Molecular clock on a neutral network

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating aspects of neutral network topology from empirical measurements of the substitution process.     

Structurally constrained protein evolution: results from a lattice simulation

We simulate the evolution of a protein-like sequence subject to point mutations, imposing conservation of the ground state, thermodynamic stability and fast folding. Our model is aimed at describing neutral evolution of natural proteins. We use a cubic lattice model of the protein structure and test the neutrality conditions by extensive Monte Carlo simulations. We observe that sequence space is traversed by neutral networks, i.e. sets of sequences with the same fold connected by point mutations. Typical pairs of sequences on a neutral network are nearly as different as randomly chosen sequences. The fraction of neutral neighbors has strong sequence to sequence variations, which influence the rate of neutral evolution. In this paper we study the thermodynamic stability of different protein sequences. We relate the high variability of the fraction of neutral mutations to the complex energy landscape within a neutral network, arguing that valleys in this landscape are associated to high values of the neutral mutation rate. We find that when a point mutation produces a sequence with a new ground state, this is likely to have a low stability. Thus we tentatively conjecture that neutral networks of different structures are typically well separated in sequence space. This result indicates that changing significantly a protein structure through a biologically acceptable chain of point mutations is a rare, although possible, event. Received 8 July 1999     

Predictions of gene family distributions in microbial genomes: evolution by gene duplication and modification

A universal property of microbial genomes is the considerable fraction of genes that are homologous to other genes within the same genome. The process by which these homologues are generated is not well understood, but sequence analysis of 20 microbial genomes unveils a recurrent distribution of gene family sizes. We show that a simple evolutionary model based on random gene duplication and point mutations fully accounts for these distributions and permits predictions for the number of gene families in genomes not yet complete. Our findings are consistent with the notion that a genome evolves from a set of precursor genes to a mature size by gene duplications and increasing modifications.     

Mutation accumulation in growing asexual lineages

The stochastic loss of entire classes of individuals bearing the fewest number of mutations-a process known as Muller's ratchet-is studied in asexual populations growing unconstrained from a single founder. In the neutral regime, where mutations have zero effect on fitness, we derive a recursion equation for the probability distribution of the minimum number of mutations carried by individuals in the least-loaded class, and obtain an explicit condition for the halting of the ratchet. Next, we consider the case of deleterious mutations, and show that weak selection can actually accelerate the ratchet beyond that achieved for the neutral regime. This effect is transitory, however, as our results suggest that even weak purifying selection will eventually lead to the complete cessation of the ratchet. These results may have important implications for problems in biology and the medical sciences.     

Population turnover and adaptation in heterogeneous environments

We study adaptive dynamics in a structured population model of asexual individuals which takes into account environmental heterogeneity among the subpopulations. The key purpose of the present work is to address how population turnovers, i.e. extinction events followed by recolonization, affect the rate of fixation of advantageous mutations. This model is a generalization of our previous model to address the interplay between environmental correlation and evolutionary forces on the adaptive process. The incorporation of population turnovers into the model enables us to make a direct correspondence between the model and host-parasite dynamics (epidemiological models). Strikingly, contrary to the intuitive and usual deleterious effect associated to extinction events, it is observed that population turnovers can in fact speed up adaptation as heterogeneity rises. On the other side, in nearly homogeneous population turnovers have a neutral effect on fixation rates, but a detrimental outcome is also achieved when extinction events become very common. In resume, population turnover outcomes on fixation rates of advantageous mutations are strongly influenced by the selective correlation among the subpopulations (demes).     

Significant residue features revealed by eigenvalue decomposition analysis of BLOSUM matrices

Here we attempt to characterize protein evolution by residue features which dominate residue substitution in homologous proteins. Evolutionary information contained in residue substitution matrix is abstracted with the method of eigenvalue decomposition. Top eigenvectors in the eigenvalue spectrums are analyzed as function of the level of similarity, i.e. sequence identity (SI) between homologous proteins. It is found that hydrophobicity and volume are two significant residue features conserved in protein evolution. There is a transition point at SI≈45%. Residue hydrophobicity is a feature governing residue substitution as SI?45%. Whereas below this SI level, residue volume is a dominant feature.     

Exact solution of an evolutionary model without aging

We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated and indicate that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups like many protozoa and coelenterates is discussed.     

Coexistence of cooperators and defectors in well mixed populations mediated by limiting resources

Traditionally, resource limitation in evolutionary game theory is assumed just to impose a constant population size. Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma, and to allow for the stable coexistence between unconditional cooperators and defectors in well-mixed populations. This is a consequence of a self-organizing process that turns the interaction payoff matrix into evolutionary neutral, and represents a resource-based control mechanism preventing the spread of defectors. To our knowledge, this is the first example of coexistence in well-mixed populations with a game structure different from a snowdrift game.     

Comparison of immunogold methodologies for the detection of low copy number viral antigens in bluetongue virus (BTV)-infected cells

Cells infected with bluetongue virus (BTV) were prepared for immunocytochemistry by freeze substitution, the progressive lowering of temperature technique and the Tokuyasu method. Sections containing virus-infected cells were incubated with specific monoclonal antibodies and colloidal gold probes to detect virus antigens of varying copy number; these BTV proteins were structural proteins VP2 and VP7 and the non-structural protein NS2. Protocols compared in this study represented those used in laboratories which handle infections agents and as such, all samples were pre-fixed with minimum concentrations of glutaraldehyde to inactivate the virus. No statistical difference was found between the gold-labelling of sections prepared by the progressive lowering of temperature technique and freeze substitution. The results showed that cryo-sections yielded the best signal-to-noise ratio for all proteins examined in this study and were therefore the most sensitive system for the detection of low copy number proteins. The data and associated inferences relate to the system described in this paper and possibly other analogous system.     

