Problem 7 - Biology: The Dynamic Science

Question

A population of mice is at Hardy-Weinberg equilibrium at a gene locus that controls fur color. The locus has two alleles, \(M\) and \(m .\) A genetic analysis of one population reveals that \(60 \%\) of its gametes carry the \(M\) allele. What percentage of mice contains both the \(M\) and \(m\) alleles? a. \(60 \%\) b. \(48 \%\) c. \(40 \%\) d. \(36 \%\) e. \(16 \%\)

Step-by-Step Solution

Answer

48%

Step 1: Understand Hardy-Weinberg equilibrium conditions

According to the Hardy-Weinberg principle, the genetic structure of a population will remain constant unless other evolutionary influences are acting upon the population. One of the key conditions for a population to be in Hardy-Weinberg equilibrium is that allele frequencies should remain constant from generation to generation in the absence of other evolutionary pressures.

Step 2: Calculate the allele frequency of the recessive allele

If 60% of the gametes carry the M allele, then 100% - 60% = 40% of the gametes will carry the m allele. This is because there are only two alleles, M and m, and their combined frequencies must add up to 100%.

Step 3: Determine the percentage of heterozygous individuals

In a population at Hardy-Weinberg equilibrium, the proportion of heterozygous individuals can be calculated using the equation 2pq, where p and q represent the frequencies of the M and m alleles, respectively. Given that p = 0.6 and q = 0.4, we calculate 2pq: \(2 \times 0.6 \times 0.4 = 0.48\). Therefore, 48% of the population contains both the M and m alleles.

Key Concepts

Allele Frequencies

Understanding allele frequencies is a cornerstone in the study of population genetics, as it pertains to the relative proportions of different genetic variants—allele—at a particular gene locus within a population. In the provided exercise, it highlights a population of mice at Hardy-Weinberg equilibrium, focusing on the gene that controls fur color with two alleles, M and m. Here, knowing that 60% of gametes carry the M allele leads to the conclusion that the remaining 40% must carry the m allele because the total must equal 100%.

This simple subtraction is profoundly important, as it sets the stage for predicting the genetic makeup in the next generation under stable conditions—no evolution, no migration, no mutation, no natural selection, and random mating. It is how scientists can estimate the genetic diversity of a population, which is fundamental for conservation biology and understanding evolutionary processes.

Moreover, allele frequencies under the Hardy-Weinberg model allow for predictions about how many individuals in a population will have certain genetic traits, which was the key in solving the given exercise.

Heterozygous Individuals

A heterozygous individual possesses two different alleles of a gene, one from each parent. In the context of the textbook exercise, these individuals have both M and m alleles for the fur color gene. Calculating the proportion of heterozygous individuals within a population is crucial for understanding the genetic variation present. The Hardy-Weinberg equation, specifically the term 2pq, is used to determine the frequency of heterozygous individuals—one of the most insightful aspects when assessing a population's genetic health.

The accurate prediction of individuals carrying both alleles, as derived from the exercise using the formula, demonstrates how genetic diversity is maintained within populations. By identifying the proportion of heterozygotes, researchers can infer much about a population's genetic structure and potential vulnerability to environmental changes or disease.

Population Genetics

The broad field of population genetics explores the genetic composition of populations and how it changes over time and space. It combines principles of Mendelian genetics and evolutionary theory to provide a framework for understanding the genetic variation observed in natural populations.

In the exercise, the Hardy-Weinberg principle is applied, which serves as a null hypothesis in population genetics. When a real population is found to be in Hardy-Weinberg equilibrium, researchers can deduce that the evolutionary forces are not actively reshaping the genetic structure. Conversely, deviations from equilibrium can signal the action of evolutionary processes like selection, gene flow, or genetic drift.

An understanding of population genetics extends beyond academics; it's applied in areas such as conservation to manage and preserve species, in medicine to understand genetic diseases, and it helps trace patterns in human ancestry. The ability to predict the genetic structure of a population under different scenarios is a powerful tool, enabling us to preserve genetic diversity, which is vital for the resilience and survival of species in changing environments.