1. Wolf populations in North America

2. Black bear distribution:

3. Scouler’s willow distribution:

4. A landscapes mosaic:

5. Only some pieces of the mosaic are suitable for a given species:

6. The populations in the landscape mosaic are not totally isolated, But only weakly connected by migrating individuals:

7. A population: a group of individuals of the same species that live and breed in the same space. A metapopulation:a group of several local populations connected by the occasional movement of individuals between populations (immigration and emigration). A deme:a population that is part of a metapopulation. Metapopulation Dynamics:The dynamics of patch occupancy. Local extinction:a deme goes extinct. Colonization:an empty but suitable habitat is repopulated by emigrants. Definitions

8. How long can a deme persist without immigration? Example: probability of local extinction is 1 in 6: p e = 1/6 = 0.1667 Probability of persisting the first year is 5 in 6: P(t=1) = 1-1/6 = 0.8333

9. Probability of persisting two consecutive years: P(t=2) = (1-1/6)*(1-1/6) = 0.6944 Probability of persisting n consecutive years: P(t=n) = (1-1/6) n How long can a deme persist without immigration?

10. Without immigration, all demes eventually go extinct, and sooner, the higher the annual extinction probability. time (years) pepe 0.2 0.5 0.8 0.9 How long can a deme persist without immigration?

11. The more demes the smaller the chance of regional extinction: (1/6) 4 = 0.00077 Probability of simultaneous extinction in 4 patches: P 4 = 1-(1/6) 4 Probability of persistence over 4 patches: P m = 1-(p e ) m Probability of persistence over m patches:

12. Time (years) Without immigration, metapopulations can go also extinct, but it takes a lot longer. Many demes lower the risk of regional extinction. Regional extinction is a lot less likely than local extinction. p e (probability of local extinction)

13. An example of a metapopulation: The endangered bay checkerspot butterfly: It’s host plant: Plantago erecta (caterpillar food)

14. Serpentine grasslands in Northern California

15. The distribution of serpentine grassland in Santa Clara County (Harrison et al. 1988) A severe drought in 1975- 1977 caused several local extinctions. Some empty patches were recolonized in 1986.

16. The Island-Mainland model: The probability of immigration is constant. mainland islands Island-mainland model: a constant “propagule rain” originating on the mainland.

17. How do we characterize the dynamics of metapopulations? 1) We only ask whether patches are occupied or not: 16 patches 4 occupied 12 empty 2) The state variable we follow is the fraction of occupied patches f. f = 4/16 = 0.25

18. The relevant rates in metapopulation dynamics: Probability of local extinction p e the probability that in a given amount of time a local population will go extinct. Probability of local colonization p i : the probability that in a given amount of time, a site will be colonized. pepe pipi

19. The rate of occupancy loss: The rate of re-colonization: The rate of change in f:

20. Fraction of occupied sites f Extinction or Immigration rate pepe Island-Mainland Model: If p i > 0 there is always a positive equilibrium: metapopulations always persist.

21. The Internal Colonization model: The probability of immigration depends on the patches occupied: islands The immigration probability is proportional to the occupied patches:

22. Internal colonization model: Metapopulations may not persist. Positive equilibrium only if p e < i.

23. Excel Worksheets: Metapopulation dynamics

24. Summary: Metapopulations are collection of populations (demes) linked by immigration. Typically, not all patches of a metapopulation are occupied. Average occupancy depends on extinction risks (p e ) and immigration probabilities (p i ). The mainland-island model assumes that p i is constant. Metapopulations cannot go regionally extinct and there always is an equilibrium with non-zero patch occupancy. The internal colonization model assumes that p i =i f. Metapopulations can go regionally extinct if p e > i. Both models assume: All sites are exactly the same. Extinction and colonization probabilities do not change over time. Local extinctions and colonizations are independent events. The spatial arrangement of the sites does not matter. Many patches (ignoring chance fluctuations in patch occupancy).