Population Growth
Chapter 11
11
Outline




Geometric Growth
Exponential Growth
Logistic Population Growth
Limits to Population Growth



Density Dependent
Density Independent
Intrinsic Rates of Increase
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Geometric Growth- pulsed reproduction
annual plant or insect

When generations do not overlap, growth can be
modeled geometrically.
Nt = Noλt




Nt = Number of individuals at time t.
No = Initial number of individuals.
λ = Geometric rate of increase (Constant ratio)
t = Number of time intervals or generations.
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Fig. 11.2
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Fig. 11.3
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Exponential Growth

Continuous population growth in an unlimited
environment can be modeled exponentially.
dN / dt = rmax N

Appropriate for populations with overlapping
generations.

As population size (N) increases, rate of population
increase (dN/dt) gets larger.
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The Exponential Growth Model

Assumes a population is growing without limits at its
maximal rate
 Rate is symbolized r and called the biotic potential
Change
over time


Intrinsic rate
of increase
Growth rate = dN/dt = riN
No. of individuals
in a population
The actual rate of population increase is
Birthrate

Deathrate
Net immigration
r = (b – d) + (i – e)
Net emigration
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Exponential Growth

For an exponentially growing population, size
at any time can be calculated as:
Nt = Noermaxt





Nt = Number individuals at time t.
N0 = Initial number of individuals.
e = Base of natural logarithms.
rmax = Per capita rate of increase (constant)
t = Number of time intervals.
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10 10
Exponential Population Growth
11 11
Logistic Population Growth

As resources are depleted, population growth
rate slows and eventually stops: logistic
population growth.


Sigmoid (S-shaped) population growth curve.
Carrying capacity (K) is the number of individuals of a
population the environment can support.

Finite amount of resources can only support a finite number
of individuals.
12 12
Logistic Population Growth
13 13
Fig. 11.9
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Fig. 11.10
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Fig. 11.11
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Fig. 11.12
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
dN/dt=rmax N

Add element that slows growth as pop size
approaches K

dN/dt=rmax N(K-N)

K
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Logistic Population Growth
dN/dt = rmaxN(1-N/K)


rmax = Maximum per capita rate of increase
under ideal conditions.
When N nears K, the right side of the equation
nears zero.

As population size increases, logistic growth rate
becomes a small fraction of growth rate.


Highest when N=K/2.
N/K = Environmental resistance.
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Limits to Population Growth

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


Boag and Grant - Geospiza fortis was
numerically dominant finch (1,200).
After drought of 1977, population fell to (180).


Food plants failed to produce seed crop.
1983 - 10x normal rainfall caused population to grow
(1,100) due to abundance of seeds and caterpillars.
21 21
Galapagos Finch Population Growth
22 22
Fig. 11.19
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Fig. 11.18
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Cactus Finches and Cactus
Reproduction

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

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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