SEIB–DGVM: A new Dynamic Global Vegetation Model using a spatially explicit individual-based approach

We report the development of a new spatially explicit individual-based Dynamic Global Vegetation Model (SEIB–DGVM), the first DGVM that can simulate the local interactions among individual trees within a spatially explicit virtual forest. In the model, a sample plot is placed at each grid box, and then the growth, competition, and decay of each individual tree within each plot is calculated by considering the environmental conditions for that tree as it relates to the trees that surround it. Based on these parameters only, the model simulated time lags between climate change and vegetation change. This time lags elongated when original biome was forest, because existing trees prevent newly establish trees from receiving enough sunlight and space to quickly replace the original vegetation. This time lags also elongated when horizontal heterogeneity of sunlight distribution was ignored, indicating the potential importance of horizontal heterogeneity for predicting transitional behavior of vegetation under changing climate. On a local scale, the model reproduced climate zone-specific patterns of succession, carbon dynamics, and water flux, although on a global scale, simulations were not always in agreement with observations. Because the SEIB–DGVM was formulated to the scale at which field biologists work, the measurements of relevant parameters and data comparisons are relatively straightforward, and the model should enable more robust modeling of terrestrial ecosystems.     

A model of surface fire,climate and forest pattern in the Sierra Nevada,California

A spatially explicit forest gap model was developed for the Sierra Nevada, California, and is the first of its kind because it integrates climate, fire and forest pattern. The model simulates a forest stand as a grid of 15×15 m forest plots and simulates the growth of individual trees within each plot. Fuel inputs are generated from each individual tree according to tree size and species. Fuel moisture varies both temporally and spatially with the local site water balance and forest condition, thus linking climate with the fire regime. Fires occur as a function of the simulated fuel loads and fuel moisture, and the burnable area is simulated as a result of the spatially heterogeneous fuel bed conditions. We demonstrate the model’s ability to couple the fire regime to both climate and forest pattern. In addition, we use the model to investigate the importance of climate and forest pattern as controls on the fire regime. Comparison of model results with independent data indicate that the model performs well in several areas. Patterns of fuel accumulation, climatic control of fire frequency and the influence of fuel loads on the spatial extent of fires in the model are particularly well-supported by data. This model can be used to examine the complex interactions among climate, fire and forest pattern across a wide range of environmental conditions and vegetation types. Our results suggest that, in the Sierra Nevada, fuel moisture can exert an important control on fire frequency and this control is especially pronounced at sites where most of the annual precipitation is in the form of snow. Fuel loads, on the other hand, may limit the spatial extent of fire, especially at elevations below 1500 m. Above this elevation, fuel moisture may play an increasingly important role in limiting the area burned.     

Scaling-up spatially-explicit ecological models using graphics processors

How the properties of ecosystems relate to spatial scale is a prominent topic in current ecosystem research. Despite this, spatially explicit models typically include only a limited range of spatial scales, mostly because of computing limitations. Here, we describe the use of graphics processors to efficiently solve spatially explicit ecological models at large spatial scale using the CUDA language extension. We explain this technique by implementing three classical models of spatial self-organization in ecology: a spiral-wave forming predator-prey model, a model of pattern formation in arid vegetation, and a model of disturbance in mussel beds on rocky shores. Using these models, we show that the solutions of models on large spatial grids can be obtained on graphics processors with up to two orders of magnitude reduction in simulation time relative to normal pc processors. This allows for efficient simulation of very large spatial grids, which is crucial for, for instance, the study of the effect of spatial heterogeneity on the formation of self-organized spatial patterns, thereby facilitating the comparison between theoretical results and empirical data. Finally, we show that large-scale spatial simulations are preferable over repetitions at smaller spatial scales in identifying the presence of scaling relations in spatially self-organized ecosystems. Hence, the study of scaling laws in ecology may benefit significantly from implementation of ecological models on graphics processors.     

Building statistical models to analyze species distributions.

