Quantitative Considerations in Mudflat Ecology

  • Peter G. BeningerEmail author
  • Inna Boldina
Part of the Aquatic Ecology Series book series (AQEC, volume 7)


Basic themes relevant to quantitative mudflat ecology are presented and explored, with examples: classical and informed-probability statistics, spatial and temporal analyses, allometric modelling, replication and pseudoreplication. The common thread is the necessity of evaluating evidence to arrive at a judgement of scientific credibility.


  1. Akaike H (1981) Likelihood of a model and information criteria. J Econ 16:3–14CrossRefGoogle Scholar
  2. Allen AP, Gillooly JF, Brown JH (2005) Linking the global carbon cycle to individual metabolism. Funct Ecol 19:202–213CrossRefGoogle Scholar
  3. Andrades R, Joyeux J-C, Andrade JM, Machado FS, Reis-Filho JA, Macieira RM, Giarrizzo T (2018) Filling the gap: length-weight and lengthlength relationships of intertidal endemic fishes of the Brazilian Province Oceanic Islands. J Appl Ichthyol 34(3):720–723CrossRefGoogle Scholar
  4. Aspden RJ, Vardy S, Perkins RG, Davidson IR, Bates R, Paterson DM (2004) The effects of clam fishing on the properties of surface sediments in the lagoon of Venice, Italy. Hydrol Earth Syst Sci 8:160–169CrossRefGoogle Scholar
  5. Bachmaier M, Backes M (2008) Variogram or semivariogram? Understanding the variances in a variogram. Precis Agric 9:173–175CrossRefGoogle Scholar
  6. Ballantyne F (2013) Evaluating model fit to determine if logarithmic transformations are necessary in allometry: a comment on the exchange between Packard (2009) and Kerkhoff and Enquist (2009). J Theor Biol 317:418–421PubMedCrossRefPubMedCentralGoogle Scholar
  7. Beninger PG, Boldina I (2014) Fine-scale spatial distribution of the temperate infaunal bivalve Tapes (=Ruditapes) philippinarum (Adams and Reeve) on fished and unfished intertidal mudflats. J Exp Mar Biol Ecol 457:128–134CrossRefGoogle Scholar
  8. Beninger PG, Boldina I, Katsanevakis S (2012) Strengthening statistical usage in marine ecology. J Exp Mar Biol Ecol 426-427:97–108CrossRefGoogle Scholar
  9. Blauw A, Benincà E, Laane R, Greenwood N, Huisman J (2012) Dancing with the tides: fluctuations of coastal phytoplankton orchestrated by different oscillatory modes of the tidal cycle. PLoS One 7(11):e49319. Scholar
  10. Boardman RC, Vann JE (2011) A review of the application of copulas to improve modelling of nonbigaussian bivariate relationships (with an example using geological data). In: Proceedings of the19th international congress on modelling and simulation. The Modelling and Simulation Society of Australia and NZ, Perth, pp 627–633Google Scholar
  11. Boldina I, Beninger PG (2013) Fine-scale spatial structure of the exploited infaunal bivalve Cerastoderma edule on the French Atlantic coast. J Sea Res 76:193–200CrossRefGoogle Scholar
  12. Boldina I, Beninger PG (2014) Fine-scale spatial distribution of the common lugworm Arenicola marina, and effects of intertidal clam fishing. Estuar Coast Shelf Sci 143:32–40CrossRefGoogle Scholar
  13. Boldina I, Beninger PG, Le Coz M (2014) Effect of long-term mechanical perturbation on intertidal soft-bottom meiofunal community spatial structure. J Sea Res 85:85–91CrossRefGoogle Scholar
  14. Boldina I, Beninger PG (2016) Strengthening statistical usage in marine ecology: linear regression. J Exp Mar Biol Ecol 474:81–91CrossRefGoogle Scholar
  15. Bradshaw GA, Spies TA (1992) Characterizing canopy gap structure in forests using wavelet analysis. J Ecol 80:205–215CrossRefGoogle Scholar
