a landscapes mosaic:. only some pieces of the mosaic are suitable for a given species:
TRANSCRIPT
A landscapes mosaic:
Only some pieces of the mosaic are suitable for a given species:
The populations in the landscape mosaic are not totally isolated,But only weakly connected by migrating individuals:
A population: a group of individuals of the same species that live and breed in the same space.
A metapopulation: a group of several local populations connected by the occasional movement of individuals between populations (immigration and emigration).
A deme: a population that is part of a metapopulation.
MetapopulationDynamics: The dynamics of patch occupancy.
Local extinction: a deme goes extinct.
Colonization: an empty but suitable habitat is repopulated by emigrants.
Definitions
How do we characterize the dynamics of metapopulations?
1) We only ask whether patches are occupied or not:
16 patches 4 occupied 12 empty
2) The state variable we follow is the fraction of occupied patches f.
f = 4/16 = 0.25
The relevant rates in metapopulation dynamics:
Probability of local extinction pe
the probability that in a given amount of time a local population will go extinct.
Probability of local colonization pi:
the probability that in a given amount of time, a site will be colonized.
pe
pi
fpe *
)1(* fpi
The rate of occupancy loss:
)1(* fpi The rate of re-colonization:
fpe *
The rate of change in f: fpfpdt
dfei *)1(
The Island-Mainland model:
The probability of immigration is constant.
mainlandislands
Island-mainland model: a constant “propagule rain” originating on the mainland.
0
0.05
0.1
0.15
0.2
0.25
0 0.2 0.4 0.6 0.8 1
I
E
Fraction of occupied sites f
Ext
inct
ion
or
Imm
igra
tion
ra
te
pe
ei
i
ppp
f
ˆ
Island-Mainland Model:
fpfpdt
dfei )1(
If pi > 0 there is always a positive equilibrium: metapopulations always persist.
The Internal Colonization model:
The probability of immigration depends on the patches occupied:
islands
ifpi The immigration probability is proportional to the occupied patches:
0
0.05
0.1
0.15
0.2
0 0.2 0.4 0.6 0.8 1
i = 0.4
i = 0.2
E
ip
f e1ˆ
Internal colonization model:
fpfifdtdf
e )1(
Metapopulations may not persist. Positive equilibrium only if pe < i.
Rescue Effect:
The probability of extinction depends on the patches occupied: extinctions are less likely the more islands are occupied.
islands
)1( fepe The extinction probability is proportional to the occupied patches:
Four possible models:
fpfpdt
dfei )1(External
colonization
Internal colonization
Independent Rescue effectextinction
)1()1( feffifdt
dffpfif
dt
dfe )1(
)1()1( feffpdt
dfi
A sink-population:
A deme within a metapopulation where mortality exceeds birth rates. Habitats remain occupied only due to immigration.
A source-population:
A deme within a metapopulation where birth rates exceed mortality. Surplus individuals leave this habitat to settle (breed) elsewhere.
Other variations
The demes may not be equal in quality. Some may have higher extinction probabilities than others, perhaps because the habitat maintains smaller populations.