Models of the geographic distributions of species have wide application in ecology. But the nonspatial, single-level, regression models that ecologists have often employed do not deal with problems of irregular sampling intensity or spatial dependence, and do not adequately quantify uncertainty. We show here how to build statistical models that can handle these features of spatial prediction and provide richer, more powerful inference about species niche relations, distributions, and the effects of human disturbance. We begin with a familiar generalized linear model and build in additional features, including spatial random effects and hierarchical levels. Since these models are fully specified statistical models, we show that it is possible to add complexity without sacrificing interpretability. This step-by-step approach, together with attached code that implements a simple, spatially explicit, regression model, is structured to facilitate self-teaching. All models are developed in a Bayesian framework. We assess the performance of the models by using them to predict the distributions of two plant species (Proteaceae) from South Africa's Cape Floristic Region. We demonstrate that making distribution models spatially explicit can be essential for accurately characterizing the environmental response of species, predicting their probability of occurrence, and assessing uncertainty in the model results. Adding hierarchical levels to the models has further advantages in allowing human transformation of the landscape to be taken into account, as well as additional features of the sampling process.     

Simulation and analysis of outbreaks of bark beetle infestations and their management at the stand level

Outbreaks of bark beetles in forests can result in substantial economic losses. Understanding the factors that influence the development and spread of bark beetle outbreaks is crucial for forest management and for predicting outbreak risks, especially with the expected global warming. Although much research has been done on the ecology and phenology of bark beetles, the complex interplay between beetles, host trees, beetle antagonists and forest management makes predicting beetle population development especially difficult. Using the recent infestations of the European Spruce Bark Beetle (Ips typographus L. Col. Scol.) in the Bavarian Forest National Park (Germany) as a case study, we developed a spatially explicit agent-based simulation model (SAMBIA) that takes into account individual trees and beetles. This model primarily provides a tool for analysing and understanding the spatial and temporal aspects of bark beetles outbreaks at the stand scale. Furthermore, the model should allow an estimation of the effectiveness of concurrent impacts of both antagonists and management to confine outbreak dynamics in practice. We also used the model to predict outbreak probabilities in various settings. The simulation results indicated a distinct threshold behaviour of the system in response to pressure by antagonists or management of the bark beetle population. Despite the different scenarios considered, we were able to extract from the simulations a simple rule of thumb for the successful control of an outbreak: if roughly 80% of individual beetles are killed by antagonists or foresters, outbreaks will rarely take place. Our model allows the core dynamics of this complex system to be reduced to this inherent common denominator.     

Design and validation of a spatially explicit simulation model for bottomland hardwood forests

Species composition in forests depends on the interaction of species traits and species availability. Yet many forest simulation models focus only on interactions of adult trees and saplings, ignoring how species become members of the community. We modify a published forest model for bottomland hardwood forests (program SWAMP [Phipps, R.L., 1979. Simulation of wetlands forest vegetation dynamics. Ecol. Modell. 7, 257–288]) to make it spatially explicit and incorporate explicit seed production and dispersal algorithms. The resulting individual-based, spatially explicit forest simulator (YAFSIM) combines mechanistic seed dispersal with growth and mortality of trees to track forest dynamics over time. We describe the structure of the model and test its validity for dynamics in small bottomland hardwood patches in the Mississippi Alluvial Valley. Dynamics of species composition and basal areas of trees predicted by Yazoo Forest Simulator (YAFSIM) were similar to those of natural second- and old-growth bottomland forests. However, diversity of simulated forest patches declined over time largely because of random dynamics acting on small, isolated populations.     

Modeled historical land use and land cover for the conterminous United States

The landscape of the conterminous United States has changed dramatically over the last 200 years, with agricultural land use, urban expansion, forestry, and other anthropogenic activities altering land cover across vast swaths of the country. While land use and land cover (LULC) models have been developed to model potential future LULC change, few efforts have focused on recreating historical landscapes. Researchers at the US Geological Survey have used a wide range of historical data sources and a spatially explicit modeling framework to model spatially explicit historical LULC change in the conterminous United States from 1992 back to 1938. Annual LULC maps were produced at 250-m resolution, with 14 LULC classes. Assessment of model results showed good agreement with trends and spatial patterns in historical data sources such as the Census of Agriculture and historical housing density data, although comparison with historical data is complicated by definitional and methodological differences. The completion of this dataset allows researchers to assess historical LULC impacts on a range of ecological processes.     

