United States Department of Analysis of Agriculture Multiresource Production Forest Service for National Assessments Rocky Mountain Forest and Range and Ap]praisals Experiment Station L.A. Joyce Fort Collins, B. McKinnon Colorado 80526 J. G. Hof T. W. Hoekstra General Technical Report RM-101

1 Management prescription C I Management prescription B Management prescription A

Ecosystem I

Adjacent ecosystems

Joint resource outputs resulting from Prescription A Abstract

This report gives an overview of the analytical methods used in in­ tegrated (multidisciplinary, multiresource, and multilevel) land management production analyses. The ecological and economic theory underlying both simulation and optimization methods are also reviewed. USDA Forest Service August 1983 General Technical Report RM-101

Analysis of Multiresource Production for National Assessments and Appraisals

L. A. Joyce, Range Scientist B. McKinnon, Forest Economist J. G. Hof, Research Forester and T. W. Hoekstra, Research Wildlife Biologist Rocky Mountain Forest and Range Experiment Station1

'Headquarters is in Fort Collins, in cooperation with Colorado State University. Contents

Page MANAGEMENT IMPLICATIONS ...... 1 INTRODUCTION ...... 1 ECOLOGICAL ANALYSES OF PRODUCTION ...... 2 Ecosystem Theory ...... 2 Ecosystem Approaches ...... 2 Ecosystem Attributes ...... 3 Environmental Indexes ...... 4 Interdisciplinary Team Approach ...... 6 Simulation Modeling ...... 6 Model Building ...... 6 Applications of Simulation Models ...... 7 Summary ...... 7 ECONOMIC ANALYSES OF PRODUCTION ...... 7 Economic Theory of Production ...... 7 Single Output Production ...... 8 Multiple Outputs and Joint Production ...... 8 Mathematical Programming ...... 9 Linear Programming ...... 9 Linear Programming and Production Theory ...... 10 History of Linear Programming Applications ...... 11 Early Applications of Linear Programming to Forestry Problems ...... 11 Goal Programming ...... 11 INTEGRA TED APPROACHES TO ANALYZING THE PRODUCTION OF NATURAL RESOURCES ...... 12 Linear Programming Multiresource Management Problems ...... 12 Multiresource Models ...... 13 The CARD-USDA Agricultural LP Model ...... 13 RCS-RAA ...... 13 FREPAS ...... 14 NIMRUM ...... 15 FORPLAN...... 16 CONCLUSIONS ...... 17 LITERATURE CITED ...... 17 Analysis of Multiresource Production for National Assessments and Appraisals

L. A. Joyce, B. McKinnon, J. G. Hof, T. W. Hoekstra, and J. Whelan

MANAGEMENT IMPLICATIONS There is no commonly accepted, ecological technique to analyze the simultaneous production of natural The dominant approach in integrated resource pro­ resources applicable in all ecosystems. Production duction analysis is optimization modeling, specifically capability/response information must be determined for multiresource linear programming modeling. Tradeoffs the optimization models quantitatively for each between alternative resource production strategies can resource, with the integration being qualitative. Ad­ be examined under a variety of decision criteria in these vances in ecological research are increasing the degree models. The theoretical basis for this approach is well­ to which the production capability/response relation­ founded in the economic theory of production. The suc­ ship can be quantified. Resource analysts must select cessful use of these models presumes the availability of the appropriate analytical technique for their specific benefit/cost information from supply/demand models, management problems. and the availability of production capability/response information from ecological models. Because this review The recent work of Wong (1980) in hierarchial model­ focuses only on the production side of integrated re­ ing suggests promising ways to include multilevel con­ source analysis, it does not consider the availability of siderations into integrated resource production benefit/cost information. analyses.

INTRODUCTION with the requirements of the Renewable Resource Research Act, Cooperative Forestry Assistance Act, and National assessments of forests, range lands, agri­ the Public Rangelands Improvement Act. cultural lands, and associated waters of the United Natural resource outputs, such as timber, wildlife, States are required by law. These assessments must be etc., can be analyzed in several different frameworks. multidisciplinary, multiresource, and multilevel. This Resource outputs can be examined functionally in terms report is an overview of the analytical techniques used of timber, range, wildlife, etc., or they can be examined in integrated land management analyses, where inte­ in a multiresource context. They can be evaluated in grated includes multidisciplinary, multiresource, and ecological terms, economic terms, or sociological terms. multilevel considerations. Resource outputs can be analyzed at the level of the Assessments, appraisals, and inventories are re­ forest, the region, or the nation. Current production of quired by a number of laws. An assessment of renew­ resource outputs can be assessed, and projected trends able resources on forests and rangelands is required by of the current production can be made, or alternatives the Forest and Rangeland Renewable Resources Plan­ for future production possibilities can be projected. ning Act of 1974 (RPA)2 as amended by the National Analytical techniques have been developed to inte­ Forest Management Act of 1976 (NFMA)3. Appraisals of grate these different tasks specified by law and these the soil, water, and related resources are required by different analytical frameworks. Optimization models the Soil and Water Resources Conservation Act of 1977 are one method used to integrate multiresource, multi­ (RCA}'. Adequate inventories and documentation for disciplinary, and future-oriented considerations. These development of policies and management of the nation's optimization models require as input predictions about federal lands are required by the Federal Land Policy future conditions, which are developed from ecological and Management Act of 1976 (FLPMA)5• The Multiple and economic simulation models. Specifically, supply/ Use-Sustained Yield Act of 1960 (MU-SY)8 requires joint demand models can provide benefit/cost (economic) in­ consideration of the major outputs from the national formation, and ecological analyses can provide produc­ forests. Accounting for the environmental impact of tion capability/response information. Social analysis management is required by the National Environmental models can predict the social impacts of the solutions Policy Act of 1969 (NEPA)7. The RPA, as amended by the given by optimization models. NFMA, requires that these assessments be coordinated Optimization models are the dominant integrated analytical technique, because they provide a framework •Public Law 93-378. United States Statutes at Large. Volume 88, for a quantitative analysis of resource production in an p. 476 (Pub. L. No. 93-378, 88 Stat. 476). economic and biological environment. Other integrated •Pub. L. No. 94-588, 90 Stat. 2949. approaches have not provided such a framework for in­ •Pub. L. No. 95-192, 91 Stat. 1407. tegrating inputs from ecological, economic, and social "Pub. L. No. 94-579, 90 Stat. 2743. '74 Stat 215, as amended; 16 U.S.C. 528-531. analyses that is consistent with the currently accepted 'Pub. L. No. 91-190, 83 Stat. 852. perspectives in ecology, economics, and social analysis. This report focuses on the production or supply side predicting the production of natural resources have gen­ of integrated resource analysis. The theory underlying erally focused on single resource outputs (Alig et al. the ecological and economic analyses is -reviewed first. 1983, Hawkes et al. 1983, and Mitchell 1983). This presentation of ecological analyses reflects the Analysis of joint production using an ecosystem ap­ state-of-the-art in its concentration on those theoretical proach to natural resource management is relatively re­ approaches which have been applied in a limited cent (Van Dyne 1969), and quantitative techniques are number of cases. There is no commonly accepted ecolog­ in early stages of development. Progress in this area has ical technique to analyze the simultaneous production of been hampered by insufficient and inadequate data, and natural resources in an ecosystem. In contrast, there by lack of ecological theory. Long-term records of are standard analytical techniques to analyze the pro­ ecosystem response to management under controlled duction of natural resources in an economic framework. conditions are rare. Although advances in ecological These techniques have been expanded to analyze multi­ theory continue to be made, there is no single, unifying resource production. These multiresource optimization theory about ecosystem structure and function that modeling techniques are reviewed last, and include a could be applied to all ecosystems. review of those techniques which attempt to include This review focuses on those theoretical ecological multilevel considerations. analyses which have been used to examine the impact of management. Different approaches in ecological research have increased understanding of ecosystem ECOLOGICAL ANALYSES OF PRODUCTION functioning, and this understanding has been used to ex­ amine the impact of management on the ecosystem's Land management activities affect the structure and productive capacity. Ecosystem-level models, such as function of an ecosystem. Changes in the ecosystem the large-scale simulation models of the International cause changes in resource outputs (fig. 1). Analytical Biological Program, attempt to quantify all pertinent techniques predicting single resource production quan­ aspects of the ecosystem and track the impacts of tify those pathways in figure 1 pertaining to the single management on the entire system. Another approach resource, such as timber or wildlife. A consideration of has been to quantify attributes of the ecosystem which the impact of this single resource management on other could act as indicators of ecosystem health. When the pathways, and the joint production of resource outputs complexities become too great to quantify, more in­ is necessary to evaluate the impact of management on tuitive approaches, such as an interdisciplinary team, the ecosystem. This is often done intuitively by have been used to estimate the impact of management. managers in the field. The problem is quantifying the Because of the diversity of approaches, the resource interaction of these pathways. Quantitative techniques analyst must select that technique which best describes

Management prescription C the impact of the particular management activity being Management prescription B considered. Management prescription A

Ecosystem Theory

Ecosystem I Ecologists have struggled to define a theoretical struc­ ture for ecological research (Haug 1981), and these continuing struggles approach the problem from two directions. The first approach views the ecosystem as a system and attempts to define a general theory of ecosystem behavior applicable to all types of eco­ Adjacent systems. The theoretical work of Miller (1978) is an ecosystems appropriate example of this category. The second ap­ proach focuses on attributes of the ecosystem and at­ tempts to define the relationships of the parts in order to ...... describe the whole. Large-scale simulation models, such as the shortgrass prairie model, ELM (Innis 1978), are examples of this approach.

