More about the simulations

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More about the simulations
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Process-based simulations
Population size and spatial structure, birth
rate, survival rate
Parameters
Description of the process
Mechanistic description of the processes of
interest.
Outcome of the process
Modelled pattern, i.e. model outcome on condition
the parameters.
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Stochasticity in natural processes

• Outcomes of the processes vary. What consitutes
  this variation?
• Parameter stochasticity
• If vital process parameters changes, outcome of
  the process changes
• Example populations reproductive rate decreases
  -gt less dispersal
• Environmental stochasticity
• Prevailing environmental conditions may change
• Example less windy weather -gt less long-distance
  wind dispersal of seeds
• Inherent stochasticity
• Stochasticity in the processes themselves
• Example in a small population, population size
  fluctuates just by chance
• gt demographic stochasticity

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An advantage of simulations demographic
stochasticity

• For example lets consider death rate p ( 0 lt p
  lt 1 )
• Population size is N, number of dead is D
• Deterministic world D Np
• Stochastic world D Binom(N, p)
• P(Dd)

• Relevant particularly for small populations
  fluctuations in population size -gt extinction
  risk -gt DEMO 1

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Individual-based simulations

• Individuals are discrete and not alike
• From an individuals perspective, process of
  death would be

Individual X
1 - p
p
Dead
Alive
Choice is a binomial random number
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Spatially explicit simulations
Spatial stochasticity Neighborhood effects
Non-explicit outcomes can still be derived
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Here R comes in

• Random number tools
• Matrix calculations
• Spatial graphics, e.g. image plots
• If some of the needed simulation procedures are
  slow, they can be
• Modelled separately and simulation outputs can
  then be red in to R
• Coded in C and compiled under R
• If some function/procedure is often needed e.g.
  by several people
• gt create a new R package for that
• gt It can be published in R web
• gt DEMO 2