text:
Why do genetic drift generates negative linkage disequilibrium?
The very first sentence of the abstract of this article is:

"In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci."

Question
Why does genetic drift generate negative linkage disequilibrium?

Im still a bit confused about this.. I understand that low variance should mean that negative equilbria are less affected by selection, and therefor favoured by drift, but I don't understand what causes the low variance to begin with..

@user2810298 I believe negative disequilibria means "associations between deleterious and beneficial alleles" Keightley & Otto, Interference...; whereas I believe positive disequilibria means those between deleterious and deleterious (or, beneficial and beneficial). I think if one has a deleterious allele and a beneficial allele, their fitness effects are canceled out, hence causing low variance.

@Vibius Is there a precise sense in which fitness effects can `cancel out'?

Genetic drift is the change of allele frequencies in a population due to random sampling during reproduction. This can cause some allele combinations to become more or less common than would be expected without drift, thus creating a disequilibrium. However, it's the combination of genetic drift AND selection that generates negative (instead of positive) disequilibria. From the discussion of the article you linked to:

Selection eliminates positive disequilibria more efficiently than it eliminates negative disequilibria, because negative disequilibrium reduces the genetic variance upon which selection acts. Consequently, the average disequilibrium over loci ... becomes negative over time.

Drift can cause negative or positive disequilibria, not just negative, by changing allele frequencies through random sampling error. Since selection acts on variance and negative equilibria correlate with low variance, they are not affected by selection as much as positive disequilibria. Thus genetic drift favours a negative linkage disequilibrium only in the presence of selection. Does that make it clearer? Perhaps I'm not understanding what you're asking (wouldn't be the first time today).


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Viruses: Adaptation to a new host through repeated host jumps
A friend told me, during a 3 minute discussion, that viruses that are endemic in host $A$ and make repeated jumps to host $B$ but can't be transmitted between individuals of species $B$, may slowly adapt (through these repeated jumps) to be able to be transmitted between individuals of host $B$ and become epidemic.
I don't know much about epidemiology. I don't understand how a virus population that is endemic to host $A$ may adapt to host $B$ with repeated jumps while the viruses that jump to host $B$ are dead end because they cannot be transmitted further more. Or Are these viruses able to jump back to host $A$ to bring back their newly acquired adaptations to host $B$?
Also, I might misunderstand the meaning of "repeated host jumps transmission". I first thought it meant repeated jumps from a reservoir population in host $A$ to host $B$, but it is also possible that it describes the dynamic of a virus population that is adapted to jump from species to species and they actually gain this ability by keeping jumping and jumping. But then, how could a virus species get adapted to jump from species to species? I'm a bit confused…. Can you give me some hints about this process of cross-species transmission through repeated jumps?

A friend told me, during a 3 minute discussion, that viruses that are
  endemic in host A and make repeated jumps to host B but can't be
  transmitted between individuals of species B, may slowly adapt
  (through these repeated jumps) to be able to be transmitted between
  individuals of host B and become epidemic.

This is...mostly true. A good example is avian influenza - there are a number of human infections linked to contact with infected poultry, but the virus is not particularly good at sustaining long chains of human-to-human transmission, likely due to differences in the respiratory tract between humans and birds.

I don't know much about epidemiology. I don't understand how a virus
  population that is endemic to host A may adapt to host B with repeated
  jumps while the viruses that jump to host B are dead end because they
  cannot be transmitted further more. Or Are these viruses able to jump
  back to host A to bring back their newly acquired adaptations to host
  B?

What they mean by repeated jumps, or what they should mean, is not a virus hopping back and forth, but a virus going from A to B many times. This is my problem with your friend's statement, it's not so much a "slow adaptation" as, well, random chance.
Imagine that there's a mutation in Virus A, which lives in chickens, that will make it well adapted to live in human beings. It's an extremely rare mutation, so the dominant strain of Virus A is maladapted for human to human transmission. That means most Virus A infections in humans will be the non-productive kind, that will infect a person, but not go on to infect other people. But, with enough rolls of the dice, a human might get the human-favored Virus A, and since there's now intense selective pressure for that strain of the virus within its new human host, it might establish itself and take off.

