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New Visualization Techniques

Vol.34 No.1 February 2000
ACM SIGGRAPH


The Role of Visualization in Understanding a Complex Forest Simulation Model



Douglas H. Deutschman
San Diego State University
Catherine Devine, Linda A. Buttel
Cornell University

Introduction

Ecological research is changing as scientists confront the complexities of natural and human-influenced ecosystems. Early ecological research was dominated by the concepts of equilibrium and determinism [30]. Ecosystems were thought to be stable "super-organisms," fine-tuned by thousands of years of mutual adaptation. In such a world, ecosystems can be completely described with static measures of equilibrium population densities. Although this view has been challenged since its inception, it is only in the past 25 years that it has been displaced as the dominant paradigm in ecology. Today, ecologists describe ecosystems as a dynamic collection of individuals responding in different ways to local interactions, broad-scale environmental change and frequent accidents of history [18, 23, 30]. Although the behavior of the ecosystem is partially understandable from population densities, ecosystem dynamics are variable and complex.

Ecologists use an increasingly sophisticated toolbox of techniques to characterize these complex dynamics. Field surveys and laboratory experiments measure the responses of individuals under varied conditions. Thus the mean response as well as the variance in response can be estimated. Improved statistical analyses allow ecologists to describe spatial structure, temporal dynamics and complex spatio-temporal patterns. Finally, mathematical models are being developed that can simulate the complex local interactions of thousands of individuals in a dynamic, heterogeneous environment [9, 17, 34].

Improvements in computer hardware and software have facilitated this shift toward increasing complexity. Today, ecologists are seldom limited by hardware, and software to acquire, store and analyze data has improved dramatically in the past decade. In addition, computational models of ecological systems are becoming common [14]. Models are tools to express our understanding of mechanisms governing the structure and function of ecological communities [20]. Models can also be used to make predictions, determine the robustness of these predictions, reveal system properties and highlight weaknesses in our knowledge [8, 25]. Complex ecological models have several important drawbacks including the need for huge amounts of input data, propagation of errors and difficulty interpreting the often voluminous model output [10, 11, 13]. As a result, increased model complexity and detail may not lead to increased understanding [10, 16, 22].

Role of Visualization in Ecological Models

Improvements in visualization are a vital (but under-valued) factor in analyzing the output from simulation models. In statistics, the idea that a necessary part of the analysis is visualizing the data is well established [see, for example, Anscombe’s pivotal paper, "Graphs in Statistical Analysis," 1973 in the American Statistician and 7, 32, 33.] Tufte argues that modern graphics do much more than replace statistical tables. He sees graphics as the simplest and most powerful instruments for reasoning about quantitative information.

Visualization plays two distinct roles in the scientific process: analysis and communication. Understanding of complex relationships (from field data as well as computational models) is difficult. Traditional static descriptors, like mean population densities of several species, are not sufficient. Instead, short-term temporal trends and local variation in densities are necessary to understand the system. Visualization facilitates understanding by providing the researcher with improved insight into the system. This process guides the development of appropriate statistical descriptors and analyses of spatial and temporal patterns.

Communication of the results from a complex simulation model is another major challenge. Presenting page after page of model code, parameter values and tabular model output is not useful. Critical peer review of the model is hampered by the ability of a reviewer to probe the model. Visualization improves the reviewer’s ability to grasp dynamics and quickly evaluate its strengths and weaknesses. Visualization also bridges the communication gap between theoretical and field ecologists by facilitating the field ecologist’s ability to see the ecological results and not get lost in the abstract mathematics and/or computation that underlies the model.

Visualization of a Forest Model

Over the past five years, tremendous effort has been invested in developing a forest model (SORTIE) completely defined by field measurements on individual trees [10, 26, 27]. SORTIE is a stochastic computer simulation model of northeastern forests that describes local competition among nine species of trees in terms of the responses of individuals. Conceptually, SORTIE is a simple model. Light (the limiting resource) is measured for each tree in the simulated landscape by means of a detailed algorithm that provides a single measure of season-long light availability. This index of light availability integrates information about a tree’s neighborhood based on the density, size, position and species of all neighboring trees. The light available to each tree is then used to calculate the growth rate and risk of mortality of each tree. Surviving trees produce seedlings as an increasing function of tree size, and the seedlings are dispersed away from the parent tree. In SORTIE, broad-scale forest dynamics emerge as the collective result of these localized interactions among seedlings, saplings and mature canopy trees.

Each of SORTIE’s functional relationships is estimated from species-specific field data. Since SORTIE is stochastic, multiple simulations (with different random number seeds) are needed to describe the behavior of the model for each set of parameter values. In the simulations presented here, the forest landscape was a square, 300 meters on a side (area = 9 hectares) typically containing several thousand trees of varying sizes on the landscape at any given time. Model runs employed a five-year time step and reported the density and total basal area (a measure of tree density weighted by each individual tree’s size) of each species throughout the 1000-year run. The simulation also outputs data on the availability of light at the forest floor using a 600 x 600 regular grid. Additionally, a complete map of the forest was output each time step. As a result, a single simulation resulted in over 10,000 density values, 720,000 light values and 200 detailed stem maps. Graphing and visualizing the complex interactions in this model were vital to understanding the emergent behavior of the forest [9].

