The third paper of my papers that the students asked me about was:
Holling, C.S. 1992. Cross-scale morphology, geometry and dynamics of ecosystems. Ecological Monographs. 62(4):447-502.
That paper was inspired by my 1986 chapter The resilience of terrestrial ecosystems; local surprise and global change, which I reviewed earlier. I designed the paper to be a test of the basic structure proposed in the 1986 chapter. That is, that there are fast/slow dynamics and cross scale interactions occurring in a dynamic hierarchy. If so, then all ecosystems should be dominated by variables that cluster or lump around a small number of scales and frequencies. The original argument was that measurements of sets of any kind of data from an ecosystem would cluster into a small number of “lumps”. The lumps would be shaped by breaks in the speeds and spatial scales of organizing variables across the Panarchy, and by the discontinuities inherent in the non-linear adaptive cycle.
The paper examines the most easily collected data I could think of – that is of the body mass weights of mammals and birds in different boreal latitude biomes- forest, prairie and marine. The test exceeded the capacity of any traditional statistical technique but the data did show clear indications of lumpiness. Moreover the lumpiness, at some scales, was unique to the ecosystem being sampled. Although the initial hypothesis was essentially that a landscape structure created the lumps, other hypotheses (e.g. founder effect, phylogeny, trophic size concentration) were proposed and tested. Only the landscape argument, or more accurately, the hierarchical/panarchical hypothesis, held up. The rest failed.
Fascinating relationships occurred when mammal body mass lumps were compared to those of birds, suggesting very different numbers of dimensions to their search- mammals as one dimensional searchers (they search a path!), birds as three (they search a volume!). A lot more testing is needed but the speculation is fascinating and fun. The causes of size dependent home range data of herbivores and carnivores suddenly became clear and coherent. The lump categories or lump patterns emerged as a signature of the structure of each ecosystem. I tend to see these as an analogue to spectral images characterizing chemical systems.
Later work by colleagues studying other ecosystems confirmed and extended the basic idea. Craig R. Allen has a big set of data from ecosystems around the world, all of which show the lumpy structure (Allen and Holling 2002). And his demonstration of body mass lumps in mammals, birds and reptiles of the Everglades also shows that the structure is very robust. That is, extinct species of one size are replaced by new species of similar sizes. Complex systems (as in the tropics) result in complex lump patterns (Carla Restrepo et al, 1997), lumps suddenly add a cross scale dimension to the role of biodiversity (Peterson et al. 1998), the extinction of large mammals 11,000 years ago in the new world, was actually an extinction of lumps associated with transformation of coarse scale landscape (Lambert and Holling 1998). Havlicek and Carpenter (2001) examined their marvelous data from years of data collection in their experimental lakes areas in Wisconsin, and see the same lumpy structure and demonstrate that the structure is strongly conserved. Raffaelli (Raffaelli et al. 2000) shows littoral organisms are organized in body mass lumps in an experimental set up whose manipulations show strong persistence of the lump structure.
Craig R. Allen has become a leader in the field, and shows that there is an amazing correlation of separately measured attributes of species in ecosystems with the lump structure. Basically he demonstrates that invasive species, endangered species, migratory and nomadic ones strongly correlate with the edge of body mass clumps as separately measured. More broadly, he also demonstrates that population variability in both space and time is highest at these gaps (Allen et al. 1999 and Allen 2006). This high correlation consistently emerges from data obtained in different ecosystems from around the world.
Finally, the same lumpy structures are seen in social and economic data concerning city size and firm size (Bessey 2006, Garmestani et al 2005, 2006 ) and international gross domestic product (Rusty Pritchard, unpublished).
Buz (W.A.) Brock, a well known economist who identifies non-linear attributes as central to economic behavior, hypothesizes that some aspects of economic growth theory suggest causes similar to those I have suggested for ecosystems. I suspect the same is true of the size of organizations. It will be interesting to test whether cities, organizations and economies on the edge of lumps, have the same features of living on the edge of crisis and opportunity as do organisms. If so, that would be extraordinarily significant for policies of development, whether for expansion of local business, regional settlement, or poverty alleviation.
