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7

When I think about your question of natural examples of XOR, it pushes me to think about what type of natural environments (i.e., evolutionary pressures) would lead to the selection of an XOR equivalent. When we implemented a synthetic XOR by "double flipping" one transcription terminator as a type of gene expression "check valve" it was the case that I ...


5

First of all, here is a program which simulates the evolution of the G-matrix over multiple generations, it's a few years old (they seem to have stopped developing it) and I've only played with it briefly. This could solve how to model the evolution of the G-matrix. Fisher's fundamental theorem is a great place to start off with the theory of this: The ...


4

What you are describing usually falls under the category of computational biology or just mathematical biology. Unfortunately, the biggest part of this field is bioinformatics, or the application of statistical and/or dynamical programming techniques to sequence data. You exclude this in your question, and I would agree with you that it is a "boring" topic ...


4

This is derived from studying how heterozygosity changes over time. The standard equation for change in heterozygosity ($H$) with constant population size ($N$) is: $H_t = \left(1 - \frac{1}{2N}\right)^tH_0$ When $N$ varies between generations you use the product of this formula: $H_t = \left(1 - \frac{1}{2N_0}\right)\left(1 - ...


3

Fishers Geometric Model (FGM) is a theoretical prediction about the adaptation process in traits. There are a number of things to establish before attempting comprehend FGM. Firstly, shifts in an adaptive landscape, in natural scenarios, are generally quite small. Because populations have been evolving for such a long time and the small shifts in adaptive ...


3

You either want a introductory book in evolutionary biology or a book that provide models/formulations of evolutionary processes In my first class of evolutionary biology I had this textbook: Futuyama, Evolution I think it gives a good start to the field and offers a good overview of the difference subfields. If you think you already knows enough about the ...


3

This question has been around for a while, so I'll try to start with a partial answer. The basic assumptions of the standard Wright-Fisher-Model are: Constant population size $N$. Discrete, non-overlapping generations. Neutrality (e.g. all individuals are equally likely to reproduce) I prefer looking at the model for haploid/chromosomes. If you bundle ...


3

I am presenting a speculative approach since nobody has mentioned about any existent models yet. Assuming that selection is based on performance in certain tasks; performance is a function of traits which in-turn is a function of genotype. Performance is a non-linear function of genotype and selection imposes a cutoff/bandpass filter on the performance ...


3

This is a little tricky. First of all lets be clear about 'bringing together favorable alleles' (or any alleles) represented by site mutations on 2 chromosomes: --------A------------------ X ------------------B-------- If the two dashed lines are two copies of the same chromosome, then a recombination event at X may produce: ...


2

Have you looked into "Fundamental of Molecular Evolution" by Dan Graur & Li. Another suggestion in line of population genetics and different evo. theories would be - Evolutionary Genetics: Concepts and Case studies (Multi-author book. Editor Fox & Wolf)


2

I don't think that you need to look further than the Price equation, which is basically a proof of a generalized version of Fisher's fundamental theorem. Price had a series of papers in the 70's that derived and applied the Price equation (e.g. Price, 1970; Price, 1972a), but most relevant for your question in probably Price (1972b). A nice summary of ...


2

Measuring the electrical signals (=nerve signals) from the heart is frequently done in medicine, it is called electrocardiography. It looks like this (from the same article): Influencing the heartbear can also be done and is done by pacemakers. Depending on the patients necessities the can permanently stimulate the heart or do this only, when certain ...


2

Well, there are some questions regarding what population. I don't have 50 rep, so I can't really ask for clarifications; populations range a lot, from your typical avoidance of inbreeding (laws against cousin marriage) to Tamils with their high rates of first cousin marriage (so high that they don't have any pedigree inbreeding depression due to selection, ...


2

What you are looking for sounds like the mechanism for a fold-change detector. I would recommend looking at these two papers: The incoherent feedforward loop can provide fold-change detection in gene regulation As an example of this working in a real system, I recommend looking at the NFkB pathway, as recently detailed by Suzanne Gaudet: Fold Change of ...


1

Fry (2010) borrowed his variables from Kidwell et al. (1977). Kidwell defines the fitness of each genotype as, $w_{m1}$, $w_{f1}$ = male and female fitness of the A$_1$A$_1$ genotype. $w_{m2}$, $w_{f2}$ = male and female fitness of the A$_1$A$_2$ genotype. $w_{m3}$, $w_{f3}$ = male and female fitness of the A$_2$A$_2$ genotype. Kidwell then establishes ...


