Problem 4 - Biology Concepts and Applications

Question

Certain dominant alleles are so essential for normal development that an individual who is homozygous recessive for a mutant recessive form can't survive. Such recessive, lethal alleles can be perpetuated in the population by heterozygotes. Consider the Manx allele \(\left(M^{L}\right)\) in cats. Homozygous cats \(\left(M^{L} M^{L}\right)\) die when they are still embryos inside the mother cat. In heterozygotes \(\left(M^{L} M\right),\) the spine develops abnormally. The cats end up with no tail (Figure 10.19 ). Two \(M^{L} M\) cats mate. What is the probability that any one of their surviving kittens will be heterozygous?

Step-by-Step Solution

Answer

The probability of a surviving kitten being heterozygous is \(\frac{2}{3}\).

Step 1: Identify the Genotypes

In this problem, we are dealing with the Manx allele (\(M^L\)). The possible genotypes for two \(M^L M\) heterozygous cats that mate are: \(M^L M^L\), \(M^L M\), and \(M M\). However, \(M^L M^L\) is lethal, and these individuals do not survive.

Step 2: Create a Punnett Square

Set up a Punnett Square for the mating of two \(M^L M\) cats. Each parent can pass either the \(M^L\) or \(M\) allele. The possible combinations are: \(M^L M^L\), \(M^L M\), \(M^L M\), and \(M M\).

Step 3: Determine Surviving Genotypes

The genotype \(M^L M^L\) results in embryonic death, so we exclude these from our calculations. The viable genotypes are \(M^L M\) and \(M M\).

Step 4: Calculate Probability of Heterozygotes

Out of the three non-lethal combinations, two are \(M^L M\) (heterozygotes). Therefore, the probability of a surviving kitten being heterozygous \(M^L M\) is \(\frac{2}{3}\).

Key Concepts

Punnett square

A Punnett square is a simple diagram used in genetics to predict the possible genotypes of offspring from a particular set of parents. It is a grid that helps us visualize how the alleles from two parents can combine. This tool is especially useful in scenarios involving genetic traits, such as the Manx allele example.To understand the probabilities of offspring inheriting certain characteristics, we fill in the Punnett square by taking one parent's alleles along the top and the other parent's alleles down the side. This allows for all possible combinations of alleles to be explored within the grid, ensuring a comprehensive overview. Each box inside the square represents a potential genotype of an offspring.For the situation of two heterozygous Manx cats, each parent contributes either the Manx allele \( M^L \) or the normal allele \( M \). The grid includes all combinations: \( M^L M^L \), \( M^L M \), \( M^L M \), and \( M M \). While the \( M^L M^L \) genotype is lethal, predicting this outcome still assists in determining the overall genetic picture for the surviving kittens.

heterozygotes

In genetics, heterozygotes are individuals who possess two different alleles for a specific gene. This is in contrast to homozygotes, who have identical alleles for a trait. In the context of the Manx cats, heterozygotes are expressed as \( M^L M \).These heterozygous individuals are crucial because they can sustain lethal recessive alleles within a population. Even though the \( M^L M^L \) genotype leads to embryonic death, the \( M^L M \) genotype survives and manifests characteristics such as a unique spinal development, resulting in tail-less cats. Heterozygotes play a significant role in maintaining genetic diversity. They allow lethal alleles to persist in the gene pool, as these alleles can be concealed when coupled with a dominant, non-lethal allele. Understanding the frequency and impact of heterozygous individuals offers insight into hereditary conditions and trait propagation in populations.

genotypes

A genotype refers to the genetic makeup of an organism, specifically the allelic composition for a given trait. This genetic code determines various aspects of an organism's appearance and function. In the Manx cat scenario, we evaluate three potential genotypes: \( M^L M^L \), \( M^L M \), and \( M M \).The important factor here is the expression of these genes. The \( M^L M^L \) genotype is lethal and results in non-viable offspring. Consequently, only \( M^L M \) and \( M M \) genotypes are evident in living kittens. Each genotype leads to different phenotypic expressions. For instance, \( M^L M \) results in a tailless cat, while \( M M \) manifests a normal tail. Understanding these genetic compositions can help predict the likelihood of various traits appearing in offspring. The non-lethal genotypes indicate a higher chance of survival and a continuing presence of the Manx trait, albeit always in a restricted pattern due to the lethal nature of the homozygous dominant alleles. Using this insight, breeders and scientists can better grasp genetic principles and manage breeding strategies effectively.