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Modelling spatial and temporal variability in a zero-inflated variable: The case of stone pine (Pinus pinea L.) cone production

Author

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  • Calama, Rafael
  • Mutke, Sven
  • Tomé, José
  • Gordo, Javier
  • Montero, Gregorio
  • Tomé, Margarida

Abstract

Modelling masting habit, i.e. the spatial synchronized annual variability in fruit production, is a huge task due to two main circumstances: (1) the identification of main ecological factors controlling fruiting processes, and (2) the common departure of fruit data series from the main basic statistical assumptions of normality and independence. Stone pine (Pinus pinea L.) is one of the main species in the Mediterranean basin that is able to grow under hard limiting conditions (sandy soils and extreme continental climate), and typically defined as a masting species. Considering the high economical value associated with edible nut production, the masting habit of stone pine has been a main concern for the forest management of the species. In the present work we have used annual fruit data series from 740 stone pine trees measured during a 13 years period (1996–2008) in order: (a) to verify our main hypothesis pointing out to the existence of a weather control of the fruiting process in limiting environments, rather than resource depletion or endogenous inherent cycles; (b) to identify those site factors, stand attributes and climate events affecting specific traits involved in fruiting process; and (c) to construct a model for predicting spatial and temporal patterns of variability in stone pine cone production at different spatial extents as region, stand and tree. Given the nature of the data, the model has been formulated as zero-inflated log-normal, incorporating random components to carry out with the observed lack of independence. This model attains efficiencies close to 70–80% in predicting temporal and spatial variability at regional scale. Though efficiencies are reduced according to the spatial extent of the model, it leads to unbiased estimates and efficiencies over 35–50% when predicting annual yields at tree or stand scale, respectively. In this sense, the proposed model is a main tool for facilitating decision making in some management aspects such as the quantification of total amount of cones annually supplied to nut industry, design of cone harvest programs or the optimal application of seedling felling.

Suggested Citation

  • Calama, Rafael & Mutke, Sven & Tomé, José & Gordo, Javier & Montero, Gregorio & Tomé, Margarida, 2011. "Modelling spatial and temporal variability in a zero-inflated variable: The case of stone pine (Pinus pinea L.) cone production," Ecological Modelling, Elsevier, vol. 222(3), pages 606-618.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:3:p:606-618
    DOI: 10.1016/j.ecolmodel.2010.09.020
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    References listed on IDEAS

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    1. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    2. Belasco, Eric J. & Ghosh, Sujit K., 2008. "Modeling Censored Data Using Mixture Regression Models with an Application to Cattle Production Yields," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6341, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
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    1. Mercè Guàrdia & Anna Teixidó & Rut Sanchez-Bragado & Neus Aletà, 2021. "An Agronomic Approach to Pine Nut Production by Grafting Stone Pine on Two Rootstocks," Agriculture, MDPI, vol. 11(11), pages 1-12, October.
    2. Huber, P. & Hujala, T. & Kurttila, M. & Wolfslehner, B. & Vacik, H., 2019. "Application of multi criteria analysis methods for a participatory assessment of non-wood forest products in two European case studies," Forest Policy and Economics, Elsevier, vol. 103(C), pages 103-111.
    3. Calama, Rafael & Puértolas, Jaime & Madrigal, Guillermo & Pardos, Marta, 2013. "Modeling the environmental response of leaf net photosynthesis in Pinus pinea L. natural regeneration," Ecological Modelling, Elsevier, vol. 251(C), pages 9-21.
    4. Manso, Rubén & Pardos, Marta & Keyes, Christopher R. & Calama, Rafael, 2012. "Modelling the spatio-temporal pattern of primary dispersal in stone pine (Pinus pinea L.) stands in the Northern Plateau (Spain)," Ecological Modelling, Elsevier, vol. 226(C), pages 11-21.
    5. Liu, Juxin & Ma, Yanyuan & Johnstone, Jill, 2020. "A goodness-of-fit test for zero-inflated Poisson mixed effects models in tree abundance studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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