Mathematics Seminars 2020

Mathematical modeling of annual plants

Speaker: Tomoatsu Sugiyama


Mathematical model is a representation in mathematical terms of the behavior of real devices and objects. It is used in many contexts such as physics, engineering, biology, finance and others. In this presentation, I show an example from a mathematical model of biology. It shows the population number at (n+1)-th generation by using the population information at n-th and (n − 1)-th generations.

What we should know about a mathematical model is that it is not necessary a tool which guess correct number of something. Some of them might be a such tool. But many are different. That is because we use parameters and approximation. For example, I use four parameters in the mathematical model given in my presentation. Among those parameters, I use ∂ to mean the probability that seeds can survive through a winter. Although I always multiply ∂ to the population when the time in the figure comes to next spring from the winter, I do not believe it is always the same number because ∂ would have many factors which make ∂ to change, such as temperature, humidity, place and others. Not to mention, other winters and other places may have different values of ∂. Nonetheless, we use ∂ in a mathematical model.

Mathematical model is even useful even if it cannot lead to an accurate number. Mathematical model is abstract and treat just important parts which affect the result. In this meaning, mathematical model is useful to grasp the core. Also, mathematical model tell us a method for solving a problem. Consider an easy mathematical model, y = ax. If we want to raise y, we can know what we should do is raising a or x. Although it is sometimes clear before making a mathematical model, we can know the way with evidence.