The hare-lynx population cycle as seen through the 'eyes' of the Canadian lynx

1. The hare-lynx population cycle as seen through the 'eyes' of the Canadian lynx A review of more than half a century's research Nils Chr. Stenseth Center for Ecologicaland EvolutionarySynthesis (CEES) Dept. of Biology, Universityof Oslo, Norway n.c.stenseth@bio.uio.no

2. Charles Elton (1924, 1942) started it all ... after which it has become a standard text-book example ...

3. The Lynx species Canadian lynx (Lynx canadensis) Iberian lynx (Lynx pardinus) Eurasian lynx (Lynx lynx) Bobcat (Lynx rufus) Maps and pictures from Big Cats Online (dialspace.dial.pipex.com/agarman/bco)

4. Raven & Johnson 1996: Biology

5. Krebs 2001: Ecology

6. Futuyma 1998: Evolutionary Biology

7. Edelstein-Keshet 1988: Mathematical Models in Biology

8. Dynamics of lynx and its main prey species (at least in North America) has … ... influenced ecology profoundly, not the least in connection with the enigma of the population cycles seen in many northern species ... such as the voles and lemmings ... phenomena which may or may not be similar to the hare-lynx cycle ....

9. The lynx’s food-web … data from south of the Hudson Bay in Canada Stenseth et al., Proc. Natl. Acad. Sci. 1997

10. The snowshoe hare food-web … data from south of the Hudson Bay in Canada Stenseth et al., Proc. Natl. Acad. Sci. 1997

11. The hare and the lynx see their food web slightly differently • The hare sees all its enemies (and doesn’t care who kills it) • The hare also sees all its food species (and doesn’t really care who provides its dinner) • The hare is also somewhat self-regulated • Hence, an order three process. • The lynx gets its dinner from a great variety of prey species – but primarily from the hare • The lynx is also somewhat self-regulated • Hence, an order two process Stenseth et al., Proc. Natl. Acad. Sci. 1997

12. A (general) vegetation-hare-predator model Vegetation: Vt+1= VtFv (Vp, Hp, ev) Hares: Ht+1= HtFh (Vp, Hp, Pp, eh) Predators: Pt+1= PtFp (Hp, Pp, ep) Stenseth et al., Proc. Natl. Acad. Sci. 1997

13. What do the experimental results tell us? ... and do they tell us the same story as the statistical time- series analysis?

14. Evidence for three trophic level effects The experiment by Krebs et al. (Kluane lake 1987-94) Treatment I Treatment II Treatment III Reducing predators AddingfoodReducing predators| and addingfood 2x increaseof hares 2x increaseof hares 10x increaseof hares Snowshoe hare populations: Squeezed from below and above Statisticalmodel ht+1 = a0 + a1 ht + a2 ht-1 + a3 ht -2 + e ... i.e., an order 3 process pt+1 = b0 + b1 pt + b2 pt-1 + e ... i.e., an order 2 process Krebs et al., Science 1995; Stenseth, Science 1995

15. Lynx time series 1920-1994 1820-1940 Stenseth et al., Proc. Natl. Acad. Sci. 1998

16. Fur returns are good proxies for actual abundance Stenseth et al., Proc. Natl. Acad. Sci. 1998

17. Predator-prey model with phase-dependence is equivalent to yt = (ai,0bi,2 + ai,1bi,0) + (2 - ai,1 - bi,1)yt-1 + (ai,1 + bi,1 - ai,1bi,1 - ai,2bi,2 - 1)yt-2 + et non-linear Phase dependency: threshold model Lower Upper b2,2 yt-2 b1,2 yt-2 yt-2 yt-2 Hares: Ht+1= Htexp[ai,0 - ai,1xt - ai,2yt] Predators: Pt+1= Ptexp[bi,0 - bi,1yt - bi,2xt] Stenseth et al., Proc. Natl. Acad. Sci. 1998

18. Phase-dependence Rochester, Alberta Kluane Lake, Yukon Functional response Phase dependency Stenseth et al., Proc. Natl. Acad. Sci. 1998

19. The non-linearity is due to phase-dependent relations between the hare and the lynx Functional response This phase-dependency may furthermore be due to fluctuating weather conditions … indeed, snow-condition enters as a significant covariate producing a similar functional response

20. … the snow condition may be a key factor in structuring the dynamic interaction between the hare and the lynx Source: Rudolfo's Usenet Animal Pictures Gallery

21. .. but most likely more than only the snow condition … ... We need a package of weather variables... ... the North Atlantic Oscillation may be such a package ... Stenseth et al. (2003) Studying climate effects on ecology through the use of climate indices: the North Atlantic Oscillation, El Niño Southern Oscillation and beyond. Proc. R. Soc. Lond. B (in press)

22. … but the NAO didn’t come as a result of my first “pet story” ….

