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

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-3

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-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.

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0.2

0.4

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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