This document outlines the basic assumptions of metapopulation models and compares different types of metapopulation models. It discusses how metapopulation models assume space is discrete with habitat patches that are large enough for local populations to persist for generations. Basic models also assume equal patch size and isolation with migration not affecting dynamics. More complex spatially explicit and realistic models incorporate factors like patch quality and distance between patches.

1. Assumptions of metapopulations

2. Outline Basic metapopulation assumptions Factors that affects local population dynamics Model assumptions advantages and disadvantages

3. Basic Metapopulation Assumptions Space is discrete, and it is possible to distinguish between the matrix and habitat patches Habitat patch units are large and permanent enough to allow for persistence of local populations for at least a few generations

4. More basic assumptions Habitat patches are of equal size and are equally isolated Migration has no real effect on dynamics 2 ways to think of migration

5. Density Dependence Per capita growth rate depends on past and/or present population densities not all populations are strongly affected all the time Morris and Doak, 2002

6. Extinction Risk of extinction increases with decreasing population size Allee Effect-Reduced per capita growth rate at low population density Habitat fragmentation- reduces patch area can be easily modeled

7. Migration Need a sufficiently high rate of migration for metapopulations to persist as a result of recolonizations If migration rate is too high, may accelerate metapopulation extinction Rescue Effect/Propagule Rain

8. Colonization Habitat Fragmentation- reduces level of patch connectivity can be easily modeled

9. Spatially Implicit (Levins) Model Assume: infinite, discrete habitat patches with no variation stochastic, asynchronous local dynamics local dynamics be ignored all patches are equally connected via migration patches are empty or occupied Hanski and Gilpin 1997

10. Levins Model dP/dt= cP(1-P)-eP Equilibrium when P hat = 1-e/c Highlights that recolonization must occur at at a high enough rate to compensate for extinctions

11. Advantages and Disadvantages of the basic Levins model + Easy mathematically and conceptually - Can only answer a limited number of questions because it ignores so many variables (generally can only be used for metapopulations close to a steady state)

12. Spatially Explicit Models Assume: many patches (arranged as cells in a lattice) patches may be occupied or empty no variation in patch size and quality migration is distance dependent Hanski, 1999 Fig. 5.3A

13. Spatially Explicit Model Probability that a cell will become occupied = γ(y-x) Where gamma is the rate of emigration and y-x is the distance between x and y

14. Advantages and Disadvantages + Local behavior is same from patch to patch, so dynamics can be easily modeled. - Can not simply describe the state of the metapopulation by the fraction of patches occupied (need to use a vector- much more complicated)

15. Spatially Realistic Model finite number of relatively small patches in comparison with the total landscape randomly scattered patches assume real patch attributes (area, location, etc) patch area and isolation affect extinction and recolonization occupied patches inflict colonization pressure on all empty patches declines with distance Hanski, 1999 Fig. 5.3

16. Spatially Realistic Model d p i /dt= C i ( t)[1-p i ]- e i p i (d p i /dt= rate of change in patch i ) pi= probability that patch i is occupied C i (t)= colonization rate in patch i, taking connectivity between all patches into account ei= extinction rate in patch i , which is a function of the area of patch i

17. Advantages and Disadvantages + More realistic; can make quantitative predictions about dynamics - More complicated; A lot of data has to be assumed; Starts to move away from the metapopulation concept

18. Works cited Driscoll, D. 2007. How to find a metapopulation. Can. J. Zool., 85 : 1031-1048. Hanski, I. 1999. Metapopulation ecology. New York: Oxford University Press. Hanski, I and Gaggiotti, O (Eds.). 2004. Ecology, genetics, and evolution of metapopulations. New York: Elsevier Academic Press. Hanski, I and Gilpin, M (Eds.). 1997. Metapopulation biology: Ecology, genetics, and evolution . New York: Academic Press. Hanski, I and Gilpin, M, 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society, 42 : 3-16. Morris, W and Doak, D. 2002. Quantitative Conservation Biology . Sunderland: Sinauer Associates, Inc. Nie, L and Mei, D. 2007. Fluctuation-enhanced stability of a metapopulation. Physics Letters A, 371 : 111-117.