## Competition for light in forest population dynamics: from computer simulator to mathematical model.(English)Zbl 1370.92140

Summary: In this article we build a mathematical model for forest growth and we compare this model with a computer forest simulator named SORTIE. The main ingredient taken into account in both models is the competition for light between trees. The parameters of the mathematical model are estimated by using SORTIE model, when the parameter values of SORTIE model correspond to the ones previously evaluated for the Great Mountain Forest in USA. We see that the best fit of the parameters of the mathematical model is obtained when the competition for light influences only the growth rate of trees. We construct a size structured population dynamics model with one and two species and with spatial structure.

### MSC:

 92D25 Population dynamics (general) 92C80 Plant biology 92-08 Computational methods for problems pertaining to biology

SORTIE
Full Text:

### References:

 [1] Adams, T.P., Purves, D.W., Pacala, S.W., 2007. Understanding height-structured competition in forests: Is there an $$R^*$$ for light? Proc. R. Soc. B 274, 3039-3048. [2] Angulo, Ó.; de la Parra, R. B.; López-Marcos, J. C.; Zavala, M. A., Stand dynamics and tree coexistence in an analytical structured modelthe role of recruitment, J. Theor. Biol., 333, 91-101, (2013) · Zbl 1397.92414 [3] Botkin, D. B., Forest dynamicsan ecological model, (1993), Oxford University Press [4] Botkin, D. B.; Janak, J. F.; Wallis, J. R., Some ecological consequences of a computer model of forest growth, J. Ecol., 60, 849-872, (1972) [5] Cammarano, M., Co-dominance and succession in forest dynamicsthe role of interspecific differences in crown transmissivity, J. Theor. Biol., 285, 46-57, (2011) · Zbl 1397.92715 [6] Cheaïb, A.; Mollier, A.; Thunot, S.; Lambrot, C.; Pellerin, S.; Loustau, D., Interactive effects of phosphorus and light availability on early growth of maritime pine seedlings, Ann. Forest Sci., 62, 575-583, (2005) [7] de Roos, A. M.; Persson, L., Competition in size-structured populationsmechanisms inducing cohort formation and population cycles, Theor. Popul. Biol., 63, 1-16, (2003) · Zbl 1101.92322 [8] Delcourt, P. A.; Delcourt, H. R., Long-term forest dynamics of the temperate zonea case study of late-quaternary forests in eastern north America, (1987), Springer New York [9] Deutschman, D. H.; Levin, S. A.; Pacala, S. W., Error propagation in a forest succession modelthe role of fine-scale heterogeneity in light, Ecology, 80, 6, 1927-1943, (1999) [10] Ducrot, A., Travelling waves for a size and space structured model in population dynamicspoint to sustained oscillating solution connections, J. Differ. Equ., 250, 410-449, (2011) · Zbl 1217.34108 [11] Engel, K. J.; Nagel, R., One-parameter semigroups for linear evolution equations, (1999), Springer Science & Business Media [12] Falster, D. S.; Brännström, Å.; Dieckmann, U.; Westoby, M., Influence of four major plant traits on average height, leaf-area cover, net primary productivity, and biomass density in single-species forestsa theoretical investigation, J. Ecol., 99, 148-164, (2011) [13] Kobe, R. K.; Pacala, S. W.; Silander, J. A.; Canham, C. D., Juvenile tree survivorship as a component of shade tolerance, Ecol. Appl., 5, 2, 517-532, (1995) [14] Köhler, P., Huth, A., 1998. An individual based rain forest model - concepts and simulation results. In: Kastner-Maresch, A., Kurth, W., Sonntag, M., Breckling, B. (Eds.), Individual-based Structural and Functional Models in Ecology. Bayreuther Forum Ökologie, vol. 52. Bayreuther Institut für terrestrische Ökosystemforschung, Bayreuth, pp. 35-51. [15] Kohyama, T., Size-structured tree populations in gap-dynamic forest - the forest architecture hypothesis for the stable coexistence of species, J. Ecol., 81, 131-143, (1993) [16] Kohyama, T.; Takada, T., The stratification theory for plant coexistence promoted by one-sided competition, J. Ecol., 97, 463-471, (2009) [17] Kohyama, T. S.; Takada, T., One-sided competition for light promotes coexistence of forest trees that share the same adult height, J. Ecol., 100, 1501-1511, (2012) [18] Kolb, T. E.; Steiner, K. C.; McCormick, L. H.; Bowersox, T. W., Growth response of northern red-oak and yellow-poplar seedlings to light, soil moisture and nutrients in relation to ecological strategy, Forest Ecol. Manag., 38, 65-78, (1990) [19] Kramer, K.; Leinonen, I.; Loustau, D., The importance of phenology for the evaluation of impact of climate change on growth of boreal, temperate and Mediterranean forests ecosystemsan overview, Int. J. Biometeorol., 44, 67-75, (2000) [20] Levin, S. A.; Grenfell, B.; Hastings, A.; Perelson, A. S., Mathematical and computational challenges in population biology and ecosystems science, Science, 275, 334-343, (1997) · Zbl 1225.92058 [21] Liu, J.; Ashton, P. S., Individual-based simulation models for forest succession and management, Forest Ecol. Manag., 73, 157-175, (1995) [22] Loustau, D.; Crepeau, S.; Guye, M. G.; Sartore, M.; Saur, E., Growth and water relations of three geographically separate origins of maritime pine (pinus pinaster) under saline conditions, Tree Physiol., 15, 569-576, (1995) [23] Magal, P., Ruan, S., 2009. Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. In: AMS eBook Collections. Memoirs of the American Mathematical Society, vol. 202. American Mathematical Society, Providence, Rhode Island. · Zbl 1191.35045 [24] Magal, P., Zhang, Z., 2017. State-dependent delay differential equation modelling forest growth I: semiflow properties, in preparation. · Zbl 1416.35278 [25] Obiang, N. L.E.; Ngomanda, A.; Hymas, O.; Chézeauxl, É.; Picard, N., Diagnosing the demographic balance of two light-demanding tree species populations in central africa from their diameter distribution, Forest Ecol. Manag., 313, 55-62, (2014) [26] Oliver, C. D.; Larson, B. C., Forest stand dynamics, (1990), McGraw-Hill Inc [27] Pacala, S. W.; Canham, C. D.; Saponara, J.; Silander, J. A.; Kobe, R. K.; Ribbens, E., Forest models defined by field measurementsestimation, error analysis and dynamics, Ecol. Monogr., 66, 1, 1-43, (1996) [28] Pacala, S. W.; Canham, C. D.; Silander, J. A., Forest models defined by field measurementsi. the design of a northeastern forest simulator, Can. J. Forest Res., 23, 1980-1988, (1993) [29] Pacala, S. W.; Canham, C. D.; Silander, J. A.; Kobe, R. K., Sapling growth as a function of resources in a north temperate forest, Can. J. Forest Res., 24, 2172-2183, (1994) [30] Porté, A.; Bartelink, H. H., Modelling mixed forest growtha review of models for forest management, Ecol. Model., 150, 141-188, (2002) [31] Pretzsch, H, 2009. Forest Dynamics, Growth and Yield: From Measurement to Model. Springer, Berlin, Heidelberg. [32] Ribbens, E.; Silander, J. A.; Pacala, S. W., Seedling recruitment in forestscalibrating models to predict patterns of tree seedling dispersion, Ecology, 75, 6, 1794-1806, (1994) [33] Ricker, W. E., Stock and recruitment, J. Fish. Res. Board Canada, 11, 5, 559-623, (1954) [34] Ricker, W.E., 1975. Computation and interpretation of biological studies of fish populations. In: Bulletin of the Fisheries Research Board of Canada, vol. 191. Fisheries and Marine Service, Ottawa. [35] Shugart, H. H.; West, D. C., Development of an Appalachian deciduous forest succession model and its application to assessment of the impact of the chestnut blight, J. Environ. Manag., 5, 161-179, (1977) [36] Shugart, H. H., A theory of forest dynamicsthe ecological implications of forest succession models, (1984), Springer-Verlag New York [37] Smith, H. L., Reduction of structured population models to threshold-type delay equations and functional differential equationsa case study, Math. Biosci., 113, 1-23, (1993) · Zbl 0797.92024 [38] Smith, H. L., A structured population model and a related functional differential equation: global attractors and uniform persistence, J. Dyn. Differ. Equ., 6, 1, 71-99, (1994) · Zbl 0794.34061 [39] Strigul, N.; Pristinski, D.; Purves, D.; Dushoff, J.; Pacala, S., Scaling from trees to foreststractable macroscopic equations for forest dynamics, Ecol. Monogr., 78, 4, 523-545, (2008) [40] Teck, R.M., Hilt, D.E., 1991. Individual-tree diameter growth model for the northeastern United States. Research paper NE-649, US. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station, Radnor, PA. [41] Trichet, P.; Loustau, D.; Lambrot, C.; Linder, S., Manipulating nutrient and water availability in a maritime pine plantationeffects on growth, production, and biomass allocation at canopy closure, Ann. Forest Sci., 65, 8, 814, (2008) [42] Valladares, F.; Niinemets, Ü., Shade tolerance, a key plant feature of complex nature and consequences, Annu. Rev. Ecol. Evol. Syst., 39, 237-257, (2008) [43] Yokozawa, M.; Hara, T., Foliage profile, size structure and stem diameter-plant height crowded plant populations, Ann. Bot., 76, 271-285, (1995) [44] Zavala, M. A.; Angulo, Ó.; de la Parra, R. B.; López-Marcos, J. C., An analytical model of stand dynamics as a function of tree growth, mortality and recruitmentthe shade tolerance-stand structure hypothesis revisited, J. Theor. Biol., 244, 440-450, (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.