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Elton, C.S.1
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C. S. Elton, Br. J. Exp. Biol. 2, 119 (1924); Voles, Mice and Lemmings (Clarendon, Oxford, 1942); see also (3).
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Voles, Mice and Lemmings
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3
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84970599878
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See P. A. P. Moran [Aust. J. Zool. 1, 163 (1953)], who fitted a linear autoregressive model of order two, which exhibits quasi-periodicity, but was well aware of its inadequacy. In particular, he pointed out the inhomogeneity of the fitted residuals, which violated the assumption of a common and constant variance for the white noise term in the fitted model. As an interesting historical point, it should be noted that Moran learned about the lynx data when he visited Charles Elton and Dennis Chitty in the Bureau of Animal Population at Oxford after World War II.
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Moran, P.A.P.1
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5
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E. Ranta, V. Kaitala, P. Lundberg, Science 278, 1621 (1997); E. Ranta, V. Kaitala, J. Lindström, Ecography 20, 454 (1997).
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Ranta, E.1
Kaitala, V.2
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E. Ranta, V. Kaitala, P. Lundberg, Science 278, 1621 (1997); E. Ranta, V. Kaitala, J. Lindström, Ecography 20, 454 (1997).
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Ecography
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Ranta, E.1
Kaitala, V.2
Lindström, J.3
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7
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0004275183
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Chapman and Hall, London
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The focus on one particular lynx series has to some extent distracted both ecologists and statisticians up to the present from the fact that similar time series exist for the entire continent [but see T. Royama, Analytical Population Dynamics (Chapman and Hall, London, 1992)].
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(1992)
Analytical Population Dynamics
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Royama, T.1
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10
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0345360301
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Statistics Canada; Dominion Bureau of Statistics 1965; Statistics Canada 1983-1995
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Statistics Canada; Dominion Bureau of Statistics 1965; Statistics Canada 1983-1995.
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14
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0344928906
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note
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21 classifications of the 21 lynx series. A "black-box" approach means doing an exhaustive search for the optimum combination in some sense - an approach troubled by multiple comparison in statistical modeling. Instead, we focus on two sets of combinations, one based on ecological features and the other on climatic condition.
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16
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0031830116
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E. Post and N. C. Stenseth, J. Anim. Ecol. 67, 537 (1998); M. C. Forchhammer, N. C. Stenseth, E. Post, R. Langvatn, Proc. R. Soc. London Ser. B 265, 341 (1998); E. Post and N. C. Stenseth, Ecology 80, 1322 (1999).
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J. Anim. Ecol.
, vol.67
, pp. 537
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Post, E.1
Stenseth, N.C.2
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17
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0032557019
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E. Post and N. C. Stenseth, J. Anim. Ecol. 67, 537 (1998); M. C. Forchhammer, N. C. Stenseth, E. Post, R. Langvatn, Proc. R. Soc. London Ser. B 265, 341 (1998); E. Post and N. C. Stenseth, Ecology 80, 1322 (1999).
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(1998)
Proc. R. Soc. London Ser. B
, vol.265
, pp. 341
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Forchhammer, M.C.1
Stenseth, N.C.2
Post, E.3
Langvatn, R.4
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18
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0033045072
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E. Post and N. C. Stenseth, J. Anim. Ecol. 67, 537 (1998); M. C. Forchhammer, N. C. Stenseth, E. Post, R. Langvatn, Proc. R. Soc. London Ser. B 265, 341 (1998); E. Post and N. C. Stenseth, Ecology 80, 1322 (1999).
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Ecology
, vol.80
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Post, E.1
Stenseth, N.C.2
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19
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0003566072
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Clarendon Press, Oxford
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H. Tong, Non-Linear Time Series: A Dynamical System Approach (Clarendon Press, Oxford, 1990); H. Tong, Threshold Models in Non-Linear Time Series Analysis (Springer-Verlag, Berlin, 1983). The model given by Eq. (1) is a SETAR(2;2,2) model. For a nontechnical presentation of the SETAR models, see Stenseth et al. [N. C. Stenseth, K.-S. Chan, E. Framstad, H. Tong, Proc. R. Soc. London Ser. B 265. 1957 (1998)].
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(1990)
Non-linear Time Series: A Dynamical System Approach
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Tong, H.1
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20
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0004089297
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Springer-Verlag, Berlin
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H. Tong, Non-Linear Time Series: A Dynamical System Approach (Clarendon Press, Oxford, 1990); H. Tong, Threshold Models in Non-Linear Time Series Analysis (Springer-Verlag, Berlin, 1983). The model given by Eq. (1) is a SETAR(2;2,2) model. For a nontechnical presentation of the SETAR models, see Stenseth et al. [N. C. Stenseth, K.-S. Chan, E. Framstad, H. Tong, Proc. R. Soc. London Ser. B 265. 1957 (1998)].
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(1983)
Threshold Models in Non-linear Time Series Analysis
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Tong, H.1
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21
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0032558710
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H. Tong, Non-Linear Time Series: A Dynamical System Approach (Clarendon Press, Oxford, 1990); H. Tong, Threshold Models in Non-Linear Time Series Analysis (Springer-Verlag, Berlin, 1983). The model given by Eq. (1) is a SETAR(2;2,2) model. For a nontechnical presentation of the SETAR models, see Stenseth et al. [N. C. Stenseth, K.-S. Chan, E. Framstad, H. Tong, Proc. R. Soc. London Ser. B 265. 1957 (1998)].
