Diameter growth models for mixed-species stands of Coastal British Columbia including thinning and fertilization effects

In this study, diameter growth models for three species growing in mixed-stands of Coastal British Columbia (BC), Canada, under a variety of silvicultural treatments were developed. The three species were: Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western redcedar (Thuja plicata Donn). A Box and Lucas model (1959) was initially fitted to the diameter growth series for each tree, as this model is very flexible and was based on processes reflective of the metabolic processes governing tree growth. Next, a random coefficients modelling approach (i.e., parameter prediction approach) was used to modify the estimated parameters for each species using functions of tree size and stage of development, site productivity, and inter-tree competition variables, while accounting for temporal correlation within trees. Impacts of fertilization on diameter growth were estimated by including the time since fertilization as an additional variable. Since state variables that are changed as a result of thinning were already in the model, accurate results post-thinning were obtained with no changes to the model. For the combined effects of thinning and fertilization, a two-step additive approach was used, where the state variables were changed following thinning and the diameter increment was modified for fertilization using the time since fertilization variable. Results indicated that multiple treatments sustain a change in growth for a longer time period following treatment than thinning or fertilization alone.     

Introducing effects of temperature and CO2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO₂ on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO₂, stand density and the tree's competition status in a stand of Scots pine (Pinus sylvestris), silver birch (Betula pendula) and Norway spruce (Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO₂ elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained.The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO₂. These calculations revealed that the growth response of individual trees to elevated temperature and CO₂ can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.     

Examination of conflicts and improved strategies for the management of an endangered Eucalypt species using Bayesian networks

Bayesian decision support tools are becoming increasingly popular as a modelling framework that can analyse complex problems, resolve controversies, and support future decision-making in an adaptive management framework. This paper introduces a model designed to assist the management of an endangered Eucalypt species, the Swamp Gum (Eucalyptus camphora). This tree species is found in the Yellingbo Nature Conservation Reserve (YNCR), an isolated patch of forest in the Yarra Valley (Victoria, Australia), where E. camphora has become increasingly threatened by dieback. In order to maintain and rehabilitate existing trees and encourage regeneration, management strategies and action plans have concentrated on restoring the hydrological regime, which has been altered due to agricultural activities within the catchment. However, research suggests that nutrient enrichment from surrounding horticulture and livestock is having a greater impact on the health of the trees. A Bayesian network model has been developed for E. camphora and used to explore the differences between these two hypotheses. Model outputs suggest that the influencing factors of E. camphora condition are (a) spatially specific and (b) differ according to the group conducting the study in the YNCR. Given the poor quality of data and knowledge available, further research is required to identify the causal factors of dieback. The model offers a framework to guide future integrative and iterative monitoring and research in the YNCR.     

More asymmetric tree competition brings about more evapotranspiration and less runoff from the forest ecosystems: A simulation study

The present paper reports how stand size-structure dynamics due to competition between different-sized trees affect long-term forested water balance in Japanese cool-temperate planted stands (evergreen coniferous Cryptomeria japonica and deciduous coniferous Larix kaempferi stands) using a fully coupled multi-layered meteorological surface physics—terrestrial ecosystems model. The simulation captured the well-known annual variation in leaf area index (LAI) accurately with stand age in monocultured and even-aged stands; the occurrence of maximum LAI during the early growth stage and then a gradual decline followed by a steady state after the maximum LAI. The simulations also detected a high dependency of annual evapotranspiration (AETr) on LAI with stand age that is well known by prior observational researches. In the C. japonica (shade-tolerant late-successional species) stand, the relationship between annual net primary productivity of an individual tree (NPP_ind) and individual tree mass (w) changed from linear to a convex curve during self-thinning, indicating that the degree of asymmetric tree competition intensified with forest stand development. The higher degree of competitive asymmetry characterized by the convex-shaped NPPind-w relationship produced greater size inequality, i.e., the formation of trees stratified by height. Under such conditions, AETr and annual transpiration (ATr) were mainly regulated by larger trees. On the other hand, the NPPind-w relationships in the L. kaempferi (shade-intolerant early-successional species) stand were linear throughout the simulated period, indicating the lower degree of competitive asymmetry. Under such conditions, the growth of intermediate-sized trees was enhanced and these trees became a dominant source of AETr (and also ATr) during self-thinning. Furthermore, the sensitivity analysis of the effects of ecophysiological parameters such as foliage profile (i.e., vertical distribution of leaf area density) of an individual tree (distribution pattern is described by the parameter η), the maximum carboxylation velocity (V_cmax0) and biomass allocation pattern of individual plant growth (μ₁) on AETr, ATr and annual runoff (AR_off) showed that the temporal trends of AETr, ATr, AR_off and NPPind-w relationships were completely the same as those in the control simulations. However, the NPPind-w relationship during self-thinning indicated higher degrees of competitive asymmetry when η or V_cmax0 were greater than those in the control simulation and generated greater AETr and ATr and thus smaller AR_off. We found that more asymmetric tree competition brings about greater size inequality between different-sized trees and thus more evapotranspiration and less runoff in a forest stand. Overall, our simulation approach revealed that not only LAI dynamics but also plant competition, and thus size-structure dynamics, in a forest ecosystem are essential to long-term future projections of forested water balance.     

