Climatic Influences on the Flowering Phenology of Four Eucalypts: A GAMLSS Approach

  • Irene L. Hudson
  • Susan W. Kim
  • Marie R. Keatley
Chapter

Abstract

This chapter represents one of the first attempts to utilize phenological data to detect non-linear responses of flowering to climate change using GAMLSS. We use the flowering of four species (Eucalyptus leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa) as a case study. Regardless of cyclicity of flowering over time, this study shows that each species flowering is significantly influenced by temperature and this effect is non-linear. Stepwise GAMLSS showed that the main temperature driver of E. leucoxylon is minimum temperature (P<0.0001), maximum temperature for E. polyanthemos (P<0.0001), both minimum and maximum temperature (P<0.0001) for E. tricarpa, and mean temperature for E. microcarpa (P<0.0001). Rainfall was not a significant predictor of flowering. GAMLSS allowed for identification of upper/lower thresholds of temperature for flowering commencement/cessation; for the estimation of long and short-term non-linear effects of climate, and the identification of lagged cyclic effects of previous flowering.

Flowering intensity of all species was positively and significantly correlated with last month’s flowering (P<0.0001); and with flowering 12 months earlier for E. polyanthemos and E. microcarpa. Flowering of E. polyanthemos was negatively and significantly correlated with flowering intensity 2 and 4 months prior; in the case of E. microcarpa with flowering 6 and 8 months earlier. Overall, E. microcarpa and E. polyanthemos flower more intensely in response to predicted increases in mean and maximum temperature, respectively. E. leucoxylon flowers less intensely with predicted increases in minimum temperature; E. tricarpa flowers less intensely with increased maximum temperature, but more intensely with increased minimum temperature (after accounting for maximum temperature).

Keywords

Climate change Cubic smoothing splines Generalised additive model for location Scale and shape (GAMLSS) Multiple time series Thresholds 

