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A co-evolutionary cellular automata for the integration of spatial and temporal scales in forest management… Mathey, Anne-Hélène 2006

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A co-evolutionary cellular automata for the integration of spatial and temporal scales in forest management planning  By  ANNE-HELENE MATHEY B.Sc, Universite Joseph Fourier, 1999 M . S c , University of British Columbia, 2001  A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies  (Forestry)  UNIVERSITY OF BRITISH C O L U M B I A October 2006 © Anne-Helene Mathey, 2006  ABSTRACT The scope of forest management has broadened to encompass ever more values and services. Designing decision support tools to provide for them involves incorporating a number of spatial and dynamic processes. This thesis presents a case for more holistic numerical planning tools which can handle spatial objectives and inter-temporal trade-offs. A novel algorithm based on cellular automata (CA) is designed to address forest planning objectives that are both spatial and temporal and subject to global constraints. In this decentralized framework, the landscape management goals are achieved through a coevolutionary decision process between interdependent stands. The problem considered is maximization of cumulative harvest volume and amount of clustered old forest subject to stable flow and minimum old growth retention. Applied to a small test area, the model demonstrates short computation time and shows sensitivity to both local constraints and global goals and constraints. The implementation requirements of forest planning models are an issue that affects both the efficacy and the efficiency of planning tools. It is argued that object-oriented implementations could efficiently integrate the spatial and temporal data required by the various processes underpinning forest planning tools. A n object-oriented design for the previously developed CA-based algorithm proves capable of considering spatial relationships with consistent allocation of clustered old growth areas. The object orientation permits a fast computation of both local and global limitations on local decision making and speedy modification of the problem definition (local and global requirements or spatial resolution).  Finally, the CA-based planning approach is used on a large scale planning problem to investigate different policy scenarios. The problem under investigation is the impact on volume flow and net present value of introducing intensive forest management (IFM) and clustering harvest activities. The main trade-off in this study was found to be between volume and net present value. In this context, IFM is used to meet the harvest targets from a smaller land base but at increased costs. Spatially clustering harvest activities, however, greatly increases the output net present value of a plan.  Keywords: cellular automata; clustering; decentralized planning; decision support tools; evolutionary algorithm; evolutionary game; forest management; geographic information systems; intensive forest management; multiple scales; object-oriented design; old growth forest; selforganization; spatial forest planning; strategic planning; sustainable forest management.  T A B L E OF CONTENT ABSTRACT  ii  TABLE OF CONTENT  iv  LIST O F T A B L E S  vi  LIST O F FIGURES  vii  ACKNOWLEDGMENTS  ix  CO-AUTHORSHIP STATEMENT  xi  1  INTRODUCTORY CHAPTER  1.1 Introduction 1.2 Sustainability 1.2.1 Sustainability and capital 1.2.2 Sustainability as a function of value system 1.3 Potential impacts of IFM on forest values 1.3.1 Forest values and forest management strategies 1.3.2 Intensive forest management 1.4 Planning and Planning tools 1.4.1 Purpose ofplanning 1.5 Research Objectives 1.5.1 Objectives 1.5.2 Thesis structure 1.6 References  1  1 3 3 6 7 7 9 11 11 12 12 14 16  2 R E - E V A L U A T I N G OUR APPROACH T O FOREST M A N A G E M E N T PLANNING: A COMPLEX JOURNEY 23  2.1 Overview 2.2 Introduction 2.3 Environmental sustainability 2.4 Social sustainability 2.5 Economic sustainability 2.6 Decision support tools and SFM planning 2.7 Decentralized forest management planning 2.7.1 Problem statement 2.7.2 Methods 2.8 Sample case 2.8.1 Results 2.9 Discussion 2.10 Conclusion 2.11 References 3  F O R E S T PLANNING USING C O - E V O L U T I O N A R Y C E L L U L A R A U T O M A T A  3.1 Overview 3.2 Introduction 3.3 Application of cellular automata in forest planning 3.4 Unconstrained forest-planning 3.4.1 Model formulation  23 23 24 26 27 28 30 30 31 33 34 37 38 40 45  45 46 49 53 53 iv  3.4.2  3.5 3.6 3.6.1 3.6.2  3.7 3.8 3.9 3.10  Co-evolutionary optimization: from local decisions to coordinated management  Constrained forest planning Problem instance Analysis of results for the unconstrained forest planning Analysis of results for the constrained forest planning  Analysis of tradeoffs between harvest volume and old forest preservation Computational analysis and a comparison with Simulated Annealing Conclusion References  4 O B J E C T - B A S E D C E L L U L A R A U T O M A T A M O D E L F O R F O R E S T PLANNING PROBLEMS  4.1 4.2 4.3 4.3.1 4.3.2  4.4 4.4.1  4.5 4.6 4.7 4.8 4.9  Overview Introduction Methodology Cellular automata model for forest planning Model implementation  Problem instance Study area and problem formulation  Model Outputs Sensitivity Analysis Discussion Conclusion References  5 OPPORTUNITIES A N D COSTS O F INTENSIFICATION A N D C L U S T E R I N G O F F O R E S T M A N A G E M E N T ACTIVITIES  5.1 5.2 5.3 5.3.1 5.3.2 5.3.3  5.4 5.5 5.5.7 5.5.2 5.5.3  5.6 5.7 5.8 5.9 6  Overview Introduction Problem Description Forest management in the boreal forests of Ontario Management options Spatial allocation  Model Formulation Problem instance Study area Management requirements Management scenarios  Comparative evaluation of scenarios Discussion Conclusions References  CONCLUDING CHAPTER  6.1 6.2 6.3 6.4  Summary of results Conclusion Future Research References  57  59 64 65 68  74 77 79 81 86  86 87 91 91 94  100 100  103 105 Ill 112 113 119  119 120 123 123 124 125  126 129 129 131 131  134 139 142 144 147  147 155 156 158  v  LIST OF T A B L E S Table 3-1  Incentive and penalty recalculation frequencies  Table 3-2 Combined objective values and computation time characterizing two constrained optimization heuristics Table 5-1  Summary of alternative management scenarios  69  79 133  Table 5-2 Difference in the amount of land harvested between scenarios that do and do not include intensive forest management 136  vi  LIST OF FIGURES Figure 1-1  Stocks and flows of resources as they relate to forest systems (adapted from van  Kooten and Bulte, 2000; Hediger, 2000)  5  Figure 1-2  Land Allocation Strategies  11  Figure 1-3  Linkage between planning and knowledge/values  12  Figure 1-4 Scenario analysis process for the evaluation of intensive forest management 14 Figure 2-1 Progress of the objective function value through iterations for weights set at 0.4 for volume harvested and 0.6 for the old forest conservation. The line represents the progress for one run and the box plot represents the spread of the objective function value at iterations 1, 50, 100, 500, 1000, 2000, 3000, and 4000 35 Figure 2-2 Volume flow over the planning horizon through iterations for weights set at 0.4 for volume harvested and 0.6 for the old forest conservation. The line represents the progress for one run and the box plot represents the spread of the objective function value at iterations 1, 50, 100, 500, 1000, 2000, 3000, and 4000 36 Figure 2-3 Final solution obtained for a simulation run with approximately 4000 iterations. Black lines delimitate areas that are not under management. Light grey cells represent lakes. Dark grey cells are old forest areas and white cells are younger forests 37 Figure 3-1  A flowchart of the co-evolutionary algorithm for a constrained planning problem  63  Figure 3-2 Progression of (a) the stand harvest volume index, (b) the stand OG index, and (c) the stand value index through iterations for the unconstrained problem. Box plots are produced every 300 iterations and summarize the results of 250 runs. Each box represents the median, 25th and 75th percentiles with the 10th and 90th percentiles as vertical lines 67 Figure 3-3 Progression through iterations of (a) the volume harvested, and (b) the amount of OG stands in the planning period 1. The lines represent the constraint levels. Box plots are produced every 400 iterations over 250 runs. Each box represents the median, 25th and 75th percentiles with the 10th and 90th percentiles as vertical lines 70 Figure 3-4 Progression of (a) the harvest value index, (b) the OG index and (c) the stand combined objective value through iterations when constraints are applied. Box plots are produced every 400 iterations over 250 runs. Each box represents the median, 25th and 75th percentiles with the 10th and 90th percentiles as vertical lines 73 Figure 3-5 Tradeoffs between cumulative harvest volume and OG index, (a) Unconstrained (A) and constrained (+) co-evolutionary optimization tradeoffs; (b) close-up of constrained (+) coevolutionary optimization tradeoffs 75 Figure 4-1  Platform for forest management planning  90  Figure 4-2  Integration of CA model and GIS raster datasets and processes  95  vn  Figure 4-3  Representation of a forest within an object-based CA framework. (The large black  arrows represent inheritance and white arrows represent composition) Figure 4-4  Study area located in Northern Ontario, Canada, with its land use categories  98 101  Figure 4-5 Distributions of the amount of (a) old growth and (b) harvest volume over time 104 Figure 4-6 Frequency of (a) harvest events, and (b) old growth in stand cells. Based on 200 runs with 12000 iterations each for the cell resolution of 9 hectares and X = 0.6 105 Figure 4-7  Distributions of the amount of (a) old growth and (b) harvest volume over time  Figure 4-8 Comparison of the objective function values between outputs for 9-ha and 16-ha resolutions and for relative weight associated with harvest value X = 0.4 and X = 0.6  107 108  Figure 4-9 Comparison of model outputs between 9-ha and 16-ha resolutions for relative weight associated with harvest value A = 0.4 and X = 0.6 108 Figure 4-10  Frequency of (a) harvest events, and (b) old growth based on 200 runs with 12000  iterations each for three different problems: 9 ha/ >-=0.4, 16 ha/X=0.4 and 16 haA.=0.6 Figure 5-1  Study area. Age class distribution (left) and ownership and road cover (right)  110 130  Figure 5-2 Net present value and cumulative harvested volume generated for each scenario 135 Figure 5-3 Location of harvested stands, young and mature stands and old growth in Period 3 for Scenario 7 (no road costs sharing) and Scenario 8 (road costs sharing) 136 Figure 5-4 Number of stands in no-management, extensive, basic and intensive management at the end of the planning horizon 137 Figure 5-5  Number of old growth stands over time for each scenario  138  Figure 5-6  Harvest flow for each scenario  139  Figure 6-2 Object oriented computer implementation of the CA-based evolutionary planning algorithm  153  viii  ACKNOWLEDGMENTS The undertaking of this thesis has confirmed a long-held suspicion: I have yet much more to learn, to unlearn and to relearn. But I can learn. And what I learn I can share. It is wonderful. I wanted to write some deep and beautiful words, some words that would convey my gratitude to all that have made this endeavor possible but, comes the end, I find myself speechless. It is clumsily therefore that I will give my thanks. First I am grateful to the forests. Forests have been and, I hope, will continue to be constant teachers. Forests have called to question my relationship to Nature, my relationship with other human beings and my relationship with time. There is much we expect from forests and these expectations force us to face up to our values. Now I want to thank Emina Krcmar, without whom the research presented in this thesis would not have been possible. It is a cliche thank-you maybe but one that means everything to me. Emina, thank you for trusting in my ideas, thank you for encouraging me and thank you pushing me to make those ideas reality. You went much beyond the call of advisor duty and I will always treasure our conversations and debates as a source of inspiration. I am also grateful to John Innes for providing pragmatic advice and support when my graduate student's illusions fell flat. He also provided me with the gift of being part of his research group, which is inestimable. Thank you John and my apologies for the American spelling of the thesis! M y thanks also go to Ilan Vertinsky who supported me throughout my Ph.D degree and did his best to get me to ground my fanciful ideas into reality. He could not keep my foray into theology to transpire in my writing - the messianic tone, but with his help I did manage to engage in some practical questions in this thesis. I want to thank Suzana Dragicevic who helped me realize and expand the potential of my methodology where I could not see it. I am also indebted to David Tait. We shared some of the best conversations I have had in the course of my graduate studies, broadening my outlook, reminding me of the limitations and idiosyncrasies of any modeling approach, and especially my own. I have now a vague sense of the definition of cybernetics, i f only because I have lost track of whether I am driving my thesis work or whether my thesis work has been driving me.. ..I also thank my wonderful colleagues in John Innes's research group, in particular Denise Allen, Garth Greskiw, Judi Krzyzanowski, Erin McGuigan, Alyson McHugh, Sonia Murray, Craig Nitschke and Joleen Timko. They endured my cursing at my ix  computer for three straight years, laughed with me and commiserated with me. They broadened my perspective on scientific research and forestry in innumerable ways. They were family. Among them, Craig Nitschke was my brother in arms and in coffee drinking. I am forever grateful for his positive and stimulating friendship. Judi, Denise and Erin provided me with new insights into the laws of thermodynamics and I will try not to forget the lessons I learnt during those three years. I want to thank Rob Kozak for his sympathy, his discussion, his cigarettes and enough mocking to endear him to me for a long long time. I am very grateful to Thomas Maness who believed in me despite my "dreadful writing" handicap; his unwavering encouragements and friendship will hopefully survive the defense of this thesis... In the end, I want to thank all those persons who had to deal with me in my daily life. This is no small feat: my parents, Catherine LeGoff and Jean Mathey, my brothers, Alban Mathey and Nicolas LeGoff, and my aunt, Elisabeth Goutman, provided the love and nurturing environment it took to awake my curiosity for life and foster enough tenacity to pursue one's dreams. Many thanks to those friends whose support shone a bright light in the dark times: the Sleeman family, and Jon Sleeman in particular, who believes that everything is absurd and vain. Even i f I never really believed him, I owe him for the great conversations and the great beer. Cedric Babe taught me simplicity and his steadfast belief that life is to be lived without further due changed my outlooks. When I got home dejected for one reason or another, or, even worse, when I got home excited about my work and that was all I could talk about, he listened. I thank Aaron Bergbusch for bringing music in my life and providing emotional distraction. Less glamorous but so necessary, I was fortunate to have the material support from a number of granting agencies, the Natural Sciences and Engineering Research Council of Canada, the Sustainable Forest Management Network, The Society for Conservation and GIS, Environmental Systems Research Institute (ESRI). I am also grateful to The Canadian Ecology Centre, Mattawa, Ontario and Tembec Inc., who provided me with support to conduct a case study in Northern Ontario. "Landscape consists in the multiple, overlapping intricacies and forms that exist in a given space at a moment in time. Landscape is the texture of intricacy, and texture is my present subject. Intricacies of detail and varieties of form build up into textures. A bird's feather is intricacy; [...] the bird in space in relation to air, forest, continent, and so on, is a thread in the texture.[...] The texture of space is a condition of time. Time is the warp and matter the weft of the woven texture of beauty in space and death is the hurtling shuttle. [...] The wonder is - given the errant nature of freedom and the burgeoning texture in time - the wonder is that all the forms are not monsters, that there is beauty at all, grace gratuitous" Annie Dillard (Pilgrim at Tinker Creek)  CO-AUTHORSHIP STATEMENT Chapter 2 (Paper I): Title: Re-evaluating our approach to forest management planning: a complex journey Co-authors: Emina Krcmar and Ilan Vertinsky Role of co-authors: manuscript preparation Chapter 3 (Paper II): Title: Forest planning using co-evolutionary cellular automata Co-authors: Emina Krcmar, David Tait, Ilan Vertinsky and John Innes Role of co-authors: manuscript preparation Chapter 4 (Paper III): Title: Object-based implementation of a decision support tool for complex forest planning problems Co-authors: Emina Krcmar, Suzana Dragicevic and Ilan Vertinsky Role of co-authors: manuscript preparation Chapter 5 (Paper IV): Title: Potential contribution of intensive forest management and economies of scale to forest management Co-authors: Emina Krcmar, John Innes and Ilan Vertinsky Role of co-authors: manuscript preparation  xi  1  INTRODUCTORY C H A P T E R  1.1 Introduction Human beings depend on natural resources directly for basic needs such as food and heat or indirectly for the production of transformed goods from primary materials. Stocks of natural resources have long appeared to be inexhaustible. However, the combination of exponential population growth and increasing industrialization has made the human toll on natural resources ever more noticeable. The fisheries collapses on both coasts of Canada is a striking example of this pressure. As human development continues along its current course, there arise greater demands on both resource utilization and conservation if there are to be sufficient resources available in the future (van Kooten and Bulte, 2000; Sedjo, 1999; World Commission on Environment and Development (WCED), 1987). Consequently, making decisions to strike a balance between demands and thereby reach towards sustainability has become a primary goal of natural resource management. Perhaps one of the most typical examples of conflicting demands is the case of forest resources. In particular, in Canada, the forestry sector in the boreal forest is faced by increased public demand for non-timber forest amenities (Reed and Baskerville 1990; Binkley 1997; Sedjo 1999). Concurrently, the global economic context for wood products has been changing. Although the trend in wood demand has remained upward (FAO 2001; Fox, 2000; Sedjo, 1999), evolving technologies, globalization and increased international trades, along with a shifting of supplying regions have all contributed to put Canadian forestry industry in a difficult situation (Porter and Martin 2000). These global trends put further pressure to increase the competitiveness of the Canadian forestry sector. One of the avenues that has been strongly advocated to achieve competitiveness has been to increase  timber production levels with Intensive Forest Management (IFM) (NRCan 2001; NRCan, 2001; Canadian senate sub-Committee on Boreal Forest, 1999). The initial motivation for this thesis was to evaluate the extent to which IFM could indeed maintain and improve timber production as part of a sustainable forest management ethic by allowing, for instance, conservation goals are met or economic benefits are generated. IFM, as equated to intensive forestry, is "the practice of forestry to obtain a high level of volume and quality of outturn per unit area through the application of the best techniques of silviculture and management" (Cote, 2003). On principle, IFM could thus ameliorate wood supply and contribute to freeing land for uses other than timber production (Binkley, 1997). However, IFM is a very controversial management option that divides forest management authorities. For instance, certification standards (e.g., as proposed by the Forest Stewardship Council) do not approve of many management practices designed to increase wood production and only recognize IFM as sustainable in limited cases (Friedman, 1999; Lucier and Shepard, 1997). Meanwhile, several jurisdictions, including the Canadian government, recommend IFM alongside extensive management and protected areas as a sustainable strategy (NRCan 2001; NRCan, 2001; Canadian senate sub-Committee on Boreal Forest, 1999). In the maze of differing opinions, the controversial nature of IFM forces decision makers to clarify their goals of forest management and the grounds on which they will analyze decision alternatives. IFM is a particularly sensitive issue; its evaluation requires taking a stand on what sustainable forest management entails for a particular area or jurisdiction before analyzing how IFM ties into this notion.  2  1.2  Sustainability  A consensus exists that natural resources should be sustained, especially the ones supporting human life. Sustainability is thus a core concept for natural resources management. However, there is little clarity about what exactly is to be sustained and for how long (Costanza and Patten, 1995). For instance, is it the services provided to us by the natural resources that we wish to maintain? Is it the existence of the natural resource itself? Or both? There does not seem to be any easy answer to the definition of sustainability, as attested by the number of studies dedicated to this issue (Global Sustainability @ RMIT university 2003; van Kooten and Bulte, 2000; Murcott, 1997; Jacobs, 1991).  1.2.1  Sustainability and capital  One way of looking at what is involved in the concept of forest resources sustainability is the notion of capital. The notion of capital is limiting, some would argue offensive, since it implies a simplification of natural resources as "production factors" only. The recognition that forests have values beyond production factors is now widespread: forests are also valued for their ecological and spiritual role, or just for their existence. However, simply leaving all forests untouched - as advocated by many naturalists and preservationists, is hardly possible at this point: there are goods and services that humans demand and expect from the forest and this entails a more utilitarian and interventionist approach in many cases (Davis et al. 2001). While keeping in mind that the value of forests extends beyond its involvement in economic activities, I will therefore articulate the issue of sustainable forest management around the notion of capital since this thesis is concerned with timber producing forest lands. I will  3  however expand the definition of capital to "a stock that yields a flow of valuable goods or services" (Costanza and Daly, 1992). Sustainability can then be expressed as a state in which the stock of capitals is maintained (van Kooten and Bulte, 2000). Natural resources in general, and timber-producing forest resources in particular, are complex systems with environmental as well as social and economic roles, and one can conceptualize them as the aggregation of natural and human (economic and social) capitals (Figure 1-1). These categories are not meant to be restrictive and they can overlap; for example, natural resources constitute both natural capital with regard to ecosystem functioning and human capital with regard the production and extraction of goods and services. The realization that natural resources are complex systems with overlaps among their different components has two main implications: the first is that all components of natural resources are interconnected. If the forest soil is depleted, it is very unlikely that tree growth will be satisfactory for timber exploitation purposes. This inference has brought about such paradigms as integrated forest management and ecosystem management. The second implication is that different types of capital can be substituted for one another. To maintain a given fish species in a forest area, artificial spawning grounds (involving financial and labor capital) could replace the loss of habitat (natural capital) due to development or timber extraction.  4  FOREST SYSTEM  Figure 1-1 Stocks and flows of resources as they relate to forest systems (adapted from van Kooten and Bulte, 2000; Hediger, 2000)  It is the extent to which the different types of capital can be substituted that defines whether it is the resource or its derived utility that we wish to sustain. Broadly, the different types of sustainability range from weak sustainability where the various forms of capitals are perfectly substitutable for one another (neo-classical paradigm) to 'strong' sustainability, where the various types of capital are perfectly complementary and no substitution is possible (ecological paradigm).  5  1.2.2 Sustainability as a function of value system The willingness to accept or reject substitution between capitals and thus the adoption of one sustainability perspective or another is a value judgment. It involves a relationship to the environment that establishes how the different capitals are perceived and evaluated (van Kooten and Bulte, 2000; Pezzey, 1997). In effect, substitution is only possible within certain limits because there is no substitute for some types of natural capital (e.g. water, soil). In those cases, we may be able to identify certain minimum thresholds necessary to sustain a given natural resource (Brown et al., 1999). Based on these minimum thresholds, there are a few different perspectives on how to take sustainable decisions (e.g. minimax principle, precautionary principle, safe minimum standard). The identification of these minimums requires knowledge of the relevant ecosystem processes and an understanding of the physical environment in which decisions are made (Gough and Ward, 1996). However, taking these decisions also requires an acknowledgement that social preferences are at the core of how we define the 'right' balance between utilization and conservation of natural resources. Even i f we assume that we can identify and meet some minimum expectations, there remain many trade-offs among the different aspects of sustainability. To be able to undertake triple-bottom line accounting of forest management, the triple bottom line must be defined. Sustainability, and as a corollary, sustainable forest management, are often falsely used as stand-alone paradigms. They are umbrella terms under which particular sets of values and their agreed degree of substitutability should be defined. In order to evaluate the worth of a particular management strategy, the values and trade-offs at stake need to be made explicit.  6  1.3 Potential impacts of IFM on forest values  1.3.1  Forest values and forest management strategies  As mentioned previously, the concept of sustainability depends to a large extent on the perception of the values at stake. In the past century, the perception of forests has broadened from a seemingly infinite resource centered on timber production to one which sees the forest as a finite source of multiple values. Forests are now also valued for their ecological functions, as well as their recreational and spiritual roles. For instance, the red and white pine forests of Ontario that were long considered an inexhaustible source of lumber gold are now valued as a scarce ecosystem of particular aesthetic and wildlife value. The values of forests evolve with time and so does the concept of sustainable forest management. Management paradigms have shifted from sheer exploitation to sustained yields in the 1950's (Kennedy 1947; Sloan 1945) to incorporate other demands with "multiple-use management" by the end of the 1960's (Agnoletti, 2000; Williams, 2000; Ross, 1995; Legg, 1988). Keeping on enlarging the scope of forest values and thus the goals of sustainable forest management, the 1990's saw the rise of "sustainable forest management", from which sprouted the "ecosystem management" and "integrated forest management" paradigms (National forest strategy (NFSC 2003) and Canada Forest Accord ( C C F M 2003; C C F M 1998; C C F M 1992). These emphasize the maintenance of ecological integrity of the forest ecosystem along with the other - more human centered - values (Ciancio and Nocentini, 2000). Currently, there are two principal alternative management strategies aimed at producing the many goods and services expected from forests. Following European thinking that it is one of the best ways to address both timber production and environmental concerns (Koch and  7  Skovsgaard, 1999), multiple-use forest management has been widely applied i n Canada since the 1960's (Drushka, 2003). However, the combination o f increasing regulatory constraints to satisfy environmental concerns and low silvicultural inputs has led to ingress into unlogged, less productive stands (Binkley, 1997) (Drushka, 2003) as demonstrated by the discussions o f logging north o f the 51st parallel in eastern Canadian provinces. This progress is accompanied by a growing number o f land-use conflicts (Binkley, 1997). Another reason for the mitigated feelings about multiple-use management arises from the social sentiment that wilderness equates "untouched land" (Cronon, 1995). Since multiple-use management results in relatively low-level but ubiquitous disturbance (e.g., it requires an extensive network o f roads), it positively obliterates wilderness. Further reasons for the failure o f multiple-use management include the mutually exclusive nature o f some management alternatives (Drushka, 2003) and the lack o f a common measurement unit for all management benefits - commercial and non-commercial (Binkley, 1997). There is no clear way o f assessing i f optimal benefit has been achieved or not through multiple-use management. It has been suggested that multiple benefits from the forest might be better achieved through land-use specialization, with spatial and/or temporal zoning, than through multiple-use forest management (Vincent and Boscolo, 2002; Binkley, 1997; Sedjo and Botkin, 1997; Hunter and Calhoun, 1996; Vincent and Binkley, 1993; Swallow et al, 1990). N E B I E (Natural disturbance, Extensive, Basic, Intensive, and Elite, (Bell, 2003)) and T R I A D (Hunter and Calhoun, 1996) are examples o f this paradigm, where one or more values are to be obtained from sections o f the forest, while protecting all values over the entire forest (Sedjo and Botkin, 1997).  