### Lecture 11-Popn Regulation Ch14b

```Ch. 14
Population Growth and Regulation
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Exponential Population Growth - Fig 14.5
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Exponential
Outline
Expectations!
Doubling time
Regulation
Density dependent
Applications - yield
Density independence
Human populations
Doubling Time
Doubling Time - Money
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t2 = [loge2]/r
Rule of Thumb for money
Doubling time = 70/annual interest rate
\$1,000 invested at 10% interest
• Note r = logeλ
• t2 = [loge2]/r
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7 years - \$2,000
14 years - \$4,000
21 years - \$8,000
28 years - \$16,000
35 years - \$32,000
42 years - \$64,000
49 years - \$128,000
56 years - \$256,000
63 years - \$512,000
Population Growth
Population Growth
• Introduce organisms to new habitats
• Starlings Fig. 13.17
• Introduce organisms to new habitats
• Gypsy Moth
t2 = [loge2]/[logeλ]
Field vole example - text λ=24
t2 = 0.69/3.18
t2 = 0.22 years (79 days)
Smith & Smith 2006
1
Population Growth
Population Growth
• Introduce organisms to new habitats
• Scotts Pine
• Introduce organisms to new habitats
• Whooping Cranes
Molles 2008
Smith & Smith 2006
Regulation
Regulation
• Introduce organisms to new habitats
• Reindeer
• Introduce organisms to new habitats
• Yeast
Smith & Smith 2006
Molles 2008
Regulation
• Introduce organisms to new habitats
• Paramecium and Barnacles
Molles 2008
Molles 2008
2
250
Logistic Growth Curve - Fig. 14.17
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K
200
150
N
100
Logistic
Growth
50
0
0
5
10
15
20
Time
Exponential
Logistic Growth Curve
N
dN/dt
dN/dt
• dN/dt = rN(1-N/K)
K
N
• N(t) =
Logistic
K/(1+e-r(t-i))
Time
Time
Logistic Growth Curve
• N(t) = K/(1+e-r(t-i))
• dN/dt = rN(1-N/K)
K
N
Time
3
• b and d
Rate (b or d)
Density Dependent Regulation
• How can r be adjusted?
Rate (b or d)
Density Dependent Regulation
d
b
N or ρ
Rate (b or d)
Density Dependent
Predators?
N or ρ
d
Rate
d
b
b
K
K
Density Dependent
b
Density Dependent
N or ρ
Food?
d
N or ρ
Density Dependent Regulation - Examples
• Insects Fig. 14.19
Rate
d
b
K
N or ρ
4
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Birds Fig. 14.20
• Mammals Fig. 14.21, 22
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Mammals Fig. 14.21, 22
• Mammals
Smith & Smith 2006
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Death rate - functional predator response
Smith & Smith 2006
Molles 2008
5
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Death rate - functional predator response
• Birds Fig. 14.20
Smith & Smith 2006
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Plants Fig. 14.23
• Plants
Smith & Smith 2006
Density Dependent Regulation - Examples
Density Dependent Regulation - Examples
• Plants Fig 14.24
• Plants - Self thinning Fig 14.25
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Density Dependent Regulation - Examples
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K
200
150
N
100
Logistic
Growth
50
0
0
5
10
15
20
Time
Activity Space - Figure 9.4
K
N
0
5
10
15
20
Time
Density Independent Regulation
Density Independent Effect
• Environmental factors - Fig. 14.13
• Environmental factors
• Gibbs and Grant 1989
Smith & Smith 2006
7
Density Independent Effects
Density Independent Effects
• Environmental factors
• Deer
• Is this regulation?
Human Populations
Human Populations
• Pearl and Reed - Fig14.19
• Fig 14.1
Rate (b or d)
Smith & Smith 2006
d
b
N or ρ
Tuesday
• Chapter 15
8
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