Ecosystem Approaches

Ecosystem-level theories represent frameworks inte­ grating ecosystem structure and function. The ap­ proaches differ in their theoretical assumptions and their degree of quantification. Examples of these ecosystem-level theories include: the system dynamics Figure 1.-Management prescriptions, ecosystem structure, and approach of Gutierrez and Fey (1980), the living systems resource outputs. theory of Miller (1978), the linear modeling approaches

2 of Patten (1975, 1976), and the energy analysis of H. T. ance on these attributes. This understanding can then Odum (1971). Further development of these theories may be used to examine the impact of management on the suggest a unifying theoretical framework for the individual attributes as an indicator of the impact of analysis of joint production in an ecosystem. Currently, management on the entire ecosystem. some of these approaches (H. T. Odum 1971) are being A thorough review of ecosystem attributes and their applied to natural resource problems and have provided numerous and diverse models is not possible here. valuable information to planners (Littlejohn 1977). Instead, the-types of models that have been used to Because of the success of H. T. Odum's (1971) approach, describe these attributes in a resource management ap­ it is briefly summarized. plication are briefly described. H. T. Odum and co-workers at the University of The ecosystem attributes of habitat space and carry­ Florida state that all systems obey three laws of energy. ing capacity have been used extensively to analyze the The first law of thermodynamics was restated by Odum effects of management on wildlife and fish populations. and Odum (1976) as the law of conservation of energy in Habitat space is defined as the distributional rela­ an ecosystem. "The energy entering a system must be tionship of species to environment Uohnson 1977), and accounted for as being stored there or as flowing out" the selection of a habitat has been modeled as a function (Odum and Odum 1976). The second law of thermody­ of environmental pattern, competition, or population namics was restated as the law of degradation of densities (Rosenzweig 1981). Carrying capacity of a energy. "In all processes some of the energy loses its species refers to that population size which is asymptoti­ ability to do work and is degraded in quality" (Odum and cally approached when growth of a population is repre­ Odum 1976). To these two laws Odum and Odum (1976) sented mathematically by a logistic equation. The added a third law, first conceptualized by Lotka in 1925. behavior of a population around its carrying capacity Referred to as the Maximum Power Principle, this law varies, depending upon the population control mech­ states, "That system survives which gets most energy anisms of that species. and uses energy most effectively in competition with Population growth is a function of interacting abiotic other systems." It is this third law which suggests those and biotic limiting factors Uohnson 1977), and the types ecosystems survive which maximize the input of energy of models predicting population growth are as diverse and use it most efficiently to meet survival needs. as the populations themselves. The types of models in­ The impact of channelization of the Gordon River, clude differential equation models (May 1973), matrix near Naples, Fla., was assessed using Odum's approach models (Usher 1972), and simulation models containing (Littlejohn 1977). The relationship between the changing several different mathematical formulations. Factors in­ patterns of land use and regional water regimes was corporated in these models include variable birth and quantitatively expressed, and the role of wetlands in death rates, competition, predation, density of popula­ maintaining aquifer stability was evaluated in three tion, and spatial complexity of the environment. Hawkes alternative land-use scenarios, including full devel­ et al. (1982) reviewed this literature on models of habitat opment. The model demonstrated the impact of devel­ space, carrying capacity, and populations in natural opment on aquifer stability and provided opportunities resource management. to test several water management plans. The Collier A species niche can be described as the environ­ County Commissioner adopted, in principle, the final mental dimensions in which that species alone can exist. contract report8 as a development plan for the region. This would include temperature ranges, humidity and salinity ranges, and biological factors such as prey species. Based on the premise that two species cannot Ecosystem Attributes co-exist in exactly the same niche, species interactions are examined by measuring niche dimensions, such as Many ecosystem processes have been described and bill length and width of birds. Franz and Bazzaz (1977) mathematically modeled. Because ecology is a young used the theory of niche differentiation to determine the science, the theoretical interpretation of each process relative impact of alternative reservoir designs on vege­ or attribute may not be universally agreed upon, and, in tation in the backwater zone of the reservoir. The occur­ fact, the significance of the attribute may be in question. rence of each tree species was described in a prob­ Johnson (1977) presented a set of ecosystem attributes ability distribution as a function of flood frequency at commonly recognized by ecologists. These attributes in­ each of three points along the river. These distributions cluded: niche; habitat; carrying capacity; community characterized the ability of each species to survive and characteristics such as diversity, trophic organization, grow, given the particular frequency of flood stages at and populations; competition; succession; resilience; that point along the river. Changes in flood stage fre­ growth; nutrient cycling and energy flow; and evolution. quencies, resulting from each reservoir design, were Ecological studies have described parts of ecosystem simulated with each of these species distributions to structure and function in terms of these attributes (E. P. determine species changes along the gradient and, thus, Odum 1971, Krebs 1972, and Ricklefs 1979). Further community impact. Recommendations were made for the studies have examined the effect of ecosystem disturb- design that produced the least impact in community composition. •odum, H. T., C. Littlejohn, and W. C. Huber. 1972. An environ­ ment evaluation of the Gordon River area of Naples, Florida, and the The matter of how to describe diversity, at either the impact of development plans. Department of Environmental Engi­ species level or the ecosystem level, has received con­ neering Sciences, University of Florida, Gainesville. siderable debate (Ricklefs 1979). Measurements of plant

3 and animal species diversity provide an overall estimate Montana habitat types including lodgepole pine, ponder­ of the variety or number of species (species richness) osa pine .. Douglas-fir, subalpine fir, whitebark pine, and and their relative abundances (evenness of distribution). spruce communities (Kessell and Potter 1980); Appala­ There are many sampling problems associated with field chian deciduous forest (Shugart and West 1977); north­ measurements of diversity, and all of the diversity in­ eastern hardwoods (Botkin et al. 1972); aspen (Cattelino dexes appear to be sensitive to these problems (Ricklefs et al. 1979); and grassland (Gutierrez and Fey 1980, 1979). Bledsoe and Van Dyne 1972). None of these models in­ Hurlbert (1971) discussed the many semantic, concep­ clude wildlife or fish population changes. tual, and technical problems associated with the Energy flow and nutrient cycling have received much measurement and interpretation of species diversity. He study at the ecosystem level in recent years. As both concluded that communities with different species com­ nutrients and energy flow through the ecosystem, each positions are not intrinsically arranged in linear order has been used as a currency to include all ecosystem on a diversity scale. Therefore, although a diversity component interactions in one model. index may show a correlation with other properties of a Richey (1977) studied the phosphorus cycle of a lake community or environment, that correlation is not evi­ using a simulation model. The model building process in­ dence that the index is either appropriate or useful. Sim­ volved interactions with field work, where parameters ilarly, two or more sets of data could have the same rela­ suggested in the model-building process were m~asured tive abundances of totally different species and still in the field. Once the model was constructed, certain have identical diversity index values. questions were asked of it. For example, "Is it important Species diversity on an island has been shown to be a to know the flux as well as the concentration of function of the total land area of the island and the phosphorus in determining its importance in a lake?" distance from the mainland (MacArthur and Wilson (Richey 1977). The response of the model to such ques­ 1967) and can be viewed as an equilibrium between im­ tions was used to suggest further experimental work. migration and migration. Islands can be interpreted as Several simulation models of energy flow and of nutrient units of land surrounded by a barrier such as water, or cycling have been used in a similar manner in other human development. Island biogeography theory has types of ecosystems. been further refined by field and mathematical simula­ Energy flow and nutrient cycling have also been stud­ tion experiments. Shaffer (1981) outlined the implica­ ied to understand the effects of management on eco­ tions of this theory in the determination of the minimum system processes. For example, a model describing the viable population size of a species, and various authors sulfur cycle of a grassland system was used to examine in Soule and Wilcox (1980) addressed the implications of the effects of increased sulfur dioxide from a nearby this theory in the management of wildlife and the design coal-powered electricity plant (Coughenour et al. 1980). of wildlife reserves. Resilience is the ability of an ecosystem to recover Mathematical models have been developed to de­ from an external perturbation. Ecosystem response to scribe trophic structure and the impact of change on perturbation is usually nonlinear and is a function of the that structure. May (1973) recognized four primary magnitude, frequency, and type of perturbation. Quan­ features of trophic structure: the number of species in­ tifying this attribute has been difficult because of the in­ volved, the nature of their interconnections, the number adequate understanding of the ways ecosystems re­ of connections per species, and the intensity of interac­ spond to stress. Cooper and Zedler (1980) recognized the tions between web members. Paine (1980) stressed the importance of this concept in environmental impact and importance of the intensity of interactions between web incorporated it into their process, although subjectively. members. According to Paine, trophic links are unequal Johnson (1977) included the attribute evolution in his in strength. The relative strength of interaction is par­ list, and what is, perhaps, most important for natural tially the result of the consumer's density and partially resource models is not the process of evolution itself, but the result of the limitation on the predation process the concept that systems evolve. While the effects of imposed by prey size. Strong interactions can be deter­ evolution may take a long time to actually see, the proc­ mined experimentally by examining the impact which ess is going on continually. This evolutionary viewpoint removing a species has on a community. Human activity is evident in Holling's (1978) work on analytical tech­ has indirectly tested this theory about the importance of niques for environmental impact assessment which can interaction strength, and the effect of a species reintro­ readily incorporate change. duction was successfully predicted from this theory (Paine 1980). Most mathematical models of food webs do not incorporate interaction strength. The importance of Environmental Indexes this concept suggests that those models that examine interaction strength will become increasingly valuable Environmental indexes synthesize information on the (Paine 1980). impact of an activity on the environment. Two general The patterns of plant populations in succession have categories of indexes can be seen: (1) those indexes been theorized for all ecosystems (E. P. Odum 1971) and which synthesize several environmental measurements, quantified for several ecosystems. Simulation models of such as an air pollution index, and (2) those indexes plant succession exist for a variety of ecosystem types: which synthesize the intuition and experience of field western coniferous forest (Reed and Clark 1979); nine experts or managers, such as quality of life indexes.

