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- 1. Assumptions of metapopulations
- 2. Outline <ul><li>Basic metapopulation assumptions </li></ul><ul><li>Factors that affects local population dynamics </li></ul><ul><li>Model assumptions </li></ul><ul><ul><ul><li>advantages and disadvantages </li></ul></ul></ul>
- 3. Basic Metapopulation Assumptions <ul><li>Space is discrete, and it is possible to distinguish between the matrix and habitat patches </li></ul><ul><li>Habitat patch units are large and permanent enough to allow for persistence of local populations for at least a few generations </li></ul>
- 4. More basic assumptions <ul><li>Habitat patches are of equal size and are equally isolated </li></ul><ul><li>Migration has no real effect on dynamics </li></ul><ul><ul><ul><li>2 ways to think of migration </li></ul></ul></ul>
- 5. Density Dependence <ul><li>Per capita growth rate depends on past and/or present population densities </li></ul><ul><ul><ul><li>not all populations are strongly affected all the time </li></ul></ul></ul>Morris and Doak, 2002
- 6. Extinction <ul><li>Risk of extinction increases with decreasing population size </li></ul><ul><ul><ul><li>Allee Effect-Reduced per capita growth rate at low population density </li></ul></ul></ul><ul><ul><ul><li>Habitat fragmentation- reduces patch area </li></ul></ul></ul><ul><ul><ul><ul><li>can be easily modeled </li></ul></ul></ul></ul>
- 7. Migration <ul><li>Need a sufficiently high rate of migration for metapopulations to persist as a result of recolonizations </li></ul><ul><li>If migration rate is too high, may accelerate metapopulation extinction </li></ul><ul><li>Rescue Effect/Propagule Rain </li></ul>
- 8. Colonization <ul><li>Habitat Fragmentation- reduces level of patch connectivity </li></ul><ul><ul><ul><li>can be easily modeled </li></ul></ul></ul>
- 9. Spatially Implicit (Levins) Model <ul><ul><ul><ul><ul><li>Assume: </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><li>infinite, discrete habitat patches with no variation </li></ul></ul></ul></ul><ul><ul><ul><ul><li>stochastic, asynchronous local dynamics </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>local dynamics be ignored </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><li>all patches are equally connected via migration </li></ul></ul></ul></ul><ul><ul><ul><ul><li>patches are empty or occupied </li></ul></ul></ul></ul>Hanski and Gilpin 1997
- 10. Levins Model <ul><li>dP/dt= cP(1-P)-eP </li></ul><ul><li>Equilibrium when P hat = 1-e/c </li></ul><ul><li>Highlights that recolonization must occur at at a high enough rate to compensate for extinctions </li></ul>
- 11. Advantages and Disadvantages of the basic Levins model <ul><li>+ Easy mathematically and conceptually </li></ul><ul><li>- 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) </li></ul>
- 12. Spatially Explicit Models <ul><ul><li>Assume: </li></ul></ul><ul><ul><ul><li>many patches (arranged as cells in a lattice) </li></ul></ul></ul><ul><ul><ul><li>patches may be occupied or empty </li></ul></ul></ul><ul><ul><ul><li>no variation in patch size and quality </li></ul></ul></ul><ul><ul><ul><li>migration is distance dependent </li></ul></ul></ul>Hanski, 1999 Fig. 5.3A
- 13. Spatially Explicit Model <ul><li>Probability that a cell will become occupied = γ(y-x) </li></ul><ul><li>Where gamma is the rate of emigration and y-x is the distance between x and y </li></ul>
- 14. Advantages and Disadvantages <ul><li>+ Local behavior is same from patch to patch, so dynamics can be easily modeled. </li></ul><ul><li>- Can not simply describe the state of the metapopulation by the fraction of patches occupied (need to use a vector- much more complicated) </li></ul>
- 15. Spatially Realistic Model <ul><li>finite number of relatively small patches in comparison with the total landscape </li></ul><ul><li>randomly scattered patches </li></ul><ul><li>assume real patch attributes (area, location, etc) </li></ul><ul><li>patch area and isolation affect extinction and recolonization </li></ul><ul><ul><ul><li>occupied patches inflict colonization pressure on all empty patches </li></ul></ul></ul><ul><ul><ul><ul><ul><li>declines with distance </li></ul></ul></ul></ul></ul>Hanski, 1999 Fig. 5.3
- 16. Spatially Realistic Model <ul><li>d p i /dt= C i ( t)[1-p i ]- e i p i </li></ul><ul><li>(d p i /dt= rate of change in patch i ) </li></ul><ul><li>pi= probability that patch i is occupied </li></ul><ul><li>C i (t)= colonization rate in patch i, taking connectivity between all patches into account </li></ul><ul><li>ei= extinction rate in patch i , which is a function of the area of patch i </li></ul>
- 17. Advantages and Disadvantages <ul><li>+ More realistic; can make quantitative predictions about dynamics </li></ul><ul><li>- More complicated; A lot of data has to be assumed; Starts to move away from the metapopulation concept </li></ul>
- 18. Works cited <ul><li>Driscoll, D. 2007. How to find a metapopulation. Can. J. Zool., 85 : 1031-1048. </li></ul><ul><li>Hanski, I. 1999. Metapopulation ecology. New York: Oxford University Press. </li></ul><ul><li>Hanski, I and Gaggiotti, O (Eds.). 2004. Ecology, genetics, and evolution of metapopulations. New York: Elsevier Academic Press. </li></ul><ul><li>Hanski, I and Gilpin, M (Eds.). 1997. Metapopulation biology: Ecology, genetics, and evolution . New York: Academic Press. </li></ul><ul><li>Hanski, I and Gilpin, M, 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society, 42 : 3-16. </li></ul><ul><li>Morris, W and Doak, D. 2002. Quantitative Conservation Biology . Sunderland: Sinauer Associates, Inc. </li></ul><ul><li>Nie, L and Mei, D. 2007. Fluctuation-enhanced stability of a metapopulation. Physics Letters A, 371 : 111-117. </li></ul>

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