populations population growth nt + 1 = nt + b – d + i – e
TRANSCRIPT
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Populations
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Population growth
• Nt + 1 = Nt + B – D + I – E
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Population growth
• Nt + 1 = Nt + B – D + I – E
• Nt + 1 = Nt + B – D (assume no I and E)
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Time: 0 1 2 3 4Cells: 1 2 4 8 16
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Time: 0 1 2 3 4 5Cells: 1 2 4 8 16 32
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Time: 0 1 2 3 4 5 6Cells: 1 2 4 8 16 32 64
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Time: 0 1 2 3 4 5 6 7Cells: 1 2 4 8 16 32 64 128
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Time: 0 1 2 3 4 5 6 7Cells: 1 2 4 8 16 32 64 128
“J” shaped or exponential growth
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Exponential growth: # increase by constant factor (R or reproductive rate) each time interval
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Nt = N0Rt
R = 2, N0 = 1, t = 5
Nt = 1 * 25 = 32
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Nt = N0Rt
R = 2, N0 = 1, t = 5
Nt = 1 * 25 = 32Mathematical model for non-overlapping (discrete) populations
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dN/dt = rNr = intrinsic rate of increaser = birth rate (b) – death rate (d)
Mathematical model for overlapping populations
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r > 0 population will grow
r = 0 population won’t change
r < 0 population will shrink
dN/dt = rN
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Fig. 52.8 The exponential model for population growth
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Fig 52.9
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Fig 52.20
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Fig 52.16
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Cod in north Atlantic
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Fig. 52.11 The patterns of exponential and logistic population growth
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For: r=0.1 K=100
if N = 10 dN/dt = .1 (10) [(100 - 10)/100]= .1 (10) (.9)= .9
if N = 99 dN/dt = .1 (99) [(100 - 99)/100]= .1 (99) (.01)= .099
dN/dt = r N [(K - N)/K]
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What do I need to know about these models?
Exponential Logistic
Pattern: J-shaped S-shaped
Equation*: dN/dt = rN dN/dt = rN[(K-N)/K]
Assumptions: -growth rate constant growth rate decreases
with pop size
-unlimited env. carrying capacity
* Know what each term means and how changes in the terms affect the pattern of population growth.
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Sometimes population growth is independent of density
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Fig 52.18
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Larch budmoth
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Fig. 52.3
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Fig. 52.22
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A Life Table
Number Probability of #Offspring bornAge aged x survival to x to females aged x
0 600 1.0 0
1 300 0.5 0
2 240 0.4 2
3 60 0.1 3
4 30 0.05 5
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Age group (x)
Nx bx lx
0 600 0 1
1 300 0 .5
2 240 2 .4
3 60 3 .1
4 30 5 .05
lxbx
Σ lxbx = 1.35
0
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.3
.25
Lifetime offspring per individual female