Measures of success in a class of evolutionary models with fixed population size and structure

Allen, Benjamin; Tarnita, Corina E.

doi:10.1007/s00285-012-0622-x

Cited by 81 publications

(153 citation statements)

References 85 publications

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“…While computational graph theorists have examined many subtleties pertaining to deme structure [4,[13][14][15][16][17][18][19][20], and for frequency-dependent selection in particular [5,[21][22][23][24][25][26], the broader issue of fixation probability and its relationship to the rate of evolution has received little attention.…”

Section: Introductionmentioning

confidence: 99%

The effect of population structure on the rate of evolution

2013

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Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by 'star graphs', that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.

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Section: Introductionmentioning

confidence: 99%

The effect of population structure on the rate of evolution

2013

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“…These assumptions can be highly specific, applying only to particular biological situations, or broad, applying to a wide range of scenarios. Modeling frameworks that rely on general (yet precise) assumptions have recently emerged as a powerful tool for studying the evolution of populations structured spatially (39)(40)(41)(42), by groups (43), and physiologically (44)(45)(46); the evolution of continuous traits (47)(48)(49); and inclusive fitness theory itself (in cases where fitness effects are additive and other requirements are satisfied) (7,19). Although these frameworks can be used to obtain general results, none of them is universal or assumption-free.…”

Section: Common-sense Approaches To Evolutionary Theorymentioning

confidence: 99%

Limitations of inclusive fitness

Allen

Nowak

Wilson

2013

Proc. Natl. Acad. Sci. U.S.A.

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Until recently, inclusive fitness has been widely accepted as a general method to explain the evolution of social behavior. Affirming and expanding earlier criticism, we demonstrate that inclusive fitness is instead a limited concept, which exists only for a small subset of evolutionary processes. Inclusive fitness assumes that personal fitness is the sum of additive components caused by individual actions. This assumption does not hold for the majority of evolutionary processes or scenarios. To sidestep this limitation, inclusive fitness theorists have proposed a method using linear regression. On the basis of this method, it is claimed that inclusive fitness theory (i) predicts the direction of allele frequency changes, (ii) reveals the reasons for these changes, (iii) is as general as natural selection, and (iv) provides a universal design principle for evolution. In this paper we evaluate these claims, and show that all of them are unfounded. If the objective is to analyze whether mutations that modify social behavior are favored or opposed by natural selection, then no aspect of inclusive fitness theory is needed.social evolution | Hamilton's rule | cooperation | kin selection

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“…Evolutionary games have a long history of being studied on spatial lattices (28,(39)(40)(41)(42) and, more recently, on graphs (7,27,43,44). The crucial quantity that needs to be calculated to evaluate natural selection is the fixation probability, ρ, of a newly introduced mutant that arises at a random position on the graph.…”

Section: Significancementioning

confidence: 99%

Computational complexity of ecological and evolutionary spatial dynamics

Ibsen-Jensen

Chatterjee

Nowak

2015

Proc. Natl. Acad. Sci. U.S.A.

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There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant) will take over a resident population? We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP).evolutionary games | fixation probability | complexity classes E volution occurs in populations of reproducing individuals. Mutation generates distinct types. Selection favors some types over others. The mathematical formalism of evolution describes how populations change in their genetic (or phenotypic) composition over time. Deterministic models of evolution are based on differential equations. They assume infinitely large population size and ignore demographic and other stochasticity. The more precise descriptions of evolutionary dynamics, however, use stochastic processes, which take into account the intrinsic randomness of when and where individuals reproduce and how many of their offspring survive. They also describe populations of finite size.A well-known stochastic process of evolution was formulated by Moran in 1958 (1). In any one-time step, a random individual is chosen proportional to fitness for reproduction and a random individual is chosen for death. The offspring of the first individual is added to the population. The total population size remains constant and is given by N. The original process was formulated for constant fitness, which means the fitness value of individuals does not depend on the relative abundance of various types in the population; it is a fixed number. The crucial question is: What is the probability that a newly introduced mutant will generate a lineage that takes over the entire population? This quantity is called the fixation probability. For the original Moran process, the...

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Measures of success in a class of evolutionary models with fixed population size and structure

Cited by 81 publications

References 85 publications

The effect of population structure on the rate of evolution

The effect of population structure on the rate of evolution

Limitations of inclusive fitness

Computational complexity of ecological and evolutionary spatial dynamics

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