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Quantile regression for modelling the impact of climate in cork growth quantiles in Portugal

Abstract

The annual growth and the thickness of cork are known to be highly variable between trees located in the same geographical location. Researching how climate variables affect different trees within the same site is a step forward for the management of cork production since current knowledge focusses only on the average tree response. Quantile regression methodology was applied for the first time to a large data set containing measurements of cork growth, sampled in 35 stands across the cork oak distribution area in Portugal. This methodology proved to be useful for testing the hypothesis raised: does climate affect differently the annual cork growth, and ultimately cork thickness of individual trees located in the same stand? Estimating the amount of cork produced by one stand that has the required thickness for the production of natural cork stoppers is essential to support cork oak management. However, no model, before this work, had been developed to provide managers with this information. A downward parabolic relationship between annual cork growth and annual precipitation was determined for all quantiles, with optimum annual average precipitation value ranging from 1103 to 1007 mm. April to August monthly temperatures, spring average temperature or summer average temperature, showed a negative relationship with annual cork growth, in particular for lower quantiles. Maximum annual temperature was shown to negatively affect annual cork thickness, in particular for the trees under the 6th quantile. The ratio between annual precipitation and average temperature, that define the Lang index (LI), showed a downward parabolic relationship with annual cork growth. Best cork growth conditions are found for Lang index values around 60, corresponding for the transition between semi-arid climate and humid climate. The application of the final model developed for estimating cork thickness of an eight years’ cork growth period allowed the prediction and mapping of the percentage of cork suitable for natural cork stopper production. It showed that higher values are expected in the Southern and Central coastal regions and along the Tagus River basin. The Northern coastal and mountain regions, characterised by Lang index values higher to 60 (humid climates), present lower estimated values for the percentage of cork suitable for natural cork stopper production. The estimated values are expected to be reduced under climate change scenarios in the Southern and Central coastal regions.

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References

  1. Acácio V, Holmgren M, Jansen PA, Schrotter O (2007) Multiple recruitment limitation causes arrested succession in mediterranean cork oak systems. Ecosystems 10:1220–1230. https://doi.org/10.1007/s10021-007-9089-9

    Article  Google Scholar 

  2. Akaike H (1981) Likelihood of a model and information criteria. J Econ 16:3–14

    Article  Google Scholar 

  3. Almeida A, Tomé J, Tomé M (2010) Development of a system to predict the evolution of individual tree mature cork caliber over time. For Ecol Manage 260(8):1303–1314

    Article  Google Scholar 

  4. Andrade C, Fraga H, Santos JA (2013) Climate change multi-model projections for temperature extremes in Portugal. Atmos Clim Lett 15(2):149–156. https://doi.org/10.1002/asl2.485

    Article  Google Scholar 

  5. Aranda I, Pardos M, Puértolas J, Jiménez MD, Pardos JA (2007) Water-use efficiency in cork oak (Quercus suber) is modified by the interaction of water and light availabilities. Tree Physiol 27(5):671–677. https://doi.org/10.1093/treephys/27.5.671

    Article  PubMed  Google Scholar 

  6. Besson CK, Lobo-do-Vale R, Rodrigues ML, Almeida P, Herd A, Grant OM, David TS, Schmidt M, Otieno D, Keenan TF, Gouveia C, Mériaux C, Chaves MM, Pereira JS (2014) Cork oak physiological responses to manipulated water availability in a Mediterranean woodland. Agric For Meteorol 184:230–242. https://doi.org/10.1016/j.agrformet.2013.10.004

    Article  Google Scholar 

  7. Bivand R, Keitt T, Rowlingson B, (2019) rgdal: Bindings for the 'Geospatial' Data Abstraction Library. R package version 1:4–4. https://CRAN.R-project.org/package=rgdal

  8. Bohora SB, Cao QV (2014) Prediction of tree diameter growth using quantile regression and mixed-effects models. For Ecol Manage 319:62–66. https://doi.org/10.1016/j.foreco.2014.02.006

    Article  Google Scholar 

  9. Borges JG, Oliveira AO, Costa MA (1997) A quantitative approach to cork oak forest management. For Ecol Manage 97(3):223–229. https://doi.org/10.1016/S0378-1127(97)00064-9

    Article  Google Scholar 

  10. Cade BS, Noon BR (2003) A gentle introduction to quantile regression for ecologists. Front Ecol Environ 1(8):412–420

    Article  Google Scholar 

  11. Cade BS, Terrell JW, Schroeder RL (1999) Estimating effects of limiting factors with regression quantiles. Ecology 80:311–323

