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 .