Sufficient conditions for emergent synchronization in protocell models

In this paper, we study general protocell models aiming to understand the synchronization phenomenon of genetic material and container productions, a necessary condition to ensure sustainable growth in protocells and eventually leading to Darwinian evolution when applied to a population of protocells.Synchronization has been proved to be an emergent property in many relevant protocell models in the class of the so-called surface reaction models, assuming both linear- and non-linear dynamics for the involved chemical reactions. We here extend this analysis by introducing and studying a new class of models where the relevant chemical reactions are assumed to occur inside the protocell, in contrast with the former model where the reaction site was the external surface.While in our previous studies, the replicators were assumed to compete for resources, without any direct interaction among them, we here improve both models by allowing linear interaction between replicators: catalysis and/or inhibition. Extending some techniques previously introduced, we are able to give a quite general analytical answer about the synchronization phenomenon in this more general context. We also report on results of numerical simulations to support the theory, where applicable, and allow the investigation of cases which are not amenable to analytical calculations.     

From survivors to replicators: evolution by natural selection revisited

For evolution by natural selection to occur it is classically admitted that the three ingredients of variation, difference in fitness and heredity are necessary and sufficient. In this paper, I show using simple individual-based models, that evolution by natural selection can occur in populations of entities in which neither heredity nor reproduction are present. Furthermore, I demonstrate by complexifying these models that both reproduction and heredity are predictable Darwinian products (i.e. complex adaptations) of populations initially lacking these two properties but in which new variation is introduced via mutations. Later on, I show that replicators are not necessary for evolution by natural selection, but rather the ultimate product of such processes of adaptation. Finally, I assess the value of these models in three relevant domains for Darwinian evolution.     

Selfishness versus functional cooperation in a stochastic protocell model

How to design an “evolvable” artificial system capable to increase in complexity? Although Darwin’s theory of evolution by natural selection obviously offers a firm foundation, little hope of success seems to be expected from the explanatory adequacy of modern evolutionary theory, which does a good job at explaining what has already happened but remains practically helpless at predicting what will occur. However, the study of the major transitions in evolution clearly suggests that increases in complexity have occurred on those occasions when the conflicting interests between competing individuals were partly subjugated. This immediately raises the issue about “levels of selection” in evolutionary biology, and the idea that multi-level selection scenarios are required for complexity to emerge. After analyzing the dynamical behaviour of competing replicators within compartments, we show here that a proliferation of differentiated catalysts and/or improvement of catalytic efficiency of ribozymes can potentially evolve in properly designed artificial cells where the strong internal competition between the different species of replicators is somewhat prevented (i.e., by choosing them with equal probability). Experimental evolution in these systems will likely stand as beautiful examples of artificial adaptive systems, and will provide new insights to understand possible evolutionary paths to the evolution of metabolic complexity.     

Selection without replicators: the origin of genes, and the replicator/interactor distinction in etiobiology

Genes are thought to have evolved from long-lived and multiply-interactive molecules in the early stages of the origins of life. However, at that stage there were no replicators, and the distinction between interactors and replicators did not yet apply. Nevertheless, the process of evolution that proceeded from initial autocatalytic hypercycles to full organisms was a Darwinian process of selection of favourable variants. We distinguish therefore between Neo-Darwinian evolution and the related Weismannian and Central Dogma divisions, on the one hand, and the more generic category of Darwinian evolution on the other. We argue that Hull’s and Dawkins’ replicator/interactor distinction of entities is a sufficient, but not necessary, condition for Darwinian evolution to take place. We conceive the origin of genes as a separation between different types of molecules in a thermodynamic state space, and employ a notion of reproducers.     

Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization

Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities.     

The evolution of trade‐offs: where are we?

