "B"
We know that initially the population has 10 blue homozygous recessive (10 bb), 40 red heterozygous (40 Bb) and 10 red homozygous dominant (10 BB)
Then we're told that 10 Bb are "caught and pinned" and therefore, we can assume the won't participate in the next offspring generation.
Now, que population has 10 blue homozygous recessive (10 bb), 30 red heterozygous (30 Bb) and 10 red homozygous dominant (10 BB), with a total of 50 individuals
So, how can we calculate the genotype distribution for the next generation?
First, we need to know the genotype frequencies in this new situation, considering that a frequency it's calculated as the number of individuals with a given phenotype over the total population.
- f(bb)=(nº of bb individuals)/(total population)=10/50=1/5
- f(Bb)=30/50=3/5
- f(BB)=10/50=1/5
Then, we can calculate the allelic frequencies from the genotypic ones, based on how the allele can be passed to the next generation.
- f(b)=f(bb)+(1/2)*f(Bb)=1/5+(1/2)*(3/5)=(2/10)+(3/10)=5/10=1/2
- f(B)=f(BB)+(1/2)*f(Bb)=1/5+(1/2)*(3/5)=(2/10)+(3/10)=5/10=1/2
Note that we can check the calculations are correct, as the sum of the frequencies of all the alleles of a gene, it should be equal to 1 (f(b)+f(B)=1)
Now, we need to calculate the new genotypic frequencies for the next generation.
However, it is not possible to calculate genotypic frequencies from the allelic ones, unless we assume a mathematical model for the behaviour of the population.
With the information we're given, we can assume that the population it's in the Hardy-Weinberg equilibrium. This model can be applied to genes with mendelian behaviour in population with certain characteristics and it states the allelic frequencies don't change from a generation to another.
Among other assumptions, the species must be diploid, mating should be random, generations shouldn't overlap, the population must be big enough to ignore the effect of genetic drift and there aren't any other processes involved that can affect the allelic frequencies (such as mutation, selection or migration).
We can now calculate the new genotypic frequencies. As the matings are random, the probability of a genotype depends on the ways of achieving it.
For example, to obtain the a bb genotype, both parents should contribute with the allele b. So:
- f(bb)=[f(b)]^2= (1/2)^2=1/4 => f(bb)=25%
In an analogous reasoning, we can deduce that:
- f(BB)=[f(B)]^2= (1/2)^2=1/4 => f(BB)=25%
- f(Bb)=2*f(b)*f(b)=1/2 => f(Bb)=50%
In summary we can say the genotype distribution of genotypes would be 25% of blue homozygous recessive (bb), 50% red heterozygous (Bb) and 25% red homozygous dominant (BB).