In evolutionary biology, attention to the relationship between stochastic organisms and their stochastic environments has leaned towards the adaptability and learning capabilities of the organisms rather than toward the properties of the environment. This article is devoted to the algorithmic aspects of the environment and its interaction with living organisms. We ask whether one may use the fact of the existence of life to establish how far nature is removed from algorithmic randomness. The paper uses a novel approach to behavioral evolutionary questions, using tools drawn from information theory, algorithmic complexity and the thermodynamics of computation to support an intuitive assumption about the near optimal structure of a physical environment that would prove conducive to the evolution and survival of organisms, and sketches the potential of these tools, at present alien to biology, that could be used in the future to address different and deeper questions. We contribute to the discussion of the algorithmic structure of natural environments and provide statistical and computational arguments for the intuitive claim that living systems would not be able to survive in completely unpredictable environments, even if adaptable and equipped with storage and learning capabilities by natural selection (brain memory or DNA).

Zenil, Hector; Gershenson, Carlos; Marshall, James A.R.; Rosenblueth, David A. 2012. "Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments." Entropy 14, no. 11: 2173-2191.

Algorithmic information theory (AIT) allows us to study the inherent structure of objects, and qualify some as ‘random’ without reference to a generating distribution. The theory origin...

In the volume, Chaitin proposes a new field of study he calls "metabiology," or the study of "the random evolution of artificial software (computer programs) instead of natural software (DNA)." He regards DNA as a computer ...

Last Friday, UWO hosted a Distinguished Colloquium talk by Gregory Chaitin, who was talking about a proposal for a new field he calls “metabiology”, which he defined in the talk (and on...

For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has even attempted to answer it until now.

In this illuminating and provocative book, Gregory Chaitin argues that we can’t be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.

Few people remember Turing's work on pattern formation in biology (morphogenesis), but Turing's famous 1936 paper On Computable Numbers exerted an immense influence on the birth of molecular biology indirectly, through the work of John von Neumann...

Evolution is one of the greatest problems in science, and a flourishing research endeavor. Over the past century, sophisticated mathematical tools and mathematical insights have been used in the pursuit of better understanding of the theory; in almost all cases they were of the sort usually employed in physics. Computational techniques and ideas have also been gloriously applied, albeit mostly for processing as in genomics and phylogeny.

The premise of this course is that computational/algorithmic thinking, and the kind of mathematics that underlies it, can be productively applied to some of the most important problems in Evolution. Corollary, it is important for computational/algorithmic thinkers to understand Evolution.

MOSES is a system for learning programs from input data. Given a table of input values, and a column of outputs, MOSES tries to learn a program, the simplest program that can reproduce the output given the input values. The programs that it learns are in the form of a “program tree” — a nested concatenation of operators, such as addition or multiplication, boolean AND’s or OR’s, if-statements, and the like, taking the inputs as arguments. To learn...

Evolution through mutation and selection in populations of asexually replicating entities is modeled by ordinary differential equations (ODEs) that are derived from chemical kinetics of replication. The solutions of the mutation-selection equation are obtained in terms of the eigenvectors of the value matrix W = Q.F with Q being the matrix of mutation frequencies and F the diagonal matrix of fitness values. The stationary mutant distribution of the population is given by the largest eigenvector of W called quasispecies Y. In absence of neutrality a single variant, the master sequence Xm, is present at highest concentration. The stationary frequency of mutants is determined by their Hamming distance from the master, by their fitness values, and by the fitness of their neighbors in sequence space...

While evolution has inspired algorithmic methods of heuristic optimisation, little has been done in the way of using concepts of computation to advance our understanding of salient aspects of biological phenomena. We argue that under reasonable assumptions, interesting conclusions can be drawn that are of relevance to behavioural evolution. We will focus on two important features of life--robustness and fitness--which, we will argue, are related to algorithmic probability and to the thermodynamics of computation, disciplines that may be capable of modelling key features of living organisms, and which can be used in formulating new algorithms of evolutionary computation.

Some Computational Aspects of Essential Properties of Evolution and Life

Computation and its Limits is an innovative cross-disciplinary investigation of the relationship between computing and physical reality. It begins by exploring the mystery of why mathematics is so effective in science and seeks to explain this in terms of the modelling of one part of physical reality by another. Going from the origins of counting to the most blue-skies proposals for novel methods of computation, the authors investigate the extent to which the laws of nature and of logic constrain what we can compute. In the process they examine formal computability, the thermodynamics of computation and the promise of quantum computing.

In this book Philip Grime and Simon Pierce explain how evidence from across the world is revealing that, beneath the wealth of apparently limitless and bewildering variation in detailed structure and functioning, the essential biology of all organisms is subject to the same set of basic interacting constraints on life-history and physiology. The inescapable resulting predicament during the evolution of every species is that, according to habitat, each must adopt a predictable compromise with regard to how they use the resources at their disposal in order to survive. The compromise involves the investment of resources in either the effort to acquire more resources, the tolerance of factors that reduce metabolic performance, or reproduction. This three-way trade-off is the irreducible core of the universal adaptive strategy theory which Grime and Pierce use to investigate how two environmental filters selecting, respectively, for convergence and divergence in organism function determine the identity of organisms in communities, and ultimately how different evolutionary strategies affect the functioning of ecosystems. This book reflects an historic phase in which evolutionary processes are finally moving centre stage in the effort to unify ecological theory, and animal, plant and microbial ecology have begun to find a common theoretical framework.

Metabiology… a mathematics of evolution? Biology is creative. Look around at the natural world and you will find the ingenious solutions that life has adopted to fill every imaginable niche. While... (Metabiology… a mathematics of evolution?