Environmental Engineering Reference
In-Depth Information
to calculate how invested money
“grows” because of compound inter-
est that is accrued. So,
N
(
t
) could be
the amount of money in an account
after some fixed time
t
, based on the
initial principle or deposit
N
(0), and
the annual percentage rate (APR) or
interest rate
r
.
Let us now explore some proper-
ties of population growth using this
equation. Suppose that we had a
species with an initial population size
of ten individuals, that the species breeds once each year, and that the mean
fitness was such that the population grew at a rate of 10 percent per year.
Population size after five, ten, fifteen, twenty-five, and fifty years is respec-
tively 16.5, 27.2, 44.8, 121.8, and 1484 (figure 4.1a).We can change the con-
ditions from this baseline by increasing initial population size by one
individual. This translates into 148 more individuals than in the baseline
population by year 50 (figure 4.1a).We can decrease the mean fitness in the
population such that the population grows only by 9 percent.This results
in 584 fewer individuals than in the baseline by year 50.The lesson here is
that species populations can appear to be persisting at low densities for some
time.Then, seemingly out of nowhere they can become highly abundant.
Small changes in starting conditions can lead to dramatic difference over
the long run. Over long-enough time periods, the geometric growth
process can lead to prodigious numbers of individuals.
Species populations do not, however, continue to increase in abundance
indefinitely. Eventually population size tends to level off at some upper
bound (e.g., figure 4.1b) because individuals in the population must com-
pete for a finite amount of resources or space. But how exactly is it that
competition holds population abundances constant?
Individuals residing in a location must vie for their share of space or for
their share of resources.As population size rises, that share diminishes in pro-
portion to the number of individuals in the population. So, the higher the
population size, the greater the intensity with which individuals must com-
pete.Thus, rising population density continually feeds back to decrease in-
dividual fitness.
We can better understand the feedback process if we decompose fitness
As population size rises, that share
diminishes in proportion to the
number of individuals in the popu-
lation. So, the higher the popula-
tion size, the greater the intensity
with which individuals must com-
pete. Thus, rising population den-
sity continually feeds back to
decrease individual fitness.
