Evolutionary dynamics on any population structure

Allen, Benjamin; Lippner, Gábor; Chen, Yuting; Fotouhi, Babak; Momeni, Naghmeh; Yau, Shing–Tung; Nowak, Martin A.

doi:10.1038/nature21723

Cited by 424 publications

(503 citation statements)

References 65 publications

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“…Social interactions, which are typically multilateral (50) and nonlinear (51,52), cannot be expressed by a single benefit and cost. Complex population structures (43,46,53,54) cannot be captured by a single relatedness quantity. Assortment among relatives often has a positive effect on cooperation (41,(44)(45)(46)(47), but in other cases it has a negative effect (48,55) or no effect at all (42,45).…”

Section: Discussionmentioning

confidence: 99%

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Nowak

McAvoy

Allen

et al. 2017

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

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Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, B, multiplied by relatedness, R, exceeds the cost to self, C. Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to BR − C. This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities B, R, and C should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters B and C depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.amilton's rule is a widely known concept in evolutionary biology. It has become standard textbook knowledge and is encountered in undergraduate education. For many, Hamilton's rule expresses the intuition that cooperation evolves more easily when there are frequent interactions among relatives, because relatives are likely to share the cooperative trait. However, Hamilton's rule goes beyond this intuition by positing a quantitative condition, BR − C > 0, which is said to predict whether or not a trait will be selected. Specifically, it is claimed that the change in average trait value from one time point to the next is proportional to BR − C .We immediately encounter the question of how the "benefit," B , the "relatedness," R, and the "cost," C , are calculated for a given system. Surprisingly, there is no consensus about the correct method. A variety of derivations have been proposed over the years (1-10), which define B , R, and C in distinct (nonequivalent) ways. In the empirical literature, peer reviewers often disagree over which method should be used in a particular manuscript (11).A number of recent papers (7, 9, 10) have endorsed a particular formulation (4, 5) as the exact, general, and even "canonical" version of Hamilton's rule. This formulation, called "Hamilton's rule-general" (HRG) (12, 13), is claimed to be as general as natural selection itself (7,14). The derivation, which we recapitulate below, is simple and contains only a few steps.The mathematical investigation of HRG reveals three astonishing facts. First, HRG is logically incapable of making any prediction about any situation because the benefit, B , and the cost, C , cannot be known in advance. They depend on the data that are to be predicted. At the outset of an experiment, B and C are unknown, and so there is no way to say what Hamilton's rule would predict. Once the experiment is ...

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Section: Discussionmentioning

confidence: 99%

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Nowak

McAvoy

Allen

et al. 2017

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

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“…Our generalized, axiomatic definition of information enables this framework to be applied to a variety of physical, biological, social, and economic systems. In particular, we envision applications to spin systems [1,17,83,84], gene regulatory systems [85][86][87][88][89][90][91], neural systems [92][93][94], biological swarming [95][96][97], spatial evolutionary dynamics [82,98,99], and financial markets [22,59,81,[100][101][102][103][104][105].…”

Section: Potential Applicationsmentioning

confidence: 99%

Multiscale Information Theory and the Marginal Utility of Information

Allen

Stacey

Bar‐Yam

2017

Entropy

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Complex systems display behavior at a range of scales. Large-scale behaviors can emerge from the correlated or dependent behavior of individual small-scale components. To capture this observation in a rigorous and general way, we introduce a formalism for multiscale information theory. Dependent behavior among system components results in overlapping or shared information. A system's structure is revealed in the sharing of information across the system's dependencies, each of which has an associated scale. Counting information according to its scale yields the quantity of scale-weighted information, which is conserved when a system is reorganized. In the interest of flexibility we allow information to be quantified using any function that satisfies two basic axioms. Shannon information and vector space dimension are examples. We discuss two quantitative indices that summarize system structure: an existing index, the complexity profile, and a new index, the marginal utility of information. Using simple examples, we show how these indices capture the multiscale structure of complex systems in a quantitative way.

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“…Understanding evolution and ecology in such spatially extended systems is a challenging and long-studied problem [29–33]. Recent studies have demonstrated rich dynamics when inter-cellular interactions are defined on heterogeneous complex networks [34–36], where spatial structure can (for example) promote invasive strategies in tumor models [35] or modulate fixation times on random landscapes [34]. Remarkably, in the weak selection limit, evolutionary dynamics can be solved for any population structure [36], providing extensive insight into game-theoretic outcomes on complex networks.…”

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confidence: 99%

Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance

Jong

Wood

2018

Phys. Rev. Lett.

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Spatial heterogeneity plays an important role in the evolution of drug resistance. While recent studies have indicated that spatial gradients of selection pressure can accelerate resistance evolution, much less is known about evolution in more complex spatial profiles. Here we use a stochastic toy model of drug resistance to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. Interestingly, there exists an intermediate regime—characterized by comparable rates of migration and mutation—in which the rate of fixation can be either accelerated or decelerated depending on the spatial profile, even when spatially averaged selection pressure remains constant. Finally, we demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Our results may lay the groundwork for optimized, spatially-resolved drug dosing strategies for mitigating the effects of drug resistance.

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Evolutionary dynamics on any population structure

Cited by 424 publications

References 65 publications

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Multiscale Information Theory and the Marginal Utility of Information

Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance

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