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Population Growth
(Ch. 11)
Population Growth
• 1) Geometric growth
• 2) Exponential growth
• 3) Logistic growth
Geometric Growth
• Growth modeled geometrically
– Resources not limiting
– Generations do not overlap
• Recall:
• 1)  = Nt+1 / Nt
• 2)  = Ro
Geometric Growth
• Growth modeled geometrically
– Resources not limiting
– Generations do not overlap
• Equation: Nt = No t
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Nt = Number inds. @ time t
No = Initial no. inds.
 = Geometric rate of increase
t = Number time intervals
Geometric Growth
• Phlox (annual plant)
Fig. 11.3
Exponential Growth
• Growth modeled exponentially
– Resources not limiting
– Generations overlap
• Recall:
1) Per Capita Rate of Increase (r)
2) r = (ln Ro) / T
3) r = b – d
Exponential Growth
• Equation: dN / dt = rmax N
• dN / dt means “change in N per unit time”
• Recall r: per capita rate of increase (Ch. 10)
• rmax: Special case of r (intrinsic rate of increase).
b - d under optimum conditions
– b = birth rate and d = death rate (rates per individual
per unit time)
• As N increases, dN/dt gets larger.
Exponential Growth
• For exponential growth:
Nt = N0 ermaxt
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Nt = No. inds. at time t.
N0 = Initial no. inds.
e = Base natural logarithms
rmax = Intrinsic rate of increase
t = Number time intervals
Resources not limiting
Geo:
Nt = No t
Exponential Growth: Example
• Whooping crane
Exponential Growth: Example
• Hunting/habitat destruction
• Federally listed
Endangered(1967). Down to
22!!
Fig. 11.6
Exponential Growth: Example
• Raising birds: costumes
avoid imprinting on
humans
Exponential Growth: Example
• Teaching young birds to
migrate (Wisconsin to
Florida)
1996
Geometric or Exponential?
Nt = N0 ermaxt
Nt = No t
Geometric
Exponential
Generations
Geometric or Exponential?
Nt = No t
Nt = N0 ermaxt
Geometric
Exponential
Separate
Generations
Overlap
λ=1
Population stable
r=0
λ>1
Population growing
r>0
λ<1
Population shrinking
r<0
Logistic Population Growth
• Unlimited resources?? nothing lasts
forever…
• As resources depleted: logistic population
growth.
Logistic Population Growth
• As resources depleted, logistic population
growth (generations overlap)
– Sigmoid (S-shaped) curve.
– Carrying capacity (K): number environment can
support.
Fig. 11.8
Ex
Logistic Population Growth
• Yeast growth (limited alcohol)
• Max. 17% (34 proof)
Fig. 11.9
Logistic Population Growth
Equation: dN/dt = rmax N (1-N/K)
• rmax = Intrinsic rate of increase (ideal
conditions)
• N = population size @ time t
• K = carrying capacity
• Or: dN/dt = rmax N (K-N)
K
How does this work?
• dN/dt = rmax N (K-N)
K
• N small: rmax N (K-0) or ≈ rmax N (1)
K
At small N, acts like exponential growth!
• N big: rmax N (K-K) or ≈ rmax N (0)
K
At larger N, growth slows: stops at K
Logistic Population Growth
1-N/K is
“scaling
factor”
When N nears
K, dN/dt
nears zero.
Fig. 11.13
Logistic Population Growth
• r: actual (realized)
reproductive rate
(b-d)
• Max. @ small N
• When N=K, r=0
• So b=d and b-d=0
• Above K? r
negative
Fig. 11.14
dN/dt = rmaxN (1-N/K)
Concepts!
• Population growth (# added per
unit time) highest when N=K/2
• Maximum sustainable yield:
largest sustainable harvest
Concepts!
• N/K: reflects environmental resistance
– Factors that limit population size
Environmental resistance
– Density-dependent factors: depend on density (N/K)
• Disease, Resource competition
– Density-independent factors: not related density
• Natural disasters (hurricane, fire, flood)
dN/dt = rmaxN (1-N/K)
Organism Size and Population
Density
• A search for patterns……
Size
– Size vs. density (neg. correlation)
– Generation time vs. size?
Gen time
Generation
time vs. size
rmax
• Positive correlation
• Log-log scale
size vs. rmax?
Size
rmax vs. size
• Negative correlation
• Note log:log scale
Human Population
• How many?
• Where?
• Age distributions and growth potential
How many?
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Human Population
How many?
7.09 billion (6/17/13)
7.02 billion (6/11/12)
6.925 billion (6/19/11)
6.448 billion (6/18/05)
Check it out now at:
• http://www.census.gov/ipc/www/idb/worldpopinfo.php
Where (continent)?
• Where?
Human Population
Fig. 11.23
Fig. 11.22
Human Population
• Where?
Human Population
• Age distributions and growth potential, 2008
Fig. 11.24
Human Population
• “Population bomb”: potential of population
to explode as people age
2000/2001-Present - New Silent Generation or Generation
Z 1980-2000 - Millennials or Generation Y 1965-1979 Generation X 1946-1964 - Baby Boom
1925-1945 – Silent Generation
1900-1924 – G.I. Generation
Human Population
• Human pop. curve: shape?
• What Earth’s K for humans?
Human Population
• Depends in part on lifestyle!
– Ecological footprint: resource use
– Biocapacity: resource supply
– Deficit if use>supply: US largest deficit
Course sequence
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Natural history (Done!)
Individuals (Done!)
Populations (Done! Except Life Histories)
Species interactions (You are here!)
Communities/ecosystems
Geographic/global ecology
5 main types of interactions among species:
Effect on
species A
Effect on
species B
Competition
-
-
Predation
+
-
Parasitism
+
-
Commensalism
+
0
Mutualism
+
+
Type of interaction
Species Interactions:
Competition (Ch. 13)
Competition (Ch. 13)
• Definition:
– Individuals attempt to gain more resource in
limiting supply
– (-,-) interaction: both participants get less
• Intraspecific: Within species.
• Interspecific: Between species.
Competition
• Interference Competition:
– Individuals interact with each other
• Resource (Exploitation) Competition:
– Individuals interact with resource