A comparison of three empirically based, spatially explicit predictive models of residential soil Pb concentrations in Baltimore, Maryland, USA: understanding the variability within cities

In many older US cities, lead (Pb) contamination of residential soil is widespread; however, contamination is not uniform. Empirically based, spatially explicit models can assist city agencies in addressing this important public health concern by identifying areas predicted to exceed public health targets for soil Pb contamination. Sampling of 61 residential properties in Baltimore City using field portable X-ray fluorescence revealed that 53 % had soil Pb that exceeded the USEPA reportable limit of 400 ppm. These data were used as the input to three different spatially explicit models: a traditional general linear model (GLM), and two machine learning techniques: classification and regression trees (CART) and Random Forests (RF). The GLM revealed that housing age, distance to road, distance to building, and the interactions between variables explained 38 % of the variation in the data. The CART model confirmed the importance of these variables, with housing age, distance to building, and distance to major road networks determining the terminal nodes of the CART model. Using the same three predictor variables, the RF model explained 42 % of the variation in the data. The overall accuracy, which is a measure of agreement between the model and an independent dataset, was 90 % for the GLM, 83 % for the CART model, and 72 % for the RF model. A range of spatially explicit models that can be adapted to changing soil Pb guidelines allows managers to select the most appropriate model based on public health targets.     

Aphid population response to agricultural landscape change: A spatially explicit,individual-based model

A spatially explicit individual-based simulation model has been developed to represent aphid population dynamics in agricultural landscapes. The application of the model to Rhopalosiphum padi (L.) population dynamics is detailed, including an outline of the construction of the model, its parameterisation and validation. Over time, the aphids interact with the landscape and with one another. The landscape is modified by varying a simple pesticide regime, and the multi-scale spatial and temporal implications for a population of aphids is analysed. The results show that a spatial modelling approach that considers the effects on the individual of landscape properties and factors such as wind speed and wind direction provides novel insight into aphid population dynamics both spatially and temporally. This forms the basis for the development of further simulation models that can be used to analyse how changes in landscape structure impact upon important species distributions and population dynamics.     

Spatially explicit modeling of overstory manipulations in young forests: Effects on stand structure and light

Young forests can be manipulated in diverse ways to enhance their ecological values. We used stem maps from two dense, second-growth stands in western Washington and a spatially explicit light model (tRAYci) to simulate effects of five silvicultural manipulations on diameter distribution, species composition, spatial patterning, and light availability. Each treatment removed 30% of the basal area, but differed in how trees were selected for removal. Three primary treatments were thin from below (removing the smallest trees), random thin (removing trees randomly), and gap creation (removing all trees in circles ∼1 tree height in diameter). Two additional treatments combined elements of these approaches: random ecological thin (a mixture of thin from below and random thin) and structured ecological thin (a mixture of thin from below and gap creation).     

Spatial hyperdynamism in a post-disturbance simulated forest

Competition–colonization models can address the population dynamics of remnants following habitat destruction. Spatially explicit versions have produced qualifications of the extinction debt issue and limited hyperdynamism in populations following habitat destruction. Although spatially explicit, these efforts examined few indicators of the spatial structure of the landscape. An existing model is modified here to represent a difference in niche adaptations as well as the competition–colonization tradeoff. Several landscape metrics are calculated at each iteration. Although the addition of niche differentiation did not change the qualitative outcome of the model, the spatial metrics show that some aspects of landscape structure, i.e., average patch area and proximity, become hyperdynamic and remain so. Small fluctuations in species populations are magnified in their spatial expression because the landscape is simplified.     

Forest production model for upland black spruce stands—Optimal site occupancy levels for maximizing net production

