Optimal Rotation Age Research Articles

Species choice and the risk of disease and insect attack: evaluating two methods of choosing between longleaf and other pines

Summary Management of near-to-nature forests is frequently supplanted by faster-growing ‘industrial’ plantations on the basis of the latter’s superior economic return. These latter species often produce higher volumes of usable biomass in shorter periods of time. Increased yields come with a price, however. While some species provide a superior net present value, they may require a higher cash flow position on the part of the landowner. Other species may possess superior production capabilities but are susceptible to insect and disease attack. Under such conditions, less productive ‘native’ species might produce a satisfactory rate of return considering their reduced risk of attack. We examine two methods of evaluating differences in effective yield and rate of return. The first method, expected value analysis, is a deterministic method that uses decision tree methodology coupled with pre-determined probabilities of outcome for a given series of events and choices. The second method is a matrix model using stochastic transitions between healthy trees and different states of poor health. Markov processes are used to drive simulations of insect and disease attack, and then calculate net present value and optimal rotation age. We keep the final per-unit product price fixed to simplify the analysis and better validate the comparison between the deterministic and stochastic methods. We use longleaf (Pinus palustris Mill.), loblolly (P. taeda L.), shortleaf (P. echinata Mill.) and slash (P. elliottii Engelm.) pines as the species in our comparison. Longleaf is the slowest growing, but it is less prone to attack than the other three. Using more recent Forest Inventory and Analysis (FIA) data, both our Markov analysis and expected value analysis found loblolly and slash pines to be superior economic performers. Earlier FIA surveys support the selection of loblolly and slash over longleaf, but suggest that higher fusiform incidence might push the investment decision towards longleaf pine, particularly vis-a-vis slash pine at higher site indices. Both analysis methods provided the same outcomes, so long as they used the same data. Given this result, a decision tree methodology is a reasonable method for evaluating the economics of species choice in forest restoration activities.

Review - Roger A. Sedjo (2003): Economics of Forestry

Review - Roger A. Sedjo (2003): Economics of Forestry

Economic analysis of slash pine forest carbon sequestration in the southern U. S.

Abstract The impact of a carbon subsidy and tax policy on slash pine (Pinus elliottii) plantations is investigated using a modified Hartman model. Such a policy is shown to increase the optimal rotation age, land expectation value and the supply of sequestered carbon. The supply of carbon increases at a decreasing rate with the price of carbon. The supply of sawtimber increases while the supply of pulpwood decreases. The increase in land expectation value was substantial, suggesting inclusion of carbon sequestration benefits and emission costs would benefit private forestland owners. As the value of forestland increases in response to a carbon policy, more land could be devoted to forestry as opposed to other land uses such as agriculture and urban development.

Forest Rotations and Stand Interdependency: Ownership Structure and Timing of Decisions

This paper extends the Hartman model to study the optimal rotation age of two interdependent stands when the stream of amenities produced from the two stands may be complements or substitutes, both in space and over time. In the presence of stand interdependence both the ownership structure and the sequence of decision making matters. Rotation age choices are examined and compared under a variety of equilibria, including Nash, Stackelberg, and sole owner cases which differ as to the level of commitment by landowners to their choices. We show that the sole owner's rotation age is longer than the rotation age solved under both Nash and Stackelberg assumptions if the stands are spatial complements, but shorter if they are substitutes. The precise relationship between the Nash and Stackelberg rotation ages, and the qualitative properties of rotation ages in terms of timber prices, regeneration costs, and interest rates, also depend on how spatial substitutability and complementarity between stands evolves through time.

Optimal spatial harvest planning under risk of windthrow

This study solves the problem of optimal spatial harvest planning when forest stands are faced by risk of windthrow and the risk depends explicitly on the features of the stand and its neighbours as well as on the geographical structure and orientation of the forest. First, we estimate the optimal rotation age and expected net present value for a range of discount rates and windthrow hazards for an unprotected stand. Next, the influence of shelter is evaluated for a ‘forest’ with two stands. Two different windthrow probability models are analysed. Relative to the one-stand case, the optimal rotation age and the corresponding net present value change significantly when an extra stand is included. This is due to the shelter effect reducing the risk of windthrow. Shelter also increases the optimal rotation age from the lower limit, being the optimal rotation age of a single stand, towards the upper limit being the case without risk. The optimal rotation age is shown to depend on geographic orientation as well as the age difference between the two stands of the ‘forest’. For forests with a higher number of stands, the optimal rotation ages may increase considerably due to the shelter effect. To illustrate this, we investigate the optimal harvest policy for a ‘forest’ with four stands where one of the stands is surrounded by the three others. The sensitivity towards geographic orientation is again analysed. Finally, a ‘forest’ with 16 stands is investigated to exemplify how an optimal short-term policy can be identified for an even higher number of stands, though the optimal harvest ages cannot be calculated within reasonable time.

