A forest simulation approach using weighted Voronoi diagrams. An application to Mediterranean fir Abies pinsapo Boiss stands

Begoña Abellanas, Manuel Abellanas, Arne Pommerening, Dolores Lodares, Simón Cuadros

Abstract


Aim of study: a) To present a new version of the forest simulator Vorest, an individual-based spatially explicit model that uses weighted Voronoi diagrams to simulate the natural dynamics of forest stands with closed canopies. b) To apply the model to the current dynamics of a Grazalema pinsapo stand to identify the nature of its competition regime and the stagnation risks it is currently facing.

Area of study: Sierra del Pinar de Grazalema (S Spain)

Material and methods: Two large plots representative of Grazalema pinsapo stands were used to fit and validate the model (plus 6 accesory plots to increase the availability of mortality data). Two inventories were carried out in 1998 and 2007 producing tree size and location data. We developed a forest simulator based on three submodels: growth, competition and mortality. The model was fitted, evaluated and validated for Grazalema plots. The simulation outputs were used to infer the expected evolution of structural diversity of  forest stands.

Main results: Vorest has proved to be a good tool for simulating dynamics of natural closed stands. The application to Grazalema pinsapo stands has allowed assessing the nature of the main processes that are driving its development pathway. We have found that the prevailing size-asymmetric competition dominates the self-thinning process in small-sized trees. At the same time, there is an active tree-size differentiation process.

Research highlights:

  • Vorest has proved to be a good tool for simulating natural stands with closed canopies.
  • The Grazalema pinsapo stand under consideration is currently undergoing a natural process of differentiation, avoiding long-term stagnation.

Keywords: Vorest; stand dynamics; individual-based forest model; spatially explicit forest model; pinsapo.


Keywords


Vorest; stand dynamics; individual-based forest model; spatially explicit forest model; Pinsapo.

Full Text:

PDF HTML XML

References


References

Abellanas B, Coca M, Cuadros S, Oliet J, 2005. Análisis de la diversidad estructural del pinsapar puro en la sierra de grazalema. Influencia sobre la dinámica de la regeneración. Actas del IV Congreso Forestal Español. SECF, 4CFE05-004-T1: 115.

Abellanas B, Abellanas M, Vilas C, 2007. Vorest: Modelización de bosques mediante diagramas de Voronoi. Actas XII Encuentro de Geometría Computacional: 2249-256. Valladolid, España.

Abellanas B, Abellanas M, Pommerening A, Lodares D, 2012. Vorest: un modelo de simulación basado en diagramas de Voronoi. Cuadernos de la Sociedad Española de Ciencias Forestales, 34: 27-37.

Alba-Sánchez F, López-Sáez JA, Benito-De Pando B, Linares JC, Nieto-Lugilde D, López-Merino L, 2010. Past and present potential distribution of the Iberian Abies species: a phytogeografic approach using fossil pollen data and species distribution model. Diversity Distrib 16: 214-218. http://dx.doi.org/10.1111/j.1472-4642.2010.00636.x

Antos JA, Parish R, Conley K, 2000. Age structure and growth of the tree-seedling bank in subalpine spruce-fir forests of south- central British Columbia. Am Midl Nat 143: 342–354. http://dx.doi.org/10.1674/0003-0031(2000)143[0342:ASAGOT]2.0.CO;2

Antos JA, Parish R, 2002. Structure and dynamics of a nearly steady-state subalpine forest in south-central British Columbia, Canada. Oecologia 130: 1, 126-135. http://dx.doi.org/10.1007/s004420100787

Arista M, 1995. The structure and dynamics of an Abies pinsapo forest in Southern Spain. Forest Ecol Manag 74: 81-89. http://dx.doi.org/10.1016/0378-1127(94)03507-S

Aurenhammer F, Edelsbrunner H, 1984. An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognition 17(2): 251-257. http://dx.doi.org/10.1016/0031-3203(84)90064-5

Bauer S, Wyszomirski T, Berger U, Hildebrandt H, Grimm V, 2004. Asymmetric competition as a natural outcome of neighbor interactions among plants: results from the field-of_neighborhood modelling approach. Plant Ecol 170: 135–145. http://dx.doi.org/10.1023/B:VEGE.0000019041.42440.ea

Bella IE, 1967. Crown width/diameter relationships of open-growing jack pine on four site types in Manitoba, Canada. Dep. Forest & Rural Development Research Notes 23(1): 5-6.

