scholarly journals A tortoise–hare pattern seen in adapting structured and unstructured populations suggests a rugged fitness landscape in bacteria

2015 ◽  
Vol 112 (24) ◽  
pp. 7530-7535 ◽  
Author(s):  
Joshua R. Nahum ◽  
Peter Godfrey-Smith ◽  
Brittany N. Harding ◽  
Joseph H. Marcus ◽  
Jared Carlson-Stevermer ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Structured Populations ◽  
Adaptive Landscape ◽  
Multiple Peaks ◽  
Structured Population ◽  
Shifting Balance ◽  
Genetic Epistasis ◽  
Rugged Topography ◽  
Landscape Genetic ◽  
Average Fitness

In the context of Wright’s adaptive landscape, genetic epistasis can yield a multipeaked or “rugged” topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to fix rapidly on one, which may not be the highest peak. In a spatially structured population, on the other hand, beneficial mutations take longer to spread. This slowdown allows distant parts of the population to explore the landscape semiindependently. Such a population can simultaneously discover multiple peaks, and the genotype at the highest discovered peak is expected to dominate eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the fable of the tortoise and the hare, the structured population (tortoise) starts relatively slow but eventually surpasses the unstructured population (hare) in average fitness. In contrast, on single-peak landscapes that lack epistasis, all uphill paths converge. Given such “smooth” topography, breadth of search is devalued and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the tortoise–hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a tortoise–hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright’s shifting balance process.

scholarly journals How the tortoise beats the hare: Slow and steady adaptation in structured populations suggests a rugged fitness landscape in bacteria

2014 ◽  
Author(s):  
Joshua R. Nahum ◽  
Peter Godfrey-Smith ◽  
Brittany N. Harding ◽  
Joseph H. Marcus ◽  
Jared Carlson-Stevermer ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Structured Populations ◽  
Adaptive Landscape ◽  
Multiple Peaks ◽  
Structured Population ◽  
Shifting Balance ◽  
Genetic Epistasis ◽  
Rugged Topography ◽  
Landscape Genetic ◽  
Average Fitness

In the context of Wright's adaptive landscape, genetic epistasis can yield a multi-peaked or "rugged" topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to rapidly fix on one, which may not be the highest peak. Contrarily, beneficial mutations in a population with spatially restricted migration take longer to fix, allowing distant parts of the population to explore the landscape semi-independently. Such a population can simultaneous discover multiple peaks and the genotype at the highest discovered peak is expected to fix eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the Tortoise-Hare fable, the structured population (Tortoise) starts relatively slow, but eventually surpasses the unstructured population (Hare) in average fitness. In contrast, on single-peak landscapes (e.g., systems lacking epistasis), all uphill paths converge. Given such "smooth" topography, breadth of search is devalued, and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the Tortoise-Hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we then explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a Tortoise-Hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright's Shifting Balance Process.

Network Centric Warfare as Complex Optimization: An Evolutionary Approach

2016 ◽  
Vol 15 (2) ◽  
pp. 93-105
Author(s):  
Zoltán Jobbágy
Keyword(s):  
Optimization Problem ◽  
Fitness Landscape ◽  
Balance Theory ◽  
Military Operations ◽  
Shifting Balance Theory ◽  
Number Of Genes ◽  
Shifting Balance ◽  
Complex Optimization ◽  
Optimal Values ◽  
Different Characteristics

Military operations are very complex undertakings. However, complexity is not a feature unique to military operations. When biologists wanted to understand the properties of gene mutation they also faced complexity. Confronted by a large number of genes featuring different characteristics, a difficult-to-decode interac- tion among those genes, and an environment that could not be excluded as a factor, Sewell Wright introduced the shifting balance theory, also known as the theory of the fitness landscape. The theory allows complexity to be seen as a process that rests on adaptation and mutation. These two processes are also central to military operations as it is imperative to offset the changing conditions coming both from the environment and the interaction with the enemy. In the article the author uses Wright’s theory to help see military operations as a complex optimization problem that includes approximations and estimations regarding optimal values.

