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Article Contents

The conceptual model, the role of quantitative models in ecological research, when should a quantitative model be developed, building quantitative ecological models, nuts and bolts of assembling a quantitative ecological model, deterministic or stochastic, a way forward, acknowledgments, references cited, common pitfalls and potential solutions, decisions about model implementations.

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An Introduction to the Practice of Ecological Modeling

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Leland J. Jackson, Anett S. Trebitz, Kathryn L. Cottingham, An Introduction to the Practice of Ecological Modeling, BioScience , Volume 50, Issue 8, August 2000, Pages 694–706, https://doi.org/10.1641/0006-3568(2000)050[0694:AITTPO]2.0.CO;2

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Modeling has become an important tool in the study of ecological systems, as a scan of the table of contents of any major ecological journal makes abundantly clear. A number of books have recently been published that provide excellent advice on model construction, building, and use (e.g., Gotelli 1995 , Gurney and Nisbet 1998 , Roughgarden 1998 ) and add to the classic literature on modeling ecological systems and their dynamics (e.g., Maynard Smith 1974 , Nisbet and Gurney 1982 ). Unfortunately, however, littleany—of this growing literature on ecological modeling addresses the motivation to model and the initial stages of the modeling process, information that beginning students would find useful.

Fast computers and graphical software packages have removed much of the drudgery of creating models with a programming language and opened new avenues of model construction, use, and even misuse. There are many reasons why a student might want to consider modeling as a component of his or her education. Models provide an opportunity to explore ideas regarding ecological systems that it may not be possible to field-test for logistical, political, or financial reasons. Often, learning occurs from apparently strange results and unexpected surprises. The process of formulating an ecological model is extremely helpful for organizing one's thinking, bringing hidden assumptions to light, and identifying data needs. More and more, students want to “do something” with modeling but are not sure how to get started.

The goals of this article are to outline issues concerning the value of ecological models and some possible motivations for modeling, and to provide an entry point to the established modeling literature so that those who are beginning to think about using models in their research can integrate modeling usefully. We therefore envision the typical reader to be an advanced undergraduate, a beginning graduate student, or a new modeler. We first consider some of the values of models and the motivation for modeling. We then discuss the steps involved in developing a model from an initial idea to something that is implemented on a computer, outlining some of the decisions that must be made along the way. Many excellent texts and journal articles deal with the technical details of models and model construction; we do not attempt to replace this literature, but rather try to make the reader aware of the issues that must be considered and point to some of the sources we have found particularly useful.

We begin with the assumption that the reader has decided that he or she would like to “do something” with modeling as part of his or her research (Figure 1) . It is important to recognize the difference between models and the modeling process. A model is a representation of a particular thing, idea, or condition. Models can be as simple as a verbal statement about a subject or two boxes connected by an arrow to represent some relationship. Alternatively, models can be extremely complex and detailed, such as a mathematical description of the pathways of nitrogen transformations within ecosystems. The modeling process is the series of steps taken to convert an idea first into a conceptual model and then into a quantitative model. Because part of what ecologists do is revise hypotheses and collect new data, the model and the view of nature that it represents often undergo many changes from the initial conception to what is deemed the final product.

The discussion that follows is organized to consider issues in a sequence similar to what a new modeler would encounter. Because individuals' backgrounds differ, the sequence is not fixed. We map one possible route through the sorts of decisions that will most likely need to be considered; this course is derived from our individual experiences plus the collective knowledge of our reviewers. We begin with conceptual models because many people, even self-labeled nonmodelers, formulate conceptual models.

The development of a conceptual model can be an integral part of designing and carrying out any research project. Conceptual models are generally written as diagrams with boxes and arrows, thereby providing a compact, visual statement of a research problem that helps determine the questions to ask and the part of the system to study. The boxes represent state variables , which describe the state or condition of the ecosystem components. The arrows illustrate relationships among state variables, such as the movement of materials and energy (called flows ) or ecological interactions (e.g., competition). Shoemaker (1977) provides an excellent discussion about how to develop conceptual models.

The development of a conceptual model is an iterative process. The skeleton of a conceptual model begins to take shape when a general research question is formulated. For example, suppose the goal of a research project is to determine the relationship between different strategies for stocking exotic salmon in the Great Lakes and the concentrations of potentially toxic contaminants in the salmon and their alewife prey. The initial conceptual model might consist of two linked boxes labeled “alewife” and “chinook salmon,” with an additional arrow labeled “stocking” pointing to the salmon's box (Figure 2a) . We have chosen to place two-way arrows between the boxes to reflect the flow of biomass and contaminants from alewife to salmon and the effect of salmon on the alewife; an alternative model might have used only one arrow, since the flow of material between boxes is the result of predation by salmon on alewife. Details would then be added to the conceptual model based on the answers to questions such as, Are there other important species besides alewife and chinook salmon? What mechanistic processes should be included? What environmental factors influence each species? What currency should be used to describe compartment interactions (e.g., elements, biomass, individuals, energy)?

After making refinements driven by such questions, the conceptual model might have alewife, chinook salmon, rainbow smelt, and lake trout (Figure 2b) , although the research interest might still be with the original two species. The next round of refinements to the conceptual model might be based on available data or consultation with ecologists who have studied the interactions of the four species shown in Figure 2b . For example, if contaminant concentrations are a function of prey body size, and if predators seek certain size classes of prey, then size structure might be added to the model to more accurately reflect these ecological features and to better simulate contaminant intake by predators (Figure 2c) . Depending on the nature of the research question, the addition of size structure might be made for just the alewife and chinook salmon. This simple example assumes that there are changes only in the state variables, but there could also be changes in the relationships among the state variables.

In general, a parsimonious approach is best for creating an appropriate conceptual model. The model should strike a balance between incorporating enough detail to capture the necessary ecological structure and processes and being simple enough to be useful in generating hypotheses and organizing one's thoughts. Creating a good conceptual model forces an ecologist to formulate hypotheses, determine what data are available and what data are needed, and assess the degree of understanding about key components of the system. Because outside viewpoints and questions often force clarification of biases and assumptions, discussing the evolving conceptual model with colleagues can be helpful. Group construction of a conceptual model can also be a useful consensus-building tool in collaborative research ( Walters 1986 , Carpenter 1992 ). Conceptual models should therefore be included in dissertation and grant proposals, especially in the early stages of project development. Revisions of the initial conceptual model then become focal points for discussion in subsequent meetings of the dissertation committee or research planning group.

A quantitative model is a set of mathematical expressions for which coefficients and data have been attached to the boxes and arrows of conceptual models; with those coefficients and data in place, predictions can be made for the value of state variables under particular circumstances. Ecologists use quantitative models for various purposes, including explaining existing data, formulating predictions, and guiding research. Simple quantitative models can be solved with pencil and paper (see mathematical ecology textbooks such as Pielou 1977 , Hallam and Levin 1986 , and Edelstein-Keshet 1988 ), but most ecological models are now implemented on a computer.

Quantitative ecological models can guide research in a number of ways. Constructing a quantitative model and running simulations may help in the design of experiments ( Carpenter 1989 , Hilborn and Mangel 1997 ), for example, to evaluate experimental power for different hypothesized effect sizes. Sensitivity analysis of a quantitative model can reveal which processes and coefficients have the most influence on observed results and therefore suggest how to prioritize sampling efforts. Quantitative models can even be used to generate “surrogate” data on which to test potential environmental indicators or evaluate potential sampling schemes. Most important, quantitative models translate ecological hypotheses into predictions that can be evaluated in light of existing or new data.

Ecologists often use quantitative models to formulate predictions about the systems they study. Some predictive models are empirical, meaning that they represent relationships determined strictly by data. Because empirical models are not based on a knowledge of underlying mechanisms, they are most useful within the bounds of the data with which they are developed ( Weiner 1995 ). A well-known empirical model from aquatic ecology predicts the level of summer chlorophyll from spring total phosphorus ( Dillon and Rigler 1974 ). Other predictive models are more mechanistic, based on hypotheses about the particular ecological processes that cause an observed pattern. The incorporation of key ecological features, such as size-selective predation and increasing contaminant concentrations with increasing prey body size (to use an example similar to that in Figure 2 ), leads to the prediction of a tradeoff between decreasing concentrations of PCBs in salmon and the probability of survival of salmon prey (Figure 3; Jackson 1997 ). In the absence of these mechanistic ecological details, lower contaminant concentrations are predicted in predators ( Jackson 1996a , 1996b ).

Predictive models can become quite complex, especially when their forecasts are used as the basis for resource management and policy decisions. Examples include global climate models, fisheries management models for setting catch and harvest quotas, watershed management models for nutrient control strategies, and risk assessment models for environmental engineering. Often, these complex predictive models are used to generate predictions for scenarios for which actual tests are difficult or impossible to run for ecological, social, or economic reasons.

Like a conceptual model, a quantitative model is rarely an end in itself. Often learning results from considering a changing suite of several quantitative models, or several formulations of processes within a particular model ( Pascual et al. 1997 ). The assessment of different models and processes allows an evaluation of the assumptions specific to those formulations and processes. In this context, it is useful to remember that models are only tools and not reality, and there is no “correct” model.

Models should follow from specific research questions rather than questions following from models. Thus, the decision to build a quantitative model from a conceptual model should occur only after a clear, focused research question has been distilled from initial ideas. A full-scale quantitative model should be created only when each of the following questions can be answered with a yes:

Will a quantitative model add to the scientific content of the study?

Is there sufficient motivation to devote the necessary time to develop a quantitative model?

Will the investment in modeling enhance the quality of knowledge produced?