Berger U, Hildenbrandt H, Grimm V, 2004. Age-related decline in forest production: modelling the effects of growth limitation, neighbourhood competition and self-thinning. J Ecol 92: 846-853.

http://dx.doi.org/10.1111/j.0022-0477.2004.00911.x

Botkin DB, Janak JF, Wallis JR, 1972. Some ecological consequences of a computer model of forest growth. J Ecol 60: 849-872.

http://dx.doi.org/10.2307/2258570

Coca M, Abellanas B, Cuadros S, Oliet JA, Miguel. A, 2001. Caracterización estructural del pinsapar de la Sierra de Grazalema. Actas del III Congreso Forestal Español. Ed. Junta de Andalucía, TRAGSA, SECF: 257-264.

Cuadros S, Oliet JA, Abellanas B, Coca M, Padrón E, 2003. La regeneración en el pinsapar de la Sierra de Grazalema. II: Estructura y dinámica del regenerado consolidado en el pinsapar puro. Cuadernos de la Sociedad Española de Ciencias Forestales 15(2): 27-32.

Cuadros S, Ramírez A, Abellanas B, 2005. Epidometría basada en análisis de imagen y apoyada en un sig. Cuadernos de la Sociedad Española de Ciencias Forestales 19: 85-90.

Eichhorn MP, 2010. Spatial organisation of a bimodal forest stand. J Forest Res 15: 391–397. http://dx.doi.org/10.1007/s10310-010-0200-2

Ek AR, 1974. Dimensional relationships of forest and open-grown trees in Wisconsin.Univ. Wisconsin Forest Research Notes 181. 7pp.

Farr WA, Demars DJ, Dealy JE, 1989. Height and crown width related to diameter for open-grown western hemlock and Sitka spruce. Can J Forest Res 19: 1203-1207. http://dx.doi.org/10.1139/x89-181

Grabarnik P, Särkkä A, 2011. Modelling the spatial and space-time structure of foreststands: How to model asymmetric interaction between neighbouring trees. Procedia Environ Sci 7: 62–67. http://dx.doi.org/10.1016/j.proenv.2011.07.012

Gray L, He F, 2009. Spatial point-pattern analysis for detecting density-dependent competition in a boreal chronosequence of Alberta. Forest Ecol Manag 259: 98-106. http://dx.doi.org/10.1016/j.foreco.2009.09.048

Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, Goss-Custard J, Grand T, Heinz S.K, Huse G, 2006. A standard protocol for describing individual-based and agent-based models. Ecol Modelling 198: 115-126. http://dx.doi.org/10.1016/j.ecolmodel.2006.04.023

Grimm V, Berger U, Deangelis DL, Polhill JG, Giske J, Railsback SF, 2010. The ODD protocol: A review and first update. Ecol Modelling 221: 2760-2768. http://dx.doi.org/10.1016/j.ecolmodel.2010.08.019

Hara T, 1992.Effects of the mode of competition on stationary size distribution in plant populations. Ann Bot 69: 509-513.

Hasenauer H, 1997. Dimensional relationships of open-grown trees in Austria. Forest Ecol Manag 96: 197-206. http://dx.doi.org/10.1016/S0378-1127(97)00057-1

Illian J, Penttinen A, Stoyan H, Stoyan D, 2008. Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley &Sons, Ltd. West Sussex. 534 pp.

Krajiceck JE, Brinkman KA, Gingrich SF, 1961. Crown competition- a measure of density. Forest Sci 7: 35-42.