  16. Broughton SA, Bryan KM (2009) Discrete Fourier analysis and wavelets. Applications to signal and image processing. Wiley, Hoboken, 360 pGoogle Scholar
  17. Brown B, Herbert Wilson Jr W (1997) The role of commercial digging of mudflats as an agent for change of infaunal intertidal populations. J Exp Mar Biol Ecol 218:49–61CrossRefGoogle Scholar
  18. Burnham K, Anderson D (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer, New York, 514 pGoogle Scholar
  19. Carpenter SR (1990) Large-scale perturbations: opportunities for innovation. Ecology 71:2038–2043CrossRefGoogle Scholar
  20. Carpenter SR (1998) The need for large-scale experiments to assess and predict the response of ecosystems to perturbation. In: Groffman P (ed) Successes, limitations, and frontiers in ecosystem science. Springer, New York, pp 287–312CrossRefGoogle Scholar
  21. Carrière JF (2006) Copulas. In: Sundt B, Teugels JL (eds) Encyclopedia of actuarial science. Wiley, Chichester, 1944 pGoogle Scholar
  22. Chapman MG, Tolhurst TJ, Murphy RJ, Underwood AJ (2010) Complex and inconsistent patterns of variation in benthos, micro-algae and sediment over multiple spatial scales. Mar Ecol Prog Ser 398:33–47CrossRefGoogle Scholar
  23. Chatfield C (2016) The analysis of time series: an introduction, 6th edn. Chapman & Hall/CRC, Boca Raton, 333 pGoogle Scholar
  24. Christensen R (2005) Testing Fisher, Neyman, Pearson, and Bayes. Am Stat 59:121–126CrossRefGoogle Scholar
  25. Cleary DR (2003) An examination of scale of assessment, logging and ENSO-induced fires on butterfly diversity in Borneo. Oecologia 135:313–321PubMedCrossRefPubMedCentralGoogle Scholar
  26. Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London, 266 pGoogle Scholar
  27. Cottenie K, De Meester L (2003) Comment to Oksanen (2001): reconciling Oksanen (2001) and Hurlbert (1984). Oikos 100:394–396CrossRefGoogle Scholar
  28. Colegrave N, Ruxton GD (2018) Using biological insight and pragmatism when thinking about pseudoreplication. Trends Ecol Evol 33:28–35PubMedCrossRefPubMedCentralGoogle Scholar
  29. Cressie N (2015) Statistics for spatial data, Revised edition. Wiley-Interscience, New York, 928 pGoogle Scholar
  30. Cressie NK, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, Hoboken, 624 pGoogle Scholar
  31. Cryer JD, Chan KS (2008) Time series regression models. In: Cryer JD, Chan KS (eds) Time series analysis with applications in R. Springer, New York, pp 249–276CrossRefGoogle Scholar
  32. Dale MRT, Fortin MJ (2009) Spatial autocorrelation and statistical tests: some solutions. J Agric Biol Environ Stat 14:188–206CrossRefGoogle Scholar
  33. Dale MRT, Fortin M-J (2014) Spatial analysis: a guide for ecologists, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  34. Dale MRT, Mah M (1998) The use of wavelets for spatial pattern analysis in ecology. J Veg Sci 9:805–814CrossRefGoogle Scholar
  35. Dale MRT, Dixon P, Fortin MJ, Legendre P, Myers DE, Rosenberg MS (2002) Conceptual and mathematical relationships among methods for spatial analysis. Ecography 25:558–577CrossRefGoogle Scholar
  36. Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math 41:909–996CrossRefGoogle Scholar
  37. Davies GM, Gray A (2015) Don’t let spurious accusations of pseudoreplication limit our ability to learn from natural experiments (and other messy kinds of ecological monitoring). Ecol Evol 5:5295–5304PubMedPubMedCentralCrossRefGoogle Scholar
