Question

In an isolated mountain village, the gene frequencies of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{O}\) blood alleles are \(0.95,0.04\), and \(0.01\), respectively. If the total population is 424 , calculate the number of individuals with \(\mathrm{O}, \mathrm{A}, \mathrm{B}\), and \(\mathrm{AB}\) type blood.

Short answer

In the isolated mountain village, there are approximately \(1\) individual with O type blood, \(391\) individuals with A type blood, \(1\) individual with B type blood, and \(16\) individuals with AB type blood.

Step-by-step solution

Calculate the Frequency of the O Allele

First, we will calculate the frequency of the O allele. As mentioned earlier, we can find this by subtracting the total of A and B frequencies from 1: O frequency = \(1 - (A \space frequency + B \space frequency)\) O frequency = \(1 - (0.95 + 0.04)\) O frequency = \(0.01\) Now we know the O allele frequency is 0.01.

Calculate the Number of Individuals with O Type Blood

O type blood is characterized by having two O alleles. Using the Hardy-Weinberg equilibrium formula, we can calculate the proportion of this genotype in the population by squaring the O frequency: O type individuals proportion = (O frequency)^2 O type individuals proportion = \((0.01)^2\) O type individuals proportion = \(0.0001\) Now, we can find the number of individuals with O type blood by multiplying this proportion by the total population: O type individuals = O type individuals proportion × Total population O type individuals = \(0.0001 × 424\) O type individuals = \(0.0424\) Since we cannot have a fraction of a person, we round it up to the nearest whole number, which is 1.

Calculate the Number of Individuals with A Type Blood

A type blood is characterized by having two A alleles (AA genotype) or one A and one O allele (AO genotype). We'll calculate them separately and then sum the two results: AA individuals proportion = (A frequency)^2 AA individuals proportion = \((0.95)^2\) AA individuals proportion = \(0.9025\) AO individuals proportion = 2 × A frequency × O frequency AO individuals proportion = \(2 × 0.95 × 0.01\) AO individuals proportion = \(0.019\) A type blood proportion = AA individuals proportion + AO individuals proportion A type blood proportion = \(0.9025 + 0.019\) A type blood proportion = \(0.9215\) Now, we can find the number of individuals with A type blood by multiplying this proportion by the total population: A type individuals = A type blood proportion × Total population A type individuals = \(0.9215 × 424\) A type individuals ≈ \(391\)

Calculate the Number of Individuals with B Type Blood

B type blood is characterized by having two B alleles (BB genotype) or one B and one O allele (BO genotype). We'll calculate them separately and then sum the two results: BB individuals proportion = (B frequency)^2 BB individuals proportion = \((0.04)^2\) BB individuals proportion = \(0.0016\) BO individuals proportion = 2 × B frequency × O frequency BO individuals proportion = \(2 × 0.04 × 0.01\) BO individuals proportion = \(0.0008\) B type blood proportion = BB individuals proportion + BO individuals proportion B type blood proportion = \(0.0016 + 0.0008\) B type blood proportion = \(0.0024\) Now, we can find the number of individuals with B type blood by multiplying this proportion by the total population: B type individuals = B type blood proportion × Total population B type individuals = \(0.0024 × 424\) B type individuals ≈ \(1\)

Calculate the Number of Individuals with AB Type Blood

AB type blood is characterized by having one A and one B allele. We'll now calculate the proportion of this genotype in the population: AB individuals proportion = A frequency × B frequency AB individuals proportion = \(0.95 × 0.04\) AB individuals proportion = \(0.038\) Now, we can find the number of individuals with AB type blood by multiplying this proportion by the total population: AB type individuals = AB individuals proportion × Total population AB type individuals = \(0.038 × 424\) AB type individuals ≈ \(16\)

Present the Results

Finally, we have calculated the number of individuals with different blood types in this isolated mountain village: O type blood individuals: \(1\) A type blood individuals: \(391\) B type blood individuals: \(1\) AB type blood individuals: \(16\)

Key concepts

Allele Frequency Calculation

Calculating allele frequencies is fundamental in understanding genetics and is central to the Hardy-Weinberg equilibrium. In genetics, an allele is one of two or more versions of a gene. Allele frequencies measure how common an allele is in a population and are calculated by dividing the number of occurrences of a specific allele by the total number of alleles for that gene in the population.

To distill it further, consider a gene with two alleles, A and B, and a population where the A allele appears 60 times, and the B allele appears 40 times. The total number of alleles would be 100 (60 A alleles + 40 B alleles). The frequency for allele A would be 0.60 (60/100), and for B, it would be 0.40 (40/100).

In our exercise with blood types, we used the given frequencies of A, B, and O alleles in a population to eventually calculate the number of individuals with each blood type. Understanding allele frequencies is a prerequisite for this and many other genetic calculations.

Genotypic Proportion

Genotypic proportion refers to the percentage of individuals in a population who have a specific genotype. This is a key concept in studying population genetics and can help predict the distribution of genetic traits. In our Hardy-Weinberg example, genotypic proportions are calculated using allele frequencies and certain assumptions, such as random mating and no evolutionary influences (e.g., mutation, selection, genetic drift)

Now consider a population and its genotype for a particular gene. If allele A appears with a frequency of 0.7 and allele B appears with a frequency of 0.3, the expected proportion of the AA genotype is \(0.7^2 = 0.49\), BB genotype is \(0.3^2 = 0.09\), and for the heterozygous AB genotype, it is \(2 * 0.7 * 0.3 = 0.42\), assuming Hardy-Weinberg equilibrium.

In the context of blood type, as we have done in the textbook exercise, genotypic proportions determine the number of individuals with each blood type genotype within the population. Translating these proportions into numbers can inform healthcare strategies, like blood bank storage protocols, in the community involved.

Blood Type Genetics

Blood type genetics is based on the ABO blood group system, which is determined by the presence or absence of antigens on red blood cells. The ABO system has three alleles: \(I^A\), \(I^B\), and \(i\), which combine to give four possible blood types: A, B, AB, and O. Blood type A individuals can have genotypes \(I^AI^A\) or \(I^Ai\), B types \(I^BI^B\) or \(I^Bi\), AB types have \(I^AI^B\), and type O have \(ii\).

Inherited from our parents, the combination of alleles determines our blood type, which is crucial for blood transfusions and understanding genetic inheritance patterns. In our exercise, we demonstrated how to calculate the number of individuals with each blood type in a population using allele frequencies. This application of Hardy-Weinberg principles to blood type genetics is especially important in fields of medicine and forensic science for identifying and understanding population structures.