Theoretical models that explain a system using mathematical equations.

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Definition of Linkage Desiquilibrium (LD)

According to [wiki][2], linkage disequilibrium $D$ equals $$D = x_{11} - p_1\cdot q_1$$ where: $$ \begin{matrix} \text{Haplotype} & \text{Frequency}\\ A_1B_1 & ...
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25 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 ...
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70 views

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 ...
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108 views

Heterozygosity and overdominance

Consider $m$ loci with heterozygote advantage (overdominance) such that the fitness of the two homozygotes is $1-\frac{s}{2}$ and the fitness of the heterozygotes is $1+\frac{s}{2}$, where $s>0$. ...
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96 views

Population genetics and the fitness probability distribution. Why is the arithmetic mean all we need?

When recording change in allele frequency in diploid, bi-allelic, infinite and panmixic population we usually use this kind of equation: $\delta_p = \frac{p * q *( p (w11 - w12) + q * (w12 - ...
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56 views

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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79 views

Heterozygosity under genetic drift

The wright-Fisher model of genetic drift is: $$p_{ij} = \binom{2N}{j}\left(\frac{i}{2N}\right)^j \left(1- \frac{i}{2N}\right)^{2N-j} $$ ,where $\binom{2N}{j}$ is a binomial coefficient. From this ...
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48 views

Additive genetic variance with $n$ loci

The genetic variance of a quantitative trait (the quantitative trait in question is fitness) can be express as the sum of two components, the dominance and additive variance: $$\sigma_D^2 + ...
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76 views

Additive genetic variance with $n$ alleles

The genetic variance of a quantitative trait (the quantitative trait in question is fitness) can be express as the sum of two components, the dominance and additive variance: $$\sigma_D^2 + ...
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145 views

Why does the slope of parent-offspring regression equals the heritability in the narrow sense?

Background ---- Notations and assumptions ---- let $W_{ij}$ be the fitness associated to the genotype $AiAj$. $x$ is the frequency of the allele $A1$ in the population. The frequency of the allele ...
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110 views

How much does the distance between a transcription factor binding site and a promoter influence transcription?

Assume we have a synthetic construct with a minimal (inducible) promoter that requires activation for significant transcription to occur. Realistically, how important is the distance between an ...
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33 views

Effective population size when the population sizes varies from season to season

Let's think of a species which has four generations per year and which population size changes from season to season so that the population size is 100 in summer, 200 in spring, 50 in autumn and 20 in ...
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249 views

When does weak selection produce qualitatively different results from strong selection?

In evolutionary game theory, it is typical to model organisms as having a base fitness that is modified slightly by the game interaction. The ratio of the game effect versus the base fitness ...
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85 views

Is there a standard reference for the importance of tumor heterogeneity?

In a recent post, Philip Gerlee highlighted the two biggest contributions of mathematical oncology to cancer research: (1) increasing focus on the progress of cancer as an evolutionary process, and ...
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43 views

What is the relation between plasmid concentration and mRNA levels?

Suppose a simple synthetic construct, consisting of a constitutive promoter and a single gene: One of the simplest ways to model GFP transcription is to use an ODE: $\frac{d [GFP_{mRNA}]}{dt} = a - ...
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32 views

Visualisation of phylogeography

I am working on phylogeography on one model species and I am a beginner. You can imagine one species that came on locality more than 5 mya (million years ago). It was a good environment, so the ...
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129 views

Genetic Drift: Models, assumptions and empirical observations

There two main mathematical models to describe the process of genetic drift are Moran model and Wright-Fisher model. My questions concern the assumptions of these models, the existence of other ...
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265 views

Natural examples of XOR functions at the cellular level

We can often think of cells as a sort of circuit on macromolecules, and can show that they can accurately and robustly implement functions like $\text{MAJ}(x_1,...,x_n)$ (return $1$ if more than half ...
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62 views

Chaos theory and population cycles

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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27 views

An over-simplified model of cell division and its relation to stem cells

I am a mathematician, and I decided to try to model cell division with math and see what conclusions came out of it. I had some questions concerning stem cells that came up in the model. In an ...
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122 views

The Assumption of Weak Selection?

I was reading this question and I failed to fully understand the introductory part of it. The OP (@Artem Kaznatcheev) says: Most analytic models like to assume weak selection because it allows ...
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246 views

Could be an union/synergy between Math, Computer Science and Marine Biology?

I'm studing for my bachelor's degree in Natural Science and I have to chose the path for my future life. I have to chose the right kind of graduate studies. Since I love computer science, maths and ...
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118 views

Definitions and examples of some math-releated ecology branches

I would like to have an example of application and a brief description/definition (two or three lines) of the following fields. I would like to understand the exact differences between them. Other ...
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197 views

Models of quorum sensing for multi-agent systems

Quorum sensing is a system of stimulus and responses correlated to population density that is used by bacteria to coordinate gene-expression. I am looking for a simple computational/mathematical model ...
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268 views

Survivorship Curves: Type II curve mortality rate is not constant?

In graphs of survivorship curves, I'm seeing that the Type II curves are straight lines, and the supplementary text says that the mortality rate is constant (i.e. the slope of the line is constant). ...
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106 views

Examples of references for mathematical approaches in bioinformatics that are applicable to linguistics?