There are clear advantages to the incorporation of quantitative modeling in a research program. We have already touched on some of these benefits, such as formulating predictions and identifying data needs or knowledge gaps. Models are also useful for organizing one's thinking about a problem. Once a conceptual model is converted to a quantitative model and used, new questions may arise as a result of interesting and unexpected results. However, the time it takes to build a useful quantitative model should not be underestimated. Model building becomes easier with practice, but modelers should expect to spend several weeks or months constructing, parameterizing, testing, and running a modestly complex model. (The time spent depends to some degree on the software used, which is discussed more below.)

Once an ecologist has decided to build a quantitative model, how should he or she choose the type of model to build? Some general classes of models used in ecology include energy and mass balance models (e.g., Hewett 1989 ), population genetics models (e.g., Roughgarden 1979 ), optimization and game theory models (e.g., Mangel and Clark 1988 ), individual-based population models (e.g., DeAngelis and Gross 1992 ), size- or age-structured population models (e.g., Caswell 1989 ), community and ecosystem models (e.g., Scavia and Robertson 1980 ), and landscape models (e.g., Baker 1989 ). Because the degree of detail varies widely within these broad categorizations (Table 1) , we recommend reading papers that discuss the merits of various modeling approaches (e.g., Levins 1966 , DeAngelis and Waterhouse 1987 , DeAngelis 1988 ). An overview of model types and formulations can also be obtained from a survey course in mathematical modeling, and we strongly recommend taking such a course as soon as the idea to “do something” with models arises. The specific types of models being considered may suggest further course work. For example, differential equations are used in many models, matrix algebra underlies size- and age-structured models, and geographical information systems (GIS) are needed to work with many spatial and metapopulation models.

The choice of model type and detail will depend on the system studied, the questions asked, and the data available. Quantitative models can quickly become complex and clear problem definition is essential to keeping the model focused. A good conceptual model is invaluable for deciding what ecological detail to include and what to ignore. For example, suppose an ecologist is studying two forest stands: One stand is intact, whereas a presumedly important seed disperser has been removed from the other. Has the removal of the seed-dispersing animal caused any changes in the population of a particular tree species in the experimental stand? There are several ways in which quantitative modeling can be used to address this question. A simple age-structured model (e.g., Caswell 1989 ) of the tree population may be useful if the ecologist wants to look for changes in age structure. Alternatively, a spatially explicit model might be needed if the ecologist wants to explore differences in spatial pattern. If the ultimate goal is to test the findings from the quantitative model in the field, then the model that is developed will dictate the types of data that will need to be collected from the two forest stands.

Once the general type of quantitative model has been chosen, the ecologist must determine the appropriate level of abstraction for the model. Consulting papers on the value of simple ( Fagerström 1987 , Scheffer and Beets 1993 ) versus complex ( Logan 1994 ) models may help guide this decision. Good models never include all possible compartments and interactions ( Fagerström 1987 , Starfield 1997 ), and the complexity of a model depends very much on the purpose and question addressed by the model. There are tradeoffs between the generality of a model and its practical utility for a particular situation ( Levins 1966 ). A highly abstract model with few parameters may be best to test general ecological hypotheses. However, for specific questions, such as whether changes in fire frequency have affected the spatial pattern of a species, a detailed spatial model coupled to GIS data may be required. Thus, a model's structure should be consistent with both the question(s) asked and the measurements made ( Costanza and Sklar 1985 , Ludwig and Walters 1985 , DeAngelis et al. 1990 ). Data for many populations are collected by size or developmental stage or at fixed time intervals, leading naturally to models with size or stage structure and certain time steps (see the box on page 700 for more on time steps). With too little detail in the model, the mechanisms driving the response of interest may not be captured. On the other hand, too much detail makes a model difficult to parameterize (determine coefficients for equations) and to validate ( Beck 1983 , Ludwig and Walters 1985 , DeAngelis et al. 1990 ). An active area of research therefore considers how to reduce model complexity while retaining essential system behavior ( Rastetter et al. 1992 , Cale 1995 ).

Once the decision to build a quantitative model has been made, and issues of model complexity and structure have been dealt with, it is necessary to develop algebraic formulations (equations) for model processes, to establish means for solving them, and to choose parameters for each equation before implementing the model on a computer. Thinking about these issues in advance may save a modeler from having to go back and redevelop portions of the model.

The importance of keeping good notes

The litmus test for a model description is that a relatively experienced modeler must be able to reproduce the model and its output, just as experiments should be capable of being replicated. Therefore, it is important to document decisions about equation forms, parameter values, and computational details, as well as any sources of information used to make these decisions. Good notes taken during model building will save hours combing the literature to rediscover the source of assumptions or parameter values.

Choosing equations

One of the initial steps in converting a conceptual model to a quantitative model involves quantifying the arrows between the state variables. This process actually involves two steps: choosing appropriate equations and determining the parameters for those equations. Equations represent mathematically the interactions among or transfers of energy or materials between state variables in a model. For example, equations 1 , 2 , and 3 represented different (hypothesized) ways to describe the process of predator consumption. Parameters are constants in the equations that make the algebraic expressions correspond to actual data.

Equations appropriate to a particular situation may be available in the literature. Certain constructs (e.g., feeding relationships, energetic equations) are common to many ecological models, although they may need to be reparameterized for different systems. Many relationships can be found in modeling textbooks, including Models in Ecology ( Maynard Smith 1974 ), Ecological Implications of Body Size ( Peters 1983 ), Handbook of Ecological Parameters and Ecotoxicology ( Jorgensen et al. 1991 ), Dynamics of Nutrient Cycling and Food Webs ( DeAngelis 1992 ), A Primer of Ecology ( Gotelli 1995 ), and Primer of Ecological Theory ( Roughgarden 1998 ). First principles (i.e., physical laws) can also provide useful relationships. Mathematically important differences among alternative formulations may or may not be important for a particular situation. If the particular form of an equation is of concern, the effects of each formulation on model results can be explored as part of the modeling exercise.

Computational issues associated with equations

Difference equations are simply solved by recursion; that is, later predictions depend on earlier predictions. Differential equations describe continuous processes, but must nevertheless be solved in discrete time steps on a computer. The two principal methods used to solve differential equations are the Euler and the Runge-Kutta methods. The Euler method steps through the differential equation as if it were a difference equation by using information at the beginning of each time interval to calculate values at the next time interval. The Euler method can be unstable when the interval between solutions (the step size) is small, because rapid accumulation of errors prevents convergence on the real solution. The Euler method may also be unstable at large step sizes because small changes in rates and local maxima and minima in the solution may be missed, which can be particularly problematic if the differential equations are nonlinear ( Press et al. 1992 ). Runge-Kutta algorithms also start with the information at the beginning of a time interval but then sample the solution at several points between the beginning and end of the interval. For most differential equation models, the Runge-Kutta is more accurate than the Euler method, and fourth-order Runge-Kutta is particularly recommended ( Press et al. 1992 ). Graphical and algebraic explanations of the Euler and Runge-Kutta algorithms appear in Press et al. (1992 ) and in textbooks on numeric methods in computing (e.g., Atkinson 1989 ). Variable step-size methods can be used to find the optimum balance between accuracy and computational speed by using small step sizes when variables are rapidly changing and long step sizes when variables are changing slowly.

A deterministic model has no random components; for the same initial conditions and time period projected, it always gives the same result. In contrast, a stochastic model incorporates at least one random factor, and thus the results are different every time the model is run. One type of stochastic model assumes that the values of some or all parameters vary through time or across individuals and are therefore described by probability distributions. Each time the model is run, the parameter values are drawn from their specified probability distributions. Other stochastic models add random errors following each calculation to simulate the effects of environmental variability. One reason to add stochasticity is to produce realistic variability in the trajectories of the state variables through time, either because the variance as well as the average value is of interest or because the effect of variability in one state variable on another state variable is of interest. Model results might be cast in terms of probabilities—for example, as the percentage of simulations in which a certain outcome (such as a catastrophic population crash) was attained. A stochastic model is not necessarily more “correct” than a deterministic model, and it is more work to create. It does provide additional information, but whether this information is of value depends on the purpose of the model. We recommend Nisbet and Gurney (1982) as the starting point for an introduction to deterministic and stochastic models.

Selecting modeling software

Implementation of a quantitative model on a computer requires the modeler (or the computer program) to keep track of many details. Some of these details, while necessary for the model to run, are irrelevant to the model predictions (e.g., allocating computer memory for arrays and matrices, creating a user interface, and writing output). Other details, such as how variables are initialized, how random numbers are generated, the order in which equations are solved, and the algorithm (computer instructions) used for solving them, do affect the predictions. We discuss some of these details further in the boxes on FPAGE 697 and 699.

The computer software selected should be determined by the degree to which the modeler wishes to control these details. At one extreme are general programming languages (e.g., C, Basic, Fortran, Pascal) that allow the modeler complete control over the model construction but also require the modeler to handle all of the sometimes tedious details. Model building gets easier with practice and by reusing bits of previously generated code, but it can still be quite time-consuming even for relatively experienced programmers. Prewritten routines for random numbers, matrix algebra, and other algorithms are available for most programming languages, reducing the need to reinvent some wheels (e.g., Numerical Recipes; Press et al. 1992 ). If this option is chosen, coursework in at least one programming language might be helpful; general programming concepts and skills translate across languages.

At the other extreme are graphical programs (e.g., STELLA, SimuLink, ModelMaker) that allow the user to create the computer program (the model) by choosing icons from a menu while the software handles the details. Models can be constructed quickly, but there are limits on what can be built and the implementation details are often hidden from the user. This final point is a significant weakness of graphical modeling packages, and we therefore tend to create our own models using programming languages. However, intelligent use of modeling packages can permit incorporation of modeling into a study with far less effort than building a model from scratch.

