Spatial synchrony and extinction risk in metapopulations: a spatial “hydra effect”

1. Spatial synchrony and extinction riskin metapopulations: a spatial “hydra effect” Jeremy Fox University of Calgary dynamicecology.wordpress.com David Vasseur Yale University

2. The “hydra effect”

3. The usual story: intermediate dispersal rates maximize metapopulation persistence Indep. patches (async.) Coloniz.-extinction (async.) “One big patch” (sync.) Big patch persistent Metapopulation persistence time Big patch extinction-prone Zero/low Intermediate High Dispersal rate

4. Intermediate dispersal rates maximize metapopulation persistence Yaari et al. 2012

5. Intermediate dispersal maximizes metapopulation persistence Huffaker 1958 Holyoak and Lawler 1996:

6. Protist microcosms: a model system for spatial synchrony Euplotes patella Tetrahymena pyriformis

7. Cyclic dynamics are easily synchronized (“phase locked”) by dispersal 1500 Prey density (ml-1) 0 0 72 0 72 Day • Dispersal rates <0.5%/prey generation can give synchrony Vasseur & Fox 2009; Fox et al. 2011, unpublished

8. Measles Gypsy moth Lynx Collared lemming Wren Spatial synchrony in nature Blasius et al. 1999, Johnson et al. 2006, Rohani et al. 1999, Paradis et al. 2000, Krebs et al. 2002

9. A puzzle: How are asynchronous colonization-extinction dynamics possible? An answer: A spatial hydra effect Local extinctions are desynchronizing • Anything that reduces synchrony promotes recolonization, and thus persistence • Empirical examples of colonization-extinction dynamics involve extinction-prone subpopulations • Empirical examples of synchrony at low dispersal rates involve persistent subpopulations

10. An illustration of the spatial hydra effect • Nicholson-Bailey host-parasitoid model with demogr. stochas. (Yaari et al. 2012) • 4 patches • Global density-independent dispersal of both spp. after births & deaths • At end of timestep: random subpop. destruction

11. Subpopulation dynamics under low dispersal, no subpop. destruction Host subpopulation abundance Timestep

12. Subpopulation dynamics under intermediate dispersal, no subpop. destruction Host subpopulation abundance Timestep

13. Subpopulation dynamics under high dispersal, no subpop. destruction Host subpopulation abundance Timestep

14. Subpopulation dynamics under high dispersal with random subpopulation destruction Host subpopulation abundance Timestep

15. A spatial hydra effect 90 Subpopulation destruction rate 0 0.025 0.5 0.075 0.1 Metapopulation persistence time (mean) 0 0.0001 0.001 0.01 0.1 1 Dispersal rate (log scale)

16. Conclusions and future directions • Hydras are real Really exists. • Effect can vary in strength, be swamped by other effects • -Matter & Roland 2010 Proc Roy Soc B • Biological details only matter via effects on colonization and extinction rates

17. Weak spatial hydra effect 800 Stochastic Ricker Stochastic logistic map Destruct. rate 0 Mean metapop. persist. time 0.025 0.05 0.075 0.1 0 0 1 0 1 Dispersal rate

18. Low rates of “stepping stone” dispersal phase lock entire metapopulations 1.8 MoranDisp. n n y n n y y y 0.9 Mean prey synchrony ±SE 0 1 2 3 4 5 Spatial lag Fox et al. 2011 Ecol. Lett.

19. Even low dispersal rates can rapidly synchronize cycling populations Fox et al. unpublished