A Review and Synthesis of Bivariate Non-Linear Models to Describe the Relative Variation of Ecological, Biological and Environmental Parameters

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• 作者：Vassilis G. Aschonitis (1)
  Giuseppe Castaldelli (1)
  Marco Bartoli (2)
  Elisa A. Fano (1)
  
  1. Department of Life Sciences and Biotechnology ; University of Ferrara ; Via L. Borsari 46 ; 44121 ; Ferrara ; Italy
  2. Department of Life Sciences ; University of Parma ; Viale G.P. Usberti 33/A ; 43124 ; Parma ; Italy
  
• 关键词：Bell ; shaped curves ; Sigmoid curves ; Double sigmoid curves ; Bilinear curves ; Periodical curves ; Relative variation
• 刊名：Environmental Modeling & Assessment
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：20
• 期：2
• 页码：169-182
• 全文大小：1,199 KB
• 参考文献：1. Chen, Y, Jackson, DA, Harvey, HH (1992) A comparison of von Bertalanffy and polynomial functions in modeling fish growth data. Canadian Journal of Fisheries and Aquatic Sciences 49: pp. 1228-1235 CrossRef
  2. Motulsky, HJ, Ransnas, LA (1987) Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB Journal 1: pp. 365-374
  3. Nocedal, J, Wright, S Numerical optimization. In: Glynn, P, Robinson, SM eds. (1999) Springer series in operations research. Springer, New Yorkpp. 634
  4. Cauchy, A. (1847). M茅thode g茅n茅rale pour la r茅solution des syst猫mes d鈥櫭﹒uations simultan茅es. / Compte Rendu des S茅ances de L鈥橝cad茅mie des Sciences XXV, Vol. A, 25, 536鈥?38.
  5. Meza, JC (2010) Steepest descent. WIREs Computational Statistics 2: pp. 719-722 CrossRef
  6. Levenberg, K (1944) A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics 2: pp. 164-168
  7. Marquart, DW (1963) An algorithm for least-squares estimation of non linear parameters. Journal of the Society for Industrial and Applied Mathematics 11: pp. 431-441 CrossRef
  8. Raes, D, Steduto, P, Hsiao, TC, Fereres, E (2009) AquaCrop鈥攖he FAO crop model to simulate yield response to water: II. Main algorithms and software description. Agronomy Journal 101: pp. 438-447 CrossRef
  9. Park, R.A., & Clough, J.S. (2004). AQUATOX (Release 2): modeling environmental fate and ecological effects in aquatic ecosystems. Technical documentation, EPA/823/R-04/002. Office of Water, United States Environmental Protection Agency, Washington, DC.
  10. Neitsch, S.L., Arnold, J.G., Kiniry, J.R., Srinivasan, R., & Williams, J.R. (2010). Soil and water assessment tool. Input/output file documentation. Version 2009 Agricultural Research Service, Texas, USA pp. 604
  11. Simunek, J, Genuchten, M, Sejna, M (2013) The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably saturated media, version 4.16 HYDRUS software Ser. Department of Environmental Sciences. University of California Riverside, Riverside
  12. Chen, WW, Niepel, M, Sorger, PK (2010) Classic and contemporary approaches to modeling biochemical reactions. Genes & Development 24: pp. 1861-1875 CrossRef
  13. Zeide, B (1993) Analysis of growth equations. Forest Science 39: pp. 594-616
  14. Castaldelli, G, Aschonitis, VG, Lanzoni, M, Gelli, N, Rossi, R, Fano, EA (2014) An update of the length-weight and length-age relationships of the European eel (Anguilla anguilla, Linnaeus 1758) in the Comacchio Lagoon, northeast Adriatic Sea, Italy. Journal of Applied Ichthyology 30: pp. 558-559 CrossRef
  15. Archontoulis, SV, Miguez, FE (2013) Nonlinear regression models and applications in agricultural research. Agronomy Journal 105: pp. 1-13 CrossRef
  16. Grimm, KJ, Ram, N, Hamagami, F (2011) Nonlinear growth curves in developmental research. Child Development 82: pp. 1357-1371 CrossRef
  17. Zwietering, MH, Jongenburger, I, Rombouts, FM, Riet, K (1990) Modeling of the bacterial growth curve. Applied and Environmental Microbiology 56: pp. 1875-1881
  18. Lopez, S, Prieto, M, Dijkstra, J, Dhanoa, MS, France, J (2004) Statistical evaluation of mathematical models for microbial growth. International Journal of Food Microbiology 96: pp. 289-300 CrossRef
  19. Aschonitis, VG, Lekakis, EH, Petridou, 螡C, Koukouli, SG, Pavlatou-Ve, A (2013) Nutrients fixation by algae and limiting factors of algal growth in flooded rice fields under semi-arid Mediterranean conditions: case study in Thessaloniki plain in Greece. Nutrient Cycling in Agroecosystems 96: pp. 1-13 CrossRef