The concepts of emergent and collective properties in individual-based models—Summary and outlook of the Bornhöved case studies

Ecology requires the conceptual and technical ability to analyse complex and dynamic systems consisting of a high and variable number of components and relations. These components are part of a variable interaction structure in a spatially heterogeneous context. The components of ecological interaction networks can give rise to self-organised, and scale-dependent interaction patterns and processes, which are the underlying causes of the overall ecological systems states.The individual-based modelling approach provides a widely applicable simulation framework based on a ‘hierarchy theory’ view of ecological systems.Here, we summarise and generalise the theoretical implications of the modelling studies presented in this volume in the field of terrestrial and aquatic, animal and plant ecology. The case studies cover a representative profile of processes related to ecological applications, such as food web interactions, population dynamics, dispersal, energy physiology, nutrient allocation and mutual impact of morphological and physiological development. The generic approach applied in this context allows a hierarchical representation of ecological systems and their components. Model results are obtained as self-organised structural relation networks and as aggregated quantitative states. In order to address different model characteristics we distinguish collective and emergent properties. Collective properties are those that are attributed equally to different organisation levels of the system. Emergent properties result from the activities of lower level entities on a higher organisation level, while not being present on the lower level. They can be subdivided into aggregational and connective properties. Emergent properties that are aggregational are those which emerge as a result of an aggregation procedure by an observer on the higher level which does not make sense or is not applicable on lower levels. Emergent properties that are connective, however, are based on an interaction network of lower level entities, which brings about the specific system characteristic.This classification of model results will allow to generalise the achievements and potential of the individual-based modelling approach in ecology.     

From single fine roots to a black alder forest ecosystem: How system behaviour emerges from single component activities

Based on empirical findings in a natural black alder ecosystem in Northern Germany we developed an individual based model that integrates components of a black alder ecosystem interacting on different levels of organisation. The factors determining seasonal fine root biomass development of forest ecosystems are not yet fully understood.We used an object oriented model approach to investigate this complex matter for black alder trees. Processes like growth, storage, respiration, transport, nutrient mineralisation and uptake as well as interactions among these factors are described on the level of functionally differentiated plant organs (fine roots, coarse roots, stem, branches, leaves) and soil units. The object structure of the model is determined by spatial relations between plant modules as well as between plant modules and their local environment modules.As results of model application we found that (i) on the organ level, spatio-temporal plasticity of (root) growth allocation is related to spatio-temporal variation of resource availability, (ii) on the plant level, balanced root:shoot growth appears in response to variation of available resources light and nutrients, (iii) on the population level, tree stand development (population structure, self-thinning) resulted from coexistence and competition between plant individuals.For the understanding of the root compartment it seems relevant that the model implementation of local scale fine root dynamics is consistent with a self-organised large scale spatial heterogeneity of fine root activity pattern. On the other hand, fine-root dynamics cannot be explained as a result of autonomous dynamics. A reference to above-ground processes is a necessary condition and the overall plant seems to act as an integrator providing boundary conditions for local activity pattern. At the same time fine-root characteristics are of some importance for properties on hierarchically higher levels, e.g. co-existence in a tree population or element cycling in the ecosystem.As a conclusion, modelling of the spatio-temporal dynamics of tree root systems appears as a paradigmatic example of scale and organisation level integrating processes.     

Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests

Forestry science has a long tradition of studying the relationship between stand productivity and abiotic and biotic site characteristics, such as climate, topography, soil and vegetation. Many of the early site quality modelling studies related site index to environmental variables using basic statistical methods such as linear regression. Because most ecological variables show a typical non-linear course and a non-constant variance distribution, a large fraction of the variation remained unexplained by these linear models. More recently, the development of more advanced non-parametric and machine learning methods provided opportunities to overcome these limitations. Nevertheless, these methods also have drawbacks. Due to their increasing complexity they are not only more difficult to implement and interpret, but also more vulnerable to overfitting. Especially in a context of regionalisation, this may prove to be problematic. Although many non-parametric and machine learning methods are increasingly used in applications related to forest site quality assessment, their predictive performance has only been assessed for a limited number of methods and ecosystems.In this study, five different modelling techniques are compared and evaluated, i.e. multiple linear regression (MLR), classification and regression trees (CART), boosted regression trees (BRT), generalized additive models (GAM), and artificial neural networks (ANN). Each method is used to model site index of homogeneous stands of three important tree species of the Taurus Mountains (Turkey): Pinus brutia, Pinus nigra and Cedrus libani. Site index is related to soil, vegetation and topographical variables, which are available for 167 sample plots covering all important environmental gradients in the research area. The five techniques are compared in a multi-criteria decision analysis in which different model performance measures, ecological interpretability and user-friendliness are considered as criteria.When combining these criteria, in most cases GAM is found to outperform all other techniques for modelling site index for the three species. BRT is a good alternative in case the ecological interpretability of the technique is of higher importance. When user-friendliness is more important MLR and CART are the preferred alternatives. Despite its good predictive performance, ANN is penalized for its complex, non-transparent models and big training effort.     

Modelling the impact of defoliation and leaf damage on forest plantation function and production

After presenting a short review of process-based model requirements to capture the plant dynamic response to defoliation, this paper describes the development and testing of a model of crown damage and defoliation for Eucalyptus. A model that calculates light interception and photosynthetic production for canopies that vary spatially and temporally in leaf area and photosynthetic properties is linked to the forest growth model CABALA. The process of photosynthetic up-regulation following defoliation is modelled with a simple conditional switch that triggers up-regulation when foliar damage or removal causes the ratio of functional leaf area to living tissue in the tree to change.We show that the model predicts satisfactorily when validated with trees of Eucalyptus nitens and Eucalyptus globulus from a range of sites of different ages, subject to different types of stress and different types of defoliation events (R² = 0.96 across a range of sites). However, the complexity of particular situations can cause the model to fail (e.g. very heavy defoliation events where branch death occurs).It is concluded that while the model will not cope with all situations, an appropriate level of generality has been captured to represent many of the physiological processes and feedbacks that occur following defoliation or leaf damage. This makes the model useful for guiding management interventions following pest attack and allows the development of scenarios including climate change impact analyses and decision-making on the merits of post-defoliation fertilisation to expedite recovery.     

Nitrogen versus phosphorus limitation in a subtropical coastal embayment (Moreton Bay; Australia): Implications for management

An approach combining nutrient budgets, dynamic modelling, and field observations of phytoplankton and nitrogen (N₂)-fixing Lyngbya majuscula following changes in wastewater N loads, was used to demonstrate that Moreton Bay is potentially phosphorus (P) limited. Modelling and nutrient budgeting shows that benthic N-fixation loads are high, allowing the system to overcome any potential N-limitation. Phytoplankton biomass has shown little change from 1991 to 2006 in the sections of Moreton Bay most impacted by wastewater effluents, despite a large reduction in wastewater N loads from 2000 to 2002. This is consistent with modelling that also showed no reduction in primary productivity associated with reduced N loads. Most importantly, there have been rapid increases in the occurrence of N-fixing L. majuscula in Moreton Bay as wastewater P loads have increased relative to wastewater N loads. This is also consistent with modelling. This work supports the premise that there may be fundamental differences in nutrient limitation of primary production between subtropical and temperate coastal systems due to differences in the importance of internal nitrogen sources and sinks (N-fixation and denitrification). These differences need to be recognised for optimum management of coastal systems.     

Emergent properties modelled with the functional structural tree growth model ALMIS: Computer experiments on resource gain and use

The functional structural tree growth model ALMIS uses the individual based modelling approach and is implemented in the object-oriented programming language SIMULA. All features (state variables) and functions (processes) are specified locally, on the level of the single plant organs. Increasing numbers of “copies” (objects) of these elementary units, Internodes, Leaves, Meristems, Roots, and Root tips, form the growing tree. Various procedures (e.g. Photosynthesis, Nutrient_uptake, Transport, Storage, Mobilisation, Respiration, Growth) are employed to describe carbon and nutrient uptake, and matter fluxes between the different plant organs. Combining plant physiology and architecture, ALMIS allows studying the effect of single ecophysiological and structural processes on whole tree growth and in the tree–environment system. Some of these effects, driven by microclimate, self-shading, variable nutrient availability, variable transport dynamics, and branching patterns are exemplified. From the interactions at the organ and sub-organ levels new features emerge at higher levels of plant organisation. These so-called emergent properties are, for example, lifetime spectrum of single organs, space filling (“architecture”) and self-thinning of the crown. The most prominent emergent properties are the different growth forms of trees resulting from simulations under various conditions. Their causal interrelations are discussed in detail.     

