Using information theory, we propose an estimation method for traits parameters in a Darwinian evolution model for species with on trait or multiple traits. We use the Fisher's information to obtain the errors on the estimation for one species with one or multiple traits. We perform simulations to illustrate the method.
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious `mutations' spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time deterministic nonlinear dynamics, and long-time evolutionary behavior with exponentially distributed rare events, discrete jumps among punctuated equilibria, and catastrophe.
In their well-known textbook (Vincent & Brown, 2005), Vincent and Brown suggested an attractive approach for studying evolutionary dynamics of populations that are heterogeneous with respect to some strategy that affects the fitness of individuals in the population. The authors developed a theory, whose goal was to expand the applicability of mathematical models of population dynamics by including dynamics of an evolving heritable phenotype trait subject to natural selection. The authors studied both the case of evolution of individual traits and of mean traits in the population (or species) a…
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such mutation rates are common in multicellular organisms including humans, however they are not explicitly considered in most population genetics models. Under these assumptions the drift shows properties distinct from the classical drift models, which ignore realistic mutation rates: i) All (non-lethal) variants of a site have a characteristic average frequencies, …
Darwin's book, Origin of the Species has been a source of public controversy for more than hundred and fifty years. Court cases and mountains of words have not dispelled this controversy. In this paper, a quantitative approach using simple mathematics shows that the concept of evolution by natural selection using only random choice of variables does work. The procedure applied to the optical equations forming the phenotype of a spider eye produces an eye design modeled after the measurements by Land and Barth.
We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped the Aitchison geometry. As an immediate consequence we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Finally, using the Fokker-Planck equation and Wasserstein-contraction estimates, we study the long time behavior of the stochastic replicator equation, as an example of a non-gradient drift diffusion on the Aitchison simplex.
It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer (HGT). At a certain point, however, life made a transition to the modern era of individuality and vertical descent. Here we present a minimal model for this hypothesized "Darwinian transition." The model suggests that HGT-dominated dynamics may have been intermittently interrupted by selection-driven processes during which genotypes became fitter and decreased…
We re-examined data from the classic Luria-Delbruck fluctuation experiment, which is often credited with establishing a Darwinian basis for evolution. We argue that, for the Lamarckian model of evolution to be ruled out by the experiment, the experiment must favor pure Darwinian evolution over both the Lamarckian model and a model that allows both Darwinian and Lamarckian mechanisms. Analysis of the combined model was not performed in the original 1943 paper. The Luria-Delbruck paper also did not consider the possibility of neither model fitting the experiment. Using Bayesian model selection, …
In here presented in silico study we suggest a way how to implement the evolutionary principles into anti-cancer therapy design. We hypothesize that instead of its ongoing supervised adaptation, the therapy may be constructed as a self-sustaining evolutionary process in a dynamic fitness landscape established implicitly by evolving cancer cells, microenvironment and the therapy itself. For these purposes, we replace a unified therapy with the `therapy species', which is a population of heterogeneous elementary therapies, and propose a way how to turn the toxicity of the elementary therapy into…
The evolution of cooperation has been a perennial problem for evolutionary biology because cooperation is undermined by selfish cheaters (or "free riders") that profit from cooperators but do not invest any resources themselves. In a purely "selfish" view of evolution, those cheaters should be favored. Evolutionary game theory has been able to show that under certain conditions, cooperation nonetheless evolves stably. One of these scenarios utilizes the power of punishment to suppress free riders, but only if players interact in a structured population where cooperators are likely to be surrou…
Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial "suicide bomber" game in terms of the phase portraits of population dynamics, for parameter combinations that cover all interesting games for two-players, and seven of the 38 possible phase portraits of the three-player game. We compare these predictions to simulations of these competitions in finite well-mixed populations, but also allowing for probabilistic ra…
This paper outlines the implications of neural-level accounts of insight, and models of the conceptual interactions that underlie creativity, for a theory of cultural evolution. Since elements of human culture exhibit cumulative, adaptive, open-ended change, it seems reasonable to view culture as an evolutionary process, one fueled by creativity. Associative memory models of creativity and mathematical models of how concepts combine and transform through interaction with a context, support a view of creativity that is incompatible with a Darwinian (selectionist) framework for cultural evolutio…
Culture evolves, not just in the trivial sense that cultures change over time, but also in the strong sense that such change is governed by Darwinian principles. Both biological and cultural evolution are essentially cumulative selection processes in which information (whether genetic or cultural) is sieved, retained and then transmitted to the next generation. In both domains such a process will result in recognizable lineages and tree-like phylogenies so characteristic of Darwinian evolution. Because a principle of inheritance (i.e., faithful replication of information) holds in both domains…
Although Darwinian models are rampant in the social sciences, social scientists do not face the problem that motivated Darwin's theory of natural selection: the problem of explaining how lineages evolve despite that any traits they acquire are regularly discarded at the end of the lifetime of the individuals that acquired them. While the rationale for framing culture as an evolutionary process is correct, it does not follow that culture is a Darwinian or selectionist process, or that population genetics provides viable starting points for modeling cultural change. This paper lays out step-by-s…
Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is transmitted to children. Here we propose a model where we simulate both the dynamics of wealth in a population and the evolution of a trait that determines how wealth is transmitted from parents to offspring, in a darwinian context.
