# Tagged Questions

Models that analyse biological systems or processes using the tools of applied mathematics.

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### Current along an axon

When an action potential is induced on a neuron, the local transmembrane potential jumps from $E_{\mbox{rest}}$, the resting potential of the neuron, to $E_{\mbox{eq}}$, the equilibrium potential of ...
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### What is the difference between a mechanistic and a statistical predictive model?

The simplest description of the difference between these two approaches that I have found are on this site who summarise the difference as: Mechanistic model: a hypothesized relationship between the ...
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### Analytical Methods for Estimating Probability of Fixation

The probability of fixation $P$ of an allele is an very important measure and there exists several solutions to estimate this probability. Each method has its own assumptions and it is often hard to ...
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### How many traits can a multivariate breeders equation handle?

The multivariate breeders equation (MBE) by Lande predicts the change in a trait $\Delta \bar z$ (response) as $\Delta \bar z = G \beta$ where $G$ is a genetic variance-covariance matrix and ...
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### Expected time for a neutral allele to reach a frequency of $p_1$ when starting at frequency $p_0$

Kimura and Ohta (1968) showed that the expected time for a neutral allele to reach fixation (given that it will reach fixation) is $$\bar t(p_0)=-4N\left(\frac{1-p_0}{p_0}\right)\ln(1-p_0),$$ where ...
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### Mathematical modelling of omics data [closed]

I'm interested in modelling host-pathogen interactions using mathematics. I know there are good resources in Pubmed but seems I'm looking for a book or introductory reviews. My background in maths is ...
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### How to compute the regression of individual fitness on individual phenotype

Consider a population structured in groups of two individuals. Individuals' interactions follow an additive prisoner's dilemma: \begin{array}{c |c |c|} & C & D \\ \hline \text{Cooperate (} C ...
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### Are there any examples of how to apply evolutionary models?

Apologies if this question it too open-ended; evolutionary biology is not my primary field. I have been reading a lot about the use of statistical mechanics in analyzing evolutionary dynamics. As an ...
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### Basic Modelling in Quantitative Genetics

I am pretty bad in thinking quantitative genetics models. I am trying to get some basic understanding of modelling the evolution of a quantitative trait. I am therefore asking for help to analyze a ...
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### Parameters for Fitzhugh-Nagumo model of Action Potential

I'm a high school student who's currently in AP Biology, so my background in biology is quite limited. I'm interested in mathematically modelling action potentials. Doing a quick google search, I ...
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### Biostatistics: Pollen dispersal directionality

What Information am I looking for? Think about a tree that is sending pollen all over the place. Because of wind, most pollen grain will go toward one direction. Imagine, we split the 2D area around ...
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### What is the probability of fixation for a mutant under fluctuating selection?

Here is an answer which explain how one can model the frequency of an allele that is under fluctuating selection (selection that varies through time). Not, thinking about fluctuating selection, there ...
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### Modeling inclusive fitness

Consider a population of two altruist with coefficient of relatedness $r$. The average inclusive fitness of this population will be $w_{0} + br -c$. Like in this example, assignment of inclusive ...
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### Hamilton's inclusive fitness approach

The underlying intuition of Hamilton's model of inclusive fitness is that we should study social behaviors from the point of view of actors -- rather than the recipients. To build his model, Hamilton ...
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### What governs the distribution of blood vessels?

Whenever someone is sick, doctor places 2 fingers on wrist & observes the heart-beat-rate by feeling pulses of a certain artery. To me it seems the distribution of blood vessels are pretty ...
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### Best software for protein in electric field modeling?

I'm trying to find a free, or cheap, software program to model the movement of a heterotrimeric protein in an alternating electric field. The dipole and crystal structure of the trimer are known. ...
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### ratio between heat transfer coefficient and thermal conductivity [closed]

Consider the Robin boundary condition for the diffusion/heat equation $\mathrm{u_t=a(t)u_{xx}+f(x,t)}$: $$\mathrm{-k(t)u_x(0,t)=h(t)u(0,t)}$$ or $$\mathrm{u_x(0,t)+\frac{h(t)}{k(t)}u(0,t)=0}$$ ...
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### Core Biological concepts explained to a Computer Scientist?

I am a computer scientist delving into Bioinformatics and I need to gain insight in biological phenomena. How would you explain three core concepts as: Evolution, Selection and Variation, to a ...
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### How does temperature influence the rate of protein degradation?

For computer modeling purposes, I am looking for some referenced quantitative measurements of the effect(s) of temperature on biochemical reactions. Question In particular, my question is: How does ...
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### Mathematical models of lineage selection

I'm interested in the concept of lineage selection (Aboitiz, 1991) as an explanation for why traits would be selected for that enhance the rate at which evolution can occur, rather than directly ...
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### Is there a biological neuron that spikes in response to hyperpolarizing currents?

As some background I've been building Electrophysiological models of neurons, and in the process stumbled upon a model, that in all respects is biologically plausible, but has a bizarre property I ...
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### Book recommendation on population/evolutionary genetics?

I have recently been involved in collaborations that require me to model the population genetics of eukaryotic populations. I fear I may either be "re-inventing the wheel" or making conceptual ...
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### Chaos theory and population cycles of odd periodicity

I have just begun to read about Chaos theory and have come across the statement that "Period three implies chaos." My question: Does any odd period imply chaos or only 3? If so, how can populations ...
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### Why sigmoid curves appear in quantitative analysis of many biological phenomena? [closed]

I know two examples: 1-The binding of hemoglobin to oxygen (binding of oxygen to one site of hemoglobin induces conformational changes which increase the affinity of the other sites for oxygen - the ...
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### Is there a standard formula/calculation for sexual dimorphism?

Is there a standard, or most accepted, way to present a value for sexual dimorphism? For example, one could use $$\frac{\text{Female value}}{\text{Male value}} -1$$ This would give negative values ...
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### Model for fluctuating selection

Is there any mathematical model to predict the behaviour and long-term consequence of counter-acting selection at different time scale? For example, let's consider the bi-allelic gene A, with alleles ...
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### Mutation-Selection-Drift Equilibrium

mutation-selection-drift equilibrium is one of the most important concept of population genetics. I could easily find the calculations for mutation-secltion equilibrium and for mutation-drift ...
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### Why can blood vessel contraction be described as a second order system?

Suppose that the x-axis represents time, and the y-axis vessel diameter. Then this graph is claimed to roughly describe what happens when the blood pressure increases, then decreases. When the ...
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### Hill's function for translational regulation

Transcriptional regulation is generally modeled as a Hill's function (similar to Michaelis-Menten Kinetics): $$\frac{dm_X}{dt}=\alpha _{m_X}.\frac{R}{K+R} -\beta _{m_X}.m_X$$ Where $m_X$ is the mRNA ...
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### Hamilton's derivation of direct fitness from his 1970 paper

In his 1970 paper "Selfish and Spiteful Behaviour in an Evolutionary Model", Hamilton uses Price's equation to derive his well-known rule $rb -c >0$. My question is about one of the steps in his ...
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### General time reversible model of evolution and Felsenstein model

I would like to get suggestions for the books related to General time reversible model of evolution and Felsenstein model etc. Specifically the mathematical treatment of these topics and concepts ...
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### Modeling intracellular interactions between sender and receiver bacteria

I am involved in a modelling task of a biological process described as follows: -- "Objective: to model behavior of a sender receiver type system The process goes as follows Pre-signal [PS] is in ...