I teach and research in a university zoology department. When I first took up my job over 20 years ago, some of my students told me that they took zoology (or biology) because they would not have to “do any maths.” I found this attitude deeply shocking: in my view analysing biological phenomena in a quantitative manner gave insights into the beauty of biology that no other approach could match. Of course, I was biased; I had graduated with a bachelor’s degree in mathematics before studying for my postgraduate qualifications in biology.
In the intervening two decades, the role of mathematics in biology, especially in biological research, has grown enormously. The long-standing use of statistical analysis of experimental data has, of course, become more sophisticated and new-fangled concepts such as Bayesian analysis have become commonplace and not just in the fields, like ecology, that always had a statistical bent. Perhaps even more fundamentally, many parts of pure mathematics – algebra and calculus – are now fully in the mainstream of biologically relevant mathematics. Many areas of biology in which mathematical tools and models were absent or marginally important now rely on mathematics and its application for their most central questions.
For example, one area in which I carry out research is phylogenetics, the study of evolutionary trees that show how different species (or groups of species) are related to each other, rather like family trees show how people are related. Back in the dark ages (the 1960s and before) evolutionary biologists drew their trees freehand, according to how they personally interpreted the data (usually derived from morphology or fossils). Today, such an approach is just not scientifically acceptable. Like thousands of scientists worldwide, I use DNA-sequences as the data to feed into various computer programs that carry out several analyses. For example, once the sequences from the different species are matched to each other correctly (“aligned”), we need to have a way of searching through the unbelievably gargantuan number of possible trees to find those (or the one) that are (or is) best supported by the data. No amount of intuition or even hand calculation could achieve this goal and, indeed, such approaches would waste most of the information we have in the sequence data. In order to make the best use of our data and draw the most accurate conclusions, we need these computer programs, which are built on rather sophisticated algebra and algorithms.
In the fields of medical research, too, things have changed. Recently I was involved in a study of the consequences of dietary restriction on lifespan. Many scientists have wondered if restricting calories can extend life expectancy, especially in humans, but the experimental data (on various animal models) was not very clear. Our study, led by Gravida Investigator, Shinichi Nakagawa, carried out what is called a meta-analysis, discovering that the effect is more pronounced in females and in model species (laboratory mice, drosophila flies, etc.). Meta-analysis feeds the results of previous studies into a combined analysis to derive an overall conclusion. Meta-analytic results are often far more powerful than single studies because they make use of so much data, but they rely on some careful mathematics, to ensure that all the factors in different experiments are properly accounted for.
Of course, the fact that mathematics now pervades more and more of biology does not mean that we all have to become mathematicians any more than car drivers must become mechanics. But as biologists, we do need to be familiar with the basics of mathematical approaches and we must learn how to drive the mathematical programs that analyse our data. And researchers above all must have some facility for talking to mathematicians, who are the very people who will be inventing the next generation of mathematical tools to analyse the increasingly vast amounts of biological data being generated in laboratories around the world.
So, as biologists, we all need some quantitative skills, and it is never too early to think about developing those skills. High-school pupils contemplating a career in biology should ensure they take mathematics as far as possible. Those students wanting to go on to study biology at university should try to take both the statistics and calculus flavours. Such careful planning will open all sorts of options about the direction of study and possible jobs. But perhaps at least as satisfying will be a greater understanding of the majestic complexity inherent in so much of modern biology.