Theoretical Ecology

, Volume 9, Issue 2, pp 129–148 | Cite as

An updated perspective on the role of environmental autocorrelation in animal populations

  • Jake M. Ferguson
  • Felipe Carvalho
  • Oscar Murillo-García
  • Mark L. Taper
  • José M. Ponciano
ORIGINAL PAPER

Abstract

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study, we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.

Keywords

Environmental variation Time series Autocorrelation Extinction risk Environmental tracking 

References

  1. Abbott KC, Ripa J, Ives AR (2009) Environmental variation in ecological communities and inferences from single-species data. Ecology 90(5):1268–1278CrossRefPubMedGoogle Scholar
  2. Akçakaya H, Halley J, Inchausti P (2003) Population-level mechanisms for reddened spectra in ecological time series. J Anim Ecol 72(4):698–702CrossRefGoogle Scholar
  3. Amarasekare P, Savage V (2012) A framework for elucidating the temperature dependence of fitness. Am Nat 179(2):178–191CrossRefPubMedGoogle Scholar
  4. Andrewartha HG, Birch LC (1954) The distribution and abundance of animals. University of Chicago Press, ChicagoGoogle Scholar
  5. Ariño A, Pimm S (1995) On the nature of population extremes. Evol Ecol 9:429–443CrossRefGoogle Scholar
  6. Austin M (2007) Species distribution models and ecological theory: a critical assessment and some possible new approaches. Ecol Model 200(1–2):1–19CrossRefGoogle Scholar
  7. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of the 1/f noise. Phys Rev Lett 59(4):381–384CrossRefPubMedGoogle Scholar
  8. Box G, Jenkins G, Reinsel G (2011) Time series analysis: forecasting and control. Wiley, New YorkGoogle Scholar
  9. Brännström A, Sumpter DJT (2005) The role of competition and clustering in population dynamics. Proc R Soc B Biol Sci 272(1576):2065–2072CrossRefGoogle Scholar
  10. Caswell H, Cohen JE (1995) Red, White and Blue: environmental Variance spectra and coexistence in metapopulations. J Theor Biol 176:301–316CrossRefGoogle Scholar
  11. Cohen J (1995) Unexpected dominance of high frequencies in chaotic nonlinear population models. Nature 378(7):610–612CrossRefPubMedGoogle Scholar
  12. Cohen J, Newman C, Cohen A, Petchey O L, Gonzalez A (1999) Spectral mimicry: a method of synthesizing matching time series with different Fourier spectra. Circuits Syst Signal Process 18(3):431–442CrossRefGoogle Scholar
  13. Cuddington K, Yodzis P (1999) Black noise and population persistence. Proc R Soc B Biol Sci 266:969–973CrossRefGoogle Scholar
  14. Cyr H (1997) Does inter-annual variability in population density increase with time? Oikos 79(3):549–558CrossRefGoogle Scholar
  15. Davidson J, Andrewartha H (1948) The influence of rainfall, evaporation and atmospheric temperature on fluctuations in the size of a natural population of Thrips imaginis (Thysanoptera). J Anim Ecol 17(2):200–222CrossRefGoogle Scholar
  16. de Valpine P, Hastings A (2002) Fitting population models incorporating process noise and observation error. Ecol Monogr 72(1): 57CrossRefGoogle Scholar
  17. Dennis B, Costantino R (1988) Analysis of steady-state populations with the gamma abundance model: application to Tribolium. Ecology 69(4):1200–1213CrossRefGoogle Scholar
  18. Dennis B, Otten MRM (2000) Joint effects of density dependence and rainfall on abundance of San Joaquin kit fox. J Wildl Manag 64(2):388–400CrossRefGoogle Scholar
  19. Dennis B, Ponciano JM, Lele SR, Taper ML, Staples DF (2006) Estimating density dependence, process noise, and observation error. Ecol Monogr 76(3):323–341CrossRefGoogle Scholar