Visualization of these simulations needed to accurately depict the spatial pattern, size and condition of each individual tree. A single forest map contained data on location (X,Y), species identity (displayed with color) and several quantitative attributes of the tree including stem diameter, height, crown width, crown depth and light penetration through the crown. The visualizations also needed to represent the availability of light at the forest floor and its dependence on the composition of the neighborhood. Several different visualizations were developed, each displaying different subsets of information. Animations were generated for some of the simulations. The animations are an incredibly powerful way to visualize dynamics. Although we do not refer to the animations in this article, they are published on the Internet in Science Online, the electronic counterpart to Science [9]. Here, we demonstrate the power of three-dimensional visualizations in illustrating how the key interactions among trees drive this complex model of a forest community.



Figure 2: Visualization of the simulated forest under two different regimes. Tree position, tree height and tree diameter are mapped to the opaque inner cylinder. The canopy dimensions (diameter and depth) and light interception (opacity) are mapped to the translucent outer cylinder.


Figure 3: The dynamic relationship between canopy trees and light availability at the forest floor. Only the trunks of adult trees are displayed since they intercept most of the light. Light at the forest floor is calculated every five meters resulting in a 600 x 600 grid of values. Light availability at the forest floor is displayed on a logarithmic grayscale with full sun (white), partial shade (eight shades of gray) and deep shade (black). In undisturbed forests (a), beech and hemlock create localized patches of deep shade. In disturbed forests (b), recently disturbed areas are much brighter, even after the maturation of the yellow birch canopy.

Role of Disturbance in the Forest

In many forests, the availability of light at the forest floor is a critical determinant of tree recruitment [2, 15]. Canopy gaps create localized areas of increased light on fine spatial and temporal scales. Gaps can be created by the mortality of canopy trees and by many types of disturbances such as wind storms, ice storms and hurricanes [1, 5]. There has been broad debate about the role of fine-scale pattern in forest gaps [3, 6, 24, 28, 31]. Some forest ecologists argue that there are complex patterns of seedling recruitment based on the size and shape of the gap and the species composition of the surrounding trees. Other ecologists acknowledge that gaps are variable, but assert that most of the variability is unimportant. Gaps function as a relatively homogeneous place where there is enough light to allow seedlings to reach the canopy. The SORTIE model uses a fine-scale estimate of local light availability for each individual seedling and sapling. Thus, it does not assume that gaps are homogeneous. Simulations with the SORTIE model can be used to evaluate the role of canopy gaps in mediating forest development.

To test this hypothesis, a series of simulations were performed that incorporated two distinct types of canopy gaps. In one set of simulations, no multi-tree gaps were created on the landscape although single-tree gaps formed naturally as the result of adult mortality. In these simulations (referred to as the undisturbed simulations) canopy gaps were small and short-lived. In contrast, disturbed simulations were subjected to a strong, multi-tree disturbance regime modeled as circles in which all trees were destroyed. This disturbance regime created significantly larger, brighter, more homogenous gaps but was not meant to represent any particular natural disturbance.

The standard way to answer this question is to analyze the mean behavior of the nine species growing in the forest. In the undisturbed-forest simulations (mean of eight different runs), fast growing species like black cherry, white pine and red oak reach the canopy first, attaining higher initial basal areas (See Figure 1a - Black Cherry). As the light reaching the forest floor declines, canopy recruitment of shade intolerant seedlings fails and the more shade tolerant species (mainly beech, hemlock and to a lesser extent, yellow birch) increase in relative abundance (See Figure 1a). At the end of the 1000-year simulation, beech dominates the undisturbed forest. In the disturbed-forest simulations, the frequent creation of larger canopy gaps by disturbance leads to the dramatically enhanced performance of yellow birch (See Figure 1b). This suggests that large canopy gaps play a very different role in the model than small, single-tree gaps.

Is this the whole story? Visualization of a single simulation provides much deeper insights. The undisturbed forest shows striking spatial pattern (See Figure 2). The canopy is fairly uniform with infrequent, small gaps and evenly spaced trees. However, species distributions within the forest are not random. There is a pronounced clustering of trees with neighbors of the same species. Beech and hemlock show very strong intra-specific clustering. The disturbed forest visualization reveals further structure. Gaps can be seen both as open space, and as clusters of yellow birch trees in various stages of maturity. Large gaps are filled almost exclusively by yellow birch, suggesting that heterogeneity in the gap is unimportant at those scales. Animations also reveal that most of the change in the forest occurs at the boundaries between clumps of different species. Beech and hemlock slowly encroach on yellow birch clusters. Beech displaces hemlock on even slower time scales. These visualizations provide answers to some research questions (e.g. large gaps function differently than small gaps) and open new questions (e.g. why are beech and hemlock tightly clustered?).

