Modelling ecological effects of climate fluctuations through the statistical modelling of longterm t

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Modelling ecological effects of climate
fluctuations through the statistical modelling of
long-term time series data
Nils Christian StensethCentre for Ecological and
Evolutionary Synthesis (CEES)Department of
BiologyUniversity of Oslo, Norway
based on work together with several collaborators
2nd International Conference on Mathemathical
Biology - Alcalá Sept 2003
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Focus on climate and ecology
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Ecological effects on ecological dynamics
density-dependence versus density-independence
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Outline
1. 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
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Reading the fingerprint of density dependence and
density independence (such as climate) from
biological time series
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The North Atlantic Oscillation (NAO)the
difference in athmospheric pressure between the
Azores and Iceland
Iceland
the Azores
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The North Atlantic Oscillation (NAO)negative and
positive phases
low NAO
high NAO
NAO index 1860-2000
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Modelling the effect(s) of climate fluctuations
(and harvesting) on population dynamics
some theoretical background
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Single-species dynamics
low b
high b
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Single-species dynamics
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Single-species dynamics
How to incorporate climatic variability in
population dynamic models- additively
or non-additively
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Single-species dynamics with climate effect
(here NAO)

• Non-additive effect of climate
• Non-linear intrinsic and extrinsic processes

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Single-species dynamics possible effects of
changing climate
b(NAO)
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An example the soay sheep off the coast of
Scotland- one single species
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Soay sheep at Hirta, St Kilda
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Soay sheep dynamics depend on NAO
Nt Nt-1(R0/?1(Nt-1/K)b??t
a0 a1(xt-1 - k) e1,t if xt-1 ? k a0
a2(xt-1 - k) e2,t if xt-1 gt k
xt
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Soay sheep dynamics depend on NAO
Using a FCTAR-model
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Soay sheep dynamics depend on NAO
Low NAO
High NAO
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One species ? to two species
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Changing competetive relationships
k1 n1 a12n2
dn1

r1n1
k1
dt
k2 (NAO) n2 a21n1
dn2

r2n2
k2(NAO)
dt
n1 log(N1 ), n2 log(N2 )
Sætre et al., 1999 Stenseth et al., Science 2000
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Changing competetive relationships
Sætre et al., 1999 Stenseth et al., Science 2000
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Grey-sided vole in Hokkaido
Seasonal forcing and ecological dynamics (back
to within-population dynamics)
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Hokkaido voles
Cold and warm currents determine differential
seasonal patterns
Stenseth et al., PRSB, 2002
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Seasonal forcing an example of regime shift
a bifurcation
xt b0 b1xt-1 b2xt-2
Nt Nt-1exp(aw0aw1xt-1aw2xt-2)(1-t)
exp(as0as1xt-1as2xt-2)t
Stenseth et al., Res. Pop. Ecol. 1998
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Hokkaido voles observations only the fall data
AR2 models
Stenseth et al., PRSB, 2002
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Hokkaido voles observations
xt a1xt-1 a2xt-2 et
Stenseth et al., PRSB, 2002
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Hokkaido voles can we predict the observed
patterns?
Stenseth et al., PRSB, 2002
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Hokkaido voles predictions
xt a1xt-1 a2xt-2 et
Nt Nt-1 Rsummer Rwinter
Rsummer C1exp(as1 log(C2) (1 aw1 aw1t)
xt-1aw2 (1 t)xt-2 as2 xt-2)t Rwinter
C2exp(aw1xt-1 aw2xt-2 )(1 t)
a1 1 aw1 ( as1 as1aw1 aw1)t
as1aw2t2a2 aw2 (as1aw1 as2 aw2)t
as1aw1t2
Stenseth et al., PRSB, 2002
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Hokkaido voles
xt1 a0 1 a1(Climt)xt 1
a2(Climt)xt-1 ?t1
Stenseth et al., PRSB, 2002
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Hokkaido voles more detailed databoth spring
and fall data
Stenseth et al., PNAS, in review
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Hokkaido voles observations
Stenseth et al., PNAS, in review
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Hokkaido voles predictions
Melt-off highly variable in the mountains
Stenseth et al., PNAS, in review
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Seasonal forcing is an example of regime shift
a bifurcation
Stenseth et al., Res. Pop. Ecol. 1998
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Season length determines the population
dynamicschanging from non-cyclic to
cyclici.e.,a bifurcation
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Season length is determined by the
climatei.e.,the dynamic bifurcation is casued
by climatically driven seasonal forcing
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Conclusions

• 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.
• Climatic variation affect ecological dynamics
  (e.g., Soay sheep) through behavioral changes
  having dynamic effects
• Climatic variation affect ecological dynamics
  (e.g., Hokkaido voles) through the length of the
  seasons having dynamic effects

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Methodological coda

• 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.
• For this, monitoring data is essential and the
  statistical modeling thereof is important.
• Mathematical modeling is important to understand
  the dynamic consequences of possible climate
  change