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Nils Chr. StensethCenter for Ecological and Evolutionary Synthesis
(CEES)Dept. of Biology, University of Oslo, Norway
n.c.stenseth@bio.uio.no
The hare-lynx population The hare-lynx population cycle as seen through the cycle as seen through the 'eyes' of the Canadian lynx'eyes' of the Canadian lynx
AA review of review of more than more than
half a half a century's century's researchresearch
... 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. 1997
The lynx’s food-web
… data from south of the Hudson Bay in Canada
Stenseth et al., Proc. Natl. Acad. Sci. 1997
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. 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
A (general) vegetation-hare-predator model
Stenseth et al., Proc. Natl. Acad. Sci. 1997
Vegetation: Vt+1= Vt Fv (Vp, Hp, v)
Hares: Ht+1= Ht Fh (Vp, Hp, Pp, h)
Predators: Pt+1= Pt Fp (Hp, Pp, p)
What do the experimentalresults tell us?
... and do they tell us the samestory as the statistical time-
series analysis?
The experiment by Krebs et al. (Kluane lake 1987-94)
Treatment I Treatment II Treatment III
Reducing predators Adding food Reducing predators| and adding food
2x increase of hares 2x increase of hares 10x increase of hares
Evidence for three trophic level effects
Snowshoe hare populations: Squeezed from below and above
Statistical model
ht+1 = 0 + 1 ht + 2 ht-1 + 3 ht -2 + ... i.e., an order 3 process
pt+1 = 0 + 1 pt + 2 pt-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. 1998
1820-1940
1920-1994
Fur returns are good proxies for actual abundance
Stenseth et al., Proc. Natl. Acad. Sci. 1998
Predator-prey model with phase-dependence
Hares: Ht+1= Ht exp[ai,0 - ai,1xt - ai,2yt]
Predators: Pt+1= Pt exp[bi,0 - bi,1yt - bi,2xt]
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 + t
is equivalent to
Stenseth et al., Proc. Natl. Acad. Sci. 1998
yt-2
2,2 y
t-2
yt-2
1,2 y
t-2
LowerUpperPhase dependency: threshold model
non-linear
Phase-dependence
Stenseth et al., Proc. Natl. Acad. Sci. 1998
Functional responsePhase dependency
Rochester, Alberta Kluane Lake, Yukon
The non-linearity is due to phase-dependent relations
between the hare and the lynx
Functional responseThis 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
CLIMATECLIMATEVARIABILITYVARIABILITY
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 1897-1934
Pacific Continental Atlantic L2 L3 L5 L7 L11 L12 L14
L2 0 1.00
1 1 0 0 0 0
L3 0.75
0 1.00
0 0 -1 -1 -1
L5 0.78 0.80
0 1.00
0 -1 -1 -1
L7 0.66 0.59 0.81
0 1.00
-1 -1 -2
L11 0.75 0.60 0.48 0.50
0 1.00
0 0
L12 0.78 0.55 0.48 0.56 0.83
0 1.00
0
L14 0.50 0.29 0.21 0.21 0.57 0.79
0 1.00
Ph
ase-synch
ron
y between a pair of tim
e-series
Co
rrel
atio
n b
etw
een
a pa
ir of
tim
e-se
ries
Stenseth et al., (unpublished)
Synchrony 1920-1994
Pacific Continental Atlantic L15 L16 L17 L18 L19 L20 L21 L22
L15 0
1.00 0 2 2 3 1 1 -1
L16 0.46
0 1.00
2 1 2 1 0 0
L17 0.40 0.30
0 1.00
0 1 0 -1 -2
L18 0.69 0.19 0.53
0 1.00
1 0 -1 -2
L19 0.42 -0.17 0.29 0.71
0 1.00
0 -2 -2
L20 0.53
0.00 0.50 0.87 0.74
0 1.00
-1 -1
L21 0.77 0.27 0.51 0.78 0.60 0.68
0 1.00
0
L22 0.70 0.36 0.37 0.49 0.36 0.38 0.71
0 1.00
Ph
ase-synch
ron
y between a pair of tim
e-seriesC
orr
elat
ion
bet
wee
n a
pair
of ti
me-
serie
s
Stenseth et al., (unpublished)
The statistically derived time-series models have been used to generate
synthetic data
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
r,0 + r,1 yr,t-1 + r,2 yr,t-2 + r ft + r+r,t yr,t-2 r+ ++++
r,0 + r,1 yr,t-1 + r,2 yr,t-2 + r ft + r+r,t yr,t-2 r- ----
yr,t =
Stenseth et al., (unpublished)
The models used to generate synthetic data
r,0 + r,1 yr,t-1 + r,2 yr,t-2 + r ft + r+r,t yr,t-2 r+ ++++
r,0 + r,1 yr,t-1 + r,2 yr,t-2 + r ft + r+r,t yr,t-2 r- ----
yr,t =
Parameter values used in each of the three regions:
Stenseth et al., (unpublished)
Pacific Continental Atlantic
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
Ph
ase-synch
ron
y between a pair of tim
e-seriesC
orr
elat
ion
bet
wee
n a
pair
of ti
me-
serie
s
0.68
0.73
0.87
0.43
0.87
0
00.67
-1.110
Observed 1897-1934
00.91
0.59-0.09
0.89
0.25-1.20
01.60
0
Observed 1920-1994
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.)
-100 105 110 115 120
01 2 3 4
etc...
emigration
years
density
Relative difference
in Fst
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., 2000. PRSB.)
Genetics of mink and muskrat
Lynx Mink Muskrat
Pictures/maps from:www.washington.edu/burkemuseum/
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 andOle 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 .....
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