Unsuspected implications arising from assumptions in simulations: insights from recasting a forest growth model in system dynamics
© Vanclay; licensee Springer. 2014
Received: 30 July 2013
Accepted: 29 October 2013
Published: 26 February 2014
Familiarity with a simulation platform can seduce modellers into accepting untested assumptions for convenience of implementation. These assumptions may have consequences greater than commonly suspected, and it is important that modellers remain mindful of assumptions and remain diligent with sensitivity testing.
Familiarity with a technique can lead to complacency, and alternative approaches and software can reveal untested assumptions. Visual modelling environments based on system dynamics may help to make critical assumptions more evident by offering an accessible visual overview and empowering a focus on representational rather than computational efficiency. This capacity is illustrated using a cohort-based forest growth model developed for mixed species forest.
The alternative model implementation revealed that untested assumptions in the original model could have substantial influence on simulated outcomes.
An important implication is that modellers should remain conscious of all assumptions, consider alternative implementations that reveal assumptions more clearly, and conduct sensitivity tests to inform decisions.
KeywordsForest growth model Validity of assumptions Visual modelling environment Fortran Simile System dynamics Swindle
Modellers generally try to implement ecological concepts faithfully and completely, but there is inevitably a tendency for model implementation to be influenced by technology, both hardware and software. This tendency is often subtle, with small artefacts introduced into a simulator with little discussion, deemed prudent to achieve efficiency or expediency. Whilst modelling, like management, is usually a compromise to deliver timely and useful results, the danger of technological limitations is that they are often subtle, understated and untested. A search of the literature suggests that authors are more likely to discuss compromises made because of data limitations than those introduced because of software limitations, perhaps because of the ease of applying a familiar approach (i.e., a ‘golden hammer’, Brown et al.,1998). This is somewhat worrisome, because minor compromises introduced for convenience in implementation may introduce substantial and unsuspected effects into simulated predictions. Where such consequences are suspected, they may be remedied during model evaluation, but two dangers remain: firstly that many modellers do not suspect the extent to which their chosen software influences their implementation or the magnitude of the consequences that may arise; and as a result they tend not to discuss these assumptions in simulator documentation. Discussions informing this paper suggest that many modellers discount and dismiss these dangers and their consequences too readily, despite empirical evidence of their importance. This paper seeks to alert modellers to these dangers and to encourage greater reporting of assumptions and compromises in both model design and in their implementation in simulators (sensu Pretzsch et al 2002).
This paper explores some aspects of compromises made during the implementation of a simulator, drawing on a published growth model for north Queensland rainforests (Vanclay, 1989a). The most-widely used version of this simulator was written in standard Fortran-77 and executed under Unix on a Vax 11-780 computer system, a platform relatively free of limitations and well understood by many modellers. This simulator was not naïve implementation, but was a deliberate decision informed by familiarity with Wirth’s (1985) work on the importance of data structures, by knowledge of diverse programming languages (e.g., Fortran, Pascal, Simula, and Simscript), by feedback received through earlier publication of several forest growth models, and by familiarity with other modelling approaches (Vanclay, 1983). The model was widely emulated (e.g., Ong and Kleine, 1996; Alder and Silva, 2000), and was instrumental in informing changes in forest management (Preston and Vanclay, 1988; Vanclay, 1996a). But a re-evaluation of the simulator as part of an undergraduate teaching program has revealed that some untested assumptions implicit in the Fortran implementation become more evident when the model is implemented in other platforms. This paper draws attention to two issues important in modelling: the need for critical review of assumptions implicit in model implementation, and the utility of considering alternative formulations to encourage explicit recognition of such assumptions.
