The Emergence of Environmental Homeostasis in Complex Ecosystems

The Earth, with its core-driven magnetic field, convective mantle, mobile lid tectonics, oceans of liquid water, dynamic climate and abundant life is arguably the most complex system in the known universe. This system has exhibited stability in the sense of, bar a number of notable exceptions, surface temperature remaining within the bounds required for liquid water and so a significant biosphere. Explanations for this range from anthropic principles in which the Earth was essentially lucky, to homeostatic Gaia in which the abiotic and biotic components of the Earth system self-organise into homeostatic states that are robust to a wide range of external perturbations. Here we present results from a conceptual model that demonstrates the emergence of homeostasis as a consequence of the feedback loop operating between life and its environment. Formulating the model in terms of Gaussian processes allows the development of novel computational methods in order to provide solutions. We find that the stability of this system will typically increase then remain constant with an increase in biological diversity and that the number of attractors within the phase space exponentially increases with the number of environmental variables while the probability of the system being in an attractor that lies within prescribed boundaries decreases approximately linearly. We argue that the cybernetic concept of rein control provides insights into how this model system, and potentially any system that is comprised of biological to environmental feedback loops, self-organises into homeostatic states.Author Summary: Life on Earth is perhaps greater than three and a half billion years old and it would appear that once it started it never stopped. During this period a number of dramatic shocks and drivers have affected the Earth. These include the impacts of massive asteroids, runaway climate change and increases in brightness of the Sun. Has life on Earth simply been lucky in withstanding such perturbations? Are there any self-regulating or homeostatic processes operating in the Earth system that would reduce the severity of such perturbations? If such planetary processes exist, to what extent are they the result of the actions of life? In this study, we show how the regulation of environmental conditions can emerge as a consequence of life's effects. If life is both affected by and affects it environment, then this coupled system can self-organise into a robust control system that was first described during the early cybernetics movement around the middle of the twentieth century. Our findings are in principle applicable to a wide range of real world systems - from microbial mats to aquatic ecosystems up to and including the entire biosphere.