8  1.3.2  Intensive forest management  In specialized land-use allocation, uses range from near exclusive timber production zones to complete reserve areas. For simplification purposes, zones can be conceptually divided between timber production zones and conservation zones. Intensive forest management (IFM) is one of the possible management alternatives of timber production zones. This strategy aims at producing more forest benefits, in terms of timber yield and/or value. This entails investments beyond those necessary to satisfy minimum management objectives. Intensive forest management can thus apply to such situations as site restoration, forest landscaping or commercial plantations. In Canada, IFM specifically refers to management alternatives aimed at maximizing wood flow, minimizing production costs, increasing the quantity and/or quality of the fiber produced, and achieving all the former on a decreased operating land base (Cote, 2003; NRCan 2001; Lautenschlager, 2000; Hagner, 2000; O M N R , 1999; Helm, 1998). This definition of IFM will be used in the remaining of the thesis, IFM comprises a set of silvicultural systems where treatments, alone or in combination, will increase the yield of a stand beyond that of free-growing status (i.e., whose growth is not impeded by competition from other vegetation) (BC MoF 2002). These systems may include site preparation, planting of genetically improved/modified stock, brushing, fertilization and pre-commercial and commercial thinning within even-aged systems. The use of genetically modified material, fertilizers and chemical herbicides is a particularly sensitive issue and the subject of many debates among stakeholders because of their effects on the social, economic and natural aspects of forests. Land-use designations under the zoning strategy that IFM is part of may more efficiently address the control of collateral environmental damage than would otherwise be possible 9  with management regulations, and site quality is thus more likely to be conserved as sensitive areas are excluded from such management (Binkley, 1997).Increased forestland available to fulfill non-timber objectives is a key contribution o f I F M to sustainable forest management (Hermann and Lavender, 1999). The larger and more numerous areas exempt from harvesting are more likely to achieve habitat, recreation and conservation goals (Binkley, 1999; Burton, 1995) over the landscape, particularly since this reduces the risks associated with choosing inappropriate reserve size or inter-reserve distance (Shafer, 2001).  In conclusion, the inclusion of I F M in a zoning strategy could be a sustainable practice but it may result in as much discontent as multiple-use forest management i f the diverse demands on forest are not acknowledged - and met (Sherry and Johnson, 1999). It is essential that I F M be evaluated within an integrated management framework, i.e., where all others uses and management actions are accounted for and where the ecology o f the forest system as well as the requirements from the various stakeholders are considered (Oliver, 1999).  The focal question then becomes: How much should be allocated to which use and where? Several alternative patterns have been proposed (Figure 1-2), often based on educated guesses or policy constraints.  Multiple  Canada senate (1998)  Burton (1995)  Lands for Life (OMNR 1999)  M= Multiple-use I = Intensive forest management P = Protected areas, reserves and unmanaged  10  Figure 1-2  L a n d Allocation Strategies  To analyze the value of IFM based on how much, where and when IFM is implemented, the first requirement is to contextualize the analysis to a particular area with particular forest ecology and structure and a particular set of practices, goals and regulations. In effect, the exercise requires the use of a land-use planning tool.  1.4 Planning and Planning tools  1.4.1  Purpose of planning  Decision-makers manipulate forest resources in order to reach towards what they perceive as sustainable management. Strategic planning is concerned with the "long-range goals and policies for resource allocation" (Turban and Meredith 1991). Planning enables the projection of a course of actions that will satisfy the objective. "Goals and constraints [...] are the drivers o f this decision process" and the resulting plan essentially identifies the choice and scheduling o f actions that will satisfy the goals (Davis et al., 2001). Planning "translates our knowledge about how the world works into activities that will promote [human] values" (Davis et al., 2001) and thus lies within a future oriented context (Figure 1-3). Forest management and its planning therefore constitute the most direct way to face demands and trade-offs regarding forests.  11  Current state  Desired future state  Figure 1-3 Linkage between planning and knowledge/values  Planning thus requires knowledge of the environment and of the impacts of management actions. In addition, it also requires an acknowledgement that social preferences are at the core of how we define the 'right' balance between utilization and conservation of forest resources.  1.5 Research  Objectives  1.5.1 Objectives The initial objective of my research was to evaluate the benefits of implementing IFM on a large forest management unit. Large scale implementation of IFM has not been undertaken in the boreal forest and a traditional quantitative, purely deductive approach is precluded by the lack of existing data. Hypotheses regarding the actual impact of IFM on different values cannot be tested. In such cases, the exploratory modeling paradigm constitutes a compromise with a purely quantitative approach. Exploratory modeling, as "the use of series of [...] computational experiments to explore the implications of varying assumptions and hypotheses" (Bankes, 1993), is the framework upon which this thesis is articulated. As a 12  corollary of exploratory modeling, scenario analysis is a tool to evaluate decision alternatives for problems bounded by uncertainty (Shoemaker, 1993). To explore how the inclusion of IFM as part of a management strategy could affect the management outcomes, this thesis focus on several objectives following a scenario analysis framework (Figure 1-4): (1) the identification of the values that may most affect strategic planning; (2) the identification of a set of scenarios related to management objectives; (3) the elaboration of a planning tool which can handle spatial objectives and inter-temporal trade-offs between management objectives and constraints, in particular those that will be affected by the inclusion of IFM in the management scenarios.  13  Question: how could the inclusion of IFM affect the potential outcomes of forest management?  . Clarify decision(s) facing the forest managers.  1. How much land to allocate to which utilization, where?  i  2.Identify and  2. The key forces most directly influencing land allocation relate to financial return, growth and yield, expected, capital and human resource availability, regulation constraints, socio-political constraints and natural processes (disturbances, succession).  3. Identify factors likely to influence the key forces driving decision.  3. The factors likely to influence the future direction of financial return are price for wood and cost of operations and the factors likely to influence regulation or sociopolitical constraints are demands for environmental services.  analyze key forces: what musN • • be known in order to make this decision?  , Analyze Factors to: • Establish their current trajectory and possible future branching points. • Determine the range of uncertainty surrounding these future possibilities. • Assess the impact of one trend upon another.  4. Inductive approach: the focus is on identifying a few important "impacting factors" and postulating a value (e.g. preference for conservation vs. timber harvest, economies of scale, price of wood etc.).  5. The task, then, is to analyze the outcome of potential decision alternatives for different combinations of "impacting factors" values.  5. Define scenario logics.  6. Model: Description of the outcome decisions under the different scenarios previously generated.  J  Figure 1-4 Scenario analysis process for the evaluation of intensive forest management. 1.5.2 Thesis structure In order to address the issue of IFM evaluation and that of a planning tool capable of supporting such analysis, this thesis focus successively address the thesis objectives:  Chapter 2 (Paper I ) determines what the requirements are for a planning tool to match the sustainable forest management paradigm in its broader concept: i.e., to address social, economic and environmental aspects of forests. Chapter 3-4 (Papers I I - I I I ) aims at developing a planning approach capable of meeting these requirements. Chapter 3 describes a decentralized approach to solving forest management problems that involves spatial and temporal trade-offs and local and global constraints. Chapter 3 further provides a comparative analysis of the CA-based algorithm with a simulated annealing algorithm. Chapter 4 presents an object-oriented framework that is capable of efficiently supporting this planning tool. This chapter also covers the issue of resolution choice and the portability of the planning framework. Chapter 5 (Paper I V ) applies the planning framework developed in the previous chapters. Chapter 5 explores the potential of intensive forest management to increase the flexibility/adaptability of strategic planning where forest management seeks to achieve multiple and conflicting objectives over space and time. This study compares the impact of intensive forest management when issues such as economies of scale and land conservation are considered. Specifically, some questions I seek to answer are: what is the cost of implementing IFM i f IFM is used to increase volume production and the conservation area is increased? Can location and clustering of harvest blocks decrease these costs?  15  1.6  References  Agnoletti, M . , 2000. Introduction: the development of forest history research. In Methods and approaches in forest history. Agnoletti, M . and Anderson, S., (Eds.), C A B I Publishing, Wallingford, U K . pp. 1-20. Bankes, S., 1993. Exploratory Modeling for Policy Analysis. Operations Research 41: 435449. British Columbia Ministry of Forests (BC MoF), 2002. Glossary of forestry terms. http://www.for.gov.bc.ca/PAB/PUBLCTNS/GLOSSARY/glossary.htm2002. Last accessed in 2005. Bell, F.W., 2003. Intensive Forest Management Science Partnership: NEBIE Plot Network. In Meeting emerging ecological, economic, and social challenges in the Great Lakes region: popular summaries. Great Lakes Forest Alliance 2003 summit. Buse, L. J. and Perera, A . H . (Eds.), Queen's Printer for Ontario, Sault Ste. Marie, pp. 115-116. Binkley, C.S., 1997. Preserving nature through intensive plantation forestry: The case for forestland allocation with illustrations from British Columbia. Forestry Chronicle 73: 553559.  Brown, J.R., Herrick, J., and Price, D., 1999. Managing low-output agroecosystems sustainably: the importance of ecological thresholds. Canadian Journal of Forest Research 29:1112-1119.  16  Burton, P.J., 1995. The Mendelian compromise: a vision for equitable land use allocation. Land Use Policy 12: 63-68. Canadian senate sub-Committee on Boreal Forest, 1999. Competing realities: The Boreal Forest at Risk. 35th Parliament of Canada ed. Report of the Standing Senate Committee on Agriculture and Forestry, Ottawa. C C F M , 1992. Canada Forest Accord, http://nfsc.forest.ca/accords/accordl.html. National Forest Strategy Coalition. Last accessed 2006 C C F M , 1998. Canada Forest Accord, http://nfsc.forest.ca/accords/accord2.html. National Forest Strategy Coalition. Last accessed 2006 C C F M , 2003. Canada Forest Accord, http://nfsc.forest.ca/accords/accord3 .html. National Forest Strategy Coalition. Last accessed 2006 Ciancio, O. and Nocentini, S., 2000. Forest management from positivism to the culture of complexity. In Methods and approaches in forest history, IUFRO Series No 3. Agnoletti, M . and Anderson, S. (Eds.), C A B I Publishing, Wallingford, U K . pp. 47-58.  Costanza, R. and Daly, H.E., 1992. Natural Capital and Sustainable Development. Conservation Biology 6: 37-46. Costanza, R. and Patten, B.C., 1995. Defining and predicting sustainability. Ecological Economics 15: 193-196. Cote, M . (Editor), 2003. Dictionary of forestry. Special edition XII World Forestry Congress. Ordre des ingenieurs forestiers du Quebec, Ottawa. 17  Cronon, W. (Editor), 1995. Uncommon ground: toward reinventing nature. W.W. Norton & Co., New York.  Davis, L.S., Johnson, K . N . , Bettinger, P.S., and Howard, T.E. (Editors), 2001. Forest Management. Fourth Edition ed. McGraw-Hill, New York. Drushka, K . 2003. Canada's forests: a history. McGill-Queen's University Press, Montreal and Kingston. Food and Agriculture Organization of the United Nations (FAO), 2001. State of the world's forests. Rome, IT Fox, T.R., 2000. Sustained productivity in intensively managed forest plantations. Forest Ecology and Management 138: 187-202. Friedman, S.T., 1999. Forest regeneration practices - How regional certification standards compare. Journal of Forestry 97: 23-32.  Global Sustainability @ RMIT University, 2003. Bibliography: descriptions of sustainability. http://www.global.rmit.edu.aU/tbl/2.2_keytexts.pdf. Royal Melbourne Institute of Technology. Last accessed 2005.  Gough, J.D. and Ward, J.C., 1996. Environmental decision-making and lake management. Journal of Environmental Management 48: 1-15.  Hagner, M . , 2000. Current forest management trends in Scandinavia. In Intensive forest management in Ontario; summary of a 1999 science workshop. Bell, F. W., Pitt, D. G., Irvine, M . , Parker, W. C , Buse, L. J., Stocker, N . , Towill, W. D., Chen, H., Pinto, F., Brown, 18  K., DeYoe, D., McDonough, T., Smith, G., and Weber, M . (Eds.), Queen's printer for Ontario, Sault Ste. Marie, pp. 16-17. Hediger, W., 2000. Sustainable development and social welfare. Ecological Economics 32: 481-492. Helm, J.A., 1998. The Dictionary of Forestry. Society of American Foresters, Bethesda. Hunter, M.L.Jr. and Calhoun, A. J. K., 1996. A triad approach to landuse allocation. In Biodiversity in managed landscapes. Szaro, R. C. and Johnston, D. (Eds.), Oxford University Press, New York. pp. 477-491. Jacobs, M . , 1991. The Green Economy: Environment, Sustainable Development and the Politics of the Future. Pluto Press, London. Kennedy,H., 1947. Report of the Ontario Royal Commission on Forestry. Koch, N.E. and Skovsgaard, J.P., 1999. Sustainable management of planted forests: some comparisons between Central Europe and the United States. New Forests 17/18: 11-22.  Lautenschlager, R.A., 2000. Can intensive silviculture contribute to sustainable forest management in northern ecosystems. Forestry Chronicle 76: 283-295.  Legg, S., 1988. Re-writing the history of forestry? Changing perceptions of the forest management in the new world. In Australia's ever changing forests: proceedings of the first national conference on Australian forest history, Canberra, 1988. Frawley, K. J. and Semple, N . M . (Eds.), Department of Geography and Oceanography, Canberra, pp. 223-336.  19  Lucier, A . A . and Shepard, J.P., 1997. Certification and regulation o f forestry practices in the United States: Implications for intensively managed plantations. Biomass & Bioenergy 13: 193-199.  Murcott, S., 1997. Appendix A : Definitions o f Sustainable Development. A A A S Annual Conference, IIASA "Sustainability Indicators Symposium," Seattle, W A 2/16/97. Available at http://www.sustainableliving.org/appen-a.htm. Last accessed 2005.  National Forest Strategy Coalition ( N F S C ) , 2003. National Forest Strategy (2003-2008), A Sustainable Forest: The Canadian Commitment. http://nfsc.forest.ca/strategies/strategy5.html.  Last accessed 2005.  Natural Resources Canada (NRCan), 2001. Forest 2020: A Budding Dialogue in Canada. In The state o f Canada's Forests. Sustainable forestry: a reality in Canada. Government o f Canada, Ottawa, pp. 74-76.  Natural Resources Canada (NRCan), 2001. State o f Canada's Forests 2000-2001: Sustainable Forestry: A Reality in Canada. 11th annual report.  Oliver, C D . , 1999. The future o f the forest management industry: highly mechanized plantations and reserves or a knowledge-intensive integrated approach. Forestry Chronicle 75: 229-245.  Ontario Ministry o f Natural Resources ( O M N R ) , 1999. Ontario Forest Accord - A foundation for progress. Queen's Printer for Ontario, Toronto, O N .  20  Pezzey, J.C.V., 1997. Sustainability constraints versus "optimality" versus intertemporal concern, and axioms versus data. Land economics 73: 448-466. Porter, M.E. and Martin, R.L., 2000. Canadian Competitiveness: Nine Years after the Crossroads. Paper presented at the CSLS Conference on the Canada- U.S. Manufacturing Productivity Gap, Ottawa. Ross, M . M . , 1995. Forest Management in Canada. Canadian Institute of Resources Law, Faculty of Law, University of Calgary, Calgary, A B . Sedjo, R.A., 1999. The potential of high-yield plantation forestry for meeting timber needs. New Forests 17/18: 339-359. Sedjo, R.A. and Botkin, D., 1997. Using Forest Plantations to Spare Natural Forests. Environment 39: 14-20. Sherry, E.E. and Johnson, C.J., 1999. The forgotten forest: Revisiting the forestland allocation strategy. Forestry Chronicle 75: 919-927. Shoemaker, P., 1993. Multiple Scenario Development: Its Conceptual and Behavioral Foundation. Strategic Management Journal 14: 193-213.  Sloan, G.M., 1945. Report of the Commissioner, the Chief Justice of British Columbia, relating to the Forest Resources of British Columbia. Swallow, S.K., Parks, P.J., and Wear, D.N., 1990. Policy-relevant nonconvexities in the production of multiple forest benefits. Journal of Environmental Management 19: 264-280.  Turban, E. and Meredith, J.R., 1991. Management Science, 5th ed, Irwin, Boston, M A .  van Kooten, G.C. and Bulte, E.H., 2000. The Economics of Nature: Managing Biological Assets. Blackwell Publishers, Oxford, U K . Vincent, J.R. and Binkley, C.S., 1993. Efficient multiple-use forestry may require land-use specialization. Land economics 69: 370-376. Vincent, J.R. and Boscolo, M . , 2002. Potential welfare gains under specialized forest management. 2002 World Congress of Environmental and Resource Economists ed. Monterey, C A . Williams, M . , 2000. Putting 'flesh on the carbon-based bones' of forest history. In Methods and approaches in forest history. Agnoletti, M . and Anderson, S. (Editor), C A B I Publishing, Wallingford, U K . pp. 35-46. World Commission on Environment and Development (WCED), 1987. Our Common Future. Oxford University Press, Oxford.  22  2  RE-EVALUATING OUR A P P R O A C H TO F O R E S T MANAGEMENT PLANNING: A C O M P L E X J O U R N E Y  2.1  1  Overview  The evolution of the forest values from timber supply to ecological and social values is leading to the redefinition of the Sustainable Forest Management (SFM) paradigm. In parallel, scientific knowledge is expanding and uncovering the interconnectedness of the various processes that support these values. We thus have many wishes and much knowledge but do we have the decision support tools that will pull them together to promote SFM? After a broad review of the evolution of decision support tools in forest management, this paper presents a case for more holistic numerical planning tools. To illustrate that such tools can be designed, we propose a simple decentralized approach. In this approach, a landscape management strategy evolves based on local decisions, integrating spatial and aspatial, multiperiod and period-specific goals. Such tools could become a useful platform for sustainable forest management planning.  2.2  Introduction  The process of decision-making in forest management describes the selection of a course of action that will be undertaken in a particular forest. Each alternative course of action connects to a particular set of anticipated future forest conditions. It is the desirability associated with each set that drives the selection process. Planning is essentially the tool that links actions to outcomes and outcomes to desirability (Davis et al, 2001). Planning  A version of this chapter has been published. Mathey, A . - H . , Krcmar, E . and Vertinsky I., 2005. Re-evaluating our approach to forest management planning: a complex journey. Forestry Chronicle 81(3): 295-296. 1  23  therefore requires knowledge of the environment and of the impacts of management actions. In addition, it also requires an acknowledgement that social preferences are at the core of how we define what constitutes a "desirable" outcome. The concept of "desired future forest", however, is not a static paradigm. Between the 1920's and the 1990's alone, a period no longer than the length of a standard harvest rotation in temperate latitudes, the perception of forests has broadened from a seemingly infinite resource and a focus on timber values to view them as a scarce source of multiple values (Agnoletti and Anderson, 2000). Management has accordingly adjusted from resource exploitation to sustained yield, multiple-use management, and finally Sustainable Forest Management (SFM). The S F M paradigm emphasizes the maintenance of the ecological integrity of the forest ecosystem while generating desired services and products. The first objective of this paper is to present a broad overview of how decision support tools have adapted to the new S F M requirements. To this end, we broadly examine the changes in conservation, social and economic demands on forest management and some parallel scientific developments. The second objective is to present an alternative planning tool as an example of a decision support methodology that is capable of acting as a platform for the holistic context of S F M .  2.3  Environmental  sustainability  In the 1960's, the alarm of scientists at the rate of species loss and the increasing public concern over environmental resources led to the rapid development of conservation biology and eventually to official protection positions (Fiedler and Kareiva, 1998; Meffe et al, 1997; U N C E D , 1992). Since the initial protection measures focused on species (e.g. U S A  Endangered Species Act), it has become increasingly clear that species could not be protected without consideration of the underlying ecological processes that support their existence. As a result of advances in such fields as community and landscape ecology, forests are now recognized as complex systems; they are the product of a number of interacting ecological processes that occur at various temporal and spatial scales (Sherry and Johnson, 1999; Voller and Harrison, 1998). The design of particularly sized and shaped reserves with a distribution through space and time ensures conservation along with the adaptive management of the rest of the forest matrix (Shafer, 2001; Oliver, 1999; Schwartz, 1999). Once the targets for conservation are identified in a particular area, coarse-filter strategies are often the approach of choice (Voller and Harrison, 1998). This improves planning efficiency at the strategic level and avoids a complete species-by-species planning process. A coarsefilter approach is also proactive in limiting the potential for further species endangerment. Disturbance ecology and landscape ecology have developed an array of measures to quantify and monitor the environment spatial patterns in the environment (landscape ecology metrics). These metrics can be used to design reserve areas and adaptive management practices. Ensuring that the requirements of conservation targets at finer scales are met constitutes the final step of any conservation strategy.  Implications for forest planning The conservation goals of S F M require that the planning techniques developed for landscape ecology and conservation biology be integrated into forest planning. As a direct consequence, planning needs to be spatial to adequately model the different levels at which forestry  25  practices can impact the landscape. This can also reduce issues such as road planning in sensitive ecosystems (stand-level) or fragmentation of old growth forests (landscape-level). Temporal variations of physical patterns must also be measurable to compare them with natural disturbance cycles. In short, it must be possible to evaluate the degree to which conservation goals are met in the forest management plan at various spatial and temporal scales.  2.4  Social  sustainability  Social acceptability towards forestry has had a powerful impact on forest management that reaches beyond conservation and can affect all forest operations. Some changes were the direct consequences of public lobbying against the forest industry (court decisions, social actions by NGO's, media attention). Other changes were the indirect consequence of political choices, eventually expressed through government regulation or legislation (e.g., the Forest Act in the USA). Faced with the evidence that social acceptability is essential to the success or failure of forest management strategies (Clawson, 1975), substantial research was initiated to clarify the social processes underlying forest management. Social acceptability was found to relate to both the outcomes and the process of planning. However, acceptable outcomes are difficult to evaluate: there are usually multiple forest stakeholders with multiple value systems (Stankey and Clark, 1992), which are not fixed but change depending on the spatial, cultural, institutional and temporal contexts (Berkes and Folke, 1998). Regardless of outcome acceptability, forest management strategies may further  26  be rejected on the basis of the planning process itself, and the lack of trust in the planning team (Shindler et al. 2002).  Implications for forest planning It follows that S F M ideally encompasses the multiplicity of stakeholders and their values and should result from a consensus. This may involve re-evaluating planning as a continuous process where the planning team is able to elicit trust and to continue the relationship with stakeholders during plan implementation. In this context, the ability of decision support systems to generate optimal solutions may not be as crucial as their capability in providing visualization of management alternatives as a basis for discussion.  2.5  Economic  sustainability  In the more specialized setting of economics, society also impacts forestry insofar as it affects the allocation of forest resources. This is exemplified by the trend towards buying wood from certified forests. However, the social demand for specific forest products is only one of the factors that have modified the economic situation of the forestry sector over the past decades. Technological advances, economic recessions, globalization of the industry and changing consumer demographics have all contributed to the industry producing only what it could sell (Cohen and Kozak, 2002; Porter and Martin 2000). The utilization of species previously considered worthless, the emergence of new suppliers and new markets, and trade disputes are all examples of the changing economic context.  27  Paralleling these changes, a number of new economic concepts have been developed which may lead to a redefinition of forest economics models: these include the role of institutions, non-static preferences, multiple levels of utility, co-evolution between natural and social systems or the effect of uncertainty on maximization (Kant, 2003; Jacobs, 1991).  Implications for forest planning The necessity to tighten the connection between the elements of the value chain, from forest management to wood processing to markets, means that the decision support system must be amenable to scenario analyses. Platforms that can accommodate alternative market outlooks could enhance the ability of forest management to satisfy the economic goals of S F M . Decision support tools must further be able to model the co-evolution between natural and economic processes in order to propose more effective plans. Incorporation of dynamic parameters is useful not only to reflect alternative market scenarios but also to integrate changing social preferences.  