Developmental structuring of phenotypic variation: A case study with a cellular automata model of ontogeny.

Developmental mechanisms not only produce an organismal phenotype, but they also structure the way genetic variation maps to phenotypic variation. Here, we revisit a computational model for the evolution of ontogeny based on cellular automata, in which evolution regularly discovered two alternative mechanisms for achieving a selected phenotype, one showing high modularity, the other showing morphological integration. We measure a primary variational property of the systems, their distribution of fitness effects of mutation. We find that the modular ontogeny shows the evolution of mutational robustness and ontogenic simplification, while the integrated ontogeny does not. We discuss the wider use of this methodology on other computational models of development as well as real organisms.

Autocatalytic chemical networks at the origin of metabolism.

Modern cells embody metabolic networks containing thousands of elements and form autocatalytic sets of molecules that produce copies of themselves. How the first self-sustaining metabolic networks arose at life's origin is a major open question. Autocatalytic sets smaller than metabolic networks were proposed as transitory intermediates at the origin of life, but evidence for their role in prebiotic evolution is lacking. Here, we identify reflexively autocatalytic food-generated networks (RAFs)-self-sustaining networks that collectively catalyse all their reactions-embedded within microbial metabolism. RAFs in the metabolism of ancient anaerobic autotrophs that live from H2 and CO2 provided with small-molecule catalysts generate acetyl-CoA as well as amino acids and bases, the monomeric components of protein and RNA, but amino acids and bases without organic catalysts do not generate metabolic RAFs. This suggests that RAFs identify attributes of biochemical origins conserved in metabolic networks. RAFs are consistent with an autotrophic origin of metabolism and furthermore indicate that autocatalytic chemical networks preceded proteins and RNA in evolution. RAFs uncover intermediate stages in the emergence of metabolic networks, narrowing the gaps between early Earth chemistry and life.

Dynamics of a birth-death process based on combinatorial innovation.

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth-death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters (P, α). This process exhibits a characteristic 'hockey-stick' behaviour: a long period of relatively little growth followed by a relatively sudden 'explosive' increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity.

The Influence of Modularity, Seeding, and Product Inhibition on Peptide Autocatalytic Network Dynamics.

Chemical networks often exhibit emergent, systems-level properties that cannot be simply derived from the linear sum of the individual components. The design and analysis of increasingly complex chemical networks thus constitute a major area of research in Systems Chemistry. In particular, much research is focused on the emergence of functional properties in prebiotic chemical networks relevant to the origin and early evolution of life. Here, we apply a formal framework known as RAF theory to study the dynamics of a complex network of mutually catalytic peptides. We investigate in detail the influence of network modularity, initial template seeding, and product inhibition on the network dynamics. We show that these results can be useful for designing new experiments, and further argue how they are relevant to origin of life studies.

Niche emergence as an autocatalytic process in the evolution of ecosystems.

The utilisation of the ecospace and the change in diversity through time has been suggested to be due to the effect of niche partitioning, as a global long-term pattern in the fossil record. However, niche partitioning, as a way to coexist, could be a limited means to share the environmental resources and condition during evolutionary time. In fact, a physical limit impedes a high partitioning without a high restriction of the niche's variables. Here, we propose that niche emergence, rather than niche partitioning, is what mostly drives ecological diversity. In particular, we view ecosystems in terms of autocatalytic sets: catalytically closed and self-sustaining reaction (or interaction) networks. We provide some examples of such ecological autocatalytic networks, how this can give rise to an expanding process of niche emergence (both in time and space), and how these networks have evolved over time (so-called evoRAFs). Furthermore, we use the autocatalytic set formalism to show that it can be expected to observe a power-law in the size distribution of extinction events in ecosystems. In short, we elaborate on our earlier argument that new species create new niches, and that biodiversity is therefore an autocatalytic process.

Autocatalytic Sets and RNA Secondary Structure.

