scholarly journals Adaptive fitness landscape for replicator systems: to maximize or not to maximize

2018 ◽  
Vol 13 (3) ◽  
pp. 25 ◽  
Author(s):  
Alexander S. Bratus ◽  
Yuri S. Semenov ◽  
Artem S. Novozhilov
Keyword(s):  
Natural Selection ◽  
Fitness Landscape ◽  
Evolutionary Process ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Basic Model ◽  
Mean Fitness ◽  
The Mean ◽  
The Hill ◽  
Fisher’S Fundamental Theorem

Sewall Wright’s adaptive landscape metaphor penetrates a significant part of evolutionary thinking. Supplemented with Fisher’s fundamental theorem of natural selection and Kimura’s maximum principle, it provides a unifying and intuitive representation of the evolutionary process under the influence of natural selection as the hill climbing on the surface of mean population fitness. On the other hand, it is also well known that for many more or less realistic mathematical models this picture is a severe misrepresentation of what actually occurs. Therefore, we are faced with two questions. First, it is important to identify the cases in which adaptive landscape metaphor actually holds exactly in the models, that is, to identify the conditions under which system’s dynamics coincides with the process of searching for a (local) fitness maximum. Second, even if the mean fitness is not maximized in the process of evolution, it is still important to understand the structure of the mean fitness manifold and see the implications of this structure on the system’s dynamics. Using as a basic model the classical replicator equation, in this note we attempt to answer these two questions and illustrate our results with simple well studied systems.

Wright’s Adaptive Landscape, Fisher’s Fundamental Theorem

2018 ◽  
Author(s):  
Samir Okasha
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Evolutionary Biology ◽  
Weak Sense ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Classical Formulation ◽  
The Hill ◽  
Fisher’S Fundamental Theorem ◽  
Fitness Maximization

Fitness maximization, or optimization, is a controversial idea in evolutionary biology. One classical formulation of this idea is that natural selection will tend to push a population up a peak in an adaptive landscape, as Sewall Wright first proposed. However, the hill-climbing property only obtains under particular conditions, and even then the ascent is not usually by the steepest route; this shows why it is misleading to assimilate the process of natural selection to a process of goal-directed choice. A different formulation of the idea of fitness-maximization is R. A. Fisher’s ‘fundamental theorem of natural selection’. However, the theorem points only to a weak sense in which selection is an optimizing process, for it requires that ‘environmental constancy’ be understood in a highly specific way. It does not vindicate the claim that natural selection has an intrinsic tendency to produce adaptation.

scholarly journals Joint phenotypes, evolutionary conflict and the fundamental theorem of natural selection

2014 ◽  
Vol 369 (1642) ◽  
pp. 20130423 ◽  
Author(s):  
David C. Queller
Keyword(s):  
Natural Selection ◽  
Species Interactions ◽  
Fundamental Theorem ◽  
Genetic Variance ◽  
Inclusive Fitness ◽  
Evolutionary Conflict ◽  
Mean Fitness ◽  
The Mean ◽  
Multiple Species ◽  
Fisher’S Fundamental Theorem

Multiple organisms can sometimes affect a common phenotype. For example, the portion of a leaf eaten by an insect is a joint phenotype of the plant and insect and the amount of food obtained by an offspring can be a joint trait with its mother. Here, I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species. Selective conflict between the interactants occurs when selection takes opposite signs on the joint phenotype. The mean fitness of a population changes not just through its own genetic variance but also through the genetic variance for its fitness that resides in other species, an update of Fisher's fundamental theorem of natural selection. Some similar results, using inclusive fitness, apply to within-species interactions. The models provide a framework for understanding evolutionary conflicts at all levels.

scholarly journals GENETIC LOAD IN NATURAL POPULATIONS: IS IT COMPATIBLE WITH THE HYPOTHESIS THAT MANY POLYMORPHISMS ARE MAINTAINED BY NATURAL SELECTION?