Heterogeneity of Light at the Forest Floor

The tight clustering of beech and hemlock was an unexpected result of the model, not seen until the model was visualized. A survey of the ecological literature provides strong support for this pattern, suggesting it is not an artifact of the model [12, 27, 29]. Two explanations are possible for the tight clustering of beech and hemlock. Either the resources needed for successful beech and hemlock establishment are greatest underneath their own species, or beech and hemlock have very limited dispersal. In SORTIE, trees compete for a single limiting resource, light. Thus, a visualization that displays simultaneously the location of adult trees and the light underneath them will provide direct evaluation of the first hypothesis.

In order to visualize both the mature trees and the light at the forest floor, it was necessary to strip away some details about the forest. The most effective visualization ended up being one in which seedlings were ignored and mature canopy trees were represented without their crowns. This thinned representation allowed for the simultaneous display of the light available at the forest floor (See Figure 3). In undisturbed forests, there are few areas of high light. The darkest areas are associated with high densities of beech and hemlock (See Figure 3a). The difference in shade cast by these three species is even more obvious in the disturbed forest (See Figure 3b). Areas of the forest with dense yellow birch trees still allow modest light to penetrate to the forest floor. In contrast, areas dominated by beech and hemlock are very dark.

This visualization suggests that the first hypothesis is wrong. Beech and hemlock cast deep shade, and thus adult clustering is not driven by improved resources underneath the adults. The visualizations also suggest that there is significant heterogeneity under the closed canopy. The observation that the forest canopy is fairly closed and uniform (as implied by Figure 2) is misleading. Individual species intercept vastly different amounts of light, leading to complex patterns of light availability at the forest floor.







Figure 4: Dispersal of beech, hemlock and yellow birch. In order to visualize patterns of seedling dispersal all information was removed except the position and height of adult trees and seedlings. In undisturbed simulations (a-c), the tight clumps of beech seedlings are in stark contrast to the widely dispersed yellow birch seedlings. In disturbed simulations (d-f), the difference between beech and yellow birch seedlings is enhanced by the increased clustering of adult trees due to disturbance.

Dispersal Limitation of Forest Trees

Dispersal limitation is the second potential explanation of the clumped behavior of beech, hemlock and yellow birch. In fact, there is a fair amount of evidence from many plant communities for a trade-off between competitive strength and dispersal [21]. In forests limited by light, the trees with the greatest ability to tolerate shade are often competitively superior but severely limited by dispersal. In SORTIE, beech and hemlock are typical shade tolerant competitors [2, 19]. Yellow birch, on the other hand, is a typical gap (or fugitive) species. It is an inferior competitor, but has greater dispersal allowing it to "find" areas of higher resources better than beech or hemlock.

In order to visualize the relationship between seedlings and adults, another visualization was developed. In this display (See Figure 4) information about crown size and shape, light availability and the position of competitively inferior species are removed. In undisturbed forests, the case for recruitment limitation seems clear. Beech and hemlock seedlings cluster tightly underneath adults (See Figure 4a). Visualization of beech trees and seedlings is compelling. In areas with no beech adults, beech seedlings are conspicuously absent (See Figure 4b). In striking contrast, yellow birch seedlings seem to be scattered completely at random (See Figure 4c). Although adult yellow birch may be slightly clumped, the seedlings are dispersed throughout the landscape. This is consistent with a gap species. In disturbed forests, the patterns are enhanced by the increased opening of the canopy through disturbance (See Figure 4d). Beech seedlings are tightly clustered under adults (See Figure 4e) while yellow birch seedlings are scattered throughout the forest (See Figure 4f). It is clear from these final figures, that beech and hemlock cluster because of dispersal limitation, but yellow birch clusters form in disturbed areas with higher light.

Discussion

Visualizations of the forest model provide compelling evidence for recruitment limitation for beech and hemlock and light limitation for yellow birch. This is consistent with the competition-colonization trade-off that is well known in ecology. The visualizations also provide clear insight into the different roles that trees of different species play in the forest. Although the canopy may seem fairly uniform, the light available under the canopy varies as a function of local species composition. All of these features of the forest emerge from a model parameterized completely at the level of trees. The visualizations suggest that SORTIE’s behavior emerges naturally and realistically from the complex local interactions among trees. The visualizations also allow for the efficient communication of the model’s structure, function and predictions. To understand the forest, we have to see the forest and the trees.

Begon et al state "Doing science at the community level presents daunting problems because the database may be enormous and complex. A first step is usually to search for patterns in community structure and composition. The need to develop procedures for describing and comparing communities has dominated the development of community ecology" [4, page 680]. Visualization provides a powerful tool to elucidate pattern. Ecologists and visualization experts need stronger relationships to develop visualization methods relevant to ecology and accessible to ecologists [14]. We hope this article provides a small step toward improved dialog between ecologists and visualization experts.

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Douglas H. Deutschman is Assistant Professor of Biology at San Diego State University. He specializes in the analysis of the complex dynamics of biological populations, communities and ecosystems.

Douglas H. Deutschman
Department of Biology
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-4614

Catherine Devine, Linda A. Buttel
Cornell Theory Center
Cornell University

The copyright of articles and images printed remains with the author unless otherwise indicated.