Modelling complex migration

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• Modelling complex migration
• Michael Bode

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Migration in metapopulations

• Metapopulation dynamics are defined by the
  balance between local extinction and
  recolonisation.

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Overview

• Metapopulation migration needs to be modelled as
  a complex and heterogeneous process.
• 2. We can understand metapopulation dynamics by
  direct analysis of the migration structure using
  network theory.

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Different migration models

1. Time invariant models.
2. Well-mixed migration.
3. Distance-based migration.
4. Complex migration.

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Time invariant models

• Re-colonisation probability is constant
• Probability of metapopulation extinction is
  underestimated.

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Well-mixed migration (the LPER assumption)

• All patches are equally connected.
• The resulting metapopulation is very homogeneous

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Distance-based migration(The spatially real
metapopulation)

• Migration strengths are defined by inter-patch
  distance.
• The result is symmetric migration,
• where every patch is connected.

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Will complex migration patterns really affect
metapopulation persistence?

• Both metapopulation (a) and (b) have the
• same total migration
• same number of migration pathways
• Only the migration pattern is different

Pr(Extinction)
Amount of migration
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Complex migration

• 1. Metapopulations can be considered networks
• We can directly analyse the structure of the
  metapopulations to determine their dynamics
• Using these methods we can rapidly analyse very
  large metapopulations

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Network metrics

• How can we characterise a migration pattern?
• Clustered/Isolated?
• Asymmetry?

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Determining the importance of network metrics
Construct a complex migration pattern
Calculate the network metrics
Use Markov transition metrics to determine the
probability of metapopulation persistence
Do the metrics predict metapopulation dynamics?
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Predicting metapopulation extinction probability

• Average Path Length ( )
• Asymmetry of the metapopulation migration (Z)
• (Where M is the migration matrix)

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Predicting metapopulation extinction probability
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Predicting incidence using patch centrality

• Ci (shortest paths to i)

0.4
0.8
0.4
0.3
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Predicting patch incidence using Centrality
Bars indicate 95 CI
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Implications patch removal
Probability of remaining metapopulation extinction
Single patch removed
High
Low
Centrality of patch removed
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Implications sequential patch removal
Average strategy
Unperturbed metapopulation
Probability of remaining metapopulation extinction
Single strategy
Removal by Centrality
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2
4
1
Number of patches removed
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Limitations and extensions

• Lack of logical framework.
• Incorporating differing patch sizes.
• Modelling abundances.

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Simulating metapopulation migration patterns
Regular Lattice
Complex network
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