Early models in the form of alignment charts (e.g., Reineke, 1927) were transparent in their application, if not their development, but the advent of statistical and computer-based models (e.g., Buckman, 1962; Clutter, 1963) commenced a subtle trend of incomplete disclosure of simulator details in published documentation. Whilst this is generally not deliberate, text-based publication of component functional relationships is rarely sufficient to reproduce a simulator (Robinson and Monserud, 2003), because many details intimate to a particular implementation may affect predictions (Villa et al., 2009). Guidelines (e.g., Pretzsch et al.,2002) have improved the standard of documentation, but there are limits on the extent to which text-based descriptions can adequately and efficiently describe computer-based implementations. Visual ‘icon-based’ modelling environments, typically based on system dynamics, can help to reveal model structure and reduce the ‘black box’ syndrome (Smith et al., 2005). One key advantage of these visual modelling environments is that the diagram is both the model and the simulator, unlike some early applications where system dynamics flowchart was merely documentation about the model (e.g., Kalgraf 1979). Unfortunately, the potential of these new tools for model design and simulator function has received little attention. Researchers have investigated how simulation results may depend on the functional form of tree growth equations (e.g., Elkin et al., 2012), but have not adequately addressed how simulators may also depend on host software used to implement the model. It is surprising that these potential dependencies have not been researched, because several popular modelling platforms have different unique features. For instance, Stella (Doerr, 1996; Eskrootchi and Oskrochi, 2010) has a conveyor-stock that handles time-lags efficiently (e.g., Blackwell et al., 2001), whilst Simile (Muetzelfeldt and Massheder, 2003; Muetzelfeldt, 2010) offers multiple-instance submodels that facilitate individual-based modelling, so it seems likely that these features may influence the implementation of models on respective platforms.
Vanclay’s (1989a) model for simulating growth and yield of tropical rainforest is widely cited and has provided the inspiration for several other forest growth simulators still in use today (e.g., Ong and Kleine, 1996; Alder and Silva, 2000), but the traditional journal article presentation of this model remains silent about some key details concerning the design and implementation of this simulator. Although this model has been superseded (Vanclay, 1994a), it retains considerable utility for teaching because of its relative simplicity. An alternative implementation of this simulator using the visual modelling environment Simile is revealing, informative and more pedagogic than the original Fortran code and journal article. Although visual system-dynamics modelling tools have been available and used increasingly for over two decades (Bossel, 1991; Doerr, 1996; Garcia, 2013), their role in informing and sharing information remains underutilized. This paper discusses new insights offered through the Simile presentation of this model, and refutes the assertion (Dufour-Kowalski et al.,2012) that visual modelling environments such as Simile are not well suited for forest growth modelling.
The best way to share information about a model is to share the simulator itself, in a form that is open-source and implemented in a generic easily-understood way. However, many useful computer languages are accessible only to a small number of practitioners, and important details of simulators coded in these languages may be hidden like the proverbial ‘needle in a haystack’ (Muetzelfeldt, 2004; Villa et al.,2009). Thus there is limited benefit in sharing proprietary computer code, unless the simulator is well documented and the language widely utilized and freely available. These hidden aspects of computer-based simulators may well be a ‘skeleton in the closet’: many experienced modellers have anecdotes about the importance of untested ‘calibration factors’ or about unintended consequences of particular data structures (e.g., Hamilton, 1994), but these are rarely documented in the formal literature, allowing these oversights to be perpetuated.
Muetzelfeldt’s interest in dynamic representation of ecological relationships (e.g., Muetzelfeldt et al.,1989) led to the development of Simile, a visual modelling environment useful for modelling ecological and agricultural systems (Muetzelfeldt and Taylor, 1997; Muetzelfeldt and Massheder, 2003). Simile employs a declarative modelling approach and saves models as structured text files, able to be processed by other software (Muetzelfeldt, 2004). It offers several constructs useful for modelling plant growth and related concepts (Prabhu et al.,2003; Vanclay, 2006a), as well as more abstract issues (e.g., Haggith et al.,2003). Thus Simile provides an interesting vehicle to illuminate, compare and share existing models (Davey et al.,2009). Simile is not unique in this ability, and Vensim is an alternative that has been used to implement forest growth simulators (e.g., Garcia and Ruiz, 2003).
Rainforests provide an informative case study because many of their characteristics pose challenges in modelling: the large number of species, the wide range of stem sizes and growth patterns, and the paucity of calibration data all amplify inherent challenges (Vanclay, 1991d; Clark and Clark, 1999; Picard and Franc, 2003). Vanclay’s (1989a) model for Queensland rainforests is a frequently cited example, and illustrates several insights that may be gained by recasting a simulator from its original Fortran into a visual system dynamics representation.
