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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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V. Life's Corporeal Evolution Develops, Encodes and Organizes Itself: An EarthWinian Genesis Synthesis

6. Dynamic Fractal Network Ecosystems

Ricotta, Carlo. Self-Similar Landscape Metrics as a Synthesis of Ecological Diversity and Geometrical Complexity. Ecological Modelling. 125/2-3, 2000. A hypothesis in search of a unified science rooted in a nature suffused by universal, multifractal patterns.

Rietkerk, Max and Johan van de Koppel. Regular Pattern Formation in Real Ecosystems. Trends in Ecology and Evolution. 23/3, 2008. Another quantification by way of “striking cross-ecosystem similarities” of an innate propensity for structural self-organization throughout nature.

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. (169)

Rinaldo, Andrea, et al. Cross-Scale Ecological Dynamics and Microbial Size Spectra in Marine Ecosystems. Proceedings of the Royal Society of London B. 269/2051, 2002. More evidence of a universal self-similarity in nature.

Why should a continuous spectrum of organism size emerge from the ecological and evolutionary processes that have shaped ecosystems over evolutionary time?...Such features may have their dynamic origin in the self-organization of complex adaptive systems, possibly to self-organized critical phenomena, because they are robust in the face of environmental fluctuations. (2051) That such a complex web of interacting factors, acting locally and over evolutionary time, should result in such universal patterns begs explanation, and suggests a tendency of ecosystems to self-organize into states that lack a characteristic size – regardless of initial conditions and of transient disturbances. (2057)

Ritchie, Mark. Scale, Heterogeneity, and the Structure and Diversity of Ecological Communities. Princeton: Princeton University Press, 2009. The fluid, intricate, diversity of land, sea and aerial fauna and flora has been evident since their naturalist study began. A Syracuse University biologist here proposes that an integral theoretical synthesis, aided by a rush of recent advances, may at last be possible. As its unifying theme and motif, the ubiquitous presence of a nested self-similarity, properly understood and quantified, can now be affirmed. As a significant aspect, it is not only animal distributions from bacteria and beetles to tuna, ungulates, and eagles that are so fractal in kind, even the terrestrial or nautical environs they reside in expresses such geometries. So may one muse that circa 2010 a consistently repetitive, indeed untangled Nature is in fact revealed, which then manifests, we are invited to observe, an independent mathematical source as an open testament for us to avail and carry forward?

In this book, I propose a new framework for predicting the structure and diversity of ecological communities that might help synthesize previous theory and data. This framework emerges out of incorporating two critical elements of the inductive approaches, scale and heterogeneity, into the analytical mathematical formalism of the more deductive approaches. (2) The emphasis on scale and heterogeneity requires a tool that can simply describe the complex physical structure of nature: fractal geometry. Fractal geometry assumes that distributions of physical material and conditions and/or biological organisms in the environment are statistically similar across a range of meaningful spatial scales. (2)

Calculating mathematical properties of fractals is relatively straight-forward; the real question is how fractal is nature? More specifically, do organisms live in an environment where resources are distributed in a fractal-like manner? When the distributions of different habitats and resources have been measured, the answer is often yes. (25) If habitats have fractal distributions, then it would be logical to assume that the organisms that occupy those habitats might also have fractal distributions. For example, the prairie grass Bouteloua gracilis in New Mexico has a fractal distribution with an estimated dimension of 1.88. (27)

Rocha, Juan, et al. Cascading Regime Shifts Within and Across Scales. Science. 362/1379, 2018. Stockholm Resilience Centre ecological scholars including Simon Levin provide a latest finesse of complex ecosystems as they interact and transition within local and planetary bioregions and climates. The work merited a review Seeing a Global Web of Connected Systems by Marten Scheffer and Egbert van Nes (362/1357), second quote.

The potential for regime shifts and critical transitions in ecological and Earth systems, particularly in a changing climate, has received considerable attention. However, the possibility of interactions between such shifts is poorly understood. Rocha et al. used network analysis to explore whether critical transitions in ecosystems can be coupled with each other, even when far apart (see the Perspective by Scheffer and van Nes). They report different types of potential cascading effects, including domino effects and hidden feedbacks, that can be prevalent in different systems. Such cascading effects can couple the dynamics of regime shifts in distant places, which suggests that the interactions between transitions should be borne in mind in future forecasts. (Rocha summary)

The Arab Spring, the invention of penicillin, and the recent mass bleaching of coral reefs are reminders that much of the change in nature and society happens in just a tiny portion of time. Understanding why and when such critical transitions happen remains notoriously difficult. In this issue, Rocha et al mine a database of shifts in social and ecological systems and conclude that about half of them may be causally linked on different scales. Their results highlight the importance of unraveling hidden connections in the web of ecological and social systems on which we depend. (Scheffer abstract)

Rogers, Tanya, et al. Chaos is not Rare in Natural Ecosystems. Nature Ecology and Evolution. July, 2022. TR, National Marine Fisheries Service, along with Bethany Johnson and Stephan Munch, UC Santa Cruz provide a 2020s report that while Darwin’s bank remains tangled, our latest nonlinear sciences can reveal the present of an orderly basis. See also Yonatan, Yogev, et al. Complexity-Stability Trade-off in Empirical Microbial Ecosystems by Yogev Yonatan, et al in this same issue for a similar contribution..

