Abstract
Self-Organising Map (SOM) clustering methods applied to the monthly and seasonal averaged flowering intensity records of eight Eucalypt species are shown to successfully quantify, visualise and model synchronisation of multivariate time series. The SOM algorithm converts complex, nonlinear relationships between high-dimensional data into simple networks and a map based on the most likely patterns in the multiplicity of time series that it trains. Monthly- and seasonal-based SOMs identified three synchronous species groups (clusters): E. camaldulensis, E. melliodora, E. polyanthemos; E. goniocalyx, E. microcarpa, E. macrorhyncha; and E. leucoxylon, E. tricarpa. The main factor in synchronisation (clustering) appears to be the season in which flowering commences. SOMs also identified the asynchronous relationship among the eight species. Hence, the likelihood of the production, or not, of hybrids between sympatric species is also identified. The SOM pattern-based correlation values mirror earlier synchrony statistics gleaned from Moran correlations obtained from the raw flowering records. Synchronisation of flowering is shown to be a complex mechanism that incorporates all the flowering characteristics: flowering duration, timing of peak flowering, of start and finishing of flowering, as well as possibly specific climate drivers for flowering. SOMs can accommodate for all this complexity and we advocate their use by phenologists and ecologists as a powerful, accessible and interpretable tool for visualisation and clustering of multivariate time series and for synchrony studies.
Similar content being viewed by others
References
Abu-Asab MS, Peterson PM, Shelter SG, Orli SS (2001) Earlier plant flowering in spring as a response to global warming in the Washington DC. area. Biodivers Conserv 10:597–612
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19:716–723
Baragona R (2001) A simulation study on clustering time series with meta-heuristic methods. Quad Stat 3:1–26
Bawa KS, Kang H, Grayum MH (2003) Relationships among time, frequency, and duration of flowering in tropical rain forest trees. Am J Bot 90(6):877–887. doi:10.3732/ajb.90.6.877
Bezdek JC, Pal NR (1998) Some new indexes of cluster validity. IEEE Trans Syst Man Cybern B: Cybern 28(3):301–315
Biernacki C, Celeux G, Govaert G (2000) Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans Pattern Anal Mach Intell 22:719–725
Borchert R, Renner SS, Calle Z, Navarrete D, Tye A, Gautier L, Spichiger R, von Hildebrand P (2005) Photoperiodic induction of synchronous flowering near the Equator. Nature 433(7026):627–629
Both C, Bouwhuis S, Lessells CM, Visser ME (2006) Climate change and population declines in a long-distance migratory bird. Nature 441(7089):81–83
Brockwell PJ, Davis RA (1991) Time series: theory and methods. Springer Series in Statistics, 2nd edn. Springer, New York
Brooker MIH, Kleinig DA (2001) Field guide to eucalypts Hawthorn. Bloomings Books, Victoria
Carpenter GA, Grossberg S (1987) A massively parallel architecture for a self-organizing neural pattern recognition machine. Comput Vis Graph Image Process 37:54–115
Cheeseman P, Stutz J (1996) Bayesian classification (AutoClass): theory and results. In: Fayyard UM, Piatetsky-Shapiro G, Smyth P, Uthurusamy R (eds) Advances in knowledge discovery and data mining. AAAI/MIT Press, Cambridge, MA
Cleland EE, Chuine I, Menzel A, Mooney HA, Schwartz MD (2007) Shifting plant phenology in response to global change. Trends Ecol Evol 22(7):357–365
Costa JAF (2010) Clustering and Visualizing SOM Results. In: Intelligent Data Engineering and Automated Learning – IDEAL 2010, vol 6283. Lecture Notes in Computer Science. Springer Berlin, pp 334–343. doi:10.1007/978-3-642-15381-5_41
Davidson NJ, Reid JB, Potts BM (1987) Gene flow between threeeucalypt species at Snug Plains. Pap ProcR Soc Tasmania 121:101–108