Trade-offs are a core component of many evolutionary models, particularly those dealing with the evolution of life histories. In the present paper, we identify four topics of key importance for studies of the evolutionary biology of trade-offs. First, we consider the underlying concept of 'constraint'. We conclude that this term is typically used too vaguely and suggest that 'constraint' in the sense of a bias should be clearly distinguished from 'constraint' in the sense of proscribed combinations of traits or evolutionary trajectories. Secondly, we address the utility of the acquisition-allocation model (the 'Y-model'). We find that, whereas this model and its derivatives have provided new insights, a misunderstanding of the pivotal equation has led to incorrect predictions and faulty tests. Thirdly, we ask how trade-offs are expected to evolve under directional selection. A quantitative genetic model predicts that, under weak or short-term selection, the intercept will change but the slope will remain constant. Two empirical tests support this prediction but these are based on comparisons of geographic populations: more direct tests will come from artificial selection experiments. Finally, we discuss what maintains variation in trade-offs noting that at present little attention has been given to this question. We distinguish between phenotypic and genetic variation and suggest that the latter is most in need of explanation. We suggest that four factors deserving investigation are mutation-selection balance, antagonistic pleiotropy, correlational selection and spatio-temporal variation, but as in the other areas of research on trade-offs, empirical generalizations are impeded by lack of data. Although this lack is discouraging, we suggest that it provides a rich ground for further study and the integration of many disciplines, including the emerging field of genomics.     

The origin of replicators and reproducers

Replicators are fundamental to the origin of life and evolvability. Their survival depends on the accuracy of replication and the efficiency of growth relative to spontaneous decay. Infrabiological systems are built of two coupled autocatalytic systems, in contrast to minimal living systems that must comprise at least a metabolic subsystem, a hereditary subsystem and a boundary, serving respective functions. Some scenarios prefer to unite all these functions into one primordial system, as illustrated in the lipid world scenario, which is considered as a didactic example in detail. Experimentally produced chemical replicators grow parabolically owing to product inhibition. A selection consequence is survival of everybody. The chromatographized replicator model predicts that such replicators spreading on surfaces can be selected for higher replication rate because double strands are washed away slower than single strands from the surface. Analysis of real ribozymes suggests that the error threshold of replication is less severe by about one order of magnitude than thought previously. Surface-bound dynamics is predicted to play a crucial role also for exponential replicators: unlinked genes belonging to the same genome do not displace each other by competition, and efficient and accurate replicases can spread. The most efficient form of such useful population structure is encapsulation by reproducing vesicles. The stochastic corrector model shows how such a bag of genes can survive, and what the role of chromosome formation and intragenic recombination could be. Prebiotic and early evolution cannot be understood without the models of dynamics.     

TOWARDS A GENERAL THEORY OF GROUP SELECTION

The longstanding debate about the importance of group (multilevel) selection suffers from a lack of formal models that describe explicit selection events at multiple levels. Here, we describe a general class of models for two‐level evolutionary processes which include birth and death events at both levels. The models incorporate the state‐dependent rates at which these events occur. The models come in two closely related forms: (1) a continuous‐time Markov chain, and (2) a partial differential equation (PDE) derived from (1) by taking a limit. We argue that the mathematical structure of this PDE is the same for all models of two‐level population processes, regardless of the kinds of events featured in the model. The mathematical structure of the PDE allows for a simple and unambiguous way to distinguish between individual‐ and group‐level events in any two‐level population model. This distinction, in turn, suggests a new and intuitively appealing way to define group selection in terms of the effects of group‐level events. We illustrate our theory of group selection by applying it to models of the evolution of cooperation and the evolution of simple multicellular organisms, and then demonstrate that this kind of group selection is not mathematically equivalent to individual‐level (kin) selection.     

