Post on 18-Jan-2016
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Populations
Population growth
• Nt + 1 = Nt + B – D + I – E
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
r > 0 population will grow
r = 0 population won’t change
r < 0 population will shrink
dN/dt = rN
Fig. 52.8 The exponential model for population growth
Fig 52.9
Fig 52.20
Fig 52.16
Cod in north Atlantic
Fig. 52.11 The patterns of exponential and logistic population growth
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]
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.
Sometimes population growth is independent of density
Fig 52.18
Larch budmoth
Fig. 52.3
Fig. 52.22
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
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
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.25
Lifetime offspring per individual female