modelling complex migration michael bode. migration in metapopulations metapopulation dynamics are...
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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
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.
Different migration models
1. Time invariant models.
2. Well-mixed migration.
3. Distance-based migration.
4. 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.
)),(()()( jidfijmjim
Will complex migration patterns really affect metapopulation persistence?
Pr(
Ext
inct
ion)
Amount of migration
Both metapopulation (a) and (b) have the
• same total migration
• same number of migration pathways
Only the migration pattern is different
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
Network metrics
How can we characterise a migration pattern?
• Clustered/Isolated?
• Asymmetry?
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?
Predicting metapopulation extinction probability
• Average Path Length ( )
• Asymmetry of the metapopulation migration (Z)
(Where M is the migration matrix)
N
i
N
jijLN
L1 1
2
1L
TMMMZ 2
1
Asymmetry (Z)
Symmetric
Asymmetric
Predicting metapopulation extinction probability
Predicting incidence using patch centrality
• Ci = (shortest paths to i)
0.3
0.8
0.4
0.4
84.1
8.03.08.04.04.0
Predicting patch incidence using Centrality
Bars indicate 95% CI
Implications: patch removal
Centrality of patch removedHighLow
Single patch removed
Pro
babi
lity
of r
emai
ning
met
apop
ulat
ion
extin
ctio
n
Implications: sequential patch removalP
roba
bilit
y of
rem
aini
ng m
etap
opul
atio
n ex
tinct
ion
Number of patches removed
32 41
Average strategy
Unperturbed metapopulation
Single strategy
Removal by Centrality
Limitations and extensions
• Lack of logical framework.
• Incorporating differing patch sizes.
• Modelling abundances.
Simulating metapopulation migration patterns
Regular Lattice Complex network