Neutral Evolution of Mutational Robustness

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. This quantifies the extent to which populations evolve mutational robustness: the insensitivity of the phenotype to mutations. Since the average neutrality is independent of evolutionary parameters---such as, mutation rate, population size, and selective advantage---one can infer global statistics of neutral network topology using simple population data available from {\it in vitro} or {\it in vivo} evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with our theoretical predictions.Comment: 7 pages, 3 figure

Statistical properties of neutral evolution

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered, and fluctuates strongly from one branch of the evolutionary tree to another, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are also due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results could improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences.Comment: 17 pages, 11 figure

Neutral evolution

Glavna teza teorije neutralnosti, da je većina evolucijskih promjena na molekularnoj razini rezultat nasumičnog genetičkog drifta selektivno neutralnih (ekvivalentnih) alela, imala je golem utjecaj na populacijsku genetiku. Tvorac teorije, Motoo Kimura, pritom ne negira značaj prirodne selekcije u evoluciji morfoloških i fizioloških karakteristika. Ipak, teorija je u početku bila potpuno neprihvatljiva za neodarviniste te je izazvala brojne rasprave. Iako danas brojni molekularni podaci govore u korist teorije, u vrijeme njena nastanka njihova dostupnost bila je ograničena, te stoga slobodno možemo tvrditi da je Kimurin rad bio vizionarski. Pretpostavka o konačnosti veličine prirodnih populacija bila je ključni korak u nastanku teorije. Što je populacija manja, to je snažnije djelovanje genetičkog drifta. No, stopa neutralne evolucije ne ovisi o veličini populacije, već o stopi nastanka neutralnih mutacija. Evolucijska stopa određenog proteina konstantna je u različitim linijama koje potječu od zajedničkog pretka, što je osnova molekularnog sata. Teorija neutralnosti ipak ne može objasniti sve evolucijske pojave. Postojeća genetička raznolikost populacija i vrsta često je bolje razjašnjena teorijom približne neutralnosti, koja uzima u obzir veličinu populacije i mogućnost istovremenog djelovanja drifta i selekcije. Pritom ishod evolucije ovisi o relativnoj snazi tih dviju sila. Uostalom, glavna razlika između "selekcionista" i "neutralista" je u tome koju od tih sila smatraju ključnim pokretačem evolucije. Teorija približne neutralnosti na neki način pomiruje ta dva stajališta.The main thesis of the neutral theory, which presumes that most of evolutionary changes on molecular level are driven by random genetic drift of selectively neutral (equivalent) alleles, had a huge influence on population genetics. Theory creator, Motoo Kimura, in doing so, doesn't deny significance of natural selection in evolution of morphological and physiological traits. Nevertheless, in the begining, the theory was completely unacceptable for neo-Darwinians and has caused many debates. By the time his theory firstly emerged, unlike now, there were only few molecular methods that could prove the theory so we can undoubtedly claim that Kimura's work was a visionary one. Presumption of finality of natural population was the crucial step towards the making of theory. The smaller the population is, the stronger is the effect of genetic drift. But the rate of neutral evolution doesn't depend on population size, but on the neutral mutation rate. The evolutionary rate of a given protein is constant in different lines that diverge from a common ancestor, so each protein evolves according to its own molecular clock. The neutral theory of molecular evolution can not explain all evolutionary phenomena. Present genetic diversity of populations and species is better explained by the nearly neutral theory, which considers the population size and the possibility of common influence of genetic drift and natural selection. The outcome of evolution depends on relative strength of above mentioned forces. After all, the main difference between "neutralists" and "selectionists" is relative importance of drift and selection, which is, in some way, conjoined into the nearly neutral theory

The edge of neutral evolution in social dilemmas

The functioning of animal as well as human societies fundamentally relies on cooperation. Yet, defection is often favorable for the selfish individual, and social dilemmas arise. Selection by individuals' fitness, usually the basic driving force of evolution, quickly eliminates cooperators. However, evolution is also governed by fluctuations that can be of greater importance than fitness differences, and can render evolution effectively neutral. Here, we investigate the effects of selection versus fluctuations in social dilemmas. By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging 'edge of neutral evolution' that delineates regimes of neutral and Darwinian evolution. Our results reveal that cooperation is significantly maintained in the neutral regimes. In contrast, the classical predictions of evolutionary game theory, where defectors beat cooperators, are recovered in the Darwinian regimes. Our studies demonstrate that fluctuations can provide a surprisingly simple way to partly resolve social dilemmas. Our methods are generally applicable to estimate the role of random drift in evolutionary dynamics.Comment: 17 pages, 4 figure

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.Comment: 4 pages, 2 figure

Scale-free networks are not robust under neutral evolution

Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution. The guiding principle for this is robustness in the resulting phenotype. The numerical results show that a power-law distribution is not stable under such an evolution, and the network approaches a homogeneous form where the overall distribution of connectivities is given by a Poisson distribution.Comment: Submitted for publicatio

Neutral evolution and turnover over centuries of English word popularity

Here we test Neutral models against the evolution of English word frequency and vocabulary at the population scale, as recorded in annual word frequencies from three centuries of English language books. Against these data, we test both static and dynamic predictions of two neutral models, including the relation between corpus size and vocabulary size, frequency distributions, and turnover within those frequency distributions. Although a commonly used Neutral model fails to replicate all these emergent properties at once, we find that modified two-stage Neutral model does replicate the static and dynamic properties of the corpus data. This two-stage model is meant to represent a relatively small corpus (population) of English books, analogous to a `canon', sampled by an exponentially increasing corpus of books in the wider population of authors. More broadly, this mode -- a smaller neutral model within a larger neutral model -- could represent more broadly those situations where mass attention is focused on a small subset of the cultural variants.Comment: 12 pages, 5 figures, 1 tabl