    Article  Google Scholar 

  12. Camilo-Alves CSP, Vaz M, Clara D, Ribeiro NMA (2017) Chronic cork oak decline and water status: new insights. New Forests 48:753–772. https://doi.org/10.1007/s11056-017-9595-3

    Article  Google Scholar 

  13. Camilo-Alves C, Dinis C, Vaz M, Barroso JM, Ribeiro NA (2020) Irrigation of young cork oaks under field conditions—testing the best water volume. Forests 11(1):88. https://doi.org/10.3390/f11010088

    Article  Google Scholar 

  14. Caritat A, Molinas M, Gutierrez E (1996) Annual cork-ring width variability of Quercus suber L. in relation temperature and precipitation (Extremadura, southwestern Spain). For Ecol Manage 86:113–120

    Article  Google Scholar 

  15. Caritat A, Gutiérrez E, Molinas M (2000) Influence of weather on cork-ring width. Tree Physiol 20:893–900. https://doi.org/10.1093/treephys/20.13.893

    CAS  Article  PubMed  Google Scholar 

  16. Coelho MB, Paulo JA, Palma JHN, Tomé M (2012) Contribution of cork oak plantations installed after 1990 in Portugal to the Kyoto commitments and to the landowners economy. Forest Policy Econ 17:59–68. https://doi.org/10.1016/j.forpol.2011.10.005

    Article  Google Scholar 

  17. Corona P, Dettori S, Filigheddu MR, Maetzke F, Scotti R (2005) Site quality evaluation by classification tree: an application to cork quality in Sardinia. Eur J Forest Res 124(1):37–46. https://doi.org/10.1007/s10342-004-0047-1

    Article  Google Scholar 

  18. den Herder M, Moreno G, Mosquera-Losada R, Palma JHN, Sidiropoulou A, Freijanes JJS, Crous-Duran J, Paulo JA, Tomé M, Pantera A, Papanastasis VP, Mantzanas K, Pachana P, Papadopoulos A, Plieninger T, Burgess PJ (2017) Current extent and stratification of agroforestry in the European Union. Agr Ecosyst Environ 241:121–132. https://doi.org/10.1016/j.agee.2017.03.005

    Article  Google Scholar 

  19. Dervilis N, Worden K, Cross EJ (2015) On robust regression analysis as a means of exploring environmental and operational conditions for SHM data. J Sound Vib 347:279–296. https://doi.org/10.1016/j.jsv.2015.02.039

    Article  Google Scholar 

  20. Ducey MJ, Knapp RA (2010) A stand density index for complex mixed species forests in the northeastern United States. For Ecol Manage 260:1613–1622. https://doi.org/10.1016/j.foreco.2010.08.014

    Article  Google Scholar 

  21. Dunnington D (2017) prettymapr: Scale Bar, North Arrow, and Pretty Margins in R. R package version 0.2.2. https://CRAN.R-project.org/package=prettymapr

  22. Faias SP, Paulo JA, Palma JHN, Tomé M (2018) Understory effect on tree and cork growth in cork oak woodlands. Forest Syst 27(1):e02S. https://doi.org/10.5424/fs/2018271-11967

    Article  Google Scholar 

  23. Faias SP, Paulo JA, Tomé M (2019) Drivers for annual cork growth under two understory management alternatives on a podzolic cork oak stand. Forests 10(2):133. https://doi.org/10.3390/f10020133

    Article  Google Scholar 

  24. Fragoso R, Marques C, Lucas MR, Martins MB, Jorge R (2011) The economic effects of common agricultural policy on Mediterranean montado/dehesa ecosystem. J Policy Model 33(2):311–327. https://doi.org/10.1016/j.jpolmod.2010.12.007

    Article  Google Scholar 

  25. Gandour M, Khoujab ML, Toumic L, Trikia S (2007) Morphological evaluation of cork oak (Quercus suber): Mediterranean provenance variability in Tunisia. Ann For Sci 64:549–555. https://doi.org/10.1051/forest:2007032

    Article  Google Scholar 

  26. Ghalem A, Barbosa I, Bouhraoua RT, Costa A (2018) Climate signal in cork-ring chronologies: case studies in Southwestern Portugal and Northwestern Algeria. Tree-Ring Research 74(1):15–27. https://doi.org/10.3959/1536-1098-74.1.15

    Article  Google Scholar 

  27. Hidalgo PJ, Marín JM, Quijada J, Moreira JM (2008) A spatial distribution model of cork oak (Quercus suber) in Southern Spain: a suitable tool for reforestation. For Ecol Manage 255:25–34

    Article  Google Scholar 

  28. Hijmans, R. J., 2019. Raster: Geographic Data Analysis and Modeling. R package version 2.8–19. https://CRAN.R-project.org/package=raster