Between these two extremes are programming packages that include functions to handle many of the details but still leave some control to the modeler (e.g., Matlab; see Roughgarden 1998 ) and spreadsheets (e.g., Excel; see Weldon 1999 ). This intermediate approach may appeal to those who want to know how equations are being solved without becoming mired in the syntax of a programming language.

Parameter estimation and model calibration

Parameter estimation is the process of finding parameter values for each equation in the quantitative model. The source of parameter values depends on how the model is going to be used. If the model is being developed to explore the consequences of different parameter values, then the model will be run for a wide range of different parameters without reference to particular ecological systems. However, if a model is being developed to predict behavior in a particular system, then usually a single (mean) value will be chosen for each parameter. In this case, parameter values are estimated by fitting equations to the data from the system, or perhaps from data available in the literature. Sometimes data are not available, in which case a modeler might estimate parameters by an iterative process of matching model output to observed system behavior. This latter practice is referred to as tuning (calibration) by direct search, and the parameters are altered until the model produces a reasonable fit with observations of the state variables. Tuning can be done systematically or by trial and error. Either way, keeping good notes is essential. Parameters determined by direct search are best viewed as hypotheses to be tested as data become available.

When parameters are estimated from observed data, the modeler seeks the parameters that lead to the best fit between an equation and the observed data (e.g., Hilborn and Mangel 1997 ). The least-squares criterion and maximum likelihood estimation are the two most commonly employed methods for this kind of parameter estimation. Least-squares estimates of parameters minimize the value of the squared deviations between the simulated and observed data; these estimates can be used for just about any deterministic component of a model for which distributions are near normal and variance is constant throughout the range of an independent variable ( Brown and Rothery 1993 ). However, for models that are nonlinear in the parameters, least squares may produce biased parameter estimates; for these models, maximum likelihood may yield better parameter estimates. Maximum likelihood algorithms determine the parameter values that maximize the probability that the observations would have occurred if the parameters were correct ( Hilborn and Walters 1992 ). Unlike least squares, maximum likelihood does not require that error terms be normally distributed ( Hilborn and Mangel 1997 ). It is beyond the scope of this article to review parameter estimation techniques, but useful information on that subject can be found in Draper and Smith (1981) , Hilborn and Walters (1992) , and Hilborn and Mangel (1997) .

Debugging, sensitivity analysis, and validation

Once a quantitative model is assembled, it must be tested to ensure that it is functioning properly; that process is called “debugging.” We recommend that the equations be calculated by hand to ensure that the code is performing as it should—that is, arrays and matrices are properly indexed, equations are properly calculated, and so forth. Each module or subroutine of a model developed with a programming language should be tested separately before the completed model is run. Output should be tabulated, state variables graphed, and intermediate parameter and rate values monitored to ensure that they are realistic during simulations. One also should check that the model behaves as expected in situations for which the analytical solution is known.

Sensitivity analysis explores whether the conclusions would change if the parameters, initial values, or equations were different. Consequently, sensitivity analyses can be used to guide further research (for example, to identify those parameters that would be worth the investment of additional field measurements or experiments), to corroborate the model, and to improve parameter estimates. There are three basic approaches to sensitivity analysis: varying parameter values one at a time, systematic sampling, and random sampling ( Hamby 1994 ). Swartzman and Kaluzny (1987) provide an excellent discussion of the advantages and disadvantages of each of these approaches. The simplest sensitivity analysis examines the effect of each parameter on model dynamics individually ( Bartell et al. 1986 ). The model is typically deemed sensitive to a particular parameter if changing that parameter's value by 10% leads to more than a 10% change in the output from the baseline scenario. Because analysis of one parameter at a time will not identify sensitive interactions among parameters, it may also be worthwhile to explore the effects of variation in two or more parameters at the same time using either systematic or random sampling ( Swartzman and Kaluzny 1987 ). When many parameters may interact, random sampling may be the best approach. Random sampling is most often done with Monte Carlo techniques (e.g., Swartzman and Kaluzny 1987 , Bartell et al. 1988 ), whereby, during each of perhaps 1000 model runs, a value for each parameter is “sampled” from a range or probability distribution. Model runs then undergo partial correlation analyses, which yield estimates of the contribution of each parameter to the overall variance in the output. Parameters with high partial correlations have the most influence on results.

In addition to doing a sensitivity analysis on parameter values, the model should be checked for sensitivity to initial conditions and equations. For example, the model can be initialized with different species ratios or size structures to find out whether output is driven by these choices. Model sensitivity to alternative equations for relationships among state variables can also be checked by rerunning the model with different equations and seeing whether the conclusions change.

Once a model works, the modeler may need to ask whether it sufficiently resembles reality, but whether that question can be answered at all is a matter of considerable philosophical debate ( Mankin et al. 1975 , Oreskes et al. 1994 , Rastetter 1996 , Rykiel 1996 ). Nevertheless, at some point the researcher must decide that the model is good enough and no more tinkering is necessary. For many system-specific ecological models, this decision is made based on comparisons of simulated data with field or experimental data. If the simulated data are sufficiently similar to the observed data, then the model is judged to be validated or corroborated, and simulations with the model proceed. If the simulated data do not match the observed data, then further work is necessary. Objective criteria for model validation include the standard error of model predictions and the proportion of variance explained by the model ( Caswell 1976 , Power 1993 ). It is preferable to have independent data for model corroboration and calibration, although in practice independent data are often hard to find, particularly for whole ecosystems.

Modeling offers exciting possibilities for the exploration of ideas that are not easily pursued through field experimentation or laboratory studies. Ecologists, for example, use models to simulate the systems they study and to investigate general theories of the way those systems operate. Moreover, simulation of systems with models helps identify data needs and knowledge gaps.

Many research programs can benefit from the integration and development of conceptual and quantitative models. The process of creating a conceptual model begins with a question; from there, the researcher formulates hypotheses, evaluates available and needed data, and assesses the degree of understanding of the system under consideration. Then the conceptual model is converted to a quantitative model; that process is iterative, evolving as new data and ideas are discovered.

We cannot possibly cover every aspect of ecological modeling—which is both a skill and a process—in one short article. We do hope, however, that we have successfully raised the issues that a beginning modeler must consider, provided an entry point to the modeling literature, and discussed the role of modeling in ecological research.

We thank Steve Carpenter for numerous suggestions during the writing of the manuscript. We are grateful to many people at the Center for Limnology, University of Wisconsin–Madison, for support during our model building years there (especially David Christensen, Xi He, Daniel Schindler, Craig Stow, and Rusty Wright). We thank Steve Carpenter, George Gertner, Lloyd Goldwasser, Bruce Kendall, Russell Kreis, Bill Nelson, John Nichols, Daniel Schindler, and, in particular, Rebecca Chasan, Wayne Getz, and an anonymous reviewer for their thoughtful reviews of the manuscript. L. J. J.'s research with simulation models was funded by the Natural Sciences and Engineering Research Council of Canada and by the Wisconsin Sea Grant Institute under grants from the National Sea Grant College Program, National Oceanic and Atmospheric Administration, US Department of Commerce, and from the State of Wisconsin (Federal grant NA90AA-D-SG469, project R/MW-41). K. L. C.'s initial research with simulation models was funded by a predoctoral fellowship from the National Science Foundation. K. L. C. also thanks the National Center for Ecological Analysis and Synthesis, which is funded by NSF (DEB94-21535); the University of California at Santa Barbara; and the State of California for financial and logistical support while preparing this paper for publication.

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This troubleshooting box outlines some common mistakes made during model construction. It is not an exhaustive list. We hope that the novice modeler will profit from our experience in solving these problems, which arise largely from writing one's own code in a programming language.

Pay careful attention to units, scaling, and conversions. For example, translating prey eaten by one trophic level (units of mass) to a mortality rate for another (numbers) requires a conversion and change of units. We go through our equations and write the dimensions and units to ensure that we are making appropriate conversions. Units and dimensions for empirically derived relationships tend to be built into regression parameters (e.g., ungulate biomass [kg] derived from grass productivity [g · m −2 · d −1 of carbon]). Problems often arise when different state variables operate on different spatial scales, which is sometimes less obvious than when the variabes operate on different time scales. Fish, for example, occupy a volume (g · m −3 ) but may eat benthic invertebrates that occupy a surface (g · m −2 ), requiring rescaling when computing trophic transfers. Apparent conversion problems can also be caused by failure to properly share variables among subroutines.

Be careful with time steps and model stability, especially for models with differential equations. The modeler typically must choose a single step size (e.g., hourly, daily, monthly, yearly) over which to have the algorithm solve the equations, even though the time step appropriate for evaluating one process (e.g., hourly nutrient uptake by phytoplankton) may not be appropriate for evaluating another (e.g., annual growth of fishes). Equations whose dynamics suffer when independent variables change on widely disparate time scales are known as “stiff” equations. Problems often occur because small roundoff or truncation errors in one variable lead to enormously inflated errors in another; such problems can be diagnosed by evaluating output variables at a variety of step sizes. An alternative approach to manually manipulating step size is to use an algorithm with an adaptive step size ( Press et al. 1992 ), which gives smoother dynamics but takes more work to program. One can also explicitly divide the model into “fast” and “slow” components and then update the fast components much more frequently than the slow components.

Pay attention to setting and resetting values. Arrays and matrices are a common source of computer bugs, thus warranting extra attention to their dimensioning, initializing, and indexing. We assign values to parameters before they are used rather than relying on the software to initialize them. We also check that parameters and initial conditions obtained from an input file are properly read and assigned. After the lapse of important time periods, we check that variables have been zeroed or renewed as appropriate. For example, in a model in which seed germination for a plant proceeds only when certain environmental conditions are met, the value for seedlings should be set to zero each time germination fails rather than (unintentionally) taking the value from the previous year. Similarly, when all individuals in a particular size or age class die or are eaten, the variables tracking their characteristics must be properly reset to prevent carryover effects when a new cohort arrives. Populations modeled with real numbers will approach but not equal zero when subjected to a constant mortality rate, and should be set to zero after some minimum population size is attained. Inspecting graphs of state variables will elucidate what is happening.

