Maintaining an Optimal Flow of Forest Products under a Carbon Market: Approximating a Pareto Set of Optimal Silvicultural Regimes for Eucalyptus fastigata

Oliver Chikumbo, Thomas J. Straka

Department of Forestry and Natural Resources, Clemson University, Clemson, USA.
Scion, Rotorua, New Zealand.

DOI: 10.4236/ojf.2012.23017                

Abstract

A competitive co-evolutionary Multi-Objective Genetic Algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes for Eucalyptus fastigata. The three objectives to be maximised included, sawlog, pulpwood and carbon sequestration payment. Three carbon price scenarios (3CPS), i.e. NZ $25, NZ $50 and NZ $100 for a tonne of CO₂ sequestered, were used to assess the impact on silvicultural regimes, against a fourth non-carbon Pareto set of efficient regimes (nonCPS), determined from a cc-MOGA with two objectives, i.e. competing sawlog and pulpwood productions. Carbon prices included in stand valuation were found to influence the silvicultural regimes by increasing the rotation length and lowering the final crop number before clearfell. However, there were no significant changes in the frequency, timing, and intensity of thinning operations amongst all the four Pareto sets of solutions. However, the 3CPS were not significantly different from each other, which meant that these silvicultural regimes were insensitive to the price of carbon. This was because maximising carbon sequestration was directly related to the biological growth rate. As such an optimal mix of frequency, intensity, and timing of thinning maintained maximum growth rate for as long as possible for any one rotation.

Keywords

Optimal Control; Competitive Co-Evolutionary Multi-Objective Genetic Algorithm (cc-MOGA); Pareto Front; Forest Holding Value; Kruskal-Wallis Test; Multiple Comparison Procedure