  20. Engen S, Be Sæther, Armitage K, Blumstein DT, Clutton-Brock T, Dobson F, Festa-Bianchet M, Oli MK, Ozgul A (2013) Estimating the effect of temporally autocorrelated environments on the demography of density independent age structured populations. Methods Ecol Evol 4:573–584CrossRefGoogle Scholar
  21. Farrior C, Tilman D, Dybzinski R, Reich P, Levin S, Pacala S (2013) Resource limitation in a competitive context determines complex plant responses to experimental resource additions. Ecology 94(11):2505–2517CrossRefPubMedGoogle Scholar
  22. Ferguson JM, Ponciano JM (2014) Predicting the process of extinction in experimental microcosms and accounting for interspecific interactions in single-species time series. Ecol Lett 17:251– 259CrossRefPubMedPubMedCentralGoogle Scholar
  23. Ferguson JM, Ponciano JM (2015) Evidence and implications of higher-order scaling in the environmental variation of animal population growth. Proc Natl Acad Sci 112(9):2782–2787CrossRefPubMedPubMedCentralGoogle Scholar
  24. Fowler MS, Ruokolainen L (2013) Confounding environmental colour and distribution shape leads to underestimation of population extinction risk. PLoS One 8(2):e55855Google Scholar
  25. Garcia-Carreras B, Reuman D (2011) An empirical link between the spectral colour of climate and the spectral colour of field populations in the context of climate change. J Anim Ecol 80:1042–1048CrossRefPubMedGoogle Scholar
  26. Geritz SA, Kisdi E (2004) On the mechanistic underpinning of discrete-time population models with complex dynamics. J Theor Biol 228(2):261–269CrossRefPubMedGoogle Scholar
  27. Gonzalez A, Holt RD (2002) The inflationary effects of environmental fluctuations in source–sink systems. Proc Natl Acad Sci 99(23):14:872–14:877CrossRefGoogle Scholar
  28. Goodman D (1987) The demography of chance extinction. In: Soule ME (ed) Viable populations for conservation. Cambridge University Press, Cambridge, pp 11–34CrossRefGoogle Scholar
  29. Halley JM (1996) Ecology, evolution and-noise. Trends Ecol Evol 11(1):33–37CrossRefPubMedGoogle Scholar
  30. Halley JM, Inchausti P (2004) The increasing importance of 1/f-noises as models of ecological variability. Fluct Noise Lett 4(2):R1– R26CrossRefGoogle Scholar
  31. Heino M, Sabadell M (2003) Influence of coloured noise on the extinction risk in structured population models. Biodivers Conserv 110(3):325Google Scholar
  32. Hilfinger A, Paulsson J (2011) Separating intrinsic from extrinsic fluctuations in dynamic biological systems. Proc Natl Acad Sci USA 12(29):167–172Google Scholar
  33. Holt R (2009) Bringing the Hutchinsonian niche into the 21st century: ecological and evolutionary perspectives. Proc Natl Acad Sci USA 106(2):19:659–19:665CrossRefGoogle Scholar
  34. Holt RD, Barfield M, Gonzalez A (2003) Impacts of environmental variability in open populations and communities: “inflation” in sink environments. Theor Popul Biol 64(3):315–330CrossRefPubMedGoogle Scholar
  35. Hooker HD (1917) Liebig’s law of the minimum in relation to general biological problems. Science 46(1183):197CrossRefPubMedGoogle Scholar
  36. Hosking J (1981) Fractional differencing. Biometrika 68(1):165– 176CrossRefGoogle Scholar
  37. Huey R, Stevenson R (1979) Integrating thermal physiology and ecology of ectotherms: a discussion of approaches. Am Zool 366:357–366CrossRefGoogle Scholar
  38. Inchausti P, Halley J (2001) Investigating long-term ecological variability using the global population dynamics database. Science 293(5530):655–657CrossRefPubMedGoogle Scholar
  39. Inchausti P, Halley J (2002) The long-term temporal variability and spectral colour of animal populations. Evol Ecol Res 4:1033–1048Google Scholar
  40. Johnson J (1925) The Schottky effect in low frequency circuits. Phys Rev 541(1918):71–85CrossRefGoogle Scholar
