APPENDIX 2. Evaluation of modeling approaches

Conceptual models

Analytical framework for integrating multi-disciplinary research. As noted in the main text, research was underpinned by the development of a conceptual model describing the impacts of human activities on different components of biodiversity, which considered the relationships between different types of anthropogenic disturbance, habitat characteristics and ecological processes at the scale of both landscapes and individual forest patches (Fig. 1). The model was developed at the outset of the research programme, and provided a valuable framework for planning and implementing research activities, as well as guiding both data collection and modelling work. However, the model did not provide a basis for developing an overall integrated model of human impacts on biodiversity, as was initially considered at the outset of the research. This is because of the difficulty of measuring or modelling some of the ecological processes concerned, such as natural selection and dispersal / migration of individuals (although some insight into the latter was provided by molecular marker studies).

The selection of habitat characteristics in the model was very much influenced by spatial metrics emerging from the discipline of landscape ecology, yet in the light of the research results obtained, stand-scale variables such as stand structure and composition also emerged as important indicators of human impacts, and with hindsight should have been explicitly included in the model. The latest phase of the research (the ReForLan project) has therefore developed a new conceptual model to provide an analytical framework for the research, which incorporates these variables (Newton 2008a). In addition, this revised model has been developed according to the DPSIR framework (EEA 1998), to facilitate the identification of suitable indicators for monitoring progress towards SFM objectives (with a particular focus on forest restoration).

Edge effects. In the case of research on edge effects, little progress has been made in developing quantitative models, but two conceptual models have recently been developed (Ries et al. 2004, Harper et al. 2005). Although our research highlighted some limitations in these models, they provided a useful framework for integrating and comparing the results of site-specific studies, and therefore for developing and testing generalisations. As noted by Ries et al. (2004), much work remains to be done regarding the development and rigorous parameterization of models relating to edge responses and their links with conservation management.

Ries et al. (2004) also highlight the fact that limited progress has been made in scaling up edge responses to the landscape scale. Such scaling is required for edge responses to contribute significantly to the development of management and conservation strategies (Sisk and Haddad 2002). Current approaches to scaling up edge responses focus on estimating the distance of edge influence within a patch (the ‘core area’ model, Laurance and Yensen 1991), or on describing parameters as a function of distance from an edge (the effective area model, Sisk et al. 1997). We employed both of these methods in our research (Echeverría et al. 2007a,b, 2008, Cayuela et al. 2006a,b,c,d). However, neither of these approaches can incorporate variable edge responses relating to landscape-scale interactions such as edge orientation or patch size (Ries et al. 2004).

Genetic variation
The integration of information on genetic variation with other measures of biodiversity represents a significant challenge. The problem is partly one of scaling: processes influencing genetic variation can operate at a range of scales, from landscapes to individuals, or even individual genes or gene complexes. Understanding of the ecological genetics of tree species is supported by a large body of empirical theory, but as noted here, results obtained for widely distributed north-temperate taxa appear to have limited applicability to species of the geographic areas where our research was undertaken (Premoli et al. 2007). Nevertheless, data from molecular markers can provide valuable information about ecological processes such as dispersal and migration, and helped refine the conceptual understanding of the impacts of forest fragmentation (Newton 2007b).

One of the limitations of data obtained from molecular markers is that they are usually unrelated to adaptive variation. Ideally, conservation decisions should take account of patterns of adaptive variation, as this is likely to be crucial for the evolutionary viability of populations (Newton 2007a). Little research has been directed towards analysis of adaptive variation in tree species native to the study areas described here, but available data indicate that substantial population differentiation exists (Bekessy et al. 2002; Souto and Premoli 2007). Development of a modelling toolkit for SFM (Sturtevant et al. 2007) might therefore usefully include tools for integrating both quantitative and molecular marker variation with other biodiversity measures.

Statistical models

Although not explicitly considered by Sturtevant et al. (2007), statistical modeling approaches provide a useful component of a modeling toolkit for SFM. For example, we employed statistical modeling approaches (particularly logistic regression) for analysis of forest loss and fragmentation (Echeverría et al. 2007a,b, Wilson et al. 2005, Cayuela et al. 2006a,c). This enabled the drivers of both forest loss and fragmentation to be identified, and forecasts of potential future land cover change to be developed. A comprehensive analysis of such underlying drivers is required in order to inform future policy decision-making and land-use planning, and in order to provide an understanding of the processes of forest loss rather than solely patterns (Bürgi et al. 2004). Here we use the term “drivers” to refer to spatial pattern drivers, or landscape features, that influence where forest loss and fragmentation is likely to occur.