The objective of this study was to develop a forest production model for determining optimal density management regimes for upland black spruce (Picea mariana (Mill.) B.S.P.) stands based on the maximization of net production. This objective was attained via the development of an allometrically extended stand density management diagram (SDMD), which was used to describe the mass dynamics of biotic and abiotic tree components by initial density regime, site quality and fine root turnover rate. Specifically, periderm, stem, branch, foliage and abiotic crown masses were estimated employing multivariate allometric regression functions based on data derived from 125 destructively sampled trees. Below-ground mass estimates were obtained using generalized allometric relationships derived from the literature. Abiotic masses included three basic components: (1) allometrically estimated retained woody debris consisting of abiotic crown structures that remained attached to the main stem; (2) fine woody debris arising from needle loss, root turnover, and abscission of modular components; (3) coarse woody debris arising from trees which incurred mortality through self-thinning. The algorithmic version of the model (1) simultaneously calculates periodic annual net production estimates (Mg/ha/year) by 10-year intervals over 100-year rotation lengths for eight initial density conditions, (2) given (1), determines the occupancy level for which net production is maximized for each stage of development (decade interval), and (3) given (2), determines the optimal size–density trajectory within the context of a SDMD. Additionally, results derived from multiple model simulations employing a range of initial densities (1500, 1650,…, 16,350 stems/ha), site indices (9, 10,…, 15 m) and fine root turnover rates (0.2, 0.3,…,0.8 proportion/year), indicated that black spruce productivity was maximized when site occupancies were maintained slightly below the zone of imminent competition mortality. Instructions for acquiring an executable version of the model through the Internet are also included.     

A family of spatial biodiversity measures based on graphs

While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two non-independent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neighbourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice of neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen.     

Evaluation of the forest growth simulator SILVA on dominant trees in mature mixed Silver fir–Norway spruce stands in South-West Germany

Forest growth simulators go beyond a mere tabulation of empirical measurements by employing biometric models that functionally describe the dependence of forest growth of the initial forest structure, growth conditions and management regime. This makes them very flexible and allows predicting growth reactions for unknown and/or complex forest growth scenarios. When simulation outcomes are to be used in silvicultural strategic planning, the results are of direct and delicate importance, and the correct simulator performance must be ascertained. This is especially so when the considered forest situation differs from the forest data used to parameterise the model (e.g. different geographical region).In this article, the forest growth simulator SILVA (version 2.2) was validated for 55 long-term experimental plots of mature mixed Silver fir–Norway spruce stands in southwest Germany (Picea abies, Abies alba). The evaluation was restricted to the upper canopy trees during the survey period 1989–2004. Following the general evaluation criteria for ecological models from [Vanclay, J.K., Skovsgaard, J.P., 1997. Evaluating forest growth models. Ecol. Mod. 98, 1–12], a specific methodology was developed to evaluate the simulated height and diameter growth on the basis of forest growth principles.The qualitative analysis proved the SILVA growth algorithms to be in accordance with physiologically based standard growth equations. The quantitative evaluation was limited by incomplete knowledge of the site conditions. To overcome this problem, the experimental plots were regarded as a “heterogeneous growth series” which allows analysing the growth behaviour in a more general way. It could be shown that for the given data set, the SILVA simulations produced an overestimation of height growth (median: +61% spruce, +12% fir), and an underestimation of diameter growth and competition sensitivity (median: ?16% spruce, ?70% fir). The errors partially compensated in the volume growth resulting in an overall over-/underestimation of +9% for spruce and ?58% for fir (median).The unbalanced height and diameter growth cannot be compensated by a change in the site conditions because this affects both height and diameter growth either positive or negative. Hence, an adjustment of selected parameterisation values appears to offer the best solution to adapt SILVA to the considered forest situation. This approach of adaptive parameterisation is discussed against a more general background of deductive vs. inductive forest growth modelling.     

Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling.

Advances in computing power in the past 20 years have led to a proliferation of spatially explicit, individual-based models of population and ecosystem dynamics. In forest ecosystems, the individual-based models encapsulate an emerging theory of "neighborhood" dynamics, in which fine-scale spatial interactions regulate the demography of component tree species. The spatial distribution of component species, in turn, regulates spatial variation in a whole host of community and ecosystem properties, with subsequent feedbacks on component species. The development of these models has been facilitated by development of new methods of analysis of field data, in which critical demographic rates and ecosystem processes are analyzed in terms of the spatial distributions of neighboring trees and physical environmental factors. The analyses are based on likelihood methods and information theory, and they allow a tight linkage between the models and explicit parameterization of the models from field data. Maximum likelihood methods have a long history of use for point and interval estimation in statistics. In contrast, likelihood principles have only more gradually emerged in ecology as the foundation for an alternative to traditional hypothesis testing. The alternative framework stresses the process of identifying and selecting among competing models, or in the simplest case, among competing point estimates of a parameter of a model. There are four general steps involved in a likelihood analysis: (1) model specification, (2) parameter estimation using maximum likelihood methods, (3) model comparison, and (4) model evaluation. Our goal in this paper is to review recent developments in the use of likelihood methods and modeling for the analysis of neighborhood processes in forest ecosystems. We will focus on a single class of processes, seed dispersal and seedling dispersion, because recent papers provide compelling evidence of the potential power of the approach, and illustrate some of the statistical challenges in applying the methods.     