Effects of migration on the evolutionary game dynamics in finite populations with community structures

We investigate the impacts of migration on the evolutionary game dynamics in finite populations with community structures in the framework of evolutionary game theory. In contrast to deterministic dynamics, our model incorporates stochastic factors induced by the finite population size. Based on the analysis of the stationary distribution of the evolutionary process in the limit of rare mutations, we prove that it is most likely to find the population in the community where all individuals have the lower migration rate. Furthermore, we show that reducing the difference between the migration rates of distinct communities can increase the first hitting time to the homogeneous absorbing state and can prolong the coexistence time of different species, promoting the conservation of biodiversity.     

Coevolutionary motion and swarming in a niche space model of ecological species interactions

Organisms are involved in coevolutionary relationships with their competitors, predators, preys and parasites. In this context, we present a simple model for the co-evolution of species in a common niche space, where the fitness of each species is defined via the network of interactions with all other species. In our model, the sign and type of the pairwise interactions (being either beneficial, harmful or neutral) is given by a pre-determined community matrix, while the interaction strength depends on the niche-overlap, i.e. the pairwise distances between species in niche space. The evolutionary process drives the species toward the places with the higher local fitness along the fitness gradient. This gives rise to a dynamic fitness landscape, since the evolutionary motion of a single species can change the landscape of the others (known as the Red Queen Principle). In the simplest case of only two-species we observe either a convergence/divergence equilibrium or a coevolutionary arms race. For a larger number of species our analysis concentrates on an antisymmetric interaction matrix, where we observe a large range of dynamic behaviour, from oscillations, quasiperiodic to chaotic dynamics. In dependence of the value of a first integral of motion we observe either quasiperiodic motion around a central region in niche space or unbounded movement, characterised by chaotic scattering of species pairs. Finally, in a linear food-chain we observe complex swarming behaviour in which the swarm moves as a whole only if the chain consists of an even number of species. Our results could be an important contribution to evolutionary niche theory.     

Molecular evolution of toxin genes in Elapidae snakes

The venom of the sea krait, Laticauda semifasciata, consists primarily of two toxic proteins, phospholipase A₂ (PLA₂) and a three-finger-structure toxin. We have cloned both toxic protein genes, including the upstream region. PLA₂ genes contain three types of inserted sequences: an AG-rich region, a chicken repeat 1-like long interspersed nucleotide element sequence and an intron II 3′ side repeat sequence. The molecular divergence of L. semifasciata PLA₂ genes was defined on the basis of the inserted sequences and their sequence homology. The length of intron I in the three-finger-structure toxin genes differs from species to species. The alignment analysis of intron I of the three-finger-structure toxin genes revealed that the intron I sequence of the ancestral gene comprised ten genetic regions. A hypothetical evolutionary process for the three-finger-structure toxin genes has also been developed.     

Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach

The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.      

Nucleotide sequence changes in human genome: detection by single-strand conformation polymorphism analysis

Mobility shift of single-stranded DNA molecules with a single-base substitution in polyacrylamide gel electrophoresis due to a change of secondary and tertiary structures provides a simple, sensitive method, single-strand conformation polymorphism (SSCP) analysis, for detection of nucleotide sequence changes in DNA. The method with the quite unique principle can detect single-nucleotide substitutions, insertions or deletions of a short nucleotide sequence and loss of genes in human cancers and other genetic diseases. The great progress of the Human Genome Project has revealed thousands of genes associated with these diseases and led to an increasing need for detection of mutations and SNPs in large numbers of DNA samples. The recent development of high-throughput SSCP technologies will enable to meet this need even in a clinical setting.     

Heterogeneous distribution of metabolites across plant species

We investigate the distribution of flavonoids, a major category of plant secondary metabolites, across species. Flavonoids are known to show high species specificity, and were once considered as chemical markers for understanding adaptive evolution and characterization of living organisms. We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved among several families: the power-law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. In order to explain the possible origin of the heterogeneity, we propose a simple model with, essentially, a single parameter. As a result, we show that two respective power-law statistics emerge from simple evolutionary mechanisms based on a multiplicative process. These findings provide insights into the evolution of metabolite diversity and characterization of living organisms that defy genome sequence analysis for different reasons.     

Sharp Asymptotics for Fixation Times in Stochastic Population Genetics Models at Low Mutation Probabilities

This article describes new models in population genetics that extend the neutral Wright–Fisher model by including strong selection and mutation. Fixation times are studied in the limit of small mutation probabilities within the framework of Markov chains with rare transitions. The main result outlines the role of the discrete geometry of the fitness landscape and provides a mean for estimating the expected number of generations for an individual with better fitness value to appear. Some connections to evolutionary algorithms are discussed as well.     

Does sex induce a phase transition?

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.     

Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.     

Speed of adaptation in structured populations

Adaptation of populations takes place with the occurrence and subsequent fixation of mutations that confer some selective advantage to the individuals which acquire it. For this reason, the study of the process of fixation of advantageous mutations has a long history in the population genetics literature. Particularly, the previous investigations aimed to find out the main evolutionary forces affecting the strength of natural selection in the populations. In the current work, we investigate the dynamics of fixation of beneficial mutations in a subdivided population. The subpopulations (demes) can exchange migrants among their neighbors, in a migration network which is assumed to have either a random graph or a scale-free topology. We have observed that the migration rate drastically affects the dynamics of mutation fixation, despite of the fact that the probability of fixation is invariant on the migration rate, accordingly to Maruyama's conjecture. In addition, we have noticed a topological dependence of the adaptive evolution of the population when clonal interference becomes effective.