Modeling of land-cover changes such as deforestation requires combining spatially explicit ecological data with information on socio-economic factors. One of the main limitations to this approach is the lack of accurate data on relevant socio-economic variables, although this situation is continually improving within our study areas. A further limitation is that the outputs of statistical regression must be interpreted with caution; many socio-economic and environmental variables are correlated with each other, and the identification of a significant statistical relationship does not necessarily indicate causality between the variables included in the model. A further point is that the output of statistical models can readily be coupled with other models, such as models of forest dynamics at the stand or landscape scale.

SPARs

In order to evaluate the potential loss of species richness resulting from forest loss and fragmentation, statistical models describing the latter processes were combined with SPARs (Rey Benayas et al. 2007). These represent a form of empirical model, although recently efforts have been made at developing underlying theory (McGill and Collins 2003). SPARs have been widely used for this purpose, but despite their popularity, they suffer from a number of limitations (Sala et al. 2005). Most important of these is the fact that extinctions forecast by such analyses do not occur immediately after a reduction in habitat area. Rather, analyses indicate the number of species that would be expected to go extinct when species numbers reach an equilibrium in a reduced area of habitat (Sala et al. 2005). Evidence suggests that many decades may be required for this equilibrium to be reached (Helm et al. 2006). Furthermore, some species may still be able to survive in an area following conversion of habitat to some other land cover type, making species loss difficult to estimate using this technique (Sala et al. 2005). Another main limitation is that SPARs predict species numbers rather than species composition. It is possible for substantial changes in species composition to occur with little or no change in species richness, yet in conservation terms, it is the species composition that may be of greatest interest (Lindenmayer and Franklin 2002).

Stand dynamics

Three main approaches have been employed for examining the dynamics of forest stands, as summarized below.

FORMIND was developed in the late 1990s at the University of Kassel, Germany specifically for exploring the dynamics of lowland tropical rain forest. It is now one of the most widely applied models for such species-rich forests, having been applied to study the effects of logging, fragmentation, and climate change in Malaysia (Köhler et al. 2001, Köhler and Huth 2004, Huth et al. 2004, 2005), sustainable timber harvesting in Venezuela and Paraguay (Kammesheidt et al. 2001, 2002), and fragmentation effects in French Guyana (Köhler et al. 2003). FORMIND is an individual-oriented forest growth model, which simulates the spatial and temporal dynamics of uneven-aged mixed species forest stands (Kammesheidt et al. 2001, Köhler et al. 2001, 2003).

The following description of the model is based on that presented by Rüger et al. (2007a). FORMIND simulates a forest (in annual time steps) as a mosaic of interacting grid cells with a size of 20 m × 20 m, which is the approximate crown size of a large mature tree. Light availability is the main driver of individual tree growth and forest succession, and within each grid cell all trees compete for light and space following the gap model approach. Each grid cell is divided into horizontal layers for the explicit modelling of the competition for light. The carbon balance of each individual tree is modelled explicitly, including the main physiological processes (photosynthesis, respiration) and litter fall. Growth process equations are modified from the models FORMIX3 and FORMIX3-Q (Ditzer et al. 2000, Huth and Ditzer 2000, 2001). Allometric functions relate above-ground biomass, stem diameter, tree height, crown diameter and stem volume. Tree mortality can occur either through self-thinning in densely populated grid cells, senescence, gap formation by large falling trees, or medium-scale windthrows. Tree regeneration rates are effective rates of recruitment of small trees at a diameter at breast height (dbh) threshold of 1 cm, with seed loss through predation and seedling mortality already being implicitly incorporated. Water and nutrient availability are assumed to be homogeneous and there is no inter-annual variability of climatic conditions in the model.