Test random number generators before using them. Random number generators vary in quality and should be tested before use. A statistics package can be used to analyze the results of 10,000 or so sequential random numbers to ensure that the mean, standard deviation, and distribution are as specified and the shape is as expected. If qualitatively different results occur when initializing the random number generator at the beginning of the program versus the beginning of each replicate, we look for another random number generator. We recommend reading Press et al.'s (1992 ) discussion of random-number generating algorithms. One way to keep random numbers the same from run to run, which is useful when developing or debugging a model, is to start each simulation with the same “seed” (the initial number from which the random numbers are generated). When the time comes to use different seeds, the computer's clock can be used for the seed value.

Issues concerning how numbers are stored and updated, how calculations are sequenced, and how inputs and outputs are made may seem unimportant to the novice modeler, but our experience is that computational details merit attention early in the modeling process because they can have substantial implications for model use and behavior.

The nature of inputs and outputs determines how easily a model is used and analyzed. If inputs are part of the model code, the model must be recompiled (translated from text into instructions the computer executes) each time the inputs are changed. If inputs are read in as a separate file (which takes more work to program), the model can be run many times with different inputs without recompiling. It is worth formatting output with the planned analysis in mind—select formats amenable to processing with statistical or graphics software. Excessive output slows the simulation time, but representative subsets of intermediate calculations should be inspected to ensure that everything is reasonable.

The sequence in which events proceed can affect results. Events that happen simultaneously in nature must occur in sequence in computer models. For example, if the organism or size class that is first in numerical order in a vector of state variables is always the first for which foraging is evaluated, it may unintentionally be the one that gets the most food!

Separating old from new values allows sequential calculations of simultaneous events to proceed correctly. Newly calculated values should be assigned to temporary variables so that subsequent calculations are not based on a mixture of old and new state variables. The value of the state variables should be updated with the values in the temporary variables only after all calculations have been completed for that time step.

Decide whether to model populations as whole or real numbers. Neither choice is perfect. Using real numbers gives fractions of individuals, whereas using integers presents stochasticity and rounding problems. For example, if the number of survivors is calculated by multiplying the survival rate by the number of starting individuals and then rounding to the nearest integer, then a single individual with a survival rate of 0.8 will live forever! It would be better to use 0.8 as a probability and then do the equivalent of flipping a coin—that is, draw a random number.

Decide how many stability checks and assurances to build into a model. The inherent mathematical and architectural constraints of computers can lead to unexpected model behavior ( Acton 1996 ). It is important to anticipate both mathematically illegal operations (e.g., division by zero) that would cause the simulation to crash and circumstances that would cause the simulation to become invalid. For example, it might be appropriate to stop the simulation if one species in a multispecies model goes extinct, to build in a means for its reestablishment if it goes extinct, or to build in a refuge or alternate food supply so that extinction is prevented. These types of stability guarantees should be used prudently. Excessive stabilizing components can hide programming errors or even dominate model dynamics; on the other hand, if used sparingly, they can prevent the frustration of having a long simulation rendered useless by a circumstance for which a stability check could easily have been programmed.

Table 1. Ecological models for representing populations

Figure 1. Flow chart summarizing the process of creating an ecological simulation model. The model building process distills current knowledge into a conceptual framework, which forms the scaffolding for the model's construction. A number of steps involve iterations or refinements that follow from consulting data, experienced modelers, or other ecologists. Once there is output from the model, the original idea or state of knowledge may be modified and additional model refinements, data collection or experiments might be planned. Benefits of the modeling process include eliminating alternatives, identifying gaps in knowledge, identifying testable hypotheses, and indicating avenues for additional experimentation and data collection

Figure 2. Example of the iterative nature of building a conceptual model from an initial idea. The first iteration (a) describes a simple relationship between one predator and prey. One arrow identifies biomass and contaminants as the material flowing from alewife to chinook salmon, and the other arrow identifies predation as an important ecological process structuring the alewife population. In this example, interest is in how the rate at which salmon are stocked affects the relationship between salmon and alewife. Additional information at the second iteration might indicate that the dynamics of the salmon and alewife (a) are also affected by rainbow smelt and lake trout, which are subsequently incorporated into the conceptual model (b). Finally, information on contaminant concentrations as a function of body size and more detail on predator preference of prey might indicate that age or size structure should be included (c). Depending on the goal of the modeling exercise, detailed age structure might be examined for the original two species of interest. In b and c, the double-headed arrows indicate state variables that directly interact. In c, the wide gray arrows represent the movement of fish to older age classes. Box labels represent the age of fish; YOY are young-of-year. Two quantitative models might be constructed: one for conceptual model b and one for conceptual model c

Figure 3. PCB concentrations (solid line) of age class 4+ chinook salmon and the probability of an alewife population crash (dashed line) for chinook salmon stocking rates and a Shepherd stock-recruitment relationship. PCB concentrations are the result of 200 model runs to year 2015, at each stocking rate, based on bootstrapped estimates of the Shepherd stock-recruitment relationship from 14 years of data for Lake Ontario. The arrow indicates 1994 stocking rates. The dotted line around the chinook salmon PCB concentrations represents +/− 2 SE

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Ecological Systems Theory

Ecological Systems Theory (EST), also known as human ecology, is an ecological/ system framework developed in 1979 by Urie Bronfenbrenner (Harkonen, 2007). Harkonen notes that this theory was influenced by Vygotsky’s socio-cultural theory and Lewin’s behaviorism theory. Bronfenbrenner’s research focused on the impact of social interaction on child development. Bronfenbrenner believed that a person’s development was influenced by everything in the surrounding environment and social interactions within it. EST emphasizes that children are shaped by their interaction with others and the context. The theory has four complex layers called systems, commonly used in research. At first, ecological theory was most used in psychological research; however, several studies have used it in other fields such as law, business, management, teaching and learning, and education.

Previous Studies

EST has been used in many different fields, however, commonly, it is used in health and psychology, especially in child development (e.g., Heather, 2016; Esolage, 2014; Matinello, 2020). For instance, Walker et al. (2019) used an EST framework to examine risk factors for overweight and obese children with disabilities. The study focused on how layers of an ecological system or environment can negatively affect children with special needs in terms of weight and obesity. They found that microsystem such as school, family home, and extracurricular activities can impact overall health through physical activities and food selectivity. Furthermore, the second layer, mesosystem (e.g., family dynamic and parental employment), also can lead to an increase in children’s weight because of a lack of money to buy nutritious food. In addition, children may be socially isolated and excluded in ways that cause stress, and their parents might use food to reinforce or comfort them. The third layer the study adopted was the macrosystem. For example, some cultures discriminate against children with disabilities so that they face more difficulty gaining access to health services.

In the field of language teaching, Mohammadabadi et al. (2019) researched factors influencing language teaching cognition. They used an ecological framework to explore the factors influencing language teachers at different levels. They adopted the four systems from Bronfenbrenner’s theory for studying the issue. This study found that the ecological systems affect language teaching.  For example, the microsystem included a direct influence on teachers’ immediate surroundings, such as facilities, emotional mood, teachers’ job satisfaction, and linguistic proficiency. The mesosystem defined interconnections between teachers’ collaboration and their prior learning experience. The exosystem included the teaching program and curriculum and teachers’ evaluation criteria, while the macrosystem addressed the government’s rules, culture, and religious beliefs. In other words, researchers use EST to guide the design of their studies and to interpret the results.

Model of EST

Concepts, Constructs, and Propositions

The four systems that Brofenbrenner proposed are constructed by roles, norm and rules (see Figure 1). The first system is the microsystem. The microsystem as the innermost system is defined as the most proximal setting in which a person is situated or where children directly interact face to face with others. This system includes the home and child-care (e.g., parents, teacher, and peers). The second is the mesosystem. The mesosystem is an interaction among two or more microsystems where children actively participate in a new setting; for instance, the relationship between the family and school teachers. The third is the exosystem. This system does not directly influence children, but it can affect the microsystem. The effect is indirect. However, it still may positively or negatively affect children’s development through the parent’s workplace, the neighborhood, and financial difficulties. The outermost system is the macrosystem. Like the exosystem, the macrosystem does not influence children directly; however, it can impact all the systems such as economic, social, and political systems. The influence of the macrosystem is reflected in how other systems, such as family, schools, and the neighborhood, function (Kitchen et al., 2019). These four systems construct the EST which considers their influences on child or human development.

Bronfenbrenner (cited in Harkonen, 2007) noted that those environments (contexts) could influence children’s development constructively or destructively. As the proposition, the system influences children or human development in many aspects, such as how they act and interact, their physical maturity, personal characteristics, health and growth, behavior, leadership skills, and others. At the end of the ecological system improvement phase, Bronfenbrenner also added time (the chronosystem) that focuses on socio-history or events associated with time (Schunk, 2016). In summary, the views of this ecological paradigm is that environment, social interaction, and time play essential roles in human development.

Using the Model

There are many possible ways to use the model as teachers and parents. For teaching purposes, teachers can use the model to create personalized learning experiences for students. The systems support teachers and school administrators to develop school environments that are suitable to students’ needs, characteristics, culture, and family background (Taylor & Gebre, 2016). Because the model focuses on the context (Schunk, 2016), teachers and school administration can use the model to increase students’ academic achievement and education attainment by involving parents and observing other contextual factors (e.g., students’ peers, extra-curricular activities, and neighbor) that may help or inhibit their learning.