Evolution of mutational robustness

We review recent advances in the understanding of the mutation-selection balance of asexual replicators. For over 30 years, population geneticists thought that an expression derived by Kimura and Maruyama in 1966 fully solved this problem. However, Kimura and Maruyama's result is only correct in the absence of neutral mutations. The inclusion of neutral mutations leads to a wealth of interesting new effects, and, in particular, to a selective pressure to evolve robustness against mutations. We cover recent literature on the population dynamics of asexual replicators on networks of neutral genotypes, on the outcompetition of fast replicators by slower ones with better mutational support, and on the probability of fixation at high mutation rates. We discuss empirical evidence for the evolution of mutational robustness, and speculate on its relevance for higher organisms.     

Stochasticity generates an evolutionary instability for infectious disease

Traditional models of disease evolution are based upon the deterministic competition between strains that confer complete cross-immunity, and predict the selection of strains with higher basic reproductive ratios ( R ₀). In contrast, evolution in a stochastic setting is determined by a complex mixture of influences. Here, to isolate the impact of stochasticity, we constrain all competing strains to have an equal basic reproductive ratio – thereby eliminating deterministic selection. The resulting stochastic models predict an evolutionary unstable strategy, which separates a region favouring the evolution of rapid-transmission (acute) strains from one favouring persistent (chronic) strains. We find this to be a generic phenomenon with strain evolution consistently driven towards extremes of epidemiological behaviour. Even in the absence of an equal R ₀ constraint, such stochastic selective pressures operate in addition to standard deterministic selection and will therefore influence the evolutionary behaviour of disease in all scenarios.     

On the origin of DNA genomes: evolution of the division of labor between template and catalyst in model replicator systems

The division of labor between template and catalyst is a fundamental property of all living systems: DNA stores genetic information whereas proteins function as catalysts. The RNA world hypothesis, however, posits that, at the earlier stages of evolution, RNA acted as both template and catalyst. Why would such division of labor evolve in the RNA world? We investigated the evolution of DNA-like molecules, i.e. molecules that can function only as template, in minimal computational models of RNA replicator systems. In the models, RNA can function as both template-directed polymerase and template, whereas DNA can function only as template. Two classes of models were explored. In the surface models, replicators are attached to surfaces with finite diffusion. In the compartment models, replicators are compartmentalized by vesicle-like boundaries. Both models displayed the evolution of DNA and the ensuing division of labor between templates and catalysts. In the surface model, DNA provides the advantage of greater resistance against parasitic templates. However, this advantage is at least partially offset by the disadvantage of slower multiplication due to the increased complexity of the replication cycle. In the compartment model, DNA can significantly delay the intra-compartment evolution of RNA towards catalytic deterioration. These results are explained in terms of the trade-off between template and catalyst that is inherent in RNA-only replication cycles: DNA releases RNA from this trade-off by making it unnecessary for RNA to serve as template and so rendering the system more resistant against evolving parasitism. Our analysis of these simple models suggests that the lack of catalytic activity in DNA by itself can generate a sufficient selective advantage for RNA replicator systems to produce DNA. Given the widespread notion that DNA evolved owing to its superior chemical properties as a template, this study offers a novel insight into the evolutionary origin of DNA.     

Evolution without speciation but with selection: LUCA, the Last Universal Common Ancestor in Gilbert's RNA world

This is not an attempt to analyze the Last Universal Common Ancestor (LUCA) to understand the origin of living systems. We do not know what came before Gilberts' RNA world. Our analysis starts with the RNA world and with genes (biological replicators alla Dawkings) made up of RNA proteins with enzymatic catalytic functions within units that are not yet modern cells. We offer a scenario where cellular entities are very simple and without individuality; they are only simple primary units of selection (the first level of selection) in which replicators compete in the most Darwinian manner, totally deprived of cooperation and interactions among genes. The information processing system of this RNA world is inaccurate and inefficient when compared to that found in organisms that came later. Among the "genes" and the entities that harbor them, high mutation rate was the most prevalent source of variability and the only inheritance was through lateral gene transfer of mobile elements. There were no chromosomes or any other genomic organization. As millions of years accumulated, complex and organized biological structures and processes evolved thanks to the variability mustered up mostly by lateral gene transfers and mutations. With micro- and mini-satellites, lateral gene transfers became indispensable devices of selection to mold variability. Competition and Darwinian selection gave way to a new transition in evolution, one I consider ineluctable, in which cooperation among interactive genes prevailed for the sake of higher fitness. Compartmentalization constituted a major transition in evolution that spurted new types of genome organization. Minichromosomes is one of these; cellular membranes and cytoplasmic structures completed the picture of the primitive cell. However, the much talked about phylogenetic tree does not exit in that ancient LUCA. The tree has no organism at its base; only clusters of genes evoke a fragile beginning for the increasingly complex cell types that were to emerge later.     

