Questions relating to biological theory or theoretical developments that deals with biological processes.

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4
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1answer
56 views

Proof of the equivalence between two ways of defining ESS

Background Two common ways of defining what an Evolutionary Stable Strategy (ESS) are: First definition: Consider a population composed of populations playing two strategies, $\mathbf{p}$ and ...
2
votes
1answer
49 views

I know how to solve these equations, but I'm not sure what t' represents?

I am investigating the Wilson Cowan neuron population model, and I can follow most of it, but I'm not sure what is meant by t' in the equation for proportion of neurons in the refractory period. The ...
1
vote
0answers
31 views

Values of Miu_max and Ks from parameter estimation?

Background I have this simple biomass growth model: $$ \mu = \mu_{max}\cdot \left(\frac{S}{K_S+S}\right) \cdot \left(\frac{1}{1+S/K_{iS}}\right) \cdot \left(\frac{K_{iP}}{K_{iP}+P}\right) \\ ...
1
vote
0answers
48 views

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 ...
3
votes
1answer
182 views

Do the claims in this paper have any degree of validity?

The paper The waiting time problem in a model hominin population talks about a problem of waiting time, etc. Is the methodology of this numerical simulation, and the conclusion right or is it wrong? ...
1
vote
0answers
34 views

metabolic heat generation and exercise intensity

Is there a relationship between bio heat equation (found here) and exercise intensity as described here That is I am trying to include the effect from exercises to the tempertaure variation in skin. I ...
2
votes
1answer
22 views

relationship between cytokines

This is for a mathematical research. I am building a model to identify severe dengue patients through the interaction of cytokines S1P,IL1b,TNFa,PAF and IL10. For this I would like to know if there ...
3
votes
0answers
35 views

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 \\ ...
3
votes
3answers
237 views

Can/Have cancer cells be/been used in stem cell culture lines?

Since Cancer cells have unlimited growth potential, can they be induced towards totipotency and pluripotency? If so, can cancer cells be used in stem cell culture because of similar properties of ...
6
votes
0answers
63 views

Variance in Fst in the infinite island model

The most famous result in the study of structured populations come from Sewall Wright. He showed that in an island model, where each subpopulation is of size $N$ and the migration rate is $m$, then ...
2
votes
0answers
25 views

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} ...
5
votes
2answers
103 views

Stochastic parameters in population growth equations

I'm more of a mathematician than a biologist, so I had a question about an application of the population growth equation to real-life models, and thus would like to ask biologists for their insights. ...
1
vote
1answer
49 views

Can DNA base pairs go through each other? [closed]

Consider the simplified version of the motion one DNA base pair held together by a hydrogen bond: Use u and v to denote the displacements of the bases from their equilibrium position along the ...
2
votes
0answers
28 views

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 ...
2
votes
1answer
153 views

Are there any theories using thermodynamics/statistical mechanics or information theory principles to modelling in ecology?

So far, I've only known one: the MaxEnt theory. It uses the maximum information entropy developed by information theorist, which in turn inspired by the thermodynamics from physics, to predict the ...
2
votes
1answer
174 views

How does one calculate the amount of oxygen produced by trees?

I'm currently working on a project to measure the impact of tree planting. Calculating the amount of oxygen seems harder than I imagined. Of-course there's the type and size of the tree and the ...
2
votes
1answer
3k views

How to interpret the breeders equation?

The univariate breeders equation is defined as, $\ R = h^2 s$ where $\ R $ is the response, $\ h^2 $ is the heritability (additive genetic variation), $\ s $ is the selection differential. The ...
1
vote
1answer
59 views

How to determine the relationship of competition or cooperation?

I am currently studying the interaction of Twitter memes (two or many), such as competition and cooperation. Is there any model or method in biology that can identify the types of the relationship, ...
10
votes
1answer
216 views

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 ...
2
votes
1answer
76 views

Discrete vs Continuous Replicator Dynamics

The replicator eqn in the case of discrete non-overlapping generations and asexual reproduction is given by the discrete replicator eqn: $$x_i(t+1) = x_i (t)\frac{f_i(t)}{\bar f (t)}$$ where $x_i$ is ...
3
votes
1answer
1k views

Index of ecological niche overlap

For this question I am interested in the Pianka's Index of ecological niche overlap. What is the Pianka's Index? How does it work? How can one calculate this index? How often is it used? In what ...
2
votes
0answers
49 views

Variance in reproductive success and effective population size

Background The effective population size $Ne$ is the size of the Wright-Fisher population that experience the same amount of drift than the population under consideration. The higher the variance in ...
6
votes
1answer
174 views

Effects of selection on effective population size

Background The effective population size ($N_e$) is a central concept of evolutionary biology and is influenced by several parameters. For example: sex ratio bias affects $N_e$ $\left(N_e = ...
9
votes
3answers
409 views

Do biological phenomena follow Gaussian statistics?

