Spatial synchrony of population fluctuations: causes and consequences

1. Spatial synchrony of population fluctuations: causes and consequences Jeremy Fox University of Calgary Website: homepages.ucalgary.ca/~jefox/Home.htm Blog: dynamicecology.wordpress.com Collaborator: David Vasseur, Yale University With thanks to: Tara Janes, Jessica Scharein, Joyce MacNeil, Stephen Hausch, Jodie Roberts, Geoff Legault

2. "An odd kind of sympathy": Huygens' clocks

3. Synchrony

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

5. Causes of spatial synchrony • Dispersal • Spatially-synchronous environmental fluctuations (Moran effect) • Interspecific interactions

6. Patch 2 Patch 1 P2 P1 Dispersal Envi. flucts. Envi. flucts. N2 N1 Demogr. stochas. Growth Mortality Predation Dispersal Stochastic predator-prey model

7. Model predictions for prey synchrony • Dispersal is synchronizing • Moran effect is synchronizing • Predation increases the synchronizing effect of dispersal Vasseur & Fox 2009 Nature

8. Sync. envi., no dispersal Sync. envi., + dispersal Patch 1 Patch 2 Model prey density Time (arbitrary units) Predator-prey oscillations are synchronized (‘phase locked’) by dispersal • No predatorsno cycleslittle effect of dispersal

9. Summary of model predictions • Dispersal is synchronizing • Moran effect is synchronizing • Predators that generate oscillations greatly increase the synchronizing effect of dispersal -Statistical signature of phase locking

10. Protist microcosm experiment • 2x2x2 factorial design crossing pres./abs. of dispersal, Moran effect, predator • Microcosms: 80 ml, semi-continuous cultures • Prey: Tetrahymena pyriformis • Predator: Euplotes patella • Experimental units: pairs of bottles • Dispersal of 10% of individuals, 3x/week • Daily temperature fluctuations (independent or perfectly synchronous) • Small samples taken on weekdays • 6 replicate bottle pairs/ttmt. combination

11. Conducting dispersal events

12. 1200 30 Temp. (°C) Eupl./ml Tet./ml 20 600 10 0 0 0 9 18 27 36 45 54 63 Illustrative population dynamics 104 30 Tet./ml (log scale) Temp. (°C) 103 20 102 0 9 18 27 36 45 54 63 Day Day

13. Experimental results vs. model predictions Vasseur & Fox 2009 Nature

14. Phase-locked oscillations 700 Patch 1 Patch 2 Tetrahymena/ml 0 0 63 Day

15. Prey densities did not track temperature fluctuations 104 30 Tet./ml (log scale) Temp. (°C) 103 20 102 0 9 18 27 36 45 54 63 Day

16. Lynx Dispersal Moran effect Species interactions Population dynamics (cyclic vs. not) Summary so far Synchrony

17. Phase drift at low dispersal rates: data Prey density (ml-1) Day Fox et al. in press Plos One

18. Phase drift at low dispersal rates: model Fox et al. in press Plos One

19. Scaling up

20. Synchrony usually decays with distance Synchrony Distance between populations • Links between pattern of decay and underlying mechs.? Ranta et al. 1995

21. Questions • Why does synchrony decay with distance? • Decay of environmental synchrony • Limited dispersal distance • Phase locking across long distances?

22. Exptl. units: 1 2 3 4 5 6 Methods • Predators + prey • 2 x 2 factorial design (y/n Moran effect, y/n dispersal) • Stepping-stone dispersal • Moran effect with spatially-decaying synchrony

23. Illustrative prey dynamics +M +D +M -D -M +D -M -D Log(Tetra./ml + 1) Time

24. + dispersal - dispersal • Dispersal increases sync. • Spat. decay of sync. in +Moran ttmts. • Higher sync. at even lags (init. conds.) • High mean sync. (init. conds.) Prey synchrony 1.8 MoranDisp. n n y n n y y y 0.9 Mean prey synchrony ±SE • No Moran x disp. interaction • Same effect at all lags (phase locking) • Moran eff. increases short-distance sync. 0 1 2 3 4 5 Spatial lag Fox et al. 2011 Ecol. Lett.

25. Take-home points • Dispersal generates long-distance phase locking • Distance-decay of synchrony due to Moran effect • Same likely true in many natural systems • Short-distance dispersal either phase-locks cycles, or produces little synchrony at all

26. Summary: Spatial predator-prey cycles work like this:

27. Consequences of synchrony for metapopulation persistence: the spatial “hydra effect”

28. The “hydra effect”

29. 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

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

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

32. 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

33. 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

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

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

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

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

38. 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)

39. Hydra effect summary • 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 • -local extinctions affect coloniz. rate via effect on synchrony

40. Future directions • Interplay of determinism and stochasticity • Embedding of Euplotes-Tet. cycle in larger food webs • Environmental heterogeneity • Larger spatial arrays? • Hydra effect under different forms of envi. stochasticity • Comparisons with nature • -changes in synchrony as cycles collapse?

41. 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

42. Prey synchrony vs. dispersal rate Even low dispersal rates can rapidly synchronize cycling populations Fox et al. unpublished Fox et al. in press Plos One

43. 1 2 3 4 5 6 r(1,2) r(3,6) Data analysis 1. Calculate prey synchrony (cross-correl. of log abundance) for every pair of jars in an array -predator abundances too noisy to analyze 2. Calculate mean sync. at every spatial lag within an array -vector of 5 cross-correl. coeffs. 3. z-transform to normalize 4. MANOVA for treatment effects, follow-up ANOVAs 5. Spatial decay: regress z-transformed cross-correlation on spatial lag, ANOVA on slopes

44. 4 Mean Euplotes/ml 2 Log(Euplotes/ml +1) 0 0 25 50 Day Illustrative predator dynamics Day

45. No dispersal + dispersal No dispersal + dispersal Desync. Sync. Little desync. Direct demonstration of dispersal-generated phase locking “Leading” patches “Trailing” patches

46. Phase drift at the cycle nadir in the absence of dispersal

47. Illustrative examples of prey synchrony 1400 Indep. envi., no disp. Sync. envi., + disp. 1000 Tet./ml Tet./ml No predators 0 0 63 0 Day Day 0 63 1000 700 + predators Tet./ml Tet./ml 0 0 0 63 0 63 Day Day

48. Dispersal × predator interaction not due to prey tracking synchronized predators Indep. envi. Sync. envi. No disp. Pred. disp. Prey disp. Both disp. Model prey synchrony -pred. +pred. -pred. +pred.

49. Dispersal No disp. Predator synchrony Vasseur & Fox 2009 Nature

50. Monte Carlo simulns. Exptl. data Robust qualitative match between model and data Vasseur & Fox 2009 Nature