2.6  Decision support tools and SFM  planning  With current management considering more than just timber production, the traditional use of stand-level cost-benefit type analyses in forest management planning (Bare et al, 1984) has become obsolete (Reed 2000). After the inception of environmental concerns, these analyses were superseded by top-down planning models associated with centralized procedures such as mathematical programming (Martell et al, 1998; Weintraub and Bare, 1996). Top-down planning models address the aggregate objectives of forest management  efficiently (e.g., harvest flow). However they do so without explicit consideration of the system's constituent elements. Top-down procedures therefore imply a strong understanding of the relationships between local processes and global properties. Too many local exceptions may compromise these relationships (e.g., stream buffers, traps, private cottages, or culturally sensitive areas...) to the extent that the strategic plan thus generated can be unachievable (McDill, 1992); Spatial planning schemes were subsequently introduced; however, when combined with centralized approaches, the size of the resulting combinatorial problem became an issue (Martell et al, 1998). Hierarchical modeling (Weintraub and Cholaky, 1991) and using heuristics (Nelson, 2003) helped to resolve this problem. Progress has since been made towards integrating multiple goals at various scales. Yet, decision support tools rarely simultaneously address all the scales and processes relevant to forest management goals. For instance, it is possible, albeit difficult, to formulate spatial goals such as the size, shape and distribution of reserve clusters (Venema et al, 2005; Stewart et al, 2004; Ananda and Herath, 2003), to integrate multiple stakeholders (Stewart et al, 2004) or to generate visual quality scenarios (Sheppard et al, 2004). However, few planning tools address scheduling of actions and fulfill both aspatial goals (e.g., harvest or cash flows) and spatial goals such as dynamic and contiguous reserve areas on the land base (see Baskent and Keles, 2005; Bettinger and Chung, 2004). Decentralized bottom-up approaches could better capture the interconnectedness between local processes and decisions and regional ones (Strange et al, 2002). In this paper, we sketch a decentralized planning methodology that could have the potential to simultaneously address scheduling of forestry operations while considering volume flow, net present value,  dynamic parameters (social preference or market outlooks) and spatial arrangement (location and clustering) of conservation areas.  2.7  Decentralized forest management  2.7A  Problem statement  planning  A forest plan, over a given planning horizon, consists of a prescribed schedule of treatments. There is one schedule for each stand that comprises the forest. In this paper, we present an iterative algorithm that begins with an initial plan and, with each iteration, attempts to improve the overall forest plan. The scheme is based on the notion of cellular automata (CA). A cellular automaton is an abstract machine with a state selected from a finite set of states and a set of transition rules. Applied at discrete time intervals, they determine the automaton's subsequent states based on the cell's own state and the states of its neighbors (Toffoli and Margolus, 1987). C A models are generally constructed as a collection of cells that form a lattice. The decentralized transition rules and the spatial interdependence of the lattice cells account for C A ' s self-organization and scale-integration capabilities. These capabilities make C A an efficient tool in modeling complex systems such as urban development, population dynamics, vegetation succession, forest fires, spatial economics and, of particular interest, afforestation decisions (Strange et al. 2002). We propose that C A may further be used for forest management planning.  30  2.7.2 Methods A forest plan can be represented by a C A model by treating each stand (represented by a raster cell) as a cellular automaton. The state of a stand is one of the many alternative schedules of treatments that could be applied to the stand. Examples of states range from the no-treatment state with no actions scheduled for the length of the planning horizon to the harvest of the stand at the beginning of the planning horizon and again at the end of the planning horizon. Each alternative stand treatment schedule is an alternative state. A forest plan thus consists of the assignment of a management state to every cell. The neighbors of each stand could be those stands that border or that are within a certain geometric distance from the stand. A state transition function would determine the new (possibly the same) treatment schedule for a stand as a function of the current forest plan as it applies to the stand and its neighbors. The forest plan evolves by iteratively generating new stand schedules (states) using the state transition function in individual stands. In our scheme, the state transition function chooses the stand schedule that maximizes an objective function. Formally, an individual lattice point or stand, / , is a member of the set of all stands L which represents the forest. We let N(l) represent the set of neighbors of the stand / . Then, n e N(l) implies that the stand n is a neighbor of the stand / . Each stand / is in a particular state s(l) where the state represents a particular schedule of stand level treatments. A forest plan will be represented by the set C = (s(/) | / e L,}. A stand's state is evaluated as a weighted average of two components. We refer to the first component as the location-independent or aspatial component. It represents the expected utility generated by the stand state/schedule that is independent of the states of neighboring 31  stands. Contributions to this component could be the net present value or the volume flow of scheduled harvests. The second component of value is the synergistic expected utility associated with a schedule that results from the spatial context of the neighboring schedules. One contribution to this component could be an old growth value that is enhanced if neighboring stands are simultaneously old. Similarly, adjacent cut blocks could decrease harvesting and treatment costs and could induce scale economies. A stand's value is computed as: v{ (l), l) = W  Ms(0J)+  aspalia  S  W  I/B/fa/  5 v ( 5 ( / ) , /)  Equation 1  where s(l)  is the stand's schedule  /  identifies the individual stand  aspatian spatial  w  w  a  weighting factors (proportion) for the relative contributions of the spatial and aspatial contributions to the total stand value r  e  av (s(l), l)  is the local value of a stand 1 with schedule s. The stand / contributes to the local value through stand specific attributes such as its initial inventory, site quality, and distance from processing facilities  sv {s(l), /)  is the spatial/context determined value of a stand 1 with a schedule s. Again the value may depend on stand specific attributes.  A configuration's value is thus: V(C) = £ v ( s ( / ) , / ) =  J^flv^/yj+^^O,/)]  Equation 2  The above system becomes a C A model with the addition of a state transition function and a state updating procedure. The state transition function selects as the next state/schedule, the  32  schedule that maximizes (the subscript associated with a schedule indexes iterations in the cellular automata updating): V(J,. (/),/) = max v(s(l)J) +1  s e S  . Equation 3  For each iteration, the initial iterative scheme consists of a probabilistic updating procedure where the state transition function is applied to randomly selected cells. This updating procedure may not converge to a stationary configuration. Improving the value for one stand may lower the value of neighboring stands, which can generate an oscillation of 'improvements' going back and forth between neighboring stands. By modifying the updating procedure and introducing asynchronous updating, the evolution of the plan with transitions could converge. In each iteration, one cell is randomly selected for updating. The schedule of a selected cell will only be changed if the value of the stand improves. The cell is 'replaced' and another cell is randomly selected for update. This process allows other cells to experience the new environment and to react to it, hence coevolving. The iterative process essentially stops when all cells are checked without any update occurring or after a fixed number of iterations.  2.8  Sample case  A small test area was used to test the algorithm. It consisted of about 4400 ha of forest divided in 9ha-cells in the boreal forest of Northern Ontario. The sample contained seven different forest types, including birch forests, spruce-dominated forests, hardwood forests, mixed hardwoods and pine forests. Each forest type has specific potential management options and associated growth and yield information. To simplify the computation of the 33  forest management problem, the number of strategies was reduced by considering only combinations of different silvicultural regimes of predefined treatment sequences with harvest schedules. Silvicultural regimes considered included "no-management", extensive, basic even-aged, intensive even-aged and, elite even-aged regime. In this sample case, the objectives were reduced to one aspatial and one spatial goal with two different time perspectives. The value consisted of a weighted average of the harvest volume generated over the entire planning horizon and of the number and compactness of old forest areas in each planning period. There were no constraints. The weights associated with each value were assumed to remain constant. The model code was built on ESRI ARC/INFO software and consisted of a number of files coded in Arc Macro programming Language (AML) and C++. The grid was populated with an initial landscape strategy and forest unit attributes. The starting configuration was created on the basis of geographic data files derived from the forest management unit using ARC/INFO.  2.8.1 Results The simulation was performed on a Pentium(R) 4. The computation time was approximately 4 hours for 50 runs with up to 4000 iterations. Each run had a different initial configuration. The number of iterations required for the algorithm to reach the highest possible average objective value was found to be between 2000 and 3000 iterations (Figure 2-1). Beyond 3000 iterations, no noticeable improvement of the objective value was apparent. The variation in  34  the objective function across runs was higher during the initial stages of the algorithm but progressively stabilized (Figure 2-1).  0  1000  2000  3000  4000  Iteration Figure 2-1 Progress of the objective function value through iterations for weights set at 0.4 for volume harvested and 0.6 for the old forest conservation. The line represents the progress for one run and the box plot represents the spread of the objective function value at iterations 1, 50,  100, 500, 1000, 2000, 3000, and 4000.  The improvement of the overall strategy seemed to be prominently the result of an improvement in the harvest flow during initial iterations (Figure 2-2). The irregular progression of the harvest flow in later iterations and its higher variability across runs (Figure 2-2) compared to the objective function value in the same iterations (Figure 2-1) both suggested that the clustering of old forest became more prominent in the later iterations.  35  Figure 2-2 Volume flow over the planning horizon through iterations for weights set at 0.4 for volume harvested and 0.6 for the old forest conservation. The line represents the progress for one run and the box plot represents the spread of the objective function value at iterations 1, 50, 100, 500, 1000, 2000, 3000, and 4000.  The preference for old forest conservation was identical in all periods of the planning horizon, which seems to limit concentrating harvests to the first and final periods. However, the inclusion of external constraints or incentives would be necessary to ensure a more balanced flow of timber. Figure 2-3 presents the old forest pattern of the area throughout planning periods. Old forest tended to be found in aggregate patches.  36  Figure 2-3 Final solution obtained for a simulation run with approximately 4000 iterations. Black lines delimitate areas that are not under management. Light grey cells represent lakes. Dark grey cells are old forest areas and white cells are younger forests.  2.9  Discussion  As mentioned earlier, ecological processes and decision making operate at a variety of scales and cell size may thus influence the spatial patterns generated by C A . Chen and Mynett (2003) found that the principal spatial scale of the studied system was the most appropriate method to decide C A cell size. The size of nine hectares was found to represent adequately the operations unit and stand polygons in the study area and was thus chosen. However, sensitivity analysis is required to verify the influence of size on the simulation output. A corollary implication of cell size influence is that it should be adjusted i f this approach is applied to another area. The cellular nature of the model makes it very portable for use in diverse forest regions. In addition to cell size, the cell states and transition rules could also be adjusted to adequately reflect stand dynamics and decision options available in the area. The C A approach has the capability to include any state relevant to a forest management area and to adapt transition rules to reflect the processes that influence forest changes in this area, which further allows 37  the approach presented in this paper to be expanded to more realistic settings with the inclusion of economic objectives, stochastic processes (e.g., fire), or other decisions choices (e.g., selective logging). In terms of practical implementation, C A thus constitutes one means to integrate mathematical optimizations and search techniques with the experience and knowledge of experts. Its affinity with the raster models of geographical information systems also facilitates visualization of planning outcomes for public input. Most centralized and prescriptive methods developed in planning reflect the belief that humans can control the forest resource to produce the desired or optimal outcome. In contrast, contemporary knowledge suggests that forests are complex co-evolutionary systems with changing functional controls in the ecosystem, in the economy and in the society (Ludwig, 2001; Holling et al, 1998). The cellular structure and the interdependence engendered from the transition rules imply that any specific element of the system reacts to, and adjusts its behavior in response to, changes occurring in other elements. Therefore, all elements of the system are, in time, influenced by all changes in the system. A decentralized approach might not simplify the complexity associated with forest systems but it might better represent it.  2.10  Conclusion  Although preliminary, the C A methodology developed in this paper shows that it is possible to simultaneously consider landscape level goals (harvest flow) and spatial goals (compact old forest reserves) with local decisions (stand scheduling). The simplistic C A evolving scheme presented in this paper showed that components from various spatial and temporal  38  contexts can be integrated. This property makes it possible to directly integrate knowledge and metrics developed by experts from fields such as landscape ecology. The inter-temporal 'pre-cognition' of the evolving scheme and the ability to re-evaluate the plan in each time period makes it possible to model dynamic events such as catastrophes, market changes or dynamic preference parameters. Such a decentralized approach is potentially a good platform for modeling complex forest systems.  39  2.11  References  Agnoletti, M . and Anderson, S. (Editors), 2000. Methods and approaches in forest history. C A B I Publishing, Wallingford, U K . Ananda, J. and Herath, G., 2003. The use of the Analytic Hierarchy Process to incorporate stakeholder preferences into regional forest planning. Forest Policy and Economics 5: 13-26. Bare, B.B., Briggs, D.G., Roise, J.P., and Schreuder, G.F., 1984. A Survey of Systems Analysis Models in Forestry and the Forest Products Industries. European Journal of Operational Research 18: 1-18. Baskent, E.Z. and Keles, S., 2005. Spatial forest planning: A review. Ecological Modelling 188: 145-173. Berkes, F. and Folke, C. (Editors), 1998. Linking Social and Ecological Systems: Management Practices and Social Mechanisms for Building Resilience. Cambridge University Press, Cambridge, U K . Bettinger, P. and Chung, W., 2004. The key literature of, and trends in, forest-level management planning in North America, 1950-2001. International Forestry Review 6: 40-50.  Chen, Q. and Mynett, A.E., 2003. Effects of cell size and configuration in cellular automata based prey-predator modelling. Simulation Modelling Practice and Theory 11: 609-625.  Clawson, M . 1975. Forests for whom and for what? John Hopkins University Press, Baltimore and London.  40  Cohen, D.H. and Kozak, R.A., 2002. Research and Technology: Market Driven Innovation in the Twenty-First Century. The Forestry Chronicle 78: 108-111.  Davis, L.S., Johnson, K . N . , Bettinger, P.S., and Howard, T.E. (Editors), 2001. Forest Management. Fourth Edition ed. McGraw-Hill, New York. Fiedler, P.L. and Kareiva, P.M. (Editors), 1998. Conservation biology for the coming decade. Second Edition ed. Chapman and Hall, New York. Holling, C.S., Berkes, F., and Folke C , 1998. Science, sustainability and resource management. In Linking Social and Ecological Systems. Berkes, F. and Folke, C. (Eds.), Cambridge University Press, Cambridge, U K . pp. 342-362. Jacobs, M . 1991. The Green Economy: Environment, Sustainable Development and the Politics of the Future. Pluto Press, London. Kant, S., 2003. Extending the boundaries of forest economics. Forest Policy and Economics 39-56. Ludwig, D., 2001. The era of management is over. Ecosystems 4: 758-764.  Martell, D.L., Gunn, E.A., and Weintraub, A., 1998. Forest management challenges for operational researchers. European Journal of Operational Research 104: 1-17.  McDill, M.E., 1992. Linking strategic, tactical, and operational forest planning techniques: Opportunities and problems in Minnesota. In Proceedings of the Society of American Foresters National Convention.October 25-27 1992, Richmond, Virginia. The Society, Bethesda, M D . pp. 376-381. 41  Meffe, G.K., Carroll, C.R., and contributors , 1997. Principles of Conservation Biology. Second Edition ed. Sinauer Associates Inc., Sunderland, Massachussetts. Nelson, J.D., 2003. Forest-level models and challenges for their successful application. Canadian Journal of Forest Research 33: 422-429. Oliver, C D . , 1999. The future of the forest management industry: highly mechanized plantations and reserves or a knowledge-intensive integrated approach. Forestry Chronicle 75: 229-245. Porter,M.E. and Martin,R.L. 2000. Canadian Competitiveness: Nine Years after the Crossroads. Paper presented at the CSLS Conference on the Canada- U.S. Manufacturing Productivity Gap, Ottawa. Reed, F.L.C. Is enhanced forestry worth the investment? Getting the analytical framework right. http://www.wsca.ca/Resources/Articles/2000/Les%20Reed.htm. Accessed in 2000.  Schwartz, M.W!, 1999. Choosing an appropriate scale for conservation efforts. Annual Review Ecology and Systematics 30: 83-108.  Shafer, C.L., 2001. Inter-reserve distance. Biological Conservation 100: 215-227.  Sheppard, S.R.J., Picard, P., and D'Eon, R., 2004. Meeting visual quality objectives with operational radial-strip partial cutting in coastal British Columbia: a post-harvest assessment. The Forestry Chronicle 80: 215-223.  Sherry, E.E. and Johnson, C.J., 1999. The forgotten forest: Revisiting the forestland allocation strategy. Forestry Chronicle 75: 919-927. 42  Shindler,B.A., Brunson,M., and Stankey,G.H. 2002. Social acceptability of forest conditions and management practices: a problem analysis. Gen. Tech. Rep. PNW-GTR-537. Stankey, G.H. and Clark, R.N. 1992. Social aspects of new perspectives in forestry: a problem analysis. Grey Towers Press, Milford, PA. Stewart, T.J., Janssen, R., and van Herwijnen, M . , 2004. A genetic algorithm approach to multiobjective land use planning. Computers and Operations Research 31: 2293-2313. Strange, N . , Meilby, H., and Thorsen, B.J., 2002. Optimization of land use in afforestation areas using evolutionary self-organization. Forest Science 48: 543-555. Toffoli, T. and Margolus, N . 1987. Cellular Automata Machines: A New Environment for Modeling. MIT Press, Cambridge, M A . United Nations Conference on Environment and Development (UNCED). 1992. Agenda 21: the Rio Declaration on Environment and Development, Statement of Forest Principles. In: Report of the United Nations Conference on Environment and Development, Rio de Janeiro, 3-14 June 1992. United Nations Commission on Environment and Development Secretariat, Geneva.  Venema, H., Calamai, P., and Fieguth, P., 2005. Forest structure optimization using evolutionary programming and landscape ecology metrics. European Journal of Operations Research 164: 423-439. Voller, J. and Harrison, S. (Editors), 1998. Conservation biology. Principles for forested landscapes. Second Edition ed. U B C Press, Vancouver.  43  Weintraub, A. and Bare, B.B., 1996. New issues in forest land management from an operations research perspective. Interfaces 26: 9-25. Weintraub, A. and Cholaky, A., 1991. A hierarchical approach to forest planning. Forest Science 37: 439-460.  44  3 F O R E S T PLANNING USING CO-EVOLUTIONARY C E L L U L A R AUTOMATA 2  3.1  Overview  The spatial distribution of forest management activities has become increasingly important with, most notably, rising concerns for biodiversity. Addressing both timber production and non-timber goals requires planning tools that support spatially explicit decision-making. The paper examines the capability of a co-evolutionary cellular automata (CA) approach to address forest planning objectives that are both spatial and temporal with global constraints. In this decentralized self-organizing planning framework, each forest stand and its associated management treatment over the planning horizon is represented as a cellular automaton. The landscape management goals are achieved through a co-evolutionary decision process between interdependent stands. A novel, computationally efficient C A algorithm for asynchronous updating of stand states is developed. The specific problem considered in the paper is maximization of cumulative harvest volume and amount of clustered old forest. The global constraints considered are stable harvest flow and minimum amount of old growth in each period of the planning horizon. Applied to a test area from the Northeastern forest region of Ontario, Canada, the model demonstrates short computation time and consistent results from multiple runs. It also compares favorably with outputs from a simulated annealing search. The CA-based algorithm successfully identifies sustainable forest outputs over the planning horizon. It shows sensitivity to both local constraints, strategic goals and strategic constraints and generates spatially explicit forest plans.  A version of this chapter has been accepted for publication pending revisions and has been resubmitted. Mathey, A . - H . , Krcmar, E., Tait, D., Vertinsky, I., and Innes, J. (2006). Forest Ecology and Management 2  45  3.2  Introduction  Sustainable forest management recognizes and seeks to maintain a wide array of ecological as well as economic and social forest functions, both locally and globally (UNCED, 1992). The challenge in forest management planning is to accommodate timber production with other, non-timber goals such as the protection of biodiversity and ecosystem health. To this end, traditional stand-level cost-benefit-type analyses need to be combined with forest or regional-level analyses in order to adequately select among forest management alternatives. As forest management interacts with ecological processes at multiple spatial and temporal scales, combined analyses can be difficult to conduct (Martell et al, 1998; Nelson, 2003). These issues are usually handled through either top-down or bottom-up planning approaches (Shands et al, 1990).  Top-down planning is the most frequent approach to reconcile processes and goals at different spatial and temporal levels. This approach is often associated with centralized procedures that track the global performance of decision combinations to select the best alternative. Centralized top-down procedures have traditionally been favored in strategic planning with an extensive use of large non-spatial mathematical programming models (Martell et al, 1998). However, an increasing number of location-specific concerns (e.g., environmental buffers, proximity to road network, adjacency, size and distribution of reserve patches) have made the inclusion of spatial considerations in planning necessary. For strategic plans to be useful, their spatial implementation must be feasible. Spatial details typically generate a large number of search combinations.  The use of heuristic methods has greatly facilitated solving the resulting computationally 46  difficult planning problems. The most frequently applied heuristics are simulated annealing (Lockwood and Moore, 1993), Monte Carlo search (Clements et al, 1990; Boston and Bettinger, 1999), tabu search (Murray and Church, 1995; Bettinger et al, 1997; Richards and Gunn, 2003), genetic algorithms (Lu and Eriksson, 2000) or combinations of several heuristics (Boston and Bettinger, 2002). Despite the increasing effectiveness of heuristic methods, it remains difficult to formalize spatial objectives such as clustering, connectivity and continuity of set-aside forestland throughout the planning horizon with centralized procedures (Bettinger et al, 2002; Nelson, 2003; Pukkala and Kurttila, 2005). The heuristics used in centralized procedures are based on the evaluation of the global objective values for different management plans. If the global objective value is not satisfactory for a given plan, lower-level decisions are changed until an acceptable objective value is obtained.  Another way of finding a satisfactory management plan is to build information from the lower levels (i.e., individual stands). Such bottom-up planning offers the advantage of directly addressing local spatial goals and constraints. In order to achieve an acceptable level of the global objective, some coordination of lower-level decisions is required. In spatial systems decisions taken at nearby locations can affect each other's contribution to the global objective more than decisions taken at distant locations (Strange et al, 2001; Hoganson and Borges, 1998; Hoganson et al. 1998). This implies that the solution space could be explored in parallel by evaluating local decisions and taking into account their interactions. Given the increasing complexity of forest systems, a decentralized approach based on local-level decisions is a natural way to address strategic forest planning. A decentralized bottom-up framework may address the spatial goals of forest management computationally more efficiently than a centralized framework. Cellular automata (CA) modeling is a decentralized 47  framework capable of representing discrete dynamical systems whose behavior is specified in terms of local relations (Toffoli and Margolus, 1987). This modeling tool has been almost exclusively used for process simulation and for the exploration of complex systems in physics, geography and biology. If C A models are to be used for planning purposes, the incorporation of guiding rules is needed to ensure that not only local (stand-level) objectives, but also global (landscape-level) goals are met. Strange et al. (2001) developed a planning tool centered on a CA-based evolutionary optimization algorithm, which solves spatial problems involving one-time afforestation decisions (Strange et al. 2002). Mathey et al. (2005) extended the work on using C A for planning by designing an evolutionary C A algorithm to address inter-temporal aspects of forest planning in addition to spatial issues. The newly developed co-evolutionary optimization algorithm was applied to solving spatial multi-period planning problems. The current paper addresses global constraints within this decentralized optimization framework and proposes a modification of both the transition rules and updating method that is capable of guiding the decentralized optimization process toward meeting global objectives while also satisfying landscape scale (global) constraints.  This study describes the co-evolutionary algorithm for both an unconstrained and a constrained forest planning problems and compares its performance with a simulated annealing algorithm. The specific forest planning problem considered is the maximization of a weighted combination of the cumulative harvest volume and a measure of the clustering of old forest stands, while keeping stable harvest flow over time and maintaining a minimum amount of old forest stands. Volume maximization and stable harvest flow reflect timberrelated objectives of forest planning. Ecological objectives of forest management are expressed by both maintaining a minimum amount of old forest and at the same time 48  promoting the clustering of old forest stands. Maintaining the clusters of old forest is important for several reasons. First, old forests are most severely impacted by timber management, both through direct degradation and through fragmentation (Harris, 1984). Second, old forests constitute a specific habitat that a number of plant and animal species depend, partially or entirely. Preserving habitat for these species requires continuity of areas of stands of old forests over the planning horizon (Seymour and Hunter 1999; Ohman, 2000). Both forest ecologists and managers acknowledge the importance of conserving clusters of old forests (Spies and Franklin, 1996) even if the question of their location, size and distribution is still contentions (Shafer, 2001; Schwartz, 1999).  