The dominant paradigm in origin of life research is that of an RNA world. However, despite experimental progress towards the spontaneous formation of RNA, the RNA world hypothesis still has its problems. Here, we introduce a novel computational model of chemical reaction networks based on RNA secondary structure and analyze the existence of autocatalytic sub-networks in random instances of this model, by combining two well-established computational tools. Our main results are that (i) autocatalytic sets are highly likely to exist, even for very small reaction networks and short RNA sequences, and (ii) sequence diversity seems to be a more important factor in the formation of autocatalytic sets than sequence length. These findings could shed new light on the probability of the spontaneous emergence of an RNA world as a network of mutually collaborative ribozymes.

Autocatalytic confusion clarified.

There is frequent confusion about the terms autocatalytic reaction, autocatalytic cycle, and autocatalytic set. As the use of the same adjective implies, these three systems do indeed share common properties, in particular their potential for exponential growth. However, the ways in which they achieve this potential are different, giving rise to different internal network structures and dynamics. Therefore, care should be taken which term is used in which context. Here, we explain and discuss the similarities and differences between the three systems in detail, in an effort to avoid any further confusion. We then also discuss the relevance of these autocatalytic systems for possible origin of life scenarios, with an emphasis on how autocatalytic sets may have played an important role in this.

Evolution of Autocatalytic Sets in Computational Models of Chemical Reaction Networks.

Several computational models of chemical reaction networks have been presented in the literature in the past, showing the appearance and (potential) evolution of autocatalytic sets. However, the notion of autocatalytic sets has been defined differently in different modeling contexts, each one having some shortcoming or limitation. Here, we review four such models and definitions, and then formally describe and analyze them in the context of a mathematical framework for studying autocatalytic sets known as RAF theory. The main results are that: (1) RAF theory can capture the various previous definitions of autocatalytic sets and is therefore more complete and general, (2) the formal framework can be used to efficiently detect and analyze autocatalytic sets in all of these different computational models, (3) autocatalytic (RAF) sets are indeed likely to appear and evolve in such models, and (4) this could have important implications for a possible metabolism-first scenario for the origin of life.

Autocatalytic sets and biological specificity.

A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from within that system. RAF (reflexively autocatalytic and food-generated) theory provides a formal way to study such processes. Beginning with Kauffman's notion of "collectively autocatalytic sets," this theory has been further developed over the last decade with the discovery of efficient algorithms and new mathematical analysis. In this paper, we study how the behaviour of a simple binary polymer model can be extended to models where the pattern of catalysis more precisely reflects the ligation and cleavage reactions involved. We find that certain properties of these models are similar to, and can be accurately predicted from, the simple binary polymer model; however, other properties lead to slightly different estimates. We also establish a number of new results concerning the structure of RAFs in these systems.

Conditions for evolvability of autocatalytic sets: a formal example and analysis.

We provide a formal but visually clear example of how a set of minimal necessary conditions for evolvability of autocatalytic sets is satisfied in a simple model of chemical reaction systems. Furthermore, we show how these conditions can be captured and analyzed with RAF theory, and how the results can be generalized with a somewhat more elaborate example. Finally, we argue that our results clearly support the hypothesis that autocatalytic sets can be evolvable, and that this might even be an expected property of such sets.

Minimal autocatalytic networks.

Self-sustaining autocatalytic chemical networks represent a necessary, though not sufficient condition for the emergence of early living systems. These networks have been formalised and investigated within the framework of RAF theory, which has led to a number of insights and results concerning the likelihood of such networks forming. In this paper, we extend this analysis by focussing on how small autocatalytic networks are likely to be when they first emerge. First we show that simulations are unlikely to settle this question, by establishing that the problem of finding a smallest RAF within a catalytic reaction system is NP-hard. However, irreducible RAFs (irrRAFs) can be constructed in polynomial time, and we show it is possible to determine in polynomial time whether a bounded size set of these irrRAFs contain the smallest RAFs within a system. Moreover, we derive rigorous bounds on the sizes of small RAFs and use simulations to sample irrRAFs under the binary polymer model. We then apply mathematical arguments to prove a new result suggested by those simulations: at the transition catalysis level at which RAFs first form in this model, small RAFs are unlikely to be present. We also investigate further the relationship between RAFs and another formal approach to self-sustaining and closed chemical networks, namely chemical organisation theory (COT).

