Growth and yield models for uneven-aged stands: past, present and future

Abstract Growth and yield modeling has a long history in forestry. Methods of measuring the growth of uneven-aged forest stands have evolved from those developed in France and Switzerland during the last century. Furthermore, uneven-aged growth and yield modeling has progressed rapidly since the first models were pioneered by Moser and Hall (1969) (Moser Jr., J.W., Hall, O.F., 1969. For. Sci. 15, 183–188). Over the years, a variety of models have been developed for predicting the growth and yield of uneven-aged stands using both individual and stand-level approaches. Modeling methodology not only has moved from an empirical approach to a more ecological process-based mechanistic approach, but also has incorporated a variety of techniques, such as, (1) systems of equations, (2) nonlinear stand table projections, (3) Markov chains, (4) matrix models, and (5) artificial neural network models. However, modeling the growth and yield of uneven-aged stands has received much less attention than that of even-aged stands. This paper reviews the current literature regarding growth and yield models for uneven-aged stands, discusses basic types of models and their merits, and reports recent progress in modeling the growth and dynamics of uneven-aged stands. Furthermore, future trends involving integration of new computer technologies (object-oriented programming and user-friendly interfaces), tree visualization techniques, and the spatially explicit application of Geographical Information Systems (GIS) into uneven-aged modeling strategies are discussed.

[1]  Joseph Buongiorno,et al.  Long- and short-term effects of alternative cutting regimes on economic returns and ecological diversity in mixed-species forests , 1993 .

[2]  Guy Eddon,et al.  Active Visual Basic 5.0 , 1997 .

[3]  R. Monserud,et al.  A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria , 1996 .

[4]  W. Leak.  Long-term structural change in uneven-aged northern hardwoods , 1996 .

[5]  M. Apps,et al.  Boreal forest responses to climate-change scenarios along an ecoclimatic transect in central Canada , 1996 .

[6]  W. Post,et al.  Influence of climate, soil moisture, and succession on forest carbon and nitrogen cycles , 1986 .

[7]  J. Aber,et al.  Predicting the effects of different harvesting regimes on productivity and yield in northern hardwoods , 1979 .

[8]  Jari Miina,et al.  Optimizing thinning and rotation in a stand of Pinus sylvestris on a drained peatland site , 1996 .

[9]  R. Hüttl,et al.  Nutrient Uptake and Cycling in Forest Ecosystems , 1995, Developments in Plant and Soil Sciences.

[10]  H. Gholz.  Applications of Physiological Ecology to Forest Management , 1997 .

[11]  K. J. Mitchell,et al.  Dynamics and Simulated Yieldof Douglas-fir , 1975 .

[12]  John S. Kush,et al.  Crown and basal area relationships of open-grown southern pines for modeling competition and growth , 1992 .

[13]  John W. Moser,et al.  A Generalized Framework for Projecting Forest Yield and Stand Structure Using Diameter Distributions , 1983 .

[14]  Joe Landsberg,et al.  Physiological ecology of forest production , 1986 .

[15]  Jari Perttunen,et al.  LIGNUM: a model combining the structure and the functioning of trees , 1998 .

[16]  Daniel B. Botkin,et al.  Predicting the effects of different harvesting regimes on forest floor dynamics in northern hardwoods , 1978 .

[17]  S. Running,et al.  A general model of forest ecosystem processes for regional applications I. Hydrologic balance, canopy gas exchange and primary production processes , 1988 .

[18]  J. L. Clutter.  Compatible growth and yield models for loblolly pine , 1963 .

[19]  Guillermo A. Mendoza,et al.  A transition matrix forest growth model for evaluating alternative harvesting schemes in Indonesia , 1986 .

[20]  K. Skog,et al.  Growth model for uneven-aged loblolly pine stands : simulations and management implications , 1998 .

[21]  R. D. Nyland,et al.  Effects of diameter distribution on the growth of simulated uneven-aged sugar maple stands , 1987 .

[22]  James P. Kimmins,et al.  The use of soil organic matter as a criterion of the relative sustainability of forest management alternatives: a modelling approach using FORECAST , 1997 .

[23]  Timo Pukkala,et al.  Effect of spatial pattern of trees on the growth of Norway spruce stand. , 1991 .