Furthermore, the EST model can support parents to educate and guide their children. It can prompt parents to assist their children in choosing their friends and finding good neighborhoods and schools. Additionally, they can build close connections to teachers, so they know their children’ skills and abilities. By involving themselves in schools, parents can positively influence their children’s educational context (Hoover & Sandler, 1997).

For research purposes, researchers can test and modify or refine the EST proposition, or they can find additional ways to measure it. Researchers also can develop questionnaires from the components or concepts and construct of EST. Additionally, the four levels of EST can be used by researchers to frame qualitative, quantitative, and mixed research (Onwuegbuzie, et.al., 2013).

At first, EST was used in children’s development studies to describe their development in their early stages influenced by the person, social, and political systems. Currently, EST is broadly applied in many fields. Schools or educational institutions can use EST to improve students’ achievement and well-being. Interaction between the family, parents, teachers, community, and political system will determine students’ development outcomes.

Esolage, D. L. (2014). Ecological theory: Preventing youth bullying, aggression, and victimization.  Theory into Practice. 53 , 257–264.

Harkonen, U. (2007, October 17). The Bronfenbenner ecological system theory of human development. Scientific Articles of V International Conference PERSON.COLOR.NATURE.MUSIC , Daugavpils University, Latvia, 1 – 17.

Heather, M.F. (2016). An ecological approach to understanding delinquency of youth in foster care . Deviant Behavior, 37 (2), 139 – 150.

Hoover-Dempsey, K. V., & Sandler, H. M. (1997). Why do parents become involved in their children’s education? Review of Educational Research , 67(1), 3–42. https://doi.org/10.3102/00346543067001003

Kitchen, J. A, (list all authors in reference list) (2019). Advancing the use of ecological system theory in college students research: The ecological system interview tool.  Journal of College Students Development, 60  (4), 381-400.

Martinello, E. (2020). Applying the ecological system theory to better understanding and prevent child sexual abuse.  Sexuality and Culture, 24 , 326-344

Mohammadabadi, A., Ketabi, S., & Nejadansari, D. (2019). Factor influencing language teaching cognition.  Studies in Second Language Learning and Teaching. 9 (4), 657 – 680.

Onwuegbuzie, A.J., Collins, K.M.T., & Frels, R.K. (2013). Foreword. International Journal of Multiple Research Approaches, 7 (1), 2-8.

Schunk, D. H. (2016). Learning theory: An educational perspective .  Pearson.

Taylor, R. D., & Gebre, A. (2016). Teacher–student relationships and personalized learning: Implications of person and contextual variables. In M. Murphy, S. Redding, & J. Twyman (Eds.), Handbook on personalized learning for states, districts, and schools (pp. 205–220). Temple University, Center on Innovations in Learning.

Walker, M., Nixon, S., Haines. J., & McPherson, A.C. (2019). Examining risk factors for overweight and obesity in children with disabilities: A commentary on Bronfenbrenner’s ecological system framework. Developmental Neurorehabilitation, 22 (5), 359 – 364.

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Latest Trends in Modelling Forest Ecosystems: New Approaches or Just New Methods?

• Modelling Productivity and Function (A Almeida, Section Editor)
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Purpose of Review

Forest models are becoming essential tools in forest research, management, and policymaking but currently are under deep transformation. In this review of the most recent literature (2018–2022), we aim to provide an updated general view of the main topics currently attracting the efforts of forest modelers, the trends already in place, and some of the current and future challenges that the field will face.

Recent Findings

Four major topics attracting most of on current modelling efforts: data acquisition, productivity estimation, ecological pattern predictions, and forest management related to ecosystem services. Although the topics may seem different, they all are converging towards integrated modelling approaches by the pressure of climate change as the major coalescent force, pushing current research efforts into integrated mechanistic, cross-scale simulations of forest functioning and structure.

We conclude that forest modelling is experiencing an exciting but challenging time, due to the combination of new methods to easily acquire massive amounts of data, new techniques to statistically process such data, and refinements in mechanistic modelling that are incorporating higher levels of ecological complexity and breaking traditional barriers in spatial and temporal scales. However, new available data and techniques are also creating new challenges. In any case, forest modelling is increasingly acknowledged as a community and interdisciplinary effort. As such, ways to deliver simplified versions or easy entry points to models should be encouraged to integrate non-modelers stakeholders into the modelling process since its inception. This should be considered particularly as academic forest modelers may be increasing the ecological and mathematical complexity of forest models.

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Introduction

Forests are one of the most complex ecosystems on Earth’s biosphere, as they host a large proportion of terrestrial biodiversity and exist at the interface between the atmosphere and the pedosphere. In addition, forests are defined as such because the dominant organisms are trees, which are long-lived immobile individuals that are usually large [ 1 ]. These features provide opportunity for forests to develop specific spatial and temporal structures that have direct influence on how the ecosystem functions (i.e., nutrient, water and energy cycles, gene flows, population, and successional changes).

All this natural complexity poses a true challenge for representing forest structure and functioning in scientific and technical studies, as well as for science-based management [ 2 ]. Traditionally, forest models have focused on the dominant organisms (trees) and how they grow, survive, and are distributed [ 3 ••]. This approach has been dominant since the beginning of early quantitative forestry in the eighteenth century. However, for the last few decades, it has been well known that understanding how trees function is not enough to understand how forests function, as other forest components (understory, wildlife, soil, and microbial communities) are also influencing trees. Hence, forest models have constantly evolved to incorporate some of forests’ complexity into their algorithms in order to produce the estimations that model developers consider necessary to meet their objectives.

The development of the first forest growth simulator marked the beginning of a new approach to estimate tree growth. Since then, modelling has evolved from the data-based approach of using statistical tools to transform observed data (“empirical models”) into an approach in which an understanding of causal relationships between variables was added to statistical relationships in order to predict variables of interest (“process-based models”) [ 4 ]. Soon after, the advantages and disadvantages of both approaches were identified [ 5 , 6 ], and with the aim of solving them, an intermediary approach was proposed [ 7 ]. Since then, forest models have evolved considerably, and in the last few years, important technical developments have revolutionized the forest modelling field [ 8 ], such as the following: the continuous increment of computing power [ 9 ]; the development of new statistical methods [ 10 ]; the great expansion in techniques for data acquisition such as LiDAR, spectral, hyperspectral, thermal, or radar sensors that can be applied at broad scales [ 11 ]; or the development of autonomous continuous measurement devices for soil, vegetation, and atmospheric variables [ 12 ]. Therefore, the aim of this review is to identify the current focuses in forest modelling that are capturing most of the research effort.

Current Main Topics in Forest Modelling

To identify the current trends in forest modelling, we first carried out a search in the Web of Science database ( https://www.webofscience.com/wos/woscc/advanced-search ) for the years 2018 to 2022 using the terms “forest modelling,” “forest function,” “forest distribution,” “forest adaptation,” and “modelling forest function” (with their alternative spellings) in the title and keywords of documents. We identified a total of 4933 documents. Among those, we selected 154 papers that were reviews of different modelling topics. After screening for relevance, the selected review papers used for our narrative review were reduced to 79.

On a second phase, to objectively identify the most popular topics in the most recent literature, we used the visualization tool VOSviewer [ 13 ] with the database of 4933 documents to map the relationships between their keywords. However, as the statistical term “random forests” was distorting the database (data not shown), we removed the documents with this term. As a result, we retained 2040 documents for keyword mapping with VOSviewer v1.6.18 (Centre for Science and Technology Studies, Leiden University, the Netherlands, http://www.vosviewer.com ). We limited the minimum number of occurrences for each keyword displayed in the map to 30 (Fig.  1 ). As a result, 20 different keywords were selected. This search was not intended to be a formal or in-depth quantitative review but merely a way to gain an unbiased and up-to-date insight on current popular modelling trends.

Keyword map showing relationships between the 20 most common keywords in documents related to forest modelling published in the Web of Science in the 2018–2022 period. Different line and dot colors indicate different clusters of terms. Dot size is proportional to the frequency of each keyword, and line thickness is proportional to the frequency of co-occurrence of connected keywords

As main result of the keyword mapping, we found the term “climate change” as the most cited. Climate change also stood out in a central position among all other terms. In addition, four different clusters of terms were identified, with climate change being the main connector among them. The first cluster (in red in Fig.  1 ) could be considered as built around quantitative assessments of vegetation biomass (or carbon) using remote-sensing techniques (either aerial or terrestrial). The second cluster (in yellow in Fig.  1 ) was composed of the relationships between growth, productivity, and climate. The third cluster (in blue in Fig.  1 ) was limited to more technical terms related to model building. Finally, the fourth cluster (in green in Fig.  1 ) was related to ecosystem services and management, in combination with climate change. Below, we discuss the main trends in each of these clusters in the following sections, based on the 79 review papers identified as relevant.

Climate Change: the Main Driver for Forest Modeling

It is not surprising that climate change is at the center of current forest modelling efforts, a pattern already noticed in other recent reviews [ 14 ]. This result could just reflect the generalized wish by forest researchers to link their work to the current widespread scientific polices focused on addressing climate change, but it could also genuinely indicate the need for understanding how complex systems such as forests will behave under unknown climate conditions. Climate change is being observed as a major force behind many changes in current and future forest environmental changes [ 15 , 16 , 17 , 18 ]. Such changes will affect in different ways the key factors driving tree physiology, and therefore, new modelling approaches need to disaggregate climate influences on those drivers. Hence, understanding detailed effects of climate change, alone or in combination with other major drivers for change such as land-use change or biodiversity loss, is obviously the ultimate goal of much of the current modelling effort.