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.

scholarly journals Negotiation and appeasement can be more effective drivers of sociality than kin selection

2016 ◽  
Vol 371 (1687) ◽  
pp. 20150089 ◽  
Author(s):  
Andrés E. Quiñones ◽  
G. Sander van Doorn ◽  
Ido Pen ◽  
Franz J. Weissing ◽  
Michael Taborsky
Keyword(s):  
Genetic Relatedness ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Conditional Cooperation ◽  
Negotiation Strategies ◽  
Structured Population ◽  
The Face ◽  
Kin Structure ◽  
Invasion Analysis ◽  
Individual Based Simulation

Two alternative frameworks explain the evolution of cooperation in the face of conflicting interests. Conflicts can be alleviated by kinship, the alignment of interests by virtue of shared genes, or by negotiation strategies, allowing mutually beneficial trading of services or commodities. Although negotiation often occurs in kin-structured populations, the interplay of kin- and negotiation-based mechanisms in the evolution of cooperation remains an unresolved issue. Inspired by the biology of a cooperatively breeding fish, we developed an individual-based simulation model to study the evolution of negotiation-based cooperation in relation to different levels of genetic relatedness. We show that the evolution of negotiation strategies leads to an equilibrium where subordinates appease dominants by conditional cooperation, resulting in high levels of help and low levels of aggression. This negotiation-based equilibrium can be reached both in the absence of relatedness and in a kin-structured population. However, when relatedness is high, evolution often ends up in an alternative equilibrium where subordinates help their kin unconditionally. The level of help at this kin-selected equilibrium is considerably lower than at the negotiation-based equilibrium, and it corresponds to a level reached when responsiveness is prevented from evolving in the simulations. A mathematical invasion analysis reveals that, quite generally, the alignment of payoffs due to the relatedness of interaction partners tends to impede selection for harsh but effective punishment of defectors. Hence kin structure will often hamper rather than facilitate the evolution of productive cooperation.

scholarly journals An inclusive fitness analysis of synergistic interactions in structured populations

2012 ◽  
Vol 279 (1747) ◽  
pp. 4596-4603 ◽  
Author(s):  
Peter Taylor ◽  
Wes Maciejewski
Keyword(s):  
Frequency Dependence ◽  
Allele Frequency ◽  
Inclusive Fitness ◽  
Selective Advantage ◽  
Structured Populations ◽  
Weak Selection ◽  
Synergistic Interactions ◽  
Fitness Effects ◽  
Structured Population

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner's dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p . We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.

scholarly journals NUMERICAL CONTINUATION OF EQUILIBRIA OF PHYSIOLOGICALLY STRUCTURED POPULATION MODELS I: THEORY

2001 ◽  
Vol 11 (06) ◽  
pp. 1101-1127 ◽  
Author(s):  
MARKUS A. KIRKILIONIS ◽  
ODO DIEKMANN ◽  
BERT LISSER ◽  
MARGREET NOOL ◽  
BEN SOMMEIJER ◽  
...  
Keyword(s):  
Local Stability ◽  
Numerical Procedure ◽  
Structured Populations ◽  
Numerical Continuation ◽  
Structured Population Models ◽  
Structured Population ◽  
Local Stability Analysis ◽  
Interaction Variables ◽  
Physiologically Structured Populations ◽  
Physiologically Structured Population Models

The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe such populations, we use integral equations coupled with each other via interaction (or feedback) variables. Additionally we allow interaction with unstructured populations, described by ordinary differential equations. The interaction variables are chosen such that if they are given functions of time, each of the resulting decoupled equations becomes linear. Our numerical procedure to approximate an equilibrium which will use this special form of the underlying equations extensively. We also establish a method for local stability analysis of equilibria in dependence on parameters.

Assessing the Likelihood of Recurrence during RNA Evolution in Vitro

2004 ◽  
Vol 10 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Niles Lehman
Keyword(s):  
Fitness Landscape ◽  
Initial Point ◽  
Living System ◽  
Test Tube ◽  
Adaptive Landscape ◽  
Local Optimum ◽  
Evolution Experiment ◽  
Efficient Selection ◽  
Insight Into

Recurrence is the possibility of resulting in the same endpoint multiple times when a living system is allowed to evolve repeatedly starting from a given initial point. This concept is of concern to both evolutionary theoreticians and molecular biologists who use nucleic acid selection techniques to mimic biotic and computorial processes in the test tube. Using the continuous in vitro evolution methodology, many replicate experimental evolutionary lineages with populations of catalytic RNA were performed to gain insight into the parameters that could affect recurrence. The likelihood that the same genotype will result in parallel trials of an evolution experiment in vitro depends on several factors, including the phenotype under selection, the size and composition of the initial diverse pool of nucleic acids used in the experiment, the degree of mutation possible during the experiment, the shape of the fitness landscape through which the population evolves, and the strategies used to invoke selection and to search the landscape, among others. By considering these factors, it can be predicted that recurrence is more likely when a small, wild-type-based starting pool is used with efficient selection and search strategies involving little online mutagenesis within a rugged adaptive landscape with a strong local optimum. The recurrence experiments performed here on the 150-nucleotide ligase ribozyme demonstrate that it repeatedly jumps from one peak in a fitness landscape to another, apparently hurdling a deep fitness valley. These predictions can and should be tested by additional multiple replicates of actual evolution experiments in the laboratory.

