One major area of interest in mathematical biology is population dynamics. A population is the number of individuals of a particular species in a certain area; population dynamics deals with the study of short- and long-term changes in certain biological variables in one or several populations.

Population dynamic studies have actually been around for centuries. For example, weight or age comparisons of human or other animal populations—or even how such populations grow and shrink over time—have long been areas of study. With regard to human populations, the two simplest kinds of input in a population study are birth and immigration rates, and the two basic outputs are death and emigration rates. If the inputs are greater than the outputs, the population will grow; if the outputs are greater than the inputs, the population will shrink.

Gregor Mendel was an Austrian monk who, in the 19th century, developed matrices of characteristics in pea plants he was breeding, which led to his founding the science of genetics.