MULTIPLE USE VALUES AND OPTIMAL STEADY STATE AGE DISTRIBUTIONS

Forest management today, generally, focuses not only on wood values but also on the many other amenities and services provided by growing forests. The significance of these multiple use values was recognized by Hartman [1976] who derived a formula for the optimal rotation for a single stand when the services provided by the stand throughout its life are considered in addition to the value of the final harvest. Some more recent work has focused on the case of multiple stands where the amenity values at a point in time depend on the age distribution of the stands at that time. One approach to harvesting multiple stands for wood values alone is the forestry maximum principle developed by Heaps [1984] and Wan [1985]. It will be shown here how the forestry maximum principle can be modified to incorporate the amenity services provided by the growing forest. The optimal steady state age distributions for the multiple stand forest can then be identified and described with the help of Hartman's rotation formula.     

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

The mathematical theory of endosymbiosis,II: Models of the Fungal Fusion hypothesis

A dynamical model of evolution of vascular plants via the Fungal Fusion hypothesis is presented. As in previous work on carbon flux in forest stands, solutions of the Volterra–Hamilton equations representing production of biomass satisfy Huxley’s Allometric Law and are stable curves, but the explicit form of the production cost functional presented here, is simpler. Evolution of the dynamics takes place in stages, via random perturbation of cost produced by genetic drift at the molecular level, natural selection and time-sequencing changes in development. The relationship to the lichen symbiocosm is discussed. Our model presents a new feature, namely, in the final evolutionary stages, physiological production variables are expressed as nonlinear transformations of products of development in earlier epochs. Finally, we point out that, neither the parabolic cone nor the right circular cone method of measurement of carbon production is needed for the mostly young forest stand data gathered by Fonseca in the Mata Atlântica. The cylindrical approximation is sufficient for the most part. Old growth forests, however, will require the more mathematically elaborate techniques.     

红树林自然保护区湿地生态系统的数学模型及其应用

研究了红树林自然保护区自然环境和人类社会活动对于生态系统的影响,考虑了生物之间的相互关系,将生物量、生物生长的面积等作为主要指标,建立了常微分方程组模型,对生态系统的变化情况进行了描述,借助稳定性分析对方程进行了研究,并进行了数值模拟。根据理论分析和数值模拟的结果,对保护区的林木恢复工作提出了合理的建议。     

Sustainable dynamics of size-structured forest under climate change

This work investigates the impact of global climate change on the sustainable growth of forest, namely, on its aggregated characteristics such as the number of trees, the basal area, and the amount of carbon sequestrated in the stand. The forest dynamics is described by a nonlinear size-structured population model. The existence of a steady state regime is proven and explicit formulas for the aggregated characteristics are obtained. A numeric simulation on realistic data illustrates and extends the analytic results obtained.     

A BIOECONOMIC APPROACH TO THE FAUSTMANN–HARTMAN MODEL: ECOLOGICAL INTERACTIONS IN MANAGED FOREST

Abstract This paper develops a bioeconomic forestry model that makes it possible to take ecosystem services that are independent of the age structure of trees into account. We derive the Faustmann–Hartman optimal harvesting strategy as a special case. The bioeconomic model is then extended to account for the fact that forest harvesting decisions impact on other ecological resources, which provide benefits for the wider community. The paper focuses on impacts associated with disturbance caused by logging operations and habitat destruction due to tree removal. This enables us to explore the interactions between forest management and the dynamics of ecological resources. The optimal rotation rule is obtained as a variation on the traditional Faustmann–Hartman equation, where an additional term captures the potential benefits derived from the growth of the ecological resource valued at its shadow price. The steady‐state solutions to the problem and sensitivity to model parameter are identified using numerical analysis.     

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.     

The impact of environmental regulations on forest product trade in China

Forest product trade plays an important role in the development of the Chinese forest industry. The trading value of forest product has shown a yearly growth rate of 12% during the last five recent years. Stringent environmental regulations in China have a profound impact on raw material supplies and industrial production in the forest sector; however, their impact on the forest product trade is still unclear. This study applies fixed and random effects models as well as a seemingly unrelated regression model to investigate the impact of environmental regulations on the trade of forest product from 2002 to 2015. The results indicate that the stringent environmental regulations promoted the import but restricted the export of forest product in general. Specifically, the stringent environmental regulations stimulated the import but had an ambiguous impact on the export of the paper product. The stringent environmental regulations had also stimulated the import of wood product but inhibited the export. In contrast, wooden furniture had been affected minimally; only export got slightly negatively affected by environmental regulations. Recommendations for resource managers:

• Trade‐offs between economic growth and environmental regulations are needed to smoothly promote the forest product trade in China.
• Paper and wooden furniture product sectors are less likely to be affected by stringent environmental regulations, because high value‐added products could compensate for environmental costs.
• The wood product sector is more likely to be negatively affected by stringent environmental regulations because environmental costs could severely impact the competitiveness of low value‐added products.

