Lecture 9Fragmented landscapes
Landscape ecologyAgroecology
A B C
Macropterous Carabidae Brachypterous CarabidaeDimorphic Carabidae
Fragmented landscapes
Idiosyncratic species Idiosyncratic species
Not nestedHigh species turnover
Slightly nestedModerate species turnover
Highly nestedLow species turnover
Extinction driven system Random system Colonization driven system
Colonization
Persistence
Nebria brevicollis Notiophilus biguttatus Carabus nemoralis
Predictable species occurrences
Glanville fritillary
Melitaea cinxia
The metapopulation of Melitaea cinxia
A B
C D
Mainland – island pattern
Patchy regional distribution
Patchy regional distribution without dispersal
A combination of these patterns
Different types of metapopulations
)(KNK
rNdtdN
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.
dP K P QmP mPdt K K
dP ePdt
dP K PmP ePdt K
Immigration
Emigration
At equilibrium dP/dt = 0
K P P e0 mP eP 1K K m
dP K PiP ePdt K
dS R ScS eSdt R
ii i
dp 1 p pdt
The basic Levins modelThe 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 and extinction rate
Additional „canonical’ assumptions
ij
ii
d
i j ji, j
1A
(e A p )
ijdi
j j i ii, j i
dp am (e A p ) 1 p pdt A
The basic model of metapopulation ecology
describes the probability of occurrence in terms of mean patch distances dij, the average migration distance , and the source island area Aj
What does metapopulation ecology predict?
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-5
-4
-3
-2
-1
0
1
2
3
0 1 2 3 4 5
Connectivity
ln A
rea
Occurrences of Hesperia comma in
fragmented landscapes in
southern England (from Hanski 1994)
Blue: occurrencesRed absencesLine: 50% chance to occur
In fragmented landscapes occupancy declines nonlinear with decreasing patch area and with decreasing conncetivity
There is a lower threshold of regional (metapopulation) extinction.This threshold can be predicted from the Levin’s model if species dispersal
rates are known.
The fraction of occupied networks depends on the number of patches in a network.
Bełow a certain threshold the species goes extinct.
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40
Number of patches per network
Frac
tion
of o
ccup
ied
netw
orks Data from the
Glanville Fritillary redrawn from Thomas and Hanski (1997).Theoretical threshold
TR: regional extinction timeTL: local extinction timeK : regional number of patchesp : 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 > 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.
Regional extinction times
0
200
400
600
800
1000
1200
0 1 2 3 4 5 6 7
P K 0.5
Med
ian
time
to e
xtin
ctio
n
PHP
LR eTT 22
2
Local time to extinction Years 1 5 10 20 50
Species Occurrences Regional time to extinctionCarabus granulatus 13 2.23327E+18 1.11664E+19 2.23327E+19 4.46655E+19 1.11664E+20Pterostichus melanarius 13 2.23327E+18 1.11664E+19 2.23327E+19 4.46655E+19 1.11664E+20Pterostichus strennus (Panzer) 13 2.23327E+18 1.11664E+19 2.23327E+19 4.46655E+19 1.11664E+20Oxypselaphus obscurus (Herbst) 12 26489122130 1.32446E+11 2.64891E+11 5.29782E+11 1.32446E+12Pterostichus diligens (Sturm) 11 3704282 18521410 37042820 74085640 185214099Synuchus vivalis (Illiger) 10 22026 110132 220265 440529 1101323Patrobus atrorufus (Stroem) 10 22026 110132 220265 440529 1101323Pterostichus antracinus 9 854 4270 8541 17081 42703Pterostichus minor (Gyllenhal) 9 854 4270 8541 17081 42703Carabus nemoralis Muller 9 854 4270 8541 17081 42703Notiophilus palustris (Duftshmid) 7 21 107 214 428 1069Clivina fossor (Linnaeus) 7 21 107 214 428 1069Stomis pumicatus (Panzer) 7 21 107 214 428 1069Leistus rufomarginatus (Duftshmid) 5 3 17 35 70 175Epaphius secalis (Paykull) 5 3 17 35 70 175Notiophilus biguttatus (Fabricius) 3 1 7 15 29 73Calathus melanocephalus (Linnaeus) 3 1 7 15 29 73Calathus mollis (Marsham) 1 1 5 10 21 52Dischirius globosus (Herbst) 1 1 5 10 21 52Leistus ferrugineus (Linnaeus) 1 1 5 10 21 52Carabus hortensis Linnaeus 1 1 5 10 21 52Calathus micropterus (Duftschmid) 1 1 5 10 21 52Calathus fuscipes (Goeze) 1 1 5 10 21 52Carabus cancelatus Illiger 1 1 5 10 21 52
Extinction times of Mazuran ground beetles
Local extinction times are roughly proportional to local abundances
SPOMSIM
Today’s reading
Metapopulation: http://en.wikipedia.org/wiki/Metapopulation
Metapopulation research group: http://www.helsinki.fi/science/metapop/
Metapopulation and extinction: http://faculty.plattsburgh.edu/thomas.wolosz/metapop.htm
Landscape ecology: The state of arthttp://www.edc.uri.edu/nrs/classes/nrs534/NRS_534_readings/Turner_AnnRevEcoSys_2005.pdf