A quick answer for now (I'll add details as I find):
The infection of B from A would be zoonosis. This transfer may not have followed a classical route of infection. For example the case of hantavirus pulmonary syndrome (HPS), the zoonosis occurs throuch the rodent (primary host) droppings.
Other example is that of avian influenza- the zoonosis doesn't happen via the respiratory route but by contact with body fluids of infected birds.
Also dead end can be achieved in the case of vector borne diseases especially those of Arboviruses. There is no mechanism of spread other than through a vector.
In other cases the virus may not be produced in high titres in the secondary host to cause infections, but enough to cause mild symptoms.
It is interesting to know how the pathogen can propagate in B but cannot infect: I dont have a definitive answer for this. If a receptor/viral adsorption site is similar between the two hosts but interaction with virus is much stronger in A, then B cannot be infected unless there are loads of virions. However once adsorbed, they can propagate within the cell and go from cell to cell with a relative ease, may be by using a different mechanism. For e.g. , in case of plants the viruses can go through plasmodesmata.
Back jump should be possible unless the pathogen has mutated to fit the new host. In such cases a enzootic infection might happen and A will be dead end. For e.g. in influenza.
This article says that dead-end host (dragonfly) behavior can be manipulated by a certain parasite (Acanthocephalus lucii) to increase transmission probability to original host (perch).
PS: influenza is a very unique case as you might be aware of the genetic drifts/shifts that make it highly adaptable.
Refer this article for some details, It has a section on dead-end transmissions.

Thanks a lot for your answer. I am not sure I fully understand: Can you tell me what is usually meant by "repeated host jumps". Does it mean repeated jumps from a reservoir population in host $A$ to another host $B$. Or does it mean that virus lineage jumps repeatedly from host to host, from the bat to the dog, from the dog to the pig, from the pig to the human, etc...

i dont understand that term either.. didn't get any hit on google.. It might mean the case of influenza where the virus has jumped to and from many hosts.

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text:
Various Genetic Loads and their Definitions
In population genetics, we talk about several types of genetic loads (also called just loads). I am asking for a exhaustive list and a short definition.
Here are for example some genetic loads that come to my mind..

Mutation load
Segregation load
Drift load
Lag load

Could add gender load - the cost of sexually antagonistic selection on traits with non-zero cross-sex genetic correlations (If SA selection affects shared genetic material then one/both sexes are constrained from reaching the optimal phenotype, this is the gender load). http://rspb.royalsocietypublishing.org/content/277/1686/1345.abstract

The genetic load is a population construct, a way of quantifying the fitness reduction in a population due deviations from the optimal genotype.
One type of load comprises all the others, namely genetic load.

Genetic load is just the loss of mean fitness relative to the ideal fitness.

You forgot to include substitution load in your list, but otherwise I think you included all the main ones.

Substitution load is the total loss of mean fitness caused because favorable alleles substitute gradually by selection rather than
  instantaneously.

As for the ones you mentioned:

Mutational load is just the accumulation of deleterious alleles in a population.
Segregating load is the decrease in fitness in a population due to homozygotes being less fit.
Drift load is the fixation of deleterious alleles due to small population size. The smaller the population, the greater the risk of
  this happening.
Lag load is the loss of fitness due to a change in environment.

Another type, mentioned by rg255:

Gender load, which is the deviation from the optimum due to an allele drifting back and forth because the version that is optimal in one sex is not the one that is optimal in another.

Different load described here Lande 1976, Barton and Partridge 2000; Standing load: standing genetic variation in fitness, Migration load: new maladaptive variation due to gene flow, selection load: natural selection within a generation. Phenotypic load (Wallace, 1970)

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A question on the spike-train autocorrelation function: Do we ignore the integration where the integrand is not defined?
In Dayan and Abbott's Theoretical Neuroscience book, they defined the spike-train autocorrelation function
in section 1.4 as
$$ Q_{\rho\rho}(\tau)=\frac 1T \int_{0}^{T} \langle(\rho(t)-\langle r\rangle)(\rho(t+\tau)-\langle r\rangle)\rangle dt .$$
But to be rigorous, $\rho$ is defined only on $[0,T]$. So the integrand is only defined on, say, $[0,T-\tau]$ for $\tau>0$.
When we compute the spike-train autocorrelation function, do we extend $\rho$ periodically, or do we simply ignore the integration on the intervals where the integrand is not defined?
By the way, Dayan and Abbott said in the book that a spike lasts about $1\text{ms}$.
But it seems that the book did not mention the order of magnitude of the duration of a trial
(Some figures implicitly indicates how long an experiment lasts. But the duration varies from $80\text{ms}$ to $300\text{ms}$).
It also seems that the book did not mention the order of magnitude of the number of spikes of a trial (But this may be related to the duration of a trial. And hence it is equivalent to asking the average firing rate $\langle r\rangle$).
I also want to know the domains of $\tau$ where we care about the value of $ Q_{\rho\rho}(\tau)$.
If we do ignore the integration on the domain where the integrand of $ Q_{\rho\rho}(\tau)$ is undefined,
is $\tau$ values subject to we are interested in the value of $ Q_{\rho\rho}(\tau)$ sufficiently small (relative to the trial duration $T$),
such that the above amount can be ignored?