  41. Jonzén N, Lundberg P (2002) The irreducible uncertainty of the demography–environment interaction in ecology. Proc R Soc B Biol Sci 269:221–225CrossRefGoogle Scholar
  42. Jonzén N, Pople T, Knape J, Sköld M (2010) Stochastic demography and population dynamics in the red kangaroo Macropus rufus. J Anim Ecol 79(1):109–116CrossRefPubMedGoogle Scholar
  43. Kaitala V, Ylikarjula J, Ranta E, Lundberg P (1997) Population dynamics and the colour of environmental noise. Proc R Soc B Biol Sci 264(1384):943–948CrossRefGoogle Scholar
  44. Kamenev A, Meerson B, Shklovskii B (2008) How colored environmental noise affects population extinction. Phys Rev Lett 101(268103)Google Scholar
  45. Kearney M, Phillips BL, Tracy CR, Christian KA, Betts G, Porter WP (2008) Modelling species distributions without using species distributions: the cane toad in Australia under current and future climates. Ecography 31:423–434CrossRefGoogle Scholar
  46. Knape J, de Valpine P (2010) Effects of weather and climate on the dynamics of animal population time series. Proc R Soc B Biol Sci 278(1708):985CrossRefGoogle Scholar
  47. Knape J, de Valpine P (2011) Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance? Ecol Lett 15(1):17–23CrossRefPubMedGoogle Scholar
  48. Laakso J, Kaitala V, Ranta E (2001) How does environmental variation translate into biological processes? Oikos 92(1):119–122CrossRefGoogle Scholar
  49. Laakso J, Kaitala V, Ranta E (2003a) Non-linear biological responses to disturbance: consequences on population dynamics. Ecol Model 162(3):247–258CrossRefGoogle Scholar
  50. Laakso J, Löytynoja K, Kaitala V (2003b) Environmental noise and population dynamics of the ciliated protozoa Tetrahymena thermophila in aquatic microcosms. Oikos 102:663–671CrossRefGoogle Scholar
  51. Laakso J, Kaitala V, Ranta E (2004) Non-linear biological responses to environmental noise affect population extinction risk. Oikos 104:142–148CrossRefGoogle Scholar
  52. Lande R (1993) Risks of population extinction from demographic and environmental stochasticity and random catastrophes. Am Nat 142(6):911–927CrossRefGoogle Scholar
  53. Lewontin RC, Cohen D (1969) On population growth in a randomly varying environment. Proc Natl Acad Sci USA 62(4):1056–1060CrossRefPubMedPubMedCentralGoogle Scholar
  54. Lindén A, Knape J (2009) Estimating environmental effects on population dynamics: consequences of observation error. Oikos 118:675–680CrossRefGoogle Scholar
  55. Lindén A, Fowler M, Jonzén N (2013) Mischaracterising density dependence biases estimated effects of coloured covariates on population dynamics. Popul Ecol 55:183–192CrossRefGoogle Scholar
  56. Lögdberg F, Wennergren U (2012) Spectral color, synchrony, and extinction risk. Theor EcolGoogle Scholar
  57. Miramontes O, Rohani P (1998) Intrinsically generated coloured noise in laboratory insect populations. Proc R Soc B Biol Sci 265:785–792CrossRefGoogle Scholar
  58. Mode CJ, Jacobson ME (1987) A study of the impact of environmental stochasticity on extinction probabilities by Monte Carlo integration. Math Biosci 83(1):105–125CrossRefGoogle Scholar
  59. Montroll E, Shlesinger M (1982) On 1/f noise and other distributions with long tails. Proc Natl Acad Sci USA 79(10):3380–3383CrossRefPubMedPubMedCentralGoogle Scholar
  60. Morales JM (1999) Viability in a pink environment: why “white noise” models can be dangerous. Ecol Lett 2(4):228–232CrossRefGoogle Scholar
  61. Morris R (1959) Single-factor analysis in population dynamics. Ecology 40(4):580–588CrossRefGoogle Scholar
  62. Murdoch WW, Kendall BE, Nisbet RM, Briggs CJ, McCauley E, Bolser R (2002) Single-species models for many-species food webs. Nature 417(6888):541–543CrossRefPubMedGoogle Scholar