Why is the polymerase chain reaction resistant to in vitro evolution?

A variety of methods have been developed to amplify DNA and RNA. These methods vary in their susceptibility to evolve new molecular species differing from the starting template. PCR is exceptionally resistant to in vitro evolution, whereas methods such as Q replicase and 3SR are much less robust. This paper develops some simple mathematical models which suggest that PCR is resistant to in vitro evolution because the reaction controls replication in discrete cycles: fast replication is of little advantage during PCR because the reaction limits fast replicators as well as slow ones to a single copy per cycle. In contrast, continuous (isothermal) reactions, as in the Q replicase reaction, favor fast replicators. The advantage of fast replication is compounded in continuous reactions, because a fast replicator can complete many generations of replication during the time it takes a slow replicator to complete one generation. These models suggest that continuous amplication protocols will never achieve the robustness against in vitro evolution observed with PCR.Correspondence to: J.J. Bull     

Spatial Dynamics and the Evolution of Enzyme Production

We re-examine the problem of the evolution of protein synthesis or enzyme production using a stochastic cellular automaton model, where the replicators are fixed in the sites of a two-dimensional square lattice. In contrast with the classical chemical kinetics or mean-field predictions, we show that a small colony of mutant, protein-mediated (enzymatic) replicators has an appreciable probability to take over a resident population of simpler, direct-template replicators. In addition, we argue that the threshold phenomenon corresponding to the onset of invasion can be described quantitatively within the physics framework of nonequilibrium phase transitions. We study also the invasion of a resident population of enzymatic replicators by more efficient replicators of the same kind, and show that although slightly more efficient mutants cannot invade, invasion is a likely event if the productivity advantage of the mutants is large. In this sense, the establishment of a population of enzymatic replicators is not a `once-forever' evolutionary decision.     

Prelife catalysts and replicators

Life is based on replication and evolution. But replication cannot be taken for granted. We must ask what there was prior to replication and evolution. How does evolution begin? We have proposed prelife as a generative system that produces information and diversity in the absence of replication. We model prelife as a binary soup of active monomers that form random polymers. ‘Prevolutionary’ dynamics can have mutation and selection prior to replication. Some sequences might have catalytic activity, thereby enhancing the rates of certain prelife reactions. We study the selection criteria for these prelife catalysts. Their catalytic efficiency must be above certain critical values. We find a maintenance threshold and an initiation threshold. The former is a linear function of sequence length, and the latter is an exponential function of sequence length. Therefore, it is extremely hard to select for prelife catalysts that have long sequences. We compare prelife catalysis with a simple model for replication. Assuming fast template-based elongation reactions, we can show that replicators have selection thresholds that are independent of their sequence length. Our calculation demonstrates the efficiency of replication and provides an explanation of why replication was selected over other forms of prelife catalysis.     

Bifurcations and phase transitions in spatially extended two-member hypercycles

Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analysed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.     