[24]  Steven W. Running,et al.  Incorporating intertree competition into an ecosystem model , 1995 .

[25]  J. P. Kimmins.  Modelling the Sustainability of Forest Production and Yield for a Changing and Uncertain Future , 1990 .

[26]  J. Overpeck,et al.  Potential Magnitude of Future Vegetation Change in Eastern North America: Comparisons with the Past , 1991, Science.

[27]  R. Nisbet,et al.  Kirtland's Warbler Habitats: A Possible Early Indicator of Climatic Warming , 1991 .

[28]  William B. Leak,et al.  An Expression of Diameter Distribution for Unbalanced, Uneven-Aged Stands and Forests , 1964 .

[29]  Thomas M. Smith,et al.  A review of forest patch models and their application to global change research , 1996 .

[30]  J. W. Moser,et al.  Deriving Growth and Yield Functions for Uneven-Aged Forest Stands , 1969 .

[31]  H. Burkhart,et al.  Compatible cubic volume and basal area projection equations for thinned old-field loblolly pine plantations , 1984 .

[32]  J. P. Kimmins,et al.  Simulation of mixedwood management of aspen and white spruce in northeastern British Columbia , 1995 .

[33]  Gregory S. Biging,et al.  Evaluation of Competition Indices in Individual Tree Growth Models , 1995, Forest Science.

[34]  Steven W. Running,et al.  Numerical Terradynamic Simulation Group 4-1993 A Physiology-Based Gap Model of Forest Dynamics , 2017 .

[35]  Matthias Dobbertin,et al.  A Comparison of Distance-Dependent Competition Measures for Height and Basal Area Growth of Individual Conifer Trees , 1992, Forest Science.

[36]  Taneli Kolström,et al.  Modelling the development of an uneven‐aged stand of Picea abies , 1993 .

[37]  Jeffrey L. Moffett,et al.  Landscape management through integration of existing tools and emerging technologies , 1998 .

[38]  Wolfgang Cramer,et al.  A simulation model for the transient effects of climate change on forest landscapes , 1993 .

[39]  Richard M. Teck,et al.  Individual tree-diameter growth model for the Northeastern United States , 1991 .

[40]  Hartmut Bossel,et al.  treedyn3 forest simulation model , 1996 .

[41]  Ian J. Bateman,et al.  Using geographical information systems (GIS) and large area databases to predict Yield Class: a study of Sitka spruce in Wales , 1998 .

[42]  Harald Bugmann,et al.  The use of a European forest model in North America: a study of ecosystem response to climate gradients , 1995 .

[43]  R. Muetzelfeldt,et al.  THE SYMFOR TROPICAL FOREST MODELLING FRAMEWORK , 1998 .

[44]  F. H. Eyre,et al.  Partial Cuttings in Northern Hardwoods of the Lake States: Twenty-Year Experimental Results , 1953 .

[45]  H. Hasenauer,et al.  Predicting juvenile tree height growth in uneven-aged mixed species stands in Austria , 1997 .

[46]  T. Pukkala,et al.  A spatial yield model for optimizing the thinning regime of mixed stands of Pinus sylvestris and Picea abies , 1998 .

[47]  Hanif D. Sherali,et al.  Estimating Optimal Thinning and Rotation for Mixed-Species Timber Stands Using a Random Search Algorithm , 1985 .

[48]  Robert A. Monserud,et al.  Applicability of the forest stand growth simulator PROGNAUS for the Austrian part of the Bohemian Massif , 1997 .

[49]  George Z. Gertner,et al.  Using a Parallel Distributed Processing System to Model Individual Tree Mortality , 1991 .

[50]  P. A. Murphy,et al.  Interim Models for Basal Area and Volume Projection of Uneven-Aged Loblolly-Shortleaf Pine Stands , 1982 .

[51]  D. Carlsson.  Optimisation of even-age stand management with an emphasis on mixed stands , 1995 .

[52]  Jouni Vettenranta,et al.  Distance-dependent Models for Predicting the Development of Mixed Coniferous Forests in Finland , 1999 .

[53]  Growth-and-yield model for uneven-aged Cedrus atlantica stands in Morocco. , 1990 .

