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:

• 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

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?

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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/CThus, 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

Extinction rate (E) can be derived from estimates of extinction risk in different areas:

P(extinction) ~ Aβ

low

high

Area and isolation

Colonization rate (C) can be derived from estimates of the probability of colonizing an empty patch: patch connectivityconnectivity = F(distance to neighbors, dispersal distance)

low

high

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?– Distance decay of similarity– Dispersal

Distance

Mean

E

nvir

on

men

tal si

mila

rity

Adding more realism

• Subpopulation dynamics– 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

• 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

• Age or stage-structure• Catastrophes (disturbances)• Density dependent dispersal• Allee effects• Landscape change• Matrix variability

Metapopulation MapsNo 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

Spotted OwlSouthern California

Spotted OwlSouthern California

Spotted OwlSouthern California

Spotted OwlSouthern California

Spotted OwlSouthern California

Increase R to 1.2 & K to Increase R to 1.2 & K to 100 for $100,000100 for $100,000

Spotted OwlLarge So. Pops. R=1.2, K to 100