scholarly journals Fitness benefits of low infectivity in a spatially structured population of bacteriophages

2014 ◽  
Vol 281 (1774) ◽  
pp. 20132563 ◽  
Author(s):  
Pavitra Roychoudhury ◽  
Neelima Shrestha ◽  
Valorie R. Wiss ◽  
Stephen M. Krone
Keyword(s):  
Transmission Rate ◽  
Burst Size ◽  
Structured Populations ◽  
Host Cells ◽  
Structured Population ◽  
Spatially Structured Populations ◽  
Lysis Time ◽  
Evolution Experiment ◽  
Spatially Structured Population ◽  
And Diffusion

For a parasite evolving in a spatially structured environment, an evolutionarily advantageous strategy may be to reduce its transmission rate or infectivity. We demonstrate this empirically using bacteriophage (phage) from an evolution experiment where spatial structure was maintained over 550 phage generations on agar plates. We found that a single substitution in the major capsid protein led to slower adsorption of phage to host cells with no change in lysis time or burst size. Plaques formed by phage isolates containing this mutation were not only larger but also contained more phage per unit area. Using a spatially explicit, individual-based model, we showed that when there is a trade-off between adsorption and diffusion (i.e. less ‘sticky’ phage diffuse further), slow adsorption can maximize plaque size, plaque density and overall productivity. These findings suggest that less infective pathogens may have an advantage in spatially structured populations, even when well-mixed models predict that they will not.

scholarly journals Lexical landscapes as largein silicodata for examining advanced properties of fitness landscapes

2019 ◽  
Author(s):  
Victor A. Meszaros ◽  
Miles D. Miller-Dickson ◽  
C. Brandon Ogbunugafor
Keyword(s):  
Evolutionary Theory ◽  
Empirical Data ◽  
In Silico ◽  
Evolutionary Biology ◽  
Fitness Landscape ◽  
Evolutionary Genetics ◽  
Higher Order ◽  
Fitness Landscapes ◽  
Adaptive Landscape ◽  
Data Sets

In silicoapproaches have served a central role in the development of evolutionary theory for generations. This especially applies to the concept of the fitness landscape, one of the most important abstractions in evolutionary genetics, and one which has benefited from the presence of large empirical data sets only in the last decade or so. In this study, we propose a method that allows us to generate enormous data sets that walk the line betweenin silicoand empirical: word usage frequencies as catalogued by the Google ngram corpora. These data can be codified or analogized in terms of a multidimensional empirical fitness landscape towards the examination of advanced concepts—adaptive landscape by environment interactions, clonal competition, higher-order epistasis and countless others. We argue that the greaterLexical Landscapesapproach can serve as a platform that offers an astronomical number of fitness landscapes for exploration (at least) or theoretical formalism (potentially) in evolutionary biology.

Fisherian and Wrightian theories of speciation

Genome ◽  
1989 ◽  
Vol 31 (1) ◽  
pp. 221-227 ◽  
Author(s):  
Russell Lande
Keyword(s):  
Sexual Selection ◽  
Genetic Drift ◽  
Chromosomal Rearrangements ◽  
Adaptive Landscape ◽  
Random Genetic Drift ◽  
Premating Isolation ◽  
Sympatric Populations ◽  
Mating Preferences ◽  
Intermediate Phenotypes ◽  
Shifting Balance

Fisher's theory of sexual selection, Wright's shifting-balance theory, and recent models based on them are reviewed as mechanisms of animal speciation. The joint evolution of mating preferences and secondary sexual characters can cause rapid nonadaptive phenotypic divergence and premating isolation between geographically separated populations, or along a cline. Extensive comparative data on Drosophila species support the suggestion of R. A. Fisher and T. Dobzhansky that the evolution of mating preferences can reinforce partial postmating isolation between sympatric populations. The interaction of natural selection and random genetic drift in local populations with a small effective size can produce a rapid transition between relatively stable phenotypes separated by an adaptive valley, or between chromosomal rearrangements with a heterozygote disadvantage. Large demographic fluctuations, such as frequent random local extinction and colonization, are required for the rapid spread of new adaptations (or karyotypes) when intermediate phenotypes (or rearrangement heterozygotes) are selected against.Key words: reproductive isolation, hybridization, sexual selection, reinforcement, subdivided population, shifting balance, adaptive landscape, random genetic drift.

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