Logistic model

A resource consumption view

Consider a resource consumption model that follows the density of a single microbial species through time \(N(t)\) and the density of that species’ limiting resource \(R(t)\):

\[ \frac{dR}{dt} = -a R N \ \frac{dN}{dt} = \epsilon a R N \]

where \(a\) is ...

Yesterday (June 17th, 2015) we organized the 1^st students poster session of the Python Programming for Biologists course in Tel-Aviv University. In the poster session, the students presented the research they did using things they learned during the course (sequence data analysis, mathematical modeling of population dynamics, statistical analysis ...

Following Gordo & Charlesworth (2000).

This Wright-Fisher model starts with a haploid asexual population at a mutation-selection balance. The population size is \(N\), the mutation rate is \(u\) and the selection coefficient is \(s\).

Denote the frequency of the best class by \(x\) and its initial value \(x_0 = e^{-u/s ...

If we sample a random individual from an asexual population that had allot of time to adapt to its environment, how many deleterious mutations can we expect it to have? This distribution of deleterious mutations is the starting point of many population genetics models. In an eariler post we’ve ...

This is an “executive summary” of Denamur and Matic (2006), which is a review of the literature on the evolution of the mutation rate in bactera.

1. Deleterious mutations are 100,000-fold more frequent than beneficial mutations in E. coli.
2. Mutators have been found in various species of bacteria in frequencies ...

This is a short summary of Sniegowski and Raynes (2013), a review about the evolution of the mutation rate, with an emphasis on the Drift Barrier Hypothesis (DBH). The summary is written in my own words, with a few footnotes and highlighting that express my thoughts.

1. Because most mutations are ...

This is a summary of Lenski, Barrick and Ofria (2006). The following are direct quotes of the original article. My comments are given as footnotes, highlighting and italics.

• Organisms must have a balance between robustness and evolvability, that is, between resisting and allowing change in their own internal states.
• A ...

Overview

This post is mostly a technical summary of the paper by Tenaillon, Le Nagard, Godelle and Taddei (2000). I wrote the summary because I use it as a baseline for my own research, which involves the evolution of stress-induced mutators (Ram and Hadany 2012).

The hypothesis the paper deals ...

Overview

In an eariler post I described how the mean fitness of a population at the mutation-selection balance can be analysed. I assumed that the population is asexual, that only deleterious mutations occur, that there is no drift or recombination, and that selection is constant.

In this post I would ...

Overview

The first post on the Mutation-Selection Blog must be about the mutation-selection balance, right?

So what is the mutation-selection balance?

In evolutionary biology, selection acts to remove deleterious mutations from the population, while mutation generates new deleterious mutations. When they cancel each other out, the population is at the ...