For Geometric Populations nonoverlapping generations:

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Summary
For Geometric Populations (nonoverlapping
generations) Population size after one
generation Nt1 R0Nt Population size as some
future time Nt1Nt?t For Exponential
Populations (overlapping generations) Number
added to population dN/dt rmaxN Population
size as some future time NtN0ermaxt
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Logistic Population Growth where K is carrying
capacity of the environment (level at which
births equal deaths) When N is small, 1-N/K is
near 1 and rmaxN is unconstrained. When N
approaches K, 1-N/K approaches 0 and rmaxN
approaches 0 and growth levels off.
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Implication of Logistic Number added to
population is greatest at inflection point (1/2
K). Hence this is the population size where
the most individuals can be harvested without
decreasing population size Known as Maximum
sustained yield. Used as a guide to hunting
and harvest.
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ASSUMPTIONS OF LOGISTIC (as for exponential - no
time lags, migration, genetic variation, or age
structure) plus Constant carrying capacity
resource availability does not vary thru
time. Linear density dependence each
individual added causes and incremental decrease
in the per capita rate of pop growth.
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Summary
For Geometric Populations (nonoverlapping
generations) Population size after one
generation Nt1 R0Nt Population size as some
future time NtN0?t For Exponential Populations
(overlapping generations) Number added to
population dN/dt rmaxN Population size as some
future time NtN0ermaxt For Logistic
Populations Number added to population dN /dt
rmaxN (1-N/K)
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• 3. For a population of elk in Yellowstone Park,
  r.015 per year, N10,000, K15,000. What is the
  rate of increase for this population?

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• 3. For a population of elk in Yellowstone Park,
  r.015 per year, N10,000, K15,000. What is the
  rate of increase for this population?
• dN /dt rmaxN (1-N/K) .015 x 10,000
  (1-10,000/15,000
• .015 x 10,000 (.333) .015 x 3,333.3 50 per
  year