Here’s my list of basic math biologists that will help a biologist understand fundamental biological principles and be able to broadly read the literature. If you are working in statistics or modelling or a specialist area that is math heavy, you will obviously need to know much more.
Thanks to the contributions from others made via this Twitter thread.
This is a work in progress. I will keep updating this list, so message me if you have more to add (or remove!).
Counting might seem so basic a skill it is not worth mentioning, but counting accurately in the field and lab takes practice. Try counting penguins in a colony of thousands, cells under a microscope, or a moving school of fish and you’ll know what I mean. If you are going to work on any abundant organism, you will need to count well.
You get bonus credentials if you can count and keep track of multiple categories in your head at the same time (if you want to practice this, just get the ebird app go to a local park and try counting as many bird species as you can without looking at your phone)
We often converting among different measurement scales, whether it be length scales, concentrations, areas or volumes. Obviously this requires ability at adding, subtracting, multiplication and division. I find areas and volumes often trip people up, so I don’t take this knowledge for granted.
The linear equation is ubiquitous in biology and especially statistics. Bonus credentials for understanding y = ax + b + error
It is helpful to understand this equation well, such as how to calculate the slope of a line from two coordinates and how to find the x or y intercept.
Primarily in 2 dimensions, but bonus points for three dimensions.
Because why multiply when you can add?
It’s useful to know what a base is, that log(0) is undefined, how log10(x) relates to 10^x, that log(1) = 0, log of a number <1 is negative, log of a number more than 1 is positive, that log(a*b) = log(a) + log(b) and that log(a+b) doesn’t equal log(a) + log(b).
Exponential growth and decline are particularly common in biology (and physics, and finance, and economics…), from temperate dependent rates to population growth.
This means being able to think about the future (or the outcome of an event or experiment) in probabilistic terms, rather than definitive terms. Biology is ruled by lady luck, not by fate.
This is fundamental to statistics, but also to thinking about the outcomes of experiments.
Including additive rule, multiplicative rule and the meaning of independence and conditional independence.
It is helpful to know that a derivate defines a rate and that an integral relates to a sum. This will help you read and understand modelling papers better. I don’t think non-modelling biologists need to know the rules of differentiation or integration.
I’m still thinking about whether I also include: normal distribution (bell curve), central limit theorem, additive property of variances. I haven’t included specialist statistical concepts (e.g. p-values, or bayes theorem), but I think all of the above sets one up to understand those applications of probability. I haven’t included matrix algebra, I don’t think you need to know that unless you are working in modelling or statistics, but message me if you have examples that disagree.