4 Ott (1978) pointed out six basic uses of environmental Index method (Klopatek et al. 1980). It is based on the indexes: following: . . . 1. Resource allocation-to assist managers in allo­ 1. identifying important ecological resources Withm cating funds and determining priorities; the area, 2. Ranking of locations-to assist in comparing en­ 2. determining the extent of those resources, and vironmental conditions at different locations; 3. computing the area quality val~e by creatin~ a 3. Enforcement of standards-to determine whether matrix which combines the magmtude of a partiCu­ standards are being met; lar resource and the importance of that resource. 4. Trend analysis-to determine changes in environ­ The overall index is calculated using nationally avail­ mental quality over time; able data on vegetation, avian species, mammalian 5. Public information-to inform the public about species, and threatened and endang~red SJ?ecies. ~he environmental conditions; Ecological Index represents a hierarchical rat~ng 6. Scientific research-to reduce a large quantity of system in which all parameters are analyzed, usmg data to a form that gives insight to the researcher three levels of stratification: national, regional, and conducting a study of some environmental phe­ ecoregion section. The index filters information from nomena. one level to another. Although this index incorporates both habitat and species data, it lacks an aquatic com­ The use of environmental indexes is often contrasted ponent. However, it appears. that su~~ a. component with the use of a mathematical model in determining en­ could be included with only shght modification. vironmental impact. The construction of a mathematical The Wildlife Habitat Quality Index (USDA 1981) was model of an ecosystem may require more detailed data described in the RCA 1980 Appraisal, Part II. Indexes of and theory than is currently available. Therefore, it habitat quality, which reflect the overall :ralue of appears more attractive to use an environmental inde;x. habitat for a wide variety of vertebrate species, were Ott (1978) stressed that index development must begm developed for croplands, pasturelands, range lands, with a carefully defined concept of the purpose of the forest lands, wetlands, and aquatic areas (rivers, index and that the original purpose must be respected streams, and ponds). Availability of food and cover for when the index is used. Ott (1978) pointed out that wildlife was considered to be a function of land use. because indexes are meant to simplify, in the process of Weighted values were developed for several resources forming an index, some information is lost. This is a (e.g., forest lands, croplands) based on factors that con­ problem only when the index is later used to answer a tributed to habitat quality (e.g., grazed versus ungrazed question it was not designed to address. forest). Wildlife habitat quality was estimated usi.ng Cooper and Zedler (1980) proposed a regional envi­ data from the 1977 National Resource Inventones ronmental assessment process that involved mapping (USDA Soil Conservation Service 1977).9 W~t~r qual~ty and subjective expert ratings of the impact of an activ­ (e.g., nutrient levels, sediment loads) an? mimmum m­ ity. They felt that, no matter how small, every project stream flow requirement data were considered to be es­ should be viewed in a regional setting, so that the sential for estimating quality of fish habitat. In addition cumulative impacts likely to be missed in case-by-case to the water quality and water supply for farm ponds, appraisals would be identified. Relative levels of the size and location of the ponds were considered im­ ecosystem sensitivity were assigned to each tract of portant in limiting fish production. Estimates of fish land in the region by a team of scientists. Ecosystel? s~~­ habitat quality were made using data from the Second sitivity was characterized by three components: signifi­ National Water Assessment (U.S. Water Resources cance of the ecosystem regionally and globally, rarity or Council 1978). Information on wildlife or fish species abundance of the ecosystem relative to others in the (e.g., presence or absence, relative abundance) was not region or elsewhere, and resilience of ~he ecosyst~m. included in this method. Determining ecosystem significance reqmred evaluatmg Short1o developed a technique whereby wildlife com­ its biological importance in terms of species composi­ munities can be evaluated on the basis of vegetation tion, resource outputs, genetic reservoir, scientific structure. The physical strata in a cover type where a value, and esthetic value. Ecosystem size and occur­ species feeds and/or breeds are used to classify the rence are the factors involved in evaluating rarity. The species into cells within a species-hab:tat matrix. The resilience of an ecosystem is a measure of a system's wildlife guilds that may occur in a cover type are deter­ ability to absorb environmental stress without chan?ing mined by cluster analysis. Impacts on wildlife are t~Ien to a recognizably different ecological state. Each umt of determined by examining the changes in the physical land was rated at one of four sensitivity levels, from strata of the vegetation cover type. While the approach minimally sensitive to maximally sensitive. The sensi­ looks at species guilds, an index of total impact could be tivity ratings were meant to provide information on the computed. likely impact of an activity. Cooper and Zedler (1980) 'USDA Soil Conservation Service. 1977. Erosion Inventory In· recognized that the use of an interdisciplinary team to structions for County Base Data. Internal memo dated March 25, evaluate ecosystem sensitivity was subjective; however, 1977. 7 p. Washington, D.C. Also, USDA Soil Conservat~on Service. the degree of agreement attained among the team 1977. Erosion inventory instructions for the PSU and_ pomt data col­ members suggested this was a worthwhile approach. lection. 20 p. Internal memo dated June 1977. Washmgton, D.C. '"Short, Henry. 1981. A technol~gy for stru~t~ring, evaluating, Another example of attempting to evaluate the impor­ and predicting impacts on wildlife commumt1es. (Unpublished tance of an ecosystem can be found in the Ecological manuscript).

5 Interdisciplinary Team Approach predicting shifts in species composition of plant and animal communities, particularly terrestrial communi­ The use of a team of experts to estimate environ­ ties. Intuitive approaches integrate the person's experi­ mental indexes or assess environmental impacts has ence and knowledge in a way that is not easy to track, received much attention because of the difficulty in ob­ but that may fill some gaps that are unavoidable in taining data (Suffling 1980) and the difficulty in quanti­ forest planning or research. fying ecosystem-level relationships (Cooper and Zedler 1980). An intuitive approach, such as a team of experts, Simulation Modeling relies on the experts to integrate their experience and the current knowledge to estimate the impact of man­ Model Building agement on the ecosystem under a wide variety of situa­ tions. Intuitive approaches have been used to estimate Simulation refers to mathematical and statistical environmental variables not easily quantified and to models that have been implemented on a computer. estimate environmental variables which there is insuffi­ Their use in ecology and resource management has cient time to measure. greatly increased in the past 15 years. The process of Examples of the first situation include the estimation constructing a simulation model can be broken into five of ecosystem sensitivity proposed by Suffling (1980) and stages: conceptual, diagrammatic, mathematical, com­ the regional environmental assessment process pro­ puter programming, and validation/verification. posed by Cooper and Zedler (1980). Another example In the conceptual stage, the modeler's experience and would be the qualitative estimates of the 12 resource intuition suggests important features about the system's outputs in the FRES study (Kaiser et al. 1972). Among the structure to be modeled, given the questions being asked estimated resource outputs were air quality, soil stabil­ about the system. In the diagrammatic stage, word ity, rare and endangered species, depressed area im­ models and diagrams are used to structure the model. pact, soil quality, and flexibility for future management. The most commonly used diagrammatic model is the An example of the second intuitive approach would be "box-and-arrow" diagram, or the compartment dia­ the forest planning process in the National Forest Sys­ gram. There, boxes represent components or compart­ tem. There, a team of experts, referred to as the inter­ ments of an ecosystem, and the arrows show inputs to disciplinary team (ID team), must develop a management and outputs from each compartment (fig. 1). Inputs to a plan for a forest. The plan must ensure coordinated compartment coming from outside the ecosystem are planning among outdoor recreation, range, timber, referred to as forcing functions, or driving variables, or watershed, wildlife, fish, and wilderness opportunities. exogenous variables. State variables refer to the con­ Where quantitative estimates of the ecosystem's tents of the boxes, and the parts of the system they responses to management are necessary, the ID team is represent. The choice of which parts of the system to directed to be as quantitative as possible. Where quan­ model as state variables is made in the conceptual stage. tification is not possible, the following guidelines from The complexity represented in the diagrammatic Forest Service Manual (FSM 1920) are given. model is referred to as the degree of aggregation. For any action taken within the planning process that Because a model never can completely replicate the must rely on assumptions (or statistical inference) in lieu system, compartments of the real system may be com­ of specific data or information, the responsible official bined in the model. One example would be combining all and the interdisciplinary team shall: plant species into one compartment instead of modeling 1. Identify the specific analytical technique and asso­ each plant species. ciated assumptions used. In the mathematical stage, the structure and function 2. Document why particular assumptions were used. of the ecosystem are described in equations. The rela­ 3. State the basis upon which the analytical tech­ tionship between state variables and/or flows is deter­ niques and corresponding assumptions were se­ mined from experimental work, previous models, or the lected and the advantages and disadvantages com­ modeler's intuition. For example, the growth of a plant pared with the relevant state-of-the-art techniques. (state variable) could be represented as a function of 4. Ensure and document, to the extent practicable, sunlight, temperature, and precipitation, all driving the consistency of assumptions with those used in variables, where the function was determined from field other land and resource management planning ef­ research. forts, including the national program. The fourth stage in the modeling process is the com­ 5. Assess the consequences and implications of using puter programming stage where the mathematical equa­ the assumptions. tions are written into a computer program. The internal The team approach appealed to Cooper and Zedler logic of the computer program is checked. (1980), especially when the team members had a strong The last stage in the modeling process is the validation/ consensus in their estimations. Cooper and Zedler (1980) verification stage. The model is tested under a variety of said that mathematical models in resource management situations. An error analysis may be performed to deter­ do not adequately synthesize the appropriate informa­ mine the magnitude of error propagation in the model. A tion for impact assessment. They indicated that current sensitivity analysis may be performed to determine how models estimate the effects of environmental change on sensitive the model is to changes in the parameters of the productivity of ecosystems, but are less successful in the equations. And, finally, the model output is com-