  38. de la Peña VH, Ibragimov R, Sharakhmetov S (2006) Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series. Lecture Notes-Monograph Series. The Second Erich L. Lehmann Symposium Institute of Mathematical Statistics, Optimality, pp 183–209Google Scholar
  39. Diggle PJ (2014) Statistical analysis of spatial and spatio-temporal point patterns. CRC Press, Boca Raton, 268 pGoogle Scholar
  40. Dungan JL, Perry JN, Dale MRT, Legendre P, Citron-Pousty S, Fortin MJ, Jakomulska A, Miriti M, Rosenberg MS (2002) A balanced view of scale in spatial statistical analysis. Ecography 25:626–640CrossRefGoogle Scholar
  41. Efron B (2013) Bayes’ theorem in the 21st century. Science 340:1177–1178PubMedCrossRefPubMedCentralGoogle Scholar
  42. Elliott KH, Bull RD, Gaston AJ, Davoren GK (2009) Underwater and above-water search patterns of an Arctic seabird: reduced searching at small spatiotemporal scales. Behav Ecol Sociobiol 63:1773–1785CrossRefGoogle Scholar
  43. Falk D, Lepore F, Noe A (2012) The cerebral cortex of Albert Einstein: a description and preliminary analysis of unpublished photographs. Brain 136(Pt 4):1304–1327. Scholar
  44. Farrell-Gray CC, Gotelli NJ (2005) Allometric exponents support a 3/4-power scaling law. Ecology 86:2083–2087CrossRefGoogle Scholar
  45. Ferriere R, Cazelles B (1999) Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80:1505–1521CrossRefGoogle Scholar
  46. Finkenstadt B, Held L, Isham V (2006) Statistical methods for spatio-temporal systems. CRC Press, Boca Raton, 286 pCrossRefGoogle Scholar
  47. Flanagan AM, Flood RD, Frisk MG, Garza CD, Lopez GR, Maher NP, Cerrato RM (2018) The relationship between observational scale and explained variance in benthic communities. PLoS One 13:e0189313. Scholar
  48. Flandrin P, Gonçalves P, Abry P (2010) Scale Invariance and Wavelets. In: Abry P, Gonçalves P, Véhel JL (eds) Scaling. Fractals and Wavelets, Wiley Online Library, pp 71–102Google Scholar
  49. Forstmeier W, Wagenmakers EJ, Parker TH (2016) Detecting and avoiding likely false-positive findings—a practical guide. Biol Rev 92:1941–1968. Scholar
  50. Fortin MJ, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, CambridgeGoogle Scholar
  51. Fortin MJ, Dale M (2009) Spatial autocorrelation in ecological studies: a legacy of solutions and myths. Geogr Anal 41:392–397CrossRefGoogle Scholar
  52. Fortin MJ, Jacquez GM (2000) Randomization tests and spatially auto-correlated data. Bull Ecol Soc Am 81:201–205Google Scholar
  53. Fortin MJ, Drapeau P, Legendre P (1989) Spatial autocorrelation and sampling design in plant ecology. Vegetatio 83:209–222CrossRefGoogle Scholar
  54. Fortin MJ, Dale MRT, ver Hoef J (2002) Spatial analysis in ecology. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics. Wiley, Chichester, pp 2051–2058Google Scholar
  55. Fortin MJ, James PMA, MacKenzie A, Melles SJ, Rayfield B (2012) Spatial statistics, spatial regression, and graph theory in ecology. Spatial Stat 1:100–109CrossRefGoogle Scholar
  56. Getis A (2007) Reflections on spatial autocorrelation. Reg Sci Urban Econ 37:491–496CrossRefGoogle Scholar
  57. Getis A (2008) A history of the concept of spatial autocorrelation: a geographer’s perspective. Geogr Anal 40:297–309CrossRefGoogle Scholar
  58. Getis A (2010) Spatial Autocorrelation. In: Fischer MM, Getis A (eds) Handbook of applied spatial analysis: software tools, methods and applications. Springer, Berlin, pp 255–278CrossRefGoogle Scholar
  59. Glover DM, Jenkins WJ, Doney SC (2011) Modeling methods for marine science. Cambridge University Press, Cambridge, 588 pCrossRefGoogle Scholar
