Use proportional reasoning to support explanations of evolutionary change

Why Scientists Use Numbers to Study Evolution

Imagine you notice more dark-colored moths in your neighborhood than light-colored ones. How would you prove that the population is actually changing? You would need to count them and compare the numbers over time. This is exactly what scientists do when they study evolution (the process by which populations of organisms change over many generations).

For centuries, people noticed that living things change. But it was not until scientists started using math — especially proportional reasoning (comparing parts to a whole using ratios, fractions, or percentages) — that they could clearly explain how much and how fast populations change.

Here is the big question we will explore: How can comparing proportions help us explain why and how species change over time? Let's find out by investigating a real-world anchoring phenomenon — the peppered moth of England.

Core Principles: Proportions and Evolution

Before we dig into data, let's make sure we understand the key ideas. Evolution happens in populations (groups of the same species living in one area), not in single organisms. A population evolves when the proportion (the fraction or percentage) of a trait changes from one generation to the next.

Anchoring Phenomenon: The Peppered Moth

In the 1800s, England's industrial revolution filled the air with soot. Tree bark, which used to be pale and covered with light-colored lichen, turned dark. Scientists noticed that peppered moths came in two main forms: light-colored and dark-colored. Before pollution, the light form was common. After pollution darkened the trees, the dark form became much more common. This is our anchoring phenomenon — a shift in the proportion of moth colors that we can explain using proportional reasoning and natural selection.

Look at the chart above. In 1850, about 90% of moths were light-colored. By 1900, that dropped to only 5%. The proportion flipped because dark moths were better camouflaged on soot-covered trees. Birds ate more light moths, so light moths had lower survival. After clean-air laws removed the soot, the proportions shifted back. This pattern shows cause and effect — a change in the environment caused a change in trait frequency.

The Math Behind Trait Frequency

To use proportional reasoning, you need to calculate the trait frequency — the proportion of a population that shows a certain trait. Here is the formula.

To see if evolution has happened, compare the trait frequency at two different times. If the proportion changes, that is evidence that the population is evolving.

You can also express the change as a ratio. If the dark moth frequency went from 10% to 95%, you could say the dark moth frequency increased by a factor of 9.5 (because 95 ÷ 10 = 9.5). Ratios like this help you describe how dramatic an evolutionary change was.

Reading Data Tables: Beetle Population Study

Let's look at a second example. Imagine scientists studying a population of beetles on an island. The beetles come in two colors: green and brown. The island has mostly green plants, so green beetles are better camouflaged from bird predators.

The data show a clear pattern: the proportion of green beetles increased steadily from 50% to 95%. The change factor from Generation 1 to Generation 20 is 95 ÷ 50 = 1.9. That means the green trait became almost twice as common. This proportional evidence supports the explanation that natural selection acted on beetle color.

Worked Example: Calculating Evolutionary Change

Let's work through a full problem step by step. A scientist studying a population of 200 lizards counts 60 with striped tails and 140 with plain tails. Five years later, she counts 200 lizards again: 120 striped and 80 plain. Has the population evolved? By how much?

Strengths and Limitations of Proportional Evidence

Proportional reasoning is a powerful tool, but like any tool, it has strengths and limitations. Let's compare them.

Connecting to Advanced Ideas in Evolution

In middle school, you track trait frequencies using simple proportions. In high school and college biology, scientists go deeper. They track allele frequencies (the proportions of specific gene versions) instead of just visible traits. They also use advanced equations to predict when populations are not evolving. Let's see how what you're learning now connects to those bigger ideas.

The skills you are building now — dividing to find proportions, comparing changes, and looking for patterns — are the exact foundation for everything that comes next. Keep practicing, and these ideas will feel natural when you meet them again in high school biology!

Practice Problems

Lesson Summary