2. Introduction

Before we begin exploring the use of mathematical models in the study of population genetics, we will review some terminology that will appear in the module.

We understand the study of population genetics to be the study of the genetic basis for evolution in a population.

Biologists distinguish between diploid organisms (whose genetic material is based on two sets of chromosomes) and haploid organisms (whose genetic material is based on one set of chromosomes). In this module, we consider only diploid organisms. The process of meiosis produces gametes, which are sexually reproductive cells (eggs and sperm) that contain one copy of each chromosome. As a result, offspring receive one set of chromosomes from each parent via sexual reproduction.

Chromosomes contain genes, which are the fundamental units of heredity. Genes carry information from one generation to the next. As a result of mutations, a gene can have one or more alleles. In other words, genes can exist in one or more forms. As gametes come together in sexual reproduction, the two alleles, one from each parent, interact to produce a trait, such as eye colour in humans, or body colour in moths.

For simplicity, we consider a trait determined by one gene, for which there are two alleles. Using the example of the body colour of moths, we denote the two alleles by M and m (the M denotes melanism; an increased amount of black pigmentation). It is not hard to see that an individual moth may have one of three possible allelic compositions for the melanism gene: MM, Mm, and mm. These three different compositions are known as genotypes. Individuals with MM and mm genotypes are known as homozygous and those with the Mm genotype are heterozygous.

Each genotype corresponds with a phenotype, which is the outward expression of the gene. In any population there can be one, two, or three phenotypes. In other words, some (or all) of the genotypes may produce the same phenotype! In this module we will only consider the two and three phenotype cases.

In the two-phenotype case, we suppose that the M allele is dominant (it is capable of expressing the melanic colour trait in the presence of the m allele) and the m allele is recessive (it fails to express the white colour trait in the presence of the M allele). We thus obtain two phenotypes: black-bodied and white-bodied. Moths with MM or Mm genotypes develop black bodies whereas moths with the mm genotype develop white bodies.

In the three-phenotype case we have the following phenotypes: black-bodied, grey-bodied, and white-bodied. As above, the MM genotype results in a black-bodied moth, and the mm genotype results in a white-bodied moth. The grey-bodied moth is a result of the Mm genotype. In this case, the M allele is not completely dominant over the m allele, and the M allele is said to demonstrate incomplete dominance.

Much of the terminology used here will reappear while you are working through the module. Please refer back to this page for reference if needed.

The main question of interest is: How does the genetic make-up of a population change over time? Suppose we know that the frequency of the M allele in the population is . In other words, of the gametes in the population contain the M allele. The remaining of the gametes carry thus the m allele, and the frequency of the m allele is . Based on this information, what are the frequencies of the M and m alleles in the next generation? What are the frequencies in the fifth generation? What are the frequencies in the generation?

To start, try and answer the following questions on your own. When you're ready, click on Show to reveal the correct answer.

1) Do recessive alleles disappear eventually?

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The recessive allele in a population may or may not disappear. Similarly, the dominant allele may or may not disappear. The frequencies of the alleles in the long run are determined by the initial conditions as well as the selection pressures on each phenotype. We will see this result shortly. What is important to realize is that the terms dominant and recessive refer to the relation between two alleles, and do not describe the frequencies of the alleles as time progresses.

2) In a population with random mating that is absent of mutation, genetic drift, genetic flow, and natural selection, do allele frequencies change over time?

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In this case, allele frequencies do not change from generation to generation. This result is known as the Hardy-Weinberg Principle. We will develop this principle formally in Section 5.

In the next section, we will consider our moth example further.