6 pared with different field data that were not used in ical simulation. This difference was pointed out by Spof­ constructing the model to determine how well the model ford (1975) for aquatic systems models and Reed and mimics the real world. Clark (1979) for forest growth models. Spofford (1975) The modeler's perceptions about the ecosystem affect contrasted the water quality models, based on the the internal structure of the simulation model. Energy Streeter-Phelps approach which predicts dissolved oxy­ flow has been used to connect all ecosystem interactions gen or algal concentrations, with aquatic ecosystem in some models, while nutrient cycling has been used in models which predict trophic levels and species popula­ others. Some models focused on population fluctuations, tions. He noted that the biological mechanisms were others concentrated on the dynamics of one animal and more complex in the models of aquatic ecosystem than its environment. Environmental boundaries may be rela­ in the water quality models. The latter models were also tively small, as in the algal-fly community of a hot based on relationships which were more empirical. springs {Wiegert 1977), or large, as in the world Applications of simulation modeling vary greatly; in resource production and consumption of the world most cases, the simulation model was built for a specific (Meadows et al. 1972). The mathematical equations in ecosystem, and often for a specific set of management the model may be based on years of research, as in the problems. Van Dyne and Abramsky (1975) compiled a model of nutrient cycling in a Liriodendron forest list of models used in agricultural and natural resource (Shugart et al. 1976), or they may be based on empirical fields, including both simulation and optimization relationships where the theoretical underpinnings from models. Weigert (1975) and Frenkiel and Goodall (1978) research are lacking. reviewed the development of simulation modeling and The various modeling approaches differ in terms of critiqued simulation model building. H. T. Odum (1971) the type of mathematics used to describe the ecosystem. and Holling (1978) presented modeling frameworks and Differential equations and difference equations have several case examples. Potential users of simulation been used in simulation models of energy flow, nutrient models need to critique carefully the assumptions cycling, and population dynamics. Some algebraic underlying the simulation models. As Odum (1976) models have been constructed also. Penning de Vries noted, no theoretical framework previously existed to (1976) noted the increased acceptance of the state guarantee the same structure in each ecosystem model. variable approach as a basic element of the simulation of continuous systems. Other modeling approaches have been reviewed by Van Dyne and Abramsky (1975), Holl­ Summary ing (1978), and Shoemaker (1977). The type of analytical technique used to determine Applications of Simulation Models the impact of management depends on the problem and the resources available. Where a diversity of manage­ ment impacts or alternative sitings of one impact are Van Dyne (1980) reviewed the development of simula­ tion models, in the context of a review of systems examined, an intuitive approach, such as the ID team ecology. The term "systems ecology" refers to the approach, has been found most useful (Cooper and "ecology (which) deals with the structure and function Zedler 1980). Where one specific management activity of levels of organization beyond that of the individual or ecosystem is examined, a quantitative approach, such as simulation modeling, has been found useful (Hall and species" (Odum 1964). Van Dyne (1980) presented the following characteristics of systems ecology: and Day 1977). 1. consideration of ecological phenomena at large, spatial, temporal or organization scales; 2. introduction of methodologies from other fields ECONOMIC ANALYSES OF PRODUCTION that are traditionally unallied with ecology; 3. an emphasis on mathematical models; In economics, a large body of theory has been devel­ 4. an orientation to computers, both digital and oped concerning production analysis. This section con­ analog devices; and tains a brief review of the general theory of production 5. a willingness to develop hypotheses about the and the use of mathematical programmir:g in production nature of ecosystems. analyses of resource outputs. The application of simulation models in ecology has been an integral part of the development of systems ecology. Some of the earliest applications of ecosystem Economic Theory of Production simulations were those of Odum (1960) and Olson (1963) on an analog computer, and Garfinkel (1962) on a digital The economic theory of production deals with prob­ computer (Wiegert 1975). Since these attempts, simula­ lems of allocation and utilization of limited resources by tion modeling has diversified greatly. Simulation models individual firms. Firms are considered to be technical of ecosystems range from large, complex systems of units which transform inputs into outputs (i.e., engage in r:qur~tions to small sets of differential equations. production). Inputs are anything the firm utilizes in pro­ Modds constructed for natural resource management ducing outputs. Outputs are the commodities the firm diffr:r in structure from modeling approaches in ecolog- produces.

7 Single Output Production lsoquant line The production process that specifies the maximum slope= - _ 1_1 __1, _ output obtainable from any combination of inputs is said to be technically efficient. A mathematical expression that relates inputs and outputs through technically effi­ cient production processes is called a production func­ tion. Equation [1] represents a production function, f, for a production process involving one output, Q, and inputs _N :0 a. Optimization point (equilibrium) I1 , ••• , In- c [1]

Specific functional forms for f (both linear and non­ linear) are used in empirical estimation of production / functions. lsocost line slope= -C1 Starting with the production function as given, eco­ c2 nomic production theory assumes that firms behave in an optimizing fashion, and focuses on decisions made by the firm with regard to optimal levels of inputs and out­ puts. In the simplest case addressed by production Input 11 theory, firms are assumed to operate in competitive Figure 2.-lsoquant and isocost equilibrium. markets for both inputs and outputs (i.e., input and out­ put prices are taken as constant by the firms for all levels of inputs and outputs). The case for other types of Because the firm is a price taker in both the input and markets is also considered in classical production output markets, P, Cv and C2 are constants. The mar­ theory. For a general discussion of economic production ginal conditions for profit maximization are: theory, see a standard microeconomic text such as Hen­ derson and Quandt (1971). of of p and p oi2 [4] The firm may have to make three general production oil = cl = c2 decisions. First, it may seek to maximize output, subject On the left side of each equation, output price, P, is to a fixed budget with which to purchase inputs. Second, multiplied by the partial derivative of the production it may seek to minimize the cost of inputs, subject to pro­ function (the marginal product). This term is the value ducing a given level of output. Third, it may seek to max­ marginal product (VMP) of input 1 or input 2. VMP imize profits where both budget and output quantities shows the marginal rate of increase in revenue from us­ are variable. ing more of the given input. The terms on the right are in­ In the first two cases, the marginal condition for put prices (C10 C2) and represent the rate of increase in optimization with two inputs in equation [1] is: total cost with additions of any input. The maximum profit level is found by equating the VMP of each input [2] with that input's price. where Ci = the factor price of the ith input (Ij). The term Multiple Outputs and Joint Production on the left, the ratio of partial derivatives of the produc­ tion function (which is the ratio of marginal products of The general notation for multiple outputs and multiple the two inputs), is the rate of technical substitution inputs is given by an implicit production function: (RTS). This ratio expresses the rate at which one input can be substituted for another in production and still ob­ [5] tain the same level of output. The term on the right is the ratio of input prices. The optimal level of production is where Q and I are vectors of outputs and inputs, re­ found by equating the ratio of marginal products (RTS) spectively. Joint production exists " ... whenever the to the ratio of input prices. This solution is shown graph­ quantities of two or more outputs are technically inter­ ically in figure 2. dependent .. . . The production of joint products does In the third case, the more general problem faced by a not require an extended analysis unless they can be pro­ firm is to maximize profits, allowing both budget and duced in varying proportions. If two products are output levels to vary. Profit is equal to total revenue (PQ) always produced in a fixed proportion ... the analysis less total cost (C1I1 + C2I2). By substituting equation [1] for a single output can be applied" (Henderson and for Q in this expression of profit, the firm seeks to Quandt 1971). maximize: With fixed inputs, a product transformation curve or production frontier is implied, such as the one graph­ [3] ically portrayed in figure 3 for two outputs. The mar-

8 ginal conditions for optimization in joint production for straints and, as linear combinations of the choice m outputs and n inputs require that: variables, make up the rows in the LP matrix. The 1. the rate of product transformation between every sum of resources used by the activities must be constrained to the total resources available-often pair of outputs must equal the output price ratio, called the right-hand side or RHS. 2. the rate of technical substitution between every 3. The performance criterion for selecting the op­ pair of inputs must equal the input price ratio, and timal set of activities from all possible activities. 3. the value marginal product of each input in pro­ duction of each output must equal the input price. This objective function is a linear combination (weighted sum) of the choice variables, the weights being the numerical contribution of each to the ob­ Mathematical Programming jective function. A simple representation of a linear programming Mathematical programming is the term applied to a problem follows: group of optimization techniques including linear pro­ Maximize: gramming, goal programming, integer and mixed integer programming, quadratic programming, geometric pro­ n gramming, and dynamic programming. All of these tech­ Z= E c.x. [6] niques are designed to select an optimal solution for a i=1 r-J set of variables, often called activities. The optimal out­ come is the numerical maximum or minimum of some Subject to: specified performance criterion or objective function. This report will focus on linear programming as the n state-of-the-art technique in applied mathematical pro­ E A -X.< B· i = 1 ... m [7] j=l IJ J- I gramming, with a brief review of goal programming.