The following section describes how cellular automata can be used in forest planning. Section 3 details the co-evolutionary C A algorithm of Mathey et al. (2005) for an unconstrained forest planning problem. Section 4 presents the solution approach to constrained forest planning problems. In Section 5, we illustrate the model and solution approaches to an empirical study using a forest in northeast Ontario. The trade-offs in the model are analyzed in Section 6. Section 7 presents a comparison with a simulated annealing search algorithm and the conclusion follows in Section 8.  3.3 Application  of cellular automata in forest planning  C A models are generally constructed as a collection of cells that form a lattice (Toffoli and Margolus, 1987; Wolfram, 1994). Each cell is characterized as being in a particular state. Transition rules applied to a cell are used to compute the cell's state for the next iteration. The transition rules are a function of the cell's own state and the states of its neighbors. C A 49  models progress by discrete steps (a time interval or iteration) during which transition functions are applied to all or a subset of the lattice's cells. Two properties of C A are particularly relevant to forest planning: scale-integration and selforganization. The integration of processes and objectives from different spatial and temporal scales is a long-standing issue in forest planning: some of the management concerns are local or stand-level (e.g., timber yield, stand structure) while others are tied to the surrounding environment (e.g., landscape patterns, economics and aesthetics). Self-organization in dynamic systems refers to the spontaneous emergence of global coherence out of local interactions (Krugman, 1996). Self-organization is particularly relevant to forests where landscape patterns result from the interactions of natural disturbances, succession dynamics, and human-induced stand management decisions. The ability of C A to develop emergent characteristics enables the modeling of spatial and temporal interactions within the forest landscape, such as gap dynamics (Hubbell and Foster, 1986), fire spread (Green, 1989) and species interactions (Colasanti and Grime, 1993). C A models are also well suited to forest management allocation since any land allocation or management decision reflects the suitability of a local cell for a specific activity and also the suitability of this activity within the neighborhood of the cell.  The details of an algorithm for multi-period forest planning with constraints, which fully employs the self-organizing and scale-integration properties of C A , are presented below. Contextualized in a C A framework, the forest is characterized as a raster system with a set of uniformly sized, square stands. Each stand,/ has an associated stand type and stand age at the beginning of the planning horizon. Each stand also has an associated set of possible treatment schedules. In terms of cellular automata, the forest is the lattice or grid, the stand is  a cell and the treatment schedule for a stand represents the state o f the cell. The standspecific treatment schedules reflect the stand type associated with the raster cell together with the alternative possible schedules for stand harvesting and silvicultural treatment that could meaningfully be applied to that given stand type. For example, the set o f treatment schedules available for a raster cell that was initially a young birch stand would differ from the set o f treatment schedules that would be available for an old growth pine stand.  A cellular automata is an iterative scheme. It begins with an assignment o f initial states to all o f the cells and progresses by updating cell states according to a state transition function. In our model, an assignment o f states to stands represents a forest plan for the entire planning horizon. A forest plan, over a given planning horizon, therefore consists o f the schedule o f management treatments prescribed for each o f the forest stands.  Formally, a plan is  />: = {*,(/):  feF],  where  Pi is the forest plan for the z'th iteration. The plan is represented as the set o f treatment schedules with one schedule per stand.  s,{j) is the treatment schedule i n the f fh iteration that is associated with stand /  Treatment  schedules range from a state that represents 'no treatment' with no actions scheduled for the length o f the planning horizon through to specific schedules involving multiple harvests and silivicultural regimes applied over the planning horizon.  51  F is the forest represented as the set of stands. Each stand,/, has an associated location, set of neighbors, and initial conditions (initial stand type and stand age). In the above formalism, / a n d s are both indexing systems./is an index into the set of all stands and s is an implicit index into the set of all possible treatment schedules. A state transition function determines a new (possibly the same) treatment schedule for a stand as a function of the current stand state and its neighbors' states. The transition function cp is applied to each stand / and its neighborhood to generate the new stand state5, (/) = <?(£,.(/)), where +1  s  M  (/)  is the state of stand/in iteration z'+l  q>(-)  is the state transition function  S (/)  is a vector representing the states, in iteration /, of stand / and its neighbors.  t  The state transition function in our algorithm chooses the stand schedule that maximizes an objective function. The last element of a C A model is the updating method that defines, for each iteration  the  set of stands to which the transition function is applied. The forest plan evolves iteratively by generating new schedules (states) and applying the state transition function to individual stands as determined by the updating scheme. The forest plan P, from iteration i changes into a new plan P  M  = {s ( / ) : / e F} in iteration M  i+\. The evolution of the plan will depend on both the transition rules and updating method formulations while the process duration is determined by stopping rules. 52  3.4 Unconstrained  forest-planning  We begin by formulating an unconstrained multi-period forest planning problem and the coevolutionary optimization method developed to solve it. This algorithm was sketched in Mathey et al. (2005). This is the first detailed description and rationale presented for this algorithm. In section 4 we extend the algorithm to apply to a constrained multi-period forestplanning problem.  3.4.1  Model formulation  In this model, the state transition function evaluates all the treatment schedules for a stand and chooses the stand's next state to be the treatment schedule that generates the highest value. This evaluation is a function of the individual stand and reflects both the stand type and the initial stand inventory. The evaluation of each treatment schedule is separated into two components.  The first component represents context independent values. In general, this contextindependent component is a site-specific evaluation that generates a value. This value can depend on a rich set of stand-specific criteria that will include factors that depend on the site type and stand location. In our model we have identified these as being proportional to the total harvest for the treatment schedule over the planning horizon.  The second component represents context-dependent values. In general, we model this as site-specific values that can be modified or augmented as a function of the states of their neighboring cells. In our forest model, the context-dependent values are determined by the presence of old growth in the stand over the planning horizon. The value of old growth is enhanced i f the old growth in the stand's treatment schedule occurs at the same time as old 53  growth is scheduled to occur in neighboring stands. The context-dependent and contextindependent values are both normalized relative to each stand's potential  Formally we have  /«/")) = — —  Equation 1  where I(s(f)) is the context-independent value associated with treatment schedule s(f) for stand/ Although I(s(f)) could take into consideration factors such as cost and represent a net present value, in our model we only considered the total volume harvested over the planning horizon. In what follows, the context independent value is referred to as the harvest value. HV (s(f)) is the harvest volume in period / generated by treatment schedule s(f). HV/is a t  scaling factor that ensures that / ranges between 0 and 1. As a scaling factor, HV/is the maximum possible total harvest that could be generated by a stand type similar to that off over the planning horizon.  The harvest value for a treatment schedule is thus an index that ranges between 0 and 1. A harvest value of 0 corresponds to a treatment schedule that had no harvesting and a harvest value of 1 corresponds to a treatment schedule that achieved the maximum possible total harvest volume for all stands of that type over the planning horizon.  J,]OG { {f))+pxOGN {f)\ t  D(s(f))=-+  S  l  —  Equation 2  where, D(s(f)) is the context-dependent value associated with treatment schedule s(f). In this case D(s(f)) considers the stand's potential for providing old growth values further enhanced  by the proportion of the stand's neighbors that are simultaneously scheduled to be retaining old growth. Below, the context-dependent value is referred to as the old growth (OG) value.  OG (s(f)) is either 1 or 0 and indicates whether the stand/is old growth or not in planning t  period t under treatment schedule s(f). Old growth, in this context, represents a stand that is over some stand-specific age. The actual age varies for different stand types and species associations.  OGN (f) is a factor between 0 and 1 that is equal to the proportion of stand fs neighbors that t  are also old growth at planning period t. p is a scaling factor that can be used to modify the degree to which old growth neighbors influence the old growth value of a stand, p x OGN (f) t  represents the enhancement of the stand's old growth value that is due to the simultaneous existence of neighboring old growth stands. In our model we set p to be 1. The stand's neighborhood consists of the eight adjacent stands in the raster grid. If the stand is on an edge we only use the five adjacent stands. Corner neighbors consist of the three adjacent stands.  OG/is a scaling factor that ensures that D ranges between 0 and 1. OG/is the maximum possible enhanced old growth value that could be generated by a stand of type/over the planning horizon. The maximum possible enhanced old growth value would be generated by a stand that was old growth in each planning period and i f all of its neighbors were also old growth in each period. Numerically, OG/, is just twice the number of planning periods.  The old growth value is thus an index that ranges between 0 and 1. A schedule that would not result in a stand ever reaching old growth during the planning horizon would have a value of 0. A schedule that would result in a stand being old growth for the entire course of the planning horizon would have a minimum old growth value of 0.5. This value would reflect a 55  stand persisting as old growth over the planning horizon without any of its neighbors ever moving into old growth themselves. A stand would only achieve its full old growth potential if it retained old growth for the entire planning horizon and all of its neighbors also retained old growth for the entire planning horizon.  The value of a treatment, z(s(f)),  is calculated as a weighted average of the above two  components:  z(s(f)) = Axl(s(f))  + (1-/L)xD{s(f))  Equation 3  where X is a weighting factor that is between 0 and 1. X represents the importance attached to old growth values relative to timber production. Also, X reflects policy and is a weighting factor that influences the behavior of the algorithm. Values of X that are close to 1 will generate solutions that reflect context independent values, while values of X that are close to 0 will favor solutions that reflect context-dependent values.  For this application, the state transition function is defined as selecting the treatment schedule Si+i(f) that maximizes the stand value in equation 3:  (/) = ?($,(/))  / . = maxz(s,.(/))  c  .  Equation 4  The last element of a C A model is the iterative scheme. The iterative scheme clarifies the order that the cells in the automata - the stands in our model, are to be updated. Deterministic synchronous updating (Wolfram, 1994) is the most frequently used iterative scheme. Following this updating method, the transition rules are applied simultaneously to all cells at each iteration. Synchronous updating often leads to oscillatory behavior. A cell changes its 56  state in response to the current states of its neighboring cells. However, its neighboring cells have also, synchronously, changed their states. The new state selected by the state transition function is no longer optimum. In the next iteration, the cell changes its state back to the state that it had in the previous iteration. The algorithm gets stuck with cells flipping back and forth in response to the oscillations of their neighbors. The iterative algorithm, using deterministic synchronous updating, used for optimization purposes, is unlikely to find a good global solution when applied to planning problems.  3.4.2 Co-evolutionary optimization: from local decisions to coordinated management The state transition function formulated in the previous section searches for the schedule that maximizes the stand's value. Such local (stand-scale) optimization represents a heuristic in that it does not guarantee optimality at the landscape level. The C A literature has suggested a number of methods to relate local, cell level decision making to the global or higher-level management goals. One option imposes constraints on the stand self-organizing behavior, so that not all transitions are available to each cell (Ward et al, 1999). Another method consists in coupling C A with an optimization methodology (Garriga and Ratick, 1996): before running the C A simulation, the number of stands that will make a state transition is determined using outcomes of the optimal land allocation problem. Finally, an approach, pursued further in this study consists of manipulating the updating procedure to meet the landscape objective (Strange et al, 2001; 2002).  57  Asynchronous updating is an alternative to synchronous updating where the transition rule is applied to only one randomly chosen cell for each iteration of the algorithm. These updating schemes represent two extremes of the numerous updating schemes that can be employed. Intermediate schemes, between these two alternatives, would select, either systematically or randomly, a subset of cells to update. A l l of the iterative schemes involve various degrees of asynchronous updating. Depending on its design, the asynchronous updating will allow a stand's state to influence that stand's neighbors and, in turn, the changes in the environment (neighborhood) can influence further changes in the stand. Lewontin (1961) refers to these co-evolving changes as co-evolution. Although no updating procedure can guarantee landscape-wide optimality of the forest plan, some updating schemes may increase the likelihood of co-evolving good global solutions.  Strange et al. (2001) added randomness by using a probabilistic synchronous updating scheme. In this scheme, each stand, in each iteration, has a probability p of being updated. As a result, on average, only a proportion p of the stands will be updated. The updating of this subset of the stands is done synchronously. And finally, the probability p, of any stand being updated, decreases with each iteration. This results in fewer and fewer stands being updated with each iteration. This updating strategy has proved numerically efficient (Strange et al. 2002).  A similar approach developed in the parallel field of game theory, randomly selects a subset of players (cells), but then imposes a random order on the subset and allows the individual players to asynchronously select their moves (state transitions) (Dieckmann et al, 2000). This asynchronous updating would provide more opportunities for stand interactions and coevolution towards a global objective. 58  Following this idea, we developed an algorithm which introduces a random, asynchronous updating scheme into a C A algorithm for solving multi-period forest planning problems (Mathey et al, 2005). At the beginning of each iteration, all of the stands are randomly ordered. Stands are updated, one at a time, following this random order. A n iteration finishes when an updated stand has changed its state. Only one stand is changed per iteration. This process allows other stands in the neighborhood to experience a change and to react to it. After a stand has been updated, its neighborhood or environment is prone to potential changes. If the stand is not updated, the next stand in the order is considered for update. At the onset of the iterative process, an improvement on the value of the stands initial random state is likely to occur and most of the stands selected would change their current states. However, after a number of iterations, fewer and fewer stands would change their state since an improvement of the stand value (i.e., a higher value) would become less likely. This would only be in response to changes in the states of their neighbors. The algorithm continues until either a maximum number of iterations has been reached or no change occurs within a single iteration.  3.5 Constrained forest planning In this section, we consider the means of satisfying global constraints together with meeting landscape-wide objective(s). We expand the co-evolutionary optimization algorithm (Mathey et al 2005) to handle multi-period planning problems with constraints.  As an illustration, we have added global harvest flow constraints together with a global minimum level of required old growth in each period t. These requirements are formulated in 59  the form of landscape-wide constraints:  v l < v , ( P ) < v _ and og,(P)>og' , mm  Here, v^ and v' in  t = l,2,...,T.  denote the respective minimum and maximum harvest volume (m ) in 3  mm  period t and og' denotes the minimum amount (number of stands) of old growth in period min  /. The values v' , v^ and og' are constants reflecting policy. The values v (P) and nill  ax  min  t  og (P) represent the actual harvest volume and amount of old growth generated in period t t  under forest plan P . Optimizing the stand objective function does not always lead to an improvement of the landscape-level objective function and, especially, does not guarantee satisfying the landscape constraints. Penalty functions are a common means to guide centralized optimization procedures towards fulfilling constraints. However, in the context of a decentralized framework we need to define "penalty functions" that are efficient surrogates for the global (landscape) constraints within the local (stand) optimization process.  We incorporate violations of global level constraints as penalties or incentives that influence cell level choices. Let a p,, and y, measure the degree to which each of the constraints is h  violated in each of the harvest periods. In our model we have defined a,, (3,, and y to be: t  60  ifv,  > ; v  max max otherwise,  A=i  /og,{P) 0  xfog {P)<og[ t  m  otherwise.  These measures are used as penalty rates, in the case of (3,, and incentive rates, in the cases of a, and y to modify the stand level objective functions. These rates will encourage or t  discourage local level decisions that would contribute to a continuing violation of the global constraints. Equation (3), the sum of the context-independent and context dependent values associated with a stand's treatment schedule, becomes:  T  HV,  + (l-A'+fl)x  OGMf))+PxOGNjj) OG  Equation 5 The incentive and penalty rates augment the value of a treatment schedule in proportion to the amount that the schedule decreases a constraint violation. The modified equation (5) is used for the evaluation of the stand value and thus modifies the initial transition function (Equation 3). The inclusion of the incentive/penalty parameters can be seen to be equivalent to establishing period dependent values X in equation 2 and 3. From this perspective, a specific set of values for a,, p,, and y can be considered to represent a t  global policy choice and represent a new expression of the relative values of harvested timber versus old growth and old growth clusters. For any given policy as represented by a,, p,, or y  h  61  the C A , as an iterative scheme, co-evolves a plan. Although the cells make local level decisions, their decisions influence their neighbors' decisions and in turn their neighbors' neighbors. The C A requires a number of iterations to co-evolve a configuration of treatment schedules that represent an effective global solution for any given policy choice. If penalty parameters change too often, stands do not have the opportunity to co-evolve a forest plan. This may potentially generate a forest plan far from the globally optimal plan. On the other hand, if penalty parameters change rarely, it is hard to find a feasible solution.  In recognition of this behavior, we further modify the constrained C A algorithm with an ad hoc iterative scheme that periodically recalculates the incentive/penalty rates. The intent is to freeze the policy environment and allow the algorithm to adjust to the set of penalties and incentives by running through a number of iterations. We group the iterations into successive blocks. Within a block of iterations, we can set the frequency at which we will recalculate our incentive and penalty parameters. In our implementation, we can adjust both the size of each block and the frequency of recalculation within each block.  As an example, one block of iterations could be from iteration number 2000 to 4000. Within this block we would recalculate our measures of the constraint violations every 400 iterations. The frequency of recalculation would increase with successive blocks until, eventually, the expression of constraints a,, P,, and y, would be recalculated at every iteration.  The flowchart for the algorithm is presented in Figure 3-1. Note that this algorithm can also be used for solving unconstrained planning problems as its special case.  62  ( START  ^  Input forest L Initial Forest Plan P  0  Penalty parameters a, =0, /?, = 0, -/. = 0 Iteration blocks  k e K = {(hJ'iUJi.Jil-Un-i.Jn])  and frequencies S of recalculation of penalty parameters k  Iteration M  Block k=0  -Yes-  S2  s  Re-calculate penalty parameters  i  •Yes-  CO  a. = d' ,P, = PI,"i = y\ jk  t  : Q.  ^; to C  „  Generate a random-order list G' of cells from L Select first stand g in order G'  Evaluate g's candidate states Next stand Sf=Sf 1 +  M+1  New Plan  P=P»y  Yes  F i g u r e 3 - 1 A flowchart of the c o - e v o l u t i o n a r y algorithm for a c o n s t r a i n e d planning p r o b l e m .  63  3.6 Problem  instance  The forest planning framework described above has been applied to a test area from a forest located in the Northeastern forest region of Ontario, Canada. In this boreal region, the main forest type is dominated by black spruce (Picea mariana), but other distinct forest types and associations include poplar (Populus spp.), balsam fir (Abies balsamea), white birch (Betula papyrifera) and jack pine (Pinus banksiana), depending on the site. The test area is represented by a 18x27 grid of square stands where each stand is 9 ha with a total of 486 stands. The small size of the problem presented here allowed the generation of numerous outputs in a relatively short time and further allowed a comparison with other algorithms which would have been difficult with large-size problems. The resolution used in C A models and how it is adapted to the landscape greatly influence the results (Menard and Marceau, 2005). However, Chen and Mynett (2003) found that the bias introduced by cell size in the final outputs was only problematic if the cell size was not relevant to the scale of decision variables. The 9 ha stand size was therefore selected because it is a functional size for representing silviculture operations in the study area since stands smaller than 10 ha typically get amalgamated to surrounding stands under the current inventory system of the area.  The unconstrained problem consists of generating a forest plan that maximizes the cumulative harvest volume while preserving continuous areas of OG forest over a 100-year planning horizon divided into 10-year periods. In the constrained problem, a stable harvest flow and a minimum amount of old growth over time are also required. The forest plan consists of management treatments (states) assigned to all stands that make up the forest.  64  Each stand has an associated forest type and an initial age. Harvested stands can be treated with any one of four silvicultural regimes: no-management, extensive, basic, and intensive. The details and consequences associated with these different silvicultural regimes are a function of the stand type and the initial age that is associated with the stand. For each stand, the alternative treatment schedules consist of all possible feasible harvest periods in combination with silvicultural regimes. Feasibility, in this case, reflects the harvest operability of the stand, which is a function of the stands type, initial age class and the applied silvilcultural regimes. A stand's state corresponds to any one of the alternative possible combinations of harvest/silvicultural regime schedules. An initial forest plan is created by randomly assigning feasible states s e S to stands / e F .  The model is built upon the Arc/Info GIS software platform with a number of programs coded in Arc Macro Language ( A M L ) and C++. The initial grid was populated with a forest inventory derived from corporate Natural Resource Values Information System (NRVIS) and Forest Resource Inventory (FRI) maps standardized by the Ontario Ministry of Natural Resources. The forest inventory was rasterized to 300m x 300m cells. For each raster dataset, the value assigned to one 9 ha-cell was generated by assigning it the value of the feature that fills the majority of the cell area (majority weighing method).  3.6.1 Analysis of results for the unconstrained forest planning In this section, we present the outcomes of the unconstrained problem obtained with the weight X = 0.4 associated to the harvest volume. In order to assess the quantitative stability of the solution provided by the algorithm, the process was repeated 250 times, each time with 65  a new randomly generated initial plan. Figure 3-2a-c present how the normalized stand volume, equation (1), the normalized old growth value, equation (2), and the combined treatment schedule value, equation (3), progress with iteration of the algorithm. The results are given for the whole forest as the normalized aggregation of all stands. The harvest volume index rises until about iteration 1300, and then gradually decreases before converging to the volume generated by the final forest plan (Figure 3-2a). The O G index value increases throughout the entire iterative process (Figure 3-2b), but its rate of change becomes much slower after iteration 1300. The average stand value follows a pattern similar to the O G index curve (Figure 3-2c). The variation in both the harvest volume and the O G index values diminishes towards the end of the iterative process. The lower variation in the average stand value compared to either the volume index or the O G index, over all iterations, reflects the expected covariance between average harvest volume and average O G index.  66  0.50 -i CD  E  o  0.48 0.46 -  .1  0.44 -  E  0.40 -  O  0.38 -  TO 0.42 -  T3  CU N  15 E o z  0.36 0.34 0.32 0.30 1000  2000 3000 Iterations  4000  5000  CD  -o c 5 o  O) I  o cu N  ro E o  2000 3000 Iterations  5000  c •  o a  3 H—  ,l-.—' o  CD  S"  O  T3  CU  c  !d  E o o •o  cu N  TO  E  1000  2000 3000 Iterations  4000  5000  Figure 3-2 Progression of (a) the stand harvest volume index, (b) the stand OG index, and (c) the stand value index through iterations for the unconstrained problem. Box plots are produced every 300 iterations and summarize the results of 250 runs. Each box represents the median, 25th and 75th percentiles with the 10th and 90th percentiles as vertical lines. Dots represent the outliers. 67  The number of iterations required for the algorithm to reach the highest possible average stand value was found to be around 2000 iterations. Beyond 2000 iterations, no noticeable improvement of the average stand value was apparent (Figure 3-2c). In the initial iterations, the rapid improvement of the average stand value is the result of increases in both cumulative harvest volume and O G index values. Despite the lower weight (X - 0.4) placed on harvest volume, the volume rises until approximately iteration 1300. This behavior results from the initial random assignment of treatments to the stands. Stands with states that favor O G conditions ('no-management' regime or regimes with no scheduled harvest) are in the minority; they are also scattered. The rare and scattered stands in O G conditions have a weak influence on their neighbors and contribute less to the global objective value. This has the implication that state transitions that increase harvest volume are initially favored. Once a certain amount of O G is built up in each planning period, the impact of grouping strengthens and it becomes increasingly worthwhile to choose a forest plan that preserves neighboring O G compared to generating volume.  