Biology (9610) | Allele frequencies in populations

Allele Frequencies in Populations: The Mathematics of Evolution

Welcome to this crucial chapter in Population Genetics! This is where we bridge the gap between individual inheritance (Mendel's laws) and evolution (change over time). Instead of looking at one organism, we look at the traits present in an entire group.

Understanding allele frequencies helps us quantify how common different versions of genes are in a population and provides the mathematical basis for understanding how and why evolution occurs.

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1. Fundamentals of Population Genetics (3.3.7.1)

What is a Population?

In population genetics, a population is defined precisely:

• It is a group of potentially interbreeding organisms (all of the same species).
• They occupy a particular space at a particular time.

Think of all the wild rabbits living in a single forest—they form one interbreeding population.

The Gene Pool Concept

The concept of a gene pool is vital. It’s like a massive bank that holds all the genetic information for a population.

• A gene pool is the complete set of all alleles for every gene in a single, specific population.
• Every time an organism reproduces, it "draws" alleles from this pool and contributes new ones back.

Defining Allele Frequency

The allele frequency is simply how often a specific allele appears compared to all other alleles for that gene in the gene pool.

• It is expressed as a fraction or proportion (a decimal value between 0 and 1).
• If the frequency of allele 'A' is 0.8, it means 80% of all the alleles for that gene in the population are 'A'.

Quick Review:

If the allele frequency changes from one generation to the next, that population is evolving.

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2. The Hardy-Weinberg Principle (H-W) (3.3.7.2)

What is the Hardy-Weinberg Principle?

The Hardy-Weinberg Principle provides a mathematical model for a hypothetical, non-evolving population. It predicts that allele frequencies will remain constant (will not change) from generation to generation, assuming certain strict conditions are met.

Biologists use this as a baseline (a "null hypothesis"). If a real population’s allele frequencies do not match the H-W predictions, it suggests that evolutionary forces (like natural selection or genetic drift) are at work.

Conditions for Hardy-Weinberg Equilibrium

The principle only holds true if the population is perfectly stable. These are the strict conditions:

1. No Mutation: No new alleles are created.
2. Random Mating: Individuals must mate without preference for a particular genotype.
3. No Selection: All genotypes must have equal survival and reproductive success (no natural selection).
4. Extremely Large Population Size: Necessary to avoid chance events influencing frequencies (i.e., avoiding genetic drift).
5. No Gene Flow/Migration: No new alleles enter or leave the population.

In reality, no natural population meets all five conditions perfectly. This is why evolution happens!

The Hardy-Weinberg Equations

We use two key equations to calculate allele and genotype frequencies in a population:

1. Allele Frequency Equation:

\[p + q = 1\]

• \(p\): The frequency of the dominant allele (e.g., A).
• \(q\): The frequency of the recessive allele (e.g., a).

The total frequency of all alleles for a gene must equal 1 (or 100%).

2. Genotype Frequency Equation:

\[p^2 + 2pq + q^2 = 1\]

• \(p^2\): The frequency of the homozygous dominant genotype (AA).
• \(q^2\): The frequency of the homozygous recessive genotype (aa).
• \(2pq\): The frequency of the heterozygous genotype (Aa).

The total frequency of all genotypes in the population must equal 1 (or 100%).

Step-by-Step Guide to H-W Calculation

In most problems, you are given the frequency of the recessive phenotype (organisms showing the recessive trait).

Example: If 16% of a population has a recessive trait (aa).

1. Find the recessive genotype frequency (\(q^2\)):
   This is the easiest step, as the recessive phenotype directly corresponds to the \(q^2\) genotype.
   \(q^2 = 16\% = 0.16\)
2. Find the recessive allele frequency (\(q\)):
   Take the square root of \(q^2\).
   \(q = \sqrt{0.16} = 0.4\)
3. Find the dominant allele frequency (\(p\)):
   Use the first equation: \(p + q = 1\)
   \(p = 1 - q = 1 - 0.4 = 0.6\)
4. Find the dominant and heterozygous genotype frequencies:
   Homozygous dominant (\(p^2\)): \(0.6 \times 0.6 = 0.36\) (36%)
   Heterozygous (\(2pq\)): \(2 \times 0.6 \times 0.4 = 0.48\) (48%)

Check: \(0.36 + 0.48 + 0.16 = 1.0\). It works!

Don't worry if the calculation seems tricky at first! Remember the formula pyramid: Start at the bottom with \(q^2\), work up to \(q\), then find \(p\), and finally calculate \(p^2\) and \(2pq\).

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3. Factors Causing Changes in Allele Frequencies

When the Hardy-Weinberg conditions are broken, the allele frequencies change, leading to evolution. The syllabus highlights three key factors that cause this change:

3.1. Natural Selection (Selection for Fitness)

Natural selection occurs when certain phenotypes are better adapted to the environment, allowing those individuals to survive longer and reproduce more successfully (differential survival and reproduction).

• Alleles carried by individuals with a selective advantage will increase in frequency in the gene pool over generations.
• Alleles that decrease fitness will typically decrease in frequency.

Example: Influence of Selection in Breeding

Humans actively participate in selection to change allele frequencies, often for economic benefit:

Selection for high-yielding breeds (like cows that produce large amounts of milk or cereal crops that produce more grain) intentionally increases the frequency of beneficial alleles within those domesticated populations.

3.2. Genetic Drift (Change by Chance)

Genetic drift is the change in the frequency of alleles in a population due to pure chance or random events, not due to selection.

• Imagine a small population of flowers (A/a). If, by chance, a few plants with the dominant 'A' allele fail to reproduce (maybe they were accidentally eaten by a non-selective herbivore), the frequency of 'A' drops suddenly.
• The effect of genetic drift is much larger in small populations because random events have a disproportionately large impact on the gene pool.

Analogy: If you flip a coin 1,000 times, you expect a result very close to 500 heads. If you only flip it 5 times, getting 4 heads (80%) is a huge random swing. Small populations are like the 5 flips—prone to big random changes.

3.3. Genetic Bottlenecks

A genetic bottleneck is a severe type of genetic drift that involves a drastic, sudden reduction in population size, often due to an environmental event (like a flood, fire, or mass disease) or human activity.

• The small group of survivors may not have the same allele frequencies as the original, large population.
• The gene pool of the new population is significantly reduced (less genetic diversity).
• Even if the population later grows, the genetic diversity remains low for many generations, and the allele frequencies are permanently altered from the ancestral state.

Did you know? The northern elephant seal population dropped to about 20 individuals in the 1890s due to hunting. Although the population has rebounded to over 30,000, they have very low genetic diversity due to this historic bottleneck.