Might this not be more suited to our [psychology.se] site than here?

I searched the keyword "Dayan Abbott" and found on both sites there are questions on details of this book. The Psychology& Neuroscience SE has more questions on this book, but it seems less active than the Biology SE.

I'd not extend p but rather divide by a "trapezoid" rather than "rectangle" 1/T that would be equivalent to integrating over all the possible event times.
You're right this only matters much if the duration is relatively short.
Also for this integral you should consider spike times as discrete.
Bair, W., Zohary, E., & Newsome, W. T. (2001). Correlated firing in macaque visual area MT: time scales and relationship to behavior. Journal of Neuroscience, 21(5), 1676-1697. is also a useful read regarding normalization of cross-correlation functions.

Thanks. May I ask two more questions? By "dividing by a trapezoid", does it mean for example, dividing $T-\tau$ for $\tau>0$? And "This only matters much if the duration is relatively short.", does "this" refer to $Q_{\rho\rho}(\tau)$, i.e. we are only interested in the value of $Q_{\rho\rho}(\tau)$ when $\tau$ is small?

@Asigan Stop and go back and think about what we're representing by an autocorrelation function. Like your previous question about this book, Dayan and Abbott will tend to give you equations in place of or alongside paragraph descriptions, assuming that these are clear to understand for someone used to reading equations, but in the real world we're never going to do these things with real data using symbolic representations of integrals, we're going to count with a computer.

By "this" I mean accounting for spikes occurring in the the edges [0 tau) and (T-tau T] of the window not having full observation time. If tau<<T these edges are too small to matter. If tau is comparable to T, the edges are important. Biologically, autocorrelations at very long tau are not going to be that meaningful (for a rough order of magnitude, let's say autocorrelations are most likely to be meaningful <200 ms, but please don't hold me to that as a strict boundary.)

Sorry for this late reply. I have been thinking this problem for days. Can I interpret it as (1) In the experiment in reality, $Q_{\rho\rho}(\tau)$ is actually measured in the manner which is explained in the next paragraph of Dayan & Abbott's book: "The spike-train autocorrelation function is constructed from data in the
form of a histogram by dividing time into bins... "? (By the way I am not sure how this paragraph works. I wrote how I understood it as follows. Would you mind justifying if I understood correctly?)

Given a $\tau$, take a sufficiently small $\Delta t$. Exists an integer $m$ such that $(m-\frac12)\Delta t<\tau<(m+\frac12)\Delta t$. Consider all spike pairs $(A, B)$ such that the time of $A$ minus the time of $B$ lies in the interval $[(m-\frac12)\Delta t, (m+\frac12)\Delta t]$. Let the number of such pairs be denoted as $N_m$. Consider
$$\frac{N_m}{T\Delta t}-\frac{n^2}{T^2}$$
which equals $\frac{H_m}{\Delta t}$ on Dayan and Abbott's book.
When $\Delta t$ is taken to be very small, experiments can observe that the above expression tends to a value. This value is $Q_{\rho\rho}(\tau)$.

(2) Is it true that the formula $Q_{\rho\rho}(\tau)=\frac 1T \int_{0}^{T} \langle(\rho(t)-\langle r\rangle)(\rho(t+\tau)-\langle r\rangle)\rangle dt$ only gives an intuitive explanation of $Q_{\rho\rho}$ calculated from the histogram as Dayan & Abbott indicated, and this formula is not rigorous from a mathematical view? If it is mathematically rigorous, would you please set an example how this formula calculates $Q_{\rho\rho}(\tau)$ if we are given a sample, say, spikes at $t_1,\cdots,t_n$ in a trial with duration $[0,T]$ and $t_1,T-t_n>\tau$?

