Questions tagged [theoretical-biology]
Questions relating to biological theory or theoretical developments that deals with biological processes.
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questions with no upvoted or accepted answers
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What's a reasonable time constant for a mathematical model of a neuron?
Background
I've been studying various mathematical models of neurons. So far I've covered the classic Hodgkin-Huxley model (to describe the potential difference of a single neuron) and the integrate ...
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Games with non-uniform interaction rates
Background:
Many models in evolutionary game theory assume uniform interaction rates. For instance, consider the $2\times 2$ game:
\begin{array}{l c c}
& A & B \\
A & a & b \\
...
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References for historical momentum in asexual species definitions
For sexually reproducing organisms, the scope of a species is somewhat fixed by reproductive compatibility.
However, this all collapses for organisms that exclusively reproduce asexually.
Here, my ...
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What is a good approximate functional form for an equation relating plant growth to sunlight?
Question is in the title. I've got daily measurements of daily mean shortwave radiation at the surface, and annual measurements of plant growth (some measure, be it height or biomass or something).
...
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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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Eye color genetics
I am trying to find a model to link the phenotype eye color to its genotypes.
I know that there exists a simple model from Davenport, which explains {brown,blue} eyes. Further, there is an extended ...
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Is there a functional model of the human retina for simulation of conversion of illuminance pattern to nerve signals?
I'm looking for a model that would take a pattern of spectral irradiance over the retina as a function of time and space and convert this into the signals propagating through the fibers of the optic ...
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Conservation Law in Gene Regulatory Network modelling
I was going through the GRN modelling from Chemical and enzyme kinetics
by D. Gonze & M. Kaufman (PDF). The gene has 2 sites for activator/repressor. It say the DNA $D_0$ combines with activator/...
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3
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Is there a way to determine corresponding differential equations from fitted Hill equation parameters
I am currently doing some work with GCaMP, a genetically encoded calcium indicator. According to the literature the Hill equation parameters for GCaMP6m is $K_d=167\pm3\, \text{nM}$ and $n=2.96\pm0.04$...
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Is there any example, where cooperative behaviour of predators induce fear in prey population?
I am basically from math background and doing Ph.D in mathematical biology. So I am not so efficient in biology. But my problem based on cooperative behaviour of animals during hunting which is ...
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Kinetic mathematical model of glycolysis?
I am looking for papers containing kinetic mathematical models of glycolysis, hopefully in mammalian cells (or as close as possible, say yeast). The papers I have found do qualitative analysis (...
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Why does my simulation not support the idea that inbreeding is bad?
After reading this post, I wrote some code to simulate inbreeding.
We have a population of $N$ creatures. Each creature has two genes, which come in two forms: recessive (a) and dominant (A). The ...
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Organisms with one, two, or more than two biological parents
I am interested in the generic names of organisms with one, two, or more than two biological parents. I don't know if the latter possibility is possible in nature, but if it could be, it would ...
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Derivation of discrete replicator dynamics
Related: Discrete vs Continuous Replicator Dynamics
I am trying to perform a derivation of the discrete time replicator dynamics, but I am unable to get through Cressman's derivation in "Evolutionary ...
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What is the effective population size of a simple two deme metapopulation?
I am confused as to how to compute the effective population size $N_e$ of a theoretical structured population. Let's consider here a simple case study.
Imagine a 2-deme metapopulation. Each deme is ...
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How to understand relatedness in an infinite island model?
My understanding is that the relatedness coefficient in kin selection models measures positive assortment. That is, altruism is more likely to evolve if altruists tend to interact with other altruists....
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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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Does unequal dominance mean the X-chromosome should be a coldspot for antagonistic variation?
Sexually antagonistic genetic variation, in a simple model, will persist if the benefit to one sex is (near) equal to the cost in the other, otherwise the polymorphism will be selected out of the ...
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3
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Experimental techniques to measure protein-protein and protein-ligand structure and dynamics
We would like to compare our simulation results with experimentation. When one wants to follow experimentally the dynamics (and possibly structure) of protein-protein or protein-ligand docking (...
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Can the concept of fisherian runaway be explained using simple models?
I want to understand the concept of fisherian runaway. Dawkins' book tells about this, but it's not clear enough. It can be seen that the essence of Fisher's idea is that when a male peacock with a ...
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Ecosystem Control Theory
I've used EcoNet online tool to analyze an ecosystem. You can run the default model by pressing "run model" in order to follow my question.
Among the extended results there are 2 'Control ...
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Difference between IC50 and Michaelis-Menten constant
I am new to biology, and getting to know the term IC50, I found that there is a connection between IC50 and Michaelis-Menten constant by the Cheng-Prusoff equation
$K_{i}=\frac{\mathrm{IC}_{50}}{1+\...
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What did Masatoshi Nei 1972 mean by "However, evolution does not occur so as to assure this property at least at the nucleotide level."?
In Nei 1972 he describes what is now called Nei's standard genetic distance. This math.SE post provides an exerpt to the definition of Nei's standard genetic distance. In this paper he states
In the ...
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Genetic evolution without crossover
Can someone please point me to the origin of the system of coupled differential equations (1) in Section 2 of Shahshahani's book$^\star$?
$$ \dot{x}_i = x_i \sum_{j=1}^n m_{ij} \frac{x_j}{|x|} $$
...
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Difference between heritability on the scale of liability versus the scale of observation
I was reading a paper on disease heritability ("Estimating Missing Heritability for Disease from Genome-wide Association Studies") and it struck me that I don't have a great understanding of ...
