1. Another Paradigm Shift (Hanski and Simberloff 1997)

4. Rescue Effect

5. Bighorn sheep

6. Key Processes Extinction Colonization Turnover
usually a constant risk multiplied times number of occupied patches
Colonization
dependent on number of occupied (sources of colonists) and empty (targets) patches
Turnover
Extinction of local populations and establishement of new local populations in empty habitat patches by migrants from existing local populations
Note focus on populations not species (in contrast to island biogeography)

7. Types of Metapopulations
Levins metapopulation: “classical metapopulation”
large network similar small patches
local dynamics faster time scale than metapopulation dynamics
Mainland-island metapopulation: “Boorman-Levitt metapopulation”
System of habitat patches within dispersal distance from very large habitat patch where the local population never goes extinct

8. More Types of Metapopulations
Source-sink metapopulation
System where at low density there are subpopulations with negative growth rates (in absence of dispersal) and positive growth rates
Nonequilibrium metapopulation
System in which long-term extinction rates exceed colonization or vice-versa; an extreme case is where isolation among subpopulations is so great that dispersal (and hence recolonization) is precluded

9. M-I
Levins
patchy
nonequilibrium
(Harrison and Taylor 1997)

10. Scale Matters
Dispersal abilities of animals determine metapopulation boundaries
and point out key connections in the landscape
Chetkiewicz et al. 2006

11. Another Population Model
Source-sink Dynamics: grouping of multiple subpopulations, some are sinks & some are sources
Source Population = births > deaths = net exporter
Sink Population = births < deaths

12. <1
>1

14. Metapopulation Model Levins
p = habitat patch (subpopulation)
m = rate of local colonization
e = rate of local extinction

15. Metapopulation Model (Look familiar?)

16. Metapopulation Model Levins
p = fraction of occupied habitat patches (subpopulations)
m = rate of local colonization
e = rate of local extinction
p* = equilibrium fraction of occupied patches

17. Key Predictions Metapopulation persists if e/m<1
P increases with increasing patch area
Due to decreasing extinction
P increases with decreasing distance among patches
Due to increasing colonization

18. Metapopulations
Let’s define extinction and colonization mathematically
Extinction pe thus persistence is 1-pe
Colonization is pi with vacancy is 1-pi
We can consider the fate of a single patch over time or the entire metapopulation over time

19. Local Persistence For a single patch: pe = Pr(local extinction)
if = 0 persistence is certain
if = 1 extinction is certain
P1 = 1-pe Pr(local persistence for 1 year)
P2 = (1-pe)*(1-pe) = (1-pe)2
PT = (1-pe)T Pr(local persistence for T years)

20. Regional Persistence In an N patch system:
PN = 1-peN Pr(at least 1 patch persists)

21. Regional Persistence

22. Metapopulations
For a given patch, the likelihood of persistence for n years is simply
pn = (1 – pe)n
E.g. if a patch has a probability of persistence = 0.8 in a given year, the probability for 3 years = 0.83 = 0.512
If we had 100 patches, approximately 52 would persist and 48 would go extinct

23. Metapopulations
To consider the fate of the entire metapopulation (i.e. the probability of extinction of the entire population)
If all patches have the same probability of extinction, it is simply pex
For example, if pe=0.5 across 6 patches then Px = 1-(pe)x or 0.56 = or 1.5%

24. Adding Stochasticity Tm = expected time to metapopulation extinction
TL = expected time to local extinction
P = fraction of occupied patches at a stochastic steady state
H = # suitable habitat patches
Assuming Tm>100TL as a criteria for long-term persistence
(Nisbet and Gurney 1982, Hanski 1997)

25. Population Persistence in Butterfly Metapopulations