Genetics ◽  
1974 ◽  
Vol 77 (3) ◽  
pp. 569-589
Author(s):  
Martin L Tracey ◽  
Francisco J Ayala
Keyword(s):  
Drosophila Melanogaster ◽  
Natural Selection ◽  
Natural Population ◽  
Natural Populations ◽  
Genetic Load ◽  
Structural Genes ◽  
Invertebrate Species ◽  
Average Proportion ◽  
Mean Fitness ◽  
The Mean

ABSTRACT Recent studies of genetically controlled enzyme variation lead to an estimation that at least 30 to 60% of the structural genes are polymorphic in natural populations of many vertebrate and invertebrate species. Some authors have argued that a substantial proportion of these polymorphisms cannot be maintained by natural selection because this would result in an unbearable genetic load. If many polymorphisms are maintained by heterotic natural selection, individuals with much greater than average proportion of homozygous loci should have very low fitness. We have measured in Drosophila melanogaster the fitness of flies homozygous for a complete chromosome relative to normal wild flies. A total of 37 chromosomes from a natural population have been tested using 92 experimental populations. The mean fitness of homozygous flies is 0.12 for second chromosomes, and 0.13 for third chromosomes. These estimates are compatible with the hypothesis that many (more than one thousand) loci are maintained by heterotic selection in natural populations of D. melanogaster.

Radical Epistasis and the Genotype-Phenotype Relationship

1994 ◽  
Vol 2 (1) ◽  
pp. 117-128 ◽  
Author(s):  
David Sloan Wilson ◽  
Alexandra Wells
Keyword(s):  
Linkage Disequilibrium ◽  
Natural Selection ◽  
Assortative Mating ◽  
Evolutionary Process ◽  
Genetic System ◽  
Adaptive Landscape ◽  
Nk Model ◽  
Phenotypic Distribution ◽  
Adaptive Landscapes

Models of evolution often assume that the offspring of two genotypes, which are genetically intermediate by definition, are also phenotypically intermediate. The continuity between genotype and phenotype interferes with the process of evolution on multipeaked adaptive landscapes because the progeny of genotypes that lie on separate adaptive peaks fall into valleys of low fitness. This problem can be solved by epistasis, which disrupts the continuity between genotype and phenotype. In a five-locus sexual haploid model with maximum epistasis, natural selection in multipeak landscapes evolves a set of genotypes that a) occupy the adaptive peaks and b) give rise to each other by recombination. The epistatic genetic system therefore “molds” the phenotypic distribution to the adaptive landscape, without assortative mating or linkage disequilibrium. If the adaptive landscape is changed, a new set of genotypes quickly evolves that satisfies conditions a and b, above, for the new peaks. Our model may be relevant to a number of recalcitrant problems in biology and also stands in contrast to Kauffman's [3] NK model of evolution on rugged fitness surfaces, in which epistasis and recombination tend to constrain the evolutionary process.

scholarly journals REMARKS ON THE EVOLUTIONARY EFFECT OF NATURAL SELECTION

Genetics ◽  
1976 ◽  
Vol 83 (3) ◽  
pp. 601-607
Author(s):  
W J Ewens
Keyword(s):  
Natural Selection ◽  
Present Note ◽  
Great Majority ◽  
Linkage Equilibrium ◽  
Evolutionary Effect ◽  
Mathematical Theorem ◽  
Fitness Parameters ◽  
Mean Fitness ◽  
The Mean ◽  
Quasi Linkage Equilibrium

ABSTRACT The so-called "Fundamental Theorem of Natural Selection", that the mean fitness of a population increases with time under natural selection, is known not to be true, as a mathematical theorem, when fitnesses depend on more than one locus. Although this observation may not have particular biological relevance, (so that mean fitness may well increase in the great majority of interesting situations), it does suggest that it is of interest to find an evolutionary result which is correct as a mathematical theorem, no matter how many loci are involved. The aim of the present note is to prove an evolutionary theorem relating to the variance in fitness, rather than the mean: this theorem is true for an arbitrary number of loci, as well as for arbitrary (fixed) fitness parameters and arbitrary linkage between loci. Connections are briefly discussed between this theorem and the principle of quasi-linkage equilibrium.