  20. Oksanen, J, Minchin, PR (2002) Continuum theory revisited: what shape are species responses along ecological gradients?. Ecological Modelling 157: pp. 119-129 CrossRef
  21. H枚枚k, M, Li, J, Oba, N, Snowden, S (2011) Descriptive and predictive growth curves in energy system analysis. Natural Resources Research 20: pp. 103-116 CrossRef
  22. Lenzen, M, Dey, C, Foran, B, Widmer-Cooper, A, Ohlem眉ller, R, Williams, M, Wiedmann, T (2013) Modelling interactions between economic activity, greenhouse gas emissions, biodiversity and agricultural production. Environmental Modeling & Assessment 18: pp. 377-416 CrossRef
  23. Johansson, H, Brolin, AA, H氓kanson, L (2007) New approaches to the modelling of lake basin morphometry. Environmental Modeling & Assessment 12: pp. 213-228 CrossRef
  24. Seki, K (2007) SWRC fit鈥攁 nonlinear fitting program with a water retention curve for soils having unimodal and bimodal pore structure. Hydrology and Earth Systems Science Discussions 4: pp. 407-437 CrossRef
  25. Gatto, M, Rossi, R (1979) A method for estimating mortalities and abundances of the Valli di Comacchio eels. Memorie dell鈥橧stituto Italiano di Idrobiologia 37: pp. 107-114
  26. Yin, X, Kropff, MJ, McLaren, G, Visperas, RM (1995) A nonlinear model for crop development as a function of temperature. Agricultural and Forest Meteorology 77: pp. 1-16 CrossRef
  27. Polak, M, Tukaj, Z, Karcz, W (2011) Effect of temperature on the dose鈥搑esponse curves for auxin-induced elongation growth in maize coleoptile segments. Acta Physiologiae Plantarum 33: pp. 437-442 CrossRef
  28. Austin, MP (2002) Spatial prediction of species distribution: an interface between ecological theory and statistical modelling. Ecological Modelling 157: pp. 101-118 CrossRef
  29. Ivits, E, Buchanan, G, Olsvig-Whittaker, L, Cherlet, M (2011) European farmland bird distribution explained by remotely sensed phenological indices. Environmental Modeling and Assessment 16: pp. 385-399 CrossRef
  30. Pallavicini, P, Diaz-Fernandez, YA, Pasotti, L (2009) Smoothly shifting fluorescent windows: a tunable 鈥渙ff-on-off鈥?micellar sensor for pH. Analyst 134: pp. 2147-2152 CrossRef
  31. Kokkinou, M, Theodorou, L, Papamichail, G, Emmanuel, M (2012) Aspects on the catalysis of lipase from porcine pancreas (type VI-s) in aqueous media: development of ion-pairs. Brazilian Archives of Biology and Technology 55: pp. 231-236 CrossRef
  32. Lehman, JT, Botkin, DB, Likens, GE (1975) The assumptions and rationales of a computer model of phytoplankton population dynamics. Limnology and Oceanography 20: pp. 343-364 CrossRef
  33. J酶rgensen, SE, Mejer, H, Friis, M (1978) Examination of a lake model. Ecological Modelling 4: pp. 253-278 CrossRef
  34. J酶rgensen, SE (1976) A eutrophication model for a lake. Ecological Modelling 2: pp. 147-165 CrossRef
  35. Martin, S, Castets, M-D, Clavier, J (2006) Primary production, respiration and calcification of the temperate free-living coralline alga Lithothamnion corallioides. Aquatic Botany 85: pp. 121-128 CrossRef
  36. Peixoto, JP (1984) Physics of climate. Reviews of Modern Physics 56: pp. 365-429 CrossRef
  37. Shumway, RH, Stoffer, DS (2006) Time series analysis and its applications鈥攚ith R examples. Springer, NY
  38. Beek, CZ, Leijnse, H, Torfs, PJJF, Uijlenhoet, R (2011) Climatology of daily rainfall semi-variance in the Netherlands. Hydrology and Earth System Sciences 15: pp. 171-183 CrossRef
  39. Weibull, W (1951) A statistical distribution function of wide applicability. Journal of Applied Mechanics 18: pp. 293-297
  40. Steele, JH (1962) Environmental control of photosynthesis in the sea. Limnology and Oceanography 7: pp. 137-150 CrossRef
  41. Orr, AH (2006) The distribution of fitness effects among beneficial mutations in Fisher鈥檚 geometric model of adaptation. Journal of Theoretical Biology 238: pp. 279-285 CrossRef
  42. Zwiers, FW, Kharin, VV (1998) Changes in the extremes of the climate simulated by CCC GCM2 under CO2 doubling. Journal of Climate 11: pp. 2200-2222 CrossRef
  43. Thanutong, C, Dejdumrong, N (2013) A new scan conversion technique for B茅zier curves. Advanced Science Letters 19: pp. 1292-1295 CrossRef
