Nils Chr. Stenseth Center for Ecological and Evolutionary Synthesis ( CEES ) Dept. of Biology, University of Oslo, Norway [email protected] The hare-lynx

Nils Chr. StensethCenter for Ecological and Evolutionary Synthesis

(CEES)Dept. of Biology, University of Oslo, Norway

[email protected]

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


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


• 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


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


1820-1940

1920-1994

Fur returns are good proxies for actual abundance


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


yt-2

2,2 y

t-2

yt-2

1,2 y

t-2

LowerUpperPhase dependency: threshold model

non-linear

Phase-dependence


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


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


e-seriesC

orr

elat

ion

bet

wee

n a

pair

of ti

me-

serie

s


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 =


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:


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


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


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 .....

Documents

Nils Chr. Stenseth Center for Ecological and Evolutionary Synthesis ( CEES ) Dept. of Biology, University of Oslo, Norway [email protected] The hare-lynx