Populations: Regulation

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PopulationsRegulation

• Ruesink Lecture 5
• Biology 356

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Three basic forms of population dynamics

• Density independent
• Continuous reproduction Exponential equation
• Discrete reproduction Geometric equation
• Density dependent
• Logistic equation

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Figure 14.5
Exponential
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Figure 14.6
Geometric and exponential equations are roughly
interchangeable because r ln(l)
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Exponential or geometric population growth

• Density-independent (l does not change with
  population size)
• Resources (light, prey, enemy-free space) not
  limiting

Number
Time
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Figure 14.17
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Logistic population growth

• Density-dependent (population growth depends on
  population size)
• Resources (light, prey, enemy-free space) are
  limiting, regulating population around K
  (carrying capacity)

K
Number
Time
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Logistic population growth
K
Number

• dN/dt r N (1 N/K)
• Slow growth at low N
• Slow growth near K

Time
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Simple dynamics of DI and DD populations

• Time series
• Number of individuals (N) at each time t
• Population rate of change
• dN/dt Nt1-Nt
• Per capita rate of change
• dN/dt/N (Nt1-Nt)/Nt

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Geometric increase
Time N dN/dt dN/dt/N
0 20
1 23
2 27
3 31
4 36
5 42
6 49
7 57
8 66
9 77
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Geometric increase
Time N dN/dt dN/dt/N
0 20 23-20 3 3/20 0.15
1 23 27-23 4 4/230.17
2 27
3 31
4 36
5 42
6 49
7 57
8 66
9 77
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Geometric increase
Time N dN/dt dN/dt/N
0 20 23-20 3 3/20 0.15
1 23 27-23 4 4/230.17
2 27 4 4/270.15
3 31 5 5/310.16
4 36 6
5 42 7
6 49 8
7 57 9
8 66 11 11/660.17
9 77
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Geometric increase
Time N dN/dt dN/dt/N
0 20 23-20 3 3/20 0.15
1 23 27-23 4 4/230.17
2 27 4 4/270.15
3 31 5 5/310.16
4 36 6
5 42 7
6 49 8
7 57 9
8 66 11 11/660.17
9 77
Accelerating population increase
Constant per capita increase
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Population abundance (N)
Time
dN/dt
Density (N)
dN/dt/N
Density (N)
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Population abundance (N)
Time
dN/dt
Density (N)
dN/dt/N
Density (N)
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Logistic
Time N dN/dt dN/dt/N
0 5
1 8
2 12
3 18
4 27
5 38
6 50
7 62
8 73
9 82
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Logistic
Time N dN/dt dN/dt/N
0 5 8-53 3/50.6
1 8 12-84 4/80.5
2 12
3 18
4 27
5 38
6 50
7 62
8 73
9 82
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Logistic
Time N dN/dt dN/dt/N
0 5 8-53 3/50.6
1 8 12-84 4/80.5
2 12 6 6/120.5
3 18 9 9/180.5
4 27 11 11/270.4
5 38 12 12/380.32
6 50 12 12/500.24
7 62 11 0.18
8 73 9 0.12
9 82 6 0.07
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Logistic
Time N dN/dt dN/dt/N
0 5 8-53 3/50.6
1 8 12-84 4/80.5
2 12 6 6/120.5
3 18 9 9/180.5
4 27 11 11/270.4
5 38 12 12/380.32
6 50 12 12/500.24
7 62 11 0.18
8 73 9 0.12
9 82 6 0.07
Highest population increase at intermediate
densities
Declining per capita contribution
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Population abundance (N)
Time
dN/dt
Density (N)
dN/dt/N
Density (N)
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How to recognize density dependence

• Manipulate density of an organism
• Record individual performance across a range of
  densities

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Figure 14.19
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Figure 14.20b, c
Density dependence in sparrows
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In class assignment

• Work in groups of 4
• Fill out separate workseets
• Use the definitions and equations on your handout
• Link demography, life tables, geometric and
  logistic population growth, population
  projection, and conservation

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In class assignment

• r exponential rate of population growth
• R0 net reproductive rate
• ra exponential rate of population growth
  estimated from life tables
• r0 intrinsic rate, can be modified by DD