Slajd 1

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From patch occupancies to metapopulations
In a patch occupancy model individuals are placed
according to a certain set of rules into the
cells of a grid. A next step might allow for
migrating between cells. Such models are called
metapopulation models.
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Mainland island pattern
Patchy regional distribution
A combination of these patterns
Patchy regional distribution without dispersal
Different types of metapopulations
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The Lotka Volterra model of population growth
Levins (1969) assumed that the change in the
occupancy of single spatially separated habitats
(islands) follows the same model. Assume P being
the number of islands (total K) occupied. Q K-P
is then the proportion of not occupied islands. m
is the immigration and e the local extinction
probability.
Immigration
At equilibrium dP/dt 0
Emigration
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m, e and even K are not simple constants. They
vary in time with respect to additinal variables
c(t) f(area, habitat quality, dispersion
ability, carrying capacities, genetic
disposition, patch distances, edge effects, patch
number, morphology, reproductive rates, trophic
levels, heterogeneity, competitive effects,
temporal variability, mortality rates,
environmental influences, resources, age
distribution...)
e(t) f(area, habitat quality, dispersion
ability, carrying capacities, genetic
disposition, patch distances, edge effects, patch
number, morphology, reproductive rates, trophic
levels, heterogeneity, competitive effects,
temporal variability, mortality rates,
environmental influences, resources, age
distribution, genetic load, mate finding,
stochastic events...)
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The basic Levins model
The basic function of the theory of island
colonization of McArthur and Wilson
The models describe changes in species numbers
and occupancies in time
The last model describes the changes occurrence
probability on patch i at colonization rate m and
extinction rate e
Additional canonical assumptions
The basic model of metapopulation ecology
describes the probability of occurrrence in terms
of mean patch distances dij, the average
migration distance a, and the soucre island area
Aj
The model predicts Species occurrences in
fragmented landscapes Spatial species
turnover Extinction probabilities Temporal
species turnover
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What does metapopulation ecology predict?
Blue occurrences Red absences Line 50 chance
to occur
Occurrences of Hesperia comma in fragmented
landscapes in southern England (from Hanski 1994)
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SPOMSIM
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Regional extinction times
TR regional extinction time TL local extinction
time K regional number of patches p Mean
number of occupied patches
Long term survival is only possible when the
average proportion P/K of occupied patches is
larger than 3 K -1 /2 P gt 3K1/2
The model of Gurney and Nisbet (1978)(based on a
stochastic form of the metapopulation model of
Levins) predicts long term regional survival of a
species if the average proportion of occupied
patches is larger than 3 times K-0.5.
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Glanville fritillary Melitaea cinxia
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The fraction of occupied networks depends on the
number of patches in a network and matches the
theoretical expectations of the patch occupancy
model of Gurney and Nisbet (1978). Data from the
Glanville Fritillary redrawn from Thomas and
Hanski (1997). The vertical line indicates the
theoretical threshold from the Gurney Nisbet
model.
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Todays reading
Metapopulation http//en.wikipedia.org/wiki/Metap
opulation Metapopulation research group
http//www.helsinki.fi/science/metapop/ Metapopul
ation and extinction http//faculty.plattsburgh.e
du/thomas.wolosz/metapop.htm