Galapagos Islands

Galapagos Islands

Metapopulation Models • Species area curves (islands as case study) • Review of Island Biogeography • Extension to subpopulations  Metapopulation • Classic (Levins) • Island-mainland (Gotelli) • Core-satellite (Hanski) • Habitat loss (Lande/Karieva) • More spatially realistic • Incidence Function models • Matrix metapopulation models • (Ozgul et al. 2008 Am. Nat.)

Galapagos Islands

Island species richness # species Island area • Bigger islands have more species than small islands • “Species-Area curves” • Documented for diverse taxa • Other types of habitat also follow this pattern.....island-like (mtn. tops, forest remnants, lakes, etc.)

Species richness increases with island AREA Log scale Rich Glor Log scale MacArthur and Wilson (1967)

Galapagos land plants S = c · Az c is constant of spp./ area z is the slope z = 0.32 (~0.3 for most islands)

An extension of this idea:Island biogeography • Dynamic equilibrium theory that explains species richness of islands • Island richness determined by colonization and extinction rates (number of species thru time) • Richness increases with size (more habiats to support more species, less extinction).... decreases with isolation (less likely to be colonized)

Species richness decreases with isolation More isolated islands less likely to receive colonists (immigration low)

small Extinction more likely for small populations (small islands) MAINLAND large near Colonization more likely for closer islands far

Island biogeography MacArthur and Wilson 1967

Experimental test of island biogeography • Defaunation experiment by Simberloff and Wilson (1969 Ecology) • Methods: • Survey small mangrove islands for arthropods. • Cover islands with plastic and spray with insecticide (gets rid of all arthropods) • Observe colonization/ succession over one year. • How many and what species return?

Simberloff and Wilson’s experiment Florida Keys

Results • Species richness on islands returned to levels similar to before defaunation • Closer, larger islands had more species • The precise species identity was not consistent, only the total number of species • Order of colonization and species interactions important for “who” composes the community

And now for a big mental leap...from diversity to individual population dynamics Metapopulations • Collection of subpopulations • Proportion of sites “occupied” determined by colonization and extinction rates at each site • Connected by individual movement (dispersal between sites provides colonists) • Individual sites may be colonized in one year and extinct the next • Individual site dynamics are variable, but overall “metapopulation” can be stable Rana cascadae

Levins (1969) introduced the concept of metapopulations to describe the dynamics of this patchiness, as a population of fragmented subpopulations occupying spatially separate habitat patches in a fragmented landscape of unsuitable habitat Metapopulation structure Shaded areas provide an excess of individuals which emigrate to and colonize sink habitats (open). • A system of populations that is linked by occasional dispersal (Levins 1969). Levins, R. 1969. Bull. Ent. Soc. Am. 15:237-240.

Metapopulation dynamics

Islands? And here… Anthropogenic subpopulations

Classic metapopulation • Deterministic, but based on stochastic events—extn, colonization • Subpopulations have independent dynamics and are connected by dispersal • All patches of identical quality

Classic metapopulation General model: dp/dt = C – E p = proportion of sites occupied C = total colonization rate E = total extinction rate

Classic metapopulation Levins model (insect pests in fields) dp/dt = cip (1 –p) - ep p = proportion of sites occupied ci = rate of propagule production (internal) e = local extinction rate (constant) Available for colonization Total colonization rate Total extinction rate

Classic metapopulation Finding the equilibrium: 0 = dp/dt = cip (1 –p) – ep 0 = cip – cip2 – ep Solve for p p* = 1- e/ci Lesson: p* > 0 when ci > e p* = 1 only when e = 0

‘Propagule rain’ metapopulation Gotelli’s model (also called Island-mainland) dp/dt = ce (1 –p) - ep p = proportion of sites occupied ce = rate of propagule rain (external—doesn’t depend on p) e = local extinction rate (constant—mediated only by p)

‘Propagule rain’ metapopulation Finding the equilibrium: 0 = dp/dt = ce (1 –p) – ep 0 = ce – cep– ep Solve for p p* = ce /(ce + e)

Habitat loss models Karieva & Wennegren’s model dp/dt = ci p (1 - D - p) - ep D = fraction of total habitat destroyed (D=0 is Levins) p = proportion of sites occupied ci = rate of propagule production (internal—does depend on p) e = local extinction rate (constant—mediated only by p) X

Habitat loss models Karieva & Wennegren’s model Finding the equilibrium: 0 = dp/dt = ci p (1 - D - p) – ep Solve for p p* = 1- e/ci– D Simple direct effect of D on metapopulation dynamics X

Assumptions of classic models: • Identical patch ‘quality’ • Extinctions occur independently, local dynamics are asynchronous • Colonization spreads across patch network and all equally likely • All patches equally connected to all other patches (not spatially explicit) • No population counts or size. Only suitable vs. unsuitable, occupied or unoccupied

Classic metapopulations • Unoccupied patches common and necessary for metapopulation persistence • Local dynamics asynchronous • Subpopulations connected by high colonization  single population (synchronized dynamics) • Matrix between sites is homogeneous • Parallel to logistic model of pop growth (filling available ‘space’ up to K)

Persistence of some local populations (sinks) depends on some migration from nearby populations (sources). • Empty patches susceptible to colonization. sink source Hanski (1998) proposed 4 conditions before assuming that metapopulation dynamics explain spp. persistence Hanski, I. 1998. Nature 396:41−49.

Patches should be discrete habitat areas of equal quality i.e. homogeneous. • 2) No single population is large enough to ensure long-term survival. • 3) Patches must be isolated but not to the extent of preventing re-colonization from adjacent patches. • 4) Local population dynamics must be sufficiently asynchronous that simultaneous extinction of all local populations is unlikely. • Without 2 & 3: we have a ‘mainland-island’ metapopulation i.e. persistence depends on supply from source population, some fragments may rarely receive or supply migrants

Core-satellite metapopulation • Observation that high rates of colonization can ‘rescue’ pops nearing extinction • RESCUE EFFECT • Satellites persist because they are resupplied with individuals from occupied sites • Effectively differences in patch quality

Core-satellite metapopulation Total extinction declines as p ~ 1, propagules likely to land at all sites Hanski’s model dp/dt = cip (1 - p) - ep (1-p) p = proportion of sites occupied ci = rate of propagule production (internal—does depend on p) e = local extinction rate (constant) Total extinction rate

Core-satellite metapopulation Hanski’s model dp/dt = cip (1 - p) - ep (1-p) Finding the equilibrium: dp/dt = (ci – e) p(1 - p) Notice: If ci > e , sign is positive ( λ > 1), p  1 (stable) If e > ci, sign is negative ( λ < 1), p  0 (extinct) If e = ci , λ = 1 (neutral equilibrium)

Classic metapopulations

Adding area and isolation Hanski (1991) Hanski and Ovaskanen (2003)

Incidence Function Models More spatially realistic (uses real data) Incorporate patch size, distance matrix Stochastic Ei = e/Ax (estimated from field data) e = probability of extinction for a patch of size A (per unit time) A = patch Area x = demographic & environmental stochasticity (if large, E decreases fast with A)

Incidence Function Models Assumes that internal dynamics are ‘fast’ relative to among patch dynamics Populations within patches ‘reach’ carrying capacity almost instantly (Ei, Ci constant) Immigration to patch I proportional to connectance (proportional contribution from all occupied sites) Can evaluate the importance of patch loss on overall stability

Galapagos Islands