While the model was successfully applied to the exploration of forest dynamics in both Chile and Mexico (Rüger et al. 2007a,b; 2008), FORMIND is difficult to parameterise completely, in common with other process-based models of forest dynamics. To cope with high species richness, tree species were grouped into plant functional types according to their maximum height and light demand. While environmental parameters and allometric relations of tree geometry were relatively easy to obtain from field measurements, measurements of physiological parameters were often not available and had to be estimated. Independent field data were used to validate overall model results (Rüger et al. 2007a,b). To improve the data basis for model parameterisation and evaluation it would be desirable to obtain inventory data from larger areas, from secondary forests of different ages, as well as information about mortality rates and the frequency and extent of large-scale disturbances (Rüger et al. 2007a).

PINQUE is based on the JABOWA-FORET class of gap models, and was programmed in the open-source R language (see The R Foundation for Statistical Computing, http://www.r-project.org/). The following description is based on that provided by Golicher and Newton (2007). In common with many other individual-based forest stand simulators, the model uses a species specific function that predicts the expected diameter increment for a tree of a given diameter under optimal growth conditions. The model uses fundamental growth equation employed by JABOWA-FORET; modelled individuals do not grow at this optimum, owing to constraints imposed by shading, temperature, water or nutrient availability. In common with other gap models, a simple allometric relationship is used for estimating the shading effect of individual tree canopies. Canopy light transmission is typically calculated using an algorithm that places the trees in order of height within each patch and calculates the leaf area for each tree. Results of field and greenhouse trials were used to produce the assumed growth response of different species with respect to overall light availability. Establishment was based on the proportion of ambient light received at ground level in the model, in relation to the degree of shade tolerance of individual species.

PINQUE represents a simpler type of model than FORMIND, and is correspondingly easier to parameterise. However, once again, a number of assumptions had to be made regarding parameter values because of the lack of detailed ecological and physiological information regarding the tree species occurring in the study area. Despite such uncertainties, model simulations compared well with existing field data, and were used to refine the available empirical theory regarding the dynamics of disturbed montane forest in Mexico (Golicher and Newton 2007).

Markov model. The dynamical consequences of recruitment patterns for stand dynamics and composition can be easily explored with a Markov model, which assumes that the probability of replacement of one canopy dominant species by other is proportional to the density of juvenile individuals of the latter (Horn 1975). The transition matrix that evaluates the probability of replacement across species combinations is then multiplied by a vector that represents initial stand composition, t. The resulting product is another vector representing the expected stand composition at the next generation t + 1 (the generation time is the time that a tree can remain as a canopy dominant, or maximal age). Field data were used to parameterize a transition matrix for forest stands in Chiapas, and used to explore the successional relationships of forest stands (Zavala et al. 2007). While analytically simple, the results proved useful for understanding the potential impacts of human activities on forest composition (Zavala et al. 2007), providing information complementary to the results of other models of stand dynamics.

The main challenge in using Markov models for exploring stand dynamics relates to the problem of deriving accurate transition probabilities. Ideally, vegetation should be monitored over prolonged periods; such data are not yet available for the study areas considered here. As the probability of transition from any vegetation category to any other category (or state) must be determined, the number of model parameters is a function of the square of the number of categories in the model (Newton 2007a). There is therefore a trade-off between the increased resolution offered by incorporating a larger number of vegetation categories (or states), and the increased difficulty of accurately parameterizing a model with a larger number of transition probabilities. This is particularly problematic given that relatively rare transitions need to be estimated with equivalent precision to relatively common transitions. In addition, Markov models tend to be highly specific to the forest type (and even the particular study area) for which they were created, limiting their practical value. However, it is possible to link Markov or semi-Markov models with gap models enabling the behaviour of the model to be explored at a much larger spatial scale than would have been possible with the gap model alone (Newton 2007a). This is not something that has yet been attempted by our research team.

Landscape dynamics

A number of different modelling approaches have been employed to examine the spatial dynamics of forest cover at the landscape scale, together with associated biodiversity. To date, modelling activities have primarily focused on use of GEOMOD, but in the latest phase of the research, LANDIS-II is being used to explore the impacts of human activities on forest dynamics (Newton 2008a). In addition, a variety of different approaches are being used to analyse the spatial dynamics of the distribution of individual species, particularly in response to climate change. Brief details of each of these approaches are presented below.

