lecture 06 metapopulations spring 2013 dr ed harris
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Lecture 06 Metapopulations Spring 2013 Dr Ed Harris. 61BL3313 Population and Community Ecology. Announcements announcements: -quiz marks -Metapopulations in R lab -issues, comments?. This time Metapopulations -metapopulations in space and time -MacArthur and Wilson / equilibrium

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-quiz marks

-Metapopulations in R lab

-issues, comments?


This time


-metapopulations in space and time

-MacArthur and Wilson / equilibrium

-Levins metapop classic

-metapopulation dynamics / extinction

-assumptions and evidence



This time



-r and K selection

-energy allocation

-clutch size + spatial patterns


-bet hedging



The idea of metapopulation biology is that most species exist in an array of subpopulations

Some of the subpopulations have R < 1 (sinks) and some R > 1 (sources)

Dispersal amongst populations prevents local extinctions




-1883 – massive vocanic explosion – 40m tsunami

-40,000 people died, the island decimated of all life

-9 months later an expedition found a single spider

-1 year later, some grass shoots were found

-1886, 16 species of grass and shrubs; 1897, 49 species; 1928, 300 species

-1929, forest forced grass into small pockets



E. O. Wilson

2 processes describe the Krakatau sequence

-Extinction, recolonization

-think of a bathtub filling – water level is species richness (the # of species)

-water in is the rate of colonization of new species

-water out the drain is the rate of extinction


metapopulations in space and time

-until now we have assumed in many models that populations are widespread, large and occupy many habitats

-of course, these are rarely true, especially in recent decades as the human population has grown

-partly in reaction to this reality, spatial ecology developed


metapopulations in space and time

spatial ecology is the study of ecological process in space and time

2 different complimentary approaches

-landscape ecology – large geopgraphic scale, physical structure and patchiness of habitat

-metapopulation biology – B I D E approach


MacArthur and Wilson / equilibrium

Theory of island biogeography

-mathematical approach to species assemblage on islands of habitat

- increasingly important today as habitats become "patchier" and more island-like


MacArthur and Wilson / equilibrium

T I B Basic idea:

1 There is a relationship between habitat island area and the number of species

found there (the species–area curve);

2 local extinction is a normal, common occurrence, particularly on small

islands with small populations;

3 local diversity is based on an interplay between colonization from a

“mainland” source of species and local extinction, resulting in an “equilibrium”

number of species;

4 island size and distance from the source of species will affect the “equilibrium”

number of species. That is, large islands that are close to the mainland will

have more species than small islands far from the mainland.


MacArthur and Wilson / equilibrium

species area relationship

S = # species

A = area of island

C = constant (intercept)

z = standard constant for group of species


MacArthur and Wilson / equilibrium

species area relationship

linear equation form:


MacArthur and Wilson / equilibrium

Again, the bathtub!

-S is equilibrium number of species, where curves intersect


MacArthur and Wilson / equilibrium

Modern view of MacArthur / Wilson

-mainland-island models

-mainland is source, island is sink


Levins metapop classic

-stochastic balance between local extinction and recolonization of empty patches

-Naturally, we have a model!

c = colonization rate

E = extinction rate

P = proportion of patches occupied


Levins metapop classic


1 The local populations are identical and have the same behavior;

2 extinctions occur independently in different patches and therefore local dynamics are asynchronous;

3 colonization spreads across the entire patch network and all patches are equally likely to be “encountered;”

4 furthermore, all patches are equally connected to all other patches.


Levins metapop classic

If we solve for dP/dt = 0, we can find the equilibrium point

<some math happens>

Take home:

Colonization must be greater than extinction or the proportion of patches occupied will go to zero!


Levins metapop classic

Patch occupancy and lowered colonization rate due to reduction in the number of habitat patches


Levins metapop classic

Patch occupancy and lowered colonization rate due to reduction in the number of habitat patches

+ increased extinction rate


metapopulation dynamics / extinction

Extinction at local and metapopulation levels


metapopulation dynamics / extinction

Some evidence that metapopulation structure can stabilize population equilibrium size

Remember chatic behaviour or this model?


metapopulation dynamics / extinction

when populations are connected... (add together N)


assumptions and evidence that metapopulations exist in nature

1 The species has local breeding populations in relatively discrete habitat patches. This condition stresses that the population is spatially structured and therefore most individuals interact with others only in the local habitat patch.

2 No single local population is large enough to have a longer expected lifetime than the expected lifetime of the metapopulation itself. This excludes mainland–island populations.

3 Empty habitat patches are common. In the Glanville fritillary butterfly study in Finland, for example, 70% of approximately 1600 habitat patches have been empty at a given time (Hanski et al. 1995).

4 The habitat patches are not too isolated to prevent re-colonization. Long-distance

movements may be facilitated by habitat corridors or other mechanisms.


assumptions and evidence that metapopulations exist in nature

5 Local dynamics are sufficiently asynchronous to make simultaneous extinction of all local populations unlikely. With complete synchrony, the metapopulation only lasts as long as the local population with the lowest chance of extinction. The greater the asynchrony, the longer the metapopulation is likely to last. In a recent review of the literature, Elmhagen and Angerbjörn (2001) found eight studies (four insect species and four small mammal species) in which asynchrony of population dynamics among patches was confirmed.

6 Population turnover, local extinctions, and the establishment of new popula- tions form the basis for metapopulation dynamics, and metapopulations persist despite population turnover. Elmhagen and Angerbjörn (2001), in a review of the literature, found 22 studies confirming turnover.


assumptions and evidence that metapopulations exist in nature

7 Population size or density is significantly affected by migration. This is the basis for source–sink populations and the rescue effect (Pulliam 1988, 1996).

8 Population density, colonization rate, and extinction rates are all affected by patch size and isolation.

9 Metapopulations can affect competitive, predator–prey, and parasite–host interactions.


assumptions and evidence that metapopulations exist in nature

Some data

Melitaea cinxia

extinction data


assumptions and evidence that metapopulations exist in nature

turnover = extinction + recolonization