     

Spatial targeting of payments for ecosystem services to achieve conservation goals and promote social equity and economic impact

The objective of this research was to identify optimal spatial targeting and distributions of a fixed PES (payment systems for ecosystem services) budget that achieves the three objectives of maximizing forest‐based carbon storage to improve cost efficiency, maximizing poverty alleviation to promote equity, and maximizing economic impact to encourage economic development. We used the Central and Southern Appalachian Region as a case study to develop a county‐level framework for identifying optimal county targets and optimal budget allocations for forest‐based carbon sequestration that addresses the three objectives. The results show that optimal budgets are more geographically widespread under the multiple‐objective priority scenarios than under the single‐objective of maximizing carbon cost efficiency, and the optimal spatial distributions of the four priority scenarios do not change appreciably across priority scenarios. The quantified relationships reveal that different priority weights among the priority scenarios yield both competitive trade‐offs and synergistic relationships between the objectives.     

On agreement forests

Tree rearrangement operations are widely used to measure the dissimilarity between phylogenetic trees with identical leaf sets. The tree bisection and reconnection (tbr) distance for unrooted trees can be equivalently defined in terms of agreement forests. For both the tbr distance and the less general subtree prune and regraft (spr) distance, we use such forests to derive new upper and lower bounds on the maximal possible distance between two trees with n leaves.     

The acircuitic directed star arboricity of subcubic graphs is at most four

A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G (that is a digraph with no opposite arcs) is the minimum number of arc-disjoint directed star forests whose union covers all arcs of G and such that the union of any two such forests is acircuitic. We show that every subcubic graph has acircuitic directed star arboricity at most four.     

MODELING FOREST PRODUCTIVITY ACROSS LARGE AREAS AND LONG PERIODS

ABSTRACT. There are three classes of forest model used to simulate forest productivity across large areas and over long periods: growth and yield models, based on statistical relationships derived from measurements on trees; the so-called gap models, concerned with species succession and dynamics, and carbon balance or biomass models. The characteristics of each type are discussed and illustrated by reference to some of the more important of the models in current use. The emphasis in this paper is on the carbon balance models, particularly on a new model (3-PG), developed in a deliberate attempt to bridge the gap between growth and yield and carbon balance models, and the companion model (3-PGS) derived from 3-PG to utilize satellite data as inputs to constrain the simulation calculations and improve estimates of growth over time. 3-PG/3-PGS run on monthly time steps, driven by weather data, and avoid the problems of over-parameterization and the requirements for a great deal of input data that limit the practical value of most carbon balance models. We present test results from 3-PG against experimental data, and against forest plot (mensuration) data from large areas; also test results from 3-PGS against estimates of average forest growth over large areas, and in plantations with different planting times, using AVHRR and Landsat MSS data to constrain the model outputs. The paper discusses the problems of the variability of natural forests and the difficulties this causes in validating models intended for use over large areas. The value of remote sensing as means of overcoming this problem is considered.     

Optimal Forest Harvesting with Ordered Site Access

A long-standing problem in forestry management is the optimal harvesting of a growing population of trees to maximize the resulting discounted aggregate net revenue. For an ongoing forest, the trees are harvested and replanted repeatedly; for a once-and-for-all forest, there is no replanting after a single harvest. In this paper, we outline a new formulation for the optimal-harvest problem which avoids difficulties associated with functional-differential equations or partial differential equations of state in the relevant optimal-control problem encountered in recent studies of the ongoing-forest problem. Our new formulation is based on the observation that tree logging is necessarily ordered by practical and/or regulatory considerations (e.g., it is illegal to cut the younger trees first in some jurisdictions); random access to tree sites does not occur in practice. The new formulation is described here for the simpler problem of a once-and-for-all forest. New results for nonuniform initial age distributions and variable unit harvest costs for this simpler problem are reported herein; results for an ongoing forest will be reported in [10]. The new model is also of interest from a control-theoretic viewpoint, as it exhibits the unique feature of having time as a state variable, in contrast to its usual role as an independent variable in conventional control problems.     