  29. ICNF. 2010. Relatório Final do 5.º Inventário Florestal Nacional. Instituto da Conservação da Natureza e Floretas

  30. Koenker R (2015) Quantile regression. international encyclopedia of the social and behavioral sciences, 2nd edn. Elseiver, Amsterdam

    Google Scholar 

  31. Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46:33–50. https://doi.org/10.2307/1913643

    Article  Google Scholar 

  32. Koenker R, Machado AF (1999) Goodness of fit and related inference processes for quantile regression. J Am Stat Assoc 94:1296–1310

    Article  Google Scholar 

  33. Lacambra LCJ, Andray AB, Francés FS (2010) Influence of soil water holding capacity on the potential distribution of forest species. a case study: the potential distribution of cork oak (Quercus suber L.) in central-western Spain. Eur J Forest Res 129:111–117

    Article  Google Scholar 

  34. Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38(4):963–974. https://doi.org/10.2307/2529876

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  35. Lang R (1915) Versuch einer exakten Klassifikation der Boden in klimatischer und geologischer Hinsicht. Intern Mitt f Bodenkunde 5:312–346

    Google Scholar 

  36. Lappi J (1997) Longitudinal analysis of height/diameter curves. For Sci 43:555–570

    Google Scholar 

  37. Lim KS, Treitz PM (2006) Estimation of above ground forest biomass from airborne discrete return laser scanner data using canopy-based quantile estimators. Scand J Forest Res 19:558–570. https://doi.org/10.1080/02827580410019490

    Article  Google Scholar 

  38. Lima MIP, Santo FE, Ramos AM, Lima JLMP (2013) Recent changes in daily precipitation and surface air temperature extremes in mainland Portugal, in the period 1941–2007. Atmos Res 127:195–209. https://doi.org/10.1016/j.atmosres.2012.10.001

    Article  Google Scholar 

  39. Myers RH (1990) Classical and modern regression with applications, 2nd edn. Duxbury Classic Series

    Google Scholar 

  40. Natividade JV (1950) Subericultura. Direcção Geral dos Serviços Florestais e Aquicolas

    Google Scholar 

  41. Oliveira V, Lauw A, Pereira H (2016) Sensitivity of cork growth to drought events: insights from a 24-year chronology. Clim Change 137:261–274. https://doi.org/10.1007/s10584-016-1680-7

    Article  Google Scholar 

  42. Palma JHN, Paulo JA, Tomé M (2014) Carbon sequestration of modern Quercus suber L. silvoarable agroforestry systems in Portugal: a yieldsafe-based estimation. Agroforestry Syst 88(5):791–801. https://doi.org/10.1007/s10457-014-9725-2

    Article  Google Scholar 

  43. Palma JHN, Paulo JA, Faias SP, Garcia-Gonzalo J, Borges JG, Tomé M (2015) Adaptive management and debarking schedule optimization of Quercus suber L. stands under climate change: case study in Chamusca Portugal. . Reg Environ Change 15(8):1569–1580. https://doi.org/10.1007/s10113-015-0818-x

    Article  Google Scholar 

  44. Pasalodos M, Pukkala T, Cañellas I, Sánchez-González M (2018) Optimizing the debarking and cutting schedule of cork oak stands. Ann For Sci 75(2):61. https://doi.org/10.1007/s13595-018-0732-8

    Article  Google Scholar 

  45. Paulo JA, Tomé M (2010) Predicting mature cork biomass with t years of growth from one measurement taken at any other age. For Ecol Manage 259:1993–2005. https://doi.org/10.1016/j.foreco.2010.02.010

    Article  Google Scholar 

  46. Paulo JA, Tomé M (2017) Using the SUBER model for assessing the impact of cork debarking rotation on equivalent annual annuity in Portuguese stands. Forest Syst 26(1):11. https://doi.org/10.5424/fs/2017261-09931

    Article  Google Scholar 

  47. Paulo JA, Faias S, Gomes AA, Palma J, Tomé J, Tomé M (2015) Predicting site index from climate and soil variables for cork oak (Quercus suber L.) stands in Portugal. New Forests 46(2):293–307. https://doi.org/10.1007/s11056-014-9462-4

    Article  Google Scholar 

  48. Paulo JA, Pereira H, Tomé M (2017) Analysis of variables influencing tree cork caliper in two consecutive cork extractions using cork growth index modelling. Agrofor Syst 91(2):221–237. https://doi.org/10.1007/s10457-016-9922-2