Using the ECLPSS software environment to build a spatially explicit component-based model of ozone effects on forest ecosystems

We have developed a modeling framework to support grid-based simulation of ecosystems at multiple spatial scales, the Ecological Component Library for Parallel Spatial Simulation (ECLPSS). ECLPSS helps ecologists to build robust spatially explicit simulations of ecological processes by providing a growing library of reusable interchangeable components and automating many modeling tasks. To build a model, a user selects components from the library, and then writes new components as needed. Some of these components represent specific ecological processes, such as how environmental factors influence the growth of individual trees. Other components provide simulation support such as reading and writing files in various formats to allow inter-operability with other software. The framework manages components and variables, the order of operations, and spatial interactions. The framework provides only simulation support; it does not include ecological functions or assumptions. This separation allows biologists to build models without becoming computer scientists, while computer scientists can improve the framework without becoming ecologists. The framework is designed to operate on multiple platforms and be used across networks via a World Wide Web-based user interface. ECLPSS is designed for use with both single processor computers for small models, and multiple processors in order to simulate large regions with complex interactions among many individuals or ecological compartments. To test Version 1.0 of ECLPSS, we created a model to evaluate the effect of tropospheric ozone on forest ecosystem dynamics. This model is a reduced-form version of two existing models: , which represents an individual tree, and , which represents forest stand growth and succession. This model demonstrates key features of ECLPSS, such as the ability to examine the effects of cell size and model structure on model predictions.     

Animal dispersal modelling: Handling landscape features and related animal choices

Animal dispersal in a fragmented landscape depends on the complex interaction between landscape structure and animal behavior. To better understand how individuals disperse, it is important to explicitly represent the properties of organisms and the landscape in which they move. A common approach to modelling dispersal includes representing the landscape as a grid of equal sized cells and then simulating individual movement as a correlated random walk. This approach uses a priori scale of resolution, which limits the representation of all landscape features and how different dispersal abilities are modelled.We develop a vector-based landscape model coupled with an object-oriented model for animal dispersal. In this spatially explicit dispersal model, landscape features are defined based on their geographic and thematic properties and dispersal is modelled through consideration of an organism's behavior, movement rules and searching strategies (such as visual cues). We present the model's underlying concepts, its ability to adequately represent landscape features and provide simulation of dispersal according to different dispersal abilities. We demonstrate the potential of the model by simulating two virtual species in a real Swiss landscape. This illustrates the model's ability to simulate complex dispersal processes and provides information about dispersal such as colonization probability and spatial distribution of the organism's path.     

Calibration of the forest vegetation simulator (FVS) model for the main forest species of Ontario,Canada

The forest vegetation simulator (FVS) model was calibrated for use in Ontario, Canada, to predict the growth of forest stands. Using data from permanent sample plots originating from different regions of Ontario, new models were derived for dbh growth rate, survival rate, stem height and species group density index for large trees and height and dbh growth rate for small trees. The dataset included black spruce (Picea mariana (Mill.) B.S.P.) and jack pine (Pinus banksiana Lamb.) for the boreal region, sugar maple (Acer saccharum Marsh.), white pine (Pinus strobus L.), red pine (Pinus resinosa Ait.) and yellow birch (Betula alleghaniensis Britton) for the Great Lakes-St. Lawrence region, and balsam fir (Abies balsamea (L.) Mill.) and trembling aspen (Populus tremuloides Michx.) for both regions. These new models were validated against an independent dataset that consisted of permanent sample plots located in Quebec. The new models predicted biologically consistent growth patterns whereas some of the original models from the Lake States version of FVS occasionally did not. The new models also fitted the calibration (Ontario) data better than the original FVS models. The validation against independent data from Quebec showed that the new models generally had a lower prediction error than the original FVS models.