[54]  David A. MacLean,et al.  Computer Corner: Forester's Yield Curve Designer Software , 1998 .

[55]  H. Shugart.  A Theory of Forest Dynamics , 1984 .

[56]  A. Ek.  Nonlinear Models for Stand Table Projection in Northern Hardwood Stands , 1974 .

[57]  R. Reynolds,et al.  The Crossett Story: The Beginning of Forestry in Southern Arkansas and Northern Louisiana , 1980 .

[58]  Simulation of the development of Norway spruce stands using a transition matrix , 1988 .

[59]  Alan R. Ek,et al.  Forest growth modelling and prediction , 1988 .

[60]  Nancy R. Walters,et al.  A guide to the TWIGS program for the North Central United States. , 1988 .

[61]  K. O’Hara.  Dynamics and Stocking-Level Relationships of Multi-Aged Ponderosa Pine Stands , 1996 .

[62]  Thomas M. Smith,et al.  The potential for application of individual-based simulation models for assessing the effects of global change , 1992 .

[63]  A. R. Stage,et al.  User's guide to the Parallel Processing Extension of the Prognosis Model , 1991 .

[64]  J. J. Jansen,et al.  Contrasts between biologically-based proces models and management-oriented growth and yield models. , 1994 .

[65]  J. R. Wallis,et al.  Some ecological consequences of a computer model of forest growth , 1972 .

[66]  D. C. West,et al.  Forest Succession Models , 1980 .

[67]  T. Penttilä,et al.  Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. , 1997 .

[68]  Melinda Moeur,et al.  Spatial models of competition and gap dynamics in old-growth Tsuga heterophylla/Thuja plicata forests , 1997 .

[69]  Nicholas L. Crookston,et al.  User's guide to the western spruce budworm modeling system , 1990 .

[70]  Jerome K. Vanclay,et al.  Modelling Forest Growth and Yield: Applications to Mixed Tropical Forests , 1994 .

[71]  B. Turner,et al.  Growth and yield modelling of Australian eucalypt forests I. Historical development , 1990 .

[72]  A. Solomon,et al.  Past and future climate change: response by mixed deciduous–coniferous forest ecosystems in northern Michigan , 1992 .

[73]  D. M. Adams,et al.  A note on the interdependence of stand structure and best stocking in a selection forest , 1976 .

[74]  R. Buckman.  Growth and Yield of Red Pine in Minnesota , 1962 .

[75]  John D. Aber,et al.  Predicting the Effects of Rotation Length, Harvest Intensity, and Fertilization on Fiber Yield From Northern Hardwood Forests in New England , 1982 .

[76]  Jari Miina,et al.  Optimizing thinnings and rotation of Scots pine and Norway spruce mixtures , 1999 .

[77]  J. P. Roise,et al.  An Approach for Optimizing Residual Diameter Class Distributions When Thinning Even-Aged Stands , 1986 .

[78]  J. H. Smith,et al.  DEVELOPMENT AND TESTING OF STAND MODELS FOR DOUGLAS FIR AND LODGEPOLE PINE , 1964 .

[79]  I. Bella,et al.  A New Competition Model for Individual Trees , 1971 .

[80]  S. Pacala,et al.  Forest models defined by field measurements: I. The design of a northeastern forest simulator , 1993 .

[81]  K. Rennolls,et al.  Timber Management-A Quantitative Approach. , 1984 .

[82]  R. K. Dixon,et al.  Process modeling of forest growth responses to environmental stress , 1991 .

[83]  J. P. Kimmins.  Forest Ecology: A Foundation for Sustainable Management , 1996 .

[84]  G. Gertner,et al.  Modeling red pine tree survival with an artificial neural network , 1991 .

[85]  Timo Pukkala,et al.  Tree-selection algorithms for optimizing thinning using a distance-dependent growth model , 1998 .

[86]  Richard F. Daniels,et al.  A comparison of competition measures for predicting growth of loblolly pine trees , 1986 .

[87]  J. Gove,et al.  Optimizing the management of uneven-aged forest stands : a stochastic approach , 1992 .

[88]  Ralph L. Amateis.  An approach to developing process-oriented growth and yield models , 1994 .

[89]  Harold E. Burkhart,et al.  A Growth and Yield Model for Thinned Stands of Yellow-Poplar , 1986 .

