Population Changes

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Population Changes
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• Life history table
• x an age class
• lx proportion of the initial sample that has
  survived to a certain age .
• a Fecundity table
• mx the mean number of offspring produced by
  females in an age class
• lmx proportional number of offspring produced
  by an age class
• source of information about population dynamics

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Species with non-overlapping generations
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• For species with overlapping generations
• Things of ecological importance include
• 1. Net reproductive rate (R0)
• 2. Average generation time (T)
• 3. Per capita rate of increase (r)

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r lnRo / T -0.509 / 10.6 -0.048
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T generation time T S xlxmx / Ro
0.940
Task calculate 1. Generation time and 2. State
of population (growth) A. from R0 B. from r r
lnRo / T
0.188
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Age class structure
L to R 3n parthenogen originating from 2n
parthenogen X 2n biparental
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Age distributions
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Population Growth

• Reproductive potential of species guarantees that
  habitats can be filled.
• Population growth can be simulated by
  mathematical models if nature is simplified and
  various assumptions are met.
• Testing models generally done in a controlled
  laboratory setting.
• May be little resemblance to natural populations.

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Some Factors Affecting Model Reliability

• 1. Relationship of population growth to
  population density may not be linear.
• 2. Effects of density on increase in populations
  size may be lagged.
• 3. Environmental effects on individuals and
  populations are not constant.
• 4. Genetic variation means that some individuals
  reproduce more than others.
• 5. Population size can fluctuate by immigration
  and emigration.

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• 1. Geometric population growth
• Populations with non-overlapping generations
  pulsed growth
• Generates a J-shaped growth curve
• Found in environments with temporary unlimited
  resources, Unoccupied habitats, open niches
• Geometric growth ?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
• Populations with overlapping generations and
  continuous growth
• 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 447,529

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• Most modeling will only occasionally approach
  natural conditions.
• However, 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