Nils Chr. Stenseth Center for Ecological and Evolutionary Synthesis ( CEES ) Dept. of Biology, University of Oslo, Norway The hare-lynx population cycle as seen through the 'eyes' of the Canadian lynx A review of more than half a century's research

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

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)

Raven & Johnson 1996: Biology

Krebs 2001: Ecology

Futuyma 1998: Evolutionary Biology

Edelstein-Keshet 1988: Mathematical Models in Biology

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....

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

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

The hare and the lynx see their food web slightly differently Stenseth et al., Proc. Natl. Acad. Sci 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

A (general) vegetation-hare- predator model Stenseth et al., Proc. Natl. Acad. Sci Vegetation:V t+1 = V t F v (V p, H p,  v ) Hares:H t+1 = H t F h (V p, H p, P p,  h ) Predators:P t+1 = P t F p (H p, P p,  p )

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

The experiment by Krebs et al. (Kluane lake ) 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 p t+1 =  0 +  1 p t +  2 p t-1 + ... i.e., an order 2 process Krebs et al., Science 1995; Stenseth, Science 1995

Lynx time series Stenseth et al., Proc. Natl. Acad. Sci

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

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 Stenseth et al., Proc. Natl. Acad. Sci y t-2  2,2 y t-2 y t-2  1,2 y t-2 Lower Upper Phase dependency: threshold model non-linear

Phase-dependence Stenseth et al., Proc. Natl. Acad. Sci Functional response Phase dependency Rochester, AlbertaKluane Lake, Yukon

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

… 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

.. 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)

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

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

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

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

Stepping back a bit... The asymmetric interaction between ecology and climate CLIMATEVARIABILITY

Climatic zonation

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 (in press)

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?

Regional synchronicity Stenseth et al., (unpublished)

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

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

The statistically derived time-series models have been used to generate synthetic data y r,t = log-abundance in region r in year t f t = external forcing. f t = sin(2pwt) e r,t = independent (in time as well as in space) N(0,1) noise  r,0 +  r,1 y r,t-1 +  r,2 y r,t-2 +  r f t +  r+  r,t y r,t-2   r y r,t = Stenseth et al., (unpublished)

The models used to generate synthetic data  r,0 +  r,1 y r,t-1 +  r,2 y r,t-2 +  r f t +  r+  r,t y r,t-2   r y r,t = Parameter values used in each of the three regions: Stenseth et al., (unpublished)

PacificContinentalAtlantic Pacific 0 (0) 1 (0)0 (1) 0.54 (0.15) Continental 0.57 (0.12) 0 (0) -1 (1) 0.65 (0.14) Atlantic 0.10 (0.12)-0.04 (0.11) 0 (0) 0.48 (0.17) Synchrony in synthetic data Phase-synchrony between a pair of time-series Correlation between a pair of time-series Observed Observed Stenseth et al., (unpublished)

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

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

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? Rueness et al., Nature (in press) Stenseth et al., (unpublished)

Genetics of lynx Stenseth et al., (unpubl.) etc... emigration years density Relative difference in F st Maximum proportion of offspring Phase –dependence of emigration

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).

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 …having a similar ecological structuring as the lynx (Yao et al., PRSB.) Genetics of mink and muskrat LynxMinkMuskrat Pictures/maps from:

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

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).

Working on the dynamics of the Canadian lynx has led me into stimulating collaborative work with Ecologists: and Geneticists Statisticians: Brno 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. -Charles Krebs, Wilhelm Falck, Ottar Bjørnstad, Mark O’Donoghue, Stan Boutin, Rudy Boonstra, Nigel Yoccoz and Eric Post, -Kung-Sik Chan, Howell Tong and Ole Chr. Lingjærde, - 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.....