Predicting present and future intra-specific genetic structure through niche hindcasting across 24 millennia.

Paleoclimatic reconstructions coupled with species distribution models and identification of extant spatial genetic structure have the potential to provide insights into the demographic events that shape the distribution of intra-specific genetic variation across time. Using the globeflower Trollius europaeus as a case-study, we combined (1) Amplified Fragment Length Polymorphisms, (2) suites of 1000-years stepwise hindcasted species distributions and (3) a model of diffusion through time over the last 24,000 years, to trace the spatial dynamics that most likely fits the species' current genetic structure. We show that the globeflower comprises four gene pools in Europe which, from the dry period preceding the Last Glacial Maximum, dispersed while tracking the conditions fitting its climatic niche. Among these four gene pools, two are predicted to experience drastic range retraction in the near future. Our interdisciplinary approach, applicable to virtually any taxon, is an advance in inferring how climate change impacts species' genetic structures.

Dispersal routes reconstruction and the minimum cost arborescence problem.

We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.

Predicting template-based catalysis rates in a simple catalytic reaction model.

We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical concordance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular, we derive an analytical calculation that allows us to accurately predict the (observed) required level of catalysis in one version of the model from that in the other version, for a given probability of having self-sustaining autocatalytic sets exist in instances of both model versions. This provides a tractable connection between two models that have been investigated in theoretical origin-of-life studies.

The structure of autocatalytic sets: evolvability, enablement, and emergence.

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even economies.

Autocatalytic Sets Arising in a Combinatorial Model of Chemical Evolution.

The idea that chemical evolution led to the origin of life is not new, but still leaves open the question of how exactly it could have led to a coherent and self-reproducing collective of molecules. One possible answer to this question was proposed in the form of the emergence of an autocatalytic set: a collection of molecules that mutually catalyze each other's formation and that is self-sustaining given some basic "food" source. Building on previous work, here we investigate in more detail when and how autocatalytic sets can arise in a simple model of chemical evolution based on the idea of combinatorial innovation with random catalysis assignments. We derive theoretical results, and compare them with computer simulations. These results could suggest a possible step towards the (or an) origin of life.

New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0.

PhyML is a phylogeny software based on the maximum-likelihood principle. Early PhyML versions used a fast algorithm performing nearest neighbor interchanges to improve a reasonable starting tree topology. Since the original publication (Guindon S., Gascuel O. 2003. A simple, fast and accurate algorithm to estimate large phylogenies by maximum likelihood. Syst. Biol. 52:696-704), PhyML has been widely used (>2500 citations in ISI Web of Science) because of its simplicity and a fair compromise between accuracy and speed. In the meantime, research around PhyML has continued, and this article describes the new algorithms and methods implemented in the program. First, we introduce a new algorithm to search the tree space with user-defined intensity using subtree pruning and regrafting topological moves. The parsimony criterion is used here to filter out the least promising topology modifications with respect to the likelihood function. The analysis of a large collection of real nucleotide and amino acid data sets of various sizes demonstrates the good performance of this method. Second, we describe a new test to assess the support of the data for internal branches of a phylogeny. This approach extends the recently proposed approximate likelihood-ratio test and relies on a nonparametric, Shimodaira-Hasegawa-like procedure. A detailed analysis of real alignments sheds light on the links between this new approach and the more classical nonparametric bootstrap method. Overall, our tests show that the last version (3.0) of PhyML is fast, accurate, stable, and ready to use. A Web server and binary files are available from http://www.atgc-montpellier.fr/phyml/.

Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems.

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form "by chance" within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching.

Average Fitness Differences on NK Landscapes.

The average fitness difference between adjacent sites in a fitness landscape is an important descriptor that impacts in particular the dynamics of selection/mutation processes on the landscape. Of particular interest is its connection to the error threshold phenomenon. We show here that this parameter is intimately tied to the ruggedness through the landscape's amplitude spectrum. For the NK model, a surprisingly simple analytical estimate explains simulation data with high precision.