The realization of the first signs of climate change and the need for early action in forest management well in advance of other economic sectors (due to the long-lived nature of trees) has meant that for at least two decades, the need to provide forest models with capabilities to simulate climate change has been recognized [ 19 , 20 ]. Such need has meant that the use of simple correlational models using traditional data from permanent plots or inventories has long been seen as inadequate among the scientific community for climate change-related studies, although such an approach can be very suitable for other research and management applications [ 21 ]. In addition, other models that had implicit representation of climate influences have moved into explicit representations to keep up with the knowledge demands on climate change effects on forest systems from different stakeholders [ 22 , 23 , 24 , 25 ].

Nevertheless, for the successful implementation of climate change simulation capabilities into forest models, modelers need to move beyond direct effects on temperature and precipitation. For example, a scarce availability of models able to link climate change with ecological disturbances has been identified [ 26 ]. Similarly, most regeneration algorithms used in forest models do not capture the effect of climate change [ 27 ]. In any case, climate change needs to be directly linked to modelling physiological responses (e.g., phenology, photosynthesis, respiration) and to frequency and severity of disturbances (fire, drought, insects’ outbreaks, etc.). In turn, changes in these processes will also affect other ecosystem processes (allocation, allometry, growth at tree level, biodiversity, and competition at ecosystem level), and therefore, simulating climate change effects will indirectly be needed to improve how such processes are modelled.

Remote Sensing and Biomass Accounting

Biomass (in the form of timber, firewood, cork, fruit, resin, charcoal, etc.) has traditionally been the most important commodity obtained from forests. Therefore, it is not surprising that the different ways to estimate forest biomass and other closely related variables (i.e., timber volume, carbon) are still among the most important topics in current forest modelling efforts (Fig.  1 ). Among them, modelling strategies to sequester C stands out as one of the most important topics [ 28 ]. The large size and immobile nature of trees allow individual features such as diameter and height to be measured at different times over extended periods. Such an inventory-based approach can provide a wealth of data, but it quickly becomes a cumbersome task when large and diverse forest areas need to be assessed. However, the explosive development of remote-sensing techniques, the lowering prices of unmanned aerial vehicles, and the continuous growth in computing capabilities are generating the ability to finally obtain detailed assessment of not only the basic population features but also the structure and spatial distribution of individual trees over large areas [ 29 ••].

A model convergence towards the tree scale for meaningful C-cycle modelling, both from upscaling more physiologically oriented models and downscaling stand-level C accounting models, has been noted [ 30 •]. However, not until very recently have researchers looked for ways to incorporate structural diversity into process-based models. A detailed review on the potential and limitations of using terrestrial laser scanning to calibrate functional-structural plant models is available [ 31 •]. One of the main advantages of linking both modelling approaches is the potential to include physiological models into a realistic structure of plant communities. This could move structural modelling from individual to community level. In fact, there are suggestions that the merging of allometry, empirical observation, remote sensing, and individual-based modelling will contribute to a more unified vision of forest ecology [ 32 ]. However, to reach such a level of integration, proper processing of terrestrial laser scanning data is needed. In addition, researchers should avoid the temptation of upscaling functional-structural plant models to the landscape level, as it will be challenging due to the potential to misrepresent other ecological processes more relevant at such a spatial scale [ 33 , 34 ].

Another important challenge to incorporate more remote sensing into forest models is the need for increased measures of standardization and uncertainty in observations [ 35 ]. However, these authors also highlight the high potential of remote-sensing data to automatize carbon models, which currently need manual and time-consuming calibration. In this respect, several issues have been identified when increasing the importance of remote data acquisition of canopy structure, such as the need for standardization of modeling approaches, the need for open datasets, the need to improve allometric models, and the need for stronger validation protocols [ 29 ••].

Allometric models are as important as remote sensing to estimate timber volume, biomass, or carbon stocks. Such models have been extensively used in the past but usually using data from pure and coetaneous stands [ 14 , 35 ]. This situation introduces an important bias when estimating carbon or biomass stocks in natural forests, which are usually multispecies and multiaged, as species allometry changes in the presence of competitors [ 36 ]. Hence, using allometric equations from pure stands could be a source of uncertainty when modelling mixed stands, as there are significant differences in allometry for a given species when growing in a single- vs. multiple-species stand [ 37 ]. In addition, many of these allometric models do not include climatic or stand-level features [ 14 ], although recent research has been undertaken to address these shortcomings [ 25 , 36 ].

The combination of different remote-sensing techniques such as LiDAR and radar can help to accurately model forest structure [ 29 ••]. An additional feature of models based on remote sensing is the potential to simulate and estimate radiation levels through the canopy and on the understory based on 3D data from LiDAR measurements. For example, the division of the canopy into volumetric pixels (or “voxels”) allows for simulating the interaction between trees, understory, and radiation at individual-tree levels or even smaller scales. In fact, 3D canopy simulation can be a more reliable way to estimate energy and C fluxes than traditional inventory-based approaches [ 38 ]. In addition, such models could help in improving connections between forest and atmosphere models [ 39 ].

Additional issues when simulating C fluxes, particularly C allocation, have been identified [ 40 •]. These authors have highlighted that the common use of fixed ratios for allocating C to plant organs is a severe oversimplification under climate change, as it removes from the model the sensitivity to environmental conditions and disturbances. In addition, the usual time steps in forest models (seasonal or annual) are too large to capture C allocation dynamics and resource acquisition. In summary, the generalized use of allometry and inventory-based approaches is just not adequate to capture short-term C dynamics [ 40 •].

Patterns vs. Processes

A second main topic in current forest modelling research is the development of new and refined methodological approaches, mostly through the use of advanced mathematical or statistical tools or by borrowing them from other fields. New progress is made almost daily in deep learning methods than are revolutionizing modern ecology [ 41 ]. These methods have great potential to improve computationally costly tasks such as classification of information from remote sensing or simulation of interactions between individuals in large forest areas. The use of these advanced statistical techniques is greatly expanding modelling capabilities to link research done at multiple scales, to simulate larger regions, and to incorporate dynamic changes at shorter temporal scales (crucial for accurate C flux modelling).

The need for such increasingly powerful approaches is clear by the two keywords highlighted in our review for this cluster (“prediction” and “pattern,” Fig.  1 ). There is a dire need for tools that can provide usable predictions for managers, as the forestry sector needs to adapt to climate change even earlier than other sectors, given the long-term consequences of current management decisions [ 42 ]. Hence, using techniques to simplify model use will undoubtedly facilitate the generation of tools easy to interpret and to share with non-modelers, and that can be easily compared with expert knowledge [ 43 ]. This idea of simplification while retaining the behavior of complex process-based models is behind the developments of “model emulators” [ 44 ].

Model emulators are built to mimic the same outputs from complex (usually process-based) models, with the main objectives of reducing computing requirements. This simplification allows for integration of the emulator in other modelling platforms (and therefore connectivity with other models or submodules different from the original process-based model), to expand temporal and spatial scales not reachable with the original process-based models or to simplify interaction with model users. Such expansion of the basic model could be crucial to understand ecological patterns that emerge at higher scales and that otherwise would not have been directly inferred by the underlying process-based model [ 45 ]. Hence, emulators could be valuable tools in the future to understand ecological patterns at large scales, particularly under novel ecological conditions created by the combination of climate, biodiversity, and land-use changes.

However, the development of emulators also brings an important challenge to the field of ecological modelling. The substitution of process-based algorithms by machine-learning based decision rules offers clear advantages. Nonetheless, it could also be considered as a process to create “black box” models in which scientific understanding of ecological process is impeded, as the mechanisms behind such processes are simplified to just algorithms that have the same outcomes. A detailed review on model simplification is available [ 46 ].

Obviously, this situation highlights the need for a dual direction in scientific advancement: while emulators are clearly useful tools to study ecological patterns, ecological processes can be better studied with mechanistic process-based models (although such a division is not so clear [ 44 ]). Advancement along both lines will also support the development of “digital twins”: computer-based copies of real forests constructed to mimic the most intricate patterns and processes, with visualization of virtual stands as one of their main strengths. These digital tools are already being proposed to train managers and researchers in understanding how climate change and new management techniques could facilitate the transition of the forest sector towards novel conditions [ 47 ]. Obviously, digital twins depend not only on the simulation and visualization techniques used but also on particularly the availability of quality data to calibrate them. Here again, remote sensing, forest inventories, and traditional fieldwork data will be crucial, as the old-fashioned rule in ecological modelling is still valid: in the absence of adequate data, all different modelling options are equally valid [ 43 ].

Productivity Still a Concern

A third popular topic in current forest modelling is related to forest productivity and growth (Fig.  1 ). This indicates that, even if for more than two decades efforts have been made to add non-timber forest products to forest models (i.e., [ 48 ]), estimating forest productivity is still a major issue in the field. This research cluster is clearly focused on how tree growth is influenced by climate. One of the key features of the research on this topic are the continuous calls for development of new growth models for species and regions outside North America, Europe, and to a lesser extent Asia [ 49 , 50 ••]. An example of successful model application around the world is the spread in the use of 3-PG, which was originally developed for Australian eucalyptus plantations but has been embraced and modified for its application in multiple regions and stand types [ 51 ]. The widespread application of 3-PG by scientists and managers was recognized in 2020 by the Marcus Wallenberg Prize which was awarded to their developers ( https://mwp.org/link-to-mwp-digital-ceremony-and-symposium/ ).