References

  1. Akaike H (1974) A new look at the statistical model identification. IEEE T Automat Contr 19:716–723CrossRefGoogle Scholar
  2. Akaike H (1983) Information measures and model selection. B Int Statist Inst 50:277–290Google Scholar
  3. Akantziliotou C, Rigby RA, Stasinopoulos DM (2002) The R implementation of generalized additive models for location, scale and shape. In: Stasinopoulos M, Touloumi G (eds) Statistical modelling in Society: Proceedings of the 17th International Workshop on statistical modelling Chania, GreeceGoogle Scholar
  4. Ashton DH (1975) Studies of flowering behaviour in Eucalyptus regnans f. Muell. Aust J Bot 23:399–411Google Scholar
  5. Bassett OD, White MD, Dacy M (2006) Development and testing of seed-crop assessment models for three lowland forest eucalypts in East Gippsland, Victoria. Austalian Forestry 69:257–269Google Scholar
  6. Benjamin MA, Rigby RA, Stasinopoulos DM (2003) Generalized autoregressive moving average models. J Am Stat Assoc 98:214–223CrossRefGoogle Scholar
  7. Berger JO (1993) Statistical decision theory and Bayesian analysis. Springer, Berlin, Heidlelberg, New YorkGoogle Scholar
  8. Borghi E, de Onis M, Garza C et al. (2006) WHO child growth standards: methods and development. Stat Med 25:247–265CrossRefPubMedGoogle Scholar
  9. Chambers LE (2006) Associations between climate change and natural systems in Australia. BAMS 87:201–206CrossRefGoogle Scholar
  10. Cole TJ, Green PJ (1992) Smoothing reference centile curves: The LMS method and penalized likelihood. Stat Med 11:1305–1319CrossRefPubMedGoogle Scholar
  11. Cremer KW (1975) Temperature and other climatic influences on shoot development and growth of Eucalyptus regnans. Aust J Bot 26:27–44Google Scholar
  12. Dept. Sustainability and Environment (2008) Climate change in the North central region. In. Dept. Sustainability and Environment, East Melbourne, VictoriaGoogle Scholar
  13. Eilers PHC, Marx BD (1996) Flexible smoothing with B-splines and penalties. Stat Sci 11:89–121CrossRefGoogle Scholar
  14. Eldridge K, Davidson J, Harwood C et al. (1993) Eucalypt domestication and breeding. Oxford University Press, New YorkGoogle Scholar
  15. Fahrmeir L, Lang S (2001) Bayesian inference for generalized additive mixed models based on markov random field priors. J R Stat Soc Ser C 50:201–220CrossRefGoogle Scholar
  16. Fitter AH, Fitter RSR, Harris ITB et al. (1995) Relationships between first flowering date and temperature in the flora of a locality of central England. Func Ecol 9:55–60CrossRefGoogle Scholar
  17. Fox J (1997) Applied regression analysis, linear models, and related methods. Sage, CaliforniaGoogle Scholar
  18. Gelman A, Carlin JB, Stern HS et al. (2003) Bayesian data analysis. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  19. Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  20. Green PJ, Silverman BW (1994) Nonparametric regression and generalized linear models. Chapman and Hall/CRC, LondonGoogle Scholar
  21. Hastie T (2008) GAM: Generalized additive models. R package version 1.0. URL http://CRAN.R-project.org
  22. Hastie TJ, Tibshirani RJ (1999) Generalized additive models. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  23. Hudson IL, Barnett A, Keatley MR et al. (2003) Investigation into drivers for flowering: effects of climate on flowering. In: Verbeke G, Moelenberghs G, Aaerts M et al. (eds) Proceedings of the 18th International Workshop on Statistical Modelling Katholieke Universiteit Leuven, BelgiumGoogle Scholar
  24. Hudson IL, Rea A, Dalrymple M (2008) Climate impacts on sudden infant death syndrome: A GAMLSS approach. In: Eilers PH (ed) Proceedings of the 23rd International workshop on statistical modelling, July 7–11, 2008, Ipskamp Partners, Enschede, The NetherlandsGoogle Scholar
  25. IPCC (2007) Summary for policymakers. Climate change 2007: Impacts, adaptation and vulnerability Working Group II contribution to the Intergovernmental Panel on Climate Change fourth assessment report. Cambridge University Press, CambridgeGoogle Scholar
  26. Jiang J (2007) Linear and generalized linear mixed models and their applications. Springer, New YorkGoogle Scholar
  27. Keatley MR (1999) The flowering phenology of box-ironbark eucalypts in the Maryborough region, Victoria. Dissertation, The University of MelbourneGoogle Scholar