  63. NERC (2010) The Global Population Dynamics Database Version 2Google Scholar
  64. Petchey O (2000) Environmental colour affects aspects of single-species population dynamics. Proc R Soc B Biol Sci 267(1445):747–754CrossRefGoogle Scholar
  65. Petchey O, Gonzalez A, Wilson H (1997) Effects on population persistence: the interaction between environmental noise colour, intraspecific competition and space. Proc R Soc B 264:1841–1847CrossRefPubMedCentralGoogle Scholar
  66. Pike N, Tully T, Haccou P, Ferrière R (2004) The effect of autocorrelation in environmental variability on the persistence of populations: an experimental test. Proc R Soc Lond Ser B Biol Sci 271(1553):2143CrossRefGoogle Scholar
  67. Pimm SL, Redfearn A (1988) The variability of population densities. Nature 334:613–614CrossRefGoogle Scholar
  68. Pinheiro J, Bates D, DebRoy S, Sarkar D, R Development Core Team (2011) nlme: linear and nonlinear mixed effects modelsGoogle Scholar
  69. R Development Core Team (2012) R: a language and environment for statistical computingGoogle Scholar
  70. Ranta E, Lundberg P, Kaitala V, Laakso J (2000) Visibility of the environmental noise modulating population dynamics. Proc Biol Sci / The Royal Society 267(1455):1851–1856CrossRefGoogle Scholar
  71. Ratikainen II, Ja Gill, Gunnarsson TG, Sutherland WJ, Kokko H (2008) When density dependence is not instantaneous: theoretical developments and management implications. Ecol Lett 11(2):184–198PubMedGoogle Scholar
  72. Ricker W (1954) Stock and Recruitment. J Fish Res Board Can 11(5):559–623CrossRefGoogle Scholar
  73. Ripa J, Lundberg P (1996) Noise colour and the risk of population extinctions. Proc R Soc B Biol Sc 263(1377):1751–1753Google Scholar
  74. Rotenberg M (1987) Effect of certain stochastic parameters on extinction and harvested populations. J Theor Biol 124:455–471CrossRefGoogle Scholar
  75. Roughgarden J (1975) A simple model for population dynamics in stochastic environments. Am Nat 109 (970):713–736CrossRefGoogle Scholar
  76. Roy M, Holt RD, Barfield M (2005) Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks. Am Nat 166(2):246–261CrossRefPubMedGoogle Scholar
  77. Royama T (1977) Population persistence and density dependence. Ecol Monogr 47(1):1–35CrossRefGoogle Scholar
  78. Royama T (1981) Fundamental concepts and methodology for the analysis of animal population dynamics, with particular reference to univoltine species. Ecol Monogr 51(4):473–493CrossRefGoogle Scholar
  79. Royama T (1992) Analytical population dynamics. Chapman & Hall, LondonCrossRefGoogle Scholar
  80. Ruokolainen L, McCann K (2013) Environmental weakening of trophic interactions drives stability in stochastic food webs. J Theor Biol 339:36–46CrossRefPubMedGoogle Scholar
  81. Ruokolainen L, Fowler MS, Ranta E (2007) Extinctions in competitive communities forced by coloured environmental variation. Oikos 116:439–448CrossRefGoogle Scholar
  82. Ruokolainen L, Lindén A, Kaitala V, Fowler MS (2009) Ecological and evolutionary dynamics under coloured environmental variation. Trends Ecol Evol 24(10):555–563CrossRefPubMedGoogle Scholar
  83. Savage VM, Gillooly JF, Brown JH, West GB, Charnov EL (2004) Effects of body size and temperature on population growth. Am Nat 163(3):429–441CrossRefPubMedGoogle Scholar
  84. Schwager M, Johst K, Jeltsch F (2006) Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions. Am Nat 167(6):879–888CrossRefPubMedGoogle Scholar
  85. Shaffer M (1987) Minimum viable populations: coping with uncertainty. In: Soule M (ed) Viable populations for conservation, chap Minimum vi. Cambridge University Press, Cambridge, pp 69–86CrossRefGoogle Scholar
