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HIERARCHY and SCALING: EXTRAPOLATING INFORMATION ALONG a SCALING LADDER by JIANGUO WU Department of Life Sciences, Arizona State

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HIERARCHY and SCALING: EXTRAPOLATING INFORMATION ALONG a SCALING LADDER by JIANGUO WU Department of Life Sciences, Arizona State Canadian Journal of Remote Sensing Vol. 25, No. 4, 1999, pp. 367-380 HIERARCHY AND SCALING: EXTRAPOLATING INFORMATION ALONG A SCALING LADDER by JIANGUO WU Department of Life Sciences, Arizona State University West, Phoenix, Arizona 85069, USA can help simplify the complexity of systems SUMMARY under study, enhance ecological understand- The large number of components, nonlinear ing, and, in the same time, minimize the dan- interactions, time delays and feedbacks, and ger of intolerable error propagation in trans- spatial heterogeneity together often make lating information across multiple scales. ecological systems overwhelmingly complex. This complexity must be effectively dealt with for understanding and scaling. Hierarchy Key Words: Scale, scaling, hierarchy theory, theory suggests that ecological systems are hierarchical patch dynamics, grain, extent, ag- nearly completely decomposable (or nearly gregation, extrapolation, near- decomposable) systems because of their loose decomposability, space-time decomposition, vertical and horizontal coupling in structure pattern and process and function. Such systems can thus be sim- plified based on the principle of time-space decomposition. Patch dynamics provides a RÉSUMÉ powerful way of dealing explicitly with spatial heterogeneity, and has emerged as a unifying La complexité des systèmes écologiques est concept across different fields of earth sci- due à la combinaison du grand nombre de ences. The integration between hierarchy composantes, des interactions non linéaires theory and patch dynamics has led to the entre elles, de délais temporels ainsi que de emergence of the hierarchical patch dynamics phénomènes de rétroactions et de paradigm (HPDP). In this paper, I shall dis- l’hétérogénéité spatiale. Afin de comprendre cuss some major elements of ecological com- les systèmes écologiques et comment on peut plexity, hierarchy theory, and hierarchical passer d’une échelle d’observation à une patch dynamics, and then present a hierarchi- autre, on se doit de tenir compte de cette com- cal scaling strategy. The strategy consists of plexité. La théorie de la hiérarchie suggère three stages, each of which may involve a que les systèmes écologiques sont en fait des number of steps and methods: (1) identifying systèmes presque décomposables à cause du appropriate patch hierarchies, (2) making ob- couplage vertical et horizontal non serré de servations and developing models of patterns leur structure et de leur fonctionnement. Ces and processes around focal levels, and (3) ex- systèmes peuvent donc être simplifiés en se trapolation across the domains of scale using basant sur les principes de décomposition spa- a hierarchy of models. Identifying and tak- tio-temporelle. Le concept unificateur de plu- ing advantage of the hierarchical structure sieurs disciplines en sciences de la terre qu’est and near-decomposability of complex eco- celui de la dynamique des parcelles est une des logical systems are essential to understanding meilleures approches pour tenir compte effi- and prediction because a hierarchical ap- cacement de l’hétérogénéité spatiale. proach can greatly facilitate simplification L’intégration de la théorie de la hiérarchie et and scaling. It is hardly justifiable theoreti- du concept de la dynamique des parcelles a cally and overwhelmingly difficult technically mené à l’émergence du paradigme de la dy- to translate information directly between two namique des parcelles hiérarchiques. Dans cet distant levels (or corresponding scales), when article, je discute des notions qui se rattachent ignoring intervening levels that are relevant to à la complexité écologique, de la théorie de la the phenomenon under study. Although it hiérarchie et de la dynamique des parcelles may be possible to scale up from the cell to hiérarchiques, puis je présente une stratégie globe, or vice versa, successful approaches hiérarchique de changement d’échelles. Cette most likely have to be hierarchical. In this stratégie comporte trois étapes: (1) identifier paper I shall describe one of such approaches les parcelles hiérarchiques appropriées, (2) in which patch hierarchies are used as “scal- faire des observations et développer des ing ladders”. This scaling ladder approach modèles des structures et des processus autour des niveaux choisis, et (3) extrapoler d’une 1 Canadian Journal of Remote Sensing Vol. 25, No. 4, 1999, pp. 367-380 échelle d’observation à l’autre en employant human landscape and above) and temporal des modèles hiérarchiques. Identifier et pren- (e.g., decades and longer) scales are poorly dre en compte la structure