Recasting the model in simile
The elements of Figure 1 represent the key information needed for individual-based modelling of forests (Weiskittel et al.,2011). These data may be read from file by the growth model, with each input record forming one of many tree records or cohorts in the model, a technique used widely in forest growth modelling (Vanclay, 1994b; Porte and Bartelink, 2002). These cohorts retain the species identity, and progressively increase tree size to reflect growth, and reduce stocking to reflect mortality.
Figure 1 is not merely a diagram, but when created in Simile, is the simulator that runs and creates simulated outputs. One of the strengths of Simile is that the user interface simultaneously creates a diagrammatic overview, the executable code, and model documentation (a ‘mouseover’ displays any comment included with each symbol).
A reviewer asked whether the migration symbol ( ) could be changed from a bird to an icon that better represents tree dynamics: it can be, but such customization does not facilitate communication. To take an example from Microsoft: a user may not like the scissors icon used to denote ‘cut’ in Microsoft software, but everyone understands what this icon denotes, and shared understanding should take precedence over personal aesthetics.
Figure 4 shows the major part of the Simile implementation of Vanclay’s (1989a) model. The ba submodel at top left simply tabulates the basal area and volume per tree by size class and by species; it provides a collation role and serves no functional purpose. The series of variables at top right extract the relevant species-specific parameters for use in other functions. Four symbols at bottom right influence the number of records in the tree list, creating the initial number ( ), adding recruitment ( ), splitting records ( ), and removing redundant records ( ) when they represent an infinitesimal stocking. The key functional components of this submodel lie within the Size and Stems submodels which estimate diameter increment and mortality respectively. Between these are two variables, rate and split, that deal with serial correlation of increments and record splitting respectively. When a large cohort is split into two smaller cohorts with faster and slower than average growth, rate maintains this growth difference to preserve the serial correlation specified by the user.
This alterative way to process recruitment illustrates one of the benefits of recasting models: advances in computer technology have created more revealing ways to represent concepts, and pose fewer restrictions on computational resources, allowing modellers to focus on good representations rather than computational efficiency (Vanclay, 2003). The challenge is for modellers to break free of old paradigms and fully exploit these new opportunities, and not merely follow a well-trodden path without question. Leary (1985, p.47), commenting on a related matter, warned that “what began as an interim solution (site index) to a difficult problem (geocentric approach [to site productivity estimation]) should not now be called the solution to the original problem” and his caveat applies equally to modelling.
In the original Fortran simulator, record splitting was hard-coded to assign 1.3 times the average increment to a quarter of the stems, whilst the remaining stems were assigned 0.9 times the predicted increment. In Figure 6, these growth rates are under user control as an easily-accessible slider. The conditions for initiating record splitting and the degree of serial correlation of increments were hidden deep in the original Fortran code, but are under user control as a slider in Figure 6. These controls could be shown explicitly as separate sliders, but for compactness are here compressed into a single vector.
The Parameters submodel (Figure 6, top right) contains parameters for diameter increment (Anon, 1987), for mortality and recruitment (Vanclay, 1989a), for volume estimation (Anon, 1981), and for harvesting and logging damage (Preston and Vanclay, 1988). The practice of collating all parameters into one submodel (rather than scattering them throughout the model) facilitates verification and maintenance of the simulator. The species grouping used in this model differs slightly from Vanclay (1989a) in using the same species groups for growth, harvesting and volume estimation, whereas Vanclay’s (1989a) model used a 3-digit species code, with each digit denoting the volume, harvesting or growth equation to be applied. These differences in the species grouping are minor, and the simplification employed here makes little practical difference and improves clarity for teaching.
The Simile implementation of this model encourages exploration of simulator assumptions not possible in the original version. For instance, a slider labelled Force BA (Figure 6 top left) allows users to over-ride the calculated stand basal area and thus to explore growth patterns and possible thinning regimes by holding standing basal area constant. Such experimentation is easy to implement within Simile, and can offer new insights and better understanding of a simulator.
Alternative strategies of record splitting may have considerable influence on predictions. Whilst differences may appear rather small over a decade, they can accumulate to contribute substantial differences that may dramatically affect the timing of harvests which is typically influenced by the number of stems exceeding some threshold. This difference does not eventuate in the case of a single stem simulated as an individual tree model (granularity = 1), but can be substantial when cohorts of post-disturbance regeneration are simulated at the estate level (granularity <0.01).
