Modelling complex migration

Michael Bode

Migration in metapopulationsMetapopulation 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 modelsTime invariant models.Well-mixed migration.Distance-based migration.Complex migration.

Time invariant modelsRe-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?Pr(Extinction)Amount of migrationBoth metapopulation (a) and (b) have the same total migration same number of migration pathwaysOnly the migration pattern is different

Complex migration1.Metapopulations can be considered networksWe can directly analyse the structure of the metapopulations to determine their dynamicsUsing these methods we can rapidly analyse very large metapopulations

Network metricsHow can we characterise a migration pattern?

Clustered/Isolated?

Asymmetry?

Determining the importance of network metricsConstruct a complex migration patternUse Markov transition metrics to determine the probability of metapopulation persistenceCalculate the network metricsDo the metrics predict metapopulation dynamics?

Predicting metapopulation extinction probabilityAverage Path Length ( )

Asymmetry of the metapopulation migration (Z)

(Where M is the migration matrix)

Predicting metapopulation extinction probability

Predicting incidence using patch centrality Ci = (shortest paths to i)

0.30.80.40.4

Predicting patch incidence using CentralityBars indicate 95% CI

Implications: patch removalCentrality of patch removedHighLowSingle patch removedProbability of remaining metapopulation extinction

Implications: sequential patch removalProbability of remaining metapopulation extinctionNumber of patches removed3241Average strategyUnperturbed metapopulationSingle strategyRemoval by Centrality

Limitations and extensionsLack of logical framework.

Incorporating differing patch sizes.

Modelling abundances.

Simulating metapopulation migration patternsRegular LatticeComplex network

Can these complex migration patterns affect the metapopulations persistence? YES.

Not just metapopulation persistence different values for different patches dependent on position.

This was the rationale for changing to distance-based migration, however two close patches may not be closely connected by migration