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Spatial pattern in tropical forests. Representation of all trees with dbh > 10cm at the lowland hill dipterocarp forest in Sinharaja, Sri Lanka, for the lower 250 x 500m part of the 25ha study plot. The size of the circle is proportionally to the dbh.

Towards a Unified Spatial Theory of Biodiversity

Summary

One of the biggest and most persistent challenges in contemporary ecology is to explain the high diversity in ecological communities such as tropical forests, grasslands, coral reefs, or plankton ecosystems. The broad objective of our project is to understand the relative importance of processes and factors that govern the composition and dynamics of species-rich communities. Advances in this issue have important implications for efforts to protect terrestrial biodiversity.

Surprisingly, although most processes which are thought to contribute to species coexistence have a strong spatial component, the rich source of information on spatial patterns has only rarely been used. To accomplish our goal, we take a radically different approach than previous attempts and adopt a spatially explicit perspective that will allow us to take significant steps towards a Unified Spatial Theory of Biodiversity. We use large and high quality data sets of tropical forests, each comprising several hundred of species and >100000 trees that are mapped, monitored and censused every 5 years.

We proceed in three steps. (1) We quantify the highly complex spatial structures found in forests using recent techniques of spatial pattern analysis. (2) We build a range of individual-based spatially-explicit simulation models ranging from “pure” neutral models to detailed process-based models of tropical forest, such as FORMIND. (3) We use pattern-oriented modelling to confront these simulation models with the set of patterns identified in (1) to identify the most parsimonious models that account simultaneously for all (spatial) patterns.

    Canopy of lowland hill dipterocarp forest in Sinharaja taken from the top of a lowland hill - Sinharaja

    (about 800m asl). It shows different species in different stages of leaf flushing (light green) and early

    fruiting (pinkish - red) stages but none in the picture in bloom. Source: Nimal Gunatilleke, Universität

    Peradeniya

Approach
 

The basic idea of our project is to analyse the highly complex spatial structures that characterize species-rich tropical forests and to develop individual-based and spatially-explicit forest simulation models to generate the same type of data (i.e., maps) so that the same patterns can be quantified in the field and in the models.

We use two complementary approaches to confront models with data and identify the simplest (i.e., parsimonious) models that account simultaneously for all (spatial) patterns. The starting point of a first simple-to-complex approach is a spatially explicit model equivalent to the classical neutral models of Hubbell (2001) and Volkov et al. (2003). The results of this model will be compared to the analytical results obtained from neutral models and will serve as point of reference. In subsequent steps processes and mechanisms will be systematically added resulting in more complex models. Simultaneously, we will use a complex-to-simple approach and start with a fully individual-based version of the existing process-based forest model FORMIND (Köhler et al. 2003) and simplify this model step by step. Because the level of complexity of the most parsimonious model is unknown we approach it from two opposed directions. This also facilitates a more systematic selection of model ingredients despite the multiple and potentially infinite number of plausible models.

Our underlying assumption is that the spatial patterns capture essential and time-invariant structural attributes of undisturbed tropical forests and thus will allow us to make general statements about of the mechanism promoting coexistence. We will execute simulations over long time spans, also to determine the quasi-equilibrium of the undisturbed forest community. This will require considerable computer power.
 

However, in contrast to the common approach, the ability of the model to capture aspects of reality will not only be evaluated based on species abundance distributions and species-area curves, but on the variety of spatial patterns that are quantified from the data of the three forest plots. Using multiple patterns is a breakthrough of pattern-oriented modelling and a powerful strategy of model selection that helps to overcomes the old problem that several substantially different models may explain the same pattern. Even if each of the patterns, taken individually, has low discriminatory power (e.g., the species abundance distribution), the simultaneous match of several patterns is highly non trivial (Wiegand et al. 2003; Grimm et al. 2005). The focus on multiple patterns constrains the selected models to show structural similarities to real forests in many different aspects and at different spatial and organisational scales.
 

Individual-based and spatially-explicit forest models
We develop a family of forest models of different complexity based on the state-of-the-art techniques in forest modelling. On the one hand, we will enrich neutral models step-by-step with processes and mechanisms which are known to enhance coexistence or relevant for community dynamics. First steps in this direction have been made e.g., by Chave et al. (2002) and Zillio and Condit (2007). On the other hand we will use process-oriented forest models of the FORMIX and FORMIND family to follow a complex-to-simple approach.

In process-oriented models, forest growth is described on the basis of the carbon balance by modelling eco-physiological processes, e.g. photosynthesis of leaves, respiration, and allocation. FORMIX and FORMIND (Huth and Ditzer 2000; Kammesheidt et al. 2001; Köhler et al. 2003; Köhler and Huth 2004, 2007; Rüger et al. 2008) keep track of individual trees (but not necessarily of their exact spatial location) and have been used to simulate areas of tropical forest of 100 ha and more. Tree species are classified into functional groups (5-22 groups, e.g. Smith et al. 1997) and the model contains a process-based representation of tree growth, mortality, regeneration, and competition. These basic processes are simulated using allometry relationships, trade-offs, the light climate, and carbon balance. The FORMIX and FORMIND models have been used e.g., extensively for analysing rainforests in different tropical regions (South East Asia, South and central America, Africa), the long-term impact of disturbances , for evaluation of forest management strategies, for understanding forest dynamics and species richness, and for determination of key processes.

Pattern-oriented modelling
An important element of our integrative approach is the general strategy of pattern-oriented modelling (POM; Wiegand et al. 2003; Grimm et al. 2005). It is a research program for individual-based (or more generally bottom-up) simulation models that provides strategies for coping with the two main challenges of bottom-up modelling - complexity and uncertainty. The pattern-oriented modelling strategy attempts to make bottom-up modelling more rigorous and comprehensive.