  28. Keatley MR, Hudson IL (1998) The influence of fruit and bud volumes on eucalypt flowering: An exploratory analysis. Aust J Bot 42:281–304CrossRefGoogle Scholar
  29. Keatley MR, Hudson IL (2000) Influences on the flowering phenology of three eucalypts. In: de Dear RJ, Kalma JD, Oke TR et al.(eds) Biometeorology and urban climatology at the turn of the century selected papers from the conference ICB-ICUC’ 99, World Meteorological Organisation, Geneva, SwitzerlandGoogle Scholar
  30. Keatley MR, Hudson IL (2007) A comparison of the long-term flowering patterns of box-ironbark species in Havelock and Rushworth forests. Environ Model Assess 12:279–292CrossRefGoogle Scholar
  31. Keatley MR, Hudson IL (2008) Shifts and changes in a 24 year Australian flowering record. In: Harmony within Nature. The 18th International Congress of Biometeorology Tokyo, JapanGoogle Scholar
  32. Keatley MR, Fletcher TD, Hudson IL et al. (2002) Phenological studies in Australia: Potential application in historical and future climate analysis. Int J Climate 22:1769–1780CrossRefGoogle Scholar
  33. Keatley MR, Hudson IL, Fletcher TD (2004) Long-term flowering synchrony of box-ironbark eucalypts. Aust J Bot 52:47–54CrossRefGoogle Scholar
  34. Kim SW, Hudson IL, Keatley MR (2005) Mixture transition distribution analysis of flowering and climatic states. In: Francis AR, Matawie KM, Oshlack A, Smyth GK (eds) Statistical Solutions to Modern Problems Proceedings of the 20th International Workshop on Statistical Modelling Sydney, AustraliaGoogle Scholar
  35. Kim SW, Hudson IL, Agrawal M et al. (2008) Modelling and synchronization of four Eucalyptus species via mixed transition distribution (MTD) and extended kalman filter (EKF). In: Eilers PHC (ed) Proceedings of the 23rd International Workshop on Statistical Modelling, Ipskamp Partners, Enschede, The NetherlandsGoogle Scholar
  36. Law B, Mackowski L, Tweedie T (2000) Flowering phenology of myrtaceous trees and their relation to climate, environmental and disturbance variables in Northern New South Wales. Austral Ecology 25:160–178Google Scholar
  37. Leith H (ed) (1974) Phenology and seasonal modeling. Springer-Verlag, New YorkGoogle Scholar
  38. Lin X, Zhang D (1999) Inference in generalized additive mixed models by using smoothing splines. J Roy Statist Soc Ser B 61:381–400CrossRefGoogle Scholar
  39. Loomis RS, Connor DJ (1992) Crop ecology: productivity and management in agricultural systems. Cambridge University Press, CambridgeGoogle Scholar
  40. McKitrick MC (1993) Phylogenetic constraint in evolutionary theory: has it any explanatory power?. Ann Rev Ecol Syst 24:307–330CrossRefGoogle Scholar
  41. Menzel A (2002) Phenology: its importance to the global change community. Climatic Change 54:379–385CrossRefGoogle Scholar
  42. Menzel A, Sparks TH, Estrella N et al. (2006a) European phenological response to climate change matches the warming pattern. Global Change Biol 12:1969–1976CrossRefGoogle Scholar
  43. Menzel A, Sparks TH, Estrella N et al. (2006b) Altered geographic and temporal variability in phenology in response to climate change. Global Ecol Biogeogr 15:498–504Google Scholar
  44. Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A 135:370–384CrossRefGoogle Scholar
  45. Pfeifer M, Heirich W, Jetschke G (2006) Climate, size and flowering history determine flowering pattern of an orchid. Bot J Linn Soc 151:511–526CrossRefGoogle Scholar
  46. Pinheiro JC, Bates DM (2000) Mixed-effects models in S and S-plus. Springer, New YorkCrossRefGoogle Scholar
  47. Porter JW (1978) Relationships between flowering and honey production of Red Ironbark, Eucalyptus sideroxylon (A. Cunn.) Benth., and climate in the Bendigo district of Victoria. Aust J Agric Res 29:815–829CrossRefGoogle Scholar
  48. Primack RB (1980) Variation in the phenology of natural populations of montane shrubs in New Zealand. J Ecol 68:849–862CrossRefGoogle Scholar
  49. Pryor LD, Johnson LAS (1971) A classification of the eucalypts. Australian National University, CanberraGoogle Scholar
  50. Development Core R Team (2007) R: A language and environment for statistical computing. URL http://www.R-project.org/
  51. Rehfeldt GE, Tchebakova NM, Parfenova EI (2004) Genetic responses to climate and climate-change in conifers of the temperate and boreal forests. Recent Res Devel Genet Breed 1:113–130Google Scholar