scholarly journals Indirect genetic effects clarify how traits can evolve even when fitness does not

2018 ◽  
Author(s):  
David N. Fisher ◽  
Andrew G. McAdam
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Genetic Effects ◽  
Social Effects ◽  
Indirect Genetic Effects ◽  
The Social ◽  
Mean Fitness ◽  
Related Individuals ◽  
Fundamental Theorems ◽  
Fisher’S Fundamental Theorem

AbstractThere are many situations in nature where we expect traits to evolve but not necessarily for mean fitness to increase. However, these scenarios are hard to reconcile simultaneously with Fisher’s Fundamental Theorem of Natural Selection and the Price identity. The consideration of indirect genetic effects on fitness reconciles these fundamental theorems with the observation that traits sometimes evolve without any adaptation, by explicitly considering the correlated evolution of the social environment, which is a form of transmission bias. While transmission bias in the Price identity is often assumed to be absent, here we show that explicitly considering indirect genetic effects as a form of transmission bias for fitness has several benefits: 1) it makes clear how traits can evolve while mean fitness remains stationary, 2) it reconciles the fundamental theorem of natural selection with the evolution of maladaptation, 3) it explicitly includes density-dependent fitness through negative social effects that depend on the number of interacting conspecifics, and 4) its allows mean fitness to evolve even when direct genetic variance in fitness is zero, if related individuals interact and/or if there is multilevel selection. In summary, considering fitness in the context of indirect genetic effects aligns important theorems of natural selection with many situations observed in nature and provides a useful lens through which we might better understand evolution and adaptation.

scholarly journals The rugged adaptive landscape of an emerging plant RNA virus

2014 ◽  
Author(s):  
Jasna Lalic ◽  
Santiago F. Elena
Keyword(s):  
Fitness Landscape ◽  
Rna Virus ◽  
Large Population ◽  
Emerging Infectious Diseases ◽  
Evolutionary Process ◽  
Adaptive Landscape ◽  
Evolutionary Potential ◽  
Recombination Rates ◽  
New Host ◽  
Population Sizes

RNA viruses are the main source of emerging infectious diseases owed to the evolutionary potential bestowed by their fast replication, large population sizes and high mutation and recombination rates. However, an equally important parameter, which is usually neglected, is the topography of the fitness landscape, that is, how many fitness maxima exist and how well connected they are, which determines the number of accessible evolutionary pathways. To address this question, we have reconstructed the fitness landscape describing the adaptation of Tobacco etch potyvirus to its new host, Arabidopsis thaliana. Fitness was measured for most of the genotypes in the landscape, showing the existence of peaks and holes. We found prevailing epistatic effects between mutations, with cases of reciprocal sign epistasis being common at latter stages. Therefore, results suggest that the landscape was rugged and holey, with several local fitness peaks and a very limited number of potential neutral paths. The viral genotype fixed at the end of the evolutionary process was not on the global fitness optima but stuck into a suboptimal peak.

scholarly journals The Coevolutionary Romance of Social Learning and Parasitic Behavior

2016 ◽  
Author(s):  
Richard McElreath
Keyword(s):  
Natural Selection ◽  
Social Learning ◽  
Host Organism ◽  
Happy Ending ◽  
Host Fitness ◽  
Learned Behavior ◽  
Mean Fitness ◽  
The Mean