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Appel, D. (2001). Forest rotation lengths under carbon sequestration payments. Conference of Economists, University of Western Australia, Perth. http://129.3.20.41/econ-wp/othr/papers/0110/0110007.pdf
[2]	Asante, P., Armstrong, G. W., & Adamowicz, L. W. (2011). Carbon sequestration and the optimal forest harvest decision: A dynamic programming approach considering biomass and dead organic matter. Journal of Forest Economics, 17, 3-17. doi:10.1016/j.jfe.2010.07.001
[3]	Bellman, R. E. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
[4]	Chen, C. M., Rose, D. W., & Leary R. A. (1980). How to Formulate and solve optimal stand density over time problem for even-aged stands using dynamic programming. General Technical Report NC56, 17p.
[5]	Chikumbo, O. (1996). Applicability of dynamical modelling and theoretical control methods in tree growth prediction and planning. Ph.D. Thesis, Canberra: The Australian National University, 273p.
[6]	Chikumbo, O. (2009a). An optimal regime model using competitive coevolutionary genetic algorithms. In A. Dourado, A. Rosa, & K. Ma-dani (Eds.), Proceedings of the International Joint Conference on Computational Intelligence (pp. 210-217). Portugal: Institute for Systems and Technologies of Information, Control and Communication (ISTICC).
[7]	Chikumbo, O. (2009b). Exploration and exploitation in function optimization using stochastic generate-and-test algorithms. In H. R. Arabnia, & A. M. G. Solo, (Eds.), Proceedings of the 2009 International Conference on Genetic and Evolutionary Methods (pp. 22-27). Las Vegas, NV: CSREA Press.
[8]	Chikumbo, O. (2012). Using different approaches to approximate a Pareto front for a multi-objective evolutionary algorithm: Optimal thinning regimes for Eucalyptus fastigata. International Journal of Forestry Research, 2012, 189081. doi:10.1155/2012/189081
[9]	Chikumbo, O., & Mareels, I. M. Y. (2003). Predicting terminal time and final crop number for a forest plantation stand: Pontryagin’s Maximum Principle. In E. Tiezzi, C. A. Brebbia, & J. L. Uso (Eds.), Ecosystems and sustainable development (pp. 1227-1235). Southampton: WIT Press.
[10]	Chikumbo, O., & Nicholas, I. (2011). Efficient thinning regimes for Eucalyptus fastigata: Multi-objective stand-level optimisation using the island model genetic algorithm, Ecological Modelling, 222, 1683-1695. doi:10.1016/j.ecolmodel.2011.03.004
[11]	Coello, C.A. (1996). An empirical study of evolutionary techniques for multi-objective optimization in engineering design. Ph.D. Thesis, New Orleans, LA: Department of Computer Science, Tulane University.
[12]	De Jong, B. H. J., Tipper, R., & Montoya-Gómez, (2000). An economic analysis of the potential for carbon sequestration by forests: Evidence from southern Mexico. Ecological Economics, 33, pp. 313327. doi:10.1016/S0921-8009(99)00162-7
[13]	Faustmann, M. (1995). Calculation of the value which forest land and immature stands possess for forestry. Journal of Forest Economics, 1, 7-44.
[14]	Fonseca, C. M., & Fleming, P. J. (1993). Genetic algorithms for multiple objective optimization: Formulation, discussion and generalizetion. In S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetics Algorithms, San Mateo, CA: Morgan Kaufmann Publishers.
[15]	Gibbons, J. D. (1985). Nonparametric statistical inference (2nd ed.). New York: Marcel Dekker.
[16]	Gutrich, J., & Howarth, R. B. (2007). Carbon sequestration and the optimal management of New Hampshire timber stands. Ecological Economics, 62, 441-450. doi:10.1016/j.ecolecon.2006.07.005
[17]	Haslett, A. N. (1988). Properties and utilisation of exotic speciality timber grown in New Zealand. Part V: Ash eucalypts and Eucalyptus nitens. New Zealand Forest Research Institute, FRI Bulletin No. 119, 20p.
[18]	Hool, J. N. (1965). A dynamic programming probability approach to forest production control. Social American Forest Proceedings, 191193.
[19]	Klemperer, W. D. (1996). Forest resource economics and finance. New York, NY: McGraw-Hill, Inc.
[20]	Kruskal W., & Wallis W. A. (1952). Use of ranks in one-criterion analysis of variance. Journal of the American Statistical Association, 47, 583-621.
[21]	Ljung, L. (1987). System identification: Theory for the user. Saddle River, NJ: Prentice Hall.
[22]	Malinowska, A. B., & Torres, D. F. M. (2007). Non-essential functionals in multi-objective optimal control problems. Proceedings of the Estonian Academy of Sciences: Physics & Mathematics, 56, 336-346.
[23]	Mayo J. H., & Straka T. J. (2005). The holding value premium in standing timber valuation. Appraisal Journal, 73, 98-106.
[24]	Meade, R., Fiuza, G., & Lu, A. (2008). Forest and forest land valuation: How to value forests and forest land to include carbon costs and benefits. Wellington: NZ Institute for the Study of Competition and Regulation Inc., Victoria University of Wellington.
[25]	Menczer, F., Degeratu, M., & Street, W. N. (2000). Efficient and scalable Pareto optimisation by evolutionary local selection algorithms. Evolutionary Computation, 8, 223-247. doi:10.1162/106365600568185
[26]	Miller, J. T., Hay, A. E., & Ecroyd, C. E. (2000). Introduced forest trees in New Zealand: Recognition, role and seed source, Part 18. The Ash Eucalypts: E fastigata, E. regnans, E. obliqua, E. fraxinoides, E. delegatensis, E. fraxinoides, E. sieberi, E. oreades, E. pauciflora, E. dendromorpha and E. paliformis. NZFRI Bulletin 124.
[27]	Nelder, J. A. (1962). New kinds of systematic designs for spacing experiments. Biometrics, 18, 283-307. doi:10.2307/2527473
[28]	Newman D. H., & Wear D.N . (1993). Production economics of private forestry: A comparison of industrial and nonindustrial forest owners. American Journal of Agricultural Economics, 75, 674-684. doi:10.2307/1243574
[29]	Osborne, M. J., & Rubenstein, R. (1994). A course in game theory (p. 7). Cambridge, MA: MIT Press.
[30]	Polheim, H. (2006). GEATbx: Introduction, evolutionary algorithms: Overview, methods and operators. URL. http://www.geatbx.com
[31]	Straka, T. J. & Bullard S. H. (1996) Land expectation value calculation in timberland valuation. Appraisal Journal, 64, 399-405.
[32]	Turner, J.A., West, G., Dungey, H., Wakelin, S., Maclaren, P., Adams, T., & Silcock, P. (2008). Managing New Zealand planted forests for carbon—A review of selected management scenarios and identification of knowledge gaps, Report by Scion for the New Zealand Ministry of Agriculture and Forestry. Rotorua: Scion.
[33]	van Kooten, G. C., Binkley, C. S., & Delcourt, G. (1995). Effect of carbon taxes and subsidies on optimal forest rotation age and supply of carbon services, American Journal of Agricultural Economics, 77, 365-374. doi:10.2307/1243546
[34]	White, A. (2007). Carbon trading outlook: Any additional measures? The Bridge magazine, 7, 38-41.
[35]	Zitzler, E., Deb, K., & Thiele, L. (2000). Comparison of multi-objective evolutionary algorithms: Empirical results. Evolutionary Computation, 8, 173-195. doi:10.1162/106365600568202
[36]