Environmental Engineering Reference
In-Depth Information
Simple Population Growth
Most species are capable of reaching huge abundances.Typically, however,
they do not.Why? To answer this question, we need to consider the funda-
mental properties of population growth.
In discussing the life-as-a-game metaphor in chapter 2, I noted that the
point of the game is to contribute as many descendants as possible to future
generations.Thus, if there are two phenotypes that differ in their rate of sur-
vival and reproductive output (fitness), natural selection will favor the one
that has the higher net survival and reproduction.This is because that phe-
notype produces genetic copies of itself at a higher rate than the other phe-
notype. Fitness, then, is a measure of that rate of increase in the abundance
of a phenotype.
Suppose we now counted the
number of individuals in a population
of a phenotype after each generation
and plotted that number against time
(figure 4.1a). This would produce a
curve that begins slowly but then
rises very rapidly.This kind of popu-
lation growth is known as geometric
or exponential growth because the
number of individuals in the popula-
tion multiplies rather than adds over
time.This simple geometric process is what gives populations the potential
to reach prodigious abundances.
Future population size can be forecast if we have two bits of informa-
tion: (1) the population size at some starting time (call it time zero); and
(2) the net rate of offspring production of an average individual in a popu-
lation from one time period to the next, that is, a measure of mean popu-
lation fitness.These two bits of information can be put into a mathematical
equation describing a simple geometric growth process:
This kind of population growth is
known as geometric or exponential
growth because the number of indi-
viduals in the population multiplies
rather than adds over time. This
simple geometric process is what
gives populations the potential to
reach prodigious abundances.
N(t) = N(0)e
rt
where
N
(
t
) is population size (numbers) at some future time
t
,
N
(0) is ini-
tial population size and
r
is the net rate of increase and
e
is the base of the
natural logarithm (i.e.,
e
= 2.71828).This equation may seem a bit daunt-
ing. But the reality is that it is used in everyday life: It is the equation used