  60. Gouhier T (2014) Biwavelet: Conduct univariate and bivariate wavelet analyses (Version 0.14).
  61. Greig-Smith P (1952) The use of random and contiguous quadrats in the study of the structure of plant communities. Ann Bot 16:293–316CrossRefGoogle Scholar
  62. Grinsted A, Moore JC, Jevrejeva S (2004) Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process Geophys 11:561–566CrossRefGoogle Scholar
  63. Haining R (2003) Spatial data analysis: theory and practice. Cambridge University Press, Cambridge, 452 pCrossRefGoogle Scholar
  64. Harte J (2011) Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press, New York, 256 pCrossRefGoogle Scholar
  65. Hassler SK, Lark RM, Milne AE, Elsenbeer H (2011) Exploring the variation in soil saturated hydraulic conductivity under a tropical rainforest using the wavelet transform. Eur J Soil Sci 62:891–901CrossRefGoogle Scholar
  66. Hawkins BA (2012) Eight (and a half) deadly sins of spatial analysis. J Biogeogr 39:1–9CrossRefGoogle Scholar
  67. Hayes AF, Cai L (2007) Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation. Behav Res Methods 39:709–722PubMedCrossRefPubMedCentralGoogle Scholar
  68. Heffner RA, Butler MJ, Reilly CK (1996) Pseudoreplication revisited. Ecology 77:2558–2562CrossRefGoogle Scholar
  69. Hewitt C, Campbell ML, Davidson AD (2016) Deciphering p-values: beware false certainty. Science 353:551PubMedCrossRefPubMedCentralGoogle Scholar
  70. Hixon MA, Tissot BN (2007) Comparison of trawled vs untrawled mud seafloor assemblages of fishes and macroinvertebrates at Coquille Bank, Oregon. J Exp Mar Biol Ecol 344:23–34CrossRefGoogle Scholar
  71. Hooker RH (1905) On the correlation of successive observations. J R Stat Soc 68:696–703CrossRefGoogle Scholar
  72. Hubbard R, Bayarri MJ (2003) Confusion over measures of evidence (p’s) versus errors (α’s) in classical statistical testing. Am Stat 57:171–182CrossRefGoogle Scholar
  73. Hurlbert SH (1984) Pseudoreplication and the design of ecological field experiments. Ecol Monogr 54:187–211CrossRefGoogle Scholar
  74. Hurlbert SH (2004) On misinterpretations of pseudoreplication and related matters: a reply to Oksanen. Oikos 104:591–597CrossRefGoogle Scholar
  75. Isler K, Barbour AD, Martin RD (2002) Line-fitting by rotation: a nonparametric method for bivariate allometric analysis. Biom J 44:289–304CrossRefGoogle Scholar
  76. James PMA, Fortin M-J (2013) Ecosystems and spatial patterns. In: Leemans R (ed) Ecological systems: selected entries from the encyclopedia of sustainability science and technology. Springer Science+Business Media, New York, pp 101–124CrossRefGoogle Scholar
  77. James PMA, Sturtevant BR, Townsend P, Wolter P, Fortin MJ (2011) Two-dimensional wavelet analysis of spruce budworm host basal area in the Border Lakes landscape. Ecol Appl 21:2197–2209PubMedCrossRefPubMedCentralGoogle Scholar
  78. Joe H (1994) Multivariate extreme-value distributions with applications to environmental data. Can J Stat 22:47–64CrossRefGoogle Scholar
  79. Johnson DH (1999) The insignificance of statistical significance testing. J Wildl Manag 63:763–772CrossRefGoogle Scholar
  80. Johnson VE (2013) Revised standards for statistical evidence. Proc Natl Acad Sci 110:19313–19317PubMedCrossRefPubMedCentralGoogle Scholar
  81. Katsanevakis S (2006) Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish Res 81:229–235CrossRefGoogle Scholar
  82. Katsanevakis S, Thessalou-Legaki M, Karlou-Riga C, Lefkaditou E, Dimitriou E, Verriopoulos G (2007a) Information-theory approach to allometric growth of marine organisms. Mar Biol 151:949–959CrossRefGoogle Scholar