This re-appraisal of an established simulator should remind readers of the importance of sensitivity testing of assumptions, both explicit and implicit. Clearly, the constructs offered in software, the operating system and the hardware available may all influence the representation, implementation and performance of a simulator. It remains instructive for all modellers to constantly question whether a representation is faithful to their imagination or slave to the technology available, and to be aware that seemingly innocuous assumptios may have significant consequences for predictions.
Vanclay’s (1989a) model was a proof-of-concept that signalled a change from long-established stand-table projection approaches (Higgins, 1977) to dynamic simulation and yield scheduling (Vanclay, 1990,1994a). Most of the embedded functional relationships were subsequently enhanced: site quality assessment (Vanclay, 1989b), diameter increment (Vanclay, 1991a), mortality (Vanclay, 1991b), regeneration (Vanclay, 1992), merchantability (Vanclay, 1991c) and harvesting (Vanclay, 1989c) functions were all subsequently revised to include more species groups and more variables. However, the prototype simulator presented here in Simile offers pedagogic advantages as it embodies the design and structure of the operational version, without the additional complexity of many equations with multiple parameters (i.e., hundreds of species and dozens of equations, each with several parameters). Despite its comparative simplicity, the simulator involves assumptions that appeared innocuous in the Fortran implementation, but are now revealed in Simile to have substantial consequences for resulting predictions.
This practical example illustrates that the quality of a model cannot be judged independently of its implementation as a simulator, and that apparently minor assumptions made in implementing the simulator may have substantial influence on predictions. A motor car offers a familiar and pedagogic analogy: a perfect engine cannot perform well in an unroadworthy car, and the utility of the vehicle relies on its overall performance rather than its theoretical specifications. So it is with simulation models: the utility of a model depends in part on assumptions made during model implementation as a simulator, and it behoves modellers to reveal, document and test such assumptions. This requires some thoughtful reflection by the modelling team, as familiarity with a modelling environment may lead to the intuitive use of convenient constructs (e.g., arrays in Fortran; submodels in Simile) without a full appreciation of the consequences for predictions.
Other related experiences are also insightful: several colleagues have related anecdotes in which thoughtful bounding to avoid computation problems in a model (such as Y = max(βX, c)) has resulted in the use of the upper bound (c) in most simulations, rather than the intended function βX. Sadly, many such discoveries are discovered only accidentally and belatedly, and they are rarely reported in the literature.
This Simile representation makes the model accessible for teaching purposes, and encourages exploration into the consequences of implementation decisions such as record splitting that have received little consideration. Similar experiences have been reported during re-engineering of the landscape model LANDIS (Scheller et al.,2010). Others have shared insights gained from converting a simulator from one computer language to another (e.g., Cumming and Burton, 1993), or to a hybrid implementation combining both code-based and icon-based software (e.g., Smith et al., 2005; Lättilä et al., 2010), but such conversion appears to offer fewer insights than re-engineering or recasting a simulator in visual environments.
Familiarity with a modelling platform, whether Fortran, Simile or otherwise, can be seductive, and can lure modellers into introducing untested assumptions for convenience of implementation. As demonstrated in this paper, such assumptions may have consequences greater than suspected. Modellers should remain conscious of all assumptions, should consider alternative implementations that make assumptions evident, and should conduct sensitivity tests to inform decisions.