Leech JW, 1984. Estimating crown width from diameter at breast height for open-grown radiate pine trees in South Australia. Aust Forest Res 14: 333-337.

Linares JC, Camarero JJ, Carreira JA, 2009. Interacting effects of changes in climate and forest cover on mortality and growth on the southernmost European fir forests. Global Ecol Biogeogr 18: 485–497. http://dx.doi.org/10.1111/j.1466-8238.2009.00465.x

Linares JC, Carreira JA, 2009. Temperate-like stand dynamics in relict Mediterranean-fir (Abies pinsapo, Boiss.) forests from southern Spain. Ann Forest Sci 66: 610:1-10. http://dx.doi.org/10.1051/forest/2009040

Linares JC, 2011. Biogeography and evolution of Abies (Pinaceae) in the Mediterranean Basin: the roles of long-term climatic change and glacial refugia. J Biogeogr 38: 619-630. http://dx.doi.org/10.1111/j.1365-2699.2010.02458.x

Lundqvist L, 1994. Growth and competition in partially cut sub-alpine Norway spruce forests in northern Sweden. Forest Ecol Manag, 65: 115-122. http://dx.doi.org/10.1016/0378-1127(94)90163-5

MAGRAMA, 2015. 3º Inventario Forestal Nacional de España (IFN3). Ministerio de Agricultura, Alimentación y Medio Ambiente de España. http://www.magrama.gob.es/es/biodiversidad/servicios/banco-datos-naturaleza/informacion-disponible/ifn3.aspx

Matic S, 2001. Silver fir (Abies alba Mill) in Croatia. Ed: Akademija Sumarskih Znanosti – Hrvatske Sume, p.o. Zagreb. 895 pp.

McCarthy J, 2001. Gap dynamics of forest trees: a review with particular attention to boreal forests. Environ Rev 9, 1: 1-59. http://dx.doi.org/10.1139/a00-012

Morin H, 1994. Dynamics of balsam fir forests in relation to spruce budworm outbreaks in the Boreal Zone of Quebec. Can J Forest Res 24, 4: 730-741. http://dx.doi.org/10.1139/x94-097

Murphy ST, Pommerening A, 2010. Modelling the growth of Sitka spruce (Picea sitchensis (Bong)carr.) in Wales using Wenk’s model approach. Allg Forst J Ztg, 181(1/2): 35-43.

Newnham RM, 1964. The development of a stand model for Douglas-fir. PhD Thesis. Univ. British Columbia. Vancouver. Canada. 201 pp.

Nunes L, Tomé J, Tomé M, 2011. Prediction of annual tree growth and survival for thinned and unthinned even-aged maritime pine stands in Portugal from data with different time measurement intervals. Forest Ecol Manag 262: 1491-1499. http://dx.doi.org/10.1016/j.foreco.2011.06.050

Oheimb G, Lang AC, Bruelheide H, David H, Forrester I, Wäsche I, Yu M, Härdtle W, 2011. Individual-tree radial growth in a subtropical broad-leaved forest: The role of local neighbourhood competition. Forest Ecol Manag 261: 499-507. http://dx.doi.org/10.1016/j.foreco.2010.10.035

Okabe A, Boots B, Sugihara K, Chiu SN, 2000. Spatial Tessellations – Concepts and Applications of Voronoi Diagrams. 2nd edition. John Wiley, 671 pp. http://dx.doi.org/10.1002/9780470317013

Oliver CD, Larson BC, 1996. Forest Stand Dynamics. Ed: John Wiley and Sons, New York. 544 pp.

Paine DP, Hann DW, 1982. Maximum crown-width equations for southwestern Oregon tree species. School of Forestry Oregon State Univ. Forest Res Paper 46: 1-20.