Mechanisms of moisture stress in a mid-latitude temperate forest: Implications for feedforward and feedback controls from an irrigation experiment

While it is well established that stomata close during moisture stress, strong correlations among environmental (e.g., vapor pressure deficit, soil moisture, air temperature, radiation) and internal (e.g., leaf water potential, sap flow, root-shoot signaling) variables obscure the identification of causal mechanisms from field experiments. Models of stomatal control fitted to field data therefore suffer from ambiguous parameter identification, with multiple acceptable (i.e., nearly optimal) model structures emphasizing different moisture status indicators and different processes. In an effort to minimize these correlations and improve parameter and process identification, we conducted an irrigation experiment on red maples (Acer rubrum L.) at Harvard Forest (summers of 2005 and 2006). Control and irrigated trees experienced similar radiative and boundary layer forcings, but different soil moisture status, and thus presumably different diurnal cycles of internal leaf water potential. Measured soil moisture and atmospheric forcing were used to drive a transient tree hydraulic model that incorporated a Jarvis-type leaf conductance in a Penman–Monteith framework with a Cowan-type (resistance and capacitance) tree hydraulic representation. The leaf conductance model included dependence on both leaf matric potential, Ψ_L (so-called feedback control) and on vapor pressure deficit, D (so-called feedforward control). Model parameters were estimated by minimizing the error between predicted and measured sap flow. The whole-tree irrigation treatment had the effect of elevating measured transpiration during summer dry-downs, demonstrating the limiting effect that subsurface resistance may have on transpiration during these times of moisture stress. From the best fitted model, we infer that during dry downs, moisture stress manifests itself in an increase of soil resistance with a resulting decrease in Ψ_L, leading to both feedforward and feedback controls in the control trees, but only feedforward control for the irrigated set. Increases in the sum-of-squares error when individual model components were disabled allow us to reject the following three null hypotheses: (1) the f(D) stress is statistically insignificant (p = 0.01); (2) the f(Ψ_L) stress is statistically insignificant (p = 0.07); and (3) plant storage capacitance is independent of moisture status (p = 0.07).     

Composition of alkaloids in different box tree varieties and their uptake by the box tree moth Cydalima perspectalis

Larvae of the moth Cydalima perspectalis are specialized on box trees (Buxus spp.). Native to eastern Asia, the moth has been introduced to Europe in 2007 and is nowadays causing severe damage to box trees in private and public gardens, as well as in semi-natural box tree forests. Box trees contain highly toxic triterpenoid alkaloids which may be sequestered by specialized herbivores such as C. perspectalis. We determined the alkaloid composition in leaves of the five most common box tree varieties in Europe belonging to two Buxus species using liquid chromatography–mass spectrometry (LC–MS) metabolite profiling. We also examined whether larvae and moths of C. perspectalis accumulate alkaloids from the different box tree varieties. The differences in alkaloid composition observed between the box tree species Buxus sempervirens and Buxus microphylla were mirrored in the tissue of C. perspectalis larvae fed on either of the different box tree species, indicating uptake of alkaloids. The larvae stored large amounts of dibasic alkaloids in their body, while monobasic alkaloids were metabolized and/or excreted. Newly emerged adult moths contained no traces of alkaloids.     