  83. Katsanevakis S, Xanthopoulos J, Protopapas N, Verriopoulos G (2007b) Oxygen consumption of the semi-terrestrial crab Pachygrapsus marmoratus in relation to body mass and temperature: an information theory approach. Mar Biol 151:343–352CrossRefGoogle Scholar
  84. Kershaw KA (1973) Quantitative and dynamic plant ecology. Edward Arnold, London, pp 128–137Google Scholar
  85. Kershaw JJ, Richards E, McCarter J, Oborn S (2010) Spatially correlated forest stand structures: a simulation approach using copulas. Comput Electron Agric 74:120–128CrossRefGoogle Scholar
  86. Kim JM, Jung Y, Sungur EA, Han K, Park C, Sohn I (2008) A copula method for modeling directional dependence of genes. BioMed Central Bioinform 9:225Google Scholar
  87. Kleiber M (1932) Body size and metabolism. Hilgardia 6:315–353CrossRefGoogle Scholar
  88. Kotze DJ, Johnson CA, O'Hara RB, Vepsäläinen K, Fowler MS (2004) Editorial: The Journal of Negative Results in Ecology and Evolutionary Biology. J Negat Results Ecol Evol Biol 1:1–5Google Scholar
  89. Kraan C, van der Meer J, Dekinga A, Piersma T (2009) Patchiness of macrobenthic invertebrates in homogenized intertidal habitats: hidden spatial structure at a landscape scale. Mar Ecol Prog Ser 383:211–224CrossRefGoogle Scholar
  90. Lark RM, Webster R (2001) Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform. Eur J Soil Sci 52:547–562CrossRefGoogle Scholar
  91. Legendre P (1993) Spatial autocorrelation: trouble or new paradigm? Ecology 74:1659–1673CrossRefGoogle Scholar
  92. Legendre P, Fortin MJ (1989) Spatial pattern and ecological analysis. Vegetatio 80:107–138CrossRefGoogle Scholar
  93. Legendre P, Legendre L (2012) Numerical ecology. Developments in environmental modelling, vol 24, 3rd edn. Elsevier, Amsterdam, 1006 pGoogle Scholar
  94. Legendre P, Dale MRT, Fortin MJ, Gurevitch J, Hohn M, Myers D (2002) The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25:601–615CrossRefGoogle Scholar
  95. Legendre P, Fortin MJ, Borcard D (2015) Should the Mantel test be used in spatial analysis? Methods Ecol Evol 6:1239–1247CrossRefGoogle Scholar
  96. Long JS, Ervin LH (2000) Using heteroscedasticity consistent standard errors in the linear regression model. Am Stat 54:217–224Google Scholar
  97. Margolis L, Esch GW, Holmes JC, Kuris AM, Schad GA (1982) The use of ecological terms in parasitology. J Parasitol 68:131–133CrossRefGoogle Scholar
  98. Matheron G (1965) Les variables régionalisées et leur estimation: une application de la théorie des fonctions aléatoires aux sciences de la nature. Masson et Cie, Paris, 305 pGoogle Scholar
  99. McIntyre AD, Elliot JM, Ellis DV (1984) Introduction: design of sampling programmes. In: Holme NA, McIntyre AD (eds) Methods for the study of marine Benthos. Wiley-Blackwell, Oxford, pp 1–26Google Scholar
  100. Men W, Falk D, Sun T, Chen W, Li J, Yin D, Zang L, Fan M (2014) The corpus callosum of Albert Einstein’s brain: another clue to his high intelligence? Brain 137:e268. Scholar
  101. Mi X, Ren H, Ouyang Z, Wei W, Ma K (2005) The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns. Plant Ecol 179:1–19CrossRefGoogle Scholar
  102. Millar R, Anderson M (2004) Remedies for pseudoreplication. Fish Res 70:397–407CrossRefGoogle Scholar
  103. Moore J, Grinsted A, Jevrejeva S (2006) Is there evidence for sunspot forcing of climate at multi-year and decadal periods? Geophys Res Lett 33:1–5Google Scholar
  104. Murphy RJ, Tolhurst TJ, Chapman MG, Underwood AJ (2008) Spatial variation of chlorophyll on estuarine mudflats determined by field-based remote sensing. Mar Ecol Prog Ser 365:45–55CrossRefGoogle Scholar