[90]  B. Solberg,et al.  Analysis of optimal economic management regimes for Picea abies stands using a stage‐structured optimal‐control model , 1991 .

[91]  Changhui Peng,et al.  Simulating effects of climate change on boreal ecosystem carbon pools in central Canada , 1999 .

[92]  P. A. Murphy,et al.  Growth and Yield of Uneven-Aged Shortleaf Pine Stands in the Interior Highlands , 1985 .

[93]  D. Botkin.  Forest Dynamics: An Ecological Model , 1993 .

[94]  Andrew D. Friend,et al.  A process-based, terrestrial biosphere model of ecosystem dynamics (Hybrid v3.0) , 1997 .

[95]  H. Arthur Meyer,et al.  Structure, Growth, and Drain in Balanced Uneven-Aged Forests , 1952 .

[96]  Juli G. Pausas,et al.  A FOREST SIMULATION MODEL FOR PREDICTING EUCALYPT DYNAMICS AND HABITAT QUALITY FOR ARBOREAL MARSUPIALS , 1997 .

[97]  Alan R. Ek,et al.  Optimizing the Management of Uneven-aged Forest Stands , 1974 .

[98]  T. Pukkala.  Prediction of tree diameter and height in a Scots pine stand as a function of the spatial pattern of trees. , 1989 .

[99]  Nicholas L. Crookston,et al.  User's guide to the stand prognosis model / , 1982 .

[100]  S. Running,et al.  FOREST-BGC, A general model of forest ecosystem processes for regional applications. II. Dynamic carbon allocation and nitrogen budgets. , 1991, Tree physiology.

[101]  David R. Larsen,et al.  Diameter growth equations for fourteen tree species in Southwest Oregon , 1991 .

[102]  S. Levin,et al.  Mathematical and Computational Challenges in Population Biology and Ecosystems Science , 1997, Science.

[103]  Usda Fs,et al.  A generalized forest growth projection system applied to the Lake States region. , 1979 .

[104]  Jerome K. Vanclay,et al.  Growth models for tropical forests: a synthesis of models and methods , 1995 .

[105]  Jianguo Liu,et al.  ECOLECON: An ECOLogical-ECONomic model for species conservation in complex forest landscapes , 1993 .

[106]  H. K. Koesmarno,et al.  OFSIM: A simulation shell for forest management , 1997 .

[107]  John Pastor,et al.  Response of northern forests to CO2-induced climate change , 1988, Nature.

[108]  H. Shugart.  A Theory of Forest Dynamics , 1984 .

[109]  J. Buongiorno,et al.  Modeling forest growth with management data: A matrix approach for the Italian Alps. , 1997 .

[110]  J. D. Brodie,et al.  A Comparison of the Pattern Search Algorithm and the Modified PATH Algorithm for Optimizing an Individual Tree Model , 1990, Forest Science.

[111]  Joseph Buongiorno,et al.  A matrix model of uneven-aged forest management. , 1980 .

[112]  D. Alder.  A Distance-Independent Tree Model for Exotic Conifer Plantations in East Africa , 1979 .

[113]  V. Favrichon,et al.  Modeling the dynamics and species composition of a tropical mixed-species uneven-aged natural forest : Effects of alternative cutting regimes , 1998 .

[114]  H. Bruner,et al.  A Markov Chain Approach to the Prediction of Diameter Distributions in Uneven-aged Forest Stands , 1973 .

[115]  E. W. Jones,et al.  Planning and Control in the Managed Forest. , 1955 .

[116]  Marc Jaeger,et al.  Plant models faithful to botanical structure and development , 1988, SIGGRAPH.

[117]  S. Levin,et al.  Scaling from Trees to Forests: Analysis of a Complex Simulation Model , 1997 .

[118]  Stephen R. Shifley,et al.  A generalized system of models forecasting Central States tree growth. , 1987 .

[119]  Hubert Hasenauer,et al.  Biased predictions for tree height increment models developed from smoothed ‘data’ , 1997 .

[120]  Mathew Williams,et al.  A three-dimensional model of forest development and competition , 1996 .

[121]  John W. Moser,et al.  Dynamics of an Uneven-Aged Forest Stand , 1972 .