The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems

In the RNA world hypothesis, RNA(-like) self-replicators are suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in such replicators, i.e., the problem of parasites. Parasites, which are replicated by catalytic replicators (catalysts), but do not replicate the others, can destroy a whole replicator system by exploitation. Recently, a theoretical study underlined complex formation between replicators--an often neglected but realistic process--as a stabilizing factor in a replicator system by demonstrating that complex formation can shift the viable range of diffusion intensity to higher values. In the current study, we extend the previous study of complex formation. Firstly, by investigating a well-mixed replicator system, we establish that complex formation gives parasites an implicit advantage over catalysts, which makes the system significantly more vulnerable to parasites. Secondly, by investigating a spatially extended replicator system, we show that the formation of traveling wave patterns plays a crucial role in the stability of the system against parasites, and that because of this the effect of complex formation is not straightforward; i.e., whether complex formation stabilizes or destabilizes the spatial system is a complex function of other parameters. We give a detailed analysis of the spatial system by considering the pattern dynamics of waves. Furthermore, we investigate the effect of deleterious mutations. Surprisingly, high mutation rates can weaken the exploitation of the catalyst by the parasite.     

The extended replicator

This paper evaluates and criticises the developmental systems conception of evolution and develops instead an extension of the gene's eye conception of evolution. We argue (i) Dawkin's attempt to segregate developmental and evolutionary issues about genes is unsatisfactory. On plausible views of development it is arbitrary to single out genes as the units of selection. (ii) The genotype does not carry information about the phenotype in any way that distinguishes the role of the genes in development from that other factors. (iii) There is no simple and general causal criterion which distinguishes the role of genes in development and evolution. (iv) There is, however, an important sense in which genes but not every other developmental factor represent the phenotype. (v) The idea that genes represent features of the phenotype forces us to recognise that genes are not the only, or almost the only, replicators. Many mechanisms of replication are involved in both development and evolution. (vi) A conception of evolutionary history which recognises both genetic and non-genetic replicators, lineages of replicators and interactors has advantages over both the radical rejection of the replicator/interactor distinction and the conservative restriction of replication to genetic replication.     

Codon-substitution models for detecting molecular adaptation at individual sites along specific lineages

The nonsynonymous (amino acid-altering) to synonymous (silent) substitution rate ratio (omega = d(N)/d(S)) provides a measure of natural selection at the protein level, with omega = 1, >1, and <1, indicating neutral evolution, purifying selection, and positive selection, respectively. Previous studies that used this measure to detect positive selection have often taken an approach of pairwise comparison, estimating substitution rates by averaging over all sites in the protein. As most amino acids in a functional protein are under structural and functional constraints and adaptive evolution probably affects only a few sites at a few time points, this approach of averaging rates over sites and over time has little power. Previously, we developed codon-based substitution models that allow the omega ratio to vary either among lineages or among sites. In this paper we extend previous models to allow the omega ratio to vary both among sites and among lineages and implement the new models in the likelihood framework. These models may be useful for identifying positive selection along prespecified lineages that affects only a few sites in the protein. We apply those branch-site models as well as previous branch- and site-specific models to three data sets: the lysozyme genes from primates, the tumor suppressor BRCA1 genes from primates, and the phytochrome (PHY) gene family in angiosperms. Positive selection is detected in the lysozyme and BRCA genes by both the new and the old models. However, only the new models detected positive selection acting on lineages after gene duplication in the PHY gene family. Additional tests on several data sets suggest that the new models may be useful in detecting positive selection after gene duplication in gene family evolution.     

13 RNA fitness landscapes

The origin of life is believed to have progressed through an RNA World, in which RNA acted as both genetic material and functional molecules. Understanding early evolution requires systematic knowledge of the relationship between RNA sequence and functional activity. In particular, knowing the structure of the fitness landscape of RNA is critical in estimating the probability of the emergence of functional sequences and the role of historical accident during evolution. Much theoretical work has been devoted to fitness landscapes, but experimental maps have been relatively limited. We use in vitro selection on a pool of short RNA sequences that nearly saturates sequence space to reconstruct the form of a comprehensive fitness landscape. We also study mutations during non-enzymatic polymerization to understand how early RNA replicators would ‘move’ in sequence space.