In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). (2) The probability distribut…
The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision…
An increasing number of dissident voices claim that the standard neo-Darwinian view of genes as 'leaders' and phenotypes as 'followers' during the process of adaptive evolution should be turned on its head. This idea is older than the rediscovery of Mendel's laws of inheritance and has been given several names before its final 'Baldwin effect' label. A condition for this effect is that environmentally induced variation such as phenotypic plasticity or learning is crucial for the initial establishment of a population. This gives the necessary time for natural selection to act on genetic variati…
Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about $K\log{L}$, rather than $K^L$, where $L$ is the length of the genomic "word", and $K$ is the number of possible "letters" that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic a…
We analyze from basic physical considerations the Darwinian competition for reproduction (evolutionary dynamics) of strategists in a Public Goods Game, the archetype for $n$-agent (group) economical and biological interactions. In the proposed setup, the population is organized into groups, being the individual fitness linked to the group performance, while the evolutionary dynamics takes place globally. Taking advantage of (groups) permutation symmetry, the nonlinear analysis of the "mesoscale" Markov phase space for many competing groups is feasible to a large extent, regarding the expected …
Open-ended evolutionary dynamics remains an elusive goal for artificial evolutionary systems. Many ideas exist in the biological literature beyond the basic Darwinian requirements of variation, differential reproduction and inheritance. I argue that these ideas can be seen as aspects of five fundamental requirements for open-ended evolution: (1) robustly reproductive individuals, (2) a medium allowing the possible existence of a practically unlimited diversity of individuals and interactions, (3) individuals capable of producing more complex offspring, (4) mutational pathways to other viable i…
In complex environments, there are costs to both ignorance and perception. An organism needs to track fitness-relevant information about its world, but the more information it tracks, the more resources it must devote to memory and processing. Rate-distortion theory shows that, when errors are allowed, remarkably efficient internal representations can be found by biologically-plausible hill-climbing mechanisms. We identify two regimes: a high-fidelity regime where perceptual costs scale logarithmically with environmental complexity, and a low-fidelity regime where perceptual costs are, remarka…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are characterized with predation efficiency and death rates, to which Darwinian evolutionary adaptation is introduced. Competition for limited prey abundance drives the populations' optimization with respect to predation efficiency and death rates. We study the influence of various ecological elements on the final state, finding that both indirect competition and …
Bacteriophage Q$β$: Six Decades at the Frontier of Molecular and Viral Evolution
Centro de Astrobiología (CAB), CSIC-INTA（天体生物学中心）；Museo Nacional de Ciencias Naturales (CSIC)（国家自然科学博物馆）；Grupo Interdisciplinar de Sistemas Complejos (GISC)（复杂系统跨学科小组）
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the formation of homogeneous clusters, which is the hallmark of network reciprocity. Here we go beyond this traditional setup and study the spatiotemporal dynamics of cooperation in a population of populations. We use the prisoner's dilemma game as the mathematical model and show that considering several populations simultaneously give rise to fascinating spati…
We study models of biological evolution and investigate a key factor to yield self-organized criticality (SOC). The Bak-Sneppen (BS) model is the most basic model that shows an SOC state, which is developed based on minimal and plausible assumptions of Darwinian competition. Another class of models, which have population dynamics and simple rules for species migrations, has also been studied. It turns out that they do not show an SOC state although the assumptions made in these models are similar to those in the BS model. To clarify the origin of these differences and to identify a key ingredi…
Variation and selection are the core principles of Darwinian evolution, yet quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings: first, libraries with same sequen…
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；New England Complex Systems Institute（新英格兰复杂系统研究所）；Vrije Universiteit Brussel（布鲁塞尔自由大学）
This paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. Traditional studies encounter problems because it is difficult to describe life and cognition in terms of matter and energy, since their laws are valid only at the physical scale. However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex. The paper presents eight tentative laws of information, valid at multiple scales, which are generalizat…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed. Here we show more generally that evolving fitness distributions are attracted to a one-parameter family of distributions with a fixed parabolic relationship between skewness and kurtosis. Unlike fitness waves, this statistical pattern encompasses both positive and negative…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics. Adaptive dynamics so far has been put on a rigorous footing only for direct competition models (Lotka-Volterra models) involving a competition kernel which describes the competition pressure from one individual to another one. We extend this to a multi-resources chemostat model, where the competition between individuals results from the sharing of several resourc…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each birth event. In the present paper, we study the long-term behavior of the system in the limit of large population $(K\to \infty)$ size, rare mutations $(u\to 0)$, and small mutational effects $(σ\to 0)$, proving convergence to the canonical equation of adaptive dynamics (CEAD). In contrast to earlier works, e.g. by Champagnat and Méléard, we take the three limi…
