Weak population regulation in ecological time series

Ecology Letters

Volumn 13, Issue 1, 2010, Pages 21-31

  Ziebarth, Nicolas L ^a,b   Abbott, Karen C ^b,c   Ives, Anthony R ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c IOWA STATE UNIVERSITY   (United States)

Author keywords

Autoregressive model; Autoregressive moving average; Global Population Dynamics Database; Linear model; Non stationarity; Population regulation; Return to equilibrium; Time series analysis

Indexed keywords

LINEARITY; POPULATION DYNAMICS; POPULATION REGULATION; STOCHASTICITY; TIME SERIES; TIME SERIES ANALYSIS;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; POPULATION DYNAMICS; REGRESSION ANALYSIS; STATISTICAL MODEL; TIME;

ANIMALS; ECOSYSTEM; MODELS, BIOLOGICAL; MODELS, STATISTICAL; POPULATION CONTROL; REGRESSION ANALYSIS; TIME FACTORS;

EID: 72949115702     PISSN: 1461023X     EISSN: 14610248     Source Type: Journal    
DOI: 10.1111/j.1461-0248.2009.01393.x     Document Type: Article

References (55)

1. Abbott, K.C., Ripa, J. Ives, A.R. (2009). Environmental variation in ecological communities and inferences from single-species data. Ecology, 90, 1268 1278.
2. Andrewartha, H.G. Birch, L.C. (1954). The Distribution and Abundance of Species. Chicago University Press, Chicago.
3. Berryman, A.A. (2003). On principles, laws and theory in population ecology. Oikos, 103, 695 701.
4. Box, G.E.P., Jenkins, G.M. Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs, NJ.
5. Brook, B.W. Bradshaw, C.J.A. (2006). Strength of evidence for density dependence in abundance time series of 1198 species. Ecology, 87, 1445 1451.
6. Bulmer, M.G. (1975). Statistical analysis of density dependence. Biometrics, 31, 901 911.
7. Cheang, W.K. Reinsel, G.C. (2003). Finite sample properties of ML and REML estimators in time series regression models with long memory noise. J. Stat. Comput. Simul., 73, 233 259.
8. Den Boer, P.J. Reddingius, J. (1989). On the stabilization of animal numbers. Problems of testing. 2. Confrontation with data from the field. Oecologia, 79, 143 149.
9. Dennis, B. Otten, M.R.M. (2000). Joint effects of density dependence and rainfall on abundance of San Joaquin kit fox. J. Wildl. Manage., 64, 388 400.
10. Dennis, B. Taper, B. (1994). Density dependence in time series observations of natural populations: estimation and testing. Ecol. Monogr., 64, 205 224.
11. Feller, W. (1968). An Introduction to Probability Theory and its Applications, Vol. 1. John Wiley & Sons, New York, NY.
12. Fromentin, J.M., Myers, R.A., Bjornstad, O.N., Stenseth, N.C., Gjosaeter, J. Christie, H. (2001). Effects of density-dependent and stochastic processes on the regulation of cod populations. Ecology, 82, 567 579.
13. Gardiner, C.W. (1990). Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer-Verlag, Berlin.
14. Holyoak, M. (1992). Detection of density dependence from annual censuses of bracken-feeding insects. Oecologia, 91, 425 430.
15. Hunter, M.D. Price, P.W. (1998). Cycles in insect populations: delayed density dependence or exogenous driving variables?. Ecol. Entomol., 23, 216 222.
16. Hunter, M.D. Price, P.W. (2000). Detecting cycles and delayed density dependence: a reply to Turchin and Berryman. Ecol. Entomol., 25, 122 124.
17. Ives, A.R. (1995). Measuring resilience in stochastic systems. Ecol. Monogr., 65, 217 233.
18. Ives, A.R., Dennis, B., Cottingham, K.L. Carpenter, S.R. (2003). Estimating community stability and ecological interactions from time-series data. Ecol. Monogr., 73, 301 330.
19. Ives, A.R., Abbott, K.C. Ziebarth, N.L. (2009). Statistical evaluation of density dependence using ARMA models. Ecology, in press.
20. Kendall, B.E., Briggs, C.J., Murdoch, W.W., Turchin, P., Ellner, S.P., McCauley, E. et al. (1999). Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology, 80, 1789 1805.
21. Lande, R. (2002). Estimating density dependence in time-series of age-structured populations. Philos. Transact. R. Soc. Lond. B Biol. Sci., 357, 1179 1184.
22. Malgras, J. Debouzie, D. (1997). Can ARMA models be used reliably in ecology?. Acta Oecol. Int. J. Ecol., 18, 427 447.
23. May, R.M. (1974). Stability and Complexity in Model Ecosystems, 2nd edn. Princeton University Press, Princeton, NJ.
24. May, R.M. Oster, G.F. (1976). Bifurcations and dynamic complexity in simply ecological models. Am. Nat., 110, 573 599.