Delaporte KL, Conran JG, Sedgley M (2001) Interspecific Hybridization within Eucalyptus (Myrtaceae): Subgenus Symphyomyrtus, Sections Bisectae and Adnataria. Int J Plant Sci 162(6):1317–1326. doi:10.1086/323276
Diaz I, Dominguez M, Vega AC, Fuertes-Martinez J (2008) A new approach to exploratory analysis of system dynamics using SOM. Applications to industrial processes. Expert Syst Appl 34(4):2953–2965
Dunn JC (1974) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J Cybern 3:32–57
Eldridge K, Davidson J, Harwood C, van Wyk G (1993) Eucalypt domestication and breeding, 1st edn. Oxford University Press, New York
Fitter AH, Fitter RSR (2002) Rapid changes in flowering time in British plants, Science 296:1689–1691
Forrest J, Miller-Rushing AJ (2010) Toward a synthetic understanding of the role of phenology in ecology and evolution. Philos Trans R Soc Lond B 365(1555):3101–3112. doi:10.1098/rstb.2010.0145
Fort JC (2006) SOM's mathematics. Neural Netw 19(6–7):812–816. doi:10.1016/j.neunet.2006.05.025
Frankie GW, Baker HG, Opler PA (1974) Comparative phenological studies of trees in tropical wet and dry forests in the lowlands of Costa Rica. J Ecol 62(3):881–919
Freitas L, Bolmgren K (2008) Synchrony is more than overlap: measuring phenological synchronization considering time length and intensity. Rev Bras Bot 31:721–724
Fulcher J, Jain L, Yin H (2008) The Self-Organizing Maps: Background, Theories, Extensions and Applications. In: Computational Intelligence: A Compendium, vol 115. Studies in Computational Intelligence. Springer Berlin, pp 715–762. doi:10.1007/978-3-540-78293-3_17
Gallagher RV, Hughes L, Leishman MR (2009) Phenological trends among Australian alpine species: using herbarium records to identify climate-change indicators. Aust J Bot 57(1):1–9. doi:10.1071/BT08051
Golay X, Kollias S, Stoll G, Meier D, Valavanis A, Boesiger P (1998) A new correlation-based fuzzy logic clustering algorithm for fMRI. Mag Resonance Med 40:249–260
Gordo O, Sanz J (2005) Phenology and climate change: a long-term study in a Mediterranean locality. Oecologia 146(3):484–495. doi:10.1007/s00442-005-0240-z
Goutte C, Hansen LK, Liptrot MG, Rostrup E (2001) Feature space clustering for fMRI meta-analysis. Hum Brain Mapping 13:165–183
Griffin AR, Burgess IP, Wolf L (1988) Patterns of natural and manipulated hybridisation in the genus Eucalyptus L'Herit: a review. Aust J Bot 36(1):41–66. doi:10.1071/BT9880041
Gross CL, Mackay DA, Whalen MA (2000) Aggregated flowering phenologies among three sympatric legumes. Plant Ecol 148:13–21
Hudson I (2010) Interdisciplinary approaches: towards new statistical methods for phenological studies. Clim Change 100(1):143–171. doi:10.1007/s10584-010-9859-9
Hudson IL (2011) Meta analysis In Encyclopedia of Climate and Weather. Second edn. Editor in Chief: Stephen H. Schneider, Associate Editor in Chief: Michael Mastrandrea, Editor-in-chief: Terry L. Root. Oxford University Press. ISBN13: 9780199765324 ISBN10: 0199765324 (March 2011 publication) http://www.oup.com/us/catalog/general/subject/AtmosphericScience/Climatology/?view=usa&ci=9780199765324
Hudson IL, Keatley MR (eds) (2010) Phenological Research: Methods for Environmental and Climate Change Analysis. Springer, Dordrecht
Hudson IL, Keatley MR, Roberts AMI (2005) Statistical Methods in Phenological Research. In: Francis AR, Matawie KM, Oshlack A, Smyth GK (eds) 20th International Workshop on Statistical Modelling, Sydney, Australia, 10–15 July 2005. Proceedings of the Statistical Solutions to Modern Problems, pp 259–270. ISBN 1 74108 101 7
Hudson IL, Keatley MR, Kim SW, Kang I (2006) Synchronicity in Phenology: from PAP Moran to now. In: Australian Statistical Conference/New Zealand Statistical Association (ASC/NZSA) conference, Auckland, New Zealand, 3th-6th July 2006
Hudson IL, Kim SW, Keatley MR (2009) Climatic influences on the flowering phenology of four Eucalypts: a GAMLSS approach. In: Anderssen RS, Braddock RD, Newham LTH (eds) 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 13–17 July 2009. Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, pp 2611–2617. ISBN: 978-0-9758400-7-8