3.6.2 A n a l y s i s o f r e s u l t s for t h e c o n s t r a i n e d f o r e s t p l a n n i n g In this section, we present the model outcomes with constraints imposed on both the harvest flow and the amount of O G over time. The stable flow constraints require that the total harvest volume in each period be between 12 000 m and 15 000 m . The O G constraint is defined as maintaining at least 41 stands (about 10% of the forested area) in O G conditions at 68  all times. The problem is also solved 250 times with X = 0.4, for comparison with the unconstrained case above. The iterative process is run for 10 000 iterations. Incentives and penalties are periodically recalculated as described in Table 3-1.  Table 3-1 Incentive and penalty recalculation frequencies.  Iteration count at beginning of the block 1 2000 4000 6000 9000-  Number of iterations between recalculations of incentives and penalties within the block Initial 'burn in' period. Incentives and penalties are fixed at 0 with no recalculation 400 200 100 1  The total harvest volume, Figure 3-3 a, and the total amount of old growth, Figure 3-3b, in the forest, in the first decade, are used to reveal the behavior of the algorithm. Comparable behavior is generated in the other decades.  69  200 175 150 125 100 75 50 25 i  0 0  2000  .V. v v. £  4- T  4000 6000 Iterations  +  8000  TE-  10000  250  co  200  S  5 i i .  0  2000  L • 4000  USfi  1  1  •  6000  •  •  8000  10000  Iterations  Figure 3 - 3 Progression through iterations of (a) the volume harvested, and (b) the amount of O G stands in the planning period 1. T h e lines represent the constraint levels. Box plots are produced every 4 0 0 iterations over 2 5 0 runs. E a c h box represents the m e d i a n , 25th and 75th percentiles with the 10th and 90th percentiles a s vertical lines. Dots represent the outliers.  70  By the end of the first block of iterations the volume harvested in the first decade has reached 180 000 m . No incentives or penalties were applied during this set of iterations. The plan 3  generated at the end of the first block is the same as that described by Figure 3-2 for the unconstrained problem. There is a mix of schedules that produce harvests and provide old growth values. The large volume harvested in the first period, Figure 3a, exceeds the maximum flow constraint. This excessive volume generates a large penalty Pi that will penalize stand decisions that harvest in the first period. On the other hand, at the end of the first block of iterations, the O G constraint is satisfied. The associated incentive parameter, yi, will continue to be equal to zero. There are similar penalties and incentives associated with the other harvest periods. The large penalty parameters attached to the harvest volumes will initially dominate the other values in the stand level objective functions. In this situation the optimum stand level decisions will generally be 'no treatment'. With the introduction of the penalty parameter Pi, a significant drop in harvest volume occurs over the next block of iterations (Figure 3-3a). After 400 further iterations, the incentive/penalty rates are recalculated. Not all of the stands will have been 'updated' from their unconstrained solution. Some decades in the plan will have inadequate harvest volumes. Other decades may still have an excess harvest. The actual set of values for the incentive/penalty rates will depend on the initial inventory and the random order in which stands were selected for updating. The wide range of possibilities leads to a wide variation in first period harvest volume and an even wider variation in the number of first period old growth stands in the plan (Figure 3-3 ab).  The stands continue to self-organize in the new environment provided by the inclusion of incentive and penalty parameters while variations in both the period harvest and O G amount 71  decrease. By recalculating of the penalty parameters and stand self-organizing throughout the iterative process, both the volume and O G targets are progressively met across planning horizon and the output variations are reduced (Figure 3-3a-b). The distributions of the stand volume index, old growth index and combined stand value for the constrained case as a function of iteration are presented in Figure 3-4a-c. Throughout the first 2000 iterations, the algorithm has not included the constraints and the results are identical to those shown in Figure 3-2. Before the first introduction of the penalty parameters, the harvest volumes do not satisfy the flow constraints for most of the planning periods. They are either below the lower target or above the upper target. On the other hand, the weight 1-A, associated with O G is sufficient to satisfy the old growth target in most periods. As in the period 1 discussed above, most of the penalty parameters y' associated with O G are therefore set to zero whereas those attached to the period volume (a and p\) are t  high. The latter penalty parameters strongly influence the performance of the algorithm towards fulfilling volume constraints to the detriment of the O G value. This would explain why, over the next block of iterations (iteration 2000 to 4000) with recalculation of the incentive and penalty rates every 400 iterations, both the average harvest value index and O G index drop below their best levels achieved in the first 2000 iterations.  72  E _2  o> CO >  ro E CO N  15 E  2000  4000 6000 Iteration  8000  10000  2000  4000 6000 Iterations  8000  10000  2000  4000 6000 Iteration  8000  10000  x  CO  T3  tz  o 1  o •o  CO N  75 E  Figure 3-4 Progression of (a) the harvest value index, (b) the O G index and (c) the stand combined objective value through iterations w h e n constraints are applied. Box plots are produced every 4 0 0 iterations over 2 5 0 runs. E a c h box represents the median, 25th a n d 75th percentiles with the 10th and 90th percentiles a s vertical lines. Dots represent the outliers.  73  The stand's harvest value index decreases as the iterative process progresses toward full satisfaction of the harvest flow constraints (Figure 3-4a). The decrease in harvest due to the maximum flow constraint leads to the preservation of more OG. The average stand's O G index value rises well above its value in the unconstrained case (compare Figure 3-2b to Figure 3-lb). The introduction of the constraints generates a large reduction in the average stand value. There is a slow partial recovery as the algorithm sorts through the alternative plans. As expected, the constrained problem converges to a solution that is lower than the unconstrained plan (Figure 3-4c versus Figure 3-2c).  3.7 Analysis of tradeoffs between harvest volume and old forest preservation The approximate boundary on the set of feasible combinations of average harvest volume index and average old growth index is identified and analyzed. This boundary, also known as the production possibility frontier, illustrates the tradeoffs between these two outputs for an efficient forest plan. The boundary shows how much the average stands harvest value must be reduced to increase the average old growth index by some amount and vice versa.  Among several ways to construct the production possibility frontier, we opted to run the model that maximizes the plans value, derived from equation (3), for different values of A,, the relative weight associated with the harvest value as opposed to the old growth value. Results of running both the constrained and unconstrained algorithms for different weights attached to harvest volume are presented in Figure 3-5. Figure 3-5 displays the total old 74  growth index summed over all o f the stands against the total harvest volume for the optimum plan for a range o f 11 values o f X between 0 and 1.  350  '  *  A  A  x <D  -O C  + +  300  *** *  JZ  A  •  250 O CD  o  A A  150  (a)  i  100  300  200  400  500  600  Cumulative volume (1000 m ) 310  +  CD 300 "O  + +  sz 290 CD i  +  +  +  280  +  "D  O  270  +++  (b)  260 120  130  140  150  160  Cumulative volume (1000m ) Figure 3 - 5 Tradeoffs between cumulative harvest volume and O G index, (a) Unconstrained ( A ) and constrained (+) co-evolutionary optimization tradeoffs; (b) c l o s e - u p of constrained (+) c o evolutionary optimization tradeoffs.  Figure 3-5 a shows the tradeoffs between the two forest outputs - harvest volume and remaining O G . The curve for the unconstrained outputs is concave to the origin. In the case  75  when the weight associated to harvest volume is 1 (e.g., the weight with O G preservation is 0), the maximum cumulative harvest is 628 000 m and the O G index approximates 138. This 3  relatively high O G index is caused by a number of non-harvestable adjacent stands included in the study area. These stands do not have timber value but they still contribute to the forest ecological values generally and to the O G index specifically as they grow older. Also, stands that can not be harvested twice in the planning horizon can be retained as old growth until the last period without a significant loss in harvest volume. When the weight associated with volume is 0, there is no harvest and the O G index approximates 357. At each extreme, the model is less sensitive to changes in the weight combination. However, for values of X between 0.3 and 0.5, the model appears to be very sensitive to small changes. Again, one can generate old growth values with little loss of stand volume and vice versa for a subset of stands. Such stands will give the typical pattern that is observed at the two ends of the possibility curves. It is possible that, with weights strongly favoring one objective against the other, the spatial arrangement of cells is secondary to the organization of the final solution. With more balanced weight combinations, the spatial arrangement of cells could become more important in guiding the solution. These quantitative results are specific to the study area under consideration: the initial abundance of old forest and a priori exclusion of some areas from harvesting make it possible to satisfy provincial forest regulations and still gain significant harvest volume. To determine whether the shape of the production possibility frontier reflects the influence of spatial organization of the co-evolutionary process or original condition of the forest, more analyses would be required. Other study areas may depict tradeoff curves of different shapes.  When constraints are added to the model, they appear to bound the production possibilities to 76  3  3  a roughly piece-wise linear envelope between 120 000 m and 150 000 m (Figure 3-5). It is conceivable that, in the first section of this curve, stands are experiencing the low flow constraint in response to lower values of X that favor old growth. In the upper part of the curve, the stands reach the upper flow constraint and, given the high values of X, minor violations in favor of harvest volume are tolerated. In the flat, intermediate portion of the curve, the flow constraints are satisfied and the systems 'jumps' from the lower boundary on volume to the upper boundary on volume. Exceedance of the 150 000 m total harvest occurs 3  as a result of small violations of each periods maximum flow constraint that would be associated with the relatively low penalties compared to the relatively high X. The small deviations from a linear tradeoff are artifacts of the heuristic algorithm and the discrete nature of the problem formulation (10 year periods).  3.8 Computational analysis and a comparison with Simulated Annealing To evaluate the computational efficiency of the co-evolutionary optimization, the constrained planning algorithm presented in the previous section is solved by simulated annealing. Simulated annealing is a random search technique whose objective is to converge to a steady optimal solution. Simulated annealing is commonly used in solving forest planning problems and has been showed to yield satisfactory results (e.g., Lockwood and Moore 1993; Boston and Bettinger 1999; Bettinger et al. 2002). For comparison with our C A algorithm, we run a simulated annealing with the same parameters as described by Strange et al. (2002).  For each algorithm, the solution process was repeated 250 times, using different initial forest  77  plans. Once the simulated annealing algorithm reached a feasible solution for the constrained problem, which took on average 15510 iterations, we restricted the number of iterations to 5000. The total number of iterations for the co-evolutionary optimization algorithm was 10000, starting from the initial unfeasible forest plan. The results of the simulations are presented in Table 3-2.  78  Table 3-2 Combined objective values and computation time characterizing two constrained optimization heuristics. Method  No. of runs  Min objective value  Max objective value  Average objective value (standard deviation)  Average no. of iterations to feasible solution  Simulated Annealing  250  0.37131  0.38594  0.37937 (0.00231)  15510  Coevolutionary optimization  250  0.39394  0.40546  0.39775 (0.00236)  No. of iterations after feasible solution is reached 5,000  Total no. of iterations  Average computation time (minutes)  8.5  10,000  7.1  The comparison between simulated annealing and co-evolutionary optimization algorithm presented in this paper indicates that the CA-based algorithm potentially performs better and faster than the widely used simulated annealing. The computation time is a function of the implementation framework and therefore may not reflect any significant improvement of the co-evolutionary C A algorithm. However, it is interesting to note its better performance. The improvement likely arises from the differences in how each algorithm treats constraints: the C A algorithm treats global requirements for volume and old growth as soft constraints and allows small deviations from the targets. In its formulation, the simulated annealing algorithm does not allow constraint violation, which may lessen its overall objective function value.  3.9  Conclusion  The CA-based algorithm developed in this paper successfully estimates some forest values and their long-term sustainability and appears adequate as a tool for long-term forest 79  planning. It also demonstrates sensitivity to both local conditions and constraints as well as to strategic goals and constraints. The outputs compare well to those of simulated annealing, a more standard search technique used in forest management planning. Also, the approach proposed in this study makes the landscape an integral part of the decision making process, ensures feasibility and generates outputs that meet objectives at different scales (local, focal, global). The spatial evolutionary game aspect of the solution algorithm allows the development of landscape strategies that are consistent with both the stand management objectives and landscape goals. The co-evolutionary approach offers an integrated perspective on management by addressing trade-offs that occur across multiple temporal and spatial scales. It can address aspatial as well as spatial objectives across multiple time periods. This spatial aspect of the solving process is particularly interesting since the algorithm can solve not only for locational issues but also for clustering issues. These capabilities offers much potential for further research with a decentralized CA-based planning approach, which includes incorporation of other values and constraints such as net present value of the forest management plan and blocking of forestry operations to achieve economies of scale.  80  3.10  References  Bettinger, P., Graetz, D., Boston, K., Sessions, J., Chung, W., 2002. Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems. Silva Fennica. 36:561-584. Bettinger, P., Sessions, J., Boston, K., 1997. Using Tabu search to schedule timber harvests subject to spatial wildlife goals for big game. Ecological Modelling 94:111-123. Boston, K., Bettinger, P., 1999. A n analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems. Forest Science 45,292-301. Boston, K., Bettinger, P., 2002. 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(Eds.), Biodiversity in managed landscapes: Theory and practice. Oxford University Press, New York, N Y , pp. 296-314. Steuer, R., 1986. Multiple Criteria Optimization, Theory, Computation and Application, John Wiley & Son, Inc.  84  Strange, N . , Meilby, H., Bogetoft, P., 2001. Land use optimization using self-organising algorithms. Natural Resource Modeling 14, 541-574. Strange, N . , Meilby, H., Thorsen, B.J., 2002. Optimization of land use in afforestation areas using evolutionary self-organization. Forest Science 48, 543-555. Toffoli, T., Margolus, N . , 1987. Cellular Automata Machines: A New Environment for Modeling. MIT Press, Cambridge, M A . U N C E D (United Nations Conference on Environment and Development), 1992. Agenda 21: the Rio Declaration on Environment and Development, the Statement of Forest Principles, the United Nations Framework Convention on Climate Change and the United Nations Convention on Biological Diversity. U N C E D , Rio de Janeiro,3-14 June 1992. United Nations Commission on Environment and Development Secretariat, Geneva. Ward, D.P., Murray, A.T., Phinn, S.R., 1999. A n Optimized Cellular Automata Approach for Sustainable Urban Development in Rapidly Urbanizing Regions. In: IV International Conference on GeoComputation, Fredericksburg, V A , U S A , 25-28 July 1999.  Wolfram, S., 1994. Cellular Automata and Complexity: Collected Papers. Addison-Wesley, New York.  85  4  O B J E C T - B A S E D C E L L U L A R AUTOMATA MODEL FOR F O R E S T PLANNING P R O B L E M S 3  4.1  Overview  Various difficulties are encountered when integrating spatial and temporal goals of forest planning with dynamics of natural processes. Some of these difficulties stem from different data involved in the various processes and models to be integrated. The focus of this study is the development of a spatial decision support tool for forest management planning. The implementation of an object-based cellular automata (CA) model in a geographic information system (GIS) as a decentralized bottom-up forest planning approach is presented. Moreover, a sensitivity analysis of model parameters is performed. This planning tool effectively addresses both local spatial constraints (limitation on the type of management depending on location) and global spatial objectives (spatial clustering of old growth conservation areas) along with timber objectives and even flow constraints. The capability of this approach to consider spatial relationships in the strategic planning process is illustrated by a spatially consistent allocation of clustered old growth areas. The object orientation of the implementation permits a fast computation of both local and global limitations on local decision making. The object-orientation of the implementation allows speedy modification of either local or global requirements and is highly portable to other complex planning problem.  A version of this chapter has been submitted for publication. Mathey, A . - H . , Krcmar, E., Dragicevic, S., Vertinsky, I. (2006). Ecological Modeling 3  86  4.2  Introduction  Under the sustainable forest management (SFM) paradigm, management decisions are no longer solely guided by the amount of timber generated; decisions are also made on the basis of potential impacts on other forest values, at both stand and landscape levels (e.g. IUFRO (Innes et al. 2006); U N C E D , 1992). Previously, the decision process traditionally focused on the timing of management activities (i.e. scheduling). However, the rising social, environmental and economic concerns in the last thirty years have resulted in an increased interest in the location of management activities. This interest has required developing and applying support tools able to deal with computationally demanding spatially explicit forest planning. Heuristic-based solution approaches have been developed to counteract the computational difficulties (Nelson, 2003). The ever more advanced methods to deal with spatial forest planning have however left a number of challenging issues. Among first is the inclusion of additional spatial goals in already large combinatorial problems poses computational challenges. Spatial goals particularly difficult to address include the size and shape of reserve areas, wildlife corridors or stream buffers (Ohman and Lamas, 2005; Stewart et al, 2004; Ohman, 2000). The second issue is related to the requirements for addressing spatial goals over time. Maintaining old growth in locations adjacent to previous old growth areas or green-up constraints and adjacency constraints are examples of such goals (Nalle et al, 2004). Finally, there is a need to consider dynamics of the forest spatial structure. The natural evolution of the forest's spatial structure over time changes the degree to which the forest can accommodate demands and provide services (Gustafson, 1996). The evolution of spatial structure due to fire, natural  87  succession or insect outbreaks should also be accounted for in forest planning tools (Baskent and Keles, 2005). There exist a number of decision support tools that address specific aspects of forest management. For instance, the field of conservation biology has produced several models that address the location, size, and shape of reserves and corridors (Williams et al, 2005). Also, ecologists have developed a number of models to capture the dynamic aspects of natural processes such fires, succession and stand dynamics, gap dynamics at different scales (Perry and Enright, 2006; Ito, 2005; Malamud et al, 1998; Manrubia and Sole, 1997). Finally, advanced techniques have been generated to handle the growing complexity of scheduling problems while simultaneously accounting for several spatial concerns (Ohman and Lamas, 2005; Liu et al, 2000; Lockwood and Moore, 1993). However, designing a planning support tool that integrates scheduling of management activities, spatial goals, and natural process dynamics remains difficult (Baskent and Keles, 2005). The difficulty in integrating scheduling, location-allocation and dynamic models is that they are usually application-specific, i.e., they have their own particular data structure and associated operations which can make model sharing difficult (Yeh and Qiao, 2005). Considerable progress has been made to achieve compatibility of data requirements between different models. Initially, achieving timber-related benefits was the primary objective of forest management and scheduling of management activities to maximize timber harvest is the traditional focus of prescriptive models for forest management (Davis et al, 2001). In that case, the aggregated growing stock is the principal attribute tracked with the help of growth and yield  88  models and decisions are proposed from mathematical programming models; a relational database structure is sufficient to store and manipulate this aspatial information. With the inception of spatial goals/constraints, spatial scheduling heuristics based on the topdown approach have been developed. These techniques are supported by relational database structures that further include geographical information such as position and topology of forest stands (GIS databases) (Martell et al, 1998; Weintraub and Bare, 1996; Bare et al, 1984). This combination allows for data modeling, analysis and queries related not only to various attributes of forest stands but also to their spatial properties and relationships (Bettinger and Chung, 2004; Nelson, 2003). The spatial database can support locationallocation models in forest planning, which have multiple uses ranging from road placement, cut-block layout, identification of sensitive areas and reserve design. These, usually static, models are based on the local suitability of land parcels and typically do not hold temporal information (Williams et al, 2005). Even i f some simple dynamic spatial constraints such as adjacency can be handled (Lockwood and Moore, 1993), it is still difficult to include objectives involving dynamic patch size and shape (Baskent and Keles, 2005; Ohman and Lamas, 2005). Typically, the spatial dynamic models, which are capable of modeling changing geometries through discrete time steps, do not store information about the past or future states of the spatial database beyond the current and next time step (Erwig et al, 1999). Dynamic spatial processes in natural systems have been modeled with cellular automata (Bone et al, 2006; Colasanti and Grime, 1993), percolation models (Henley, 1993), discrete-event simulation (De Vasconcelos et al, 2002), or spatio-temporal Markov chains (Balzter et al, 1998). Dynamic models can be used to sequentially forecast changes in the forest structure and 89  provide a realistic backdrop for both location and scheduling models. Figure 4-1 illustrates the necessity to link management decision process with the changes in the decision context (socio-economic context and natural events).  Socio-economic processes  Natural processes  Forest Valuation  Succession  Markets  Fire  Costs  Insect outbreaks  I  Management processes  Forest Initial State  Landscape events  Reserve layout Silviculture Harvest  Output (dynamic) Forest State  Figure 4-1  Platform for forest management planning.  The necessity of designing spatio-temporal databases that would be capable of coordinating the data structure held by the GIS and its changes through time has long been recognized and investigated (Peuquet and Niu, 1995). In particular, a number of studies have been undertaken to explore the capability of object-based programming to store and manage  90  complex spatio-temporal data (Yeh and Qiao, 2005; Erwig et al, 1999; Raper and Livingstone, 1995). In forest management planning, Bugg et al (2002) proposes the use of objects-oriented programming to support forest management and Baskent et al (2001) actually proposed an object implementation of a top-down approach to forest planning problem combined with a simulated annealing heuristic algorithm. In that study, the forest is conceptualized using (spatial and aspatial) strata which are represented with objects. The model successfully solved for a number of priority-sorted objectives including some spatial constraints that took precedence over harvest objectives. However, the model did not address complex spatial objectives such as shapes and size of harvest blocks or reserves. The objective of this study is to present an object-based implementation of an approach based on cellular automata (CA) that can address, through time, some complex spatial objectives of forest planning.  4.3 Methodology 4.3.1 Cellular automata model for forest planning Cellular automata (CA) models have been successfully used to represent spatial and timedependent processes, particularly in the context of complex systems (Wolfram, 1994) including cities (Benenson et al, 2005; Ward et al, 1999) or natural ecosystems (Bone et al, 2006; Colasanti and Grime, 1993). Initially introduced by Von Neumann (1966) to design self-reproducing machines, C A models have been used to represent discrete dynamical systems specified in terms of local relations and evolving through discrete time steps (Couclelis, 1997). The basic elements of a C A model are cells; each cell has a neighborhood (a set of adjacent cells) and an associated state selected from a finite number of possible 91  states (Toffoli and Margolus, 1987). A l l cells involved in a model form a grid. A collection of all the cell and state combinations over the grid is called a configuration. The configuration updates at specific time intervals when some or all cells modify their states according to the given transition rules. The transition rules define the new cell state based on the cell current state and states of its neighbors. A C A model defines the numerical characteristics of a state-transition process. C A models have also been used for management decisions (Strange et al, 2002; White and Engelen 1997) and have been shown to be able to satisfactorily handle spatial objectives in land allocation problems. Strange et al. (2002) solved a one-time afforestation problem in Denmark with an evolutionary C A approach. When combined with optimization models, C A can be used to address temporal objectives (Ward et al, 1999). In forest management planning, a typical forest plan addresses spatial trade-offs, not only between one planning period and the next but also across all periods of the planning horizon. Such temporal tradeoffs may arise from requirements for even-flow of timber products or the objective of conserving land in each period (Baskent and Keles, 2005). A n alternative C A method based on an asynchronous application of transition rules and dynamic penalty/incentive functions was proposed in Chapter 3 to deal with temporal objectives and global constraints. In this approach, the cells co-evolve into the final forest plan. The premise for the development of this co-evolutionary C A model is that each cell must contribute to the improvement of landscape-wide objectives while choosing its next state. Cell cooperation within a C A framework is therefore required to address both spatial and temporal objectives. To generate a forest management plan with the CA-based model, we define a forest stand as the C A cell and the stand treatment (suite of management actions) as the cell state. One 92  example of stand treatment over the a 100-year planning horizon divided into decadal periods would be "commercial thinning in period 2 - harvest in period 3 - mechanical site preparation and planting in period 3 - tending in period 4 - harvest in period 8". The stand treatment can be modified by transition rules. The local transition rules involve choosing a state that maximizes the contribution z() of standfto the overall value of the forest plan. The transition function can be formulated as follows:  4 i(/))  = m  +  «4(/))  s<=S  = max £ [(X + a',) x /'(s, (/)) + (1 - X' + /?