1' Geometric population growth

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• 1. Geometric population growth
• In populations with discontinuous growth,
  non-overlapping generations, pulsed growth
• E.g., one reproductive episode/year with complete
  replacement.
• Generates a J-shaped growth curve
• Found in environments with temporary unlimited
  resources, Unoccupied habitats, open niches
• Geometric growth ?N (i.e., lambda x N)
• Need a value for ?, a constant
• ? geometric rate of increase
• ? Nt 1 / Nt
• Starting with a population of 5,000, the
  population is 6,000 after one episode of
  reproduction
• ? ? 6000/5000 1.2

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Using ? sequentially
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• 2. Exponential population growth
• Iteroparous populations with overlapping
  generations.
• Generates a J-shaped growth curve
• Found in environments with temporary, unlimited
  resources, Unoccupied habitats, open niches
• Exponential growth dN/dt rmaxN
• rmax maximum per capita rate of increase
  intrinsic rate of increase
• rmax would be estimated under ideal conditions of
  unlimited resources

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Unconstrained Population Growth

• Nt1 Nt Nt(r) discrete form
• Nt No(ert) continuous form
• With exponential growth across 20 years, what is
  your estimate of population size starting with
  300,000 individuals and r 0.02?
• N20 447,547

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• Although most modeling will only occasionally
  approach natural conditions,
• patterns can be observed in nature that fit
  particular growth models.

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Exponential growth of Scots pine
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Exponential growth of collared doves
A shift from exponential growth to logistic growth
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Logistic Population Growth

• Model of population growth described by an
  S-shaped curve
• Curve has an upper limit defined by the finite
  carrying capacity of the habitat.
• Density dependent factors slow, then adjust
  population growth.

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Logistic population growth
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Logistic population growth model
Contains a term that emulates nature Considers
finite resources (carrying capacity)
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• This model uses r per capita rate of increase
• One source of r from natality and mortality
• r (bo - do)
• bo individual (per capita) birth rate
• If 1 in 10 individuals produce offspring in a
  day, then bo 0.1 individual / individual / day
• do individual (per capita) death rate
• If 1 in 15 individuals die in a day, then do
  1/15 or 0.067 individual / individual / day
• r 0.1 - 0.067 0.033

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Colonization of rocks by Balanus balanoides
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Modifying for time lag

• Lag between an increase in population size and
  its effect on
• subsequent population growth.

Lag decelerates the approach to K. Growth rate
will increase past the density that should be
triggering a decline in population growth.
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Density Independent Factors and Population Growth

• Effects on population growth not related to
  population size.
• Individual variation
• Environmental variation
• Weather (temperature/precipitation) flux
• Stochasticity (chance)

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Stochastic Growth Models E.g., Possible size of a
population of 5 females after one generation
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