Hudson IL, Keatley MR, Kim SW (2010a) Climatic Influences on the Flowering Phenology of Four Eucalypts: A GAMLSS Approach. In: Hudson IL, Keatley MR (eds) Phenological Research: Methods for Environmental and Climate Change Analysis. Springer, Dordrecht, pp 213–237. doi:10.1007/978-90-481-3335-2-10
Hudson IL, Keatley MR, Kim SW (2010b) Modelling the Flowering of Four Eucalypt Species Using New Mixture Transition Distribution Models. In: Hudson IL, Keatley MR (eds) Phenological Research: Methods for Environmental and Climate Change Analysis. Springer, Dordrecht, pp 315–340. doi:10.1007/978-90-481-3335-2_14
Hudson IL, Keatley MR, Kang I (2010c) Wavelet characterization of eucalypt flowering and the influence of climate. Environmental and Ecological Statistics, (Published on line first: 27 June 2010 ) pp 1–21. doi:10.1007/s10651-010-0149-5
Johnson SD (1993) Climatic and phylogenetic determinants of flowering seasonality in the Cape flora. J Ecol 82:567–572
Junker B, Klukas C, Schreiber F (2006) VANTED: a system for advanced data analysis and visualization in the context of biological networks. BMC Bioinform 7(1):109
Keatley MR (1999) The Flowering Phenology of Box-Ironbark Eucalypts in the Maryborough Region, Victoria. PhD thesis, The University of Melbourne
Keatley MR, Hudson IL (1998) The influence of fruit and bud volumes on the flowering of eucalypts: an exploratory analysis. Aust J Bot 46(2):281–307
Keatley MR, Hudson IL (2000) Influences on the flowering phenology of three eucalypts. In 'Biometeorology and Urban Climatology at the Turn of the Century. Selected Papers from the Conference ICB-ICUC '99.' (Eds RJ de Dear, JD Kalma, TR Oke and A Aucliems) pp. 191–196. (World Meteorological Organisation: Geneva, Switzerland)
Keatley M, Hudson I (2007) A comparison of long-term flowering patterns of Box-Ironbark species in Havelock and Rushworth forests. Environ Model Assess 12(4):279–292. doi:10.1007/s10666-006-9063-5
Keatley MR, Hudson IL (2008) Shifts and changes in a 24 year Australian flowering record. In: 18th International Congress of Biometeorology, Tokyo, Japan, 22nd-26th September 2008. Harmony within Nature. p 85. http://www.icb2008.com/ScientificP.html.
Keatley MR, Fletcher TD, Hudson IL, Ades PK (2002) Phenological studies in Australia: potential application in historical and future climate analysis. Int J Climatol 22(14):1769–1780. doi:10.1002/joc.822
Keatley MR, Hudson IL, Fletcher TD (2004) Long-term flowering synchrony of box-ironbark eucalypts. Aust J Bot 52(1):47–54. doi:10.1071/BT03017
Kim SW, Hudson IL, Keatley MR (2006) Extending Mixture Transition Distribution (MTD) methods to incorporate interactions: Links to species synchrony and phenology. In: Australian Statistical Conference/New Zealand Statistical Association (ASC/NZSA) conference, Auckland, New Zealand, 3–6 July 2006
Kim SW, Hudson IL, Keatley MR, Agrawal M (2008) Modelling and synchronization of four Eucalypt species via Mixed Transition Distribution (MTD) and Extended Kalman Filter (EKF). In P. Eilers, editor, Proceedings of the 23 rd International Workshop on Statistical Modelling, 23rd International Workshop on Statistical Modelling, Utrecht, Netherlands, 7th -11th July, pp 287–292
Kim SW, Hudson IL, Keatley MR (2009) Modelling the flowering of four eucalypts species via MTDg with interactions. In: Anderssen RS, Braddock RD, Newham LTH (eds) 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 13th -17th July 2009. Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, pp 2625–2631. ISBN: 978-0-9758400-7-8
King I, Wang J, Chan L, Wang D, Martín-Merino M, Román J (2006) A New SOM Algorithm for Electricity Load Forecasting. In: Neural Information Processing, vol 4232. Lecture Notes in Computer Science. Springer, Berlin, pp 995–1003. doi:10.1007/11893028_111
