Transcript Slide 1

Spatial ecology I:
metapopulations
Bio 415/615
Questions
1. How can spatially isolated populations be
‘connected’?
2. What question does the Levins
metapopulation model answer?
3. How does patch size and isolation influence
metapopulation dynamics?
4. If population dynamics are correlated, does
metapopulation extinction risk go up or down?
5. How do metapopulation models comment on
the SLOSS debate?
Space: the final frontier
Spatial patterns dominate how ecologists
view ecological problems. We’ve
discussed many, like:
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Species-area curves
Island biogeography
Latitudinal gradient of diversity
Patterns of endemism
Space: the final frontier
Spatial ecology is the name given to
studies that depend on spatial
structure, whether implicit (separate
patches that are influenced by outside
forces) or explicit (specified spatial
structure such as patch shape or
distances).
Spatial ecology
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As Hanski (1998) notes, the contribution of space to
ecological processes can be addressed in 3 ways:
1. Separate patches of uniform structure.
2. Separate patches of varied structure and
connectivity.
3. Continuously varying landscape factors.
Is one approach better than others?
Why should we consider space in
conservation biology?
• We have 5 populations of a rare animal.
PVA says they each have a 50% chance of
going extinct in the next 10 years.
• If the populations are CLOSED and
INDEPENDENT, then the chance that
ALL populations go extinct in the next 10
years is .5x.5x.5x.5x.5 = 3%
(or ed)
But what if they aren’t independent
events?
How could populations be
‘connected’?
• Dispersal / Immigration
– Fast growing populations could augment
slow growing or endangered populations
– Disease or predators could spread from one
patch to another
– Genetic diversity could increase with
outside immigration
• Environment
– Resources or disturbances could be
correlated between patches
Simple metapopulation scenario
• Assume there are lots of ‘equal’ patches
(P) that support individuals of one
species
• Assume each population has the same
extinction risk (E) and ability to
colonize other patches (C)
• Assume no time lags or other
complications
Under what conditions (E,C) will the
metapopulation persist?
= Levins model
(Richard Levins developed metapopulation
concept around 1970)
ΔP = CP(1 – P) - EP
Change in occupied patches equals the
total colonists (C*P) times the number
of patches available (1-P) minus the
number of extinct patches (E*P).
= Levins model
When ΔP is zero, the total patches
occupied are in equilibrium, and
P = 1 – E/C
Thus, when extinction rates (E) are less
than colonization rates (C), some
patches will be occupied.
In other words, high local extinction
rates can be offset by high migration
between patches to allow species to
persist indefinitely in a metapopulation.
Digression: Huffaker 1958
Set up an experiment on the population growth of a mite
that eats oranges, and its predator (also a mite). At first,
had a hard time getting the prey to persist in the presence
of the predator, BUT…
Digression: Huffaker 1958
… after manipulating the distances between oranges,
creating corridors for dispersal, and setting up partial
barriers to the predators, he could increase the survival
rate for both species. This demonstrated the importance
of spatial configuration of ‘habitat’ patches.
Levins model: too basic?
• We wouldn’t use the Levins model to
explore the persistence of real
metacommunities. WHY?
– Patches are different
• What properties of patches influence
population persistence in an open
system?
IBT revisited in metapopulations
• Patches differ in extinction rates and
colonization rates. How is patch
variation in C and E estimated?
Colonization
rates
estimated
from measures
of patch
isolation
Extinction
rates
estimated
from
measures of
patch size
Area and isolation
high
low
Extinction rate (E) can be derived from
estimates of extinction risk in different
areas:
P(extinction) ~ Aβ
Area and isolation
low
high
Colonization rate (C) can be derived from
estimates of the probability of colonizing an
empty patch: patch connectivity
connectivity =
F(distance to neighbors, dispersal distance)
Correlated patches
Why should demographic parameters
(births, deaths, etc) be correlated
between patches?
• Large-scale environmental factors
(climate)
What is the effect of positive patch
correlation on metapopulation extinction
risk?
Disturbance-Climate Relations
Southern Oscillation & fire -Swetnam & Betancourt 1990
Demographic correlation and
extinction risk
Several small
populations can be
more persistent
than a single large
population, but only
if population
dynamics are
partially
uncorrelated. What
is the role of
dispersal here?
How do we measure correlation
of populations in different
patches?
• DISTANCE. Why?
Mean
Environmental
similarity
– Distance decay of similarity
– Dispersal
Distance
Adding more realism
• Subpopulation dynamics
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– Structured metapopulation model
Patch quality & K
Temporal trends in patch quality
Spatially explicit model
Spatially realistic model
– Spatial location (distance), Habitat quality
– Corridors
– Matrix quality and dispersal (vs. distance)
= LANDSCAPE ECOLOGY!!!
Simulation Models
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Demographic stochasticity
Distances and arrangements of populations
Initial abundance
growth rate (R), survival rate (S), SD of R, K,
temporal trend in K
• Density dependence
• Ave., max. dispersal distance, dispersal rate
• Spatial autocorrelation in environment (L)
Could be added
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Age or stage-structure
Catastrophes (disturbances)
Density dependent dispersal
Allee effects
Landscape change
Matrix variability
Metapopulation Maps
No Dispersal (L)
Dispersal (R)
K=20, R=1.2, SD=.5
Population Options (each of 5)
Environmental Correlation (L)
Dispersal
5 Populations:
Correlated Environments
Top: No Dispersal Bottom: High Dispersal
5 Populations:
Uncorrelated Environments
Top: No Dispersal Bottom: High Dispersal
5 Populations: Uncorr Env
Top: Single Large (K=100, R=1.2, SD=.6)
Bottom: 5, UnCorr, High Dispersal
5 Populations: Uncorr Env
Top: Single Large (K=100, R=1.2, SD=.6)
Bottom: 5, UnCorr, High Dispersal
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