hiérarchique ainsi understood. However, the recent literature in que la quasi-décomposition des systèmes ecology and related fields of earth sciences écologiques complexes sont essentiels à la clearly indicates an increasing emphasis on compréhension et la prédiction en écologie car studies at coarse scales and over multiple l’approche hiérarchique facilite grandement la scales. This shift in research emphasis in simplification des systèmes et le passage de ecology seems inevitable for at least two rea- l’information d’une échelle d’observation à sons. The first is that most if not all environ- une autre. Il est difficilement justifiable mental and resource management problems théoriquement et très difficile techniquement can only be dealt effectively with at broad de traduire l’information directement entre les scales on which they typically occur. The deux niveaux distants lorsque l’on ignore les second and more profound reason is that autres niveaux pertinents au phénomème étu- ecologists are now acutely aware that, in order dié. Malgré qu’il soit possible de passer de la to understand how nature works, they must cellule au globe, et vice-versa, pour que cette consider broad-scale pattern and process and démarche soit valable, elle se doit d’être relate them to those at fine scales with which hiérarchique. Le présent article décrit une telle they are most familiar. In both cases, trans- approche, soit celle de parcelles hiérarchiques, lating or extrapolating information from one qui est employée comme “échelle de scale to another, i.e., scaling, is indispensable. changements d’échelles d’observation”. Accordingly, the process of translating or ex- Cette approche peut aider à simplifier la com- trapolating information from fine to coarse plexité des systèmes étudiés et par le fait même scales is usually referred to as scaling-up, and aider à la compréhension écologique et ce tout the process in the reverse direction as scaling- en minimisant le danger de propagation down. Clearly, there is an urgent need to d’erreurs lors du passage de l’information conduct large-scale studies for capturing the d’une échelle d’observation à une autre. patterns and processes that are not evident in __________________________ fine-scale observations, and to develop strate- gies for translating information from local to “The world is both richly strange and regional and global scales. Indeed, the issues deeply simple. That is the truth of scale and scaling have taken a prominent spelled out in the graininess of reality; position in ecology (Levin, 1992; Peterson that is the consequence of modularity. and Parker, 1998). Not surprisingly, these re- Neither gods nor men mold clay cent studies have shown that scaling is usually freely; rather they form bricks.” complex, with problems and obstacles arising from a variety of situations. ¾ From Philip Morrison (1966) Why is scaling a complex matter? First, studies in landscape ecology, hydrology, INTRODUCTION meteorology, and other related earth sciences have shown that different controls and proc- Traditionally, most empirical and theoretical esses tend to dominate in distinctive, charac- studies in ecology have been conducted over teristic domains of scale in time and space. small areas and short time periods and poorly Thus, observations made on a single scale can, replicated. For example, Kareiva and Ander- at best, capture only those patterns and proc- son (1986) reported that 50% of ecological esses pertinent to that scale of observation. experiments published in the journal, Ecol- Yet, complexity arises almost inevitably when ogy, between 1980 and 1987 were conducted a description or explanation simultaneously on plots less than 1m in diameter. In a similar invokes multiple levels of organization or survey, Tilman (1989) found that only 7% of domains of scale (Simon, 1962; Allen and experiments he examined were conducted on Starr, 1982). Second, nonlinear relationships a time scale greater than five years, while 40% and feedbacks among components at the lasted less than 1 year (typically a single field same and different scales are quite common season). Up to now, only a few whole eco- in ecological systems. Strong nonlinearities systems have been subjected to experimental often lead to instability and unpredictability manipulation and usually not replicable or in large complex systems. Third, spatial het- controlled (Carpenter et al. 1995). As a re- erogeneity is ubiquitous and varies at differ- sult, patterns and processes of ecological sys- ent scales, further complicating the scaling tems that occur on broad spatial (e.g., the process. For example, while landscapes can 2 Canadian Journal of Remote Sensing Vol. 25, No. 4, 1999, pp. 367-380 be perceived as hierarchical mosaics of patches, at each level patches may interact in a variety of ways and form different patterns. COMPLEXITY OF ECOLOGICAL Patchiness and gradients usually
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