Faustmann in an uncertain policy environment

This paper deals with optimal forest rotation age and silvicultural investment under policy or regulatory uncertainty to which wasteful deforestation and lack of reforestation and afforestation efforts in the developing countries and loss of old growth forests and biodiversity in the developed countries are attributed. Incorporating a stochastic uncertainty factor into the familiar deterministic Faustmann formula yields a result that confirms with casual observations — when policy uncertainty is present, forest stands are harvested earlier and silvicultural investment is smaller than otherwise. The policy implication is that, in order to promote forest resource conservation, encourage afforestation and reforestation, and attack other forest-related problems effectively, the pervasive nature of policy uncertainty needs to be curbed.

Modelling near-natural silvicultural regimes for beech – an economic sensitivity analysis

Near-natural silvicultural regimes for beech ( Fagus sylvatica L.), in the form of uneven-aged selective felling, receive increasing interest in Denmark. This is partly due to the ability of this system to preserve the forest climate and maintain important ecological functions such as bio-geochemical cycling and biodiversity conservation. The optimal age to convert from even-aged management to uneven-aged selective felling seems to be as early as possible, about 55 years, when sufficient natural seeding can be expected. A fixed conversion period of 100 years is assumed. This regime, here analysed by the use of a so-called chessboard model, appears to be economically superior to clear felling if the regime is initiated in medium-aged stands down to the age of 55 years, assuming a high site quality and a real discount rate of 3% per annum. Uneven-aged selective felling seems to be economically superior to even-aged natural regeneration, assuming that: (i) the stumpage prices of regeneration harvests are increased by 10%, or (ii) the diameters of regeneration harvests exceed those of even-aged management by about 17% simultaneous with an identical increase of the maximum stumpage price. Clear felling seems to be the more profitable regime only if: (i) the stand is close to the economic optimal rotation age for clear felling, and (ii) when the stumpage prices of regeneration harvests achieved by use of the uneven-aged selective management regime are reduced by 10% or more due to quality defects caused by prolonged rotation ages. The above results are sensitive to variation of stumpage prices, but less so to variation of regeneration costs associated with near-natural management systems. However, the near-natural silvicultural regimes may be unable to fulfill the liquidity objectives following from the application of traditional management systems.

Use of uncertain inventory data in forestry scenario models and consequential incorrect harvest decisions

Uncertainty in long-term timber production analyses usually focus success of regeneration, growth/mortality of trees and future fluctuations of timber prices/harvest costs, while uncertainty related to inventory data is paid less attention. At the same time, evaluations of inventory methods usually stop when the error level is stated, while the uncertainty accompanied by using the data is seldom considered. The present work addresses uncertain inventory data in long-term timber production analyses. Final harvest decisions, i.e. possible outcome intervals with respect to timing and expected net present value-losses due to incorrect timing, were considered. A case study was presented where inventory data errors according to different error levels were generated randomly. The selected error levels were based on observations from practical forest inventories in Norway. The analysis tool was GAYA-JLP. The impact of errors on decisions was derived through repeated computations of management strategies maximising net present value without harvest path constraints. A real rate of discount of 3% and an error level of 15% resulted in expected net present value-losses of 1 NOK ha–1 for basal area, 63 NOK ha–1 for mean height, 210 NOK ha–1 for site quality, 240 NOK ha–1 for stand age, and 499 NOK ha–1 when random errors occurred simultaneously for all these variables. The expected net present value-losses varied considerably. The largest losses appeared for stands with ages around optimal economical rotation ages. The losses were also relatively large for young stands, while they were relatively low for overmature stands. The experiences from the case study along with considerations related to other sources of uncertainty may help us to get a more realistic attitude to the reliability of long-term timber production analyses. The results of the study may also serve as a starting point in a decision oriented inventory planning concept, in which alternatives for inventory design and intensity are based on considerations with respect to inventory costs as well as net present value-losses.

