Darwinian evolution as a dynamical principle

Kocher, Charles; Dill, Ken A.

doi:10.1073/pnas.2218390120

Cited by 10 publications

(14 citation statements)

References 59 publications

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“…Last but not least, we are presently developing a study of the non-equilibrium properties of evolution (such as entropy production) within our framework, allowing us to quantify "evolutionary irreversibility", both at a microscopic and macroscopic levels, complementing recent and exciting results [167][168][169][170].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Statistical mechanics of phenotypic eco-evolution: from adaptive dynamics to complex diversification

Sireci¹,

Muñoz²

2023

Preprint

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The ecological and evolutionary dynamics of large sets of individuals can be naturally addressed from a theoretical perspective using ideas and tools from statistical mechanics. This parallelism has been extensively discussed and exploited in the literature, both in the context of population genetics and in phenotypic evolutionary or adaptive dynamics. Following this tradition, here we construct a framework allowing us to derive ‘macroscopic’ evolutionary equations from a rather general ‘microscopic’ stochastic dynamics representing the processes of reproduction, mutation and selection in a large community of individuals, each one characterized by its phenotypic features. In this set up, ecological and evolutionary timescales are intertwined, which makes it particularly suitable to describe microbial communities, a timely topic of utmost relevance. Our framework leads, even in the limit of infinitely large populations, to a probabilistic description of the distribution of individuals in phenotypic space, as encoded in what we call ‘generalized Crow-Kimura equation’ or ‘generalized replicator-mutator equation’. We discuss the limits in which such an equation reduces to the theory of ‘adaptive dynamics’ (i.e. the standard approach to evolutionary dynamics in phenotypic space, which usually focuses on the mean or at most the variance of such distributions). Moreover, we emphasize the aspects of the theory that are beyond the reach of standard adaptive dynamics. In particular, working out, as an example, a simple model of a growing and competing population, we show that the resulting probability distribution can possibly exhibit dynamical phase transitions changing from unimodal to bimodal —by means of an evolutionary branching— or to multimodal, in a cascade of evolutionary branching events. Furthermore, our formalism allows us to rationalize these events as a cascade of ‘dynamical phase transitions’, using the parsimonious approach of Landau’s theory of phase transitions. Finally, we extend the theory to account for finite populations and illustrate the possible consequences of the resulting stochastic or ‘demographic’ effects. Altogether the present framework extends and/or complements existing approaches to evolutionary/adaptive dynamics and paves the way to more systematic studies of e.g. microbial communities as well as to future developments including theoretical analyses of the evolutionary process from the perspective of non-equilibrium statistical mechanics.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Statistical mechanics of phenotypic eco-evolution: from adaptive dynamics to complex diversification

Sireci¹,

Muñoz²

2023

Preprint

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“…1 expresses these properties in the form of a machine-like, biosphere-wide nonequilibrium (NEQ) cycle that we call the Darwinian Evolution Machine (DEM). Described in detail elsewhere (Kocher and Dill, 2023 ), the cycle operates from left to right. ( a ) At time , indicates a wild-type (status quo) population.…”

Section: Description Of Darwinian Dynamics As a Cyclic Machinementioning

confidence: 99%

“…. Peaceful coexistence is captured using a saturating function (Beddington 1975, De Angelis et al 1975, Kocher and Dill 2023, Novak and Stouffer 2021, Stouffer and Novak 2021, ( )…”

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confidence: 99%

“…( 2 ) which simply expresses two natural limits: that maximum concentrations of moms are finite and that speeds of producing offspring are finite. What's novel in the present DEM perspective is the combining of this generalized form of population-genetics Equations 1 with iterative mutation, competition and selection cycles (Kocher and Dill 2023). In the following section, we extract four principles from this DEM perspective that helps us formulate possible molecular precursors in the next sections.…”

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confidence: 99%

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Origins of life: first came evolutionary dynamics

Kocher

Dill

2023

QRB Discovery

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When life arose from prebiotic molecules 3.5 billion years ago, what came first? Informational molecules (RNA, DNA), functional ones (proteins), or something else? We argue here for a different logic: rather than seeking a molecule type, we seek a dynamical process. Biology required an ability to evolve before it could choose and optimize materials. We hypothesize that the evolution process was rooted in the peptide folding process. Modeling shows how short random peptides can collapse in water, catalyze elongation of others, powering both increased folding stability and emergent autocatalysis through a disorder-to-order process. REQUIREMENT FOR LIFE'S ORIGIN: PERSISTENT PROPAGATIONWhat was the origin of life? A pre-requisite for answering that question is to define the difference between dead and alive. Defining life has been notoriously challenging (

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“…In addition, sexual selection, like any other evolutionary force, is not determined by a single condition, such as the production of gametes. Evolution is a dynamic process in which the outcome is the result of complex non‐linear interactions between many forces, from species‐specific to ecological conditions (Kocher & Dill, 2023). Thus, we need to advance our theoretical knowledge about the evolution of sex differences (in care patterns) as a consequence of a dynamic process of the interaction between many selection forces, rather than a simplistic consequence of anisogamy reinforced by positive feedback loops.…”

Section: Introductionmentioning

confidence: 99%

Beyond classical theories: An integrative mathematical model of mating dynamics and parental care

Araujo,

Moura

2023

Journal of Evolutionary Biology

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Classical theories, such as Bateman's principle and Trivers' parental investment theory, attempted to explain the coevolution of sexual selection and parental care through simple verbal arguments. Since then, quantitative models have demonstrated that it is rarely that simple because many non‐intuitive structures and non‐linear relationships are actually at play. In this study, we propose a new standard for models of mating dynamics and parental care, emphasizing the clarity and use of mathematical and probabilistic arguments, the meaning of consistency conditions, and the key role of spatial densities and the law of mass action. We used adaptive dynamics to calculate the evolutionary trajectory of the total care duration. Our results clearly show how the outcomes of parental care evolution can be diverse, depending on the quantitative balance between a set of dynamical forces arising from relevant differences and conditions in the male and female populations. The intensity of sexual selection, synergy of care, care quality, and relative mortality rates during mating interactions and caring activities act as forces driving evolutionary transitions between uniparental and biparental care. Sexual selection reduces the care duration of the selected sex, uniparental care evolves in the sex that offers the higher care quality, higher mortality during mating interactions of one sex leads to more care by that sex, and higher mortality during caring activities of one sex favours the evolution of uniparental care in the other sex. Both synergy and higher overall mortality during mating interactions can stabilize biparental care when sexual selection reduces the care duration of the selected sex. We discuss how the interaction between these forces influences the evolution of care patterns, and how sex ratios can vary and be interpreted in these contexts. We also propose new directions for future developments of our integrative model, creating new comparable analyses that share the same underlying assumptions and dynamical frameworks.

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Darwinian evolution as a dynamical principle

Cited by 10 publications

References 59 publications

Statistical mechanics of phenotypic eco-evolution: from adaptive dynamics to complex diversification

Statistical mechanics of phenotypic eco-evolution: from adaptive dynamics to complex diversification

Origins of life: first came evolutionary dynamics

Beyond classical theories: An integrative mathematical model of mating dynamics and parental care

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