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…based on work together with several collaborators

Modelling ecological effects of climate fluctuations through the statistical modelling of long-term time series data. Nils Christian Stenseth Centre for Ecological and Evolutionary Synthesis (CEES) Department of Biology University of Oslo, Norway.

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…based on work together with several collaborators

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  1. 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

  2. Focus on climate and ecology

  3. CLIMATE VARIABILITY Ecological effects on ecological dynamics: density-dependence versus density-independence

  4. Outline 1. Some few conceptual introductory remarks 2.Large-scale climate indices (e.g., the North Atlantic Oscillation (NAO), El Nino) 3. Modellingecological 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

  5. XtXt+1 time t-2 t-1 t t+1 (i) Density dependence only Xt Xt+1 = Xt·R(Xt)  xt+1 = a0 + (1 + a1)·xt + t+1 Statistical density dependence (DD) (ii) Density dependence and climate, non-interactive (additive) effects Climt Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + (1 + a1)·xt + g(Climt) + t+1 Additive effect of climate (iii) Density dependence and climate, interactive effects Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + [1 + a1(Climt)]·xt + t+1 Climate affecting strength of DD Climt Reading the fingerprint of density dependence and density independence (such as climate) from biological time series

  6. The North Atlantic Oscillation (NAO)the difference in athmospheric pressure between the Azores and Iceland Iceland the Azores

  7. The North Atlantic Oscillation (NAO)negative and positive phases low NAO high NAO NAO index 1860-2000

  8. Modelling the effect(s) of climate fluctuations (and harvesting) on population dynamics …some theoretical background

  9. Single-species dynamics low b high b

  10. Single-species dynamics

  11. (ii) Density dependence and climate, non-interactive (additive) effects Climt Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + (1 + a1)·xt + g(Climt) + t+1 Additive effect of climate (iii) Density dependence and climate, interactive effects Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + [1 + a1(Climt)]·xt + t+1 Climate affecting strength of DD Climt Single-species dynamics How to incorporate climatic variability in population dynamic models:- additively… …or non-additively

  12. Nt R Nt+1 = 1+(aNt )b(NAO) Single-species dynamics with climate effect (here: NAO) • Non-additive effect of climate • Non-linear intrinsic and extrinsic processes

  13. Nt R Nt+1 = 1+(aNt )b(NAO) Single-species dynamics: possible effects of changing climate b(NAO)

  14. An example: the soay sheep off the coast of Scotland- one single species

  15. Soay sheep at Hirta, St Kilda

  16. Soay sheep: dynamics depend on NAO (iii) Density dependence and climate, interactive effects Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + [1 + a1(Climt)]·xt + t+1 Climate affecting strength of DD Climt 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 > k xt =

  17. Soay sheep: dynamics depend on NAO Using a FCTAR-model

  18. Soay sheep: dynamics depend on NAO Nt R Nt+1 = 1+(aNt )b(NAO) Low NAO High NAO

  19. One species  to two species

  20. 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

  21. Collared, high NAO Collared, low NAO Collared flycatcher Pied Pied Flycatcher Changing competetive relationships Sætre et al., 1999 Stenseth et al., Science 2000

  22. Grey-sided vole in Hokkaido Seasonal forcing and ecological dynamics (back to within-population dynamics)

  23. Hokkaido voles Cold and warm currents determine differential seasonal patterns Stenseth et al., PRSB, 2002

  24. Seasonal forcing – an example of ”regime shift” – a bifurcation xt = b0+ b1xt-1+ b2xt-2 Nt = Nt-1exp[(aw0–aw1xt-1–aw2xt-2)(1-t)] ·exp(as0–as1xt-1–as2xt-2)t] Stenseth et al., Res. Pop. Ecol. 1998

  25. Hokkaido voles: observations only the fall data AR2 models Stenseth et al., PRSB, 2002

  26. Hokkaido voles: observations South North xt = a1xt-1+ a2xt-2+ et Stenseth et al., PRSB, 2002

  27. Hokkaido voles: can we predict the observed patterns? Stenseth et al., PRSB, 2002

  28. Hokkaido voles: predictions xt = a1xt-1+ a2xt-2+ et Nt = Nt-1 Rsummer Rwinter Rsummer = C1exp[(–as1 [log(C2) + (1 – aw1 +aw1t) xt-1–aw2 (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

  29. Hokkaido voles (iii) Density dependence and climate, interactive effects Xt Xt+1 = Xt·R(Xt, Climt)  xt+1 = a0 + [1 + a1(Climt)]·xt + t+1 Climate affecting strength of DD Climt xt+1 = a0 + [1 + a1(Climt)]·xt+ [1 + a2(Climt)]·xt-1 + t+1 Stenseth et al., PRSB, 2002

  30. Hokkaido voles: more detailed databoth spring and fall data Stenseth et al., PNAS, in review

  31. Hokkaido voles: observations Stenseth et al., PNAS, in review

  32. Hokkaido voles: predictions Melt-off highly variable in the mountains Stenseth et al., PNAS, in review

  33. Seasonal forcing is an example of ”regime shift” – a bifurcation Stenseth et al., Res. Pop. Ecol. 1998

  34. Season length determines the population dynamicschanging from non-cyclic to cyclici.e.,a bifurcation

  35. Season length is determined by the climatei.e.,the dynamic bifurcation is casued by climatically driven seasonal forcing

  36. 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

  37. 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

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