/ )xD' (s, (/))]  (1)  where s (f) and s.(f)  states of stand fin iteration /+1 and i, respectively  i+]  (f)  s  G  S(f)  the set of possible stand states  z(s (f))and  z(5 .(/))  t, t=l,...,T  risa  M  ;  values of stand / in iteration H-l and i, respectively period (practically, it is the mid-point of a period in the planning horizon)  I' ( i (/))  spatially independent value in /  D' (SJ (/))  spatially dependent value in t  X and (1 - X)  respective weights associated to aspatial and spatial values in t  a],  are the penalty/incentive multipliers applied to the aspatial and spatial values for t and iteration /. They are derived from the level of achievement of spatial and aspatial global constraints by the whole grid.  s  fi!  The forest management plan is developed when all stands are associated to treatments that, together, achieve management goals. The development of the management plan follows an iterative process where stands successively choose a treatment partly as a function of the 93  strategies chosen by their neighbors until an overall stable strategy has been evolved by all stands. Incentive/penalty multipliers are reevaluated dynamically throughout the iterative process to progressively guide stands towards transitions that do not contribute to global constraint violations. The asynchronous C A algorithm can thus lead to the conservation and clustering of old-growth through time and to generating timber volume subject to even-flow of harvest and minimum conservation requirements. The next section discusses some of the issues related to the implementation and the data support for the CA-based forest planning model.  4.3.2 Model implementation For each cell of a grid, C A models aim to determine state z'+l from state i, with i representing an iteration. The essential tasks of C A model implementations are 1) to retrieve a cell state and 2) to apply the appropriate transition rule. When C A models are used to represent spatial processes, they are often integrated with GIS by using raster cells as the basic C A cells (White and Engelen, 2000; Couclelis, 1997). The C A cell states and states of their neighbors are derived from the information contained in overlapping raster datasets (Figure 4-2).  94  Initial GIS raster datasets  attribute x attribute attribute z_  Output GIS raster datasets  Raster algebra operations GRID operations  v^^^^^j^^fg^^z' t=i  / / / / / / / / / / y  4 ^CAgrid C ^ z ^ z  _  Transition rules  ZZZIZZZIZ / / / C A cell c e C with state s (Xc ,y , z ) c  c  c  Figure 4-2 Integration of CA model and GIS raster datasets and processes.  Figure 4-2 illustrates the key difference between C A data structure and GIS raster data models: C A models are cell-based, i.e., the C A cell embed all data related to its state and its transition rules whereas GIS raster data models are built from the theme, a data layer that represent many raster cells but with respect to one attribute only. Since standard raster datasets can store only one attribute value, implementing a C A model based on a GIS raster data structure therefore involves looping through multiple raster data layers to retrieve the information necessary to reconstitute the state of one particular cell (Figure 4-2). Once the information on the cell state is retrieved from the raster datasets, procedural languages are typically used to retrieve the appropriate transition rule, which involves conditional statements, before applying the rule. Most GIS-based C A models follow this type of implementation (Ward et ai, 1999; Wu, 1998; White and Engelen, 1997; Couclelis, 1997). Another issue with implementing C A models on a GIS platform is the fact that C A models are essentially dynamic whereas GIS data structure is static. This requires that new raster  95  data layers be created to represent the updated states of C A cells once the transition rules have been applied (Figure 4-2). For C A models with a modest number of cell states and simple transition rules, procedural languages can retrieve the appropriate information of the cell state from the raster data layers and apply the appropriate transition rule relatively fast. In forest management, however, the transition to the next cell state (i.e. the stand treatment) is a function of several stand attributes and each combination of the attributes calls for a new set of transition rules. When the attributes of neighboring stands and their states are also taken into account, further conditional statements are necessary to retrieve and apply the appropriate transition rule. The more complex the cell state and transition rules are, the more convoluted and lengthy the procedures become. A major inefficiency related to the implementation of C A models with procedural languages is the necessity to loop through a large amount of information before retrieving the relevant state and transition rules with conditional statements. This makes modification, portability, and documentation of the C A implementation difficult for complex problems. Reducing the computation time and redundancy of the code would be possible if the C A implementation was able to directly recognize the attributes and state of a particular cell and its neighbors, and directly access the transition rules associated with that specific state. A n object-based implementation of the C A models where each cell is represented by an object that manages both its states and transitions may be capable of achieving a direct application of transition rules and palliate to the aforementioned inefficiencies.  96  Object-oriented implementation A n Object is the association of a data structure, called the Data Members, and a set of operations that can be applied to these data, called the Function or Method Members (Carrano and Prichard, 2002). A n object implementation may be particularly well suited and efficient for the C A forest planning approach. In the implementation of the C A model for forest planning, each forest stand, the essential cellular automaton, is represented by an object that holds the stand current treatment as part of its data structure and is capable of changing the treatment upon execution of internal transition rules. When executing transition rules, the stands also use their neighbors' states as inputs. Since the management area consists of both forested and non-forested areas, the forest stand object can be further distinguished from the area that supports it. To implement the C A models within an object-based platform, forest stand objects, geographic cell objects and grid objects are defined (Figure 4-3). The information contained in the forest stand objects, cell objects and grid objects can be obtained from GIS raster thematic data layers (e.g. forest cover type, stand age, cell location, site quality or topology) and from other data sources (e.g., growth and yield curves, wood prices, and planning horizon) (Figure 4-3). Most of the attributes and some state variables for the cells and the stands are equivalent to the information from GIS layers for the corresponding record. Cell objects may contain forest stand objects, which run copies of embedded optimization models aimed at choosing the best treatments for the particular stand. The grid manages the execution of transition functions for all stands and the information passing between the stand object, the cell, and its surroundings; the grid also provides the global optimization parameters. A detailed explanation of the different objects presented in Figure 4-3 follows. 97  Spatial data (GIS)  Aspatial information  acquisition  1) Clarification of the problem structure - Identification of decision variables - Identification of decision parameters  preparation 2) Decision variables - identification of objectives - construction of weight matrix - decision process 3) Acquisition of decision parameters - cost/price information - growth & yield information -  old-growth definitions  Objects Oriented Implementation of CA FOREST STAND CLASSES  FOREST STAND OBJECT DATA MEMBERS: - Forest type, age etc... - Strategy state (use/ schedule combination) FUNCTION M E M B E R S - Transition rule (optimization function)  CELL OBJECT DATA MEMBERS - Edaphic attributes, - Geographic attribute - Forest stand object (optional)  FUNCTION MEMBERS Locate neighbours  J  DATA MEMBERS - Time period - Iteration number - Vector of cells FUNCTION MEMBERS - Advance time - Iterative elicitation of stand transition process - Calculate global performance  F i g u r e 4-3  R e p r e s e n t a t i o n of a forest within a n o b j e c t - b a s e d C A f r a m e w o r k . (The large black a r r o w s represent inheritance a n d white a r r o w s represent c o m p o s i t i o n ) .  A Forest Stand Object performs a number of operations, including choosing a stand  treatment schedule ( C A state transition). The data members of the forest stand object include  98  both the stand attributes such as age or forest type and treatment schedule. Even though each forest stand object has its own data structure with its own optimization models and characteristics contained within, similar transition rules can be applied to more than one stand objects. For instance all stands of the "black spruce" ecosystem type share the same set of potential silviculture regimes, the same growth and yield curves and the same old growth threshold. A l l stand objects representing the black spruce type can use a common transition rule method that is distinct from other forest stand objects with different ecosystems. In the implementation of C A co-evolutionary algorithm, a general class for forest stand objects is defined, from which a number of inherited classes for specific forest ecosystem types. A Cell Object represents a particular location on the land that may support a forest stand object. The cell object consists of data members including geographic information (e.g. location and topology), site specific attributes (e.g. site productivity) and one forest stand object if relevant. The cell methods include retrieving location information and information regarding the distance to mills and primary road networks and other landmarks of interest (e.g., sensitive habitat, parks, residential areas and roads). At the next level of abstraction is the cell surface or the Grid Object. The grid object can be construed as the actual surface of the forest management area, or as a two-dimensional list of geographic cell objects. The grid object is responsible for knowing the cell geographic locations, as well as the topological relationships between cells (their spatial arrangements). Another important function of the grid object is managing time progression, eliciting transition of stand states and monitoring the achievement of the forest-wide objectives. The grid object includes the updating function which calls the stand transition rules from the forest stand objects. Such modularity allows for the modification of the updating method 99  depending on the chosen C A algorithm. This modification can take place without any changes needed either in the cell or the forest stand codes. At each iteration, the grid sends a request to a forest stand. The forest stand does the actual state transition, but the grid coordinates the transition activity and provides the global parameters of the optimization functions, which results in the forest plan (i.e. overall configuration). These parameters include the weights associated with the respective objectives, the length of the planning horizon, the current time information and the incentive scheme to fulfill objectives within certain limits. The grid also determines the stopping rules of the C A algorithm. Besides determining the updating process (i.e. deciding when the transition rules are applied to a forest stand object), the grid establishes the rules for selecting the cells. The grid acts as a filter for processing only the cells that are actually open to transition since there is a number of cells that may be removed from management decision-making (e.g., different ownership, water bodies and protected land). This characteristic further increases the efficiency of processing the information in the C A model.  4.4 Problem Instance  4.4.1  Study area and problem formulation  A n area of 4,280 hectares, located in Northern Ontario, Canada, (Figure 4-4) is used to illustrate and test the object-based CA-model proposed earlier. The planning problem consists in maximizing the combined function of timber volume and continuous areas of old growth throughout the planning horizon. The problem further includes a requirement for stable-flow of timber harvest and a minimum area of old growth conserved in each planning 100  period. The study area encompasses several types of forest cover with different response to management treatment, growth and yield information and age thresholds to be considered old growth (OG).  Figure 4-4  Study area located in Northern Ontario, C a n a d a , with its land use categories  The Grid Object of the C A model was populated with the initial stand and geographic attributes derived from raster GIS data layers. The datasets were obtained from the inventory data of the Ontario Ministry of Natural Resources (MNR) corporate Natural Resource Values Information System (NRVIS) and the Forest Resource Inventory (FRI). The preparation and importation of data into objects was conducted in Arc/Info Workstation (ESRI 2005) with a number of Arc Macro Language ( A M L ) modules applied to raster datasets. The object-based co-evolutionary C A model was coded in C++. The model outcomes over the planning horizon are represented by raster data layers generated with Arc/Info.  101  In this application of C A model to forest planning, the state transition is defined as the state (treatment) that maximizes the combination of the harvest and conservation value. The harvest value is measured by the total harvest volume the stand generates over the planning horizon. The conservation value involves the old-growth status of both the stand and its neighbors over the horizon. For instance, a state transition which maintains the stand old growth status over time increases in value if the neighboring stands are also old growth in the same time window. The local transition rules in equation (1) are reformulated by identifying the aspatial value,  r  [s(f)), as the cumulative harvest flow generated by the stand under a  /=i  given schedule state, s(f),  over the planning horizon. The spatially-dependent value,  T  ^ Z ) ' (5,. ( / ) ) , is an old growth index based on both the old growth status of the stand itself  (=1  under a given state, s(f),  and the proportion of its neighbors also in old growth for each  period of the planning horizon. The planning horizon represents the total time span covered by the planning process. Local constraints on cells decisions are defined as no management and no intensive management are allowed within the respective 600 m, and between 600 m and 2000 m of residential and recreation areas and water bodies. The global constraints include a minimum periodic harvest level of 15,500 m , a maximum periodic harvest level of 20,500 m and a minimum of 12 percent of the forest land base in old growth status in each period. A n initial solution was created by assigning a random state (treatment schedule) to each cell. The iteration process was then allowed to work for a certain number of iterations. Reevaluation of the incentive multipliers was carried out at increasing frequency.  102  4.5 Model Outputs The results presented in the next sections illustrate the potential of the object-based C A planning approach to generate forest management plans that address spatially explicit local and global constraints and global objectives. The temporal behaviour of the outcomes is examined. The outcomes are analyzed over time in terms of the amount of old growth and harvest volume, and also in terms of the spatial allocation of harvest events and old growth. The algorithm was run 200 times, each time with 12000 iterations for the weight assigned to the harvest volume component of the combined objective function of A = 0.6 and the cell resolution of 9 hectares (300m x 300m). The initial forest plan was randomly generated for each run. Figure 4-5 illustrates the respective distributions of the amount of old growth and harvest volume over time. The old growth constraint is easily satisfied with an old growth amount above the minimum requirement in each time period (Figure 4-5a). The harvest levels from the plan tend to hit the lower bound in the first half of the planning horizon and hit the upper bound of harvest flow constraints towards the final period. The high proportion of the forest initially in old growth is clustered. It follows that it is more profitable to the objective function value to choose states that favor the old growth value than states that generate harvest volume value. As time progresses and more stands have been harvested, the amount of old growth on the landscape diminishes and harvesting stands generates higher objective values, reaching the upper bound on harvest level requirements. The harvest flow mostly satisfies the constraints with small deviations from the minimum harvest levels in Period 4 to 6 (Figure 4-5b). 103  (a)  1  2  3  4  5  6  (b)  7  8  9  10  1  2  Time (10-year periods)  3  4  5  6  .  7  8  9  10  Time (10-year periods)  —°— 9 ha resolution; X = 0.6 Constraint boundary  Figure 4-5 Distributions of the amount of (a) old growth and (b) harvest volume over time.  The frequency at which the model allocates each stand to either old growth or harvest events at the beginning, the middle and the end of the planning horizon is shown in Figure 4-6 a and b. Across 200 runs, the model consistently avoids locating harvest events in stands close to private and recreational areas or water bodies but allocates harvest events in the rest of the landscape quite variably (Figure 4-6a).  104  (a) Harvest events  Period 1  Period 5  Period 10  Figure 4-6 Frequency of (a) harvest events, and (b) old growth in stand cells. Based on 200 runs with 12000 iterations each for the cell resolution of 9 hectares and X = 0.6.  In general, the location patterns of both old growth areas and harvest events become more consistent around and after the mid-horizon (Figure 4-6). From the middle of the planning horizon onward, the model keeps in old growth those stands closer to water bodies, private land and areas previously reserved for conservation (Figure 4-6 b). While old growth is frequently located in the same stands, there is a higher variability of harvest location, particularly in the initial periods (Figure 4-6a).  4.6 Sensitivity  Analysis  Old growth is more consistently allocated on the study area than harvest event since the harvest component of the objective function is aspatial, i.e., the harvest of a stand is based solely on its potential to generate timber over the planning horizon or in a specific period. The old growth value on the other hand is context dependent. In the self-organization process, old growth is guided by both the fixed geographic elements of the landscape (e.g. 105  areas perpetually in reserve) and by the drive to cluster rather than by the initial solution. In this model, the allocation of harvest events and silviculture regimes is not as spatially controlled and their location and timing are therefore more inconsistent. A concern that arises is the model sensitivity to the initial inventory, to the initial solution and to the model parameters. The influence of resolution in C A models has been observed before (Kocabas and Dragicevic, 2006; Chen and Mynett, 2003) and experimentation with more resolutions could help define the one that is optimal to solve a given planning problem (Menard and Marceau, 2005). If the cell (decision unit) size is chosen on the basis of what makes sense operationally on the landscape, the bias of the model to resolution can be limited (Chen and Mynett, 2003). Furthermore, where large cell size is required the weight associated with the neighborhood and with the context-dependent values could also be reduced. A sensitivity analysis is performed to test the impact of cell resolution and objective weights definitions on the model outcomes. The periodic outputs for different weights on volume, X=0A and != 0.6, and different cell resolution, 9 hectare and 16 hectare are presented in Figure 4-7. Similarly to Figure 4-5, the high proportion of old growth clusters drives the objective function and limits the volume harvested in the initial periods for the 9 haA,=0.4 and 16 ha/A.=0.4 problems (Figure 4-7). As time progresses and more stands have been harvested, the amount of old growth on the landscape diminishes and harvesting stands generates higher objective values thus driving the harvest level to the upper bound (Figure 4-7). For the 16 haA.=0.6 problem, the harvest levels consistently hit the upper bound.  106  (a)  (b)  Time (10-year periods)  Time (10-year periods)  —•— 9 ha resolution; X = 0.4 16 ha resolution; X = 0.4 —•-- 16 ha resolution; X= 0.6  Figure 4-7 Distributions of the amount of (a) old growth and (b) harvest volume over time  Regardless of the weight on volume, X, both 16 ha problems generates higher amounts of old growth (Figure 4-7a). When the resolution changes the calculation of the old growth objective value still draws upon the proportion of the 8-cells neighborhood that is in oldgrowth. The neighborhood of a 9-ha cell covers 81 hectares whereas the neighborhood of a 16-ha cell covers 256 hectares. To achieve the same old growth value in the objective function (Figure 4-8c), a much larger area is required to be old growth when the model operates on larger cells (Figure 4-9a).  107  (a)  0.2  0  1  J X.=  0A  1  0 15 -  o  I  1  <D  Harvest vali  •  04  -9  0.20  o  0 5  0.00  X = 0A  1 = 0.6  X = 0.6  9-ha resolution  X = 0.4  X = 0.6  16-ha resolution  Figure 4-8 Comparison of the objective function values between outputs for 9-ha and 16-ha resolutions and for relative weight associated with harvest value A = 0.4 and A = 0.6.  Although the impact o f resolution on the overall objective function values is not large (Figure 4-8), the 'real' values generated by the solving CA-algorithm are very different (Figure 4-7 and Figure 4-9).  250  o o o  200  H  150  o > 100 H C >D rs  E  13  CJ  A.  = 0.4  X—  0.6  9-ha resolution  X=  0.4  X=  0.6  16-hectare resolution  Figure 4-9 Comparison of model outputs between 9-ha and 16-ha resolutions for relative weight associated with harvest value A = 0.4 and A = 0.6. 108  The consistent of allocation to old growth or harvest events to a given stand is also impacted by cell resolution (Figure 4-10). In all cases (Figure 4-6 and Figure 4-10), the contextdependent old growth value directly influences the location of old growth areas and indirectly the choices of silviculture regimes and harvest schedule in each cell. Although the initial solution does influence the final solution to some extent, particularly in the first planning periods, the requirement to account for inter-temporal tradeoffs (constraints on periodic harvest volume and old growth proportion) prevents unlimited growth of old growth clusters through the planning horizon. Additional spatial objectives in the planning problem definition would further prevent this from happening by reducing the solution space.  109  Resolution 9 hectares; K-0.4: (a) Harvest events ."I  I  ^v/*' ;*,t^  Occurrence frequency High  (b) Old growth  Low  Period 1  Period 5  Period 10  Resolution = 7 6 hectare A= 0.4: (a) Harvest events  I  i  S  y  l i l M t " ' " fiftilEW V l>  >  "  Occurrence frequency High  (b) Old growth Low  Period 1  Period 5  Period 10  Resolution = 16 hectare A= 0.6: (a) Harvest events  •  ink. i  ii; •  .-4 - •  Occurrence frequency  •  High  (b) Old growth Low  Period 1  Period 5  Period 10  Figure 4-10 Frequency of (a) harvest events, and (b) old growth based on 200 runs with 12000 iterations each for three different problems: 9 ha/ A=0.4, 16 ha/A=0.4 and 16 ha/A=0.6.  110  4.7  Discussion  The implementation of the C A models to forest planning on the object-based platform has many advantages over the implementation with procedural languages. One is to avoid repeatedly accessing information that is not immediately relevant and to communicate only the information necessary to the executing function such as spatial and temporal parameters. The object-based C A models do not require scrolling through numerous thematic layers or database entries before finding the information necessary to proceed with the state transition of a given stand. A l l the information needed is self-contained or communicated to the stand at execution time. An additional advantage of the object-based design is the reusability of both the code and information shared by similar objects. Similar objects are all built from the same original design, called a class. The class defines the type of data and function members a derived object will contain. We can define a forest stand class that defines the basic data and function members contained in a forest stand object. They could be age, forest cover type, current management and planned management strategy. It is further possible to derive more specific forest stand classes from this original class. Such classes could differentiate between the different forest cover types found on the landscape with different growth and yield information, old growth threshold and operable windows. As there is no need in principle to have forest stand objects contain the same list of state variables (or even have the same internal structure), then each forest object need only contain those qualities (variables) that are relevant to that forest stand. Different forest stands may have any variety of internal details but can interact as long as the information passed in messages is consistent, i.e., as long as cells are communicated the states of their neighboring cells that will influence their 111  own choice of strategy (use/schedule). Since all forest stands do not have the same level of complexity, the class functionality is practical for the implementation of C A models for forest planning.  4.8  Conclusion  The decentralized model and object-based platform presented in this paper successfully identified forest management plans for problems involving inter-temporal tradeoffs and both local and global spatial and aspatial objectives/constraints. The object orientation of the implementation permits a fast computation of both local and global limitations on cells' decision making. The object-orientation of the implementation allows speedy modification of either local or global requirements and is highly portable to other planning problem contexts. Further research would include additional environmental processes such as succession and stochastic events (fire or insect outbreaks). Additional research with the object oriented framework would include internalizing succession processes in the methods of'forest objects' which is anticipated to facilitate their computation. With respect to cellular automata, further inclusion of fires or insect outbreak would allow to analyze the resilience of any given management strategy to losses. The computation of fire has already been shown to be easily handled by C A models (Green, 1989). Other notable enhancement of the objective function for forest planning would include financial aspects of harvesting. If the scheduling of harvest was also a function of the proximity to the road network and of the size of the harvest block - such as is the case when economies of scale are desirable, it is anticipated that there would be more consistency in the location and timing of harvest events on the landscape. 112  4.9  References  Balzter, H., Braun, P.W., and Kohler, W., 1998. Cellular automata models for vegetation dynamics. 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Computers, Environment and Urban Systems 29: 133-157.  118  5  OPPORTUNITIES AND C O S T S OF INTENSIFICATION AND CLUSTERING OF F O R E S T MANAGEMENT ACTIVITIES 4  5.1  Overview  The intensification of forest management in Canada has attracted a renewed interest since the end of the 1990s, particularly so in the boreal regions. It has been advocated as a possible solution to the conundrum that increasing demand for conservation areas and increasing pressure for timber production have created. It is not the first time that intensive forest management (IFM) has gone through a period of major interest among the forest managers in Canada before falling into obsolescence with hardly any large-scale implementation (e.g. Whan 2000). Are the benefits and disadvantages of IFM for the Canadian boreal forest so unclear that conclusions about its value are impossible? This paper investigates the potential contribution of IFM for fulfilling conservation and timber flow objectives in a management unit set in the boreal forest of Ontario. We present an assessment of land allocation and management alternatives. The evaluation is undertaken by solving a long-term forest planning problem for different policy scenarios with a decentralized planning approach based on cellular automata. The results show that the cumulative volume is not higher for scenarios including the IFM as a management option. However, the area of forest harvested is lower in most periods for these scenarios. IFM does not generate more volume but rather helps to meet the harvest volume targets from a smaller forest area. The main trade off in this study was found to be between volume and net present value. Constraints on the volume flow were  A version of this chapter has been submitted for publication. Mathey, A . - H . , Krcmar, E., Innes J.L., Vertinsky I. (2006). Canadian Journal of Forest Research  4  119  met but systematically hit the lower bound. In this context, spatially clustering the harvest activities that occur in each time period increases the net present value of a plan.  5.2  Introduction  Intensification of forest management in Canada has attracted renewed interest in the past decade. 