[122]  B. Bruce Bare,et al.  Optimizing Species Composition in Uneven-Aged Forest Stands , 1987, Forest Science.

[123]  A. Groot,et al.  An individual-tree basal area growth model for black spruce in second-growth peatland stands , 1999 .

[124]  R. Waring,et al.  A generalised model of forest productivity using simplified concepts of radiation-use efficiency, carbon balance and partitioning , 1997 .

[125]  Hartmut Bossel,et al.  Generic simulation model of forest growth, carbon and nitrogen dynamics, and application to tropical acacia and european spruce , 1989 .

[126]  Robert J. McGaughey,et al.  TECHNIQUES FOR VISUALIZING THE APPEARANCE OF FORESTRY OPERATIONS , 1998 .

[127]  Y. Vuokila.  Functions for variable density yield tables of pine based on temporary sample plots. , 1965 .

[128]  Steven W. Running,et al.  Testing a Mechanistic Model for Predicting Stand and Tree Growth , 1996 .

[129]  J. Kush,et al.  Basal Area Growth of Individual Trees: A Model Derived from a Regional Longleaf Pine Growth Study , 1994 .

[130]  Dale S. Solomon,et al.  A two-stage matrix model for predicting growth of forest stands in the Northeast , 1986 .

[131]  L. Frelich,et al.  A Simulation of Equilibrium Diameter Distributions of Sugar Maple (Acer saccharum) , 1984 .

[132]  P. West.  Use of diameter increment and basal area increment in tree growth studies. , 1980 .

[133]  Robert G. Haight,et al.  Optimizing any-aged management of mixed-species stands. I, Performance of a coordinate-search process , 1990 .

[134]  Changhui Peng,et al.  Modelling the net primary productivity of temperate forest ecosystems in China with a GAP model , 1999 .

[135]  J. P. Kimmins.  Scientific foundations for the simulation of ecosystem function and managment in FORCYTE-11 , 1993 .

[136]  Bryan R. Pearce,et al.  A C++ implementation of an individual/landscape model , 1997 .

[137]  Gary J. Brand,et al.  A description of STEMS-- the stand and tree evaluation and modeling system. , 1982 .

[138]  Michael Battaglia,et al.  Process-based forest productivity models and their application in forest management , 1998 .

[139]  L. Valsta,et al.  A Scenario Approach to Stochastic Anticipatory Optimization in Stand Management , 1992, Forest Science.

[140]  Marja Kolström,et al.  Ecological simulation model for studying diversity of stand structure in boreal forests , 1998 .

[141]  F. Houllier,et al.  Growth and management of mixed-species, uneven-aged forests in the French Jura : implications for economic returns and tree diversity , 1995 .

[142]  William R. Wykoff,et al.  A Basal Area Increment Model for Individual Conifers in the Northern Rocky Mountains , 1990, Forest Science.

[143]  Jari Perttunen,et al.  LIGNUM: A Tree Model Based on Simple Structural Units , 1996 .

[144]  L. Valsta,et al.  An optimization model for Norway spruce management based on individual-tree growth models. , 1992 .

[145]  David A. Herman,et al.  Fiber 3.0: An ecological growth model for northeastern forest types. Forest Service general technical report (Final) , 1995 .

[146]  Paul A. Murphy,et al.  Uneven-Aged Silviculture for the Loblolly and Shortleaf Pine Forest Cover Types , 1996 .

[147]  Robert A. Monserud,et al.  Height Growth and Site Index Curves for Inland Douglas-fir Based on Stem Analysis Data and Forest Habitat Type , 1984 .

[148]  P. Lemmon,et al.  Volume and Diameter Growth of Ponderosa Pine Trees as Influenced by Site Index, Density, Age, and Size , 1962 .

[149]  G. Z. Gertner,et al.  Modeling individual tree survival probability with a random optimization procedure: an artificial neural network approach , 1995 .

[150]  Robert G. Haight,et al.  Optimizing Any-Aged Management of Mixed-Species Stands: II. Effects of Decision Criteria , 1990, Forest Science.

[151]  William R. Wykoff,et al.  Supplement to The User's Guide for The Stand Prognosis Model-version 5.0 , 1986 .