  52. Rigby RA, Stasinopoulos DM (1996a) MADAM macros to fit mean and dispersion additive models. In: Scallan A, Morgan G (eds) Glim4 macro library manual, release 20, Numerical Algorithms Group, Oxford, pp 68–84Google Scholar
  53. Rigby RA, Stasinopoulos DM (1996b) Mean and dispersion additive models. In: Hardle W, Schimek MG (eds) Statistical theory and computational aspects of smoothing, Physica-Verlag, Heidelberg, pp 215–230Google Scholar
  54. Rigby RA, Stasinopoulos DM (2001) The GAMLSS project: A flexible approach to statistical modelling. In: Klein B, Korsholm L (eds) New Trends in Statistical Modelling: proceedings of the 16th International Workshop on Statistical Modelling Odense, DenmarkGoogle Scholar
  55. Rigby RA, Stasinopoulos DM (2005) Generalized additive models for location, scale and shape. Appl Statist 54:507–554Google Scholar
  56. Rosenzweig C, Casassa G, Karoly DJ et al. (2007) Assessment of observed changes and responses in natural and managed systems. Climate change 2007: Impacts, adaptation and vulnerability. Contribution of Working Group II to the fourth assessment report of the Intergovernmental Panel on Climate Change. In: Parry ML, Canziani OF, Palutikof JP et al. (eds). Cambridge University Press, Cambridge, UK, pp 79–131Google Scholar
  57. Rosenzweig C, Karoly D, Vicarelli M et al. (2008) Attributing physical and biological impacts to anthropogenic climate change. Nature 453:353–358CrossRefPubMedGoogle Scholar
  58. Royston P, Altman DG (1994) Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. Appl Statist 43:429–467CrossRefGoogle Scholar
  59. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  60. Smith PL (1979) Splines as a useful and convenient statistical tool. Amer Statistician 33:57–62CrossRefGoogle Scholar
  61. Sparks TH (1999) Phenology and the changing pattern of bird migration in Britain. Int J Biometeorol 42:134–138CrossRefGoogle Scholar
  62. Sparks TH, Carey PD (1995) The responses of species to climate over two centuries: an analysis of the Marshman phenological record, 1736–1947. J Ecol 83:321–329CrossRefGoogle Scholar
  63. Sparks TH, Jeffree EP, Jeffree CE (2000) An examination of the relationship between flowering times and temperature at the national scale using long-term phenological records from the UK. Int J Biometeorol 44:82–87CrossRefPubMedGoogle Scholar
  64. Stasinopoulos DM, Rigby RA (1992) Detecting break points in generalised linear models. Comput Stat Data An 13:461–471CrossRefGoogle Scholar
  65. Stasinopoulos DM, Rigby RA (2007) Generalized additive models for location scale and shape (GAMLSS) in R. J Stat Softw 23:1–46Google Scholar
  66. Thomson JD (1980) Skewed flowering distributions and pollinator attraction. Ecology 61:572–579CrossRefGoogle Scholar
  67. Traill B (1991) Box-ironbark forests: tree hollows, wildlife and management. In: Lunney D (ed) Conservation of Australia’s forest fauna, Royal Zoological Society of NSW, Mosman, pp 119–123Google Scholar
  68. Tzaros C (2005) Wildlife of the box-ironbark country. CSIRO Publishing, CollingwoodGoogle Scholar
  69. Visser ME, Both C (2005) Shifts in phenology due to global climate change: the need for a yardstick. Proc Roy Soc London B 272:2561–2569CrossRefGoogle Scholar
  70. Walther G-R, Post E, Convey P et al. (2002) Ecological responses to recent climate change. Nature 416:389–395CrossRefPubMedGoogle Scholar
  71. Waser NM (1983) Competition for pollination and floral character differences among sympatric plant species: A review of evidence. In: Jones CE, Little RJ (eds) Handbook of experimental pollination biology, Van Nostrand Reinhold Company, New York, pp 277–292Google Scholar
  72. Wielgolaski F-E (1999) Starting dates and basic temperatures in phenological observations of plants. Int J Biometeorol 42:158–168CrossRefGoogle Scholar
  73. Yang S, Logan J, Coffey DL (1995) Mathematical formulae for calculating the base temperature for growing degree days. Agr Forest Meteorol 74:61–74CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Irene L. Hudson
    • 1
  • Susan W. Kim
    • 1
    • 2
  • Marie R. Keatley
    • 3
  1. 1.School of Mathematics and StatisticsUniversity of South AustraliaAdelaideSouth Australia
  2. 2.Institute for Sustainable Systems and TechnologiesUniversity of South AustraliaMawson LakesSouth Australia
  3. 3.Department of Forest and Ecosystem ScienceUniversity of MelbourneMelbourneAustralia

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