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 Ecological and Evolutionary Synthesis
(CEES)
Dept. of Biology, University of Oslo, Norway
n.c.stenseth@bio.uio.no
Charles Elton (1924, 1942)
started it all
... after which it has become a
standard text-book example ...
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)
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 ....
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
Stenseth et al., Proc. Natl. Acad. Sci. 1997
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
A (general) vegetation-harepredator model
Vegetation:
Vt+1= Vt Fv (Vp, Hp, ev)
Hares:
Ht+1= Ht Fh (Vp, Hp, Pp, eh)
Predators:
Pt+1= Pt Fp (Hp, Pp, ep)
Stenseth et al., Proc. Natl. Acad. Sci. 1997
What do the experimental
results tell us?
... and do they tell us the same
story as the statistical timeseries analysis?
Evidence for three trophic level effects
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
Snowshoe hare populations: Squeezed from below and above
Statistical model
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
Lynx time series
1920-1994
1820-1940
Stenseth et al., Proc. Natl. Acad. Sci. 1998
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]
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:
Stenseth et al.,
Proc. Natl. Acad. Sci. 1998
Lower
b1,2 yt-2
Upper
b2,2 yt-2
threshold model
yt-2
yt-2
Phase-dependence
Rochester, Alberta
Kluane Lake, Yukon
Phase dependency
Functional response
Stenseth et al., Proc. Natl. Acad. Sci. 1998
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, snowcondition 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
CLIMATE
VARIABILITY
Climatic zonation
Genetics of lynx
That is: (1) the Pacific region is genetically different from the
Continental region, and
(2) the Continental region is different from the Atlantic region
Rueness et al.,
Nature (in press)
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?
Remember:
Snow condition
affects the success
of hare and lynx
Regional synchronicity
Stenseth et al.,
(unpublished)
L2
L3
L5
L7
L11
L12
L14
Pacific
L2
0
1.00
Continental
L3
L5
1
1
0
0.75
0.78
0.66
0.75
0.78
L7
0
Atlantic
L11
L12
0
0
L14
0
0
0
-1
-1
-1
0
0
-1
-1
-1
0
-1
-1
-2
0
0
0
0
0
1.00
0.80
0.59
0.60
0.55
1.00
0.81
0.48
0.48
1.00
0.50
0.56
1.00
0.83
1.00
0
0.50
0.29
0.21
0.21
0.57
0.79
1.00
Phase-synchrony between a pair of time-series
Correlation between a pair of time-series
Synchrony 1897-1934
Stenseth et al.,
(unpublished)
L15
L16
L17
L18
L19
L20
L21
L22
Pacific
L15
0
1.00
L16
0
Continental
L17
L18
2
2
0
0.46
0.40
0.69
0.42
0.53
0.77
L19
L20
3
1
Atlantic
L21
L22
1
-1
2
1
2
1
0
0
0
0
1
0
-1
-2
0
1
0
-1
-2
0
0
-2
-2
0
-1
-1
0
0
1.00
0.30
0.19
-0.17
0.00
0.27
1.00
0.53
0.29
0.50
0.51
1.00
0.71
0.87
0.78
1.00
0.74
0.60
1.00
0.68
1.00
0
0.70
0.36
0.37
0.49
0.36
0.38
0.71
1.00
Phase-synchrony between a pair of time-series
Correlation between a pair of time-series
Synchrony 1920-1994
Stenseth et al.,
(unpublished)
The statistically derived time-series
models have been used to generate
synthetic data
yr,t =
br,0
+ br,1
yr,t-1 + br,2- yr,t-2 + jr -ft + yr+- er,t
yr,t-2  qr
+ + b+ y
+
+
+
br,0
r,1 r,t-1 + br,2 yr,t-2 + jr ft + yr+er,t
yr,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)
The models used to generate synthetic
data
yr,t =
br,0
+ br,1
yr,t-1 + br,2- yr,t-2 + jr -ft + yr+- er,t
yr,t-2  qr
+ + b+ y
+
+
+
br,0
r,1 r,t-1 + br,2 yr,t-2 + jr ft + yr+er,t
yr,t-2  qr
Parameter values used in each of the three regions:
Stenseth et al., (unpublished)
Synchrony in synthetic data
Observed 1897-1934
Observed 1920-1994
Correlation between a pair of time-series
0 (0)
Pacific
Continental
Atlantic
0.67
1 (0)1.60
0
0 (1) 0
0 (0) 0
0
-1.11
-1 (1) -1.20
0.54 (0.15)
Continental
0.73 0.25
0.57 (0.12)
Atlantic
0.68 -0.09
0.10 (0.12)
0.87 0.89
0.65 (0.14)
0.43 0.59
-0.04 (0.11)
0 (0) 0
0
0.87 0.91
0.48 (0.17)
Phase-synchrony between a pair of time-series
Pacific
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?
Stenseth et al., (unpublished)
Rueness et al., Nature (in press)
Genetics of lynx
density
100
105
110
0
12
34
115
120
years
etc...
emigration
Relative
difference
in Fst
Maximum
proportion
of offspring
Phase –dependence of emigration
Stenseth et al., (unpubl.)
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).
Genetics of mink and muskrat
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
…having a similar ecological structuring as the lynx (Yao et al., 2000. PRSB.)
Lynx
Mink
Muskrat
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
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:
-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.
Brno
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 climateecology interactions.