Population Growth
Chapter 11
Geometric Growth
Exponential Growth
Logistic Population Growth
Limits to Population Growth
Density Dependent
Density Independent
Intrinsic Rates of Increase
Our Future
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Geometric Growth
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When generations do not overlap, growth can
be modeled geometrically.
N t = N oλ t
Nt = Number of individuals at time t.
 No = Initial number of individuals.
 λ = Geometric rate of increase.
 t = Number of time intervals or generations.

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Exponential Growth
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Continuous population growth in an unlimited
environment can be modeled exponentially.
dN / dt = rmax N
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Appropriate for populations with overlapping
generations.
 As population size (N) increases, rate of
population increase (dN/dt) gets larger.
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Exponential Growth
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For an exponentially growing population,
size at any time can be calculated as:
Nt = Noert
Nt = Number individuals at time t.
N0 = Initial number of individuals.
e = Base of natural logarithms.
rmax = Per capita rate of increase.
t = Number of time intervals.
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Exponential Growth of Human Population
The Black Death!
www.globalchange.umich.edu/.../human_pop.html
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Logistic Population Growth
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As resources are depleted, population growth
rate slows and eventually stops, this is called
logistic population growth.
 Sigmoid (S-shaped) pop. growth curve.
 Carrying capacity (K) is the number of
individuals of a population the environment
can support.
 A finite amount of resources can only
support a finite number of individuals.
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Logistic Population Growth
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Logistic Population Growth
dN/dt = rmaxN(1-N/K)
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rmax = Maximum per capita rate of increase under
ideal conditions.
rmax occurs at extremely low population size.
Growth rate (dN/dt) is greatest when N=K/2.
When N nears K, the both (1-N/K) and r approach
zero.
N/K = Environmental resistance; defines when
resources limit further growth.
If N>K, then dN/dt is negative; population declines.
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Limits to Population Growth
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Environment limits population growth by
altering birth and death rates.
 Density-dependent factors
 Disease, Resource competition
 Density-independent factors
 Natural disasters
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Galapagos Finch Population Growth
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Boag and Grant - Geospiza fortis was
numerically dominant finch (1,200).
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After drought of 1977, population fell to
(180). Food plants failed to produce seed
crop.
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1983 - 10x normal rainfall caused population
to grow (1,100) due to abundance of seeds
for adults and caterpillars nestlings.
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Galapagos Finch Population Growth
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Cactus Finches and Cactus Reproduction
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Grant and Grant documented several ways
finches utilized cacti:
 Open flower buds in dry season to eat
pollen
 Consume nectar and pollen from mature
flowers
 Eat seed coating (aril)
 Eat seeds
 Eat insects from rotting cactus pads
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Cactus Finches and Cactus Reproduction
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Finches tend to destroy stigmas, thus
flowers cannot be fertilized.
 Wet season activity may reduce seeds
available to finches during the dry season.
 Opuntia helleri main source for cactus
finches.
 Negatively impacted by El Nino (1983).
 Stigma snapping delayed recovery.
– Interplay of biotic and abiotic
factors.
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Population Growth by Small
Marine Invertebrates
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Populations of marine pelagic tunicate
(Thalia democratica) grow at exponential
rates in response to phytoplankton blooms.
 Numerical response can increase
population size dramatically due to
extremely high reproductive rates.
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Intrinsic Rates of Increase (r)
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On average, small organisms have higher
rates of per capita increase and more
variable populations than large organisms.
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Our Future?
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