Estimating Economic Gains for Landowners Due to Time-Dependent Changes in Biotechnology

Abstract This paper presents a model for examining the economic value of biotechnological research given time-dependent changes in biotechnology. Previous papers examined this issue assuming a time-neutral change in biotechnology. However, when analyzing the genetic improvements of increasing a tree's resistance to a pathogen, this assumption is untenable. We derive analytical expressions for the optimal rotation age given non-constant changes in biotechnology. Our model is then implemented using (1) growth and yield simulations, (2) optimal rotation calculations, and (3) survey data on genetic resistance of slash pine (Pinus elliottii) to fusiform rust. Non-parametric regression models are used to estimate the economic gain functions which, for the cases considered, averaged about 1% of forestland value per year. For. Sci. 45(2):163-170.

Risk Preferences and Adaptive Harvest Policies for Even-Aged Stand Management

Abstract Uncertainty in future states of nature affects the set of feasible management alternatives as well as a forest owner's preferences among different alternatives. To incorporate uncertainty into forestry decisions, both effects should be recognized simultaneously. This study concerns the final harvest decision in even-aged stand management with stochastic stumpage prices. An expected utility maximization model is developed for determining the optimal adaptive harvest policy. Instead of assuming risk-neutrality on the side of forest owners, the model explicitly incorporates risk preferences into the determination of reservation prices. A method for estimating the set of efficient adaptive harvest policies for risk-averse forest owners is developed based on the mean-variance rule and stochastic dominance analysis. The set of efficient adaptive harvest policies is estimated and compared with the set of efficient rotation ages for two example stands. Numerical results show that any risk-averse forest owner prefers the optimal adaptive harvest policy to the optimal rotation age. By using the rule of "harvest only when the observed stumpage price is equal to or higher than the reservation price," the expected net present value can be increased, and, meanwhile, the standard deviation of the net present value can be reduced significantly. Incorporation of risk-aversion leads to reservation prices that may be lower than those that maximize the expected net present value. It indicates that risk-averse forest owners typically should harvest earlier than risk-neutral forest owners. For. Sci. 44(4):496-506.

Optimal stand management with endogenous risk of sudden destruction

The optimal thinning and rotation age policy for a stand subject to risk of destruction by windthrow is investigated. In particular, risk is not assumed exogenous as in previous research, but is modelled as endogenous to stand management. It is shown that the optimal solution when risk is endogenous differs significantly from the optimal solution to a problem where risk is assumed absent or exogenous. We find that in spite of substantial fixed costs related to thinning, the optimal number of thinnings increases and the optimal intensity of each thinning decreases. Furthermore, we find that the shortening effect of risk on the optimal rotation age is reduced substantially, when the thinning strategy is optimized subject to the effect on the risk levels. We conclude that the presence of endogenous risk strongly affects the optimal management strategy, and that an ecologically better founded approach to stand management is optimal in such cases. A group of solutions centred around a local optimum was characterized by fewer, more intense thinnings and a drastic shortening of the rotation age. If fixed costs were to increase substantially, this local optimum may become global, but still result in a longer rotation and more frequent thinnings than in the case of exogenous risk. Finally, features of the model's risk dynamics allow an analysis of the effect of changing the stand's resistance to and ability to recover from (i.e. the stand's resilience) the disturbances caused by thinnings, measured as changes in the susceptibility to windthrow. We find that in spite of the fixed costs related to thinning, a decrease in resistance or resilience makes it optimal to increase the number of thinnings, while at the same time making each thinning less intense.

Optimal forest rotation age when carbon captured is considered: theory and applications

Optimal forest rotation age when carbon captured is considered: theory and applications

Searching for an optimal rotation age for forest stand management under stochastic log prices

Due to rapid change in timber prices in the Japanese market most likely affected by imported timber from countries such as the U.S., Canada, and the Nordic countries, the domestic forest managers have been facing a large degree of future price uncertainty. Because of this, it becomes necessary to take the future price uncertainty into account within the forest management framework. In this paper, the continuous time stochastic process, i.e., the geometric Brownian motion, has been used to model the log price process. The binomial option pricing approximation was then applied to value the Sugi ( Cryptomeria japonica) and Hinoki ( Chamaecyparis obtusa) forested land under stochastic log prices in order to search for an optimal rotation age. Our experiments with the proposed two state stochastic dynamic programming model showed that when the current log price is high enough to cover all costs, an optimal rotation age from the stochastic price and deterministic price models coincides, although the total expected present net value from management activities differs. Also it was shown that as the current log price decreases, an optimal rotation age derived from the stochastic price model becomes longer than that from the deterministic price model. If the current log price further decreases, then forest management will be abandoned, and the forest stand will be converted into alternative uses.

