Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. That the underlying topology can substantially affect the results of the evolutionary process is seen most clearly in a paper by Erez Lieberman, Christoph Hauert and Martin Nowak. In evolutionary graph theory, individuals occupy vertices of a weighted directed graph and the weight wi j of an edge from vertex i to vertex j denotes the probability of i replacing j. The weight corresponds to the biological notion of fitness where fitter types propagate more readily. One property studied on graphs with two types of individuals is the fixation probability, which is defined as the probability that a single, randomly placed mutant of type A will replace a population of type B. According to the isothermal theorem, a graph has the same fixation probability as the corresponding Moran process if and only if it is isothermal, thus the sum of all weights that lead into a vertex is the same for all vertices. Thus, for example, a complete graph with equal weights describes a Moran process. The fixation probability is where r is the relative fitness of the invading type. Graphs can be classified into amplifiers of selection and suppressors of selection. If the fixation probability of a single advantageous mutation is higher than the fixation probability of the corresponding Moran process then the graph is an amplifier, otherwise a suppressor of selection. One example of the suppressor of selection is a linear process where only vertex i-1 can replace vertex i (but not the other way around). In this case the fixation probability is (where N is the number of vertices) since this is the probability that the mutation arises in the first vertex which will eventually replace all the other ones. Since for all r greater than 1, this graph is by definition a suppressor of selection. Evolutionary graph theory may also be studied in a dual formulation, as a , or as a stochastic process. We may consider the mutant population on a graph as a random walk between absorbing barriers representing mutant extinction and mutant fixation. For highly symmetric graphs, we can then use martingales to find the fixation probability as illustrated by Monk (2018). Also evolutionary games can be studied on graphs where again an edge between i and j means that these two individuals will play a game against each other. Closely related stochastic processes include the voter model, which was introduced by Clifford and Sudbury (1973) and independently by Holley and Liggett (1975), and which has been studied extensively. (Wikipedia).
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph Theory
Graph Theory: 02. Definition of a Graph
In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio
From playlist Graph Theory part-1
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
An introduction to the field of Graph Theory, the study of networks Algorithms repository: https://github.com/williamfiset/algorithms#graph-theory Slides: https://github.com/williamfiset/Algorithms/tree/master/slides/graphtheory Graph Theory Videos: https://www.youtube.com/playlist?list
From playlist Graph Theory Playlist
What is a Path Graph? | Graph Theory
What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can
From playlist Graph Theory
Graph Theory FAQs: 01. More General Graph Definition
In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o
From playlist Graph Theory FAQs
This lesson introduces graph theory and defines the basic vocabulary used in graph theory. Site: http://mathispower4u.com
From playlist Graph Theory
In this tutorial I explore the concepts of walks, trails, paths, cycles, and the connected graph.
From playlist Introducing graph theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Jake Scott: Incorporating ecological epistasis into evolutionary control of cancer
HYBRID EVENT Recorded during the meeting " Dynamics and Statistics of Cancer Evolution : Applying Mathematics to Experimental and Clinical Data " the June 07, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this vi
From playlist Virtual Conference
Lecture 1: Combinatorial problems on trees inside phylogenetic networks
🌟There is a further part to this video. If you are interested in, watch the next video🌟 ➔ https://youtu.be/y1UfsYTrlXo This video is one of the two introductory lectures (Introduction to Discrete Mathematical Biology) given by Momoko Hayamizu as part of an omnibus lecture series "Advanced
From playlist 2020 Advanced Topic in Modern Mathematical Sciences 2
Statistical Rethinking 2022 Lecture 16 - Gaussian Processes
Slides and other course materials: https://github.com/rmcelreath/stat_rethinking_2022 Intro: https://www.youtube.com/watch?v=uYNzqgU7na4 Music: https://www.youtube.com/watch?v=kXuasY8pDpA Music: https://www.youtube.com/watch?v=eTtTB0nZdL0 Pause: https://www.youtube.com/watch?v=pxPdsqrQByM
From playlist Statistical Rethinking 2022
Structure, function, and evolution of gene regulatory networks by Erik van Nimwegen
Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S
From playlist Winter School on Quantitative Systems Biology
Evolution as a Population-Genetic Process (Lecture 2) by Michael Lynch
PROGRAM FIFTH BANGALORE SCHOOL ON POPULATION GENETICS AND EVOLUTION (ONLINE) ORGANIZERS: Deepa Agashe (NCBS, India) and Kavita Jain (JNCASR, India) DATE: 17 January 2022 to 28 January 2022 VENUE: Online No living organism escapes evolutionary change, and evolutionary biology thus conn
From playlist Fifth Bangalore School on Population Genetics and Evolution (ONLINE) 2022
Matteo Smerlak - Aspects of evolutionary dynamics from viruses to whales
Our interdisciplinary group studies ecological and evolutionary dynamics across scales. In this video I present a selection of recent results that illustrate the role of mathematics in furthering our understanding of biological evolution: (1) a formalization of the concept of “selection”
From playlist Research Spotlight
Research talks by Nisheeth Vishno
Second Bangalore School on Population Genetics and Evolution URL: http://www.icts.res.in/program/popgen2016 DESCRIPTION: Just as evolution is central to our understanding of biology, population genetics theory provides the basic framework to comprehend evolutionary processes. Population
From playlist Second Bangalore School on Population Genetics and Evolution
Lec 31 | MIT 7.014 Introductory Biology, Spring 2005
Population Genetics and Evolution (Prof. Martin Polz, Guest Lecturer) View the complete course: http://ocw.mit.edu/7-014S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 7.014 Introductory Biology, Spring 2005
Fitness landscapes in theory and application by Joachim Krug
The Third Bangalore School on Population Genetics and Evolution DATE:05 March 2018 to 17 March 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore. No living organism escapes evolutionary change. Evolutionary biology thus connects all biological disciplines. To understand the processes dri
From playlist Third Bangalore School on Population Genetics and Evolution
Introduction to Graph Theory: A Computer Science Perspective
In this video, I introduce the field of graph theory. We first answer the important question of why someone should even care about studying graph theory through an application perspective. Afterwards, we introduce definitions and essential terminology in graph theory, followed by a discuss
From playlist Graph Theory
Mutation, Selection and Evolutionary Rescue in Simple Phenotype....(Lecture 1) by Guillaume Martin
PROGRAM FIFTH BANGALORE SCHOOL ON POPULATION GENETICS AND EVOLUTION (ONLINE) ORGANIZERS: Deepa Agashe (NCBS, India) and Kavita Jain (JNCASR, India) DATE: 17 January 2022 to 28 January 2022 VENUE: Online No living organism escapes evolutionary change, and evolutionary biology thus conn
From playlist Fifth Bangalore School on Population Genetics and Evolution (ONLINE) 2022