GEOMOD is a GIS-based model, which simulates land-use change by predicting the transition from one land-use state to another. Simulations can be based on both environmental and socio-economic attributes as well as spatial data of forest cover at different time intervals (Hall et al. 1995a,b; Pontius et al. 2001). One of the advantages of GEOMOD is that it requires relatively small amounts of data for calibration and validation compared to other complex dynamic models (Pontius et al. 2001). GEOMOD identifies locations where changes in land uses are most likely by using decision rules based on: (a) the pattern of geophysical variables with respect to already deforested land, (b) stratification by political sub-region, and/or (c) nearest neighbours. This rule simulates the manner in which deforestation occurs on the edges of forest patches, or in open areas of forest fragments (Echeverría et al. 2008). GEOMOD was successfully applied in southern Chile, where it demonstrated high predictive power (Echeverría et al. 2008).

LANDIS-II is based on an object-oriented modelling approach operating on raster GIS maps (He et al. 1999, Mladenoff and He 1999, Scheller et al. 2007). The principal modules of LANDIS relate to forest succession, seed dispersal, wind disturbance, fire and timber harvesting. In LANDIS, each cell is a spatial object containing species, environment, disturbance, and harvesting information (Mladenoff and He 1999). Tree species are simulated as the presence or absence of 10-year age cohorts in each cell, rather than as individual trees, greatly reducing the processing power required to perform simulations over large areas. The integration of LANDIS with GIS provides a powerful set of tools with which to explore the potential impacts of management interventions at the landscape scale, which have been used in an increasing number of forest communities in different parts of the world (Mladenoff 2004). The latest version (LANDIS-II) represents a significant development, as the model was re-engineered as an integrated modeling environment, allowing greater flexibility through the use of customized extensions for landscape disturbance and succession, among others (Sturtevant et al. 2007). The main limitation of LANDIS is perhaps its relatively simplistic representation of cohorts (Newton 2007a). We are currently parameterising LANDIS-II for four areas of in Latin America, to explore the potential impacts of fire, livestock grazing and cutting on the spatial dynamics of dry forest, and to examine the potential for forest recovery under different land management scenarios (Newton 2008a). Integration of LANDIS-II with GIS offers ready scope for exchange of spatial data with other modelling tools, such as spatial MCA.

Habitat models. Understanding what constitutes suitable habitat for a particular species is of critical importance to conservation management and planning, yet the specific habitat requirements of many species are poorly understood. Forest managers typically require habitat maps to support management decisions, and such maps may also be required at regional or national scales to inform conservation planning. A range of analytical techniques are now available for building spatial models of species distributions (Elith and Burgman 2003, Guisan and Zimmerman 2000). A number of these are being employed in our current research, including DOMAIN (Carpenter et al. 1993) and MaxEnt (Phillips et al. 2006).

PVA

Matrix models have been widely used to explore the population dynamics of individual tree species, and provide a valuable tool for exploring harvesting impacts (Newton 2007a). However, complete parameterization of a matrix model may often be very difficult to achieve. For example, accurate estimates of mortality rates may be very difficult to obtain for long-lived tree species, and the influence of density dependence is also often difficult to evaluate (Newton 2007a). Potentially the output of such models can be input to other probabilistic models, such as BBNs (Newton 2009), although this has not yet been attempted for tree species. BBNs have however proved useful for integrating socio-economic information relating to the use of tree species (Newton et al. 2006), an approach that has helped identify some recommendations regarding how the sustainable use of tree species can be achieved in practice (Newton 2008b).

Decision-support tools

Three analytical approaches are briefly described here, which we are using to integrate research results (including output from other models) in ways that can be used to support decision-making.

Bayesian Belief Network (BBN). A Bayesian Belief Network (sometimes referred to as a Bayesian network or Belief net) may be defined as a graphical model that incorporates probabilistic relationships among variables of interest. The term graphical model is used because the BBN can be represented in the form of a network diagram, to provide a visual representation of the components and dependencies of a domain. Bayesian networks evolved in the late 1980s through developments of theory developed for graphical models, particularly through the work of Pearl (1986, 1988, 1995). This research established BBNs at the interface between statistics, applied artificial intelligence and expert system development. In common with other Bayesian approaches, BBNs can be considered as tools for updating existing (a priori) information using probabilities as a measure of uncertainty. BBNs may be used as tools for building predictive models, for structuring knowledge or beliefs relating to a domain, or for supporting decision making. The application of BBNs to forest management began in the early 1990s, with Haas (1991) providing an early example.

