Ecological Modelling Advanced article Wolfgang Pittroff, University of California, Davis, California, USA Article Contents . Introduction Ellen K Pedersen, Colorado State University, Fort Collins, and Colorado Division of Fish and Game, . Reality and Real Systems Gunnison, Colorado, USA . Systems Analysis . Conceptual Model Ecological modelling is the use of systems analysis and simulation to mimic complex . Mathematical Model ecological systems by summarizing available relevant information. The process includes . Model Domain the development of conceptual and quantitative models, and the evaluation and use of the . Model Qualification model to answer the specific questions for which the model was built. Model Application . Application Example . Outlook Introduction doi: 10.1038/npg.els.0003270 Ecology is the science of the relationships between organ- isms and their environment, which comprises biotic and abiotic elements. Ecologists hold that these relationships are structured by hierarchies consisting of successive levels Reality and Real Systems of organization (Odum, 1998). The ecosystem, an organ- izational level or layer of nature, is considered to be the Ecological or ecosystem models are defined as abstractions lowest level containing all biotic and abiotic elements of real systems (Jeffers, 1988). Reality comprises all things required to ‘perform functions’ (Tansley, 1935; Odum, that are tangible. The word ‘system’, in its original meaning, 1998). The combination of these elements leads to emer- denotes the purposeful aggregation of parts – obviously in gent properties, i.e. the function of an ecosystem tran- human perception. One could argue, therefore, that a scends the sum of its individual components. A simple system that is the object of an ecological model is already a illustration of this concept is a watershed. The func- model, i.e. a picture of reality simple enough to be under- tions performed by a watershed transcend the sum of all stood by humans. Accordingly, the distinction between its geographical, botanical and hydrological properties. system and model is, in the strict sense, not appropriate. In other words, even if all elements of a particular water- However, in line with conventional terminology (Jeffers, shed were precisely understood, one could still not infer 1988), we define ‘model’ as a simplified description of a the function of the entire system without an explicit un- system. The most important required characteristic of a derstanding of the functional interrelationships of its model is to conserve an appropriate representation of func- elements. This example demonstrates that spatial and tion (emergent properties) of the system of interest. As the temporal scales of the ecosystem are defined according model is an abstraction, some details of the description of to the objectives of the ecosystem study (see Jørgensen, the system of interest can be omitted, but the description of 2002, p. 10). system function arising from emergent properties may not. There is no doubt that anthropogenic influences now A model is developed as the result of systems analysis. pervasively dominate the change of ecosystems. Human- induced change of ecosystems has produced the mass extinction of species and has caused environmental Systems Analysis degradation (in the sense of vital functions of ecosys- tems being damaged) across the planet. These detrimen- The Merriam Webster Dictionary Online (2002) defines tal developments may even manifest themselves at systems analysis as ‘the act, process, or profession of stud- the level of global climate change. Consequently, ecosys- ying an activity (as a procedure, a business, or a physio- tem management (Odum, 1998), albeit an ill-defined logical function) typically by mathematical means in order activity, is becoming a necessity. Humans manage to define its goals or purposes and to discover operations complex systems by creating models (Forrester, 1961) and procedures for accomplishing them most efficiently’. because management must be based on information However, decomposing a system in such a way that a sim- and functional understanding. Accordingly, ecological plified model conserving emergent properties can be con- modelling is essential for the management of ecolo- structed is not a formalized scientific method. Its result (the gical systems. Typically, ecological models are imple- model) is also typically not static: knowledge tends to grow, mented as mathematical (i.e. abstract) models of real perspectives change, and new information may modify old ecosystems. ‘laws’. Decomposing a system for the construction of a ENCYCLOPEDIA OF LIFE SCIENCES & 2005, John Wiley & Sons, Ltd. www.els.net 1 Ecological Modelling Many Conceptual Model Many data Many data Little understanding Good understanding The construction of a simulation model requires describing the components of a system and their interrelationships Statistics Physics such that events and processes occurring in the system can be represented in the model. Therefore, the conceptual model is also a definition of the boundaries of the resulting simulation model. An explicit understanding of the bound- Few data Few data aries of the model is essential for defining the level of res- Good understanding Little understanding olution (the lowest level on which elements and processes of Relative of amount data the system of interest are described) and the level of aggre- Systems analysis and Simulation gation (how results of the model are represented). By Few necessity, the construction of a conceptual model of an Understanding Low High ecosystem depends on the intended use of the model. How- ever, available data often determine the details of the Figure 1 Comparison of different methods to solve problems, depending implementation of a conceptual model. Consequently, the on the relative level of understanding of and the relative amount of data available for the system (from Grant et al. (1997), modified from Starfield level of resolution of the model may not match the require- and Bleloch (1991)). ments defined by the conceptual model. In such a situation, it is essential to document the level of agreement of the conceptual model with the implemented mathematical model is equivalent to reducing the dimensionality of model. This documentation is often missing. See Jørgensen observed reality (data). Two fundamentally different and Bendoricchio (2001) for additional discussion. approaches to the reduction of dimensionality in cause– There are four model archetypes: static vs. dynamic and effect relationships exist: statistics (applied to data gener- empirical vs. mechanistic. Static models do not consider ated by experimental research following Popper (1966)) and systems changing over time. Examples include certain systems analysis. Both apply an interpretation framework optimization models (linear programming). Dynamic to observed data (containing dependent and independent models are based on time-dynamic relationships. An variables), but only systems analysis attempts to describe example would be a hydrological model of a watershed functionality explicitly. However, there is a symbiotic re- describing water yield and water quality changes by a set of lationship between experimental research (statistics) and time-dynamic differential equations, e.g. as functions of systems analysis: frequently the attempt to construct a precipitation, geology, vegetation and management. model identifies knowledge gaps leading to new hypotheses The focus of empirical models is prediction, typically at and subsequent experimental research. In turn, data from low levels of resolution with processes and events highly experimental research are essential for the construction of aggregated. Mechanistic models attempt to explain by an models. Figure 1, adapted with permission from Grant et al., explicit formulation of causal relationships. In practice, the (1997), attempts to position systems analysis relative to distinction between empirical and mechanistic is blurred in physics and statistics. One could argue that a situation of ecological modelling because it depends on the level of ‘Few Data, Good Understanding’ is not really possible. resolution of the model. It is therefore inappropriate to This will be addressed below. In this context, it is relevant to use either category in the description of models without consider certain pitfalls faced by those who believe they are reference to the level of resolution and intended applica- applying Karl Popper’s understanding of science to the tion scope. biological or ecological disciplines. They must answer the The elements of a conceptual model (state, driving and question of whether Popper’s two principal requirements – auxiliary variables, material and information transfers, and i.e. theories must be (1) universal and (2) falsifiable – apply sources and sinks) as defined by Forrester (1961) constitute to hypotheses formulated as probability statements, as it the descriptive formalism of most ecological models (Grant occurs so often in ecology. Dolby (1982) presented an in- et al., 1997). However, other descriptive formalisms, e.g. depth discussion of this issue. based on energy flows (Odum, 1972) or causal input–out- Systems analysis includes testing of and experimentation put networks (Patten, 1978; Fath and Patten, 1999), have with models. This again illustrates that systems analysis been proposed. Fath et al., (2001) recently attempted a and modelling is an iterative process. Often in ecology, synthesis