# metapopulation assumptions

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Assumptions of Assumptions of metapopulationsmetapopulations

OutlineOutline

Basic metapopulation assumptions

Factors that affects local population dynamics

Model assumptions

advantages and disadvantages

Basic Metapopulation Basic Metapopulation AssumptionsAssumptions

Space is discrete, and it is possible to distinguish between the matrix and habitat patches

Habitat patch units are large and permanent enough to allow for persistence of local populations for at least a few generations

More basic assumptionsMore basic assumptions

Habitat patches are of equal size and are equally isolated

Migration has no real effect on dynamics

2 ways to think of migration

Density DependenceDensity Dependence

Per capita growth rate depends on past and/or present population densities

not all populations are strongly affected all the time

Morris and Doak, 2002

ExtinctionExtinction

Risk of extinction increases with decreasing population size

Allee Effect-Reduced per capita growth rate at low population density

Habitat fragmentation- reduces patch area

can be easily modeled

MigrationMigration

Need a sufficiently high rate of migration for metapopulations to persist as a result of recolonizations

If migration rate is too high, may accelerate metapopulation extinction

Rescue Effect/Propagule Rain

ColonizationColonization

Habitat Fragmentation- reduces level of patch connectivity

can be easily modeled

Spatially Implicit (Levins) Spatially Implicit (Levins) ModelModel

Assume:

infinite, discrete habitat patches with no variation

stochastic, asynchronous local dynamics

local dynamics be ignored

all patches are equally connected via migration

patches are empty or occupied

Hanski and Gilpin 1997

Levins ModelLevins Model

dP/dt= cP(1-P)-ePEquilibrium when Phat= 1-e/c

Highlights that recolonization must occur at at a high enough rate to compensate for extinctions

Advantages and Advantages and Disadvantages of the basic Disadvantages of the basic

Levins modelLevins model+ Easy mathematically and conceptually

- Can only answer a limited number of questions because it

ignores so many variables (generally can only be used for metapopulations close to a steady state)

Spatially Explicit ModelsSpatially Explicit Models

Assume:

many patches (arranged as cells in a lattice)

patches may be occupied or empty

no variation in patch size and quality

migration is distance dependent Hanski, 1999 Fig. 5.3A

Spatially Explicit ModelSpatially Explicit Model

Probability that a cell will become occupied= γ(y-x)

Where gamma is the rate of emigration and y-x is the distance between x and y

Advantages and Advantages and DisadvantagesDisadvantages

+ Local behavior is same from patch to patch, so dynamics can

be easily modeled.

- Can not simply describe the state of the metapopulation by the

fraction of patches occupied (need to use a vector- much more complicated)

Spatially Realistic ModelSpatially Realistic Modelfinite number of relatively small patches in comparison with the total landscape

randomly scattered patches

assume real patch attributes (area, location, etc)

patch area and isolation affect extinction and recolonization

occupied patches inflict colonization pressure on all empty patches

declines with distance

Hanski, 1999 Fig. 5.3

Spatially Realistic ModelSpatially Realistic Model

dpi/dt= Ci(t)[1-pi]-eipi

(dpi/dt= rate of change in patch i)pi= probability that patch i is occupied

Ci(t)= colonization rate in patch i, taking connectivity between all patches into account

ei= extinction rate in patch i , which is a function of the area of patch i

Advantages and Advantages and DisadvantagesDisadvantages

+ More realistic; can make quantitative predictions about

dynamics

- More complicated; A lot of data has to be assumed; Starts to

move away from the metapopulation concept

Works citedWorks citedDriscoll, D. 2007. How to find a metapopulation. Can. J. Zool., 85: 1031-1048.

Hanski, I. 1999. Metapopulation ecology. New York: Oxford University Press.

Hanski, I and Gaggiotti, O (Eds.). 2004. Ecology, genetics, and evolution of metapopulations. New York: Elsevier Academic Press.

Hanski, I and Gilpin, M (Eds.). 1997. Metapopulation biology: Ecology, genetics, and evolution. New York: Academic Press.

Hanski, I and Gilpin, M, 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society, 42: 3-16.

Morris, W and Doak, D. 2002. Quantitative Conservation Biology. Sunderland: Sinauer Associates, Inc.

Nie, L and Mei, D. 2007. Fluctuation-enhanced stability of a metapopulation. Physics Letters A, 371: 111-117.