POM explicitly follows the basic research program of science: the explanation of observed patterns. Patterns are defining characteristics of a system and are therefore often indicators of essential underlying processes and structures. Patterns contain information on the internal organization of a system, but in “coded” form. The purpose of POM is to “decode” this information (Wiegand et al. 2003). The ground breaking insight of POM is that, for complex systems, a single pattern observed at a specific scale and hierarchical level, such as the species abundance distribution, is not sufficient for model selection, i.e., to reduce uncertainty in model structure and parameters. POM therefore uses multiple patterns observed in real systems at different hierarchical levels and scales for model selection.

Spatial pattern analysis
Species-rich tropical forests comprise hundreds of tree species at different stages (i.e., recruits, seedling, sapling, intermediate, adult, dead) which result in highly complex and diverse spatial structures. Methods of statistical spatial pattern analysis (Wiegand and Moloney 2004; Illian et al. 2008) provide a powerful framework to analyze such data. An important goal of spatial pattern analysis is to determine the degree of random spatial structures in uni-, bi-, and multivariate species interactions and its critical spatial scales (Wiegand et al. 2007a, b, c).

Neutral theories predict weak interactions among species whereas alternative theories predict strong interactions among species. Reaching our goal, however, requires efficient techniques to deal with the analysis of the association of thousands of species pairs. The software Programita, provides a powerful tool to conduct such analyses and allowed the PI to significantly advance in the above goal (Wiegand et al. 2007a, b, c). Extension of this work will build the core of the pattern-analysis part of the project but will be enriched by other recent techniques (e.g., Illian et al. 2008).

Confronting models with data
This step requires extensive simulations of the forest models. In contrast to previous efforts that used simulation models we use the pattern-oriented modelling strategy which allows for rigorous and systematic analysis of simulation models. Pattern-oriented modelling uses “strong inference” (Platt 1964) by contrasting alternative models to the pattern data. To this end, alternative forest models are formulated by adding more detailed processes and mechanisms to the basic neutral model or to simplify a complex process-based version of FORMIND, and characteristic patterns of the tropical forests at both population and community levels are identified. The alternative models are then tested by how well they match the observed patterns. Alternative models failing to reproduce the patterns are rejected, and additional patterns with more falsifying power can be used to contrast successful alternatives
 

References

Chave, J., H. C. Muller-Landau, and S. A. Levin. 2002. Comparing classical community models: theoretical consequences for patterns of diversity. American Naturalist 159: 1-23.

Grimm, V., et al. 2005. Pattern-oriented modeling of agent-based complex Systems: lessons from ecology. Science 311:987-991

Hubbell, S. P. 2001. The unified neutral theory of biodiversity and biogeography. Princeton University Press, Princeton, N.J.

Huth, A.; Ditzer, T. 2000. Simulation of the growth of a Dipterocarp lowland rain forest with FORMIX3. Ecological Modelling 134: 1-25

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. 2008. Statistical analysis and modelling of spatial point patterns. John Wiley & Sons, Chichester.

Kammesheidt,L., Köhler,P., Huth,A., 2001. Sustainable timber harvesting in Venezuela: a modelling approach. J. Appl. Ecol. 38, 756-770.

Köhler, P., Chave, J., Riera, B., Huth, A. 2003. Simulating long-term response of tropical wet forests to fragmentation, Ecosystems 6, 129-143.

Köhler,P., Huth,A., 2004. Simulating growth dynamics in a South-East Asian rainforest threatened by recruitment shortage and tree harvesting. Clim. Change 67, 95-117.

Köhler,P., Huth,A., 2007. Impacts of recruitment limitation and canopy disturbance on tropical tree species richness. Ecol. Modell. 203, 511-517.

Platt, J. R. 1964. Strong inference. Science 146: 341-444.

Smith, T.M., H.H. Shugart and F.I. Woodward (eds.). 1997. Plant Functional Types: Their Relevance to Ecosystem Properties and Global Change. Cambridge University Press, Cambridge 369 pp.

Rüger,N., Williams-Linera,G., Kissling,W.D., Huth,A., 2008. Long-term impacts of fuelwood extraction on a tropical montane cloud forest. Ecosystems 11: 868–881
Volkov, I., Banavar, J.R., Hubbell, S.P., Maritan, A. 2003. Neutral theory and relative species abundance in ecology. Nature 242: 1035 – 1037.

Wiegand, T., and K. A. Moloney. 2004. Rings, circles, and null-models for point pattern analysis in ecology. Oikos 104: 209-229.

Wiegand, T., F. Jeltsch, I. Hanski, and V. Grimm. 2003. Using pattern-oriented modeling for revealing hidden information: a key for reconciling ecological theory and application. Oikos 100: 209-222.

Wiegand, T, C.V.S. Gunatilleke, I.A.U.N. Gunatilleke, and T. Okuda. 2007a. Analyzing the spatial structure of a Sri Lankan tree species with multiple scales of clustering. Ecology 88: 3088–3102.

Wiegand, T, C.V.S.. Gunatilleke, and I.A.U.N.. Gunatilleke. 2007b. Species associations in a heterogeneous Sri Lankan Dipterocarp forest. American Naturalist 170 E77–E95.

Wiegand, T, C.V.S. Gunatilleke, I.A.U.N. Gunatilleke, and A. Huth. 2007c. How single species increase local diversity in tropical forests. PNAS 104:19029–19033.

Zillio T,Condit R 2007. The impact of neutrality, niche differentiation and species input on diversity and abundance distributions. Oikos 116: 931-940.