…based on work together with several collaborators
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Transcript of …based on work together with several collaborators
Modelling ecological effects Modelling ecological effects of climate fluctuations of climate fluctuations through the statistical through the statistical
modelling of long-term time modelling of long-term time series dataseries dataNils Christian Stenseth
Centre for Ecological and Evolutionary Synthesis (CEES)Department of Biology
University of Oslo, Norway
…based on work together with several collaborators
2nd International Conference on Mathemathical Biology - Alcalá Sept 2003
Focus on climate and ecology
Ecological effects on ecological dynamics: density-dependence
versus density-independence
CLIMATECLIMATEVARIABILITYVARIABILITY
Outline1. Some few conceptual introductory remarks
2. Large-scale climate indices (e.g., the North Atlantic Oscillation (NAO), El Nino)
3. Modelling ecological effects of climate fluctuations (e.g., linear/non-linear, additive/non-additive)
4. Population ecology: The dynamics of the Soay sheep off Scotland: non-linear, non-additive climate effects
5. Two species – Community ecology: Climatic influence on competitive relationships among species
6. Population ecology: Voles in Hokkaido, Japan
7. Conclusion
Reading the fingerprint of density dependence and density independence (such as climate) from biological time series
t-2 t-1 t t+1
Xt Xt+1 time
Xt Xt+1 = Xt·R(Xt) xt+1 = a0 + (1 + a1)·xt + t+1
(i) Density dependence only
Statistical density dependence (DD)
(ii) Density dependence and climate, non-interactive (additive) effects
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + (1 + a1)·xt + g(Climt) + t+1
Climt
Additive effect of climate
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + [1 + a1(Climt)]·xt + t+1
(iii) Density dependence and climate, interactive effects
Climt
Climate affecting strength of DD
The North Atlantic Oscillation (NAO)the difference in athmospheric pressure
between the Azores and Iceland
Iceland
the Azores
The North Atlantic Oscillation (NAO)negative and positive phases
NAO index 1860-2000
high NAO
low NAO
Modelling the effect(s) of climate fluctuations (and harvesting) on population
dynamics
…some theoretical background
Single-species dynamics
bt
tt aN
RNN
)(11
0
0.05
0.1
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low b
high b
btaN
R
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tN
Single-species dynamics
bt
tt aN
RNN
)(11
Single-species dynamics
How to incorporate climatic variability in population dynamic models:- additively…
…or non-additively
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + [1 + a1(Climt)]·xt + t+1
(iii) Density dependence and climate, interactive effects
Climt
Climate affecting strength of DD
(ii) Density dependence and climate, non-interactive (additive) effects
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + (1 + a1)·xt + g(Climt) + t+1
Climt
Additive effect of climate
Single-species dynamics with climate effect (here: NAO)
Nt+1 = Nt R
1+(aNt )b(NAO)
• Non-additive effect of climate
• Non-linear intrinsic and extrinsic processes
Single-species dynamics: possible effects of changing climate
Nt+1 = Nt R
1+(aNt )b(NAO)
b(NAO)
An example: the soay sheep off the coast of
Scotland- one single species
Soay sheep at Hirta, St Kilda
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
1 9 5 5 1 9 6 5 1 9 7 5 1 9 8 5 1 9 9 5
Y e a r
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1 9 5 5 1 9 6 5 1 9 7 5 1 9 8 5 1 9 9 5
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Soay sheep: dynamics depend on NAO
Nt = Nt-1(R0/1+(Nt-1/K)bt
a0 + a1(xt-1 - k) + 1,t if xt-1 k
a0 + a2(xt-1 - k) + 2,t if xt-1 > k xt =
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + [1 + a1(Climt)]·xt + t+1
(iii) Density dependence and climate, interactive effects
Climt
Climate affecting strength of DD
Soay sheep: dynamics depend on NAO
Using a FCTAR-model
Soay sheep: dynamics depend on NAO
High NAO
Low NAONt+1 = Nt R
1+(aNt )b(NAO)
One species to two species
Sætre et al., 1999Stenseth et al., Science 2000
Changing competetive relationships
dn1
dt=
k1 – n1 –12n2
k1r1n1
dn2
dt=
k2 (NAO) – n2 –21n1
k2(NAO)r2n2
n1 =log(N1 ), n2 =log(N2 )
Pied Flycatcher
Col
lare
d fl
ycat
cher
Collared, high NAO
Collared, low NAO
Pied
Sætre et al., 1999Stenseth et al., Science 2000
Changing competetive relationships
Grey-sided vole in Hokkaido
Seasonal forcing and ecological dynamics (back to within-population dynamics)
Hokkaido voles
Cold and warm currents determine differential seasonal patternsStenseth et al., PRSB, 2002
Seasonal forcing – an example of ”regime shift” – a bifurcation
Stenseth et al., Res. Pop. Ecol. 1998
xt = b0 + b1xt-1 + b2xt-2
Nt = Nt-1exp[(aw0–aw1xt-1–aw2xt-2)(1-)] ·exp(as0–as1xt-1–as2xt-2)]
Hokkaido voles: observations only the fall data
AR2 models
Stenseth et al., PRSB, 2002
Hokkaido voles: observations
SouthNorth
Stenseth et al., PRSB, 2002
xt = 1xt-1 + 2xt-2 + t
Hokkaido voles: can we predict the observed patterns?
Stenseth et al., PRSB, 2002
Hokkaido voles: predictions
Stenseth et al., PRSB, 2002
xt = 1xt-1 + 2xt-2 + t
Nt = Nt-1 Rsummer Rwinter
Rsummer = C1exp[(–as1 [log(C2) + (1 – aw1 + aw1) xt-1–aw2 (1 – )xt-2] – as2 xt-2)]Rwinter = C2exp[(–aw1xt-1 – aw2xt-2 )(1 – )]
1 = 1 – aw1 + (– as1 + as1aw1 + aw1)– as1aw2
2 = – aw2 + (as1aw1 – as2 + aw2)– as1aw1
Hokkaido voles
Stenseth et al., PRSB, 2002
Xt Xt+1 = Xt·R(Xt, Climt) xt+1 = a0 + [1 + a1(Climt)]·xt + t+1
(iii) Density dependence and climate, interactive effects
Climt
Climate affecting strength of DD
xt+1 = a0 + [1 + a1(Climt)]·xt + [1 + a2(Climt)]·xt-1 + t+1
Hokkaido voles: more detailed databoth spring and fall data
Stenseth et al., PNAS, in review
Hokkaido voles: observations
Stenseth et al., PNAS, in review
Hokkaido voles: predictions
Stenseth et al., PNAS, in review
Melt-off highly variable in the mountains
Stenseth et al., Res. Pop. Ecol. 1998
Seasonal forcing is an example of ”regime shift” – a bifurcation
Season length determines the population dynamics
changing from non-cyclic to cyclici.e.,
a bifurcation
Season length is determined by the climate
i.e.,the dynamic bifurcation is casued
by climatically driven seasonal forcing
Conclusions
1. Indices (North Atlantic Oscillation and the like) are found to be good climate proxies useful for understanding how climatic fluctuations have affected ecological pattern and processes in the past.
2. Climatic variation affect ecological dynamics (e.g., Soay sheep) through behavioral changes having dynamic effects
3. Climatic variation affect ecological dynamics (e.g., Hokkaido voles) through the length of the seasons having dynamic effects
Methodological coda
1. Understanding what the response of ecological systems to environmental change has been in the past will help us be prepared for what might happen in the future.
2. For this, monitoring data is essential – and the statistical modeling thereof is important.
3. Mathematical modeling is important to understand the dynamic consequences of possible climate change