Klukas C (2006) The VANTED software system for transcriptomics, proteomics and metabolomics analysis. J Pestic Sci 31(3):289–292
Kohonen T (1995) Self-Organizing Maps. Springer Series in Information Sciences, 2nd edn. Springer, Heidelberg
Kohonen T (2001) Self-Organizing Maps. Third, extended edn. Springer, Heidelberg
Krebs CJ (1994) Ecology: the experimental analysis of distribution and abundance, 4th edn. Benjamin Cummings, New York
Mac Nally R, Horrocks G (2000) Landscape-scale conservation of an endangered migrant: the swift parrot (Lathamus discolor) in its winter range. Biol Conserv 92(3):335–343
Martin PR, Bonier F, Moore IT, Tewksbury JJ (2009) Latitudinal variation in the asynchrony of seasons: implications for higher rates of population differentiation and speciation in the tropics. Ideas Ecol Evol 2:9–17
Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Trans Pattern Anal Mach Intell 24(12):1650–1654
Menzel A, Fabian P (1999) Growing season extended in Europe. Nature 397:659
Menzel A, Sparks T (2006) Temperature and plant development: phenology and seasonality. In: Morison JIL, Morecroft MD (eds) Plant growth and climate change. Blackwell, Oxford, pp 70–95
Menzel A, Sparks TH, Estrella N, Koch E, Aasa A, Ahas R, Alm-Kubler K, Bissolli P, Brasavská O, Briede A, Chmielewski F-M, Crepinse Z, Curnel Y, Dahl A, Defila C, Donnelly A, Filella Y, Jatczak K, Mage F, Mestre A, Nordli Ø, Peñuelas J, Pirinen P, Remišová V, Scheifinger H, Striz M, Susnik A, van vliet AJH, Wielgolaski F-E, Zach S, Zust A (2006) European phenological response to climate change matches the warming pattern. Glob Change Biol 12:1969–1976
Miller-Rushing AJ, Hoye TT, Inouye DW, Post E (2010) The effects of phenological mismatches on demography. Philos Trans R Soc Lond B 365(1555):3177–3186. doi:10.1098/rstb.2010.0148
Möller-Levet CS, Klawonn F, Cho KH, Wolkenhauer O (2003) Fuzzy clustering of short time series and unevenly distributed sampling points, Proceedings of the 5th International Symposium on Intelligent Data Analysis, Berlin, Germany, August 28–30
Moran PAP (1953a) The statistical analysis of the Canadian lynx cycle. I. Structure and prediction. Aust J Zool 1(2):163–173
Moran PAP (1953b) The statistical analysis of the Canadian lynx cycle. II. Synchronization and meteorology. Aust J Zool 1(3):291–298
Nguyen PN, Haughton D, Hudson IL (2009) Living standards of Vietnamese provinces: a Kohonen map Case Studies in Business. Case Studies in Business, Industry and Government Statistics 2(2):109–113
Parry M, Canziani O, Palutikof J, van der Linden P, Hanson C (2008) Climate change 2007 –impacts, adaptation and vulnerability. Contribution of Working Group II to the Fourth AssessmentReport of the IPCC, Cambridge University Press, Cambridge
Pẽnelaus J, Filella I, Comas P (2002) Changed plant and animal cycles from 1952 to 2000 in theMediterranean region, Glob Change Biol 8:531–544
Piccolo D (1990) A distance measure for classifying ARMA models. J Time Ser Anal 11(2):153–163
Post E, Forchhammer M (2008) Climate change reduces reproductive success of an Arctic herbivore through trophic mismatch. Philos Trans R Soc Lond B 363:2369–2375
Prieto P, Peñuelas J, Ogaya R, Estiarte M (2008) Precipitation-dependent flowering of Globularia alypum and Erica multiflora in Mediterranean shrubland under experimental drought and warming, and its inter-annual variability. Ann Bot 102:275–285
Primack RB, Ibáñez I, Higuchi H, Lee SD, Miller-Rushing AJ, Wilson AM, Silander JA Jr (2009) Spatial and interspecific variability in phenological responses to warming temperatures. Biol Conserv 142(11):2569–2577
Pryor LD, Johnson LAS (1971) A classification of the eucalypts. Australian National University, Canberra
Rathcke B (1983) Competition and facilitation among plants for pollination. In: Real L (ed) Pollination Biology. Academic, Orlando, Florida, pp 305–329