AbstractOnce an animal begins to acquire behavior by social learning, it may be seduced by parasitic parasitic, behavior that reduces the animal’s fitness and thereby increases its own spread. However, the animal’s psychology will coevolve, potentially limiting the influence and spread of parasitic behavior. I revisit prominent models of the evolution of social learning and introduce the possibility of parasitic behavior. First, I explore a courtship between primitive social learning and parasitic behavior. Parasitic behavior can spread, but selection on the host then reduces social learning and limits its importance. Both parties are frustrated. In the second part, I study a reconciliation dynamic in which social learning becomes strategic about who it partners with. In this model, parasitic behavior can become prevalent and substantially reduce host fitness. However, it may also evolve to be mutualistic and raise the mean fitness of the host organism. When this occurs, natural selection may favor psychological susceptibility to parasitic behavior. Both social learning and socially learned behavior can enjoy a happy ending.

scholarly journals Acceleration of Evolutionary Processes by Learning and Extended Fisher's Fundamental Theorem

2021 ◽  
Author(s):  
So Nakashima ◽  
Tetsuya J. Kobayashi
Keyword(s):  
Genetic Algorithms ◽  
Natural Selection ◽  
Fundamental Theorem ◽  
Evolutionary Process ◽  
Evolutionary Processes ◽  
Individual Fitness ◽  
Learning Agent ◽  
The Impact ◽  
Fisher’S Fundamental Theorem ◽  
Population Fitness

Natural selection is general and powerful concept not only to explain evolutionary processes of biological organisms but also to design engineering systems such as genetic algorithms and particle filters.There is a surge of interest, both from biology and engineering, in considering natural selection of intellectual agents that can learn individually. Learning by individual agents of better behaviors for survival may accelerate the evolutionary processes by natural selection. We have accumulating pieces of evidence that organisms can transmit its information to the next generation via epigenetic states or memes. Also, such idea is important for engineering applications to improve the genetic algorithms and the particle filter. To accelerate the evolutionary process, an agent should change their strategy so that the population fitness increases the most. Equivalently, an agent should update the strategy towards a gradient (derivative) of the population fitness with respect to the strategy. However, it has not yet been clarified whether and how an agent can estimate the gradient and accelerate the evolutionary process. We also lack methodology to quantify the acceleration to understand and predict the impact of learning. In this paper, we address these problems. We show that an learning agent can accelerate the evolutionary process by proposing ancestral learning, which uses the information transmitted from the ancestor (ancestral information) via epigenetic states or memes. Numerical experiments show that ancestral learning actually accelerates the evolutionary process. We next show that the ancestral information is sufficient to estimate the gradient. In particular, learning can accelerate the evolutionary process without communications between agents. Finally, to quantify the acceleration, we extend the Fisher's fundamental theorem (FF-thm) for natural selection to ancestral learning. The conventional FF-thm relates the speed of evolution by natural selection to the variety of the individual fitness in the population. Our extended FF-thm relates the acceleration of the evolutionary process to the variety of individual fitness of the agent. By the theorem, we can quantitatively understand when and why learning is beneficial.

scholarly journals An Empirical Analysis of Search in GSAT

1993 ◽  
Vol 1 ◽  
pp. 47-59 ◽  
Author(s):  
I. P. Gent ◽  
T. Walsh
Keyword(s):  
Computer Experiments ◽  
Extensive Study ◽  
Hill Climbing ◽  
Average Score ◽  
Approximation Procedure ◽  
Problem Size ◽  
Simple Scaling ◽  
The Mean ◽  
Two Phases ◽  
The Hill

We describe an extensive study of search in GSAT, an approximation procedure for propositional satisfiability. GSAT performs greedy hill-climbing on the number of satisfied clauses in a truth assignment. Our experiments provide a more complete picture of GSAT's search than previous accounts. We describe in detail the two phases of search: rapid hill-climbing followed by a long plateau search. We demonstrate that when applied to randomly generated 3SAT problems, there is a very simple scaling with problem size for both the mean number of satisfied clauses and the mean branching rate. Our results allow us to make detailed numerical conjectures about the length of the hill-climbing phase, the average gradient of this phase, and to conjecture that both the average score and average branching rate decay exponentially during plateau search. We end by showing how these results can be used to direct future theoretical analysis. This work provides a case study of how computer experiments can be used to improve understanding of the theoretical properties of algorithms.

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