Spatio-temporal modelling of ground vegetation development in mountain spruce forests

More complex models of forest ecosystems are required to understand how land-cover changes can impact vegetation dynamics and spatial pattern. In order to document spatio-temporal modelling abilities, the observations conducted in the declined climax mountain Norway spruce forest during the recovery period (1995-2006) are used for simulation and spatial analysis in the GIS environment. The developed spatio-temporal model is used for simulation of forest vegetation dynamics in a mountain spruce forest in the framework of regeneration processes after stress from air pollution. In order to explore the spatial and temporal phenomena of regeneration processes, the spatio-temporal model is based on a large set of ordinary differential equations that solve dynamic processes in sets of microsites arranged in grids for each ground vegetation species and each age group of Norway spruce seedlings. The spatial extent of the explored site is composed of a set of 50 × 50 microsites. Each microsite is represented by a square with dimensions of 1 m × 1 m. The presented simulation studies are mainly focused on seedlings from the seed year 1992, in order to explore the longest monitored time series of survival. It is based on exponential growth models that are related to the environmental conditions for each microsite. The canopy gaps based on estimates of the local crown projected area, the soil type layer, and the dominant grass density are used to provide case simulation studies. The first case study simulates the influence of microsite positions in relation to the local tree crown projections on the survival of spruce seedlings. It is assumed that the density of the trees is the main factor that determines the light and heat supply to the ground level of the Norway spruce seedlings. The second case study extends the previous study to include terms that determine the growth ratio in dependence on the crown projection area. The third case study provides further extensions in order to simulate growth ratio relations to the local soil type. The fourth case study demonstrates the local influence of the dominant grasses, such as Avenella flexuosa and Calamagrostis villosa, on the natural regeneration of Norway spruce. Starting from the conditions at the sites before the recovery period, the case simulation studies are able to project the short-term succession for a regeneration decade and the approximate long-term development. In addition to the standard simulation procedures based on solution of ordinary differential equations, spatio-temporal modelling in the GIS environment is able to provide spatial data management, analysis and visualization of the data.     

Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.     

Simulating forest succession after blowdown events: The crucial role of space for a realistic management

Ecological patterns vary in space and time. Therefore, when using dynamic models in ecology, the spatial aspect should not be neglected prematurely since it could possibly change the model outcomes to a considerable extent. In view of this problem, we describe here a method how to construct a non-spatial version from a spatially explicit simulation model. The principle idea is to suppress the spatial correlations of cells in a grid in time by continuously re-assigning a random neighbourhood for each cell on the grid. Since this procedure actually eliminates the spatial dimensions, it allows to quantify the unadulterated impact of spatial processes on the model results. To illustrate an important application of this approach in the context of forest management we use a grid-based model that simulates succession of Norway spruce (Picea abies (L.) Karst.) at mountainous sites after blowdown events. The output of this model is compared with the results of the deduced non-spatial version of this model regarding the predicted amount of re-growing trees. The non-spatial version dramatically overestimates the number of spruce trees on different microsites. Thus, the uncritical use of the non-spatial model might give reason to wrong management decisions that are based on too optimistic predictions. In practice, this may lead to dangerous situations, especially in mountain forests serving as protection against avalanches and landslides. This example demonstrates the successful applicability of our approach. Our method can be interpreted as a contribution to an extended sensitivity analysis: it analyses the sensitivity of the results due to structural changes of the model. This sensitivity allows one to estimate the redundancy or the necessity of spatially explicit processes in a model with regard to the parsimony principle of modelling. Since our approach is not dependent on special features of the simulation model used here, it is assumed to be applicable for other spatial models, too, and can thus be considered of general interest for a diligent model analysis.     

Inverse modeling for effective dispersal: Do we need tree size to estimate fecundity?

The estimation of the dispersal kernel for the seedling and sapling stages of the recruitment process was made possible through the application of inverse modeling to dispersal data. This method uses the spatial coordinates of adult trees and the counts of seedlings (or saplings) in small quadrats to estimate the dispersal kernel. The unknown number of recruits produced by an adult tree (the fecundity) is estimated - simultaneously with the dispersal kernel - via an allometric linear model relating the unknown quantity with a (easily) measured characteristic of the adult tree (usually the basal area). However, the allometric relation between tree size and reproductive success in the sapling (or seedling) stage may not be strong enough when numerous, well-documented, post-dispersal processes (such as safe-site limitation for recruitment) cause large post-dispersal seedling mortality, which is usually unrelated to the size of the tree that dispersed them. In this paper we hypothesize that when tree size and reproductive success in the seedling/sapling stage are not well correlated then the use of allometry in inverse modeling is counter-productive and may lead to poor model fits. For these special cases we suggest using a new model for effective dispersal that we term the unrestricted fecundity (UF) model that, contrary to allometric models, makes no assumptions on the fecundities; instead they are allowed to vary freely from one tree to another and even to be zero for trees that are reproductively inactive. Based on this model, we examine the hypothesis that when tree size and reproductive success are weakly correlated and the fecundities are estimated independently of tree size the goodness-of-fit and the ecological meaning of dispersal models (in the seedling or sapling stage) may be enhanced. Parameters of the UF model are estimated through the EM algorithm and their standard errors are approximated via the observed information matrix. We fit the UF model to a dataset from an expanding European beech population of central Spain as well as to a set of simulated dispersal data were the correlation between reproductive success and tree size was moderate. In comparisons with a simple allometric model, the UF model fitted the data better and the parameter estimates were less biased. We suggest using this new approach for modeling dispersal in the seedling and sapling stages when tree size (or other adult-specific covariates) is not deemed to be in strong relation to the reproductive success of adults. Models that use covariates for modeling the fecundity of adults should be preferred when reproductive success and tree size guard a strong relationship.     

