niques. Mathematical biology is carried
out by mathematicians, physicists, and
biologists from various disciplines within
their fields. These scientists work on such
problems as modeling blood vessel for-
mation, with possible applications to
drug therapies; modeling the electro-
physiology of the heart; exploring
enzyme reaction within the body; and
even developing models that track the
spread of disease.
What is population dynamics?
One major area of interest in mathemati-
cal biology is population dynamics. A
population is the number of individuals of a particular species in a certain area; popu-
lation dynamics deals with the study of short- and long-term changes in certain bio-
logical 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.
How does population dynamicsuse mathematics?
Population dynamics combines observations and mathematics, especially the use of dif-
ferential equations (for more about differential equations, see “Mathematical Analysis”).
For example, to determine what the population of a certain country will be in ten years,
scientists use a mathematical model commonly called the exponential model, or the rate
of change of a population as it is proportional to the existing population. (For more
about population growth mathematics and the environment, see below.)
Who was Gregor Mendel?
Austrian monk Gregor Johann Mendel (1822–1884) performed experiments with pea
plants from 1857 to 1865 that eventually led to his discovery of the laws of heredity.
Gathering 34 different kinds of peas of the genus Pisum(all tested for their purity), he
attempted to determine the possibility of producing new variants by cross-breeding.
By self-pollinating the plants—and covering them over so there was no unplanned^315
MATH IN THE NATURAL SCIENCES
A simple Mendel matrix.