Population growth

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Population growth

• Geometric growth
• Exponential or logarithmic growth
• Logistic growth
• Carrying capacity
• Density-dependent and independent limiting
  factors

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The elephant is reckoned to be the slowest
breeder of all known animals, and I have taken
some pains to estimate its probable minimum rate
of natural increase it will be under the mark to
assume that it breeds when thirty years old, and
goes on breeding till ninety years old, bringing
forth three pairs of young in this interval if
this be so, at the end of the fifth century there
would be alive fifteen million elephants,
descended from the first pair."   
Charles Darwin, The Origin of Species
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Nt N0 ?t
Geometric growth of annual Phlox ? 2.4177
per year Year 0 N0 996 Year 1 N1
2408 Year 3 N3 14076 Year 8 N8 ?
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Geometric growth
Note that curve is stepped
(so whats ? for year 30?)
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Exponential growth Continuous population growth
in an unlimited environment dN/dt rmaxN rmax
per capita rate of increase under ideal
conditions t time In words, the change in
population size (N) at any time t equals the
maximum rate of increase multiplied by the
population size at the same time
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Nt N0ert
Exponential growth of a cattle herd r 0.365
cows (per cow per year) Year Herd
size 0 50.0 1 72.0 2
103.8 5 ? 10
1923.7 50 ?
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Exponential growth
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Whale pop. growth

• Annual migration counts from 1967-1980 indicate a
  2.5 growth rate.
• Thus from 1967-1980, pattern of growth in
  California Gray Whale pop fit exponential model
• Nt N0e0.025t

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Various values of rm
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Organism Pop. doubling time
 
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Logistic equation ( sigmoidal growth curve) d
N/dt rmN (K-N)/K rmN (1 N/K) rm
intrinsic rate of increase (rmax) K carrying
capacity (number of individuals environment can
support)
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POPClocks
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