Question

In a population of 10,000 individuals, where 3600 are \(M M\) 1600 are \(N N,\) and 4800 are \(M N,\) what are the frequencies of the \(M\) alleles and the \(N\) alleles?

Short answer

Answer: The frequency of M alleles is 0.6 and the frequency of N alleles is 0.4 in the given population.

Step-by-step solution

Count the number of M and N alleles

To count the number of M alleles, we need to consider both individuals who have only M alleles (\({MM})\) and those with both M and N alleles (\({MN}).\) As each individual carries 2 alleles, there are 2 M alleles in each \({MM}\) individual and 1 M allele in each \({MN}\) individual. Similarly, we count the number of N alleles, accounting for the \({NN}\) and \({MN}\) individuals.

Calculate the number of M and N alleles

With the information given, we can calculate the number of M and N alleles in the population as follows: Number of M alleles = \(2 * 3600 + 4800 = 7200 + 4800 = 12,000\) Number of N alleles = \(2 * 1600 + 4800 = 3200 + 4800 = 8,000\)

Calculate the total number of alleles in the population

Since each of the 10,000 individuals has 2 alleles, the total number of alleles in the population is: Total number of alleles = \(10,000 * 2 = 20,000\)

Calculate the frequencies of M and N alleles

To find the frequency of M alleles, we can divide the number of M alleles by the total number of alleles in the population. Frequency of M alleles = \(\frac{12,000}{20,000} = 0.6\) Similarly, we can find the frequency of N alleles by dividing the number of N alleles by the total number of alleles in the population. Frequency of N alleles = \(\frac{8,000}{20,000} = 0.4\) Thus, the frequency of M alleles is 0.6 and the frequency of N alleles is 0.4 in the given population.

Key concepts

Population Genetics

Population genetics is a subfield of genetics that deals with the study of genetic variation within populations and the genetic differences among various populations. It involves the examination of allele frequencies, genotypic frequencies, and how these frequencies change over time under the influence of evolutionary processes such as natural selection, mutation, genetic drift, and gene flow.

For example, when we look at a population of 10,000 individuals where the presence of two alleles, M and N, is observed, the first step in population genetics is to determine the frequency of these alleles. Allele frequency is the proportion of all copies of a gene that is made up of a particular gene variant (allele). In our case, calculating the frequency of alleles M and N provides us an understanding of how these alleles are distributed within the population.

At its core, population genetics seeks to explain the causes and consequences of genetic variation, which directly ties into how a species adapts to its environment and how this may lead to evolutionary changes over time.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a principle that provides a mathematical baseline for studying genetic variation in a population that is not evolving. This equilibrium state is achieved when allele frequencies in the population remain constant from generation to generation, provided that certain conditions such as a large breeding population, random mating, no mutation, no migration, and no natural selection are met.

Under the Hardy-Weinberg equilibrium, the expected frequencies of genotypes—such as those individuals with MM, MN, or NN combinations in our example—can be predicted using the allele frequencies. The principle is often expressed by the equation: \( p^2 + 2pq + q^2 = 1 \) where \( p \) and \( q \) represent the frequency of two alleles, and \( p^2 \) , \( 2pq \) , \( q^2 \) reflect the frequencies of the corresponding genotypes. When allele frequencies are known, as in our exercise with M and N alleles, the Hardy-Weinberg equation can be a robust tool for predicting the genetic structure of a population, assuming no other evolutionary influences are at play.

Genetic Variation

Genetic variation refers to the diversity in gene frequencies within a species. This variation is what makes each individual unique and is essential for a population's adaptability and survival. Sources of genetic variation include mutations, which can introduce new gene variants, and sexual reproduction, which recombines alleles into new configurations.

In our exercise, genetic variation is represented by the existence of M and N alleles within the population. The balance between these alleles and their distribution defines the population's genetic diversity. The higher the genetic variation, the more likely the population can withstand environmental changes and resist diseases since there's a greater chance that some individuals will carry advantageous traits.

Understanding how genetic variation is distributed and how it changes over time is crucial in fields such as conservation biology, where maintaining genetic diversity is often a key goal in preserving species.