Productivity estimations will remain crucial in the near and medium future, as commercial forestry will likely become more focused on high-yield intensively managed plantations to sequester and substitute carbon-intensive materials. Conservation forestry will increasingly expand into forest reserves around the world to increase stored carbon and protect biodiversity. In this context, the development of basic (but management-friendly) correlational models such as allometric and inventory-based models is needed [ 35 , 52 , 53 ]. However, the need to include climate in all these new models is certainly a challenge for new regions and species, as they would need either long-term data series or an extensive network of inventory plots to account for climatic influences on tree growth rates or allometry. Hence, new developments in automatic and climate-sensitive tree monitoring devices may be helpful [ 12 ].

Modelling Forests Beyond Trees

While tree growth and productivity are still an important topic, the largest cluster of research topics identified was related to modelling forest components other than trees. Most of this research is based on the clear understanding that for models to be able to handle climate change effects, it is essential to include more ecosystem components that historically have received less attention [ 21 ].

Some key issues are the improved assessment of carbon and water cycles. For example, it has been stated that those models using drought indexes that include an evaporative component work better, but also that there is just a small number of studies actually evaluating drought indexes against physiological indicators of water stress [ 54 ]. In this respect, a recent review of the way in which the representation of evapotranspiration processes has evolved in forest models has noticed a trend towards the simplification from the initial attempts, achieved by the availability of more empirical data and model evaluation tests that have allowed the refinement of simulation algorithms [ 55 ]. These authors have pointed that such simplification allows for further connections to water flow models and the scalability of such research. This is an important advance, as the common oversimplification of eco-hydrological processes in models makes linkages with socio-economic values more difficult to evaluate [ 56 •]. These authors also pointed to a lack of empirical work on effects of water availability in forest productivity. Further developments that mechanistically link hydraulic conductance with physiology, growth and mortality are taking place [ 57 , 58 , 59 ].

How biodiversity is integrated into forest models is another of the issues in this keyword cluster. Traditionally, there is a biodiversity bias towards trees in forest models [ 60 ]. This is not surprising, as biodiversity interactions (both animal and vegetal) in forests are a complex and broad field that have not been incorporated into models until relatively recently, and that still remains largely ignored in operational models used in forest management. In this regard, a lack of integration of modelling approaches at different spatiotemporal scales has been identified as a barrier to implement biodiversity into forest modelling [ 61 ]. Similarly, calls for more attention to the role of understory in key ecological processes have been raised [ 62 ], even if early examples of the importance of tree-understory interactions when simulating commercial forestry are available [e.g., 63]. It is currently advocated that the most efficient approach is to use plant functional traits that can accommodate the inherent complexity of understory communities. To do so, models must have detailed time and spatial scale to allow for the different ecophysiological behaviors (many times resource opportunistic) that understory species usually display, particularly following disturbances [ 64 ].

An important effort currently taking place in vegetation science is determining how functional traits can be applied to models to understand how species with different traits interact. An important and ongoing development is to expand the functional trait approach being developed for vegetation studies [ 65 ]. This is particularly important in highly diverse ecosystems such as tropical forests in which it is unrealistic to simulate forest dynamics with only a few dominant species.The functional trait approach is now being expanded to model species interactions including animals, particularly herbivores. However, mechanistic models of forest pests are usually based on correlations between environmental variables (e.g., degree days) and growth rates (usually at individual or population scales), and limited to some of the pest’s life cycle stages. Hence, there is a need for models able to integrate current algorithms that simulate specific pest and pathogens at different development stages to obtain meaningful estimates of their interactions with the rest of forest components [ 43 ]. More intriguingly, concerns have been raised around the usually forgotten role of megafauna in forest models [ 3 ••]. Although it has been traditionally assumed that the effects of megafauna are realized at the forest level through seed dispersal, arguments exist to also consider their impacts on nutrient cycling and plant demography, such as the role of megafauna on predation of plant reproductive organs, mortality caused by herbivory or trampling, and nutrient redistribution related to animal residues [ 3 ••]. A serious effort to better understand the role of megafauna in forests is needed, given the current situation of defaunation in many areas of the world, which in some areas is trying to be reversed by rewilding actions. The use of “herbivore functional traits” (equivalent to the already accepted concept of plant functional traits) and different ways to incorporate linkages between plant and herbivores into process-based models have been suggested [ 3 ••]. This issue is not limited to tropical or natural forests, as the influence of large herbivores on tree and shrub density in boreal [ 66 ] and temperate forests [ 67 ] has been reported, with or without management.

Other approaches to account for biodiversity include the use of habitat and species distribution models. They link the smallest (habitat) to the largest (distribution) spatial scales and provide a better understanding of the potential impacts of novel ecological conditions over the mid to long term. The dramatic increase of available data on climate, soils, and species distributions allows for finely gridded modelling at both temporal and spatial scales. This advance allows statistically based species distribution models to be linked to process-based models [ 16 , 68 ], although better understanding of absence data and improved inclusion of abiotic interactions will become crucial to estimate effects of climate change [ 69 , 70 ].

Finally, an always-important topic in forest models is the integration of management into modelling. Such integration has two clear foci: simulation of management practices and involvement of forest managers into the modelling process [ 71 ]. As forest management is inherently an ecological disturbance, including management simulation in forest modelling should not be limited to anthropogenic actions but should include natural disturbances as well. However, the main limitation that needs to be solved is the lack of information on the specific mechanisms that link climate change with disturbances [ 26 ]. This is especially important when several disturbances can be connected through cascading effects on the ecosystem [ 42 , 72 ].

Important conceptual advances in disaggregating disturbances into their constituent components and embedding disturbances into system dynamics have been recently completed [ 50 ••]. These authors have identified as important challenges the need for simulating nondeterministic competitive interactions between tree species and their responses to disturbances and suggest using life history traits to overcome this issue. However, although these linkages among disturbances have been long recognized in forestry, little research has actually incorporated them into forest models, particularly as multi-disturbance models [ 50 ••]. In addition, most models that incorporate disturbances predict probabilities for such disturbances to happen depending on different stand features, but not the disturbances effects [ 26 ]. Among disturbances, wildfire modelling is an important field by itself. As in the case of other disturbances, abiotic factors such as slope, elevation, distance to roads, or weather patterns are important for incorporating complexity at small spatial and temporal scales [ 73 ]. However, getting good quality for such small-scale variables could be a challenge in areas with dense forest cover and sparse road networks, as is the case in most tropical or boreal forests [ 74 ].

Another important step in making forest models more meaningful for stakeholders include modifying the way models are created. The focus on participatory processes in which model users and forest stakeholders interact with forest modelers during the inception of the modelling studies is being increasingly recognized as fundamental for the model to make actual impact in the forest sector [ 44 ]. This approach aims to bring nonacademic forest stakeholders into the process at the beginning, so they develop a sense of ownership of the research outcome and therefore are much more likely to implement the model outcomes. Three models for science-policy interaction have identified [ 74 ]: the “linear phase” when science informed policy-making in a unidirectional manner, the “interactive phase” when both sides found themselves in a continuous interaction, and the “embedded phase.” Our own experience is that the linear phase is still dominant in many regions, with scientists developing models and scenarios of their interest and then approaching nonacademic stakeholders with their results. Only in some scarce cases the interaction has progressed and moved into the second stage of science-policy interaction (i.e., [ 44 ]). It is then time to push towards a multi-actor approach (the second “interactive” phase of bringing science into practice). However, to achieve this goal, models need to be accessible, relevant, and user-friendly for non-modelers and address current forest management concerns to actually bring change into forestry practices [ 76 ]. A comparison on how different European decision support systems are facing these challenges has identified the need to incorporate forest owner behavior and accurate spatial analysis to better estimate landscape-level provisioning of ecosystem services [ 77 ].

Next Challenges for Forest Model Convergence

Understanding how complex ecosystems such as forests are structured and function as a system has been, still is, and will be challenging. The challenge lies in understanding how climate change affects forests, while our understanding on how to model forests under “normal” conditions is still far from complete. In addition to the most popular topics currently being explored in forest modelling discussed earlier, we have identified through our review several topics that deserve mention due to their relevance, even if they did not explicitly appear in the keyword map in Fig.  1 . Such topics include the following:

Small forests : Landscapes around the globe are becoming increasingly fractioned, making small forests of a few hectares or smaller increasingly common. Managers of such forests usually have limited resources to access and use models, and models usually lack representations of external factors (such as the vicinity of agriculture lands) that can be relevant for the functioning and structure of small forests [ 76 ].

Urban forests : As urban landscapes expand, urban forests are becoming very important in delivering a multitude of ecosystem services. However, urban forest models have been developed only for few regions around the world (i.e., USA, Europe, and China) and are mostly correlational in nature. To better assess the effects of climate change on ecosystem services, better linkages with ecophysiological mechanisms must be incorporated into urban forest models [ 49 ]. Among the potential ecosystem services that could be modelled in urban forests are not only carbon sequestration [ 78 ] but also aesthetic values [ 79 ].

The Global South : A recurrent finding in all recent forest modelling reviews is the strong bias towards North America and Europe [ 38 , 50 ••, 52 ], followed by East Asia to a lesser extent (mostly China and Japan). Some isolated modelling hotspots in the southern hemisphere are Australia (which has generated one of the most successful forest models, [ 51 ]) and Brazil (mostly focused on modelling plantation forests but also generated some work on Amazonian forests). More effort must be made to better understand the applicability of models from other regions to these areas that are underrepresented in the scientific modelling literature. This is an important research area given regional variations in terms of tree, understory and wildlife species composition, and other environmental constraints such as climate, edaphic factors, or human management models.

