# The Role of Mathematics in Biology Video

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• 0:04 Measuring Life
• 1:01 Creating Models
• 1:33 Tracking Change
• 2:12 Statistics
• 3:19 Testing Hypotheses
• 4:35 Lesson Summary
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Lesson Transcript
Instructor: Meredith Mikell
Mathematics is applied in all major fields of science, including biology. Here, we investigate the different applications of mathematics in biology and explore some examples.

## Measuring Life

Unlike physics and chemistry, biology is not usually a science associated with mathematics. But because there are quantifiable aspects of life science, mathematics plays a critical role in better understanding the natural world. Mathematical biology is a field of research that examines mathematical representations of biological systems.

Imagine that you are a biologist studying butterfly migrations. You go into the field and count a sample population in a confined region and then multiply your sample numbers by the total geographical range to get a population estimate. You then go back to your lab and review other researcher's reports of butterflies over the span of their migration pattern and use vector calculations to predict their future path. Finally, you examine previous years' data on the butterfly numbers and location to establish a probable error margin for your prediction. At every step of this process, you depend upon mathematics to measure, predict, and understand natural phenomena.

## Creating Models

One key role of math in biology is the creation of mathematical models. These are equations or formulas that can predict or describe natural occurrences, such as organism behavior patterns or population changes over time.

For scientists, mathematical models make it so much easier to view and describe a measurable phenomenon without having to stay stuck in the raw, numerical data. Most fields of medicine are also very dependent upon mathematical models, especially with regard to the frequencies of gene expression and the spreading rates of diseases.

## Tracking Change

Basic measurements of living things are often a necessary part of understanding how they change over time. This is a basic form of mathematics, but is crucial to better understanding living things.

For example, Charles Darwin famously observed different species of finches in the Galapagos Islands. In studying these birds, modern evolutionary biologists observe a progression in beak changes across a different species as the finch has specialized to eating different food sources. Accurately measuring the precise lengths and thicknesses of the beaks and averaging those differences within each population is very valuable raw data for drawing conclusions about how the species have differentiated over time.

## Statistics

A sub-field of biological science is the field of biostatistics, a field in which statistics are used to describe and explain life sciences. The purpose of statistical analyses is to find correlations, or interdependent relationships, between variables and to compare variables against each other.

For example, a marine biologist might want to know if there is a positive statistical correlation between the presence of cone snails, a common predator in marine habitats, and tulip snails, who are often preyed upon by larger snails. She may set up an experiment in which tulip snails are present in all testing areas, but cone snails are added to only a few of those areas.

Over time, she records the number of tulip snails remaining in all areas, and finds that there is a difference between areas with cone snails and areas without cone snails. But is that difference significant enough to draw conclusions about snail behavior? She then runs a series of statistical tests to see if the difference is, indeed, statistically significant.

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