Catastrophic bifurcations in a second-order dynamical system with application to acid rain and forest collapse

In this paper we present a second-order nonlinear dynamical system modelling the interactions of trees and damaging insects in a forest. With this model we discuss the influence of acidic deposition, an increase of which can cause sudden insect infestations and the collapse of the forest ecosystem. The analysis is carried out by finding the bifurcations of the system and by proving that under suitable conditions, such bifurcations can be catastrophic. The conditions for bifurcation can be explicitly given, and this facilitates the biological interpretation of the results.     

GLOBAL CLIMATE CHANGE AND OPTIMAL FOREST MANAGEMENT

A policy question of current interest is how to cope with climate change. One suggestion is to use forests to offset carbon emissions, and therefore, reduce the threat of global warming. This study develops a rigorous model of the relationship between optimal forest harvesting regimes and carbon sequestration. The theoretical analysis integrates the carbon sequestration life cycle into the Faustmann framework and develops optimal cutting rules when carbon sequestration benefits are considered. The carbon life cycle includes both the sequestration of carbon and its ultimate re-release into the atmosphere. A case study of Douglas fir applies the theoretical framework.     

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.     

Regression Tree Analysis Using TARGET

Regression trees are a popular alternative to classical regression methods. A number of approaches exist for constructing regression trees. Most of these techniques, including CART, are sequential in nature and locally optimal at each node split, so the final tree solution found may not be the best tree overall. In addition, small changes in the training data often lead to large changes in the final result due to the relative instability of these greedy tree-growing algorithms. Ensemble techniques, such as random forests, attempt to take advantage of this instability by growing a forest of trees from the data and averaging their predictions. The predictive performance is improved, but the simplicity of a single-tree solution is lost.

In earlier work, we introduced the Tree Analysis with Randomly Generated and Evolved Trees (TARGET) method for constructing classification trees via genetic algorithms. In this article, we extend the TARGET approach to regression trees. Simulated data and real world data are used to illustrate the TARGET process and compare its performance to CART, Bayesian CART, and random forests. The empirical results indicate that TARGET regression trees have better predictive performance than recursive partitioning methods, such as CART, and single-tree stochastic search methods, such as Bayesian CART. The predictive performance of TARGET is slightly worse than that of ensemble methods, such as random forests, but the TARGET solutions are far more interpretable.     

Low‐density barriers for controlling plant crowd diseases: How far and fast can pathogens spread?

We explore numerically the possibility of controlling the spread of plant diseases characterized by relatively low dispersal (crowd diseases) through the introduction of a spatial barrier with low density of susceptible hosts. We use the diffusion approximation to Kendall's spatially extended version of the Kermack–McKendrick epidemic model and illustrate our findings within the context of a representative viral disease that affects cocoa trees. RECOMMENDATIONS FOR MANAGERS:

• Our numerical results suggest that using low‐density barriers of hosts in crowd plant diseases might be an effective way of halting the spatial dispersal of pathogens. The introduction of these barriers may reduce the economic impact when compared with other methods of controlling the disease spread.
• Before using the model to approximate suitable sizes of barriers, it is necessary to execute an exhaustive assessment of the model appropriateness for any particular disease under consideration.
• Our results suggest that to improve the efficiency of low‐density barriers it is important to explore their use in combination of current alternative control methods.

     

A special problem of large scale forest management

The continuously growing need for forestry products and the limited availability of forests have raised the question of how best the forest economy should be managed. In what follows, it will be assumed that a group of cellulose factories will be built in a forest region of a country, where the forest will be cultivated, solely with the needs of the factories in mind. Since large forestry machines will be used, a selective felling of tress will not be possible; a machine removes all the trees from an area being harvested. After that, new trees are planted immediately. This obviously necessitates the forest being divided into smaller subforests, which produce raw material for the factories in a sufficiently continuous manner. the optimal dimensioning of such a system of forests in the steady state is discussed. The basic difference from present practice is the assumption that the time needed for the transportation of wood is negligible; the cost aspect is not considered in this paper.