- Alder D, Silva JNM: An empirical cohort model for management of Terra Firme forests in the Brazilian Amazon. Forest Ecol Manag 2000, 130: 141–157. 10.1016/S0378-1127(99)00196-6View ArticleGoogle Scholar
- Anonymous: Rainforest Volume Equations. Research Report No 3. Department of Forestry, Brisbane, Queensland; 1981:85.http://trove.nla.gov.au/work/13313532 ISSN: 0311-0893. National Library of Australia, index for this report series isGoogle Scholar
- Anonymous: Rainforest increment studies. Research Report No 5. Department of Forestry, Brisbane, Queensland; 1987:59–60.http://trove.nla.gov.au/work/13313532 ISSN: 0311-0893. National Library of Australia, index for this report series isGoogle Scholar
- Blackwell GL, Potter MA, Minot EO: Rodent and predator population dynamics in an eruptive system. Ecol Modell. 2001, 142(3):227–245. 10.1016/S0304-3800(01)00327-1View ArticleGoogle Scholar
- Bossel H: Modelling forest dynamics: Moving from description to explanation. Forest Ecol Manag 1991, 42: 129–142. 10.1016/0378-1127(91)90069-8View ArticleGoogle Scholar
- Botkin DB: Forest Dynamics: an ecological model. Oxford University Press, Oxford; 1993. 309 pp 309 ppGoogle Scholar
- Brown WJ, Malveau RC, McCormick HW, Mowbray TJ: AntiPatterns: Refactoring Software, Architectures, and Projects in Crisis. Wiley, New York; 1998. ISBN: 0-471-32929-0Google Scholar
- Buckman RE: Growth and yield of red pine in Minnesota. Tech. Bulletin No. 1272, U.S. Department of Agriculture, Forest Service; 1962.http://books.google.fi/books?id=j3e2J5mHYmgCGoogle Scholar
- Clark DA, Clark DB: Assessing the growth of tropical rain forest trees: Issues for forest modeling and management. Ecol Applications 1999, 9: 981–997. 10.1890/1051-0761(1999)009[0981:ATGOTR]2.0.CO;2View ArticleGoogle Scholar
- Clutter JL: Compatible growth and yield models for loblolly pine. Forest Sci 1963, 9(3):354–371.Google Scholar
- Cole DM, Stage AR: Estimating future diameters of lodgepole pine. Res. Pap. INT-131. U.S. Department of Agriculture, Forest Service. Ogden UT: Intermountain Forest and Range Experiment Station; 1972:20.Google Scholar
- Connell JH, Green PT: Seedling dynamics over thirty-two years in a tropical rain forest tree. Ecology 2000, 81: 568–584. 10.1890/0012-9658(2000)081[0568:SDOTTY]2.0.CO;2View ArticleGoogle Scholar
- Crookston NL, Dixon GE: The forest vegetation simulator: A review of its structure, content, and applications. Comput Electron Agric 2005, 49: 60–80. 10.1016/j.compag.2005.02.003View ArticleGoogle Scholar
- Cumming SG, Burton PJ: A programmable shell and graphics system for forest stand simulation. Environ Model Software 1993, 8: 219–230. 10.1016/S0266-9838(05)80003-6View ArticleGoogle Scholar
- Davey C, Ougham HJ, Millar A, Thomas H, Tindal C, Muetzelfeldt R: PlaSMo: Making existing plant and crop mathematical models available to plant systems biologists. Comp Biochem Physiol A Mol Integr Physiol 2009, 153: S225-S226.View ArticleGoogle Scholar
- Doerr HM: Stella ten years later: A review of the literature. Int J Comput Math Learning 1996, 1(2):201–224. 10.1007/BF00571080View ArticleGoogle Scholar
- Dufour-Kowalski S, Courbaud B, Dreyfus P, Meredieu C, de Coligny F: Capsis: an open software framework and community for forest growth modelling. Ann For Sci 2012, 69: 221–233. 10.1007/s13595-011-0140-9View ArticleGoogle Scholar
- Duursma RA, Robinson AP: Bias in the mean tree model as a consequence of Jensen’s inequality. For Ecol Manage 2003, 186: 373–380. 10.1016/S0378-1127(03)00307-4View ArticleGoogle Scholar
- Elkin C, Reineking B, Bigler C, Bugmann H: Do small-grain processes matter for landscape scale questions? Sensitivity of a forest landscape model to the formulation of tree growth rate. Landscape Ecol 2012, 27(5):697–711. 10.1007/s10980-012-9718-3View ArticleGoogle Scholar
