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grows larger, you earn still more interest, and the sum grows
by escalating amounts each year. The reason is that a fixed 5
percentage of a small number makes for a small increase,
but the same percentage of a large number produces a large 4
increase. Thus, as savings accounts (or populations) become
larger, each incremental increase likewise gets larger. Such 3
acceleration is a characteristic of exponential growth. Birds per route
We can visualize changes in population size by using 2
population growth curves. The J-shaped curve in Figure 3.16
shows exponential growth. Populations of organisms increase 1
exponentially unless they meet constraints. Each organism
reproduces by a certain amount, and as populations get larger, 0
there are more individuals reproducing by that amount. If
there are adequate resources and no external limits, ecologists 1970 1980 1990 2000 2010
theoretically expect exponential growth. Year
Normally, exponential growth occurs in nature only when Figure 3.16 A population may grow exponentially for a time
a population is small, competition is minimal, and environmen- when colonizing an unoccupied environment or exploiting an
tal conditions are ideal for the organism in question. Most often, unused resource. The Eurasian collared dove is currently spread-
these conditions occur when the organism is introduced to a new ing across the North American continent, propelled by exponential
environment that contains abundant resources to exploit. Mold growth. Data from Sauer, J.R., et al., 2011. The North American Breeding Bird
growing on a piece of fruit, or bacteria colonizing a recently Survey, results and analysis 1966–2009. v. 3.23.2011. USGS Patuxent Wildlife
dead animal, are cases in point. Plants colonizing regions dur- Research Center, Laurel, MD.
ing primary succession (p. 103) after glaciers recede or vol-
canoes erupt may also grow exponentially. In Hawai‘i, many reached carrying capacity (Figure 3.18). Populations of other
of the species that colonized the islands from other locations European birds that spread across North America in the past,
underwent exponential growth for a time after their arrival. One such as the house sparrow and European starling, have peaked
current example of exponential growth in the mainland United and are today beginning to decline.
States is the Eurasian collared dove (see Figure 3.16). Unlike its Many factors influence a population’s growth rate and car-
extinct relative the passenger pigeon, this species arrived here rying capacity. For animals in terrestrial environments, limiting
from Europe, thrives in human-disturbed areas, and has spread factors include temperature extremes; prevalence of disease;
across North America in a matter of years. abundance of predators; and the availability of food, water,
mates, shelter, and suitable breeding sites. Plants are often
limited by amounts of sunlight and moisture and the type of soil
Limiting factors restrain chemistry, in addition to disease and attack from plant-eating
population growth animals. In aquatic systems, limiting factors include salinity,
sunlight, temperature, dissolved oxygen, fertilizers, and pol-
Exponential growth rarely lasts long. If even a single species lutants. To determine limiting factors, ecologists may conduct
were to increase exponentially for very many generations,
it would blanket the planet’s surface! Instead, every popula-
tion eventually is constrained by limiting factors—physical,
chemical, and biological attributes of the environment that
restrain population growth. These limiting factors determine Limiting factors:
the carrying capacity, the maximum population size of a spe- Stabilized - Resource availability
cies that a given environment can sustain. Carrying population - Temperature extremes CHAPTER 3 • Ev ol u T i on, Bi odiv ER si T y, A nd Po P ul AT i on E C ology
Ecologists use the S-shaped curve in Figure 3.17 to show capacity size - Predators/parasites
Disease
how an initial exponential increase is slowed and eventually - Disease
brought to a standstill by limiting factors. Called the logistic
growth curve, it rises sharply at first but then begins to level
off as the effects of limiting factors become stronger. Eventu-
ally the collective force of these factors stabilizes the popula- Exponential growth
tion size at its carrying capacity.
We can witness this process by taking a closer look at the Population size
data for the Eurasian collared dove population, as gathered by
thousands of volunteer birders and analyzed by government
biologists through the Breeding Bird Survey, a long-running Time
citizen science project. The dove first reached North America Figure 3.17 The logistic growth curve shows how popu-
in Florida a few decades ago and subsequently spread north lation size may increase rapidly at first, then grow more
and west. Today its numbers are growing fastest in western slowly, and finally stabilize at a carrying capacity. Carrying
areas it has recently reached, and slower in eastern areas where capacity is determined both by the biotic potential of the organism
it has been present for longer. In Florida, it has apparently and by various external limiting factors. 85
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