Abstract
As tropical forests are complex systems, they tend to be modelled either roughly via scaling relationships or in a detailed manner as high-dimensional systems with many variables. We propose an approach which lies between the two whereby succession in a tropical forest is viewed as a trajectory in the configuration space of a dynamical system with just three dependent variables, namely, the mean leaf-area index (LAI) and its standard deviation (SD) or coefficient of variation along a transect, and the mean diameter at breast height (DBH) of trees above the 90th percentile of the distribution of tree DBHs near the transect. Four stages in this forest succession are identified: (I) naturally afforesting grassland: the initial stage with scattered trees in grassland; (II) very young forest: mostly covered by trees with a few remaining gaps; (III) young smooth forest: almost complete cover by trees of mostly similar age resulting in a low SD; and (IV) old growth or mature forest: the attracting region in configuration space characterized by fluctuating SD from tree deaths and regrowth. High-resolution LAI measurements and other field data from Khao Yai National Park, Thailand show how the system passes through these stages in configuration space, as do simple considerations and a crude cellular automaton model.
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Acknowledgments
We are grateful to the Department of National Parks, Wildlife and Plant Conservation for permission to work in Khao Yai, and to the superintendents of Khao Yai National Park, Prawat Woharndee and Narong Mahannop, and their staff for their cooperation. We thank Anuttara Nathalang and her staff for providing data from Mo Singto plot and for their cooperation, and Luan Jannuan for his help in reconstructing the history of the park and thus giving a precise age to the different plots we studied. We are also happy to acknowledge many fruitful discussions with Laurent Cournac, Louise H. Emmons, Natsuda Klongvessa, Florian Hartig, and Nicolas Picard. The travel grant for Dubois and Favier was funded by the Franco-Thai programme. Some parts of this work were funded by the Faculty of Science Research Grants, Kasetsart University. Finally, we thank the two anonymous referees for their valuable comments.
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Appendix
Appendix
Cellular automaton model
The model is an n x × n y cellular automaton with periodic boundary conditions. Each cell represents a 5 m × 5 m quadrat and has values of LAI and DBH. The DBH corresponds to the DBH of the largest tree in the quadrat. Each time step (representing 1 year) is composed of two sub-steps: tree-falls followed by tree growth.
In the tree-falls sub-step, each cell with a DBH larger than d o has a probability p d of dying. Such a tree is assumed to be 50 m in height and falls in a random direction, killing trees where it falls (by setting those cells to zero LAI and DBH) with probability p dtf.
In the tree growth sub-step, if the DBH is nonzero, it is incremented by Δd up to a maximum of d max at the next time step. If the LAI is nonzero, it is incremented by ΔL up to a maximum of L max. If the LAI (and therefore also the DBH) of a cell is zero and is surrounded by k cells with an LAI greater than L s (using a 4-cell neighbourhood and so k = 0, 1, … , 4), the probability that the LAI becomes ΔL at the next time step is p wa+k p f. The parameters p wa and p f (both much less than 1) correspond to the probability of germination of seeds dispersed by, respectively, wind or animals, and falling from a neighbouring tree.
Initially, all cells have zero LAI and DBH. Values of M, S and V are found from the values of LAI along a line of n x cells in the x-direction. D is found from the values of DBH in these cells and the row of cells of the same length alongside.
Values of parameters used: n x = 40, n y = 21, d o = 32 cm, Δd = 0.4 cm, d max = 70 cm, ΔL = 0.2, L max = 7, L s = 2, p d = 0.01, p dtf = 0.2, p wa = 0.04, p f = 0.01. With the exception of the last three, which are difficult to estimate from the data available to us, the parameter values were chosen to be in line with field data. p dtf clearly only has an effect once trees start dying; increasing its value results in larger fluctuations in the OGF stage. In the model, p wa and p f are assumed to be small. Increasing p wa results in a more uniform YSF stage. The effects of changing p f are more complex and are coupled to other parameter values. But overall, the qualitative features of the model output do not depend on the precise choice of parameter values.
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Chanthorn, W., Ratanapongsai, Y., Brockelman, W.Y. et al. Viewing tropical forest succession as a three-dimensional dynamical system. Theor Ecol 9, 163–172 (2016). https://doi.org/10.1007/s12080-015-0278-4
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DOI: https://doi.org/10.1007/s12080-015-0278-4