- Eskrootchi R, Oskrochi GR: A Study of the efficacy of project-based learning integrated with computer-based simulation - STELLA. Educ Tech Soc 2010, 13(1):236–245.Google Scholar
- Ford A: Modeling the environment: an introduction to system dynamics modeling of environmental systems. Island Press, Washington DC, USA; 1999. ISBN: 1-55963-600-9Google Scholar
- Garcia O: Forest stands as dynamical systems: an introduction. Mod Appl Sci 2013, 7(5):32–38.View ArticleGoogle Scholar
- Garcia O, Ruiz F: A growth model for eucalypt in Galicia, Spain. For Ecol Manage 2003, 173: 49–62. 10.1016/S0378-1127(01)00817-9View ArticleGoogle Scholar
- Haggith M, Prabhu R, Pierce Colfer CJ, Ritchie B, Thomson A, Mudavanhu H: Infectious ideas: modelling the diffusion of ideas across social networks. Small-scale Forest 2003, 2: 225–239.Google Scholar
- Hamilton DA Jr: Uses and abuses of multipliers in the Stand Prognosis Model. Gen. Tech. Rep. INT-GTR-310. U.S. Department of Agriculture, Forest Service, Intermountain Research Station, Ogden, UT; 1994:9.http://gis.fs.fed.us/fmsc/ftp/fvs/docs/gtr/multipl.pdfGoogle Scholar
- Hedayat AS, Su G: Robustness of the simultaneous estimators of location and scale from approximating a histogram by a normal density curve. Am. Stat. 2012, 66(1):25–33. 10.1080/00031305.2012.663665View ArticleGoogle Scholar
- Higgins MD: A sustained yield study of north Queensland rainforests. Department of Forestry, Brisbane, Queensland; 1977:182.Google Scholar
- Jacoby JE, Harrison S: Multi‒variable experimentation and simulation models. Nav Res Logist Q 1962, 9(2):121–136. 10.1002/nav.3800090206View ArticleGoogle Scholar
- Jensen JL: Sur les fonctions convexes et les inégualités entre les valeurs moyennes. Acta Mathematica 1906, 30: 175–193. 10.1007/BF02418571View ArticleGoogle Scholar
- Kalgraf K: The dynamics of a simple stand. Studia Forestalia Suecica. In Wood Resource Dynamics in the Scandinavian Forestry Sector Edited by: Lönnstedt L, Randers J. 1979, 152: 55–66.Google Scholar
- Kariuki M, Kooyman RM, Smith RGB, Wardell-Johnson G, Vanclay JK: Regeneration changes in tree species abundance, diversity and structure in logged and unlogged subtropical rainforest over a thirty six year period. For Ecol Manage 2006, 236: 162–176. 10.1016/j.foreco.2006.09.021View ArticleGoogle Scholar
- Köhler P, Huth A: The effects of tree species grouping in tropical rain forest modelling: Simulations with the individual based model Formind. Ecol Modell 1998, 109: 301–321. 10.1016/S0304-3800(98)00066-0View ArticleGoogle Scholar
- Lättilä L, Hilletofth P, Lin B: Hybrid simulation models–when, why, how? Expert Syst Appl 2010, 37(12):7969–7975. 10.1016/j.eswa.2010.04.039View ArticleGoogle Scholar
- Leary RA: Interaction Theory in Forest Ecology and Management. Nijnhoff, Dordrecht; 1985. 219 pp 219 ppView ArticleGoogle Scholar
- Ledermann T, Eckmüllner O: A method to attain uniform resolution of the competition variable Basal-Area-in-Larger Trees (BAL) during forestgrowth projections of small plots. Ecol Modell 2004, 171: 195–206. 10.1016/j.ecolmodel.2003.08.005View ArticleGoogle Scholar
- Muetzelfeldt R: Position paper on declarative modelling in ecological and environmental research. European Commission Directorate-General for Research, Sustainable Development, Global Change and Ecosystems; 2004.http://simileweb.com/documents/dmeer.pdf ISBN: 92-894-5212-9.Google Scholar
- Muetzelfeldt R: A generic approach for representing complex structures in biological models. Nat Precedings 2010. doi:10.1038/npre.2010.5188.1 doi:10.1038/npre.2010.5188.1Google Scholar
- Muetzelfeldt R, Massheder J: The Simile visual modelling environment. Eur J Agron 2003, 18: 345–358. 10.1016/S1161-0301(02)00112-0View ArticleGoogle Scholar