Optimal forest rotation age when carbon captured is considered: theory and applications

Carbon dioxide (CO2) is the gas most responsible for the greenhouse effect. Since trees absorb CO2 during growth, some authors have argued for the importance of considering forests not only as timber producers but also as carbon pools. The consideration of carbon uptake as a public good generates a divergence between the private and social optima. This paper presents a methodology to determine optimal forest rotation ages in this context of multiple use and to remove the divergence between these two optima. A theoretical framework, based upon compromise programming, is applied to a case study of a beech forest in Spain, within the context of the current European financial aid for afforestation programs.

ENVIRONMENTAL AND FINANCIAL SUSTAINABILITY OF FOREST MANAGEMENT PRACTICES

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or nondeclining flow of services from the forest is socially desirable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber‐productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforestation and rehabilitation costs, and the impact of the system on the productivity of the site.An application of the model is presented for lodgepole pine in Alberta. We conclude that, at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for more intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvesting on soil productivity.

Environmental and Financial Sustainability of Forest Management Practices

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or non-declining flow of services from the forest is socially desireable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber-productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforesation and rehabilitation costs, and the impact of the system on the productivity of the site. An application of the model is presented for lodgepole pine in Alberta. We conclude that at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for mroe intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvsting on soil productivity.(This abstract was borrowed from another version of this item.)

A Strategy for Multiproduct Stand Management with Uncertain Future Prices

Abstract This paper presents a strategy for stand management with multiple series of stochastic prices. When the only decision is to reject or accept a set of prices for a clearcut, the strategy is to accept and clearcut in the current period if the revealed revenue is at least as large as the current reservation revenue. This strategy is shown to be optimal when the price process is stationary and temporarily independent with the possibility of cross-product price dependence. Simulation involving red pine yields separated into two products, pulp and sawtimber, show the reservation revenue harvest strategy is far more consistent with current management practice than previous analyses involving a single product, sawtimber, have indicated. The probability distribution of optimal rotation ages is similar to a series of exponential (also called "waitingtime") distributions with new peaks at each major ingrowth event in the multiproduct yield function. The financial implications of considering pulp and sawtimber price uncertainty simultaneously are also addressed. For. Sci. 42(1):58-66.

A cost function estimating the loss due to extended rotation age

A method for estimating the economic loss in timber production resulting from extending the rotation age was studied. Basically, optimal rotation age depends on the stated objectives. If the objective comprises only timber production, the rotation age is derived from maximizing the net present value (PV) of timber production. If, on the other hand, the objective function includes, for example, the maintenance of biodiversity and scenic values, the optimal rotation age is likely to be extended. In the present study, PVs from successively extended rotation ages were estimated for a sample of economically mature stands. The PVs were based on no thinning allowed (case A), and thinning allowed in the first 5‐yr period (case B). By using regression analysis, functions were estimated that predict the inoptimality loss from extending the rotation age for both cases. Stand data collected by subjective (ocular) inventory methods were the regressors. Only the problem of economic loss in timber production from extend...

An Interactive Thinning Simulation for Red Pine Stands

Abstract This paper describes a computer program, REDPTHIN, that permits the development of optimal thinning schedules for red pine plantations in the Lake States. The optimal schedules maximize total cubic foot volume production for any initial stand condition of age, site, and basal area stocking. These optimal schedules are derived via a special dynamic programming algorithm that the author developed. User specified thinning schedules can be simulated. Optimal biological rotation age and mean annual increment can be derived from the output table. North. J. Appl. For. 12(1):43-48.

More on Forest Regulation: An LP Perspective

Abstract Optimal solutions to some 2500 linear programming formulations were compared to examine the impact of forest regulation constraints. The solutions demonstrate that regulation can be expensive, with no simple rules available to describe how a regulated forest can best be achieved or what rotation age should be used for the regulated forest. The optimal rotation age can be longer or shorter than the Faustmann rotation, but results strongly suggest that the optimal rotation will be close to the Faustmann rotation if long conversion periods are used. The cost of regulation can be sensitive to the length of the conversion period, the initial age distribution of the forest, stability constraints on harvests during the conversion period, and the range of management options and rotation ages possible. Large cost savings are sometimes possible with relatively small increases in the length of the conversion period. The need to hold land idle during the conversion period can substantially increase the cost of regulation. FOR. SCI. 39(2):321-347.