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Unformatted text preview: Population Growth Ecology, Lecture 4: Population Growth & Regulation Basic terms:
∆N = (B + I) – (D + E) Population growth models and exponential growth ∆N = (B – D) Densitydependent effects and logistic growth ∆N/∆t = (B – D) Allee effects
Predatorprey dynamics Births Deaths Population Size Emigration
Immigration 1 Life Table 2 Reproductive Table 3 4 Population Growth Population Growth Basic terms:
Per capita rate of increase (r) = b – d
If r = 0, zero population growth (ZPG)
If r > 0, the population is growing
If r < 0 the population is declining Basic terms:
Per capita birth rate (b)
Per capita death rate (d)
B=bN
D=dN
∆N/∆t = bN – dN ∆N/∆t = bN – dN
∆N/∆t = N (b–d) ∆N/∆t = rN 5 6 Exponential Growth Exponential Growth
From ﬁxed interval to instantaneous
Population size (N) ∆N/∆t = r N
dN/dt = rinst N
dN/dt = rmax N
dN/dt = r N
2,000 Population size (N) 1,500 dN
= rN
dt 1,000 500 Number of generations 0
0 5
10
Number of generations 15 7 8 Human population growth
6 5 4 3 2 The Plague 1 # individuals (billions) 7 0
8000 4000 3000 2000 1000 0 1000 2000 Year
9 10 Elephants in Kruger Park, South Africa
2,000 dN 1.0N
=
dt Population size (N) Elephant population (N) 8,000 6,000 4,000 2,000 0
1900 Effect of r on
growth 1,500 dN 0.5N
=
dt
1,000 500 0 1920 1940 1960 0 5 10 15 Number of generations Year
11 12 Regulation (density dependent) Effect of competition on
number of offspring Effect of competition on seed production Song sparrow
(Melospiza melodia) Plaintain
(Plantago major) % of juveniles with lambs 13 100 14 Density dependent forces Soay sheep of
Hirta Island 80 60 Territoriality Toxicity of waste Parasites 40 Predation 20 0
200 300 400 500 600 Population size (N)
15 16 Logistic Growth Allee Effects Limited resources and carrying capacity (K)
K = maximum population size that an environment can sustain standard (negative)
density dependence r=b–d
dN/dt = rN
dN
K–N
= rN
K
dt positive effect Population size (N) K = carrying capacity negative effect Berec et al. 2006
TREE 22(4): 185–191 Number of generations 17 18 2,000 Population size (N) Population size (N) Logistic Growth Model
K = carrying capacity dN
K–N
=r N K
dt dN
= 1.0N
dt
1,500 1,000 dN
1.0 N
dt = 500 1,500–N
1,500 0 Number of generations 0 5 10 15 Number of generations
19 20 Logistic growth in laboratory ecosystems: Overshooting (time lag) in Daphnia
Number of Daphnia / 50 mL # of Paramecium / mL Beetles, crustaceans, yeast, paramecia, prokaryotes...
1,000
800
600
400
200
0 0 5 10 15 180
150
120
90
60
30
0 0 20 40 60 80 100 120 140 160 Time (days) Time (days)
21 22 ...
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This note was uploaded on 09/16/2010 for the course BIO 1B taught by Professor Carlson,mischel,power during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Carlson,Mischel,Power

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