- Muetzelfeldt R, Taylor J: The suitability of AME (the Agroforestry Modelling Environment) for agroforestry modelling. Agro Forum 1997, 8(2):7–9.Google Scholar
- Muetzelfeldt R, Robertson D, Bundy A, Uschold M: The use of Prolog for improving the rigour and accessibility of ecological modelling. Ecol Modell 1989, 46: 9–34. 10.1016/0304-3800(89)90067-7View ArticleGoogle Scholar
- Nebel G, Dragsted J, Vanclay JK: Structure and floristic composition of flood plain forests in the Peruvian Amazon: II. The understorey of restinga forests. For Ecol Manage 2001, 150: 59–77. 10.1016/S0378-1127(00)00681-2View ArticleGoogle Scholar
- Okuda T, Kachi N, Yap SK, Manokaran N: Tree distribution pattern and fate of juveniles in a lowland tropical rain forest – implications for regeneration and maintenance of species diversity. Plant Ecol 1997, 131: 155–171. 10.1023/A:1009727109920View ArticleGoogle Scholar
- Ong PC, Kleine M: DIPSIM: Dipterocarp forest growth simulation model – a tool for forest-level management planning. In Dipterocarp Forest Ecosystems: Towards sustainable management. Edited by: Schulte A. World Scientific, Singapore; 1996:228–246. ISBN: 9810227299 ISBN: 9810227299View ArticleGoogle Scholar
- Picard N, Franc A: Are ecological groups of species optimal for forest dynamics modelling? Ecol Modell 2003, 163: 175–186. 10.1016/S0304-3800(03)00010-3View ArticleGoogle Scholar
- Porte A, Bartelink HH: Modelling mixed forest growth: a review of models for forest management. Ecol Modell 2002, 150: 141–188. 10.1016/S0304-3800(01)00476-8View ArticleGoogle Scholar
- Prabhu R, Haggith M, Mudavanhu H, Muetzelfeldt R, Standa-Gunda W, Vanclay JK: ZimFlores: a model to advise co-management of the Mafungautsi Forest in Zimbabwe. Small-scale For 2003, 2: 185–210.Google Scholar
- Preston RA, Vanclay JK: Calculation of timber yields from north Queensland rainforests. Queensland Department of Forestry, Technical Paper No 47; 1988:19.http://espace.library.uq.edu.au/eserv/UQ:8264/R008_tp47.pdfGoogle Scholar
- Pretzsch H, Biber P, Dursky J, von Gadow K, Hasenauer H, Kändler G, Kenk G, Kublin E, Nagel J, Pukkala T, Skovsgaard JP, Sodtke R, Sterba H: Recommendations for standardized documentation and further development of forest growth simulators. Forstw. Cbl. 2002, 121: 138–151. 10.1046/j.1439-0337.2002.00138.xView ArticleGoogle Scholar
- Reineke LH: A modification of Bruce’s method of preparing timber yield Tables. J Agric Res 1927, 35: 843–856.Google Scholar
- Robinson AP, Monserud RA: Criteria for comparing the adaptability of forest growth models. Forest Ecol Manag 2003, 172: 53–67. 10.1016/S0378-1127(02)00041-5View ArticleGoogle Scholar
- Scheller RM, Sturtevant BR, Gustafson EJ, Ward BC, Mladenoff DJ: Increasing the reliability of ecological models using modern software engineering techniques. Front Ecol Environ 2010, 8: 253–260. 10.1890/080141View ArticleGoogle Scholar
- Simon G: Computer simulation swindles, with applications to estimates of location and dispersion. Appl. Statist. 1976, 25: 266–274. 10.2307/2347234View ArticleGoogle Scholar
- Simulistics: Simile at a glance. Simulistics Ltd; 2013.http://www.simulistics.com/overview.htm [16 May 2013]Google Scholar
- Smith FP, Holzworth DP, Robertson MJ: Linking icon-based models to code-based models: a case study with the agricultural production systems simulator. Agricult Sys 2005, 83(2):135–151. 10.1016/j.agsy.2004.03.004View ArticleGoogle Scholar
- Stage AR: Prognosis model for stand development. Res. Pap. INT-137. U.S. Department of Agriculture Forest Service, Intermountain Forest and Range Experiment Station; 1973:32.Google Scholar
- Valle D: Incorrect representation of uncertainty in the modeling of growth leads to biased estimates of future biomass. Ecol Applications 2011, 21(4):1031–1036. 10.1890/10-0830.1View ArticleGoogle Scholar