j = 1 ... n Linear Programming

Linear programming (LP) is a mathematical program­ In this example, there are n activities, and m con­ ming technique which can be used to maximize or mini­ straints (rows). The total resource available for any row mize a linear objective function, subject to a set of linear is Bi, and the amount of it used per unit of activity j is Aij' constraints. A linear programming model has three Additionally, activities (Xi) may not take on a value less major components: than zero. The problem expressed mathematically in 1. The set of all possible activities under considera­ equations [6] and [7] could be presented in matrix form tion. These are also called the choice variables, in figure 4 for n = 4 and m = 3. The Cj are the objective and make up the columns in the LP matrix, which is function coefficients, indicating the marginal contribu­ also called the A matrix. tion of each Xi to Z. 2. The set of limitations on the resources needed to carry out the activities. These are called the con- x1 x2 x3 x4 type RHS

A11 A12 A13 A14 ~ 81 A21 A22 A23 A24 ~ 82 A31 A32 A33 A34 ~ 83

c1 c2 c3 c4 z (Maximize/ a"' minimize) :; Q_ :; 0 Figure 4.-A matrix representation of an LP problem. Several assumptions are necessary for the mathemat­ ical solution of a linear programming problem. First, all mathematical relationships in both the objective func­ tion and the constraints must be linear in the choice variables. Nonlinear relationships can be piecewise ap­ proximated with combinations of linear functions. Line­ arity is assured by two requirements-proportionality and additivity. Each activity's contribution to the objec­ Output 0 1 tive function and its rate of resource use is proportional Figure 3.-Product transfonnation curve. to that activity; that is, coefficients in both the objective

9 (Ci) and constraints (Aijl are constant for all levels of ac­ tivity Xi. The total contribution to the objective function and the total resource use of two or more activities engaged in at the same time must equal the sum of the individual contribution, or resource use, of each activity engaged in separately. Second, all choice variables must be nonnegative. Third, all choice variables must be divisible; that is, they can take on fractional values. Additional constraints may be imposed on choice variables to ensure an integer value in integer or mixed­ -"' ~ integer programming, which require different solution a. techniques than the general linear programming prob­ c lem. Fourth, all coefficients (Ci and Aijl must be specified before the model is run. Additionally, it is assumed these coefficients are known with certainty; thus, LP is a deterministic model. Fifth, only one objective function may be specified for maximization or minimization at any one time. Although the LP formulation in equations [6) and [7) implies a lack of a time dimension, this is not a general limitation of LP. Discrete time periods can be incor­ porated by adding additional rows and columns for each Input 11 time period. In this way, the LP can both allocate and Figure 5.-Linear programming isoquant. schedule the activity variables. For a very readable dis­ cussion of linear programming applied to resource plan­ ning see Kent (1980).

Linear Programming and Production Theory

A firm producing a single output may have several processes from which it can produce that output. A pro­ duction process, represented by the columns in the LP matrix, utilizes the fixed resources (Bi) in some constant proportion (Aijl· This production process is of fixed pro­ portions, divisible, and exhibits constant returns to scale (Dorfman, Samuelson, and Solow 1958). The firm chooses the optimal production process and the level of that production process. Because each process utilizes fixed resources at different but constant rates, substitu­ tion between sets of inputs can be accounted for by sub­ stitution between linear processes (i.e., between col­ umns). A "kinked" isoquant results, as shown in figure 5

for two inputs (11 , I2l· Although the smooth marginal conditions found by calculus are not used in this "kinked" case, the same Output 0 concepts of rates of substitution apply in the linear pro­ 1 Figure 6.-Linear programming product transformation curve. gramming case. Substitution takes place between activi­ ties rather than directly between inputs. theory, it may be necessary to consider a large number The standard linear programming problem also can of production process (i.e., a large number of columns in be interpreted for the case of joint production. Proc­ the LP matrix). esses (columns) may exist for simultaneously producing An important point is that linear programming more than one output. Because the resource level is generally starts one step before economic theory by fixed by the right-hand side, a production frontier can choosing a technically efficient production process as be traced out by allocating the available input to differ­ well as an economically efficient one. In this sense, LP ent processes and finding resultant output vectors. Such provides more information to a manager who is not a production frontier is shown in figure 6 for two out­ aware in advance of technically efficient production puts. With this "kinked" production frontier, the con­ processes. It can readily be used to show the implica­ cept of marginal rates of product transformation still tions of alternative choices. This aspect has made linear apply to optimal decisions. In order to approximate the programming a widely used, practical tool for manage­ smoothly curved production frontier of production ment and planning in the business sector.

10 History of Linear Programming Applications Forest managers have had long experience in plan­ ning for particular resources, especially timber. Early Applications of Linear Programming to Forestry Multiple use objectives are currently being superim­ Problems posed on the older procedures .... foresters are accustomed to working with the traditional tools and Some of the first applications of linear programming concepts of timber management and probably the to forestry problems dealt with forest and wood indus­ easiest way to obtain multiple use objectives is by tries. Paull and Walter (1955) and Paull (1956) applied building on this base. linear programming to minimize delivery transportation costs and minimize trim loss in newsprint manufactur­ ing. Bethel and Harrell (1957) used an LP to find op­ Goal Programming timum costs of alternative plywood production and distribution procedures. Jackson (1958) and Jackson and Goal programming is a mathematical programming Smith (1961) used LP to determine optimal sawing technique that can be used to find a solution to a methods in a mill. They formulated both a profit max­ resource allocation problem involving several objec­ imization and a production maximization problem. tives, subject to a set of linear constraints. Depending on Coutu and Ellertsen (1960) used LP to find the best (in­ the type of formulation, all goals may be considered come maximizing) allocation of resources among various simultaneously in a composite (and single) objective farming activities, including forestry. Some of the first function, or sequentially in a series of objective func­ scheduling applications dealt with minimizing the cost of tions. Goal programming is a particular form of linear providing pulpwood to a mill (Theiler 1959, Curtis 1962). programming where the choice variables are devia­ The traditional forest regulation problem of maximizing tional variables-showing over- or underachievement of volume subject to sustained yield constraints was formu­ the specified goal levels of output. For a more formal lated by Loucks in 1964. Kidd, Thompson, and Hoepner discussion of goal programming, see Lee (1972). (1966) formulated the regulation problem to maximize Goal programming concepts were developed by present net worth subject to various management con­ Charnes et al. in 1955 and applied widely to manage­ straints. In 1967, Nautiyal and Pearse used LP to ex­ ment problems in the business sector. Field (1973) in­ amine optimum harvest patterns, rotation length, and troduced goal programming to the forestry literature. the conversion period. Bottoms and Bartlett (1975) applied goal programming to In all of these early applications, the LP's were multiresource management of 9,050 acres of the Colo­ developed for each specific problem. In 1971, a linear rado State Forest. Their formulation used ordinal prior­ programming package (Timber RAM) was developed ity ranking of goals. which could be applied to various timber management Bell (1976) further discussed transformation of a planning problems (Navon 1971). For a more technical linear program into a goal program with a composite discussion of Timber RAM, see Alig et al. (1983). Proto­ weighted objective function. Dane, Meador, and White type RAM models for range and transportation systems (1977) used the composite weighted objective form of were developed later Gansen 1976), but not widely used. goal programming on a 158,000-acre planning unit on Although the inputs and outputs of Timber RAM are the Mt. Hood National Forest, Oregon. Schuler, timber related, Navon (1971) suggested that the model Webster, and Meadows (1977) reported on their pilot could partially evaluate the "interaction of range, application of goal programming on a 10,000-acre watershed, recreation, wildlife, and timber manage­ subunit of the Mark Twain National Forest, Missouri. ment policies." This was accomplished largely by ex­ Schuler, Webster, and Meadows (1979) suggested the cluding land from the allowable cut base and by meeting biggest problem in the application of goal programming constraints imposed by commitments to produce other involved the technical coefficients. Steuer and Schuler resources through reduction in wood yield.U Chappelle (1978), in a discussion of the same pilot study pointed out et al. (1976) argued that this approach to multiple-use further problems, encountered in goal ranking: considerations does not necessarily provide an optimal The objectives [goals] were also ranked by the plan­ solution to forestry (as opposed to timber) planning ning team. However, the ranking was strictly ordinal. problems. A cardinal ranking scheme was considered to be This incremental approach to multiple-use modeling unobtainable. This constituted the first noticeable (i.e., starting with a timber model and then modifying it) beginning of the series of difficulties that occurred in appears to have precedent in the way functional plan­ trying to find an OR/MS technique to solve this forest ning evolved toward multiple-use planning in response management problem. to the Multiple Use-Sustained Yield Act of 1960. Accord­ Dyer et al. (1979) used the Bottoms and Bartlett goal ing to Hall (1963) multiple use was initially viewed as a program to show the sensitivity of the goal programming problem of coordinating separate resource programs allocation to changes in priority levels and concluded rather than starting with an overall multiple-use pro­ that an ordinal ranking goal programming would not gram. Hall suggests this approach can be explained by solve the problem of determining objective function history: weights required to achieve a pareto optimum allocation "Johnson, K. Norman. 1980. Timber activity scheduling on the national forests: The second revolution. Paper presented at Oregon of resources. Dyer et al. (1979) also discussed the use of State University seminar, Corvallis. goal programming as a suboptimization technique; they

11 concluded it is a useful tool if used carefully and with a Linear Programming Multiresource complete understanding of its inner workings. Management Problems

