Tucker Gilman

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Migration and Competition Dynamics in a Patchy
Environment

• Tucker Gilman
• Katy Greenwald
• Rich Hambrock

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Background

• Populations are often patchily distributed
• Natural processes
• Anthropogenic habitat fragmentation
• Setting the scene
• Discrete patches
• Two competing species
• Different dispersal strategies
• Main question who wins???
• Can there be stable coexistence?

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Two species in patch i
0 lt aij lt 1 is the proportion surviving migration
from patch j to patch i
Coexistence if
Bistability if
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Two species in patch i (simplified)

• Assume
• Intrinsic birth rate is independent of patch
• Migration is constant and random between patches

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Two species in patch i
Results

• Coexistence in one patch and exclusion in another
  can result in coexistence everywhere with
  migration.
• Coexistence everywhere can end in exclusion for
  the faster migrator.
• Trivial equilibrium is stable if riltmi (1-a) for
  i 1, 2, . . . , n

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Two patches with migration
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Two patches with migration
Coexistence
Coexistence
Coexistence
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Two patches with migration
Species Y
Coexistence
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Two patches with migration
Coexistence
Coexistence
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Two patches with migration
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Two patches with migration
K1,13.75, K2,16 K1,21.21, K2,22
K1,17.5, K2,112 K1,21.21, K2,22
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Smart Migration Models
Risk Adverse Migration
Where f is a non-decreasing function with f(0)
0 and f(1) 1
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Smart Migration Models
Relative fitness
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Smart Migration Models
Density-Dependent Migration
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Smart Migration Models
Density-Dependent Migration (2 patches)
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Density dependent migration (2 patches)
Species Y
Coexistence
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Density dependent migration (2 patches)
a1
a0.99
a0.90
a0.80
a0.80
a0.61
a0.60
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Some Open questions

• Investigate the dynamics of other smart migration
  models.
• How much smarter does a smart migrator have to be
  to overcome a slower smart migrator?

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Discrete time model

• Model system pond-breeding salamanders
• Biphasic life history
• Aquatic juvenile stage
• Terrestrial adult stage

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Two species in patch i
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Two species in patch i
Adults
Kids
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Two species in patch i
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Deterministic model
m0.33
a0.75
m0.67
The fast migrant always loses.
If migration is dan- gerous, fast migrants go
extinct.
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Environmental stochasticity
Chance of drought 25 in small pond 15 in
medium pond 5 in large pond
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Further questions

• The slower migrant always wins, with all else
  equal.
• How can we induce a founder control outcome?
  (i.e., can the fast migrant ever win?)
• Change other parameters, e.g., bump up R for the
  fast species or increase a for the slow one.
• Other ways
• More patches?
• Metapopulation?
• Demographic stochasticity?