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These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…

Disordered Systems and Neural Networks · Physics 2007-05-23 Luca Peliti

We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…

Populations and Evolution · Quantitative Biology 2026-05-12 Mingtao Xia , Tom Chou

Great apes, the other living members of our hominid family, become decrepit before the age of forty and rarely outlive their fertile years. In contrast, women - even in high mortality hunter-gatherer populations - usually remain healthy and…

Populations and Evolution · Quantitative Biology 2019-07-01 Peter S. Kim , John S. McQueen , Kristen Hawkes

We analyze the growth rates of atmospheric carbon dioxide and human population, by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive…

Atmospheric and Oceanic Physics · Physics 2015-03-17 Andreas D. Hüsler , Didier Sornette

Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…

Populations and Evolution · Quantitative Biology 2008-12-04 Anders Eriksson

Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…

Populations and Evolution · Quantitative Biology 2022-06-28 Emanuele Crosato , Jeffrey N. Philippson , Shashi Thutupalli , Richard G. Morris

In this paper, we consider a mathematical model for the evolution of neutral genetic diversity in a spatial continuum including mutations, genetic drift and either short range or long range dispersal. The model we consider is the spatial $…

Probability · Mathematics 2022-10-04 Raphaël Forien

Human intelligence, the most evident and accessible form of source of reasoning, hosted by biological hardware, has evolved and been refined over thousands of years, positioning itself today to create new artificial forms and preparing to…

Artificial Intelligence · Computer Science 2025-12-09 Suayb S. Arslan

Here we study the emergence of spontaneous leadership in large populations. In standard models of opinion dynamics, herding behavior is only obeyed at the local scale due to the interaction of single agents with their neighbors; while at…

Physics and Society · Physics 2015-06-11 Guillem Mosquera-Donate , Marian Boguna

The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…

Disordered Systems and Neural Networks · Physics 2009-10-30 David R. Nelson , Nadav M. Shnerb

Generative models trained on finite data face a fundamental tension: their score-matching or next-token objective converges to the empirical training distribution rather than the population distribution we seek to learn. Using rule-valid…

Machine Learning · Computer Science 2026-05-12 Binxu Wang , Emma Lucia Byrnes Finn , Bingbin Liu

Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (heavy right-tailed offspring number distribution) is central for…

Populations and Evolution · Quantitative Biology 2026-01-16 Bjarki Eldon

How the very first nervous systems evolved remains a fundamental open question. Molecular and genomic techniques have revolutionized our knowledge of the molecular ingredients behind this transition but not yet provided a clear picture of…

Neurons and Cognition · Quantitative Biology 2017-10-31 Ronald A. J. van Elburg , Oltman O. de Wiljes , Michael Biehl , Fred A. Keijzer

About 45,000 years ago, symbolic and technological complexity of human artefacts increased drastically. Computer simulations of Powell, Shennan and Thomas (2009) explained it through an increase of the population density, facilitating the…

Physics and Society · Physics 2015-05-30 M. A. Sumour , M. A. Radwan , M. M. Shabat , Ali H. El-Astal

We consider models of growing multi-level systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy…

Physics and Society · Physics 2015-06-17 Agnieszka Czaplicka , Krzysztof Suchecki , Borja Minano , Miquel Trias , Janusz A. Holyst

How did the human species evolve the capacity not just to communicate complex ideas to one another but to hold such conversations from across the globe, using remote devices constructed from substances that do not exist in the natural…

Neurons and Cognition · Quantitative Biology 2019-07-09 Liane Gabora , Anne Russon

In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…

Probability · Mathematics 2024-07-09 Nicolas Champagnat , Vincent Hass

Darwin introduced the concept of the "living fossil" to describe species belonging to lineages that have experienced little evolutionary change, and suggested that species in more slowly evolving lineages are more prone to extinction (1).…

Genomics · Quantitative Biology 2013-02-12 Bianca Sclavi , John Herrick

Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and…

Populations and Evolution · Quantitative Biology 2009-11-13 Muyoung Heo , Louis Kang , Eugene I. Shakhnovich

Demographic transition, characterized by declines in fertility and mortality, is a global phenomenon associated with modernization. While typical patterns of fertility decline are observed in Western countries, their applicability to other…

Physics and Society · Physics 2025-01-31 Kenji Itao
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