'Intensification' describes the practice of forestry that increases the volume and/or quality of outturn per unit area (Helm, 1998). With a decreasing land base of primary forest due to past forestry operations or current protection measures, intensive forest management (IFM) undertaken on smaller commercial areas is a potential solution to maintain or even boost the supply of wood fiber. In the boreal forest, IFM has therefore been advocated in the context of land specialization to "meet the competing realities of preserving the resource, maintaining the lifestyle and values of [...] communities, extracting economic wealth and preserving ecological values" (Canadian senate sub-Committee on Boreal Forest, 1999). Independently of conservation objectives, IFM is further perceived as a means to respond to a growing world demand for wood products and could be considered as a means to balance economic goals with forest stewardship and societal concerns (Bell, 2003; NRCan, 2001). In Ontario, where most of the forestry operations take place on public land, the debate between increasing conservation areas and maintaining forestry operations resulted in a consultation process between government, environmental associations and forestry industry between 1997 and 1999. The process produced "Ontario's Living Legacy Land Use Strategy" and the associated "Ontario Forest Accord" (OMNR, 1999). The basis of the Accord is to ensure a secure environment for the forestry industry while establishing a protected areas  120  system that covers at least twelve percent of the Crown forested land base. In this context, IFM is perceived as a productive solution to a decreased operating land base. The same amount (or more) of timber could be produced from a smaller area, thus alleviating the impact of increased protected areas on wood supply. Forest science partnerships have been established to "assess the impacts of intensive forest management on increased forest growth and yield ... to assess the environmental impacts of intensive forest management, ... and to direct science activities in support of Ontario's forest management planning requirements" (OMNR, 1999). One such partnership undertook studies in the boreal forest of Ontario and found that intensive silviculture did increase growth and yield but did not provide a positive economic return, at least in the "representative stands" studied and based on the assumptions used (Insley et al. 2002). Despite the absence of a positive economic contribution at the stand scale, IFM could help better achieve other forest management objectives: the increase in timber harvest from land under IFM could lead to the reduction of the overall area under timber management and thus to the augmentation of areas allocated to reserve and conservation (von Mirbach, 2001; Hermann and Lavender, 1999; Binkley, 1997; Sedjo and Botkin, 1997). Altogether exempting large areas from harvesting could more efficiently achieve habitat, recreation and conservation goals over the landscape than regulated timber activities (Binkley, 1999; Burton, 1995), not least because they can fully remove pressure from sensitive areas, which would be protected in reserves. This would allow a comparatively straightforward control of collateral damage to the environment and/or to cultural way of life of First-Nations (e.g., culturally marked trees, trails or trap lines) than otherwise possible with management rules and regulations. 121  Whether IFM is implemented will eventually depend on factors beyond stand productivity or stand-level economic returns. If it is essential that the management decisions be feasible at the stand level, which is concerned with the manipulation of the forest resource (i.e., stand intervention), the decisions must also be profitable at the management level, which is concerned with the administration, planning and finances of the forest management area. Finally, the decision must be beneficial at the socio-political level, which is concerned with the social and political support and regulation of management (Brumelle et al, 1991). Therefore some questions that need to be answered are: can IFM make up for a decrease in future timber harvest rates due to either the age-class structure of the landscape or to the increase in protection areas? If so, how fast can we expect this increase to be, and how much would it cost? Could these costs be alleviated by concentrating harvest operations?  OBJECTIVES:  The objective of this paper is to analyze the potentials of IFM to fulfill conservation and timber flow objectives in a management unit set in the boreal forest of Ontario. The next section discusses the forest management problem in more detail. A n analysis and assessment of land allocation and management alternatives follow. The evaluation is undertaken by solving a long-term forest planning problem for different policy scenarios. In particular, we examine how maintaining old growth forest conservation affects harvest volumes and financial benefits in a boreal forest of Ontario. We also examine the impact of IFM on the discounted net revenue when there are requirements on harvest flow. Lastly, we investigate the potential of aggregating harvest areas for decreasing operations costs.  122  5.3 Problem  Description  5.3.1 Forest management in the boreal forests of Ontario In the boreal forests of Ontario, forestry operations are principally undertaken on public land. Forestry operations are often linked to or even administered by one or a few mills in the same area. One consequence is that forest managers are concerned with supplying the mills' demand for timber and doing so at the lowest possible cost (since these costs are accounted against the profits from mill operations). In addition, regulatory constraints, often conservation-related, are to be satisfied and public demands regarding lighter management around recreation or residential areas have to be met. Ontario Living Legacy requires that at least twelve percents of the forested land base be set aside for protection (OMNR, 1999). In addition, there are a number of management guidelines that require that a large amount of contiguous old forest be left in the landscape for wildlife habitat maintenance (e.g., pine marten requirements (Watt et al. 1996), which may result in reduced timber harvest. In combination with an imbalanced age-class structure with an abundance of over-mature stands, the protection requirements could lead to a timber supply "dip" within the next forty years (Bell, 2003). Therefore, the objectives of forest management in northern Ontario can be broadly categorized into (1) the maintenance of wood production, (2) the fulfillment of conservation and protection requirements and (3) an increase of net financial benefits from forestry.  123  5.3.2 Management options Customarily, the options available to achieve the aforementioned have included the exclusion of forestry operations altogether, and extensive and basic management regimes. Extensive regimes mainly consist of natural regeneration after harvest. Extensive regime is the most widely practiced with low operating and investment costs. Basic regimes apply those silvicultural activities that ensure a free growing status: site preparation, artificial and natural regeneration, and tending if required. Intensive forest management, insofar as it refers to intensive regimes, is an array of silviculture practices that, alone or in combination, will increase the yield and/or wood quality beyond that of the free-growing status (Cote, 2003). Intensive regimes activities include those of the basic regimes in addition to planting of improved stock and acceleration of artificial regeneration (stand tending). Pre-commercial thinning and commercial thinning are also options considered under intensive regimes. In Ontario, however, the use of fertilization, drainage or genetically modified organisms is not allowed. Intensive management can be construed as a subset of sustainable forest management where the allocation of land to different uses (timber and non-timber) is carefully planned to increase the value of desired forest components (not just timber) (Lautenschlager, 2000). The location and level of aggregation of uses to increase financial revenues - by generating economies of scales, and conservation values - by generating larger core areas of natural or old growth forest therefore constitute another aspect of intensive management. In the remaining of this document, IFM refers to intensive silviculture while locations of clusters of protected areas or harvest blocks are separately considered.  124  5.3.3 Spatial allocation The nature conservation and timber production objectives of the Ontario's Living Legacy (OMNR, 1999) have a number of spatial aspects that strongly influence where each type of management can be undertaken. Some of the allocation issues can be determined prior to the forest planning process by identifying the areas where little or no management is to take place. A number of guidelines limit management activities in the proximity of water bodies, recreation or residential areas and sensitive wildlife habitat. Some areas, such as permanent nature reserves, are simply excluded from management. Other allocation issues are resolved during the planning process. For instance, the focus of the conservation effort is not only on the amount of untouched forest or old growth forest; rather, the objective is to maintain large clusters of old growth forest and/or untouched forests so as to provide adequate quantity, quality and continuity of habitat for some featured species (e.g., pine marten, (Watt et al. 1996). Conservation, environmental and recreational spatially explicit objectives/constraints create discrepancies between the strategic targets of an aspatial plan and the reality of its implementation, sometimes reducing significantly the discounted net financial benefits and harvest volume that could be expected otherwise (e.g. Daust and Nelson, 1993). The impact of spatial considerations on management outcomes means that decision support tools need to be spatially explicit. Using spatially explicit planning tools can generate plans that meet the spatial requirements of conservation objectives while tracking the timber-related objectives. Spatial planning tools can further be used to minimize operation costs. In particular, one means to limit the costs of forest operations could be to undertake forestry operations in those areas that are close to 125  roads, especially primary road network, are close to processing facilities, have high volume and "neighboring aggregate resources". Harvest costs are the largest of all operation costs; they also offer the most opportunities to generate economies of scale since the simultaneous harvest of adjacent stands can result in sharing the costs for access roads (Delong et al, 2004; Rose and Chapman, 2003).  5.4 Model Formulation The forest planning problem considers two objectives. The first objective is to maximize the discounted net return (net present value) from timber harvest over the planning horizon. The second objective is to maximize the cumulative harvest volume over the planning horizon. The bi-objective problem is converted into optimization problem where the objective function is the weighted sum of the two objectives. The objective function is subject to constraints on the amount of old growth and the amount of timber required in each planning period.  max Z = X w, x NPV{s(f))+ seS  w x V{s(f))  Equation 1  2  s  Here NPV(s(f))  is the discounted net revenue obtained as a difference between revenues  and costs over the planning horizon by schedule s() applied to stand / . The revenue, R(s(f)),  depends on of different wood grades and the volume harvested. The costs  include silvicultural costs, Silv(s(f)),  and harvest costs, HC(s(f)).  Silvicultural costs  (regeneration, tending and thinning) are calculated on a per hectare basis and are assumed to be independent of the size of the treated block. For a given management regime, timing of 126  silvicultural treatments is predetermined and their costs are discounted to the time of the initializing harvest. Harvest costs include both administrative and operational components. Operational costs are associated with falling, constructing spur roads and skid trails (Delong et al, 2004) and bringing the necessary machinery on site (Rose and Chapman, 2003); they could be decreased by the simultaneous harvest of adjacent stands. A spur road is any road required to access a block that is not adjacent to a main road. Although larger harvested areas may require longer spur roads, they presumably require fewer of them, hence the economies. NPV(s(f))  over the planning horizon T\s formulated as:  N P V l A f ) ) - ±  R  ,  ^ - ™  * Q -  {  H  C  ,  {  * r t  E u q  a t i  „„2  The operational harvest cost at period / discounted at rate r, is calculated as follows: HC (*(/)) =AC {s(f)) + FC (sff)) + SkC {s(f)) + StC (*(/)) + RC {s(f)) + TC (s(f))  Equation 3 where, for harvest in period t, Administrative/ other costs  AC(s(f)) = «/*($/ha) area harvested (ha)  Falling costs  FC(s(f))  Skidding costs  SkC(s(f) =a ($/m ) * HarvestVolume (m ) + a ($/km-m ) * Harvest Volume (m ) * average skidding distance (km)  = a ($/m ) * Harvest Volume (m ) 3  3  2  3  3  3  4  3  3  Spur road transport costs  StC{s(f)] = a ($/km-m ) * Harvest Volume (m ) * average distance to major road (km)  Road-building costs  RC(s(f)) =a-6 ($/km) * distance to nearest primary or secondary road (km)  Transport costs  TC(s(f))  3  3  5  =ai ($/km-m ) * distance to the mill (km) * Harvest Volume (m ) 3  3  127  Here, a\ ($/ha) is the administrative cost per hectare; a-i ($/m ) is the cost of falling one cubic 3  meter of wood; aj ($/m ) is the distance-independent skidding cost per cubic meter; a ($/km3  4  m ) is the distance-dependent skidding cost per cubic meter and kilometer; as ($/km-m ) is 3  3  the cost of transporting one cubic meter over a kilometer of spur road; a^ ($/km) is the cost of building one kilometer of spur road; 07 ($/km-m ) is the cost of transporting one cubic meter 3  of wood for one kilometer of major road . Transport costs are dependent on the volume harvested, the road network existing and its proximity to mill facilities. Transport costs are also assumed to be independent of the size of the harvested block. V(s(f))  in Equation 1 is the cumulative harvest volume generated by schedule s(f) applied  to stand / . The problem is solved using the decentralized approach developed in Chapters 3 and 4. The basic decision-making in this approach is a stand. For the stand / , the treatment schedule s(f) is chosen to maximize the stand objective value: max z = w x NPV{s(f)) x  +w x 2  V(s(f))  Equation 4  A co-evolutionary approach reconciles local-level decisions, i.e. the choice of a treatment schedule for each stand, with global-level objectives and local and global-level constraints based on cellular automata modelling and co-evolutionary principles. Local level constraints are addressed by introducing a constraint vector prior to the transition function. This vector restricts the set of possible transitions to certain types of management based on either social factors (proximity to residential or recreational areas), physical factors (unproductive land, 128  protected ecosystem), or geographical factors (riparian or lake buffer areas, moose aquatic feeding areas). Global constraints are addressed within the transition function by using adaptive penalty/incentive multipliers that steer the stand decision towards decisions that will decrease the discrepancy between the global performance and the global constraints (see Chapter 3).  5.5 Problem 5.5.1  instance  Study area  Forest management planning in the Romeo Malette Forest (RMF) in the Northeast Region of 2  2  Ontario is presented. R M F covers approximately 6,220 km , of which 4,747 km are manageable productive forest lands subject to management (Figure 5-1). The forest is located within the boreal region, with the tree species typical to boreal forest types and distribution patterns. There are sixteen different forest ecosystem types present on R M F . These are dominated by black spruce (Picea mariana), but other distinct forest types and associations include poplar (Populus spp.), balsam fir (Abies balsamea), white birch (Betula  papyrifera)  and jack pine (Pinus banksiana), depending on the site. The forest inventory was rasterized at a 9-ha resolution to build the grid supporting the planning problem. For each raster dataset, the value assigned to one 9 ha-cell was generated by assigning it the value of the feature that fills the majority of the cell area (majority weighing method). The initial grid was populated with a forest inventory derived from corporate Natural Resource Values Information System (NRVIS) and Forest Resource Inventory (FRI) maps standardized by the Ontario Ministry of Natural Resources.  129  The planning horizon was set to 100 years, divided into decadal periods. The decision variable includes the timing of harvest and the choice of subsequent management regime. Three management regimes are considered: extensive, basic, and intensive. The silvicultural regimes (a suite of silvicultural activities) associated with each management regime are specific to a forest type. The operability windows vary according to the combination of forest type and silvicultural regime. A maximum of two harvest events can take place over the planning horizon. A no-harvest option was also generated for each stand. The coefficients a, used to calculate Equation 3 are derived from information about local operations in the Romeo Malette forest.  Legend 0  Mill  Age (years) [ ! •  [ 0-30 30 - 80  Ownership  Major road types  | | Timber m a n a g e m e n t  Highway  H Private land  Main road  J  P a t e n t land  Primary road  |  Provincial park  S e c o n d a r y road  J  Indian reserve  Tertiary road  I  Recreation reserve  Figure 5-1 Study area. A g e class distribution (left) and ownership and road cover (right)  130  5.5.2 Management requirements Beside the stand-specific characteristics (age, species composition, site quality), constraints at the stand and forest levels are used to determine the potential decision for a given stand. Local constraints consist of the exclusion of the rare red and white pine stands from management. Also, no management can be undertaken within 600 m of areas of concern (moose feeding areas, water bodies, recreational and residential areas). Only no-management, extensive and basic management can take place within 2,000 m of such areas. Global constraints include bounds on the volume harvested in each planning period and minimum protection requirements. Based on the protection and old growth maintenance guidelines presented earlier, we aggregate the forest protection requirements to the maintenance of large old forest patches in each period of the planning horizon. The minimum requirement is to retain twelve percent of the forested areas in old growth at all time. This roughly amounts to 66,000 ha of old growth retained in each planning period. The definition of old growth is based on the stand age and is forest type-specific (Uhlig et al. 2001).Deciduous-dominated stands reach the old growth stage earlier than coniferousdominated stands.  5.5.3 Management scenarios In order to analyze the potentials of IFM to improve timber benefits, volume and costs, a number of scenarios are examined. For a long time, forests were considered a production factor to mill operations, and sustained yield management was the prevalent paradigm before the inception of sustainable forest management. Sustained yield management emphasizes 131  timber values and is concerned in particular with harvest flow whereas sustainable forest management encompasses a number of other values including biodiversity, wildlife habitat or soil and water quality. Three benchmark cases were consequently investigated. The first benchmark case includes determining the maximum cumulative volume that can be produced over the horizon and identifying the corresponding values of discounted net return and old growth area. In this benchmark case, only no-management, extensive and basic regimes are considered. The two subsequent cases include determining the highest stable yield over the horizon with and without the requirement of maintaining twelve percents of forest in old growth condition. The increasing independence of woodlot operations from mill operations may allow shifting the focus of forest management away from volume production towards economic efficiency. Within this perspective, a number of scenarios were identified where the goal is to achieve the highest net return (net present value) from forest operations. The scenarios differ by the constraints related to volume flow and old growth retention. The bounds on periodic volume flow were set at 3 million m and 3.5 million m . The rationale for these bounds stems from a recent study of the Romeo Malette forest (Spatial Planning Systems 2004). We further investigate the potential of IFM to help fulfilling timber and revenue objectives and the potential of simultaneously harvesting several adjacent stands to reduce harvest costs. Finally, a scenario is included to investigate the model behaviour. In this scenario, volume and net present value are desirable outcomes of a forest management plan, which constitutes a compromise between a volume-driven management and a revenue-driven management. The cumulative harvest volume and net present value objectives are weighted equally with bounds on volume flow between 4 and 4.8 million m per period, which is the current harvest 3  132  level. The scenarios are summarized in Table 5-1. The local constraints apply to all scenarios.  Table 5-1 Summary of alternative management scenarios (w is the weight associated with the net present value objective and w is the weight associated with cumulative volume objective) 1  2  Scenario Objective weights  Global constraints  IFM option  Cost sharing for adjacent harvested stands  0  wi=0, W2=1  None  No  No  1  wi=0, W2=1  Stable flow  No  No  2  W1=0, W2=1  Stable flow; Minimum 12% of the forest in old growth in each period  No  No  3  Wi=1, W2=0  None  Yes  No  4  wi=1, W2=0  None  Yes  Yes  5  W i = 1 , W2=0  3M m <Periodic volume <3.5M m ; Minimum 12% of the forest in old growth in each period  No  No  6  W1 = 1, W2=0  3M m <Periodic volume <3.5M m ; Minimum 12% of the forest in old growth in each period  No  Yes  7  W i = 1, W2=0  3M m <Periodic volume <3.5M m ; Minimum 12% of the forest in old growth in each period  Yes  No  8  W1 = 1,W2=0  3M m <Periodic volume <3.5M m ; Minimum 12% of the forest in old growth in each period  Yes  Yes  9  Wi=.5, W2=.5  4M m <Periodic volume <4.8M m Minimum 12% of the forest in old growth in each period  No  No  3  3  3  3  3  3  3  3  3  3  133  5.6 Comparative evaluation of  scenarios  The scenarios are evaluated and compared i n terms o f the objective values (cumulative volume and net present value), o f the number o f stands in each management regime at the end o f the planning horizon, and o f the spatial allocation o f harvest areas and old growth areas i n each planning period. The harvest flow, the old growth over time and the area harvested in each period are also examined for all scenarios.  FINANCIAL AND TIMBER SUPPLY BENEFITS:  The scenarios focusing on generating volume (Scenarios 0, 1, and 2) and the scenarios focusing on increasing net present value (Scenarios 3 and 4) generate strikingly different outputs: the highest harvest volumes among all scenarios are associated with the lowest net present values and vice versa (Figure 5-2).  134  50  0  1  2  3  4  5  6  7  8  9  Scenarios Figure 5-2 Net present value and cumulative harvested volume generated for each scenario.  Scenarios only differing by whether or not they include IFM as a potential management option show little increase in cumulative volume from their counterparts but have a lower net present value (Scenarios 7, 8 vs. 5, 6 in Figure 5-2). The inclusion of IFM decreases the amount of land harvested in each period for otherwise similar scenarios (Table 5-2).  135  Table 5-2 Difference in the amount of land harvested between scenarios that do and do not include intensive forest management.  Period 1 2 3 4 5 6 7 8 9 10  Area harvested under Scenario 7 area harvested under Scenario 5 (ha) -3348 -1296 360 -837 -945 -198 -414 -360 -3798 -1773  Area harvested under Scenario 8 area harvested under Scenario 6 (ha) -2115 -900 -576 72 -18 -306 -1305 -99 -2538 -1152  The cumulative volumes of scenarios that differ only in the option to share costs for building spur road at the time of harvest show little difference (Figure 5-2). However, the net present value is systematically increased (Figure 5-2). The spatial positions of harvested stands are also affected as clustering of harvested stands to form harvest blocks occurs (Figure 5-3).  Scenario 7  Scenario 8  Figure 5 - 3 Location of harvested stands, young and mature stands and old growth in Period 3 for Scenario 7 (no road costs sharing) and S c e n a r i o 8 (road costs sharing).  136  ALLOCATION OF M A N A G E M E N T REGIMES  The scenarios that seek to maximize net present value not only have the lowest cumulative harvest volumes but also generate the highest amount of both natural forest (Figure 5-4) and old growth (Figure 5-5). The scenarios that include IFM show a general reduction in the amount of land under extensive and basic management (Figure 5-4).  35000  I I I 1  30000  -o  c  Natural state Extensive management Basic management Intensive management  25000  CO -t—'  10  20000 i  CD  Z  CD  15000  E -p  10000  5000  0  1  2  3  4  5  6  7  8  9  Scenarios Figure 5-4 Number of stands in no-management, extensive, basic and intensive management at the end of the planning horizon.  137  55000 -i  %  50000 -  vj—, / CD  •o 45000 O C  C/3 T3 C  — • — Scenario 0 Scenario 1 —Scenario 2 — ° - Scenario 3 — * - Scenario 4 —o - Scenario 5 — - Scenario 6 — » — Scenario 7 Scenario 8 —Scenario 9  40000 -  ro 35000 CO  iber of 9-h  ro  t z:  30000 25000 20000 15000 1  2  3  4  5  6  7  8  10  Planning period Figure 5 - 5 N u m b e r of old growth stands over time for e a c h scenario  OLD G R O W T H AND HARVEST F L O W OVER TIME  The minimum of 12% of old forest retention in each planning period is met for all scenarios (Figure 5-5), even in the unconstrained scenarios (scenario 0, 3 and 4). The inclusion of this constraint therefore has little impact on the planning outputs for otherwise similar scenarios (e.g., Scenarios 1 and 2, Figure 5-2). On the other hand, the inclusion of an even flow constraint or specific bounds on harvest levels decreases the cumulative harvest flow when the objective is to maximize the cumulative volume (Scenarios 2 vs. 1) and increases the cumulative volume when the objective is to maximize net present value (scenarios 5, 6 and 7, 8 vs. 3, 4) (Figure 5-2). The stable flow constraint is met for Scenarios 1 and 2 and the bounded flow constraint is met for scenarios 5 to 8 (Figure 5-6). The highest stable harvest level was identified between 7 and 7.8 million m . 138  In the case of Scenario 9, which trades off the net present value and cumulative volume objectives, the volume flow constraints are met in the initial periods with harvest levels around 4 million cubic meters but violated in the last two periods where the upper bound of 4.8 million m is exceeded (Figure 5-6). The levels of net present value and cumulative 3  volume for scenario 9 are somewhat in the middle ground between scenarios 0-2 and 3-4, which respectively focus on net present value and volume.  Planning period Figure 5 - 6 Harvest flow for e a c h scenario.  