INTEGRATED APPROACHES TO ANALYZING THE PRODUCTION OF NATURAL RESOURCES Perhaps the most successful applied attempts at in­ tegrating information across disciplines and resources A single theoretical basis for integrated analysis have been the multiresource linear programming across disciplines does not exist today. Theoretical models. The first example of such a model was D'Aquino developments attempting to provide this theoretical (1974). The basic structure of these models will be illus­ basis include Georgescu-Roegen (1977), Boulding (1977), trated in a simplified linear programming model con­ Thompson (1977), and Odum (1971). Odum (1978) uses sidering only two types of land, five management pre­ energy to integrate ecological, economic, and social scriptions, and three resources (fig. 7). systems. Applications in regional planning can be found In figure 7, the major column headings are types of in Kemp et al. (1977) and Boynton et al. (1977). The diffi­ land and/or resources. The "X/s" under the two land culties of determining the value of energy in this ap­ types are the number of acres allocated to alternative proach have been discussed by Hyman (1980). management prescriptions which could be applied in Holling (1978) developed an approach incorporating a TYPE I (X1 and X2) and TYPE II (X3, X4, X5) land. X1 quantitative description of system behavior using through X5 are choice variables defined as the number catastrophe theory, and a qualitative integration of of acres allocated to the given management prescription system behavior using workshops. The workshops have (1 through 5). been used to bring together the academicians, who The timber, wildlife, and forage rows in the matrix mathematically describe the system, and the managers represent the resource outputs of this forest system and politicians, who manage the system. The feedback which result from implementation of the management between managers, politicians, and academicians facili­ prescriptions. The land, TYPE I and TYPE II, rows are tated a deeper understanding of the system and its the inputs (acres) to this joint production system. K5 model. Applications in land planning can be found in acres of Type I land are available, and K6 acres of Type Holling (1978). II land are available. The dominant technique in integrating ecological and The timber output, wildlife output, and forage output economic analyses is the optimization modeling ap­ rows are the amounts of each of the outputs that are proach. These models can analyze the tradeoffs be­ harvested from the forest system. The "Net Benefit" tween a variety of resource production alternatives. The row is the objective which managers seek to maximize decision criteria for the tradeoff analysis can be varied given the resources available and the production rela­ also. This type of analysis presumes the input of benefit/ tionships involved. cost information and production capability/response The " X's" under the major column heading "Prod­ information. ucts" (X6 , X7 , X6) are accounting columns which collect

Type I Type II Products Constraint RHS type

xl x2 x3 x4 x5 x6 X? X a

Timber A1,1 A1,2 A1,3 A1 4 A1,5 - A1,6 K1 =0 ' = Wildlife A2,1 A2,2 A2,3 A24 A2,5 -A2,7 K2 =0 ' = Forage A31 A3,2 A3,3 A3,4 A3,5 -A3a K3 =0 ' ' = Budget A4,1 A4,2 A4,3 A4,4 A4,5 ~ K4

Type I A51 A5,2 K5 ' = Type II A6,3 A54 A6,5 K6 ' = Timber output A7,6 ~ K? Wildlife output Aa,? ~ Ka Forage output Ag,a ~ Kg

Net Ben. A10,1 A10,2 A10,3 A10,4 A10,5 A10,6 A1C,7 A10,a

Figure 7.-A simple resource allocation model where X, and X2 are the number of acres in Type I land allocated to alternative management prescriptions; X3, x., X5 are the number of acres in Type II land allocated to alternative management prescriptions; X., Xn X8 are timber, wildlife, and forage products, respectively; the '\ are production coefficients; the A,. are the objective tunc· tion coefficients; and the K, are the nght·hand sides (RHS). l

12 or transform the outputs described in some of the rows RC8-RAA into an aggregate output for the area being analyzed.12 TheA/sin columns one through five can generally be In 1972, a system of interrelated computer programs termed the impacts of the Jih management prescription was developed by the USDA Forest Service Watershed on either the row outputs or row inputs. For example, Systems Development Unit in Berkeley, Calif. The A,,, is the output of timber per acre if the first manage­ Resources Capability System (RCS) was designed to be • "used to quantitatively evaluate functional programs as ment prescription is implemented, and A5 1 is the amount of Type I land it takes to implement the minimum size they relate to the basic soil, climatic, and water prescription 1 treatment. resources. This information can then be combined in the The coefficients in row 10, the "Net Benefits" row, system with quantitative data from the various disci­ describe the change in net benefits if one unit of the jth plines and functions of resource management, plus management prescription occurs. Thus, A, ,, is the cost selected management objectives and constraints, and 0 , utilized in an interdisciplinary analysis of resource allo­ of prescription 1 and A,0 6 is the benefit derived from one unit of timber output (Xo). cation alternatives" (USDA Forest Service 1972). The Resources Capability System included several K4 is an upper limit on the amount of money to be response simulation models (water yield, sediment yield, made available for managing the area. K7 through K9 are minimum levels of timber, wildlife, and forage that are individual renewable resource models, and an economic required. analysis model) and a multiple resource allocation This simple model ignores time dimensions and other model. This allocation model became known as the complexities such as nonconstant benefit coefficients. Resource Allocation Analysis (RAA) component. It was Environmental quality indexes are also excluded from this RAA component of RCS which received most of the the example. These complexities do not pose severe attention during the mid-1970's. It included an LP model, analytic problems, and they can be brought into the its associated A-matrix generator, and its output display analysis without conceptual difficulty-though such a programs. model would be significantly larger (i.e., more rows and The RAA was first applied to water resource and columns). river basin development planning. By 1975, it had been used on approximately 40 land-use planning problems in the USDA Forest Service National Forest System. Most Multiresource Models of the forests using the RAA for multiple-use planning were in the West (Beaverhead, Nezperce, Montana; The CARD-USDA Agricultural LP Model Williamette, Oregon; Modoc, Klamath, Shasta Trinity, California; and Payette, Idaho). The set of computer pro­ Linear programming models are well suited to evalu­ grams was continually modified in response to user ating the response of agricultural production to chang­ needs in these various applications (Lundeen 1975). ing policy or economic perturbation on both an intrare­ The matrix generator, called MAGE5, was perhaps gional and interregional basis. A model designed to do the most unique and notable aspect of the RAA package. this has been constructed and tested by the Center for A versatile, user-specified model, it included delineation Agricultural and Rural Development (CARD) at Iowa of constraints, costs, benefits, and a single objective State University in cooperation with USDA Soil Conser­ function. The output of goods and services could also be vation Service and the USDA Economics, Statistics, and time-streamed; that is, outputs resulting from the appli­ Cooperatives Service. cation of management prescriptions could vary over Given regional and national demands for land, water, time. The same could occur for rates of capital and fertilizer, and pasture, together with the quantity of labor inputs pertaining to resource management. In resources available for use in satisfying them (i.e., con­ addition to the time-streaming option, the production of straints), the CARD-USDA model can minimize the cost timber could be simulated with a user-specified growth of producing those demands. As such, the model can be function. This was one of the first examples of a cou­ used to assess the effects of initiating new markets, pling between simulation and optimization models even changing demands and resource availabilities, modu­ though the former was self-contained in the latter. The lating costs, and altering the interaction of commodity developers had planned to provide for additional simula­ production, resource purchase, and land development tion models as a way to quantitatively describe resource activities with the relevant markets. interactions; however, this was not fully accomplished. The CARD-USDA model was delineated regionally in The specification of the objective function in RAA several ways. On the basis of soil type and management allowed for flexibility. The user could specify any of the attributes, 164 land resource regions were defined. On commodity or economic rows (or any combination of the basis of production (crops and water) 105 separate them) as an objective function (Lundeen 1975). Although producing areas were defined. Additionally, producing it was possible to minimize costs, the most commonly areas were agglomerated into 28 major marketing re­ used approach was to maximize present net worth or gions with a market center defined for each. Transfers one of the major commodities. The LP was designed to be of resources and demands between regions were at the run iteratively with changing objective functions or dif­ marketing region level. ferent right-hand side constraints. "K, through K, are set at zero to force all product output levels in­ Overall, the RAA was user-operated and controlled. to x., X,. and x•. For example, the three main components of RAA (LP