It now seems that these intriguing discoveries have potentially big consequence for questions of change and transformation in any social or biological system. The breaks across scales create the conditions for endangerment, invasiveness and the other attributes mentioned above. In effect, such places are where novelty emerges in an interaction between crisis and opportunity. It is where novel changes can occur as an adaptive cycle starts to renew after a “creative destruction”.
I argue that those body mass breaks are caused by the scale breaks in a Panarchy, as adaptive cycles move from operating at one scale range to another. That is where resource variability and unpredictability is greatest. In a boreal forest, for example, the scales dominated by distinct processes range at least from centimeters and days at the scale of needles and their defoliators, through meters and decades at the scale of whole trees and patches, to 100’s of meters and several decades for stands of even age trees, to, eventually, hundreds of kilometers and millennia for forest biomes. At each of those scale ranges, different processes dominate.
This generation of and entrainment of novelty creates options for systems, maintains the adaptive capacity of a system, and serves as a reservoir of potential functions that may be required following transformations or as normal system dynamics evolve. Such novelty is at the heart of resilience.
But there is skepticism, about lumps, at least. Manly (1996) showed that traditional conservative statistical techniques only identify at most two “lumps” in Holling’s data, where I identified 8 or more. Siemann and Brown say there are no lumps at all, although like Sousa and Connell (1985) earlier, they asked and tested entirely the wrong question. And so it goes. . . .
The fine physicist from the Santa Fe Institute, Murray Gell-Mann, suggested to me that I organize a meeting with supporters, skeptics and other experts, in order to review the whole argument and data. It is an example of the role such an integrative center like SFI can provide, and Craig Allen and I organized the session. The basic conclusion of most participants at the end of the meeting, was that the lumps were real, their number was certainly similar to the numbers I identified, their cause could be the one that I could not disprove, but that other causes might be involved as well. The participants, skeptics and supporters, agreed to test the idea further with entirely new data from new systems. Those new studies each confirmed and extended the discoveries and we have organized all of them in a new book manuscript. It is now in press in a book edited by Craig Allen and I.
I liked the whole process and argument because it is the first time I could predict anything very rigorously- that is, “what are the likely endangered, invasive, nomadic species?”! According to Craig’s analysis, the only variables that correlate with endangerment and invasiveness are time of introduction and closeness of size to the body mass lump edge (Allen et al. 1999). All the other suggestions in the literature- such as size and trophic status, do not hold up as consistent predictors. I hope that work will continue and become generalized to other systems and to inexpensive ways to monitor existing systems.
But, if so, it will take years! The results of the work seem too different from our traditions in science and statistics, where uni-modal distributions, continuity and Type I error statistics have been the standards for simplification. None of those are appropriate for tests of lumpy, discontinuous or multi-modal distributions. The necessary art of simplification has a different foundation for this work than traditional ones. But it does open a terrific new landscape of thought for further discovery.
The start of that process began 18 years ago, and led to the paper that presents the test of the reality of the Panarchy/hierarchy conclusions (Holling 1992). Now it is clear that discontinuities in patterns and processes exist and they disrupt our ability to apply popular scaling models and approaches. Such scaling methods are powerful, and have shown that there is a template that organizes eco-physiological variables of organisms. But they are a first order result. The famous graph showing metabolism vs. size of mammals from bacteria to whales is a classic example. More recent work by West et al. (1999) has discovered the physical, fractal mechanisms that define the parameters of the relationship. Tasty, indeed!