  105. Nason GP, von Sachs R (1999) Wavelets in time series analysis. Philos Trans A 357:2511–2526CrossRefGoogle Scholar
  106. Newell RIE, Bayne BL (1980) Seasonal changes in the physiology, reproductive condition and carbohydrate content of the cockle Cardium (= Cerastoderma) edule (Bivalvia: Cardiidae). Mar Biol 56:11–19CrossRefGoogle Scholar
  107. Newman M (2005) Power laws, Pareto distributions and Zipf’s law. Contemp Phys 46:323–351CrossRefGoogle Scholar
  108. Oksanen L (2001) Logic of experiments in ecology: is pseudoreplication a pseudoissue? Oikos 94:27–38CrossRefGoogle Scholar
  109. Oksanen L (2004) The devil lies in details: reply to Stuart Hurlbert. Oikos 104:598–605CrossRefGoogle Scholar
  110. Oliver M, Webster R, Gerrard J (1989) Geostatistics in physical geography. Part I: Theory. Trans Inst Br Geogr 14:259–269CrossRefGoogle Scholar
  111. Owhadi H, Scovel C, Sullivan T (2015) Brittleness of Bayesian inference under finite information in a continuous world. Electron J Stat 9:1–79CrossRefGoogle Scholar
  112. Packard GC (2012a) Is non-loglinear allometry a statistical artifact? Biol J Linn Soc 107:764–773CrossRefGoogle Scholar
  113. Packard GC (2012b) Julian Huxley, Uca pugnax and the allometric method. J Exp Biol 125:569–573CrossRefGoogle Scholar
  114. Packard GC (2016) Relative growth by the elongated jaws of gars: a perspective on polyphasic loglinear allometry. J Exp Zool (Mol Devel Evol) 326B:168–175CrossRefGoogle Scholar
  115. Packard GC (2017) The essential role for graphs in allometric analysis. Biol J Linn Soc 120:468–473Google Scholar
  116. Packard GC, Birchard GF (2008) Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates. J Exp Biol 211:3581–3587PubMedCrossRefPubMedCentralGoogle Scholar
  117. Phillips F (2016) Deciphering p-values: defining significance. Science 353:551PubMedPubMedCentralGoogle Scholar
  118. Pitt WC, Ritchie ME (2002) Influence of prey distribution on the functional response of lizards. Oikos 96:157–163CrossRefGoogle Scholar
  119. Rouyer T, Fromenti JM, Ménard F, Cazelles B, Briand K, Pianet R, Planque B, Stenseth NC (2008a) Complex interplays among population dynamics, environmental forcing, and exploitation in fisheries. Proc Natl Acad Sci 105:5420–5425PubMedCrossRefPubMedCentralGoogle Scholar
  120. Rouyer T, Fromentin J, Stenseth N, Cazelles B (2008b) Analysing multiple time series and extending significance testing in wavelet analysis. Mar Ecol Prog Ser 359:1–23CrossRefGoogle Scholar
  121. Royall RM (2004) The likelihood paradigm for statistical evidence. In: Taper ML, Lele SR (eds) The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago, pp 119–152CrossRefGoogle Scholar
  122. Salvadori G, De Michele C (2007) On the use of copulas in hydrology: theory and practice. J Hydrol Eng 12:369–380CrossRefGoogle Scholar
  123. Santos MN, Gaspar MB, Vasconcelos P, Monteiro CC (2002) Weight–length relationships for 50 selected fish species of the Algarve coast (southern Portugal). Fish Res 59:289–295CrossRefGoogle Scholar
  124. Schefzik R, Thorarinsdottir TL, Gneiting T (2013) Uncertainty quantification in complex simulation models using ensemble copula coupling. Stat Sci 28:616–640CrossRefGoogle Scholar
  125. Schmidt T (2006) Coping with copulas. In: Rank J (ed) Copulas: from theory to application in finance. Risk Books, London, pp 3–34Google Scholar
  126. Serinaldi F, Grimaldi S, Abdolhosseini M, Corona P, Cimini D (2012) Testing copula regression against benchmark models for point and interval estimation of tree wood volume in beech stands. Eur J For Res 131:1313–1326CrossRefGoogle Scholar
  127. Seuront L (2010) Fractals and multifractals in ecology and aquatic science. CRC, Boca RatonGoogle Scholar