1

Most of us have had the apoptotic process in our B-lymphocytes disrupted when we had infectious mononucleosis, caused by the EBV virus. The EBV virus (pardon the virus-virus) encodes proteins, including one that mimics a host cell protein, Bcl-2, which plays an important role in apoptosis. The set of virus 'decoy' proteins forces the infected cell to ...


1

Lot's of ways. Apoptosis is complex, but falls under two pathways ending up at caspase 3. Anywhere in the pathway may there be a problem but also in things that trigger the pathway. For example in cancer there is loss of tumour suppressors which ensure a damaged cell undergoes apoptosis or prevents replication and oncogenes which allow controlled ...


1

Long for a comment but consider this to be an extended comment and not an exact answer: At least for Poisson I can say that the random variable should fit the three Poisson postulates. Poisson RV generally describe discrete events in continuous intervals. A fitness function doesn't seem to be such a type of RV; it is a property of a population rather than ...


1

I really good intro to evolution book is The Evolution of Vertebrate Design by Leonard Radinski. Also, for a more math based approach you could look into Narrow Roads of Gene Land. These are collected papers of W.D Hamilton.


1

There are many different ways to do this, depending on what assumptions you make on e.g. stable age structure, distribution of offspring, haploidy/diploidy, population growth etc. As you probably know, there are also two main approaches to effective population sizes, namely ones based on; 1) the rate of inbreeding ($N_{e,i}$) and 2) the increase in variance ...


1

Being a typical molecular biologist, I am a little uncomfortable with classical genetics terms. I might redefine some symbols (perhaps to mean the same) [It is like talking to oneself while thinking]. There are four DNA-blocks : A1, B1, A2 and B2. Ak and Bk are adjacent blocks. [Perhaps this is same as what you defined the symbols as]. A and B are ...


1

Another important reason to have mating types is to prevent self-fertilization or self-polination that produces less capable offspring. Because of this requirement, mating types may evolve also for species that produce both types of gametes, or does not differentiate them into male and female gametes. Fertilization is only possible if gametes have different ...


1

This paper uses 4 metrics for discreet landscapes. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3240586/ Deviation from additivity: How much your genes interact (normalized). Fitness in a purely additive landscape with three genes, for example, is F=f(x)+g(y)+h(z) where f,g, and h are each functions of one variable (the x,y, and z "genes"/coordinates). ...


1

The following answer is not complete and only give some intuitive grasp on Fisher's fundamental theorem of Natural Selection. A better devlopment can be found in Ewen's book Let's first define what is the Additive Genetic Variance Consider a quantitative character that is determined entirely by a locus $A$ which two alleles are $A_1$ and $A_2$. the ...


1

Here's a paper with an historical bibliography of mathematical analyses in the introduction. As you can see when you demand a mathematical treatment of something as poorly understood as the genetic inheritance of traits, the word proof is to be used in a qualified way. In this case a multilocus fitness with variation in the population with no linkage ...


1

I think at @fileunderwater provides a good explanation of the basics math behind it, and some good references. I would like to go more into detail about the modeling decisions and benefits of assuming weak selection and why it is done in the literature. When you are making evolutionary models, especially one in evolutionary game theory, the first place is ...


1

This is my take in this, without experience of using the Taylor series to analyse evolutionary game theory problems. As you know the Taylor series expansion of $f(x)$ at point $a$ can be written as: $f(x)= f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f^{(3)}(a)}{3!}(x-a)^3 + ... + \frac{f^{(n)}(a)}{n!}(x-a)^n + ...$ Often factors above second order are ...


1

This article claims to be a new level of evidence for group selection. Its a little early to tell at this point whether the critics will be moved. They have not been in the past! sorry if this is a bit short - its late, but i'll try to come back and do more later..


1

Unfortunately, the answer depends completely on how stringent you are with "Hamilton's rule". If you just mean the equation $r \geq c/b$ then it is important to look at modern usages. In modern usage, all three of the terms $r$, $c$, and $b$ can be arbitrarily complicated. My favorite examples include when $r$ takes into account spatial structure saying that ...


1

Here is a simple proof that the probability of fixation given an infinite time is indeed p (in a finite population, otherwise there will be no fixation): Let's look at all 2N gametes in the population. Eventualy, according to the Wright-Fisher model, only one of them will be represented in the population. The probability for this gamete to be of an allele ...



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