But that is an explanation that focuses on the universal property of physical conditions that set the template. Biological and societal processes create the concentrations of opportunity along that template. That leads to the “lumpy” world representation that now has led to the new book demonstrating the existence of lumpy organization in a variety of ecosystems, in animal geographic ranges, in city sizes, migrating species, economic activities and firm sizes (Allen and Holling In Press). Note that although the evidence continues to grow, only a subset of ecosystem scale ecologists, social scientists and economists have accepted the theory and examples in a way to further test and expand theories of change. Lots of traditional ecologists are critical and do not understand the essential foundations in theory, empirical examples and societal examples.
That is because, historically, most natural scientists study systems that can be manipulated – that is, below the size of a 1m square quadrant in nature or a bench in the lab. That is how my own research started 50 years ago. That has exercised the traditional experimental scientific method with its testing of alternative hypotheses. But it does not sit comfortably with the uncertain reality of large-scale (regional to global) social/environmental systems where experiment comes only through adaptive experiments in combination with appropriately scaled policies and with alternate models of the system. That requires different, broader approaches and methods.
Allen, C. R., E. A. Forys, and C. S. Holling. 1999. Body mass patterns predict invasions and extinctions in transforming landscapes. Ecosystems 2:114-121.
Allen, C. R. and C.S, Holling, 2002. Cross-scale structure and scale breaks in ecosystems and other complex systems. Ecosystems 5: 315-318.
Allen, C. R., A. S. Garmestani, T. D. Havlicek, P. A. Marquet, G. D. Peterson, C. Restrepo, C. A. Stow, B. E. Weeks. 2006. Patterns in body mass distributions: sifting among alternative hypotheses. Ecology Letters 9(5) 630-643.
Bessey, K. M. (2002) Structure and dynamics in an urban landscape: toward a multi-scale view. Ecosystems, 5, pp. 360-375.
Garmestani, A.S., C.R. Allen, and K.M. Bessey. 2005. Time series analysis of clusters in city size distributions. Urban Studies 42: 1507-1515.
Garmestani, A. S., C. R. Allen, J. D. Mittelstaedt, C. A. Stow, and W. A. Ward. 2006. Firm size diversity, functional richness and resilience. Environment and Development Economics 11: 533-551.
Havlicek, T. D. and S. R. Carpenter. 2001. Pelagic species size distributions in lakes: are they discontinuous? Limnology and Oceanography 46:1021-1033.
Holling, C.S. 1992. Cross-scale morphology, geometry and dynamics of ecosystems. Ecological Monographs. 62(4):447-502.
Holling , C.S. and Craig Allen. 2002. Adaptive inference for distinguishing credible from incredible patterns in nature. Ecosystems 5: 319-328.
Lambert, W. D. and C. S. Holling (1998). Causes of Ecosystem Transformation at the end of the Pleistocene: Evidence from mammal body mass distributions. Ecosystems 1: 157-175.
Manly, B.F.J. 1996. Are there clumps in body-mass distributions? Ecology 77: 81-86
Peterson, G., C. R. Allen, C. S. Holling. (1998). Ecosystem Resilience, Biodiversity, and Scale. Ecosystems 1: 6-18.
Raffaelli, D., S.Hall, C. Emes and B. Manly. 2000. Constraints on body size distributions: an experimental approach using a small-scale system. Oecologia 122: 389-398.
Restrepo, C., L. M. Renjifo, and P. Marples. 1997. Frugivorous birds in fragmented neotropical montane forests: Landscape pattern and body mass distribution. Pages 171-189, in W.F. Laurance and R. O. Bierregaard, Jr., editors. Tropical Forest Remnants: Ecology, Management, and Conservation of Fragmented Communities. The University of Chicago Press, Chicago, IL.
Siemann, E., and J. H. Brown. 1999. Gaps in mammalian body size distributions reexamined. Ecology 80:2788-2792.
Sousa, W.P. and J.H. Connell. 1985. Further comments on the evidence for multiple stable points in natural communities. American Naturalist 125, 612-615.
West, G.B., J.H.Brown and B.J. Enquist. 1999. The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science 284:1677-1679.