Population Genetics

Learning objectives:

Define evolution, natural selection, and fitness

List the five conditions for a population to be at Hardy-Weinberg Equilibrium

Use the Hardy-Weinberg equations to calculate allele frequencies and genotype frequencies in a population

Determine if a population is evolving

Introduction

Evolution is defined as change in a population over time. In 1859, Charles Darwin proposed natural selection as the mechanism of evolution. For evolution to occur by natural selection, variation must exist in within the population. These differences cause some individuals to have increased survival and reproduction under certain environmental conditions. We now know that the cause of variation in physical traits is the presence of different alleles, or forms of genes.

If certain conditions are met, the ratios of different alleles and combinations of alleles remain constant over generations. When this happens, the population does not evolve. In this lab, we will look at the relationships between allele frequencies, genotype frequencies, and phenotype frequencies and how violations of these conditions cause populations to change.

Contents

Review of some important terms:

Population: a group of individuals of the same species in the same place at the same time

Gene – a section of DNA on a chromosome that codes for one trait

Allele – a different form of a gene (ex. Black or white fur)

Dominant allele – the allele that is usually expressed

Recessive allele – the allele that may be masked by the dominant allele

Haploid cell – has only one copy of each chromosome (gametes)

Diploid cell – has 2 copies of each chromosome (most eukaryote cells)

Genotype – the actual combination of alleles present for a particular trait

Homozygous – The two alleles from each parent for a trait are the same

Heterozygous – The two alleles from each parent for a trait are different

Phenotype – the physical result of the genes present

Mendelian Inheritance

For our discussion of inheritance at the individual level and population-wide frequencies, we will begin with a few assumptions about the way the trait is inherited.

the organism is diploid and reproduces sexually

the gene has two alleles. One is completely dominant over the other.

one gene determines one trait

the gene is autosomal (not sex-linked)

Gregor Mendel made predictions about patterns of inheritance at the individual level.

Example:

- In pea plants, the allele for round seeds is dominant (R) and the allele for wrinkled seeds is recessive (r).

- Using a Punnett square to predict genotype frequencies of offspring produced by a cross between 2 heterozygous parents, we find the following ratios:

R r

R RR Rr

r Rr rr

1 homozygous dominant RR

2 heterozygous Rr

1 homozygous recessive rr

RR and Rr have the dominant phenotype and rr has the recessive phenotype, so the phenotype ratio of offspring is 3 dominant: 1 recessive

Theory of Evolution

In On the Origin of Species, Darwin described the process of evolution and natural selection as the mechanism for evolution.

Evolution: Genetic change in a population over time (generations)

Natural Selection: Differential survival and reproduction under natural conditions

Evolution occurs at the population level, not at the individual level. It involves changes in the frequencies of different alleles and genotypes in the population.

Population Genetics

In the early 1900’s Godfrey Hardy and Wilhelm Weinberg independently developed two equations that describe allele and genotype frequencies in a population that is not evolving. These equations help us apply Mendel’s predictions at the population level.

Frequencies in a population are expressed as decimal numbers. For example, if a gene occurs in the dominant form 80% of the time and the recessive form 20% of the time, allele frequencies are 0.8 and 0.2.

By convention, lower-case p represents the frequency of the dominant allele in a population and lower-case q represents the frequency of the recessive allele in a population

The Hardy-Weinberg equations can be illustrated using Punnett squares and the ratios discovered by Mendel.

We will start with the case of a single pair of heterozygous parents and their offspring.

If each parent has genotype Rr, half the gametes produced by each will have the dominant allele R and the other half will have the recessive allele r.

We can use these individuals to represent the population, so the dominant allele frequency (p) = 0.5 and the recessive allele frequency (q) = 0.5.

Allele frequencies are multiplied to get genotype frequencies.

p = 0.5 r

q = 0.5

p = 0.5

p2 = 0.25 Rr

p*q = 0.25

q = 0.5 Rr

p*q = 0.25 Rr

q2 = 0.25

Frequency of homozygous dominant RR = p2 = 0.25

Frequency of heterozygous Rr = p*q + p*q = 2pq = 0.5

Frequency of homozygous recessive rr = q2 = 0.25

Symbols for representing alleles, genotypes, and phenotypes:

Alleles Genotypes Phenotypes

Dominant Recessive Homozygous dominant Heterozygous Homozygous recessive Dominant Recessive

In individuals

Example:

Round seeds are dominant, wrinkled seeds are recessive R r RR Rr rr Round seeds Wrinkled seeds

Frequency in a population p q p2 2pq q2 p2 + 2pq q2

Hardy-Weinberg equations represent allele frequencies or genotype frequencies in the population.

Because there are only two alleles (dominant or recessive) for the gene, their frequencies in the population must total 100%.

The total of the three possible genotype frequencies also equals 100%.

Equation for allele frequencies:

p + q = 1

Equation for genotype frequencies:

p2 + 2pq + q2 = 1

The Hardy-Weinberg Principle states that under certain conditions allele frequencies and genotype frequencies will remain constant through time (generation after generation).

When the frequencies of alleles for a gene do not change over time, the gene is in genetic equilibrium.

Assumptions that must be met for a population to be at Hardy-Weinberg equilibrium:

1. no mutations

2. random mating

3. large population

4. no gene flow

5. no selection

If one or more of the assumptions are not met, the population evolves.

Using the Hardy-Weinberg Equations

In the real world, we are more likely to know the phenotypes of individuals in a population than their genotypes or alleles.

Example: In a population of 50 caterpillars, 8 are green and the rest are yellow. The yellow allele is dominant. Find the allele frequencies.

In this case, we are given phenotype numbers and must first calculate their frequencies.

Green phenotype frequency = 8/50 = 0.16

Yellow phenotype frequency = 42/50 = 0.84

Because green is recessive, we know that all green caterpillars are homozygous recessive yy, so q2 = 0.16

Yellow caterpillars can be either homozygous dominant YY or heterozygous Yy, so p2 + 2pq = 0.84

To get allele frequencies, start with the known genotype, homozygous recessive

q2 = 0.16

q = = 0.4 = recessive allele frequency

p = 1-0.4 = 0.6 = dominant allele frequency