Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a new evolutionary algorithm. Optimization of a continuous objective function is analogous to searching for high fitness phenotypes on a fitness landscape. We summarize how natural selection moves a population along the non-euclidean gradient that is induced by the population on the fitness landscape (the natural gradient). Under normal approximations common in quantitative genetics, we show how selection is related to Newton's method in optimization. We find that intermediate selection is most informative of the fitness landscape. We describe the generation of new phenotypes and introduce an operator that recombines the whole population to generate variants that preserve normal statistics. Finally, we introduce a proof-of-principle algorithm that combines natural selection, our recombination operator, and an adaptive method to increase selection. Our algorithm is similar to covariance matrix adaptation and natural evolutionary strategies in optimization, and has similar performance. The algorithm is extremely simple in implementation with no matrix inversion or factorization, does not require storing a covariance matrix, and may form the basis of more general model-based optimization algorithms with natural gradient updates.
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…
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 theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the population. Deductive theory predicts how populations adapt to environmental challenge. Inductive theory describes the causes of change in populations. One starts with a given amount of change. One then assigns different parts of the total change to particular causes. Inductive theory analyzes alternative causal models for how populations have adapted to environ…
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…
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…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of evolutionary theory. Here I discuss a new conceptual link between evolution and statistical physics. I argue that natural selection can be viewed as a coarsening phenomenon, similar to the growth of domain size in quenched magnets or to Ostwald ripening in alloys and emulsions. In particular, I show that the most remarkable features of coarsening---scaling an…
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…
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…
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）
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…
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…
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…
The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We develop a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in non-equilibrium populatio…
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…
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 natural mortality (M) and purse-seine catchability and selectivity were estimated for Trachurus novaezelandiae, Richardson, 1843 (yellowtail scad)-a small inshore pelagic species harvested off south-eastern Australia. Hazard functions were applied to two decades of data describing catches (mostly stable at a mean +- SE of 315 +- 14 t p.a.) and effort (declining from a maximum of 2289 to 642 boat days between 1999/00 and 2015/16) and inter-dispersed (over nine years) annual estimates of size-at-age (0+ to 18 years) to enable survival analysis. The data were best described by a model with ei…
Reduction of information entropy along with ever-increasing complexity are among the key signatures of living matter. Understanding the onset of such behavior in early prebiotic world is essential for solving the problem of origins of life. To elucidate this transition, we study a theoretical model of information-storing heteropolymers capable of template-assisted ligation and subjected to cyclic non-equilibrium driving forces. We discover that this simple physical system undergoes a spontaneous reduction of the information entropy due to the competition of chains for constituent monomers. Thi…
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…
Stronger selection implies faster evolution---that is, the greater the force, the faster the change. This apparently self-evident proposition, however, is derived under the assumption that genetic variation within a population is primarily supplied by mutation (i.e.\ mutation-driven evolution). Here, we show that this proposition does not actually hold for recombination-driven evolution, i.e.\ evolution in which genetic variation is primarily created by recombination rather than mutation. By numerically investigating population genetics models of recombination, migration and selection, we demo…
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…