Chaotic dynamics are thought to be rare in natural populations but this may be due to earlier empirical limitations, rather than an inherent stability of ecosystems. By way of extensive simulation testing, we applied multiple chaos detection methods to a global database and found chaotic behavior in some 30% of cases. Relative chaos was more prevalent among plankton and insects and least among birds and mammals. These results demonstrate that chaos does often occur in natural populations, and thus caution against steady-state approaches to conservation and management. (Excerpt)

Roy, Monojit, et al. Broad Scaling Region in a Spatial Ecological System. Complexity. 8/5, 2003. Scale-free patterns in dynamic ecosystems suggest they are poised near a critical state, which evidence then supports.

In summary, our individual-based spatial predator-prey model exhibits a set of scaling properties characteristic of systems near criticality. (25)

Ryan, Matthew, et al. The Use of Artificial Neural Networks (ANNs) to Simulate N2O Emissions from a Temperate Grassland Ecosystem. Ecological Modelling. 175/2, 2004. Along with many other areas such as gene regulation or social cohesion, a dynamic approach based on how the brain operates is of much utility for ecosystems studies.

Artificial neural networks are sophisticated pattern recognition systems that operate by mathematically mimicking the biological human learning process (i.e. learning by experience) where they can extract and learn the hidden relationships between system inputs and resulting outputs. (189) The grouping of the individual neurons, their configuration, the interconnection between the neurons, the weightings along these connections, and the learning algorithms employed is what makes up a functioning neural network. (190)

Saavedra, Serguei, et al. A Simple Model of Bipartite Cooperation for Ecological and Organizational Networks. Nature. 457/463, 2009. Since science now proceeds on the plane of a worldwide personal humankind, rather than by one man, real discoveries being made often pass unnoticed. A case in point might be a flurry of papers (Sugihara, Griffen, Wills, Palmer, May, Heng, Misteli) on a repetitive occurrence of the same dynamic patterns and processes across widely disparate natural and social realms. In this case, with Northwestern University’s Brian Uzzi as mentor, similar “metrics” are found in plant-animal pollination networks and manufacturer-contractor business.

Our study identifies striking similarities in the general structural characteristics of networks that are formed as a result of cooperative mechanisms operating in radically different contexts, linking partners in ecological and socio-economic systems, respectively. This empirical finding motivates the proposed simple model for bipartite cooperation, which captures the most important generic features of mutualistic interaction patterns starting from a minimal set of input parameters. At the level of partner–partner interactions, equivalent behaviour in different systems appears to be driven by similar types of interaction constraints. These correspond to complementarity in traits or characteristics, a hierarchical organization limiting the range of potential partners, and the environmental context. (465-466)

Santos, F. and J. Pacheco. Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation. Physical Review Letters. 95/098104, 2005. A paper cited in Tom Siegfried’s A Beautiful Math which theoretically affirms an innate favorable bias to cooperate rather than compete.

We study the evolution of cooperation in the framework of evolutionary game theory, adopting the prisoner’s dilemma and snowdrift game as metaphors of cooperation between unrelated individuals. In sharp contrast with previous results we find that, whenever individuals interact following networks of contacts generated via growth and preferential attachment, leading to strong correlations between individuals, cooperation becomes the dominating trait throughout the entire range of parameters of both games, as such providing a unifying framework for the emergence of cooperation. (098104-1)

Schneider, David. The Rise of the Concept of Scale in Ecology. BioScience. 51/7, 2001. Ecosystems are best characterized by a dynamic hierarchy due to a power-law self-organized criticality.

Schramski, John, et al. Metabolic Theory Predicts Whole-Ecosystem Properties. Proceedings of the National Academy of Sciences. 112/2617, 2015. An update on this large project hosted by James Brown of the University of New Mexico, a co-author. Into the mid 2010s, decades of field and laboratory study are paying off with a general, robust synthesis such as this.

Understanding the effects of individual organisms on material cycles and energy fluxes within ecosystems is central to predicting the impacts of human-caused changes on climate, land use, and biodiversity. Here we present a theory that integrates metabolic (organism-based bottom-up) and systems (ecosystem-based top-down) approaches to characterize how the metabolism of individuals affects the flows and stores of materials and energy in ecosystems. The theory provides a robust basis for estimating the flux and storage of energy, carbon, and other materials in terrestrial, marine, and freshwater ecosystems and for quantifying the roles of different kinds of organisms and environments at scales from local ecosystems to the biosphere. Abstract excerpts)

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