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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 ...


6

Yes, we can say the number of species is limited as you conjecture. However, quick estimation shows that the limitation has no apparent usefulness: A reasonable estimate of the largest known genome is 150 GB (150,000,000,000 or 1.5e11 nucleobases). The limit would be 4 raised to that power. That limit is so high that it is too large for most calculators ...


6

That's an interesting conjecture about the total amount of genetic variation that is possible. I would modify a few things. First, since the size of genomes varies greatly among organisms (from 0.5 Mb to 15 Mb just for prokaryotes), there should be a fifth character in your set, representing the absence of a nucleotide. There are also issues of whether ...


6

The smallest unit that can be selected is, of course, the single nucleotide. The most striking examples of this are Single Nucleotide Polymorphisms (SNPs), many of which confer selective (dis)advantages. To take a simple example, imagine a SNP that introduces a frameshift mutation, rendering a gene incapable of producing its protein. If that protein is ...


5

There are a number of more recent papers dealing with phylogenetic methods in reconstructing language history as well, including work by Colin Renfrew and Quentin Atkinson. Here are two recent high-profile papers. Unfortunately, both are still behind paywalls, but even reading the list of papers they cite / that cite them would be a great way to answer your ...


5

Very little is known about the structure of fitness landscapes. H.A. Orr (2005; also Whitlock et al., 1995; Kryazhimskiy et al., 2009) explains that most experimental results do not actually attempt to measure the fitness landscape, but instead report just the average fitness versus time and average number of acquired adaptations versus time. This can't be ...


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 ...


3

I'm going to define a species according to the biological species concept, probably the most widely "accepted" species concept where a species is a group of individuals that reproduce, or have the potential to do so. Using a simplified example I will show you that gene*environment interactions affecting phenotype can allow separate species to occur despite ...


3

Replace the word "complexity" with any other word..."height", "weight", "resting metabolic rate", etc. and the model would still be solvable in a mathematical sense and it would read the same way. So, it's hard for me to accept the model as relevant to the evolution of complexity. I think you need to make the model have a more robust definition of ...


3

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

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 ...


2

In an evolution mutations are often random and lead to differences in phenotype that can be adaptive under certain pressures. A lot of times mutation is a random process, but here are three cases I can think of off of the top of my head where I would say the organism is 'trying' to do it: HIV is a retrovirus, which means in its viral form its genome is ...


2

Branching processes (from probability theory) were originally developed to study the extinction of family names (Galton-Watson process), but are also used to study biological extinction and general evolutionary processes. One example that applies ideas from branching processes and phylogenetic methods to reconstruct ancient languanges can be found in Forster ...


2

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 ...


2

The concept of fitness is very general. An adequate definition of fitness is hard to specify in the same way that a definition of "species" is hard to give. To be useful, scientific or technical definition of such broad concepets will often need to be so narrow that more than one is needed. A uselessly broad definition of fitness might be: "Fitness is ...


2

The question is interesting. I am afraid about the use of the word "fitness" in you question. The fitness is usually defined as the number of offsprings an individual can sire in its lifetime. Most often we talk about relative fitness which is the relative number of offspring in an individual can sire in its lifetime compare to the individual in the ...


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

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

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 ...


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

This is actually a very interesting yet difficult question to give a single precise answer to. I will try and summarize for you a "meta answer": Complexity Science Some consider complexity not to be a Biological topic as such, since it is a property that accumulates in non-biological systems e.g. economics, technology, music, language - in fact anything ...


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

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

Theoretical biology spans multiple disciplines and the unaccompanied term evolution is defined differently in each: As such chemical evolution is different from time evolution in physics and many other systems in theoretical biology that "evolve". These do play a role in theoretical biology. Also, what standard answer to evolution in the field of ...


1

Pianka's index of niche overlap is defined in his papers from 1973 and 1974, as: $O_{kl}=\dfrac{\sum_i^n{p_{il} p_{ik}}}{\sqrt{\sum_i^n{p_{il}^2} \sum_i^n{p_{ik}^2}}}$ where $O_{kl}$ is the resource overlap between species $k$ and $l$, and since the index is symmetric $O_{kj} = O_{lk}$. $p_{ib}$ represents the proportion of resource $i$ that is used by ...


1

As I see it, your question is also encompassing an inquiry for a theory of fitness. In recent years the inclusive fitness theory has seen its share of interest, which can be applied to social entities. Freely citing from wikipedia here: An organism is judged by the number of offspring it has, how they support them, and how their offspring could ...


1

update The answer is here! Original comment/answer Kimura and Ohta (1969) showed that assuming an initial frequency of $p$, the mean time to fixation $\bar t_1(p)$ is: $$\bar t_1(p)=-4N\left(\frac{1-p}{p}\right)ln(1-p)$$ similarly they showed that the mean time to loss $\bar t_0(p)$ is $$\bar t_0(p)=-4N\left(\frac{p}{1-p}\right)ln(p)$$ Combining the ...



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