Do you have any classic references for mathematical approaches in bioinformatics that are applicable to linguistics (or vice versa)? EDIT I am mainly interested in approaches to reconstruct the ...
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105 views

Suggestions for an experiment? [closed]

I would appreciate suggestions for my year-long AP Biology project. Such a project would consists of a standard experiment, to be done over the period of a year, so it would have >to be fairly ...
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219 views

Structure of fitness landscapes in the NK model

The NK model of rugged fitness landscapes consists of $N$ sites where fitness contribution of each site depends on its state $\{0,1\}$ and is epistatically affected by $K$ other sites. When defining ...
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192 views

Is local equilibrium a reasonable assumption for evolutionary processes?

Whenever I look at discussions of fitness landscapes (in particular, Kauffman's NK model) the questions tend to resemble: The population is at a local equilibrium, but another equilibrium of ...
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151 views

Are there natural selection experiments that quantitatively agree with theoretical modeling?

Has anyone ever conducted an evolution experiment and quantitatively compared it to theory? For example, has anyone ever put bacteria in a million petri dishes filled with antibiotics and calculated ...
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81 views

Modeling yeast biochemical pathway using enzyme kinetics

I need enzyme concentration and metabolites concentration values to en-corporate these values in my model and do some simulation. I searched through some database yeast metabolome database ...
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57 views

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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98 views

Understanding SIR models in epidemiology

We are doing research on a SIR model of an epidemic. For one of the subsections, we are talking about saturation content rate of a human. We would like to know if anyone has an understanding of ...
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558 views

Scoring sequence against position weight matrix

I have a weight matrix of length 20 x 15 (amino acids x sequence positions). Each element of my weight matrix is a relative probability If I have a sequence say "AAPGTGASMHSGLLW" how would I score it ...
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36 views

Range of feasible coefficients in an unlimited growth model

If you are given an unlimited growth model in the form: $\frac {dP(t)}{dt} = k P(t)$ Obviously the population growth would never be unlimited, but let's presume for the moment that we are ...
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136 views

What is the minimum population size that Hardy-Weinberg calculations can be applied to?

I'm trying to find out if a particular allele is in Hardy-Weinberg disequilibrium, but the data is poor. What's the minimum population number that you can use to get any sort of respectable ...
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50 views

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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Looking for detailed nutrient/energy flow at the bottom of the freshwater food chain

I am trying to model the production and consumption of nutrients and waste at the bottom of the food chain in freshwater ecosystems. I can only find broad information on the Internet and don't know ...
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421 views

Michaelis-Menten Kinetics: Does measuring apparent Km and Vmax take into account competing reactions?

I am learning about why it is important to measure Km and Vmax for each experimental setup because measuring the "apparent" Km and Vmax includes enzyme inhibitions of which one might not be aware. ...
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231 views

What would it take to recognize a deer by its photo?

I am trying to recognize a deer by its antlers or any other means. Elaborating: I was hoping to use their antlers to recognize them but I have heard that most deers shed their antlers every year so ...
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101 views

Lineage selection in plasmid evolution

I've been reading through Paulsson (2002) and I am not sure what he means by "lineage selection" in the second to last section. The paper deals with plasmid replication, and mostly concentrates on the ...
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22 views

Do the antlers re-grow in the same pattern every year? [duplicate]

I am a software engineer and I am trying to develop a system to identify a deer by its photograph. Most deers lose their antlers every year. I would like to know if they re-grow in the same pattern ...
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108 views

How to classify equilibrium points [closed]

I have the two differential equations: $$\frac{dN_1}{dt} = N_1(2 - N_1 - 2N_2)$$ $$\frac{dN_2}{dt} = N_2(3 - N_2 - 3N_1).$$ I worked out the equilibrium points to be at $N_1 = 0, \frac{4}{5}$ and ...
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162 views

Deterministic model of lambda-phage lysis/lysogeny [MATLAB]

Project 1 Base: Can someone please help me understand what I need from Project 1 Base code to do questions 1 and 2 from the first image? I'm new to MATLAB so a thorough explanation would be ...
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132 views

Alternatives to fittest-win and Moran processes as simple mathematical models of selection

When modeling selective sweeps as a micro-building block in models of macroevolution (not to be confused with misuses of this in creationist arguments), I use the fittest-win model of selection as a ...
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748 views

Why is 'Grudger' an evolutionary stable strategy?

I am currently reading 'The Selfish Gene' by Richard Dawkins, which I am sure many here have read. The topic are evolutionary stable strategies (ESS) regarding cooperation. I apologise for the long ...
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3answers
568 views

How exactly are game theoretical evolutionary models described during implementation for computer simulations?

When a biologist or a layman tries to reason the evolutionary explanation for something, they would simply use English with some math thrown in (for a random example, pick any explanation out of "The ...
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214 views

Short-term Lamarckism in asexual single cell organisms

I was reading through the Karr et al. (2012) whole-cell computational model. One of the things they did was to induce single-gene disruptions in their model. They observed several to be fatal, but: ...
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152 views

What software is there available for Quantitative structure–activity relationship (QSAR) pharmacological studies?

QSAR modelling in pharmacology basically hangs on using mathematical modelling to approximate the effects different molecules will have on various pharmacological targets. I would like to know what ...
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102 views

How are Genetic Circuits Modelled?

I've read a recent Nature Methods paper by Moon T.S. et al, in which a synthetic genetic circuit consisting of layered logic gates was created. For example, the paper, a circuit is modelled in Figure ...