Metapopulation modeling: Stochastic Patch Occupancy Model (SPOM) by Atte Moilanen 1. Metapopulation processes and variables 2. Stochastic Patch Occupancy Models (SPOMs) 3. Connectivity in metapopulation studies
What is metapopulation modeling used for Developing fundamental theory; understanding spatial population dynamics Producing qualitative / quantitative predictions for the needs of conservation understanding effects of fragmentation and habitat loss reserve network design metapopulation viability analysis studies of feasibility of reintroduction
Metapopulation processes and variables species interactions migration (dispersal) emigration regional stochasticity immigration colonization local dynamics and local extinction
Some factors affecting local dynamics and local extinction population size (density) emigration immigration population growth rate type of population growth patch size quality (food, breeding ) species interactions Stochastic factors environmental stochasticity demographic stochasticity catastrophes genetics human persecution habitat loss
Factors affecting emigration Patch size quality shape edge quality Population density
Factors affecting movement The habitat matrix habitat types texture of habitat pattern (distances between patches) Behavior of the species habitat specific movement and mortality rates edge effects species perceptual ability dispersal cues (conspecific attraction etc.)
Factors affecting immigration Patch detection ability of the species Patch size shape boundary quality quality Population size / density
Factors affecting colonization Number of immigrants Patch quality Population density (possible Allee effect etc.)
Factors affecting all metapopulation processes; 1. Species interactions Predation, competition, mutualism etc. May affect any metapopulation process local dynamics and local extinction rates migration behavior
Factors affecting all metapopulation processes; 2. Regional stochasticity Spatially correlated environmental stochasticity Caused by weather, disease, etc. Causes correlation in local dynamics / migration Strong effect on metapopulation persistence Effect may depend on habitat type Example: M. cinxia 1993-1994 1993, 250 populations 1994, 130 populations decline caused by larval mortality due to dry summer weather
Stochastic Patch Occupancy Models (SPOMs) Basic assumption: local dynamics are very complex to model => ignore local dynamics and only model species presence / absence in habitat patches Kareiva & Steinberg (1997): the presence/absence assumption is almost necessary in large scale ecological studies Relatively easy data collection 1st SPOM; the incidence function model (Hanski 1994)
SPOMs: general structure Extinction probability E i (t) of occupied patch All patch states updated each time unit Patch area A i Connectivity S i (t) Colonization probability C i (t) of empty patch - effect of distance on migration - current patch occupancy pattern
SPOMs: common simplifications Patches have sizes but no shape Patch quality is constant The habitat matrix is of uniform quality Regional stochasticity often ignored
local extinction: example Decreasing function of area etc. 2.0 1.5 A i = area of patch i and x are parameters E i 1.0 0.5 E i A x i 0.0 0.0 0.5 1.0 1.5 2.0 A i
SPOMs: effect of distance on migration Migration success decreasing function of distance the dispersal kernel A (negative exponential) Dd (, ) exp( d) ij B,C,D (fat tailed) 1 Dd ( ij,, ) 1 d d ij = distance from i to j ij ij D(d ij, 1.0 C 0.5 B A D 0.0 0 1 2 3 4 5 d ij
SPOMs: colonization Colonization probability of patch i, C i (t)=f(connectivity) 1.0 A: independent colonizations C() t 1 exp( ys ( t)) i B: Allee effect i C i (t) 0.5 A B C() t i [ Si( t)] [ S ( t)] S i (t) = connectivity y = parameter i 2 y 2 2 0.0 0 1 2 S i (t)
SPOMs: regional stochasticity Spatial correlation in extinctions and/or colonizations (weather etc.) One way of implementing: synchronous variation in patch areas Bad year, A i decreased - good year, A i increased Simple modeling alternatives synchronous over the entire metapopulation synchronous within patch clusters, but independent between clusters synchronous for different habitat patch classes Enormous effect on predicted metapopulation extinction probabilities
Connectivity in metapopulation studies Connectivity is a critical component of all spatial models Many different connectivity measures used in literature Almost all connectivity measures can be classified as nearest neighbor measures buffer measures IFM measures Great differences in performance
The view of a patch occupancy model
The view of a nearest neighbor (NN) connectivity measure nearest neighbor population
The view of a buffer measure Consider equally patches within a circle around the focal patch.
The view of an IFM-SPOM connectivity measure Consider all source populations Source population size has an effect Scale effect by distance Population dynamical connectivity: only consider occupied patches
The view of an IFM-SPOM population-dynamical connectivity measure original IFM empty focal patch
Comparing connectivity measures summary of results NN measures very, very bad Best performance of buffer and IFM measures approximately equal But buffer measures sensitive to estimation of buffer radius Inclusion of focal patch size always improved results