BBNs differ from most other approaches to environmental modelling by exclusively using probabilistic, rather than deterministic, expressions to describe the relationships among variables, a feature that is particularly useful in the context of risk assessment and for supporting decision making (Borsuk et al. 2004). A BBN represents a description of the probabilistic relationships among the domain’s variables, enabling the joint (or total) probability distribution of all variables to be divided into a series of conditional and unconditional distributions (Borsuk et al. 2004). The graphical nature of the network facilitates visualization of such relationships, and can foster communication among scientists, decision-makers and other stakeholders regarding the relationships between variables in a particular domain.

BBN models do not necessarily replace existing environmental, economic or social models; instead it is possible to take the outputs from such models and incorporate them in BBNs, by converting them into probability distributions. BBNs can therefore be seen as tools for integrating different kinds of knowledge or evidence, including model outputs and quantitative data, together with subjective information such as expert knowledge. In the context of developing a modelling toolkit for SFM, they may have particular value for meta-modelling. The ability to integrate both qualitative and quantitative information is widely considered to be one of the main assets of BBNs, and is particularly welcomed by researchers investigating environmental management, who may often be required to integrate socio-economic with biophysical information.

Further information on the use of BBNs in environmental modelling is provided by Newton et al. (2006) and Newton (2009).

Spatial multi-criteria analysis (MCA). This technique offers a tool for exploring spatial data (integrated with GIS) in relation to decision-making. The approach is particularly well suited to participatory research approaches, as it enables the views of different stakeholders to be integrated and explored. Analyses are typically based on use of the analytical hierarchy process (AHP) and its extensions into the spatial domain. This approach involves the construction of an evaluation matrix, which contains the possible alternatives relating to a particular decision and the criteria against which they will be evaluated. The scores for this matrix can be developed during participatory workshops with stakeholders. The different evaluation criteria are typically characterised by different importance levels, which can vary greatly between stakeholders. This element is included in the analysis by assigning subjective weights to each criterion (prioritisation). A weight can be defined as a value assigned to a criterion that indicates its importance relatively to the other criteria under consideration. Once the weights are assigned, aggregation can be performed using a decision rule that dictates how best to order the alternatives, on the basis of the intrinsic characteristics of the alternatives (criterion scores), and on the preferences of the decision-makers (criterion assessment and weights). Models typically display great sensitivity to these weights, so it is important to adopt a consensual approach in which different weighting systems are evaluated, each representing a contrasting perspective on the decision problem. The sensitivity of a particular decision to the weights and values elicited from stakeholders can be explored in the analysis.

Use of spatial data enables this technique to be integrated with other modelling approaches. For example, the ReForLan project (Newton 2008a) is employing spatial MCA to explore options for forest restoration in collaboration with stakeholders. Outputs of other spatially explicit models, such as LANDIS-II, could potentially be used as input, enabling (for example) the location of management interventions to be explored under different scenarios of environmental change. Further details of spatial MCA approaches are provided by Geneletti (2004) and Kangas et al. (2000).

Scenarios. All ecological models are based on a range of assumptions and uncertainties. Scenario planning offers a framework for developing environmental management approaches under such uncertain conditions. A scenario can be defined in this context is an account of a plausible future (Peterson et al. 2003). The development of scenarios is a recognized tool in business planning and economic forecasting, but only recently has it been applied to conservation. Peterson et al. (2003) provide a valuable introduction to the use of scenarios in a conservation context. Further information on the technique is provided by Newton (2007a).

Scenario planning provides a tool to explore the uncertainty surrounding the future consequences of a decision, by developing a small number of contrasting scenarios. Generally scenarios are developed by a range of stakeholders in a systemic process of collecting, discussing and analysing information, through a series of workshops. The technique therefore seems highly relevant to the participatory modelling approach described by Sturtevant et al. (2007). Scenarios may draw upon a variety of quantitative and qualitative information, such as the results of ecological surveys and outputs from modelling exercises. Peterson et al. (2003) suggest that the major benefits of using scenario planning for conservation are (i) increased understanding of key uncertainties, (ii) incorporation of alternative perspectives into conservation planning, and (iii) greater resilience of decisions to surprise. However, the use of this technique to support SFM is in its infancy.

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