Pommerening A, LeMay V, Stoyan D, 2011. Model-based analysis of the influence of ecological processes on forest point pattern formation- A case study. Ecol Modelling, 222: 666-678. http://dx.doi.org/10.1016/j.ecolmodel.2010.10.019

Pommerening A, Särkkä A, 2013. What mark variograms tell about spatial plant interactions. Ecol Modelling, 251: 64-72. http://dx.doi.org/10.1016/j.ecolmodel.2012.12.009

Pretzsch H, Biber P, Ďurský J, 2002. The single tree-based stand simulator SILVA: construction, application and evaluation. Forest Ecol Manag, 162(1): 3-21. http://dx.doi.org/10.1016/S0378-1127(02)00047-6

Pretzsch H, 2009. Forest dynamics, growth and yield. From measurement to model. Spriger-Verlag. Berlin. 664 pp.

R Development Core Team, 2011. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

Römisch K, 1996. Durchmesserwachstum und ebene Bestandesstruktur am Beispiel der Kiefernversuchsfläche Markersbach. In: Hempel, G. (Ed.), 8. Tagung der Sektion Forstliche Biometrie und Informatik, pp. 84–103. Biotechnische Fakultät, Abteilung Forstwirtschaft, Ljubljana, Slovenia.

Scaltsoyiannes A, Tsaktsira M, Drouzas AD, 1999.Allozyme differentiation in the Mediterranean firs (Abies, Pinaceae).A first comparative study with phylogenetic implications. Plant Syst Evol, 216(3/4): 289-307. http://dx.doi.org/10.1007/BF01084404

Smith WR, Farrar RM, Murphy RA, Yeiser JL, Meldahl RS, Kush JS, 1992. Crown and basal area relationships of open-grown southern pines for modeling competition and growth. Can J Forest Res 22: 341-347. http://dx.doi.org/10.1139/x92-044

Sterba H, Zingg A, 2001. Target diameter harvesting- a strategy to convert even-aged forests. Forest Ecol Manag 152(1-3): 95-105. http://dx.doi.org/10.1016/S0378-1127(00)00700-3

Stewart GH, Rose AB, Veblen TT, 1991. Forest development in canopy gaps in old-growth beech (Nothofagus) forests, New Zealand. J Veg Sci 2: 679–690. http://dx.doi.org/10.2307/3236178

Thorpe SC, Astrup R, Trowbridge A, Coates KD, 2010. Competition and tree crowns: A neighborhood analysis of three boreal tree species. Forest Ecol Manag 259: 1586–1596. http://dx.doi.org/10.1016/j.foreco.2010.01.035

Toda M, Yokozawa M, Emori S, Hara T, 2010. More asymmetric tree competition brings about more evapotranspiration and less run off from the forest ecosystems: A simulation study. Ecol Modelling 221: 2887-2898. http://dx.doi.org/10.1016/j.ecolmodel.2010.08.025

Uchmansky J, 2000. Resource partitioning among competing individuals and population persistence: an individual-based model. Ecol Modelling 131:21–32. http://dx.doi.org/10.1016/S0304-3800(00)00242-8

Weiner J, 1986. How competition for light and nutrients affects size variability in Ipomoea tricolor populations. Ecology, 67: 1425–1427. http://dx.doi.org/10.2307/1938699

Weiner J, 1990. Asymmetric competition in plant populations. Trends Ecol Evol 5: 360-364. http://dx.doi.org/10.1016/0169-5347(90)90095-U

Weiner J, Damgaard C, 2006. Size-asymmetric competition and size-asymmetric growth in a spatially explicit zone-of-influence model of plant competition. Ecol Res 1: 707–712. http://dx.doi.org/10.1007/s11284-006-0178-6

Woods KD, 1984. Patterns of tree replacement: canopy effects on understory pattern in hemlock – northern hardwood forests. Vegetatio 56: 87–107.

Xiang QP, Xiang QY, Guo YY, Zhang XC, 2009. Phylogeny of Abies (Pinaceae) inferred from nrlTS sequence data. Taxon 58(1): 141-152.




DOI: 10.5424/fs/2016252-08021

Webpage: www.inia.es/Forestsystems