Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a renewable resource extended throughout the environment provides the energy necessary to sustain life, including movement and reproduction. Since the resource doesn't regrow immediately, it generates competition between individuals and therefore provides a natural selection pressure from which evolution of the genetic traits is observed. As a result of this, several phenomena characteristic of living systems emerge from this model without having to introduce them explicitly. These include speciation and punctuated equilibrium, competitive exclusion, and altruistic behaviour from selfish rules.
In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker replicator equation that describes dynamics of pure strategy frequencies. I then investigate the evolution of not only frequencies of pure strategies but also of total distribution of mixed strategies. I show that the process of natural selection of strategies for all games obeys the dynamical Principle of minimum of information gain.
The Age-Specific Force of Natural Selection and Walls of Death
W. D.汉密尔顿著名的年龄特异性自然选择力公式，以依赖线性近似为代价，否定了由于突变积累而导致的衰老死亡率预测。将Evans et al.（2007）的突变累积的完全非线性人口统计模型应用于Hamilton的设置，我们发现了令人惊讶的差异。非线性相互作用在最常研究的情况下导致汉密尔顿式预测的崩溃，在其他情况下改进预测，并允许在繁殖结束之前的年龄出现死亡之墙。遗传负荷的哈勒原理有一个精确但不熟悉的概括。
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g.~births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). S…
We investigate how initial and boundary conditions influence the competition dynamics and outcome in dispersal-structured populations. The study is carried out through numerical modeling of the heterogeneous Brownian bugs model, in which individuals are characterized by diversified diffusion coefficients and compete for resources within a finite interaction range. We observed that if instead of being distributed randomly across the domain the population is initially localized within a small region, the dynamics and the stationary state of the system differ significantly. The outcome of the nat…
Modern biological tools have made it possible to unequivocally demonstrate the deep relationship among species in terms of genes and basic molecular mechanisms. In addition, results from genetic, physical and physiological approaches applied to individual model cell systems have led to the mapping of large networks of macromolecular interactions with similar general properties. Although gene, mechanism and network structure similarities among species tend to suggest the existence of important constraints applied to organisms, it is surprising that the elucidation of the precise general mechani…
We derived a new speed limit in population dynamics, which is a fundamental limit on the evolutionary rate. By splitting the contributions of selection and mutation to the evolutionary rate, we obtained the new bound on the speed of arbitrary observables, named the selection bound, that can be tighter than the conventional Cramér--Rao bound. Remarkably, the selection bound can be much tighter if the contribution of selection is more dominant than that of mutation. This tightness can be geometrically characterized by the correlation between the observable of interest and the growth rate. We als…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we study how natural selection acts on mutants that have the same reproductive rate, but experience different population structures. In our framework, mutation alters population structure, which is given by a graph that specifies the dispersal of offspring. Reproduction can be either genetic or cultural. Competin…
Understanding the rift between update rules in Evolutionary Graph Theory: The intrinsic death rate drives star graphs from amplifying to suppressing natural selection
The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic compartments - droplets of an emulsion. The selection of desirable variants is performed according to the phenotype of each compartment. The random partitioning leads to a fraction of compartments receiving more than one genotype making the whole process a lab implementation of the group selection. From a practical point of view (where efficient selection is typica…
Suppose we have $n$ different types of self-replicating entity, with the population $P_i$ of the $i$th type changing at a rate equal to $P_i$ times the fitness $f_i$ of that type. Suppose the fitness $f_i$ is any continuous function of all the populations $P_1, \dots, P_n$. Let $p_i$ be the fraction of replicators that are of the $i$th type. Then $p = (p_1, \dots, p_n)$ is a time-dependent probability distribution, and we prove that its speed as measured by the Fisher information metric equals the variance in fitness. In rough terms, this says that the speed at which information is updated thr…
Environment heterogeneity creates fast amplifiers of natural selection in graph-structured populations
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；SIB Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Inserm（法国国立健康与医学研究院）
The amplification cycle of many replicators (natural or artificial) involves the usage of a host compartment, inside of which the replicator express phenotypic compounds necessary to carry out its genetic replication. For example, viruses infect cells, where they express their own proteins and replicate. In this process, the host cell boundary limits the diffusion of the viral protein products, thereby ensuring that phenotypic compounds, such as proteins, promote the replication of the genes that encoded them. This role of maintaining spatial co-localization, also called genotype-phenotype lin…
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran p…
Population genetics models typically consider a fixed population size and a unique selection coefficient. However, population dynamics inherently generate noise in numbers of individuals and selection acts on various components of the individuals' fitness. In plant species with seed banks, the size of both the above- and below-ground compartments present noise depending on seed production and the state of the seed bank. We investigate if this noise has consequences on 1)~the rate of genetic drift, and 2)~the efficacy of selection. We consider four variants of two-allele Moran-type models defin…
Darwin's theory of evolution by natural selection does not predict long-term progress or advancement, nor does it provide a useful way to define or understand these concepts. Nevertheless, the history of life is marked by major trends that appear progressive, and seemingly more advanced forms of life have appeared. To reconcile theory and fact, evolutionists have proposed novel theories that extend natural selection to levels and time frames not justified by the original structure of Darwin's theory. To extend evolutionary theory without violating the most basic tenets of Darwinism, I here ide…
The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a simple population model in which there compete simple multicellular organisms that grow either by synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous an…
Simonton (2006) makes the unwarranted assumption that nonmonotonicity supports a Darwinian view of creativity. Darwin's theory of natural selection was motivated by a paradox that has no equivalent in creative thought: the paradox of how change accumulates when acquired traits are not inherited. To describe a process of cumulative change in which acquired traits are retained is outside of the scope of the theory of natural selection. Even the early evolution of life itself (prior to genetically mediated template replication) cannot be described by natural selection. Specifically, natural selec…
Neural codes appear efficient. Naturally, neuroscientists contend that an efficient process is responsible for generating efficient codes. They argue that natural selection is the efficient process that generates those codes. Although natural selection is an adaptive process, evolution itself, is not. Evolution consists of not only natural selection, but also neutral stochastic forces that can generate biological inefficiencies. The explanatory power of natural selection cannot be appealed to, without regards for the remaining evolutionary forces. In this paper, we aim to reformulate the expla…