  44. Dale, P. (2004). Introduction to mathematical techniques used in GIS. CRC Press, 224 pp. ISBN: 9780415334143.
  45. Michaelis, L, Menten, ML (1913) Die kinetik der invertinwirkung. Biochemische Zeitschrift 49: pp. 333-339
  46. Anastacio, PM, Nielsen, SN, Frias, AF, Marques, JC (1999) CRISP (crayfish and rice integrated system of production): 4. Modelling water, algae and oxygen dynamics. Ecological Modelling 123: pp. 29-40 CrossRef
  47. Kayombo, S, Mbwette, TSA, Katima, JHY, J酶rgensen, SE (2003) Effects of substrate concentrations on the growth of heterotrophic bacteria and algae in secondary facultative ponds. Water Research 37: pp. 2937-2943 CrossRef
  48. Antonopoulos, VZ (2010) Modelling of water and nitrogen balances in the ponded water and soil profile of rice fields in Northern Greece. Agricultural Water Management 98: pp. 321-330 CrossRef
  49. Kosugi, K (1994) Three-parameter lognormal distribution for soil water retention. Water Resources Research 30: pp. 891-901 CrossRef
  50. Goudriaan, J, Monteith, JL (1990) A mathematical function for crop growth based on light interception and leaf area expansion. Annals of Botany 66: pp. 695-701
  51. Goudriaan, J. (1994). Using the expolinear growth equation to analyze resource capture. In J.L. Monteith, R.K. Scott, M.H. Unsworth (eds.), Resource capture by crops (pp. 99鈥?00), Nottingham University Press.
  52. Yang, RC, Kozak, A, Smith, JHG (1978) The potential of Weibull-type functions as flexible growth curves. Canadian Journal of Forest Research 8: pp. 424-431 CrossRef
  53. Chalker, BE (1981) Simulating light-saturation curves for photosynthesis and calcification by reef-building corals. Marine Biology 63: pp. 135-141 CrossRef
  54. Genuchten, MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: pp. 892-898 CrossRef
  55. Richards, FJ (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10: pp. 290-301 CrossRef
  56. Bertalanffy, L (1957) Quantitative laws in metabolism and growth. Quarterly Review of Biology 32: pp. 217-231 CrossRef
  57. Yuancai, L, Maques, PC, Macedo, WF (1997) Comparison of Schnute鈥檚 and Bertalanffy-Richards鈥?growth functions. Forest Ecology and Management 96: pp. 283-288 CrossRef
  58. Erickson, GM, Rogers, KC, Yerby, SA (2001) Dinosaurian growth patterns and rapid avian growth rates. Nature 412: pp. 429-433 CrossRef
  59. Tj酶rve, E, Tj酶rve, KMC (2010) A unified approach to the Richards-model family for use in growth analyses: why we need only two model forms. Journal of Theoretical Biology 267: pp. 417-425 CrossRef
  60. Wang, X-S, Wu, J, Yang, Y (2012) Richards model revisited: validation by and application to infection dynamics. Journal of Theoretical Biology 313: pp. 12-19 CrossRef
  61. Verhulst, PF (1838) A note on population growth. Correspondence Mathematiques et Physiques 10: pp. 113-121
  62. Lipovetsky, S (2010) Double logistic curve in regression modeling. Journal of Applied Statistics 37: pp. 1785-1793 CrossRef
  63. Hau, B, Amorin, L, Bergamin-Filho, A (1993) Mathematical functions to describe disease progress curves of double sigmoid patterns. Phytopathology 83: pp. 928-932 CrossRef
  64. Amorin, L, Bergamin-Filho, A, Hau, B (1993) Analysis of progress curves of sugarcane smut on different cultivars using functions of double sigmoid patterns. Phytopathology 83: pp. 933-936 CrossRef
  65. Gompertz, B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society 182: pp. 513-585 CrossRef
  66. Yin, X, Goudriaan, J, Lantinga, EA, Vos, J, Spiertz, HJ (2003) A flexible sigmoid function of determinate growth. Annals of Botany 91: pp. 361-371 CrossRef
