Funded Grants

Cross scale organization and scale breaks in complex systems

Humans continue to increase their ability to determine the exact structure of the basic elements of complex systems. For example, the human genome has now been completely and precisely mapped. However, humans still don't understand how the simplest of emergent properties arise in these systems. Emergent properties are things like consciousness in humans, or resilience to perturbation in ecosystems, that we wouldn't have predicted to occur or exist given the sum of the parts. Despite humankinds' increasing technological know-how, properties like these remain a mystery. Their understanding remains a challenge of both basic and practical interest. Basic interest simply because humans desire to know how things function. Practical interest because complex systems are part of our everyday lives, for example in the form of ecosystems and economies, and we need to understand how they will react to the increasing stresses placed upon them, and how new systems will re-organize when they replace the old.

Complex systems are usually hierarchically organized, and possess a number of emergent properties that makes their understanding of great interest. Hierarchies are systems with multiple levels of organization where each level is semi-independent and formed from the interactions among a set of variables that share similar speeds. Communication between levels consists only of a small set of information or of material, and flows to the next higher and slower level. This structure allows wide variation in particulars within levels, and encourages adaptive change and exploration of alternatives.

Ecologists embraced the transfer of the term hierarchy to complex ecological systems and developed its application to a wide variety of ecological relationships and structures. Theoretical understanding was increased by shifting attention from the smallscale perspectives dominant in ecology, to a multi-scale landscape view that recognized the cross-scale interactions between biotic and abiotic processes.

Despite theoretical advances resulting from hierarchy theory, most current models of the organization of ecological systems implicitly represent species and their ecological functions as operating at the same scale. Ecological systems, however, are not scale invariant. Different species operate at different temporal and spatial scales, as do ecological processes. Small and fast scales are dominated by biophysical processes that control physiology and morphology, while the very largest scales are dominated by climate and geomorphological processes

The scaling of physical, biological, ecological and social phenomena has become a major focus of efforts to develop simple representations of complex systems. One approach to analyzing the cross-scale structure of ecosystems has been to search for scaling relationships derived from basic processes that capture the variation found across all scales. These efforts have identified and described a number of interesting scaling laws.

However, there has been almost no focus upon the structure and dynamics of scale breaks-- scales that are in-between two different scaling regimes. Ecological and biological hierarchies appear to exhibit multiple scale regimes. There are breaks between levels as processes controlling structure shift from one set to another. For example, the analysis of vegetation pattern on landscapes has shown that different scaling regimes exist. The analyses of animal community patterns also have revealed a cross-scale pattern of multiple scale regimes, shown by the clumping of animal characteristics such as size. Brian Walker and colleagues have shown that morphological characteristics of plants are also unevenly distributed, and that these characteristics aggregate into distinct groups that correspond to ecological functions. Analyses of community organization have revealed that species' body size, which strongly correspond to the scales at which a species lives, are unevenly distributed. These aggregations suggest that ecosystems are not simply following allometric laws, but that the interaction of plants, animals, and their environment varies with scale and produces ecological patterns that vary across scales in a discontinuous fashion. Understanding the organization and dynamics of ecosystems and other complex systems within and across scales offers the potential to assess both the resilience of ecosystems and the vulnerability of particular components. In ecosystems, the distribution of species' body masses should exhibit a pattern that reflects the system's organization and this pattern should provide information on basic ecological properties of that ecosystem. Analyses of patterns in the distribution of animal body masses demonstrate that these body mass distributions are discontinuous. That is to say, across the range of body masses an a size axis, there are areas where body masses tend to aggregate, and there are areas where no species of that particular size occurs. Because body mass correlates so strongly with a whole suite of ecological attributes of a species, like life span, step length, and home range size, it provides an excellent proxy for the scale at which these species interact with their environment. Thus, discontinuities in body mass distributions reflect discontinuities--and available scales--in the environments in which these animals live. Discontinuities in animal body mass distributions identify scale breaks in the organization of ecological systems.

In hierarchical complex systems, there are breaks between levels as processes controlling structure shift from one set to another. Scale breaks in characteristics of animal communities such as body masses correlate strongly with a set of poorly understood biological phenomena that consist of contrasting attributes. These phenomena include invasion, extinction, high population variability, migration and nomadism. In other words, high variability at the species, population and community levels. Recently, with colleagues, I demonstrated that the body masses of endangered and invasive species in a community occur at the edges of body mass aggregations 2-4 times as often as expected by chance. That correlation is consistent in all 8 data sets examined so far. Those data include four different taxa in two different ecosystems. The strong correspondence between the independent attributes of population status and body-mass pattern in three different taxa confirms the existence of discontinuous body mass distributions. It may seem initially surprising that both invasive and declining species are located at the edge of body-mass aggregations. These results suggest that something similar must be shared by the two extreme biological conditions represented by invasive species and declining species. An examination of the phenomena of nomadism in birds in an Australian Mediterranean climate ecosystem found that nomadic birds too cluster about scale breaks. The clustering of these phenomena at predictable scale breaks suggests variability in resource distribution or availability is greatest at these states. Is this true in other systems?

Careful investigation of the partitioning of diversity within and across scales, the importance of scale breaks and the phenomena associated with scale breaks may lead to fruitful avenues of investigation in the analysis of ecological, economic and social systems. For example, high (resource) variability can be bath a detriment (i.e., the association between extinct and declining species and scale breaks) or a boon (the success of invasive species at scale breaks). I suggest that this discontinuous pattern has predictive power: species, community, and population turnover in landscapes subject to human transformation tend to be located at the edge of body-mass aggregations, which may be transition zones between distinct ranges of scale. Location at scale breaks affords species great opportunity, but also potential crisis. There are several puzzles related to this association that need to be solved. Under what circumstances is it beneficial to exploit or specialize at scale breaks? When a system's resilience is exceeded (or approached?) do species/organizations associated with scale breaks unravel first? What are economic or social indicators that exhibit scale breaks? If there are such lumps in the size of firms, are the ones on the edge of lumps similarly functionally unique? In the size of cities? In the size of the gross national product of nations, or exports?

Answering these questions, and thereby better understanding the structure of complex systems such as ecosystems and urban networks, should also provide better understanding of the emergent properties that arise from these structures. Transformation of the Earth's surface, to a degree that surely exceeds the imagination of anyone living at the previous turn of the century, is proceeding without abatement or slowdown. Urban areas in the United States are sprawling at rates that exceed population growth many fold. Ecological systems are under greater and greater stress, and becoming more and more like islands. The Earth is composed of complex systems such as ecosystems, urban networks, and economies. How, or even if, these systems cope with stresses is vitally important to humanity as it proceeds wildly into the 21st century. Understanding their basic structure is the first step.