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(1998)
Proc. R. Soc. London Ser. B
, vol.265
, pp. 1957
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Stenseth, N.C.1
Chan, K.-S.2
Framstad, E.3
Tong, H.4
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22
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0030986178
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N. C. Stenseth, W. Falck, O. N. Bjørnstad, C. J. Krebs, Proc. Natl. Acad. Sci. U.S.A. 94, 5147 (1997).
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Proc. Natl. Acad. Sci. U.S.A.
, vol.94
, pp. 5147
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Stenseth, N.C.1
Falck, W.2
Bjørnstad, O.N.3
Krebs, C.J.4
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24
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0004184934
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Chapman & Hall, London
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D. R. Cox and D. V. Hinkley, Theoretical Statistics (Chapman & Hall, London, 1974); H. Akaike, in Second International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds. (Akademiai Kiado, Budapest 1973); H. Akaike, IEEE Trans. Autom. Cont. AC-19, 716 (1974).
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Theoretical Statistics
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Cox, D.R.1
Hinkley, D.V.2
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25
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0344066645
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B. N. Petrov and F. Csaki, Eds. Akademiai Kiado, Budapest
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D. R. Cox and D. V. Hinkley, Theoretical Statistics (Chapman & Hall, London, 1974); H. Akaike, in Second International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds. (Akademiai Kiado, Budapest 1973); H. Akaike, IEEE Trans. Autom. Cont. AC-19, 716 (1974).
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(1973)
Second International Symposium on Information Theory
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Akaike, H.1
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26
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0016355478
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D. R. Cox and D. V. Hinkley, Theoretical Statistics (Chapman & Hall, London, 1974); H. Akaike, in Second International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds. (Akademiai Kiado, Budapest 1973); H. Akaike, IEEE Trans. Autom. Cont. AC-19, 716 (1974).
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IEEE Trans. Autom. Cont.
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, pp. 716
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Akaike, H.1
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27
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0344497821
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note
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Using the tests described in (22) and adopting a 5% significance level, we cannot reject the hypothesis of common slopes and the hypothesis of the common ratio of intercepts for the pairs (L1 and L2) and (L4 and L5). For L6 and L7, we cannot reject the hypothesis of common slopes in the upper regimes and that the lag-2 coefficients may be the same for the two series. However, L6 and L7 appear to have a different lag-1 coefficient in the lower regime. Thus, the evidence of common dynamics for L6 and L7 is somewhat weak. For details, see (6).
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28
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0038530342
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CCEA Occasional Paper No. 14, Ottawa
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B. Wiken, D. Gauthier, I. Marshall, K. Lawton, H. Hirvonen, A Perspective on Canada's Ecosystems, CCEA Occasional Paper No. 14, Ottawa (1996).
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(1996)
A Perspective on Canada's Ecosystems
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Wiken, B.1
Gauthier, D.2
Marshall, I.3
Lawton, K.4
Hirvonen, H.5
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29
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0003545786
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publ. 1300, Environment Canada, Canadian Forestry Service, Ottawa
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J. S. Rowe, Forest Regions of Canada (publ. 1300, Environment Canada, Canadian Forestry Service, Ottawa, 1972).
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(1972)
Forest Regions of Canada
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Rowe, J.S.1
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30
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0344066651
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note
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We have investigated the constraint structure further (Table 1): assuming only a common structure in the lag-1 and lag-2 in the upper regime provides worse fit This suggests that the additional constraints [found by testing (6)] are significant Relocating 13 to the Pacific-maritime group yields an AIC slightly larger than -1819.38. This implies some fuzziness in the boundary of the three zones. One can classify L3 into the Pacific-maritime zone or the Continental zone. The case of Yukon seems rather clear cut: including it in the Pacific zone substantially increases the AIC and hence provides a poorer description.
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31
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0344497819
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Supplementary information is available at www. sciencemag.org/feature/data/1037845.shl.
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33
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0003755335
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Agriculture and AgriFood Canada/Environment Canada, Ottawa
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Ecosystem Stratification Working Group, A National Ecological Framework for Canada (Agriculture and AgriFood Canada/Environment Canada, Ottawa, 1995).
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(1995)
A National Ecological Framework for Canada
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34
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0344497818
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note
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This work was initiated while several of the authors were at the Centre for Advanced Study at the Norwegian Academy for Sciences and Letters, Oslo. N.C.S. acknowledges generous support from the Norwegian Science Council and the University of Oslo. K-S.C. acknowledges generous support from the University of Iowa. H.T. acknowledges the Engineering and Physical Sciences Research Council (UK) and the University of Hong Kong for support N.C.S. and H.T. acknowledge support from UK Biotechnology and Biological Sciences Research Council/Engineering and Physical Sciences Research Council (UK) grant 96/MM109785. R.B., S.B., and C.J.K. acknowledge support from the Natural Sciences and Engineering Research Council of Canada. E.P. acknowledges the National Science Foundation (grant DBI-93-04178) for support. M.C.F. acknowledges the Danish National Research Council for support We thank A. Kenney for preparing the figure and three anonymous reviewers for providing valuable comments, helping us to clarify our argument.
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