13 model, matrix generator, report writer) could either be ownership were possible. Of these, the task force ob­ operated as a sequential, interfaced system, or as tained and evaluated data for 956 resource units (USDA separate programs in order to aid in accomplishing Forest Service 1972b). other RCS objectives. Additional information on RCS can The resource output production under different man­ be found in USDA Forest Service (1972) and Dyrland agement strategies for each resource unit was deter­ (1973). mined by an interdisciplinary team of scientists. For each of six possible management strategies (table 1), a set of management practices were generated by the FREPAS team. Resource outputs for each resource unit for each The FREPAS (Forest-Range Environmental Production management strategy were also estimated by the team Analytical System) model was developed as part of the (table 2). Forest-Range Environmental Study (FRES), during Table 1.-Management Strategies in FREPAS (USDA Forest Service 1972b) 197D-72. The purpose of this study was to collate infor­ mation about United States rangelands and to develop a Strategy A-Environmental management without livestock. technology for evaluating such information in a way that Livestock are excluded by fencing, riding, public education, or in· would serve the planning needs of the USDA Forest centive payments. Damage to the range resource is corrected to Service (USDA Forest Service 1972b). The analytical maintain a stewardship base. The range management cost is system was to permit the manipulation of various borne by other functions, such as timber. economic, political, and social constraints on the use of Strategy B-Environmental management with livestock. Livestock is permitted at present capacity of the range environment. Invest­ different range resource units in order to determine op­ ments are made only to maintain the environment at a steward­ timal management procedures. ship level. Costs of correcting past abuse are charged to other The FRES model was a multiresource LP model with a functions. cost-minimization objective function. Required model Strategy C-Extensive management of environment and livestock. Management seeks full utilization of the animal unit months inputs included a nation-wide forest and ·range land in­ available for grazing. However, no attempt is made to maximize ventory. For each land unit, the following inputs are re­ forage production by cultural practices. quired: then current (1970) management strategies, and Strategy D-lntensive management of environment and livestock. associated resource outputs, maximum potential of Production of forage is maximized subject to the constraints of multiple use. This strategy includes reseeding and complex resource production, and minimum level of management livestock-management systems and practices. for each land unit based on legal restrictions. The data Strategy E-Maximum management of environment and livestock. base for these inputs was developed as part of the FRES Livestock production is maximized, subject only to stewardship study. Computer programs for data manipulation, of soil and water resources. Multiple use is not a constraint. matrix manipulation, LP solution, and a report writer Strategy X-Management at a substewardship level. Livestock are grazed at a level that depletes the range resource. were developed (Kaiser et al. 1972). The FRES model was run under a series of policy alternatives (e.g., budget and resource production constraints), and the Table 2.-Resource outputs estimated for each resource unit in the results, in terms of resource outputs, were compared FRES study (USDA Forest Service 1972b) with the then current (1970) situation (USDA Forest Output Unit of measure Service 1972b). FRES defined a framework for land inventory. Thirty­ four soil-vegetation units, based on Kuchler's (1964) Grazing measures classification system of potential natural vegetation, Browse and herbage Tons per acre per year formed the foundation for land classification across the Animal unit months AUM per acre per year Animal output value $ per acre per year 48 coterminous states (Garrison et al. 1977). Each soil­ Joint products vegetation unit, or ecosystem, was further divided by Wood Cubic feet per acre per year productivity (four classes) and condition (three classes). Water Acre feet per acre per year On forest ecosystems, productivity was defined by Water quality Acre feet per acre per year Storm runoff Inches per acre per year capacity to produce wood, and condition was defined by Sediment Tons per acre per year the stocking level of poles and sawtimber. On nonforest Employment Man hours per acre per year ecosystems, productivity classes were assigned accord­ Qualitative estimates ing to relative herbage production compared to the max­ Soil stability A value between '1-5 imum potential of that ecosystem. Condition classes fol­ Rare and endangered species A value between 1-5 Nongame birds A value between 1-5 lowed the concepts supporting the USDA Forest Service Carnivores and raptors A value between 1-5 definition of range condition (i.e., vegetative composition Air quality A value between 1-5 and vigor, soil erosion, and erosion-potential factors). Soil quality A value between 1-5 In addition to partitioning on the basis of potential Depressed area impact A value between 1-5 vegetation, production, and condition, land was further Cultural heritage, resident A value between 1-5 Cultural heritage, nonresident A value between 1-5 divided according to ownership. Three ownership cate­ Beauty A value between 1-5 gories were recognized: (1) National Forest System, (2) other federal, and (3) nonfederal. As a result of the 'A 5-point scale was used to measure qualitative products. The above partitioning, 1,224 unique combinations (called five points were: 1 =bad, 2 =poor, 3 =fair, 4 =good, and 5 =excel­ resource units) of ecosystem-productivity-condition- lent.

14 FREP AS, as an LP model, allocated acres of land to ownership categories, four productivity categories, and the various management strategies within each four condition classes. The ownership categories were: resource unit, subject to given resource product con­ National Forest System lands (NFS), Bureau of Land straints, in order to minimize the investment cost for Management lands, other federal lands, and state and range management and treatment (Kaiser et al. 1972). private lands. There were four productivity and four The FREPAS model assumed a static environment, and condition classes. As a result of the above partitioning, did not allow for scheduling (i.e., the model ignored the approximately 5,000 unique combinations (Resource effects of a decision's impact on opportunities during Units) of ecosystem-productivity-condition-ownership subsequent time periods). were possible. These Resource Units (RU) were assumed to exhibit homogeneous response to management. For each RU, the resource outputs under different NIMRUM management were determined by an interdisciplinary team of scientists. In FREP AS, only management strate­ The National Interregional Multiresource Use Model gies associated with range were defined (table 1). In (NIMRUM) is one of the four models in the National In­ NIMRAS, appropriate combinations of management terregional Multiresource Analytical System (NIMRAS) levels for range, wildlife, and timber representing cur­ which was developed for the 1980 RP A Assessment. The rent use were made by the ID team for each RU. Thus, purpose of NIMRAS was to help evaluate alternative na­ for example, a combined management level to "do tional programs of forest and range land management. nothing" consists of: range management AN-environ­ The models were summarized by Ashton et al. (1980) as mental management without livestock; timber manage­ follows: ment level 1-no commercial use; and wildlife manage­ The National Interregional Multiresource Use ment level1-no management. Each combination, called Model uses linear programming to allocate national a management triplet, had a set of management prac­ and regional demands for renewable resource uses tices associated with it. Six management levels, similar on the land base. This model minimizes operational to the six strategies in FREP AS, were possible for range. costs of alternative programs while achieving en­ Six management levels for timber and three manage­ vironmental restraints, range production, sustained ment levels for wildlife were defined. Table 3 lists the wood yield, and wilderness. resource outputs in NIMRUM. The second model evaluates regional employment and earnings triggered by a national program. Table 3.-Resource outputs in the NIMRUM model The third model, Futures Foregone, keeps count of (Ashton et al. 1980) future options lost in terms of the amount affecting citizens groups, rate of impact, and length of impact. Output Unit of measure The last model, Social Conflict, operates on the postulate that there will be proponents and opponents for any resource use and that some degree of conflict Herbage and browse production Pounds per acre per year is inevitable. The model uses impact information in­ Net wood growth Cubic feet per acre per year Wood harvested Cubic feet per acre per year cluding that generated from previous models and Domestic livestock grazing AUM per acre per year serves to quantify the amount and pattern of conflict. Wild ruminant grazing AUM per acre per year NIMRUM is a linear programming model which seeks Dispersed recreation use Visitor-day per acre per year Water yield Inches per acre per year to minimize the cost of allocating the nation's forest and Storm runoff Inches per acre per year range land base to alternative resource management ac­ Sediment yield Tons per acre per year tivities, so as to meet expected demands for the various Life form-water Percent of area outputs. Ashton et al. (1980) explained NIMRUM this Life form-ground Percent of area way: Life form-bushes Percent of area Life form-trees Percent of area Each allocation is a pattern of resource uses that satisfies demand projections for certain market and nonmarket outputs. In this sense, the demand for Resource management practices are the basis for goods and services is the driving force of the model. NIMRUM costs. Costs of the individual resource man­ Costs are calculated for each allocation, and these agement practices were aggregated into single resource direct the model toward its goal, the selection of the management levels, and the cost of the management least expensive resource allocation, and management level for timber, for range, and for wildlife were added pattern to meet demand. to generate total costs for the management triplet. Costs NIMRUM was the first national-level land allocation for all ownerships were assumed to be similar. Range model to account internally for resource interaction costs were based on Forest Service budget data, and (joint production). Because of the size of the national timber costs were based on the Forest Service Timber model , computations were actually carried out on two Management Practice Cost Survey conducted in 1976. subnational models-one for the East and one for the Wildlife costs were drawn from timber or range costs, West. depending on the type of vegetation manipulation under­ The NIMRUM land base was stratified according to taken for habitat management. All costs were annual 107 Kuchler potential natural communities (PNC), four averages based on a 50-year time period. Capital costs

