Question

A man is homozygous dominant for alleles at 10 different genes that assort independently. How many genotypically different types of sperm cells can he produce? A woman is homozygous recessive for the alleles of 8 of these 10 genes, but she is heterozygous for the other 2 genes. How many genotypically different types of eggs can she produce? What hypothesis can you suggest to describe the relationship between the number of different possible gametes and the number of heterozygous and homozygous genes that are present?

Short answer

The man can produce 1 type of sperm cell, while the woman can produce 4 different types of egg cells. The number of different potential gametes equals 2 to the power of the number of heterozygous genes present.

Step-by-step solution

Determine the Number of Sperm Cell Types

Since the man is homozygous dominant for alleles at 10 different genes, he can only produce one type of sperm cell for each gene, because there are no alternative alleles that can be passed on. As the genes assort independently, the total number of different types of sperm cells is the product of the different types of alleles for each gene. In this case, that is simply 1.

Determine the Number of Egg Cell Types

The woman is homozygous recessive for alleles at 8 out of 10 genes, meaning she can only produce one type of egg cell with the recessive allele for these 8 genes. However, for the remaining 2 genes where she is heterozygous, she can produce two types of egg cells (one with the dominant allele and one with the recessive allele). The total number of different types of egg cells she can produce is calculated by multiplying the number of types for each gene. Thus, for the 8 homozygous genes, she can produce only one type of egg cell each. For the 2 heterozygous genes, she can produce 2 types each. Therefore, the total number of genotypically different egg cells she can produce is 1^8 * 2^2 = 1 * 4 = 4.

Formulate a Hypothesis

The number of different possible gametes is equal to 2 raised to the power of the number of heterozygous genes in the individual. For genes that are homozygous, only one kind of allele can be passed on, so they do not contribute to the diversity of gametes.

Key concepts

Independent Assortment

The principle of independent assortment is a fundamental concept in genetics that explains how different genes independently separate from one another when reproductive cells develop. During meiosis, which is the process that produces sperm and egg cells, chromosomes are distributed randomly into each gamete.

This means that each gamete has an equal chance of receiving either the maternal or paternal chromosome. For instance, if we look at our man with homozygous dominant alleles, his genes will consistently pass on the dominant allele. Since they're all homozygous, his sperm cells won't display diversity; they'll all be the same in genotypic respect. For the woman with the heterozygous genes, however, the trait from either mom or dad can be passed on independently for each of the 2 genes she's heterozygous for, resulting in varying combinations and thus, different types of eggs.

Homozygous and Heterozygous Alleles

Genes exist in pairs of alleles, and these alleles can either be homozygous or heterozygous. When an individual has two identical alleles for a particular gene, they are said to be homozygous. In our problem, the man has homozygous dominant alleles, meaning all his alleles for the 10 genes are the same dominant type, represented symbolically as 'AA' for example.

On the other hand, if the alleles are different—one dominant and one recessive—the individual is heterozygous, depicted as 'Aa'. The woman in our scenario is homozygous recessive for 8 genes and heterozygous for 2. The difference between homozygous and heterozygous alleles is directly linked to the variety of gametes an individual can produce. Homozygosity leads to uniform gametes, as seen with the man's sperm, while heterozygosity introduces variation, as evidenced by the four types of eggs the woman produces.

Genetics and Heredity

Genetics and heredity are terms closely linked to the study of how traits are passed from parents to offspring. Through the principles of genetics, we understand that genes—which carry the instructions for traits—are the units of heredity. Each parent contributes one allele for every gene, which come together to form the offspring's genotype.

The genotype then influences the phenotype, or the physical expression of traits. Inheriting two dominant or two recessive alleles (homozygous) will result in a clear expression of the trait, while inheriting a dominant and a recessive allele (heterozygous) can result in a dominant trait expression due to dominance, but with a hidden recessive allele that can be passed to the next generation. The variability of offspring traits is highly dependent on the parental genotypes and the assortment of alleles, as illustrated by our examples of different types of sperm and egg cells produced.