Overlooked physio-ecological processes : Two important mechanisms have attracted little attention in forest models until now. One is regeneration (including masting), which is now recognized as a process that can significantly affect biomass allocation and hence carbon and energy flows. Even if detailed conceptual models on forest regeneration have been available for some time (i.e., [ 80 ]), regeneration has usually been oversimplified in forest models [ 81 ]. However, recent important advances in understanding the masting process allow for the implementation of mechanistic models [ 82 ]. Giving the inherent complexity and current incomplete understanding of the process, modelling regeneration patterns could be a more practical approach than modelling processes in order to avoid error propagation, especially if models are to be scaled up to regional or larger areas [ 83 ••]. Another overlooked topic is root growth and function. Traditionally, the simulation of fine roots has been underdeveloped compared to leaves, and hence, a common approach has used allometric relationships of fine roots to other biomass fractions [ 84 ]. However, the latest research indicates that this is not always appropriate, but also that enough data for mechanistic root models are starting to be available [ 85 ]. Given the important role of roots in carbon, nutrient and water cycles, and the influence of such cycles on tree mortality [ 86 ], a more mechanistic modelling approach would be desirable.

Uncertainty assessment : Traditionally, the study of climate change effects on forest has relied on modelling different climate scenarios, management options, and their interactions. However, such an approach does not provide a clear picture of the uncertainty around model predictions. Hence, moving from scenario assessment towards uncertainty analysis has been proposed [ 56 •, 63 ]. To do so, using predictions from different models would be useful, particularly if the models use different approaches [ 16 ]. The viability of assessing uncertainty through using envelopes of models has been demonstrated and refined [ 19 , 87 ].

Conclusions

Our review of current trends in forest modelling has shown that climate change is the main driving force that is stimulating researchers to develop new approaches and methods to model forest ecosystems and forest managers to use such models. It has also shown that we are at an exciting moment, in which the development of new statistical and measurement techniques is finally creating opportunities for developing true inter-scale models, from individuals to regions and beyond. In addition, the present need to incorporate users into the modelling process is stronger than ever, and options exist to simplify science-based models into operational models without losing accurate representation of ecological patterns. However, the need to better understand ecological process is also more important than ever as climate, biodiversity, and land-use changes move forest ecology of the Earth to novel conditions. Hence, improving the mechanistic representation of ecological process in an integrative manner that moves beyond trees will be crucial for meaningful predictions of forest ecosystem development under novel conditions. In conclusion, we have shown that the traditional division between process-based and statistical models lacks actual meaning, as the major trend is towards cross-scale integration of different modelling approaches.

Data Availability

The data presented in this study are available on request from the corresponding author.

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Blanco, J.A., Lo, YH. Latest Trends in Modelling Forest Ecosystems: New Approaches or Just New Methods?. Curr. For. Rep. 9 , 219–229 (2023). https://doi.org/10.1007/s40725-023-00189-y

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Multifaceted applications of synthetic microbial communities: advances in biomedicine, bioremediation, and industry.

1. Introduction

2. definition and importance of microbial communities, 2.1. synthetic microbial communities, 2.2. artificial communities, 2.3. semi-synthetic communities, 3. interactions in microbial communities, 4. methodologies and tools in design of synthetic microbial communities, 4.1. computational models, 4.2. importance of genetic circuits in microbial communities, 4.3. crispr, 4.4. quorum sensing (qs), 5. applications of synthetic microbial communities, 5.1. biomedicine and health, 5.2. bioremediation and industry, 6. bioethics: potential risks in implementing synthetic microbial communities, 7. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Contreras-Salgado, E.A.; Sánchez-Morán, A.G.; Rodríguez-Preciado, S.Y.; Sifuentes-Franco, S.; Rodríguez-Rodríguez, R.; Macías-Barragán, J.; Díaz-Zaragoza, M. Multifaceted Applications of Synthetic Microbial Communities: Advances in Biomedicine, Bioremediation, and Industry. Microbiol. Res. 2024 , 15 , 1709-1727. https://doi.org/10.3390/microbiolres15030113

Contreras-Salgado EA, Sánchez-Morán AG, Rodríguez-Preciado SY, Sifuentes-Franco S, Rodríguez-Rodríguez R, Macías-Barragán J, Díaz-Zaragoza M. Multifaceted Applications of Synthetic Microbial Communities: Advances in Biomedicine, Bioremediation, and Industry. Microbiology Research . 2024; 15(3):1709-1727. https://doi.org/10.3390/microbiolres15030113

Contreras-Salgado, Edgar Adrian, Ana Georgina Sánchez-Morán, Sergio Yair Rodríguez-Preciado, Sonia Sifuentes-Franco, Rogelio Rodríguez-Rodríguez, José Macías-Barragán, and Mariana Díaz-Zaragoza. 2024. "Multifaceted Applications of Synthetic Microbial Communities: Advances in Biomedicine, Bioremediation, and Industry" Microbiology Research 15, no. 3: 1709-1727. https://doi.org/10.3390/microbiolres15030113

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• Published: 29 August 2024

Ecological zoning for climate policy and global change studies

• Philip Audebert   ORCID: orcid.org/0009-0007-5244-4702 1 ,
• Eleanor Milne   ORCID: orcid.org/0000-0002-2602-1040 1 ,
• Laure-Sophie Schiettecatte 1 ,
• Daniel Dionisio 1 ,
• Maidie Sinitambirivoutin 1 ,
• Carolina Pais 1 ,
• Clara Proença 1 &
• Martial Bernoux   ORCID: orcid.org/0000-0002-2913-3590 1  

Nature Sustainability ( 2024 ) Cite this article

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• Climate-change mitigation
• Environmental impact

As climate change accelerates, nations are moving towards meeting their nationally determined contributions and reducing greenhouse gas (GHG) emissions. Reporting of this from the agriculture, forestry and other land use sector relies on data related to land use and management, climate and soil type. Where such data are unavailable, the Intergovernmental Panel on Climate Change (IPCC) provides a set of default factors, based on an extensive literature review of likely GHG emission factors and carbon stock changes disaggregated by the Food and Agriculture Organization’s global ecological zones. As understanding of global ecological zones under environmental change improves, it becomes necessary to reassess such ecological zoning approaches to enable reporting of GHG emissions to support nationally determined contributions and global change studies. Here we propose a globally consistent ecological zoning approach based on Holdridge life zones using climatic data from the Climate Research Unit on a 0.5° grid, which tackles certain limitations found in the existing guidance provided by the IPCC. A set of three global ecological zone maps based on Holdridge life zones were devised using increasing levels of aggregation, which could support sustainability studies of global environmental change, specifically climate change, and be used as a zoning approach by the IPCC.

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Data availability

All data used in this article is publicly available and correctly referenced by the authors. The authors mainly used climate data from CRU and elevation data from USGS EROS. The codes and assets are made available via the links below on Google Earth Engine. Climate data from CRU can be accessed via https://crudata.uea.ac.uk/cru/data/hrg/ . Elevation data from USGS EROS can be accessed via https://www.usgs.gov/centers/eros/science/usgs-eros-archive-digital-elevation-global-30-arc-second-elevation-gtopo30 .

Code availability

The entire code can be accessed on Google Earth Engine via https://code.earthengine.google.com/?accept_repo=users/philipaudebert/HLZs . The assets can also directly be accessed via https://code.earthengine.google.com/?asset=users/philipaudebert/HLZ/Level1 , https://code.earthengine.google.com/?asset=users/philipaudebert/HLZ/Level2 and https://code.earthengine.google.com/?asset=users/philipaudebert/HLZ/Level3 . The code can also be accessed on Github via https://github.com/phil-aud/ecological-zoning .

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Acknowledgements

The authors thank all experts from the FAO, notably the Forestry Division, Land and Water Division and the Office of Climate Change, Biodiversity and the Environment, and the IPCC for their participation in the technical consultations to validate the methodology of the proposed ecological zoning approach. No specific funding was awarded for writing up this paper. However, this paper was produced with the support of FAO and the French Development Agency (AFD).

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Philip Audebert, Eleanor Milne, Laure-Sophie Schiettecatte, Daniel Dionisio, Maidie Sinitambirivoutin, Carolina Pais, Clara Proença & Martial Bernoux

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Contributions

P.A. and E.M. were responsible for formulating the overarching research goals and aims, designing and validating the methodology and writing the paper. P.A. was responsible for implementing the computer code and supporting algorithms, ensuring the reproducibility of results, conducting the formal analysis and synthesis of study data. L.-S.S. was responsible for validating the methodological approach and writing the paper. D.D. and M.S. were responsible for testing of existing code components and for the provision of study materials. C. Proença and C. Pais were responsible for the visualization of the published work. M.B. was responsible for the supervision of the research activity.

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Correspondence to Philip Audebert .

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Extended data

Extended data fig. 1 equivalence of altitudinal belts and latitudinal regions..

Figure showing how different altitudinal belts were systematically assigned to a life zone using a life zone found in the latitudinal equivalent. Adapted from Holdridge.

Extended Data Fig. 2 Correspondence of IPCC Climate Zones and HLZs.

The stacked column chart shows the relationship between the IPCC Climate Zones and the Holdridge Life Zones where each colour represents the occurrence of a HLZ within each of the IPCC Climate Zones. The twelve IPCC Climate Zones are represented on the x-axis, whereas the y-axis represents the pixel distribution of each of the HLZ.

Supplementary information

Supplementary information.

Supplementary Tables 1 and 2. Supplementary Table 1. Equivalence table between the IPCC climate zones and ecological zones. Supplementary Table 2. Summary table of existing ecological zone maps.

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Audebert, P., Milne, E., Schiettecatte, LS. et al. Ecological zoning for climate policy and global change studies. Nat Sustain (2024). https://doi.org/10.1038/s41893-024-01416-5

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Received : 06 November 2023

Accepted : 24 July 2024

Published : 29 August 2024

DOI : https://doi.org/10.1038/s41893-024-01416-5

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