OUTLINE FOR THIS WEEK Lec 11 – 13
METAPOPULATIONS concept --> simple model Spatially realistic metapopulation models Design and Implementation Pluses/minuses
The importance of the MATRIX
CORRIDORS (as a conservation tool) THE BASICS
Levins 1970 - first used term metapopulation “a population of populations” a group of local populations that are linked by immigration and emigration
Approach
Model population persistence NOT population size
Local populations are reduced to two values 0 local extinction, 1 local persistence
Metapopulation operates at a larger spatial scale examines proportion of patches that are occupied The classical metapopulation
All patches are the same No spatial structure Large number of patches
time Change is due to
Extinction and Colonization
Metapopulations are buffered by rescue effects or recolonisation after local extinction Modelling the classical metapopulation
Extinctions = extinction rate x prop’n patches occupied = e.p
Colonization = colonization rate x prop’n unoccupied patches = cp. (1-p)
E C
0 1 p 0 p 1 At EQUILIBRIUM
Extinction = Colonization
ep = cp (1-p) Q. What influences P*= 1- e/c Extinction Graphically
Colonization C or E
0 p 1 Classical metapulations and habitat loss
Loss of a patch Reduced patch size --> a reduced colonization rate !increased! extinction !reduced! colonization
0 1 Pnew Porig
0 1 P Pnew orig The classical metapopulation model is UNREALISTIC all patches are the same size all patches are equally connected
BUT patches in nature vary in size and isolation
Spatially realistic metapopulation models
Q. Which patches are most likely to go extinct or become colonized? Patch area and isolation effects on occupancy Eg 1 Dormice - 238 woodlands in the UK
Occupancy
Area Isolation Patch area and isolation effects on occupancy Eg 2 Skipper - grass meadows in the UK
Closed = occupied
Area
Isolation The classical metapopulation model is spatially implicit all patches are the same size all patches are equally connected
BUT patches in nature vary in size and isolation
Spatially realistic metapopulation models
Patch size influences extinction Isolation and patch size influence colonisation Spatially realistic population models
MODELLING APPROACHES
Patch occupancy models Patch - 0/1 Data needed - low Application - general
STOCHASTIC PATCH OCCUPANCY MODELS Simplest case - Incidence function models
Probability a patch i is occupied
Ji = Ci / Ci+Ei
Generated from snapshot data ie presence/absence at one point in time Assumes presence/absence is a result of extinction colonisation dynamics the metapopulation is in an equilibrium state Designing and implementing an IFM YOUR SYSTEM
North
Middle
Bodie, California 76 patches South What factors will influence local extinctions? 1 2 3 How will these factors influence local extinctions?
Possible relationships – fill in graphs
1 1
0 0 Area Area What factors will influence local colonisations?
1 Distance between patches 2 Patch size of neighbouring patches providing colonizers 3 State of other patches (occupied or not)
How will those factors influence colonisation?
Basic curve Add Patch size 1 - d 1 e ! j Ci
0 0 dist dist INCIDENCE FUNCTION MODELS
Predicted patch occupancy
Ji = Ci / Ci+Ei
SO what data do we need?
state of each patch (0 or 1), patch areas Aj, distances dij
How do we estimate Ci and Ei?
Use computer Fit statistical model Observed patch occupancy to equations for Ci and Ei (y variable -0 or 1) = (eqn include data + unknown parameters) Model estimates parameters Model therefore describes shape of previous graphs Designing and implementing an IFM YOUR SYSTEM
Bodie, California 20 yr study 76 patches
Parameterised using data for 4 yrs YOU HAVE Ei = extinction probability for each patch i = min [µ/Ax, 1] where A=area and µ and x are parameters Ci = colonization probability varies with isolation (distance), area State of each patch (0ccupied or Unoccupied)
How do you predict PATCH OCCUPANCY and the PROPORTION OF PATCHES OCCUPIED in the future?
Design your simulation. Your simulation results Each network separately all patches included
Patch occupancy
North is stable but Southern networks are not Metapopulation not local dynamics predicts observed pattern Using an IFM Habitat loss 1973-1993
Glanville fritillary, a checkerspot butterfly
Aland Islands >4000 habitat patches Current patches 20% of that available 50 yrs ago 10+ yr time series on extinctions/recolonisations Using an IFM
Glanville fritillary, a checkerspot butterfly
Evaluating conditions for classic metapopulation Populations turnover - extinction is common Habitat patches support local breeding populations No single pop’n is large enough to avoid extinction Patches can be recolonized Patch dynamics are asynchronous Using an IFM
Use snapshot data to estimate parameters influencing extinction and colonisation Use model to predict patch occupancy
eqm
Extinction dynamics due to happy loss expected with a further loss of 50% Incidence function models The positive Are simple Can represent discrete networks of populations in patches that vary within a spatially realistic landscape Allow rigorous mathematical analysis Require limited data Incidence function models
The limitations Data requirements to estimate parameters
1 sufficient patches - 30+ sufficient occupied or empty patches - 10+
2! Equilibrium - no strong trend in % occupied
3 Constant extinction and colonisation rates
Q. Why? The Limitations Assume extinction and colonisation rates are constant
Pika Moilanen et al 1998 Field Vole - Crone et al 2001 Bodie, California Tvarrminne, Finland 4 years - 76 patches 5 yrs - 76 islands
Parameters vary Parameters vary 2-100 fold Area effects differ between yrs
BUT Using mean values captured dynamics of the systems The Limitations Are metapopulations common?
Hanski Many spp may be in extinction-recolonisation balance many butterflies forest insects on dead trees daphnia in rock pools frogs in ponds birds in fragmented woodlots - nuthatches small mammals on islands or in patchy habitat
Harrison and Taylor 1993, Baguet 2004 Spp in extinction-recolonisation balance are rare Examples of spp in extinction-recolonisation balance
Glanville fritillary on granite outcrops -Discrete! breeding populations -All! populations small with high risk extinction -Recolonization! possible (patches < 4km apart)
Pool frog in ponds along Baltic coast -relatively! frequent extinctions (pike predation) - ! movement between ponds rare
- ! extinctions create vacant ponds which are recolonized
Harrison and Taylor 1997 Limitations How common is equilibrium?
Patchy Non-eqm Classical declining
HIGH<--- Fragmentation ---> LOW
Baguet: common rare common Critical appraisal - CONCLUSIONS
1)! Exclusive use of classic metapopulation model theory should be avoided 2)!Management of pop’ns using IFM should be preceded by examination of assumptions regarding population turnover and equilibrium state 3)!Classic metapopulation theory is not only framework to examine consequences of habitat loss and fragmentation From Baguette 2004 Basic and Applied Ecology 5 213-2004