I have recently entered the life sciences (from physics). I am concerned about the use of p values in the life sciences literature. For example, in this article, they test 9 - 12 rats in a control ...
1
vote
0answers
14 views

Biomolecule , DNA-RNA difference [duplicate]

Why is that a RNA has uracil in place of thymine? RNA could have thymine bases but it has uracil ? What is the reason for the presence of uracil there ?
1
vote
0answers
28 views

What is the distribution of the expected number of lineages in a birth-death tree after time T?

I've been looking at The reconstructed evolutionary process by Nee et al. 1994 and they provide a number of equations dealing with the birth-death process, specifically the "reconstructed" birth-death ...
7
votes
2answers
128 views

Within and Between Allelic Class Diversity

I am reading Charlesworth et al. 1997. They talk about diversity within and between allelic classes. Nucleotide diversities ($π$) at each neutral site were estimated from the mean of $2 \sum z_t ...
4
votes
1answer
70 views

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 ...
5
votes
4answers
153 views

Is Insulin-Glucose dynamic Lotka-Volterra?

From Wikipedia: The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the dynamics of ...
2
votes
1answer
188 views

Why does the number of mutations per individuals follow a Poisson distribution?

I was reading this review. On page 11, left column, first paragraph, one can read: [..] there is a Poisson distribution of the equilibrium number of mutations per individual, if fitness effects ...
2
votes
0answers
64 views

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 ...
12
votes
0answers
119 views

What have the L-systems (Lindenmayer systems) been actually used for in biology?

Wikipedia: An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian ...
1
vote
3answers
107 views

What fraction of sites are expected to be polymorphic?

Question Consider a very long (eventually infinite) DNA sequence of neutral sites. Consider a panmictic population of constant size $N$ with a per site mutation rate of $\mu$ where all individuals ...
5
votes
0answers
77 views

Understanding F-statistics in population genetics

I am reading a classical Weir and Cockerham 1984 paper about Fst estimation. At the beginning (first page, right column), they define 3 statistics. $F$ is the correlation of genes within individuals ...
4
votes
1answer
111 views

Forward versus backward numerical simulations in population genetics

My question is closely related to this post. There are a number of existing platforms to perform numerical individual-based simulation in populations genetics. An almost exhaustive list of such ...
3
votes
1answer
484 views

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 ...
4
votes
1answer
29 views

Accuracy of best plant growth models?

Given a plant $P$, predict its height $H$ at time $t$ since planting given some environmental variables $E_1, \dots, E_n$. How accurate are the state-of-the-art models for such thing? What data is ...
2
votes
1answer
101 views

System biology and evolution: Book-recommendations

I have relatively good knowledge in evolutionary biology and in population genetics. I am getting more and more interested in the evolution of ... genetic developmental processes gene interactions ...
3
votes
1answer
131 views

Michaelis-Menten equation type - how it is derived?

Can somebody explain how is the following differential equation found? It is about the blood alcohol content. See this article (pages 3 and 4). They say the concentration of blood alcohol ...
3
votes
0answers
78 views

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 ...
3
votes
1answer
62 views

Altruism in viscous (asexual) populations

The viscosity of a population is the tendency of offspring to remain near their place of birth. Taylor 1992 ("Altruism in viscous populations") provides a model to study how viscosity affects the ...
3
votes
1answer
47 views

Anopheles arabiensis lifespan and sporogony duration

What is the longest observed lifespan of a mosquito, especially of the species Anopheles arabiensis? How long does it take for Plasmodium parasites to develop and move into the salivary glands of ...
4
votes
1answer
59 views

Modelling insecticide net efficacy loss [closed]

I am currently doing some work on modelling the effects of treated nets usage on mosquito populations. Nets do not retain their maximum efficacy forever. They lose their chemical efficacy after about ...
2
votes
2answers
217 views

Value of mathematical models in biology [closed]

Sorry if this is too much of a soft question or if it is too broad for this site. As a person who has much more experience with math than biology, I've always been really interested in the ...
2
votes
1answer
79 views

Better population models than the logistic equation [closed]

For modelling the population of a single species in a region, the logistic equation is used $$ \frac{dN}{dt} =kN\Big(1-\frac{N}{K}\Big) $$ where $N$ is the number of organisms, $K$ is the carrying ...
5
votes
1answer
74 views

Queller's 1985 version of Hamilton's rule

Queller 1985 ("Kinship, reciprocity and synergism in the evolution of social behavior") provides a generalization of Hamilton's rule that allows for non-additivity. To accomplish that, Queller writes ...
8
votes
1answer
92 views

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 ...
2
votes
2answers
293 views

What are multicell spheroids?

I'm from a maths background and I'm doing some research on mathematical models of cancer. I've come across alot of literature mentioning "multicell spheroids" in the context of avascular tumours. I ...
7
votes
3answers
156 views

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 ...
2
votes
0answers
33 views

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 ...