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Objectives
Describe the pattern of exponential growth.
Relate limiting factors and carrying capacity.
Compare and contrast density-dependent and densityindependent factors.
Identify hypotheses for the causes of population growth cycles.
Key Terms
exponential growth
limiting factor
carrying capacity
density-dependent factor
density-independent factor
The population of crows in your neighborhood can grow, decline, or
stay constant over time. If conditions were ideal for crows, the
population would grow until your neighborhood was completely
overrun with crows. Fortunately, this does not occur. The crow
population's ability to grow is limited by predators, disease, food
supply, and other factors in the crows' environment.
Exponential Growth of Populations
A population's ability to grow depends partly on the rate at which its
organisms can reproduce. Bacteria are among the fastest-reproducing
organisms. A single bacterium can reproduce every 20 minutes under
laboratory conditions of unlimited food, space, and water. After just 36
hours, this rate of reproduction would result in enough bacteria to form
a layer almost half a meter deep covering the entire planet.
In general, larger mammals reproduce at slower rates than smaller
mammals. For example, elephants produce fewer offspring than mice
and have longer time intervals between offspring. But even so, in
theory, the descendants of a single pair of mating elephants would
number 19 million elephants within 750 years.
In these theoretical examples, the bacteria and elephant populations are
undergoing exponential growth, in which the population multiplies by a
constant factor at constant time intervals. Consider the bacteria
example. The constant factor for this population is 2, because each
parent cell splits, forming two offspring cells. The constant time
interval is 20 minutes. So every 20 minutes, the population is multiplied
by 2. Graphing these data forms the J-shaped curve in Figure 35-5.
Notice that the larger the population of bacteria, the faster the
population grows—the curve gets steeper with time.
Figure 35-5
This table shows how many bacteria are in a population that
doubles every 20 minutes. The graph is another way to show
the same data.
Carrying Capacity
In nature, a population may start growing exponentially, but eventually
one or more environmental factors will limit its growth. The population
then stops growing or may even begin to decrease. For example,
consider lily pads growing and spreading across the surface of a pond.
Once the pond is covered in lily pads, no more can grow. Space is one
example of a limiting factor, a condition that can restrict a population's
growth. Other limiting factors include disease and availability of food.
Figure 35-6 shows the growth of a population of fur seals on Saint Paul
Island off the coast of Alaska. Until the early 1900s, hunting kept the
seal population small and fairly stable. Then hunting on the island was
reduced, and the seal population began to increase almost
exponentially. By about 1935, the population leveled off again.
Ecologists hypothesized that the population became limited by a
variety of factors, including disease and competition for food.
variety of factors, including disease and competition for food.
Figure 35-6
Before the early 1900s, hunting kept this
population of fur seals below the carrying
capacity of the environment. Then, after
hunting was reduced, the population grew
almost exponentially for two decades. The
population began to level off as it reached
the carrying capacity.
When such environmental factors limit a population's growth rate, the
population is said to have reached its carrying capacity. The carrying
capacity is the number of organisms in a population that the
environment can maintain, or carry, with no net increase or decrease.
As a growing population approaches carrying capacity, the birth rate
may decrease or the death rate may increase (or both), until they are
about equal. Over time the balance in births and deaths keeps the
change in the population size close to zero. Notice the S-shaped curve
of the seal population graph in Figure 35-6. The seal population
increased rapidly for a time, but then stabilized when it reached the
carrying capacity of the environment.
Factors Affecting Population Growth
In the laboratory, you can observe the effects of environmental factors
such as food availability or temperature on population growth. For
example, if you put fruit flies in a container and add the same amount
of food each day, the population rapidly increases until the daily food
supply cannot support more flies. If you place another container of fruit
flies on a sunny window ledge, the heat may cause that population to
decrease despite a sufficient food supply.
Density-Dependent Factors Factors similar to those affecting
laboratory fruit flies affect natural populations. For example, the best
nutrition for white-tailed deer is the new leaves and buds of woody
shrubs. When deer population density is low, this high-quality food is
abundant, and a large percentage of the females bear offspring. On the
other hand, when the population density increases, the nutritious food
supply becomes scarce due to overgrazing, and many females do not
reproduce at all. The availability of high-quality food is one example of
a density-dependent factor, a factor that limits a population more as
population density increases. Another example of a density-dependent
factor is a disease that spreads more easily among organisms in a dense
population than in a less dense population.
Density-Independent Factors Factors that limit populations but
are unrelated to population density are called density-independent
factors. Extreme weather events, such as hurricanes, blizzards, ice
storms, and droughts, are examples of density-independent factors.
These conditions have the same effect on a population regardless of its
size.
Figure 35-8
A population of aphids typically
grows exponentially in the wet
springs months. The population
nearly dies off in the hot, dry summer.
Weather is a density-independent
factor that limits the aphid
populations.
Population Growth Cycles
Some populations have "boom-and-bust" growth cycles: They increase
rapidly for a period of time (the "boom"), but then rapidly decline in
numbers (the "bust"). Populations of various rodents exhibit boom-andbust cycles. A striking example is lemming populations, which can
cycle dramatically every three to five years. Some researchers
hypothesize that natural changes in the lemmings food supply may be
hypothesize that natural changes in the lemmings food supply may be
the underlying cause. Another hypothesis is that stress from crowding
during the "boom" may affect the lemmings' hormonal balance and
reduce the number of offspring produced, causing a "bust."
Some populations' growth cycles appear to be influenced by those of
other populations in their environments. For example, in the forests of
northern Canada, both the lynx and the snowshoe hare follow boomand-bust cycles (Figure 35-9).
Figure 35-9
The cycling populations of snowshoe hares and
their predators, the lynx, appear to be related.
Increases in the hare population are followed
closely by increases in the lynx population.
About every 10 years, the hare population reaches a high point,
followed by a sharp decrease. The lynx, which feeds on the hare, has a
population cycle that seems to follow that of the hares. When the hare
population increases, the lynx population follows closely. You might
hypothesize that the greater availability of food enables the lynx
population to grow. Then, as more and more lynx feed on the hares, the
hare population decreases again, which in turn becomes a limiting
factor for the lynx. This complicated relationship is still not fully
understood. Are the two species directly influencing each other's
population growth? Or is there another underlying cause for the
changes, such as a cycle in the hares' food supply? The causes of boomand-bust cycles vary among species.
Concept Check 35.2
1. Describe how a population grows with unlimited food, space, and
water.
2. Describe what happens when a population reaches its carrying
capacity in a particular environment.
3. Compare density-dependent and density-independent factors, and
give an example of each.
4. What is a boom-and-bust population growth cycle? What might
cause such a cycle?
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