Biology 12

Chapter 14 Population Ecology • MHR 477

imaginary species are realistic. Clearly, there is
more to this story.
Many populations do grow exponentially, at
least for a period of time. This can often happen,
for example, when humans introduce a new
species into a favourable environment. The zebra
mussel population in North America is growing
exponentially, and the rat population that the
Easter Islanders brought with them to their new
home probably experienced exponential growth for
a time. However, exponential growth rarely lasts
long in nature. There are a variety of reasons for
this, many of which are related to the fact that
environments are rarely as unlimited as the one in
which our imaginary bacteria were growing. More
commonly,there are limits set by the environment
to the growth of any population.
Notice that in the mathematical model of
exponential growth, the growth rate (r) is constant for
a given population. Although the rate of population
increase (dN/dt) changes with the population
size (becoming faster with larger N ), the rate of
population growth is fixed. This can only be true
in conditions in which there is a sufficient supply
of food and all other resources needed for the
population to live up to its biotic potential. In nature,
however, as a population grows larger in size (and
thus denser), the resources that its members require
may start to run out. Some individuals in the
population may not be able to get the resources they
need to survive. As a result, the death rate (d) may
increase. Alternatively, individuals may be able to
find sufficient food for growth and maintenance of
body systems, but not the extra amount needed for
reproduction. Thus, the birth rate (b) may go down.
Since r=b−d, the result is that as resources
become more limited, rmay decrease as a result
of a decrease in b, an increase in d, or both.
The type of population change that occurs in
limited environments, in which ris not constant, is
called logistic growth. Unlike the J-shaped curve of
exponential growth, logistic population growth
produces what is referred to as a sigmoidal or
S-shaped curve(see Figure 14.12). Notice that the
first part of the curve resembles the pattern seen in
exponential growth. The population increases slowly
at first, since Nis small and there are relatively few
individuals to produce offspring. The rate of change
then picks up speed, because there are lots of
resources to support the population and an increased
number of individuals are available to reproduce.
At some point, however, the population becomes
so large that it starts to have an impact on the

available resources. At this point, ris affected —

although the population continues to grow, it does

so at an increasingly slower rate. After the

inflection point of the logistic growth curve (the

point where the direction of curvature changes),

rbecomes smaller and smaller, producing what

is often referred to as a “shoulder” in the curve.

Eventually, the population stops growing

altogether. This occurs when the birth rate is equal

to the death rate (b=d), r= 0 , and dN/dt= 0. At

this point the population is at the carrying capacity

of the environment (K) — the maximum population

size that can be sustained in a given environment

over a long period of time. Two separate

populations of the same species may have different

maximum sizes because of differences in the

richness of their respective environments.

Figure 14.12This figure shows a model of how a

population might grow in an environment where food

or other resources are limited.

The Logistic Growth Equation

As is true for exponential growth, it is useful to

have a generalized mathematical equation to

describe logistic population growth. And just as the

S-shaped curve starts out with a J-shaped section,

this equation begins with the exponential growth

Your Electronic Learning Partner has animation clips that

will enhance your understanding of the carrying capacity

of fish populations.

ELECTRONIC LEARNING PARTNER

Population size (

N

)

Time

slow

growth

no growth

rapid growth

carrying capacity (K)