1. Modelling complex migration Michael Bode

2. Migration in metapopulations Metapopulation dynamics are defined by the balance between local extinction and recolonisation.

3. Overview 1.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.

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

5. Time invariant models Re-colonisation probability is constant Probability of metapopulation extinction is underestimated.

6. Well-mixed migration (the LPER assumption) All patches are equally connected. The resulting metapopulation is very homogeneous

7. 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.

8. Will complex migration patterns really affect metapopulation persistence? Pr(Extinction) Amount of migration Both metapopulation (a) and (b) have the same total migration same number of migration pathways Only the migration pattern is different

9. Complex migration 1.Metapopulations can be considered networks 2.We can directly analyse the structure of the metapopulations to determine their dynamics 3.Using these methods we can rapidly analyse very large metapopulations

10. Network metrics How can we characterise a migration pattern? Clustered/Isolated? Asymmetry?

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

12. Predicting metapopulation extinction probability Average Path Length ( ) Asymmetry of the metapopulation migration (Z) (Where M is the migration matrix)

13. Asymmetry (Z) Symmetric Asymmetric Predicting metapopulation extinction probability

14. Predicting incidence using patch centrality C i = (shortest paths to i) 0.3 0.8 0.4

15. Predicting patch incidence using Centrality Bars indicate 95% CI

16. Implications: patch removal Centrality of patch removed HighLow Single patch removed Probability of remaining metapopulation extinction

17. Implications: sequential patch removal Probability of remaining metapopulation extinction Number of patches removed 3241 Average strategy Unperturbed metapopulation Single strategy Removal by Centrality

18. Limitations and extensions Lack of logical framework. Incorporating differing patch sizes. Modelling abundances.

21. Simulating metapopulation migration patterns Regular LatticeComplex network