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Modelling complex migration Michael Bode. Migration in metapopulations. Metapopulation dynamics are defined by the balance between local extinction and recolonisation. Overview. Metapopulation migration needs to be modelled as a complex and heterogeneous process.
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Modelling complex migration Michael Bode
Migration in metapopulations Metapopulation dynamics are defined by the balance between local extinction and recolonisation.
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.
Different migration models • Time invariant models. • Well-mixed migration. • Distance-based migration. • Complex migration.
Time invariant models • Re-colonisation probability is constant • Probability of metapopulation extinction is underestimated.
Well-mixed migration (the LPER assumption) • All patches are equally connected. • The resulting metapopulation is very homogeneous
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.
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
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
Network metrics How can we characterise a migration pattern? • Clustered/Isolated? • Asymmetry?
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?
Predicting metapopulation extinction probability • Average Path Length ( ) • Asymmetry of the metapopulation migration (Z) (Where M is the migration matrix)
Symmetric Asymmetry (Z) Asymmetric Predicting metapopulation extinction probability
Predicting incidence using patch centrality • Ci= (shortest paths to i) 0.4 0.8 0.4 0.3
Predicting patch incidence using Centrality Bars indicate 95% CI
Implications: patch removal Probability of remaining metapopulation extinction Single patch removed Low High Centrality of patch removed
Implications: sequential patch removal Average strategy Unperturbed metapopulation Probability of remaining metapopulation extinction Single strategy Removal by Centrality 1 2 3 4 Number of patches removed
Limitations and extensions • Lack of logical framework. • Incorporating differing patch sizes. • Modelling abundances.
Simulating metapopulation migration patterns Regular Lattice Complex network