5.7  Discussion  Somewhat surprisingly, the results from the case study indicate that the main tradeoffs of the Romeo Malette forest management are not between the timber and conservation objectives but rather between the timber supply and the financial benefit objectives. Because of the 139  negative impact of volume harvest on net present value, the planned harvest levels do not reach above the imposed lower bounds. The initial high amount of both unmanaged forest and old growth forest on the landscape ensures that the constraint on the minimum amount of old growth over time is met, even under the highest levels of harvest levels. The old growth constraint has therefore little impact on the management strategy. However, under volume-focused scenarios, the old growth levels reduce over time and a depletion of both the old growth forests and the unmanaged forest is likely to occur for longer planning horizons. Also, in the model formulation, the old growth constraint applies to all forest ecosystems collectively. If particular serai stage distributions and/or ecosystem representations were required, the old growth constraint might not be so easily met. In that case, the conservation constraints may affect the management strategy. The key objective of this study is to determine the potential of IFM to rectify a future timber shortfall due to increased conservation requirements and/or age class imbalance and to generate volume from a smaller area. The results from the case study do not support the hypothesis of a short-term timber supply on the management unit. Conservation requirements do not restrict management strategies under the investigated scenarios. However, these results are specific to this case study and should not be generalized. For the forests of smaller size and stringer conservation policy or different initial inventory, IFM could become a necessary management option to meet timber harvest requirements For the scenarios 5 to 8, which share similar constraints regarding volume flow and old growth maintenance, the extensive regime is the prevalent management, followed by basic regime (Figure 5-4). Although the cumulative volume does not increase for the scenarios that 140  include the IFM option, the harvest area is lower in most periods compared to the scenarios without the IFM option. This is particularly noticeable for scenarios that do not consider costs-sharing among simultaneously harvested adjacent stands. The role of IFM, as perceived in this case study, is to generate the minimum required volume from a smaller harvest area. However, IFM is also a more costly strategy. Under more stringent conservation requirements than those used for this case study, the harvest area may be limited, which could make IFM more attractive despite its higher cost. Clustering harvest activities is another aspect of management intensification considered in this study. The results indicate that clustering harvest activities is the single most important factor in increasing net present value under the stable flow constraint. When contiguous stands are simultaneously harvested, they share the costs of building spur roads to access the main road network. This property encourages the formation of harvest blocks from adjacent stands and reduces overall costs. However, the model does not produce unrealistically large harvest blocks and even proposes single-stand harvest in a number of cases. This can be explained by the fact that the stand management decision is a function of several characteristics of the stand beside the neighborhood influence such as operability, potential for conservation or old growth, potential to generate volume in other planning periods and other costs. For instance, stands located close to major roads are most often chosen for harvesting since this minimizes the need for, and the cost, of building spur roads. In such cases there is no incentive for grouping stands into harvest blocks. With regard to the solution technique applied to solve the case study problems, scenario 9 offers an insight into the problem of aggregate objective functions with multiple, conflicting, objectives. In the initial periods, the influence of maximizing the net present value is high 141  and decisions tend to meet this objective and only the minimum required harvest volume is generated in each time period. Because of discounting, harvests in the later planning periods hardly affect the net present value. In later periods, maximizing the combined objective rests solely on the maximization of the volume objective. Fulfilling the objective drives the coevolutionary algorithm rather than meeting the constraints, which get violated in the later periods. The outcome of this scenario emphasizes the importance of designing penalty functions associated with the constraints that do not dominate the objective function but also that are not dominated by the objective function. Another potential challenge regarding the methodology is related to the spatial representation in regular raster-like cells. The grid structure and algorithm simplify the neighborhood relationships in the sense that only the eight adjacent neighbors have a direct impact on the stand's decision. As a result, the way neighborhood is designed in the CA-based approach described here may not prove fully satisfactory if harvest blocks or old growth clusters consisting of more stands are required.  5.8  Conclusions  In the boreal forest of Ontario, the volume and value of timber generated under the local intensive silviculture practices are small. The potential gain of intensive silviculture mainly lies in helping the forest manager to fulfill management objectives when the requirements on both timber supply and conservation are high and when the forest inventory is limiting. The initial inventory, with its associated quantity of old growth and unmanaged forest, and the protection requirement both influence the level at which remedial actions such as intensive  142  silviculture needs to be undertaken to meet objectives. In the Romeo Malette case study, the abundance of old forest is such that even under the most volume-focused scenario, clusters of old growth remain in the final planning period. Although the inclusion of intensive forest management results in a net loss of revenues, it facilitates meeting harvest flow requirements from a smaller harvested area. This may prove important if harvest costs were to increase or if conservation requirements were considered beyond those of old growth retention. The degree to which IFM would be desirable would again depend on the initial inventory. The main trade off in this study was found to be between volume and net present value. Constraints on the volume flow were met but systematically hit the lower bound. In this context, clustering harvest activities increase the net present value. The decentralized methodology fosters such aggregation but does not lead to the 'cancerous' growth of harvest blocks since both the initial inventory and the potential with regard to other objectives detract from timber operations. Clustering of both protected areas and harvest operations therefore could better achieve both the conservation and the timber objective by improving the habitat value of conserved areas and decreasing the operational costs in harvested areas. The level to which the model encourages clustering of either harvest operations or conservation areas needs to be identified on a regional basis to best fit the local processes and disturbances.  143  5.9  References  Bell, F.W., 2003. Intensive Forest Management Science Partnership: NEBIE Plot Network. In Meeting emerging ecological, economic, and social challenges in the Great Lakes region: popular summaries. Great Lakes Forest Alliance 2003 summit. Buse, L. J. and Perera, A . H . (Eds.), Queen's Printer for Ontario, Sault Ste. Marie, pp. 115-116. Binkley, C.S., 1997. Preserving nature through intensive plantation forestry: The case for forestland allocation with illustrations from British Columbia. Forestry Chronicle 73: 553559. Binkley, C.S., 1999. Ecosystem management and plantation forestry: new directions in British Columbia. New Forests 17/18: 435-448. Brumelle, S., Carley, J.S., Vertinsky, I.B., and Wehrung, D.A., 1991. Evaluating silvicultural investments: a review in the Canadian context. Forestry Abstracts 52: 803-856.  Burton, P.J., 1995. The Mendelian compromise: a vision for equitable land use allocation. Land Use Policy 12: 63-68. Canadian senate sub-Committee on Boreal Forest, 1999. Competing realities: The Boreal Forest at Risk. 35th Parliament of Canada ed. Report of the Standing Senate Committee on Agriculture and Forestry, Ottawa. http://www.parl.gc.ca/36/l/parlbus/commbus/senate/Come/bore-e/rep-e/rep09jun99-e.htm. Last accessed 2006.  Cote, M . (Editor), 2003. Dictionary of forestry. Special edition XII World Forestry Congress ed. Ordre des ingenieurs forestiers du Quebec, Ottawa.  144  Daust, D.K. and Nelson, J.D., 1993. Spatial Reduction Factors for Strata-Based Harvest Schedules. Forest Science 39: 152-165. Delong, S.C., Fall, S.A., and Sutherland, G.D., 2004. Estimating the impacts of harvest distribution on road-building and snag abundance. Canadian Journal of Forest Research 34: 323-331. Helm, J.A. 1998. The Dictionary of Forestry. Society of American Foresters, Bethesda. Hermann, R.K. and Lavender, D.P., 1999. Douglas-fir planted forests. New Forests 17/18: 53-70. Insley, M . , Fox, G., and Rollins, K . 2002. The Economics of Intensive Forest Management: A Stand Level Analysis for the Romeo Malette Forest in Ontario. A Report Prepared for Tembec Inc., the Ontario Ministry of Natural Resources, and U L E R N . Lautenschlager, R.A., 2000. Can intensive silviculture contribute to sustainable forest management in northern ecosystems. Forestry Chronicle 76: 283-295. NRCan, 2001. Forest 2020: A Budding Dialogue in Canada. In The state of Canada's Forests. Sustainable forestry: a reality in Canada. Government of Canada, Ottawa, pp. 74-76. Ohman, K. and Lamas, T., 2005. Reducing forest fragmentation in long-term forest planning by using the shape index. Forest Ecology and Management 212: 346-357.  O M N R , 1999. Ontario Forest Accord - A foundation for progress. Queen's Printer for Ontario, Toronto, ON.  145  Rose, S.K. and Chapman, D., 2003. Timber harvest adjacency economies, hunting, species protection, and old growth value: seeking the dynamic optimum. Ecological Economics 44: 325-344. Sedjo, R.A. and Botkin, D., 1997. Using forest plantations to spare natural forests. Environment 39: 14-20. Spatial Planning Systems, 2004. Patchworks Analysis of IFM options for the Romeo Malette Forest. http://www.forestresearch.ca/partnership_projects/spatial_analysis/RMF%20analysis.pdf. Accessed in 2006. Stewart, T.J., Janssen, R., and van Herwijnen, M . , 2004. A genetic algorithm approach to multiobjective land use planning. Computers and Operations Research 31: 2293-2313. Uhlig,P.A., Harris,G., Craig,C, Bowling,B., Chambers,B., Naylor,B., and Beemer,G. 2001. Old-growth forest definitions for Ontario. von Mirbach, M . 2001. Can intensive forestry help promote forest conservation? Sierra Club of Canada discussion paper, Ottawa, ON. Watt, W.R., Baker, J.A., Hogg, D . M . , McNicol, J.G., and Naylor, B.J. 1996. Forest Management Guidelines for the Provision of Marten Habitat. Version 1.0. MNR#50908. Whan, E., 2000. Thirty years of intensive forest management in Ontario. Available attextithttp://www.wildlandsleague.org/ifm.pdf, retrieved on August 8, 2002.  146  6  CONCLUDING C H A P T E R  6.1 Summary of results This thesis investigates what would be the desired characteristics of a planning support tool to meet the objectives of sustainable forest management. Since the current forest management paradigm strive to include a range of environmental, social and economic services beyond timber products, decision support tools have to address these other objectives and provide the decision maker with the information required to assess the environmental, social and economic sustainability of a forest management strategy. The main requirements for planning tools are: 1) Planning tools must address the management requirements for conservation and protected areas at multiple temporal and spatial scales. 2) Planning tools must be amenable to modifications of value systems and localized alterations resulting from interactions with various stakeholders in the planning process. 3) Planning tools must approach economic assessments of costs and benefits from a wider perspective than those provided by assuming fixed prices, fixed markets and a focus on timber products. The practical repercussion of these three requirements is that planning tools need to be able to accommodate spatial objectives and to provide an outlook of the forest under different management strategies and different - and changing - conditions over the planning horizon, accounting for natural processes such as succession, natural disturbances or climate change.  147  Although much progress has been made towards including spatial objectives in planning, particularly with the use of heuristics to generate solution plans (Nelson, 2003), spatial considerations are still difficult to formulate using traditional operations research methods (Baskent and Keles, 2005; Bettinger and Chung, 2004; Ohman, 2000). When dynamic processes such as changing market prices, changing value systems or natural disturbances are added to the picture, forest management planning tends to turn to hierarchical modeling and/or meta-modeling. In both cases, the challenge is to achieve a meaningful interaction between the processes and decisions happening at different scales. Efficiently linking the many processes requires commensurate interfaces between models/problems. To achieve this linkage, I propose to use a cellular automata-based approach (CA). C A models have proven successful at simulating and linking phenomena occurring at different scales (White and Engelen, 2000). C A models can easily address the modeling of dynamic spatial issues and could therefore model the evolution of forests through time|(Colasanti and Grime, 1993; Green, 1989; Hogeweg, 1988). However, C A modeling is a weak decision technique in that it is not goal-directed; it does not focus on the choice of a state that will lead to a given global result, rather, it focus on processes; results are the outcome produced by such processes. The user must change the model and run 'what-if experiments over and over again with the aim of reaching a predefined goal state, not knowing whether it can be attained anyway. This thesis develops a novel CA-based algorithm that extends the CA-based simulation models beyond 'what i f questions. This is done by allowing the C A cells to have foresight of their future conditions (states) under each management option before choosing one.  148  A forest planning approach based on cellular automata (CA) is proposed to address the problems of formulating spatial objectives and integrating between local events and higher level goals through time. This simulation technique can be used for forest planning purposes if the forest is represented as a grid; C A cells represent stands, C A states represent management schedules and transition rules are decision-making models. The neighborhood influencing the stand's decision is constituted of the eight adjacent stands. One rationale for using a C A approach is that spatial objectives are not only related to individual stands' characteristics, they are also a function of their spatial relationship to other stands. The C A based planning framework is a decentralized planning approach where each stand makes the decision concerning its own management. A plan that fulfills global objectives will be developed eventually if the stands' individual decisions benefit the forest as a whole. A novel iterative co-evolution of stand decisions is designed to achieve this purpose. To foster coevolution among local decisions and thereby achieve satisfying results at the global level, the CA-based algorithm uses a concept that finds its roots in spatial evolutionary game theory where the decisions of individual players are most influenced by players in close vicinity. A n asynchronous updating procedure is applied to allow stands to make decisions successively and to react to previous decisions made by their neighbors. Following this scheme, all stands interact and co-evolve a final solution plan. To illustrate the feasibility of a CA-based planning tools, a first problem consisting in maximizing a weighted sum of volume and old growth conservation measures over a planning horizon is defined and solved with the C A algorithm (Chapter 2). The old growth conservation measure is of particular interest in that it is based on both the old growth status of the stand and the proportion of the stand's neighborhood also in old growth in any given 149  time period. Basically clusters of old growth are more valuable than scattered old growth. The innovation of the approach proposed in Chapter 2 is that a CA-based model is used to solve a multi-period planning problem and successfully retain clusters of old growth forest in each planning period. This approach can further accommodate non-spatial, forest-wide constraints such as stable harvest flow and minimum retention of contiguous areas of old forests. Handling of global constraints in the decentralized CA-based model is done by including penalties and incentives in the local decision making function (Chapter 3). The penalties and incentives will encourage or discourage local level decisions that would contribute to a continuing violation of the global constraints. Not unlike dynamic or adaptive penalty functions used in standard centralized approaches, the penalties and incentives applying to the stand's decision function are periodically recalculated to reflect the landscape level of satisfaction with regard to global constraint. The model is applied to a small case study of about 4400 ha of forest divided in 9ha-cells. The objective is to maximize a linearized two-objective function involving old growth conservation and cumulative volume. The results show that this approach successfully achieves clustering of old growth in each planning period while meeting the harvest volume target. The same problem (involving clustering objectives and global constraints) is solved with a simulated annealing for comparison. The CA-based algorithm compared favorably. The decentralized planning approach described in Chapter 3 is particularly innovative in that it successfully satisfies global constraints in each planning period despite locally made decisions and further achieves old growth clusters rather than fragmented old growth within each planning period. 150  If forest planning tools are to address complex spatial and inter-temporal objectives and processes with both simulation and decision aspects, there needs to be adequate data support. A data interface where outputs of different models/processes are made commensurate and can then serve as inputs to other processes could facilitate interaction between interdependent processes. Already, there has been considerable progress made in achieving compatibility of data requirements between different models. Scheduling models have evolved to accommodate spatial issues with the integration of geographic information systems and decision tools. The relational database structure thus expanded can handle a number of spatial objectives and constraints involving topology (e.g., adjacency issues) or location (e.g., riparian management). However, this data representation presents a number of challenges in addressing spatial objectives based on complex spatial relationships (e.g., size and shape of harvest blocks and of conservation reserve), in efficiently retrieving information or in representing temporal data. A n object-based implementation of data, where each data element is represented by an object enclosing its own data attributes and associated methods, could be particularly useful to form the basis for a platform capable of integrating prescriptive and spatial modeling techniques. A n object-based implementation of the co-evolutionary C A model for forest planning involves forest stand objects with data members including current age, site quality, forest type and treatment (Chapter 4). Within the C A framework, methods encapsulated in the stand object are transition rules. In the implementation of a co-evolutionary C A model for forest planning, each forest stand is represented by an object that holds its state (treatment) as part of its data structure and is capable of changing the treatment upon execution of internal transition rules (decision function). When executing transition rules, the stands also use their  151  neighbors' states as inputs. Since the management area consists of both forested and nonforested areas (e.g., roads, rivers and lakes), the forest stand object is further distinguished from the area that supports it. The implementation of the C A models within an object-based framework is illustrated in Figure 6-1. This innovative framework has the advantage of being reusable, easily linked to GIS and other databases, and is portable to other problems, other resolutions and other planning algorithms. Another advantage of the object-orientation implementation is the streamlining of information retrieval: when a stand is considered for transition, only the relevant information is accessed. This reduces the computation time typical of complex conditional statements.  152  Heuristic p l a n n i n g algorithm ( START S  acquisition  )  input forMt L  ^Penalty parameter 14 -0, /.'. -0,  Aspatial information  _J_HHPWHS5'*  /  preparation  initial Form Plan P-  'iteration blocks k i K = Hh-hUhl.)  Spatial data (GIS)  1) Clarification of the problem structure - Identification of decision variables - Identification of decision parameters 2) Decision variables - identification of objectives - construction of weight matrix • decision process  -0 (/. i.i.Q  3) Acquisition of decision parameters - cost/price information - growth & yield information - old-growth definitions  Objects Oriented Implementation of CA F O R E S T STAND CLASSES  F O R E S T STAND O B J E C T CELL OBJECT  Schedule List Operabilily ranges Ol Schedule List Qperability ranges Ol+Schedule List Operabllity ranges Old growth threshold  DATA MEMBERS - Time penod - Iteration number - Vector of cells FUNCTION M6MBSRS - Advance time - Simulate natural disturbance - Identify a strategic plan: Heuristic planning algorithm - Calculate olobal performance  Figure 6-1 Object oriented computer implementation of the CA-based evolutionary planning algorithm  The C A methodology and its object-oriented implementation are used to evaluate the potential of intensive silviculture and clustering of harvesting activities to generate financial revenues and meet management constraint on volume flow and old growth retention. A number of local constraints are also included, such as the creation of riparian and lake buffers and management limitations around recreational and residential areas and sensitive wildlife habitats. Although the results do not enable a generalized statement regarding the value of intensive silviculture, they do point to the importance of the initial inventory and the economic environment within which forest management takes place (Chapter 5). In the case study, there were no volume or value gains when intensive silviculture is practiced. Intensive silviculture actually decreases overall financial revenues. However, the practice of intensive silviculture results in meeting the harvest flow targets from a smaller area being harvested. This presents an advantage that may prove more important than the increased associated management costs. Such would be the case if harvest costs were to increase, i f conservation requirements were considered beyond those of old growth retention or if the initial inventory did not permit meeting timber flow targets under conventional management practices. The initial amount of natural and old growth forest in the case study is very large and protection requirements are not limited to timber harvest activities: the main trade off is between volume and net present value. Constraints on the volume flow were met but systematically hit the lower bound. In this context, clustering harvest activities increased the net present value. The decentralized methodology fosters such aggregation but does not lead to 'cancerous' growth of harvest blocks since both the initial inventory and the potential with regard to other objectives may detract from timber operations. Clustering of both protected areas and harvest operations therefore could better achieve both the conservation and the  154  timber objective by improving the habitat value of conserved areas and decreasing operation costs of harvested areas. The level to which the model encourages clustering of either harvest operations or conservation areas needs to be identified on a regional basis to best fit the local processes and disturbances.  6.2  Conclusion  The CA-based planning methodology proposed in this thesis is capable of handling traditional management objectives such as harvest volume, net present value and old growth retention. In addition, it is capable of successfully clustering conservation areas and harvest activities, which further enhance the value of the final plan by generating economies of scale and limiting forest fragmentation. The planning methodology handles local constraints related to inventory limitations and limitations on the type of management that can be undertaken in sensitive areas (riparian buffers, proximity to recreational and residential areas, sensitive wildlife habitat). A l l constraints and objectives, spatial and aspatial, are traded off not only within one planning period but across all periods of the planning horizon. The research presented in this thesis thus not only contributes to the body of research on cellular automata but also to the field of forestry operations research. The object-oriented data support for the implementation of the planning model has the advantage of avoiding the need to access information not directly relevant to the procedure being called. The re-usable property of the object-oriented framework provides easy transfer of the planning model to different planning problems and geographic conditions (inventory,  155  spatial and temporal resolutions, etc.). This aspect of the thesis research constitutes a tangible contribution to the field of geographic information science.  6.3 Future Research Although the application is limited to evaluating net present value, old growth, volume, stand specific management potential and limitations, it could easily be modified to include such processes as aging and succession. Further modifications could consist of varying the weights of each objective in different planning periods, or changing timber prices and management costs along the planning horizon. These additions would be a significant step toward acknowledging and planning for the dynamic environment in which forest management is to operate. The object-oriented framework could also support the design of harvest blocks or reserves that fit some shape requirements or some specific distribution (e.g., natural disturbance emulation in harvest openings). Including natural disturbances and designing management strategies that are robust in the face of unforeseen events is a further area of improvement for the framework presented in this thesis. The evolution of the forest landscape can be simulated by cycling through time periods, aging the landscape, implementing succession and coupling this evolution with a natural disturbances model. C A platforms have been successfully used to simulate fire and its spread; they have also been used to simulate the progression of insect outbreaks. These models could easily be integrated here to provide more realistic pictures of future forests. The CA-based planning algorithm could be called again at later time periods to evaluate the capacity of the then forest landscape to fulfill management objectives. A tool thus built could  156  provide a useful decision support aid when a forest landscape is considered high risk with respect to frequent fire regime, flood, or pest problems among others. The CA-based planning framework is a heuristic/simulation and its main purpose is to serve as a thinking tool, to help decision makers learn about the nature and dynamic behaviour of the real forest system and to find out how it is critically bounded, rather than to make definite statements about the future state of the system being modeled. The main premise of this thesis is that the environment in which forest management decisions are made changes over time; also, management of the forest adjusts to the new value system. B y exploring how the explicit consideration of these changes can affect the management process and its outcomes, it can limit the amount of uncertainty associated with decisions undertaken now. This study does not aim at determining what the right mix of different forest uses is. Rather, its focus lies in examining the impact of considering values as changing parameters in a general planning exercise. To date, strategic management planning techniques, whether simulation or optimization, have evolved to accommodate new needs and desires, but they are seldom designed to anticipate the changes in the objectives of forestry through time. Simulation methods seem to provide more opportunities than optimization techniques to analyze land allocation strategies when assumptions such as static discounting rate or static value system (e.g., static preference for recreation services) are removed. In the context of land-use allocations that segregate land uses, I propose to explore the flexibility/adaptability of strategic planning when the value system changes throughout the planning horizon. Value system would encompass natural and socio-economic values associated with different goods, services and environmental assets from the forest. 157  6.4  References  Baskent, E.Z. and Keles, S., 2005. Spatial forest planning: A review. Ecological Modelling 188: 145-173.  Bettinger, P. and Chung, W., 2004. The key literature of, and trends in, forest-level management planning in North America, 1950-2001. International Forestry Review 6: 40-50. Colasanti, R.L. and Grime, J.P., 1993. Resource Dynamics and Vegetation Processes - A Deterministic Model Using 2-Dimensional Cellular Automata. Functional Ecology 7: 169176. Green, D.G., 1989. Simulated Effects of Fire, Dispersal and Spatial Pattern on Competition Within Forest Mosaics. Vegetatio 82: 139-153. Hogeweg, P., 1988. Cellular Automata as paradigm for ecological modelling. Applied mathematics and computation 27: 81-100.  Nelson, J.D., 2003. Forest-level models and challenges for their successful application. Canadian Journal of Forest Research 33: 422-429.  Ohman, K., 2000. Creating continuous areas of old forest in long-term forest planning. Canadian Journal of Forest Research 30: 1817-1823.  White, R. and Engelen, G., 1997. Cellular automata as the basis of integrated dynamic regional modelling. Environment and Planning B-Planning & Design 24: 235-246.  158  White, R. and Engelen, G., 2000. High resolution integrated modelling of the spatial dynamics of urban and regional systems. Computers, Environment, and Urban Systems, 383-400.  

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