V. Life's Corporeal Evolution Develops, Encodes and Organizes Itself: An Earthtwinian Genesis Synthesis

6. Dynamic Fractal Network Ecosystems

Pigolotti, Simone, et al. Stochastic Spatial Models in Ecology. Journal of Statistical Physics. 172/1, 2018. SP, Okinawa Institute of Science, Massimo Cencini and Consiglio Nazionale delle Ricerch, Rome, Daniel Molina, Basque Center for Applied Mathematics, and Miguel Munoz, University of Granada, Spain provide a good example of later 2010s (re)unifications across this widest span from lively physical substrates to active flora and fauna environments.

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. In this review, we emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories. (Abstract excerpt)

Pimm, Stuart. The Balance of Nature? Chicago: University of Chicago Press, 1991. A leading ecologist presciently recognizes the potential for nonlinear principles to explain complex landscapes which actually do not seek an equilibrium as long thought but are dynamically self-organized.

Pinto-Ramos, D., et al.. Pinto-Ramos, D., et al. Vegetation clustering and self-organization in inhomogeneous environments. .. arXiv:2406.12581.. An international theorist team posted in Germany, Chile, Morocco and Belgium provide further quantifications as to how many manner of flora tend to array themselves so as to cope with ever changing environs.

Due to climatic changes, excessive grazing, and deforestation, arid ecosystems are vulnerable to desertification and land degradation. The vegetation cover loses spatial homogeneity as aridity increases, and the self-organized patterns collapse into a bare state. This transition could be gradual or abrupt, leading to a catastrophic shift of ecosystems. By way of a mathematical model which includes environmental inhomogeneities, we show how vegetation patterns create a hysteresis loop which corresponds to qualitative self-organized clustering responses. These behaviors can then be connected to historically significant trends of climate change in arid ecosystems.

Ranta, Esa, et al. Ecology of Populations. Cambridge, UK: Cambridge University Press, 2006. From Scandinavia, a technical study in part on the scale independent spatial and temporal self-organization of ecosystems.

Recknagel, Freidrich, ed. Ecological Informatics. Berlin: Springer, 2003. Bioinformatics is the application of computer analysis to biological phenomena such as genetic and protein networks. This book reviews a similar employ of artificial neural networks, adaptive agents, evolutionary algorithms, and so on to characterize and understand intricate, nested ecosystems. An earlier version of the subject appeared in Ecological Modelling. 146/1-2, 2001.

Ecological Informatics is defined as interdisciplinary framework promoting the use of advanced computational technology for the elucidation of principles of information processing at and between all levels of complexity of ecosystems – from genes to ecological networks… (iii)

Reuter, Hauke. The Concepts of Emergent and Collective Properties in Individual-Based Models. Ecological Modelling. 186/4, 2005. A summary paper from a special issue on flora and fauna as the epitome of dynamic, scalar, complex systems due to many relational individuals or agents. See also Reuter in Organic Societies above.

In the second half of the 20th century a crucial paradigm shift in biological theory included the perception of ecological systems as being self-organized. (491) The important thing about life is that the local dynamics of a set of interacting entities (e.g. molecules, cells, etc.) support an emergent set of global dynamical structures which stabilize themselves by setting the boundary conditions within which the local dynamics operate. (492)

Reynolds, A. M. On the Intermittent Behaviour of Foraging Animals. Europhysics Letters. 75/4, 2006. Another insight into a creative mathematical order which suffuses the natural realm. Of course, Galilei Galileo knew this long ago. See also in the same journal issue, (S. Picoli, et al) how a similar scaling pervades human complex systems.

This suggests that the scale-free and intermittent characteristics of forager movement patterns can be understood within the context of a single unified scale-free model. (520)

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)

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