Reusch DB, Alley RB, Hewitson BC (2007) North Atlantic climate variability from a self-organizing map perspective. J Geophys Res 112 (D2):D02104. doi:10.1029/2006jd007460
Roddick JF, Spiliopoulou M (2002) A survey of temporal knowledge discovery paradigms and methods. IEEE Trans Knowledge Data Eng 14(4):750–767
Root TL, Price JT, Hall KR, Schneider SH, Rosenzweig C, Pounds JA (2003) Fingerprints of global warming on wild animals and plants. Nature 421(6918):57–60
Royama T (2005) Moran effect on nonlinear population processes. Ecol Monogr 75(2):277–293. doi:10.1890/04-0770
Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464
Shaw CT, King GP (1992) Using cluster analysis to classify time series. Physica D 58:288–298
Shoichet BK, Chen Y (2009) Molecular docking and ligand specificity in fragment-based inhibitor discovery. Nat Chem Biol 5(5):358–364. doi:10.1038/nchembio.155
Shumway RH (2003) Time–frequency clustering and discriminant analysis. Stat Probab Lett 63:307–314
Singhal A, Seborg DE (2005) Clustering multivariate time-series data. J Chemom 19(8):427–438
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 44:82–87
Sparks TH, Górska-Zajączkowska M, Wójtowicz W, Tryjanowski P (2010) Phenological changes and reduced seasonal synchrony in western Poland. Int J Biometeorol. doi:10.1007/s00484-010-0355-8
Staggemeier VG, Diniz-Filho JAF, Morellato LPC (2010) The shared influence of phylogeny and ecology on the reproductive patterns of Myrteae (Myrtaceae). J Ecol 98:1409–1421
Thackeray SJ, Sparks TH, Frederiksen M, Burthe S, Bacon PJ, Bell JR, Botham MS, Brereton TM, Bright PW, Carvalho L, Clutton-Brock TIM, Dawson A, Edwards M, Elliott JM, Harrington R, Johns D, Jones ID, Jones JT, Leech DI, Roy DB, Scott WA, Smith M, Smithers RJ, Winfield IJ, Wanless S (2010) Trophic level asynchrony in rates of phenological change for marine, freshwater and terrestrial environments. Glob Change Biol 16(12):3304–3313. doi:10.1111/j.1365-2486.2010.02165.x
Thomson JD (2010) Flowering phenology, fruiting success and progressive deterioration of pollination in an early-flowering geophyte. Philos Trans R Soc Lond B 365:3187–3199. doi:10.1098/rstb.2010.0115
Vesanto J, Alhoniemi E (2000) Clustering of the self-organizing map. IEEE Trans Neural Netw 11(3):586–600. doi:10.1109/72.846731
Visser ME, Both C (2005) Shifts in phenology due to global climate change: the need for a yardstick. Proc R Soc Lond B 272(1581):2561–2569. doi:10.1098/rspb.2005.3356
Vlachos M, Lin J, Keogh E, Gunopulos D (2003) A wavelet based anytime algorithm for k-means clustering of time series. Proceedings of the Third SIAM International Conference on Data Mining, San Francisco, CA, May 1–3, 2003
Wilson JA (2002) Flowering ecology of a Box-Ironbark Eucalyptus community. PhD thesis, Deakin University
Xiong Y, Yeung D-Y (2002) Mixtures of ARMA models for model-based time series clustering, Proceedings of the IEEE International Conference on Data Mining, Maebaghi City, Japan, 9–12 December, 2002
Yin H, Gorban AN, Kégl B, Wunsch DC, Zinovyev AY (2008) Learning Nonlinear Principal Manifolds by Self-Organising Maps. In: Principal Manifolds for Data Visualization and Dimension Reduction, vol 58. Lecture Notes in Computational Science and Engineering. Springer, Berlin, pp 68–95. doi:10.1007/978-3-540-73750-6-3
Acknowledgments
The authors are very grateful to two reviewers whose comments and insights very much improved the details pertaining to the motivation for this study, the clarity of the methods and visual displays, and the interlinking and distinctions of SOMs to more traditional methodologies.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hudson, I.L., Keatley, M.R. & Lee, S.Y. Using Self-Organising Maps (SOMs) to assess synchronies: an application to historical eucalypt flowering records. Int J Biometeorol 55, 879–904 (2011). https://doi.org/10.1007/s00484-011-0427-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00484-011-0427-4