25. May, R.M., Conway, G.R., Hassell, M.P. Southwood, T.R.E. (1974). Time delays, density-dependence and single-species oscillations. J. Anim. Ecol., 43, 747 770.
26. McGilchrist, C.A. (1989). Bias of ML and REML estimators in regression models with ARMA errors. J. Stat. Comput. Simul., 32, 127 136.
27. Murdoch, W.W., Kendall, B.E., Nisbet, R.M., Briggs, C.J., McCauley, E. Bolser, R. (2002). Single-species models for many-species food webs. Nature, 417, 541 543.
28. NERC Centre for Population Biology (1999). The Global Population Dynamics Database. Available at: http://www.sw.ic.ac.uk/cpb/cpb/gpdd.html.
29. Nicholson, A.J. (1933). The balance of animal populations. J. Anim. Ecol., 2, 132 178.
30. Nicholson, A.J. (1954). An outline of the dynamics of animal populations. Aust. J. Zool, 2, 9 65.
31. Osenberg, C.W., St Mary, C.M., Schmitt, R.J., Holbrook, S.J., Chesson, P. Byrne, B. (2002). Rethinking ecological inference: density dependence in reef fishes. Ecol. Lett., 5, 715 721.
32. Pollard, E., Lakhani, K.H. Rothery, P. (1987). The detection of density-dependence from a series of annual censuses. Ecology, 68, 2046 2055.
33. Reddingius, J. Den Boer, P.J. (1989). On the stabilization of animal numbers. Problems of testing. 1. Power estimates and estimation errors. Oecologia, 78, 1 8.
34. Reinsel, G.C. (1997). Elements of Multivariate Time Series Analysis, 2nd edn. Springer, New York.
35. Rothery, P., Newton, I., Dale, L. Wesolowski, T. (1997). Testing for density dependence allowing for weather effects. Oecologia, 112, 518 523.
36. Royama, T. (1992). Analytical Population Dynamics. Chapman and Hall, London.
37. Saether, B.E., Lande, R., Engen, S., Weimerskirch, H., Lillegard, M., Altwegg, R. et al. (2005). Generation time and temporal scaling of bird population dynamics. Nature, 436, 99 102.
38. Shenk, T.M., White, G.C. Burnham, K.P. (1998). Sampling variance effects on detecting density dependence from temporal trends in natural populations. Ecol. Monogr., 68, 445 463.
39. Sibly, R.M., Barker, D., Denham, M.C., Hone, J. Pagel, M. (2005). On the regulation of populations of mammals, birds, fish, and insects. Science, 309, 607 610.
40. Sibly, R.M., Barker, D., Hone, J. Pagel, M. (2007). On the stability of populations of mammals, birds, fish and insects. Ecol. Lett., 10, 970 976.
41. Solbreck, C. Ives, A.R. (2007). Density dependence vs. independence, and irregular population dynamics of a swallow-wort fruit fly. Ecology, 88, 1466 1475.
42. Stark, J. (1999). Delay embeddings for forced systems. I. Deterministic forcing. J. Nonlinear Sci., 9, 255 332.
43. Stark, J. (2000). Observing complexity, seeing simplicity. Philos. Transact. R. Soc. Lond. A Math. Phys. Eng. Sci., 358, 41 61.
44. Staudenmayer, J. Buonaccorsi, J.R. (2005). Measurement error in linear autoregressive models. J. Am. Stat. Assoc., 100, 841 852. (Pubitemid 41276331)
45. Stuart, A. Ord, J.K. (1987). Kendall's Advanced Theory of Statistics, Vol. 1 : Distribution Theory. Oxford University Press, New York, NY.
46. Turchin, P. (1990). Rarity of density dependence or population regulation with lags?. Nature, 344, 660 663.
47. Turchin, P. (1995). Population regulation: old arguments and a new synthesis. In : Population Dynamics: New Approaches and Synthesis (eds Cappuccino, N. Price, P.W.). Academic Press, San Diego, pp. 19 40.
48. Turchin, P. (2003). Dynamical effects of plant quality and parasitism on population cycles of larch budmoth. Ecology, 84, 1207 1214.
49. Turchin, P. Berryman, A.A. (2000). Detecting cycles and delayed density dependence: a comment on Hunter & Price (1998). Ecol. Entomol., 25, 119 121.
50. United States Forest Service (2007). Gypsy Moth Digest. Available at: http://www.na.fs.fed.us/fhp/gm/defoliation/index.shtm.
51. de Valpine, P. Hastings, A. (2002). Fitting population models incorporating process noise and observation error. Ecol. Monogr., 72, 57 76.
52. Woiwod, I.P. Hanski, I. (1992). Patterns of density dependence in moths and aphids. J. Anim. Ecol., 61, 619 629.
53. Wold, H. (1938). A Study in the Analysis of Stationary Time Series. Almqvist & Wiksells, Uppsala, Sweden.
54. Yao, Q.W. Tong, H. (1994). On prediction and chaos in stochastic systems. Philos. Transact. R. Soc. Lond. A Math. Phys. Eng. Sci., 348, 357 369.
55. Zeng, Z., Nowierski, R.M., Taper, M.L., Dennis, B. Kemp, W.P. (1998). Complex population dynamics in the real world: modeling the influence of time-varying parameters and time lags. Ecology, 79, 2193 2209.