    Article  Google Scholar 

  49. Pebesma EJ, Bivand RS (2005) Classes and methods for spatial data in R. R News 5(2):9–13

    Google Scholar 

  50. Pereira H (2007) Cork: biology production and uses. Elsevier, p 336

    Google Scholar 

  51. Pierce, D. 2019. ncdf4: Interface to Unidata netCDF (Version 4 or Earlier) Format Data Files. R package version 1.16.1. https://CRAN.R-project.org/package=ncdf4

  52. Pinheiro JC, Bates DM (2000) Mixed-effects models in S and S-Plus stat and computer series. Springer, p 528

    Google Scholar 

  53. R Core Team (2018) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/

  54. Ramírez-Valiente JA, Valladares F, Delgado Huertas A, Granados S, Aranda I (2011) Factors affecting cork oak growth under dry conditions: local adaptation and contrasting additive genetic variance within populations. Tree Genet Genomes 7:285–295. https://doi.org/10.1007/s11295-010-0331-9

    Article  Google Scholar 

  55. Rousseeuw PJ (1984) Least median of squares regression. J Am Stat Assoc 79:871–880

    Article  Google Scholar 

  56. Rousseeuw PJ, Hubert M (2018) Anomaly detection by robust Statistics. WIREs Data Min Knowl Discov 8:e1236

    Google Scholar 

  57. Sampaio T, Gonçalves E, Patrício MS, Cota TM, Almeida MH (2019) Seed origin drives differences in survival and growth traits of cork oak (Quercus suber L.) populations. For Ecol Manage 448:267–277. https://doi.org/10.1016/j.foreco.2019.05.001

    Article  Google Scholar 

  58. Sánchez-González M, Calama R, Cañellas I, Montero G (2007) Variables influencing cork thickness in Spanish cork oak forests: a modeling approach. Ann For Sci 64:301–312

    Article  Google Scholar 

  59. SAS Institute Inc. 2015.SAS/STAT®14.1 User’s Guide. Cary, NC: SAS Institute Inc. Chapter 95: The QUANTREG Procedure. pp 7674 – 7755. https://support.sas.com/documentation/onlinedoc/stat/141/qreg.pdf

  60. Scharf FS, Juanes F, Sutherland M (1998) Inferring ecological relationships from the edges of scatter diagrams: comparison of regression techniques. Ecology 79(2):448–460. https://doi.org/10.1890/0012-9658(1998)079[0448:IERFTE]2.0.CO;2

    Article  Google Scholar 

  61. Schneider CA, Rasband WS, Eliceiri KW (2012) NIH Image to ImageJ: 25 years of image analysis. Nat Methods 9(7):671–675. https://doi.org/10.1038/nmeth.2089

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  62. Tiberi R, Branco M, Bracalini M, Croci F, Panzavolta T (2016) Cork oak pests: a review of insect damage and management. Annal Forest Sci 73:219–232

    Article  Google Scholar 

  63. Uribe JM, Guillen M (2020) Why and when should quantile regression be used? In: quantile regression for cross sectional and time series data springer briefs in finance. Springer

    Book  Google Scholar 

  64. Vessella F, Parlante A, Schirone A, Sandoletti G, Bellarosa R, Piovesan G, Santi L, Schirone B (2010) Irrigation regime as a key factor to improve growth performance of Quercus suber L. Scand J For Res 25:68–74. https://doi.org/10.1080/02827581.2010.485819

    Article  Google Scholar 

  65. Zang H, Lei X, Zeng W (2016) Height–diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models. Forestry 89(4):434–445. https://doi.org/10.1093/forestry/cpw022

    Article  Google Scholar 

  66. Zhang B, Sajjad S, Chen K, Zhou L, Zhang Y, Yong KK, Sun Y (2020) Predicting tree height-diameter relationship from relative competition levels using quantile regression models for Chinese fir (Cunninghamia lanceolata) in Fujian province. China Forests 11:183

    CAS  Article  Google Scholar 

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Acknowledgements

This research was funded by the Forest Research Centre, a research unit funded by Fundação para a Ciência e a Tecnologia I.P. (FCT), Portugal (UIDB/00239/2020). First author was financed by FCT under the contracts SFRH/BPD/96475/2013 and DL57/2016/CP1382/CT0027. Second author was financed by FCT under the contract SFRH/BD/133598/2017. Third author was financed by FCT under the contract FCT PD/BD/52695/2014.

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Correspondence to Joana Amaral Paulo.

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Paulo, J.A., Firmino, P.N., Faias, S.P. et al. Quantile regression for modelling the impact of climate in cork growth quantiles in Portugal. Eur J Forest Res 140, 991–1004 (2021). https://doi.org/10.1007/s10342-021-01379-8

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Keywords

  • Quercus suber L.
  • Climate change
  • Cork stopper
  • Cork growth index
  • Cork ring
  • Cork thickness