  67. Cuny, HE, Rathgeber, CBK, Kiess茅, TS, Hartmann, FP, Barbeito, I, Fournier, M (2013) Generalized additive models reveal the intrinsic complexity of wood formation dynamics. Journal of Experimental Botany 64: pp. 1983-1994 CrossRef
  68. Durner, W (1994) Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resources Research 30: pp. 211-223 CrossRef
  69. Cairns, SP, Robinson, DM, Loiselle, DS (2008) Double-sigmoid model for fitting fatigue profiles in mouse fast- and slow-twitch muscle. Experimental Physiology 93: pp. 851-862 CrossRef
  70. Roper, L.D. (2000). Using sigmoid and double-sigmoid functions for earth states transitions. Personal copy not assigned to a journal, available online: http://www.roperld.com/Science/DoubleSigmoid.pdf.
  71. Buchwald, P (2007) A general bilinear model to describe growth or decline time profiles. Mathematical Biosciences 205: pp. 108-136 CrossRef
  72. Schroeder, F (1997) Water quality in the Elbe estuary: significance of different processes for the oxygen deficit at Hamburg. Environmental Modeling and Assessment 2: pp. 73-82 CrossRef
  73. Righetto, L, Casagrandi, R, Bertuzzo, E, Maria, L, Gatto, M, Rodriguez-Iturbec, I, Rinaldo, A (2012) The role of aquatic reservoir fluctuations in long-term cholera patterns. Epidemics 4: pp. 33-42 CrossRef
  74. Kosugi, K (1996) Lognormal distribution model for unsaturated soil hydraulic properties. Water Resources Research 32: pp. 2697-2703 CrossRef
  75. Khlosi, M, Cornelis, WM, Douaik, A, Genuchten, MT, Gabriels, D (2008) Performance evaluation of models that describe the soil water retention curve between saturation and oven dryness. Vadose Zone Journal 7: pp. 87-96 CrossRef
  76. Dexter, AR, Czy偶, EA, Richard, G, Reszkowska, A (2008) A user-friendly water retention function that takes account of the textural and structural pore spaces in soil. Geoderma 143: pp. 243-253 CrossRef
  77. Aschonitis, V.G., Castaldelli, G., Lanzoni, M., Merighi, M., Rossi, R., & Fano, E.A. (2013). Eel population assessment in the Comacchio Lagoon: evidences of stock collapse. XIII S.It.E Congress Ancona, 16鈥?8 September 2013.
  78. Geiser, F (2004) Metabolic rate and body temperature reduction during hibernation and daily torpor. Annual Review of Physiology 66: pp. 239-74 CrossRef
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Environment
  Environment
  Mathematical Modeling and IndustrialMathematics
  Applications of Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1573-2967

文摘

There is a plethora of non-linear models to describe bivariate relationships related to ecological, biological and environmental problems, and this makes difficult to have a general aspect about the suitable models for a new-born dataset. Additionally, there is a special interest for bivariate non-linear models which can describe the relative variation of the dependent variable (NLR models) (i.e. these models provide a restricted range of values between 0 and 1) because they can easily be adjusted to fit different datasets which describe the same relationship. The aim of this study is to provide a review and synthesis of NLR models which can be used to describe bivariate relationships which follow bell-shaped, simple-double sigmoid, bilinear and periodical patterns. This attempt aims to save time and effort for the selection of a NLR model based on five steps (a) preparation of data, (b) visual identification of the suitable model based on pre-constructed graphs, (c) a starting point using the simpler form (base function) of the selected models which are given in complex general forms, (d) directions to increase the number of coefficients in order to improve fitting and (e) techniques to modify the given NLR models in order to derive new ones with inverted patterns.