- Vanclay JK: Techniques for modelling timber yield from indigenous forests with special reference to Queensland. M.Sc. Thesis, University of Oxford, U.K; 1983. 194 p 194 pGoogle Scholar
- Vanclay JK: A growth model for north Queensland rainforests. Forest Ecol Manag 1989a, 27: 245–271. 10.1016/0378-1127(89)90110-2View ArticleGoogle Scholar
- Vanclay JK: Site productivity assessment in rainforests: an objective approach using indicator species. In Proceedings of the Seminar on Growth and Yield in Tropical Mixed/Moist Forests, 20–24 June 1988. Edited by: Wan Razali M, Chan HT, Appanah S. Forest Research Institute Malaysia, Kuala Lumpur; 1989b:225–241.Google Scholar
- Vanclay JK: Modelling selection harvesting in tropical rain forests. J Trop For Sci 1989c, 1: 280–294.Google Scholar
- Vanclay JK: Design and implementation of a state-ofthe-art inventory and forecasting system for indigenous forests. September 24–30, 1989. In Global Natural Resource Monitoring and Assessment: Preparing for the 21st century, proceedings of the international conference and workshop. Edited by: Lund HG, Preto G. Fondazione G. Cini, Isle of San Giorgio Maggiore, Venice, Italy; 1990:1072–1078. http://espace.library.uq.edu.au/view/UQ:8268Google Scholar
- Vanclay JK: Compatible deterministic and stochastic predictions by probabilistic modelling of individual trees. Forest Sci 1991a, 37: 1656–1663.Google Scholar
- Vanclay JK: Mortality functions for north Queensland rainforests. J Trop Forest Sci 1991b, 4: 15–36.Google Scholar
- Vanclay JK: Modelling changes in the merchantability of individual trees in tropical rainforest. Commonw Forest Rev 1991c, 70: 105–111.Google Scholar
- Vanclay JK: Data requirements for developing growth models for tropical moist forests. Commonw Forest Rev 1991d, 70: 248–271.Google Scholar
- Vanclay JK: Modelling regeneration and recruitment in a tropical rainforest. Can J Forest Res 1992, 22: 1235–1248. 10.1139/x92-165View ArticleGoogle Scholar
- Vanclay JK: Sustainable timber harvesting: Simulation studies in the tropical rainforests of north Queensland. Forest Ecol Manag 1994a, 69: 299–320. 10.1016/0378-1127(94)90237-2View ArticleGoogle Scholar
- Vanclay JK: Modelling Forest Growth and Yield: Applications to Mixed Tropical Forests. CAB International, Wallingford, U.K.; 1994b.Google Scholar
- Vanclay JK: Lessons from the Queensland rainforests: Steps towards sustainability. J Sustainable Forest 1996a, 3(2/3):1–27.View ArticleGoogle Scholar
- Vanclay JK: Assessing the sustainability of timber harvests from natural forests: Limitations of indices based on successive harvests. J Sustainable Forest 1996b, 3(4):47–58. 10.1300/J091v03n04_05View ArticleGoogle Scholar
- Vanclay JK: Realizing opportunities in forest growth modelling. Can J Forest Res 2003, 33: 536–541. 10.1139/x02-117View ArticleGoogle Scholar
- Vanclay JK: Spatially-explicit competition indices and the analysis of mixed-species plantings with the Simile modelling environment. Forest Ecol Manag 2006a, 233: 295–302. 10.1016/j.foreco.2006.05.020View ArticleGoogle Scholar
- Vanclay JK: Can the lessons from the community rainforest reforestation program in eastern Australia be learned? Int Forest Rev 2006b, 8(2):256–264. 10.1505/ifor.8.2.256View ArticleGoogle Scholar
- Villa F, Athanasiadis IN, Rizzoli AE: Modelling with knowledge: a review of emerging semantic approaches to environmental modelling. Environ Model Software 2009, 24: 577–587. 10.1016/j.envsoft.2008.09.009View ArticleGoogle Scholar
- Weiskittel AR, Hann DW, Kershaw JA, Vanclay JK: Forest Growth and Yield Modeling. Wiley, New York; 2011:430. ISBN: 978-0-470-66500-8View ArticleGoogle Scholar
- Wirth N: Algorithms+Data Structures = Programs (Vol. 76). Prentice Hall, Upper Saddle River, NJ, USA; 1985. ISBN: 0130224189Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.