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"Evolution (Biology) Mathematics."
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The Calculus of Selfishness
How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the \"invisible hand\" that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation.
eBook
Sciencia : mathematics, physics, chemistry, biology, and astronomy for all
\"From the structure of the cosmos to that of the human body, the discoveries of science over the past few hundred years have been remarkable. Sciencia spans the realms of mathematics, physics, chemistry, biology, and astronomy, offering an invaluable introduction to each. Curious about quarks, quasars, and the fantastic universe around you? Ever wanted to explore a mathematical proof? Need an introduction to biochemistry? Beautifully illustrated with engravings, woodcuts, and original drawings and diagrams, Sciencia will inspire inquisitive readers of all ages to appreciate the interconnected knowledge of the modern sciences\"--Page 4 of cover.
Book
Mathematics of evolution and phylogeny
This book considers evolution at different scales: sequences, genes, gene families, organelles, genomes and species. The focus is on the mathematical and computational tools and concepts, which form an essential basis of evolutionary studies, indicate their limitations, and give them orientation. Recent years have witnessed rapid progress in the mathematics of evolution and phylogeny, with models and methods becoming more realistic, powerful, and complex. Aimed at graduates and researchers in phylogenetics, mathematicians, computer scientists and biologists, and including chapters by leading scientists: A. Bergeron, D. Bertrand, D. Bryant, R. Desper, O. Elemento, N. El-Mabrouk, N. Galtier, O. Gascuel, M. Hendy, S. Holmes, K. Huber, A. Meade, J. Mixtacki, B. Moret, E. Mossel, V. Moulton, M. Pagel, M.-A. Poursat, D. Sankoff, M. Steel, J. Stoye, J. Tang, L.-S. Wang, T. Warnow, Z. Yang, this book of contributed chapters explains the basis and covers the recent results in this highly topical area.
eBook
Analysis of Evolutionary Processes
Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. InAnalysis of Evolutionary Processes, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics.
After introducing the basics of evolutionary processes and classifying available modeling approaches, Dercole and Rinaldi give a detailed presentation of the derivation of the AD canonical equation, an ordinary differential equation that focuses on evolutionary processes driven by rare and small innovations. The authors then look at important features of evolutionary dynamics as viewed through the lens of AD. They present their discovery of the first chaotic evolutionary attractor, which calls into question the common view that coevolution produces exquisitely harmonious adaptations between species. And, opening up potential new lines of research by providing the first application of AD to economics, they show how AD can explain the emergence of technological variety.
Analysis of Evolutionary Processeswill interest anyone looking for a self-contained treatment of AD for self-study or teaching, including graduate students and researchers in mathematical and theoretical biology, applied mathematics, and theoretical economics.
eBook
Fixation probabilities in evolutionary dynamics under weak selection
In evolutionary dynamics, a key measure of a mutant trait’s success is the probability that it takes over the population given some initial mutant-appearance distribution. This “fixation probability” is difficult to compute in general, as it depends on the mutation’s effect on the organism as well as the population’s spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation’s effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant’s fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.
Journal Article
Classes of explicit phylogenetic networks and their biological and mathematical significance
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks that describe such complex processes have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of phylogenetic networks from empirical data.
Journal Article
A discrete-time dynamical system and an evolution algebra of mosquito population
Recently, continuous-time dynamical systems of mosquito populations have been studied. In this paper, we consider a discrete-time dynamical system, generated by an evolution quadratic operator of a mosquito population, and show that this system has two fixed points, which become saddle points under some conditions on the parameters of the system. We construct an evolution algebra, taking its matrix of structural constants equal to the Jacobian of the quadratic operator at a fixed point. Idempotent and absolute nilpotent elements, simplicity properties, and some limit points of the evolution operator corresponding to the evolution algebra are studied. We give some biological interpretations of our results.
Journal Article
Extended nonlinear variational like-inequalities driven by system of fractional evolutionary equations
In this article, we consider an extended evolutionary system involving fractional differential variational-like inequalities. The system consists of a nonlinear mixed variational-like inequality and an extended fractional differential equation in a complete normed linear space. We examine the non-emptiness, closedness, boundedness and convexity of solution set for the considered nonlinear mixed variational-like inequality in this setting. Furthermore, we establish upper semicontinuity and measurability of set valued solution map of the mixed quasi-variational inequality with respect to both state variable and time variable. Additionally, the existence of mild solutions for the system is shown by means of fractional operator theory, Bohnenblust-Karlin fixed point theorem for multivalued mappings and operator semigroup theory. We conclude by a numerical example, with the response times for different values of
α
.
Journal Article
Evolution of dispersal in open advective environments
We consider a two-species competition model in a one-dimensional advective environment, where individuals are exposed to unidirectional flow. The two species follow the same population dynamics but have different random dispersal rates and are subject to a net loss of individuals from the habitat at the downstream end. In the case of non-advective environments, it is well known that lower diffusion rates are favored by selection in spatially varying but temporally constant environments, with or without net loss at the boundary. We consider several different biological scenarios that give rise to different boundary conditions, in particular hostile and “free-flow” conditions. We establish the existence of a critical advection speed for the persistence of a single species. We derive a formula for the invasion exponent and perform a linear stability analysis of the semi-trivial steady state under free-flow boundary conditions for constant and linear growth rate. For homogeneous advective environments with free-flow boundary conditions, we show that populations with higher dispersal rate will always displace populations with slower dispersal rate. In contrast, our analysis of a spatially implicit model suggest that for hostile boundary conditions, there is a unique dispersal rate that is evolutionarily stable. Nevertheless, both scenarios show that unidirectional flow can put slow dispersers at a disadvantage and higher dispersal rate can evolve.
Journal Article