  86. Shumway R, Stoffer D (2006) Time series analysis and its applications. Springer, New YorkGoogle Scholar
  87. Sibly RM, Barker D, Denham MC, Hone J, Pagel M (2005) On the regulation of populations of mammals, birds, fish, and insects. Science 309(5734):607–610CrossRefPubMedGoogle Scholar
  88. Sibly RM, Barker D, Hone J, Pagel M (2007) On the stability of populations of mammals, birds, fish and insects. Ecol Lett 10:970–976CrossRefPubMedGoogle Scholar
  89. Staples DF, Taper ML, Dennis B (2004) Estimating population trend and process variation for PVA in the presence of sampling error. Ecology 85(4):923–929CrossRefGoogle Scholar
  90. Sugihara G (1995) From out of the blue. Nature 378(7):559–60CrossRefGoogle Scholar
  91. Swanson B (1998) Autocorrelated rates of change in animal populations and their relationship to precipitation. Conserv Biol 12(4):801–808CrossRefGoogle Scholar
  92. Taper M, Gogan P (2002) The northern Yellowstone elk: density dependence and climatic conditions. J Wildl Manag 66(1):106–122CrossRefGoogle Scholar
  93. Taper ML, Staples DF, Shepard BB (2008) Model structure adequacy analysis: selecting models on the basis of their ability to answer scientific questions. Synthese 163(3):357–370CrossRefGoogle Scholar
  94. Tuljapurkar S (1982) Population dynamics in variable environments. II. Correlated environments, sensitivity analysis and dynamics. Theor Popul Biol 140:114–140CrossRefGoogle Scholar
  95. Tuljapurkar S, Haridas CV (2006) Temporal autocorrelation and stochastic population growth. Ecol Lett 9(3):327–337CrossRefPubMedGoogle Scholar
  96. van de Pol M, Vindenes Y, Sæther BE, Engen S, Ens BJ, Oosterbeek K, Tinbergen JM (2011) Poor environmental tracking can make extinction risk insensitive to the colour of environmental noise. Proc R Soc B Biol Sci 278(1725):3713–3722CrossRefGoogle Scholar
  97. Vasseur DA, Yodzis P (2004) The color of environmental noise. Ecology 85(4):1146–1152CrossRefGoogle Scholar
  98. Veenstra JQ (2012) Persistence and anti-persistence: theory and software. PhD thesis, Western UniversityGoogle Scholar
  99. Wagenmakers EJ, Farrell S, Ratcliff R (2004) Estimation and interpretation of 1/f noise in human cognition. Psychon Bull Rev 11(4):579–615CrossRefPubMedPubMedCentralGoogle Scholar
  100. Wichmann M, Johst K, Moloney K, Wissel C, Jeltsch F (2003) Extinction risk in periodically fluctuating environments. Ecol Model 167:221–231CrossRefGoogle Scholar
  101. Wichmann MC, Johst K, Schwager M, Blasius B, Jeltsch F (2005) Extinction risk, coloured noise and the scaling of variance. Theor Popul Biol 68(1):29–40CrossRefPubMedGoogle Scholar
  102. Ziebarth NL, Abbott KC, Ives AR (2010) Weak population regulation in ecological time series. Ecol Lett 13(1):21–31CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jake M. Ferguson
    • 1
    • 2
  • Felipe Carvalho
    • 3
    • 7
  • Oscar Murillo-García
    • 4
    • 5
  • Mark L. Taper
    • 6
  • José M. Ponciano
    • 1
  1. 1.Department of BiologyUniversity of FloridaGainesvilleUSA
  2. 2.National Institute for Mathematical and Biological SynthesisUniversity of TennesseeKnoxvilleUSA
  3. 3.Program of Fisheries and Aquatic Sciences, School of Forest Resources and ConservationUniversity of FloridaGainesvilleUSA
  4. 4.School of Natural Resources and Environment, Wildlife Ecology and ConservationUniversity of FloridaGainesvilleUSA
  5. 5.Grupo de Investigación en Ecología Animal, Departamento de BiologíaUniversidad del ValleCaliColombia
  6. 6.Department of EcologyMontana State UniversityBozemanUSA
  7. 7.NOAA Pacific Islands Fisheries Science CenterHonoluluHawaii

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