23. Let us ask the lynx (or the data on the lynx)...

24. Ecological or climatic zonation? N. C. Stenseth et al., Science 1999

25. Canada divided by climatic regions Stenseth et al., Science 1999

26. Stepping back a bit ... CLIMATE VARIABILITY The asymmetric interaction between ecology and climate

27. Climaticzonation

28. Genetics of lynx That is: (1) thePacific region is geneticallydifferent from theContinental region, and (2) theContinental region is different from theAtlantic region Rueness et al., Nature (in press)

29. Remember:Snow condition affects the success of hare and lynx That genetic differentiation between the Pacific region and the Continental region is ”easy”: the Rockies But why the genetic differentiation between the Continental region and the Atlantic region?

30. Regional synchronicity Stenseth et al., (unpublished)

31. Synchrony 1897-1934 Correlation between a pair of time-series Phase-synchrony between a pair of time-series Stenseth et al., (unpublished)

32. Synchrony 1920-1994 Correlation between a pair of time-series Phase-synchrony between a pair of time-series Stenseth et al., (unpublished)

33. The statistically derived time-series models have beenused to generate synthetic data yr,t = br,0+ br,1yr,t-1+ br,2yr,t-2+ jrft+ yr+er,tyr,t-2 qr - - - - - br,0+ br,1yr,t-1+ br,2yr,t-2+ jrft+ yr+er,tyr,t-2 qr + + + + + yr,t = log-abundance in region r in year t ft = external forcing. ft = sin(2pwt) er,t = independent (in time as well as in space) N(0,1) noise Stenseth et al., (unpublished)

34. The models used to generate synthetic data yr,t = Parameter values used in each of the three regions: br,0+ br,1yr,t-1+ br,2yr,t-2+ jrft+ yr+er,tyr,t-2 qr - - - - - br,0+ br,1yr,t-1+ br,2yr,t-2+ jrft+ yr+er,tyr,t-2 qr + + + + + Stenseth et al., (unpublished)

35. Synchrony in synthetic data Observed1897-1934 Observed 1920-1994 0.67 0 0 1.60 0 0.73 0.25 -1.11 0 -1.20 0.89 0.87 0 0.68 -0.09 0.43 0.59 0 0.87 0.91 Phase-synchrony between a pair of time-series Correlation between a pair of time-series Stenseth et al., (unpublished)

36. Are the genetics structured similar to the ecology? ... we obtained samples … Rueness et al., Nature (in press)

37. The sampling scheme We aimed at as good coverage of the entire Canada as possible ... Rueness et al., Nature (in press)

38. The ecology and genetics of lynx Can the observed genetic spatial structuring be seen as a result of the underlying ecological dynamics which itself is determined by climatic differences? Stenseth et al., (unpublished) Rueness et al., Nature (in press)

39. Genetics of lynx density - years 100 105 110 115 120 0 1 2 3 4 e tc . .. emigration Relative difference in Fst Maximum proportion of offspring Phase –dependence of emigration Stenseth et al., (unpubl.)

40. Genetics of lynx The same result was predicted by the model reported by M. Doebeli and Dieckmann, Nature 421, 259 (2003) Our lynx studies demonstrate that the genetic differentiation hinges on the peculiar life history of the lynx (dispersing during the decrease phase when the mortality is high).

41. Genetics of mink and muskrat Lynx Mink Muskrat Pictures/maps from:www.washington.edu/burkemuseum/ Ifthepeculiaritiesofthelynxlifehistory is important, similargeneticdifferentiationsouthoftheHudson Bay is not expected for mink and muskrat …having a similarecologicalstructuring as thelynx (Yaoet al., 2000. PRSB.)

42. Conclusions • the lynx sees the world slightly differently than the hare: • The hare sees the world 3-dimentionally; • The lynx sees it 2-dimentionally • the lynx is governed by a non-linearity in the second lag • that is in its relations to the hare • the ecology is profoundly influenced by the climate (possibly through the snow conditions) • the genetics (and evolution) seems also to be influenced by climate • the lynx is indeed the model organism ecology and evolution can benefit – and indeed do benefit – from

43. Seeing the hare-lynx dynamics through the eyes of the lynx, suggest that the pattern of climate fluctuations sets the stage both regarding ecological structuring and genetic structuring. The pattern of climate fluctuations also creates an almost cryptic environmental gradient leading to genetic separation (a process being of key importance in the splitting of one species into two).

44. Brno Working on the dynamics of the Canadian lynx has led me into stimulating collaborative work with Ecologists: • Charles Krebs, Wilhelm Falck, • Ottar Bjørnstad, Mark O’Donoghue, • Stan Boutin, Rudy Boonstra, • Nigel Yoccoz and Eric Post, Statisticians: • Kung-Sik Chan, Howell Tong and • Ole Chr. Lingjærde, and Geneticists - Kjetill Jakobsen, Hans Ellegren and Eli Rueness. These curiosity-driven studies of mine and my colleagues have been generously funded by Norwegian Science Council and the University of Oslo and others ..... I'm sure we have learnt something new - insight which also might be of some immediate use, e.g., in our effort to understand the climate-ecology interactions.