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Estimate sex-specific survival from mark-recapture data using multi-site, sex-specific cormack-jolly-seber model?
I am interested in identifying sex-specific survival rates. I have a long-term dataset of individually marked birds from one breeding colony. Of these, I am able to genetically sex a subset. ...
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Can human pathogens present on plants become plant pathogens?
Since human pathogens sometimes live on the surface of plant leaves(read here and and here), and there are plant-pathogen microbes also living on leaf surfaces, is it possible for plant virulence ...
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Range for which the Verhulst-Pearl model is a good approximate
The Verhulst-Pearl model describes the growth of a population using the differential equation,
$$\frac{dN}{dt}=rN \left(\frac{K-N}{K} \right)$$
where N is the population (no. of organisms), r, the ...
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2
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Measurement equation of Tree-Step pathway model
I am not specialist in biology but I want to test a parameters estimation method (based on Kalman filter) on the Tree-Step pathway model, but I cannot find a document that gives the measurement ...
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2
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86
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Variance of Stochastic Growth Rate for Average Population Size Over Time
I'm interested in calculating the variance of the stochastic growth rate for the average population size over time,
$$\ln \beta = \lim_{t\to\infty}\dfrac{1}{t}\ln V[N(t)]$$
which shows that the ...
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2
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What model of epistasis best fit the reality?
In theoretical population genetics, it is very common to have to assume a model of epistatic interaction. The two most common models are the additive model and the multiplicative model.
Additive ...
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2
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Math backbone in biology/genetic
Are there any good books, that shows some advanced models in genetics particularly?
The problem is i don't see any good math model in genetics interactions exept combinatorics. I'd like to know what ...
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143
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Replicator equation for mixed strategies?
The the replicator equation is usually defined for pure strategies. More specifically, the replicator eqn for $n$ strategies is given by:
\begin{equation}
\dot x_{i} = x_{i} \left( \sum_{j=1}^{n} a_{...
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2
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115
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Metabolic control theory: proof of the summation theorem?
I'm looking for a rigorous proof of the summation theorem of metabolic control theory. The only sources I find are the original papers by Kacser and Burns 1973 and Heinrich and Rapoport 1974, both of ...
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Variance in reproductive success and effective population size
Background
The effective population size $N_e$ is the size of the Wright-Fisher population that experience the same amount of drift than the population under consideration.
The higher the variance ...
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2
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Textbook for quantitative biochemistry with thermodynamics, as an alternative to Voet, Voet & Pratt (Fundamentals of Biochemistry)?
I'm looking for a great textbook on biochemistry that covers core topics: relevant aspects of thermodynamics, reaction kinetics, metabolism (e.g. krebs cycle, respiration, etc.). Ideally it would also ...
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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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2
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What is the probability of fixation for a mutant under fluctuating selection?
Here is an answer which explains how one can model the frequency of an allele that is under fluctuating selection (the selection that varies through time).
Not, thinking about fluctuating selection, ...
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2
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Is there a difference between endorphins that are released while physical activity and sex/masturbation?
I observerd myself and I can identify two different types of "happines".
First - called by me - After Pleasure :
Occurs AFTER (and last long) long activity that require from me engagement focus and ...
2
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Based on which criteria should i choose the control sample to calculate delta_delta_Ct
I want to calculate the gene expression of an experiment with the Delta delta Ct method.
I have these results from two runs of a real time PCR (one for the GOI(Gene of Interest) and one for the ...
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Reverse complement of reconstruction model for assembling reads
One way to assemble fragments produced by DNA sequencing (often called reads) is to seek for the shortest common superstring that contains all the reads of a given set of reads. One model for this ...
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Universal mathematical statements in biology similar to Price Equation
I just read about Price Equation and I thoroughly enjoyed the concept, as well as the elegance of the mathematical formulation. I especially enjoyed the fact that (to quote Wikipedia) it is "a ...
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Modeling and Predicting Squirrel Populations
I was recommended to come here from the MathSE site. Here is the question:
I am interested in modeling the growth of the Eastern Fox squirrel population in Los Angeles, not only in terms of numbers ...
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How is the Allee effect modeled in the presence of a highly variable carrying capacity?
Consider a rather standard model of population dynamics in the presence of a strong Allee effect:
$$ \frac{du}{dt}=u\left(1-\frac{u}{K}\right)\left(\frac{u}{A}-1\right),$$
where $u(t)$ is population, $...
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Calculation of drug efficacy- mathematical biology approach
I am participating in a mathematical biology project.
I would like to discuss the following problem:
Let A be a drug such that $x_{o}$ chemical units of it kills 12% of $y$ cells per 1 day, I would ...
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1
vote
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answer
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Method of determining base values of traits in isolated populations
Prelude: I came across a discussion about the correct formula for calculating the average IQ of offspring, which goes something like the following
$$ 100 + \frac35 \left( \left(\text{father's IQ} + \...
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Is there any reliable data about the correlation between the size of a species and number of individuals that belong to it?
I'm curious to know if such a collection of data exists, so I could visualize it with a graph, and see how humans compare to other spieces of similar size.
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What are the interaction energies/chemical potential values for the cytoplasm - protein interactions within the cytoplasm?
I'm trying to simulate phase separation in a biological based system using a Cahn Hilliard model. I have 3 components, they are 2 theoretical enzymes and the cytoplasm. I have found plenty of sources ...
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answers
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When cancer is detectable, how many sub-clones are there at that stage?
I have read somewhere that cancer is detectable when the number of cells reaches $10^7 - 10^9$, which probably varies according to the specific tumor. At this early stage, what is the expected number ...
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