A proposal of an indicator for quantifying model robustness based on the relationship between variability of errors and of explored conditions

The evaluation of biophysical models is usually carried out by estimating the agreement between measured and simulated data and, more rarely, by using indices for other aspects, like model complexity and overparameterization. In spite of the importance of model robustness, especially for large area applications, no proposals for its quantification are available. In this paper, we would like to open a discussion on this issue, proposing a first approach for a quantification of robustness based on the variability of model error to variability of explored conditions ratio. We used modelling efficiency (EF) for quantifying error in model predictions and a normalized agrometeorological index (SAM) based on cumulated rainfall and reference evapotranspiration to characterize the conditions of application. Population standard deviations of EF and SAM were used to quantify their variability. The indicator was tested for models estimating meteorological variables and crop state variables. The values provided by the robustness indicator (I_R) were discussed according to the models’ features and to the typology and number of processes simulated. I_R increased with the number of processes simulated and, within the same typology of model, with the degree of overparameterization. No correlation were found between I_R and two of the most used indices of model error (RRMSE, EF). This supports its inclusion in integrated systems for model evaluation.     

Design of a Domain Specific Language for modelling processes in landscapes

The modelling of processes that occur in landscapes is often confronted to issues related to the representation of space and the difficulty of properly handling time and multiple scales. In order to investigate these issues, a flexible modelling environment is required. We propose to develop such a tool based on a Domain Specific Language (DSL) that capitalises on the service-oriented architecture (SOA) paradigm. The modelling framework around the DSL is composed of a model building environment, a code generator and compiler, and a program execution platform. The DSL introduces five language elements (entity, service, relation, scenario and datafacer) that can be combined to offer a wide range of possibilities for modelling in space and time at different scales. When developing a model, model parts are either built using the DSL or taken from libraries of previously built ones, and adapted to the specific model. The practical usage of the DSL is illustrated first with the Lotka–Volterra model, and then with a landscape modelling experiment on the spread of a mosquito-borne disease in the Sahelian region of West Africa. An interesting characteristic of this approach is the possibility of adding new elements into an existing model, and replacing others with more appropriate ones, thus allowing potentially complex models to be built from simpler parts.     

The spread of marine non-indigenous species via recreational boating: A conceptual model for risk assessment based on fault tree analysis

Recreational vessel movements are increasingly recognised as an important pathway for the spread of non-indigenous species (NIS) in marine environments. Research on risks posed by recreational vessels has focused on external hull fouling, yet a number of studies reveal the potential for NIS to also be transferred by a range of other vessel components. This paper uses fault tree analysis as a framework for incorporating input from a panel of international experts, to elucidate the consecutive steps that must occur for NIS to be introduced from different components of recreational boats. Our conceptual model reveals the complexity of the invasion process even when only the ‘release’ phase is considered (i.e. the release of NIS from an infected vessel into a new area). The model highlights that, in addition to external fouling of the ‘hull’ (hull, rudder and propeller), important vessel components may also include fouling, sediment or water released from the deck, internal spaces, anchors and fishing/diving gear. The extent to which these components are important is situation-specific, and depends on attributes of the vessel, location and NIS present. Hence, the comprehensive model described here could be modified or simplified to reflect the attributes that are relevant to particular circumstances. We demonstrate this principle using examples of three NIS: the colonial tunicate Didemnum vexillum and the Asian kelp Undaria pinnatifida that both have established in Port Nelson New Zealand after vessel-mediated spread, and the clubbed tunicate Styela clava that was detected on a vessel hull in the port but is not known to have established. Although the modelling and assessment of some of the events identified in the fault trees would be difficult or unrealistic, it is important to acknowledge them in order to provide a comprehensive risk assessment tool. Even where risks are largely unknown, difficult to quantify, or reflect stochastic events, this does not necessarily preclude management intervention.