How complex systems theory sheds new light on the adaptive dynamics of viral populations Viruses are everywhere, infecting all sorts of living organisms, from the tiniest bacteria to the largest mammals. Many are harmful parasites, but viruses also play a major role as drivers of our evolution as a species and are essential regulators of the composition and complexity of ecosystems on a global scale. This concise book draws on complex systems theory to provide a fresh look at viral origins, populations, and evolution, and the coevolutionary dynamics of viruses and their hosts. New viruses continue to emerge that threaten people, crops, and farm animals. Viruses constantly evade our immune systems, and antiviral therapies and vaccination campaigns can be powerless against them. These unique characteristics of virus biology are a consequence of their tremendous evolutionary potential, which enables viruses to quickly adapt to any environmental challenge. Ricard Sole and Santiago Elena present a unified framework for understanding viruses as complex adaptive systems. They show how the application of complex systems theory to viral dynamics has provided new insights into the development of AIDS in patients infected with HIV-1, the emergence of new antigenic variants of the influenza A virus, and other cutting-edge advances. Essential reading for biologists, physicists, and mathematicians interested in complexity, Viruses as Complex Adaptive Systems also extends the analogy of viruses to the evolution of other replicators such as computer viruses, cancer, and languages.

Can physics be an appropriate framework for the understanding of ecological science? Most ecologists would probably agree that there is little relation between the complexity of natural ecosystems and the simplicity of any example derived from Newtonian physics. Though ecologists have long been interested in concepts originally developed by statistical physicists and later applied to explain everything from why stock markets crash to why rivers develop particular branching patterns, applying such concepts to ecosystems has remained a challenge.

"Self-Organization in Complex Ecosystems" is the first book to clearly synthesize what we have learned about the usefulness of tools from statistical physics in ecology. Ricard Sole and Jordi Bascompte provide a comprehensive introduction to complex systems theory, and ask: do universal laws shape the structure of ecosystems, at least at some scales? They offer the most compelling array of theoretical evidence to date of the potential of nonlinear ecological interactions to generate nonrandom, self-organized patterns at all levels.

Tackling classic ecological questions--from population dynamics to biodiversity to macroevolution--the book's novel presentation of theories and data shows the power of statistical physics and complexity in ecology. "Self-Organization in Complex Ecosystems" will be a staple resource for years to come for ecologists interested in complex systems theory as well as mathematicians and physicists interested in ecology."

Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, "Phase Transitions" examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur.

Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Sole shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies.

Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems."

In 'Signs of Life', the authors apply the mathematical tools of complexity theory to model biological processes in terms of complex dynamics from which characteristic patterns of order emerge. They examine genetic networks - such as chaos in brain function and the emergent phenomenon of ant colonies - in order to explain this phenomena.