  128. Seuront L, Lagadeuc Y (2001) Multiscale patchiness of the calanoid copepod Temora longicornis in a turbulent coastal sea. J Plankton Res 23:1137–1145CrossRefGoogle Scholar
  129. Seuront L, Spilmont N (2002) Self-organized criticality in intertidal microphytobenthos patch patterns. Phys A 313:513–539CrossRefGoogle Scholar
  130. Sheng Y (2010) Wavelet transform. In: Poularikas AD (ed) Transforms and applications handbook. CRC Press, Boca Raton, p 911Google Scholar
  131. Shenko AN, Bien WF, Spotila JR, Avery HW (2012) Effects of disturbance on small mammal community structure in the New Jersey Pinelands, USA. Integr Zool 7:16–29PubMedCrossRefPubMedCentralGoogle Scholar
  132. Shumway RH, Stoffer DS (2011) Time series analysis and its applications with R examples, 3rd edn. Springer, New York, 596 pCrossRefGoogle Scholar
  133. Sokal RR, Oden NL (1978a) Spatial autocorrelation in biology: 1. Methodology. Biol J Linn Soc 10:199–228CrossRefGoogle Scholar
  134. Sokal RR, Oden NL (1978b) Spatial autocorrelation in biology: 2. Some biological implications and four applications of evolutionary and ecological interest. Biol J Linn Soc 10:229–249CrossRefGoogle Scholar
  135. Sousa T, Domingos T, Kooijman SALM (2008) From empirical patterns to theory: a formal metabolic theory of life. Philos Trans R Soc B Biol Sci 363:2453–2464CrossRefGoogle Scholar
  136. Southwood TRE, Henderson PA (2000) Ecological methods. Wiley-Blackwell, Oxford, 592 pGoogle Scholar
  137. Student (1914) The elimination of spurious correlation due to position in time or space. Biometrika 10:179–180CrossRefGoogle Scholar
  138. Stumpf MPH, Porter MA (2012) Critical truths about power laws. Science 335:665–666PubMedCrossRefPubMedCentralGoogle Scholar
  139. Sutherland WJ (1982) Spatial variation in the predation of cockles by oystercatchers at Traeth Melynog, Anglesey. II. The pattern of mortality. J Anim Ecol 51:491–500CrossRefGoogle Scholar
  140. Taper ML, Ponciano JM (2016) Evidential statistics as a statistical modern synthesis to support 21st science. Popul Ecol 58:9–29CrossRefGoogle Scholar
  141. Thrush SF, Pridmore RD, Hewitt JE (1994) Impacts on soft-sediment macrofauna: the effects of spatial variation on temporal trends. Ecol Appl 4:31–41CrossRefGoogle Scholar
  142. Tjørve E (2009) Shapes and functions of species–area curves (II): a review of new models and parameterizations. J Biogeogr 36:1435–1445CrossRefGoogle Scholar
  143. Tobler WR (1970) A computer movie simulating urban growth in the Detroit region. Econ Geogr 46:234–240CrossRefGoogle Scholar
  144. Torrence C, Compo GP (1998) A practical puide to wavelet analysis. Bull Am Meteorol Soc 79:61–78CrossRefGoogle Scholar
  145. Wang M, Upadhyay A, Zhang L (2010) Trivariate distribution modeling of tree diameter, height, and volume. For Sci 56:290–300Google Scholar
  146. West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126CrossRefGoogle Scholar
  147. White CR, Kearney MR, Matthews PG, Kooijman SA, Marshall DJ (2011) A manipulative test of competing theories for metabolic scaling. Am Nat 178:746–754PubMedCrossRefPubMedCentralGoogle Scholar
  148. Xiao X, White E, Hooten M, Durham S (2011) On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology 92:1887–1894PubMedCrossRefPubMedCentralGoogle Scholar
  149. Zeileis A, Grothendieck G (2005) Zoo: S3 Infrastructure for regular and irregular time series. J Stat Softw 14:1–27CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire de Biologie Marine, MMS, Faculté des SciencesUniversité de NantesNantesFrance

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