15 (consisting chiefly of roads) with relatively long lives section. For a comprehensive discussion of FORPLAN, were discounted at 6-5/8%. Other costs were not see Johnson et al.15 discounted. Perhaps most basic to the configuration of any LP Pickens13 noted that the objections to NIMRAS were generated by FORPLAN is the definition of analysis the result of a lack of faith in the input data. While he areas (AA's), analogous to RU's in NIMRUM, and the acknowledged that there are problems with the data, alternative management prescriptions for each analysis the use of an ID team to generate such a national data area. FORPLAN allows considerable flexibility in the set was considered the most viable approach to give the user designation of analysis areas and management best possible data with the time and resource con­ prescriptions. Analysis areas are identified by three straints imposed on the development of NIMRAS. Some user-specified land characteristics (up to 60 categories of the information required in the analysis was not avail­ of each), up to 9 working groups, up to 15 land classes, able from scientifically conducted studies, reflecting the and up to 60 existing vegetation classes. Every alter­ functional approaches taken in previous studies on man­ native management prescription specified in FORPLAN agement implications. He stressed that, for NIMRAS, the must apply to a given analysis area. In addition, alter­ data was sufficiently accurate to measure the type of native prescriptions can be included to apply to the responses they were commissioned to study. Further regeneration classes created by prescriptions with uses of the model should examine the data quality harvest practices. The time frame that applies to man­ problem. agement prescriptions as well as to resultant outputs is also quite variable, having up to 30 time periods of 1 to 20 years each. FORPLAN Also basic to the structure of any LP generated by FORPLAN is an option called "Aggregate Emphasis." The Forest Planning Model (FORPLAN) is intended for This option allows designation of groups of analysis use on every national forest (or groups of national areas that must be allocated to management prescrip­ forests) in the USDA Forest Service National Forest Sys­ tions together. This restriction is to avoid illogical situa­ tem. It is one of the analytical tools to be utilized in ful­ tions such as "an analysis area allocated to intensive filling the requirements of the National Forest Manage­ timber management production in the midst of analysis ment Act of 1976 and its subsequent regulations. areas allocated to a wilderness".ts FORPLAN is a software package that serves as a ma­ The structure of any FORPLAN-generated LP is also trix generator, an interface to the Univac 1100 FMPS14 subject to area and volume control, harvest flow (e.g., linear programming (LP) solution algorithm, and a report nondeclining yield), ending inventory, management writer of the LP solution. The type of LP which emphasis and intensity, and cultural treatment con­ FORPLAN creates varies considerably according to ap­ straints. These kinds of constraints can take on plication by the user on any given forest. Many options numerous configurations. are available in the FORPLAN package-a characteris­ Concerning timber harvest (and other timber activity) tic that is consistent with the widespread application in­ scheduling, FORPLAN can construct an LP based on tended. In general, the LP which FORPLAN generates is either of two structures Uohnson and Schnerman 1977) intended to simultaneously solve management activity which differ in the manner in which they define timber scheduling problems, land allocation problems, and out­ choice variables and handle multiple harvests within put mix problems. The basic structure is much like the the planning horizon. Model I is more conducive to keep­ simple example given previously, with the addition of ing track of location on the ground, while Model II is scheduling capabilities. Because FORPLAN evolved more conducive to minimizing model size. from a timber model called MUSYC, it retains some em­ FORPLAN has options for 10 different objective func­ phasis on timber analysis capabilities; however, the tions in the LP it generates: emphasis in application is up to the user rather than the 1. Maximize PNW for n periods-maximize dis­ software package itself. counted present net worth (net monetary income) The responsibility for determining alternative man­ over n periods under the assumption that the agement prescriptions to be applied within the forest amount of output provided does not affect its and for quantifying the ecological impact of those man­ price. agement prescriptions rests with the interdisciplinary 2. Minimize cost for n periods-minimize undis­ team (ID team). Because this information is forest­ counted monetary cost over n periods. specific, the experience of the team members on site 3. Minimize discounted cost for n periods-minimize becomes very important. In order to present the general discounted monetary cost over n periods. flavor of FORPLAN capabilities, some of its more impor­ 4. Maximize PNW under downward-sloping demand tant options/characteristics are briefly discussed in this for n periods-maximize discounted net income over n periods under the assumption that the "Pickens, James B. 1980. NIMRAS system documentation. (Un­ published report prepared for USDA Forest SeNice, Washington, amount of output offered influences the price D.C.). received. 14The use of trade and company names is for the benefit of the "Johnson, K. Norman, Daniel B. Jones, and Brian M. Kent. 1980. reader; such use does not constitute an official endorsement or ap­ Forest planning model (FORPLAN) user's guide and operations proval of any service or product by the U.S. Department of Agri­ manual. (Draft). USDA Forest Service Land Management Planning, culture to the exclusion of others that may be suitable. Fort Collins, Colo.

16 5. Maximize PNB under downward-sloping demand puts. In integrating ecological, economic, and social for n periods-maximize discounted net benefit analyses, optimization models can analyze tradeoffs be­ (approximately the discounted sum of producer's tween resource outputs and opportunities for improving plus consumer's surplus) over n periods, under the resource situation based on a variety of criteria. the assumption that the amount of output influ­ The difficulty of scope remains, however. Modeling ences the price received. relatively small areas of land (such as a National Forest) 6. Minimize deviations from goals-minimize the is appealing because of the relative detail, resolution, penalty incurred through nonachievement of the and accuracy that can be achieved. However, regional goals specified. and national concerns are different than local concerns 7. Maximize output i for n periods-maximize one of and joint strategies between small land units may be the scheduled or nonscheduled outputs over n highly desirable. The need for centralized decisionmak­ periods. ing is a primary motivation for national planning efforts 8. Minimize output i for n periods-minimize one of such as RPA. the scheduled or nonscheduled outputs over n There are essentially three alternative approaches to periods. this dilemma. First, a national model could be utilized, 9. Maximize PNW for individual stands-specifying capturing whatever level of resolution possible. This is this objective function produces a report giving roughly the approach taken in the NIMRUM effort. Sec­ the maximum discounted net income (PNW) over ond, one could simply "add up" the results of small­ the planning horizon projected for each analysis scale models, such as FORPLAN. Third, a middle-ground area containing timber available for harvest, con­ solution would be a multilevel approach as outlined by sidering each prescription and possible time of Wong (1980). entry and harvest. Basically, the idea is to utilize models such as 10. Maximize PNW for individual stand with detail­ FORPLAN at the lowest levels of analysis and analyze specifying this objective function produces a only alternative output vectors at higher levels. That is, report giving the maximum PNW for each all production possibilities analysis occurs only at the analysis area containing timber available for lowest level, and the higher level models simply harvest, as done under objective 9. It also pro­ "choose" from the different possibilities that are deter­ duces the PNW for each prescription designated mined to be feasible. This type of approach is discussed for each analysis area, considering all possible elsewhere in more detail as a possible assessment anal­ times of entry and harvest. ysis tool.16 For objective functions 4 and 5, FORPLAN can gener­ ••u.s. Department of Agriculture, Forest Service. 1981. Problem ate a piecewise approximated downward-sloping de­ analysis: Integrated resource analysis for national assessments. mand curve for timber. Fixed prices are assumed for all 150 p. Staff paper- National Resource Analysis Techniques Proj­ ect, Rocky Mountain Forest and Range Experiment Station, Fort other outputs. At this time, costs can be assigned per Collins, Colo. acre for timber-related management prescriptions and per unit output for all outputs (including timber). It is LITERATURE CITED anticipated that the capability to assign costs per acre for all management prescriptions will soon be available Alig, Ralph J., Paul A. Morris, and Bernard J. Lewis. in FORPLAN. An option to include fixed costs is also 1983. Aggregate timber supply analysis. USDA Forest available in FORPLAN. Service General Technical Report RM-100. Rocky Output constraints or output targets are an important Mountain Forest and Range Experiment Station, Fort part of the LP models generally developed with FOR­ Collins, Colo. PLAN. These targets set minimum or maximum levels of Ashton, Peter G., James B. Pickens, Coryell Ohlander, outputs to be obtained in the LP solution and literally and Bruce Benninghoff. 1980. Many resources, many drive the model in some instances. Inclusion of these uses: A system analysis approach to renewable targets is directly mandated by the NFMA regulations. resource development. Water Resources Bulletin 16:738-744. Bell, Enoch F. 1976. Goal programming for land use CONCLUSIONS planning. USDA Forest Service General Technical Report PNW-53, 12 p. Pacific Northwest Forest and Optimization models provide a method to integrate the Range Experiment Station, Portland, Oreg. ecological, economic, and social impact analyses, and to Bethel, James S., and Clean Harrell. 1957. The applica­ identify opportunities based on selected criteria. The tion of linear programming to plywood production and predictions from simulation models can be used as input distribution. Forest Products Journal7(7):221-227. for the optimization model. Specifically, the supply/ Bledsoe, L. J., and G. M. Van Dyne. 1971. A compartment demand models can provide the benefit/cost (economic) model of secondary succession. p. 48(}513. In Systems information, and the ecological analyses can provide the analysis and simulation in ecology, Vol. 1. B. C. Patten, production capability/response information for the editor. 607 p. Academic Press, New York, N.Y. optimization models. The social analyses can predict Botkin, D. B., J. F. Janak, and J. R. Wallis. 1972. Some social impacts of the solutions provided by an optimiza­ ecological consequences of a computer model of tion model. Public participation also provides social in- forest growth. Journal of Ecology 60:849-873.

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20 Agriculture-CSU, Fort Collins Joyce, L. A., B. McKinnon, J. G. Hof, and T. W. Hoekstra. 1983. Joyce, L. A., B. McKinnon, J. G. Hof, and T. W. Hoekstra. 1983. Analysis of multiresource production for national assessments and Analysis of multiresource production for national assessments and appraisals. USDA Forest Service General Technical Report appraisals. USDA Forest Service General Technical Report RM-101, 20 p. Rocky Mountain Forest and Range Experiment Sta­ RM-101, 20 p. Rocky Mountain Forest and Range Experiment Sta­ tion, Fort Collins, Colo. tion, Fort Collins, Colo.

This paper gives an overview of the analytical methods that have This paper gives an overview of the analytical methods that have been used in integrated (multidisciplinary, multiresource, and been used in integrated (multidisciplinary, multiresource, and multilevel) land management production analyses. The ecological and multilevel) land management production analyses. The ecological and economic theory underlying both simulation and optimization methods economic theory underlying both simulation and optimization methods are also reviewed. are also reviewed.

Keywords: Integrated land management, multiresource production Keywords: Integrated land management, multiresource production analyses analyses

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Joyce, L. A., B. McKinnon, J. G. Hof, and T. W. Hoekstra. 1983. Joyce, L. A., B. McKinnon, J. G. Hof, and T. W. Hoekstra. 1983. Analysis of multiresource production for national assessments and Analysis of multiresource production for national assessments and appraisals. USDA Forest Service General Technical Report appraisals. USDA Forest Service General Technical Report RM-101, 20 p. Rocky Mountain Forest and Range Experiment Sta­ RM-101, 20 p. Rocky Mountain Forest and Range Experiment Sta­ tion, Fort Collins, Colo. tion, Fort Collins, Colo.

This paper gives an overview of the analytical methods that have This paper gives an overview of the ·analytical methods that have been used in integrated (multidisciplinary, multiresource, and been used in integrated (multidisciplinary, multiresource, and multilevel) land management production analyses. The ecological and multilevel) land management production analyses. The ecological and economic theory underlying both simulation and optimization methods economic theory underlying both simulation and optimization methods are also reviewed. are also reviewed.

Keywords: Integrated land management, multiresource production Keywords: Integrated land management, multiresource production analyses analyses