1. Howell Tong conference The importance of TAR- modeling for understanding the structure of ecological dynamics: the hare-lynx population cycle as an example Nils Chr. Stenseth and others Howell Tong Conference Nils Chr. Stenseth Centre of Ecological and Evolutionary Synthesis (CEES) Institute of Biology, University of Oslo, Norway

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

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

4. Howell Tong conference Raven & Johnson 1996: Biology

5. Howell Tong conference Krebs 2001: Ecology

6. Howell Tong conference Futuyma 1998: Evolutionary Biology

7. Howell Tong conference Edelstein-Keshet 1988: Mathematical Models in Biology

8. Howell Tong conference … and, of course, Howell Tong’s time series book at OUP …

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

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

11. Howell Tong conference What do the experimental data tell us?... and what do observational (time-series) data tell us? … and do they tell the same story?

12. Howell Tong conference The experiment by Krebs et al. (Kluane lake 1987-94) Treatment ITreatment IITreatment III Reducing predatorsAdding foodReducing predators and adding food 2x increase of hares2x increase of hares10x increase of hares Evidence for three trophic level effects Snowshoe hare populations: Squeezed from below and above Statistical model h t+1 =  0 +  1 h t +  2 h t-1 +  3 h t -2 + ... i.e., an order 3 process Krebs et al., Science 1995; Stenseth, Science 1995 p t+1 =  0 +  1 p t +  2 p t-1 + ... i.e., an order 2 process

13. Howell Tong conference As the lynx sees its food web … … data from south of the Hudson Bay in Canada. Stenseth et al., Proc. Natl. Acad. Sci. 1997

14. Howell Tong conference … and as the snowshoe hare sees its food-web … data from south of the Hudson Bay in Canada. Stenseth et al., Proc. Natl. Acad. Sci. 1997 Predators Food species

15. Howell Tong conference That is, the hare and the lynx see their food web slightly differently Stenseth et al., Proc. Natl. Acad. Sci. 1997 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

16. Howell Tong conference Robert May – Lord May of Oxford – has worked on the same topic: May, R.M. 1973. Time-delays versus stability in population dynamics with two and three trophic levels. Ecology 54 : 315-325. Bob May says (in an e-mail to me on July 6, 2004): “Send him my very best wishes for the success of the meeting, and my most sincere apologies for not being able to be there with you”

17. Howell Tong conference Lynx time series Stenseth et al., Proc. Natl. Acad. Sci. 1998 1820-1940 1920-1994

18. Howell Tong conference Fur returns are good proxies for actual abundance Stenseth et al., Proc. Natl. Acad. Sci. 1998

19. Howell Tong conference Predator-prey model with phase-dependence Hares:H t+1 = H t exp[a i,0 - a i,1 x t - a i,2 y t ] Predators:P t+1 = P t exp[b i,0 - b i,1 y t - b i,2 x t ] y t = (a i,0 b i,2 + a i,1 b i,0 ) + (2 - a i,1 - b i,1 )y t-1 + (a i,1 + b i,1 - a i,1 b i,1 - a i,2 b i,2 - 1)y t-2 +  t is equivalent to y t-2  2,2 y t-2 y t-2  1,2 y t-2 Lower Upper Phase dependency: threshold model non-linear Stenseth et al., Proc. Natl. Acad. Sci. 1998

20. Howell Tong conference Phase-dependence Stenseth et al., Proc. Natl. Acad. Sci. 1998 Functional response Phase dependency Rochester, AlbertaKluane Lake, Yukon

21. Howell Tong conference 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

22. Howell Tong conference Understanding the phase dependency was a direct result of statistical modelling Stenseth et al., PNAS 1998

23. Howell Tong conference … 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

24. Howell Tong conference Let us ask the lynx (or the data on the lynx)... Is there any spatial structuring of these time- series data?

25. Howell Tong conference What is the spatial structuring force(s)? Stenseth et al., Science 1999

26. Howell Tong conference Canada divided by climatic regions Stenseth et al., Science 1999

27. Howell Tong conference Climatic zonation Stenseth et al., Science 1999

28. Howell Tong conference This grouping was a result of statistical modelling Stenseth et al., Science 1999

29. Howell Tong conference Are the genetics structured similar to the ecology?... we obtained samples … Rueness et al., Nature (2003)

30. Howell Tong conference The sampling scheme We aimed at as good coverage of the entire Canada as possible... Rueness et al., Nature (2003)

31. Howell Tong conference That is: (1) the Pacific region is genetically different from the Continental region, and (2) the Continental region is different from the Atlantic region Genetics of lynx Rueness et al., Nature (2003)

32. Howell Tong conference 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?

33. Howell Tong conference Snow is a key factor for the trophic interaction between hare and lynx ‘X’ = locations (stations) that exhibit statistical significance at the 5% level Difference in frequency of winter warm spells between opposite polarity of the NAO Stenseth et al., Proc. Natl. Acad. Sci. (in press)

34. Howell Tong conference Understanding the link between the grouping of the lynx dynamics, climate and snow condition – and how that operates through the direct hare-lynx food-web link – was a direct result of statistical modelling Stenseth et al., PNAS 2004a,b

35. Howell Tong conference All having a similar ecological structuring as the lynx (Yao et al., 2000. PRSB.) Genetics of mink and muskrat LynxMinkMuskrat Pictures/maps from: www.washington.edu/burkemuseum/ If the peculiarities of the lynx life history is important, similar genetic differentiation south of the Hudson Bay is not expected for mink and muskrat

36. Howell Tong conference Working on the dynamics of the Canadian lynx has led me into stimulating collaborative work with Ecologists: and Geneticists Statisticians: -Charles Krebs, Wilhelm Falck, Ottar Bjørnstad, Mark O’Donoghue, Stan Boutin, Rudy Boonstra, Hildegunn Viljugrein, Nigel Yoccoz and Eric Post, -Kung-Sik Chan, Howell Tong and Ole Chr. Lingjærde - Kjetill Jakobsen, Hans Ellegren, Eli Rueness and Dorothee Ehrich.