@Asigan Autocorrelation is the chance of seeing a spike at lag Tau relative to another spike, normalized by the overall firing rate. That's what you should see when you read the equation. If you don't have infinite observation time, then there are some lags Tau relative to some spikes that you do not actually observe so you shouldn't count them as if there are no spikes there.

I think the Bair paper I linked to would be useful, have you read it? I don't like the phrase "mathematically rigorous", it's not useful when you're doing science instead of math.

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What preceded ATP synthase?
ATP Synthase is ubiquitous throughout life on earth and so most probably evolved within the last universal common ancestor (LUCA) before that lineage diversified into the various kingdoms of life.
It is suggested that the functional domains comprising the ATP Synthase complex were cobbled together from pre-existing sub-units, each with with a related activity (e.g. the union of a proton motor with a DNA Helicase with ATPase activity), which seems reasonable, although a bit vague in the details.
The fact that a primitive ATP Synthase arose in the first place suggests that ATP already had a central role in cellular metabolism and so begs the question, what preceded ATP Synthase in the role of generating ATP in the LUCA cell?

ATP Synthase is NOT ubiquitous throughout life on earth. It is lacking from most anaerobic organisms.

There are metabolic processes in which ATP is synthesised without the involvement of ATP synthase. The best examples are, in fact, two steps in the glycolytic pathway, catalysed by phosphoglycerate kinase and pyruvate kinase. This is why, in the absence of any aerobic metabolism, many organisms (like yeast for example) can grow quite happily, producing two molecules of ATP for each molecule of glucose that is metabolised.
Presumably this process is what enabled ATP to gain its central role in energy metabolism without any need for an ATP synthase.

We don't know much about early evolution of life. However it is believed that energetic molecules (analogous to ATP) may have evolved before everything else. These energetic molecules may have driven different metabolic reactions (which need not be catalyzed by big protein enzymes). Also, it is believed that natural chemical gradients would have been used by primitive life-forms to obtain the energy.
You can have a look at this article. I am pasting the list of references/recommended reading mention in this article so that you may search for them individually even if this article is not accessible any longer.

- Allen, J. F. The function of genomes in bioenergetic organelles. Philosophical Transactions of the Royal Society of London B: Biological Sciences 358, 19–37 (2003)

- Efremov, R. G., Baradaran, R. & Sazanov, L. The architecture of respiratory complex I. Nature 465, 441–445 (2010) doi:10.1038/nature09066

- Lane, N., Allen, J. F. & Martin, W. How did LUCA make a living? Chemiosmosis in the origin of life. Bioessays 32, 271–280 (2010) doi:10.1002/bies.200900131

- Lane, N. & Martin, W. The energetics of genome complexity. Nature 467, 929-934 (2010)
- Martin, W. & Russell, M. On the origin of biochemistry at an alkaline hydrothermal vent. Philosophical Transactions of the Royal Society of London B: Biological Sciences 362, 1887–1925 (2007)
- Mitchell, P. Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism. Nature 191, 144–148 (1961) doi:10.1038/191144a0
- Orgel, L. Are you serious, Dr Mitchell? Nature 402, 17 (1999) doi:10.1038/46903
- Russell, M. J. First life. American Scientist 94, 32–39 (2006)
- Silverstein, T. The mitochondrial phosphate-to-oxygen ratio is not an integer. Biochemistry and Molecular Biology Education 33, 416–417 (2005)

Is this really a chicken–egg question? It just seems to be asking whether a simpler method of ATP generation preceeded the ATP synthase and if so what. Isn't this actually acknowledging the solution to the real chicken/egg problems with ATP, such the need for ATP in the synthesis of the adenine ring of ATP? Your list of references is very useful, but can I suggest you provide more context by naming the "energetic molecules" you mention.

@David point taken. The energetic molecules that I mention haven't really been identified. It is just hypothetical. This is probably mentioned in one of the references. Nonetheless, I'll try to look up and provide some more context asap.


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Formal definition of an animal
The Wikipedia entry for animal defines it as a “multicellular eukaryotic organism in the biological kingdom, Animalia”. I do not find this definition very clear. In particular, it seems almost circular, as if an animal is anything we define to be an animal.
I tried finding a different definition, but the Oxford dictionary definition doesn’t seem to me to be any more satisfactory:

“a living organism that feeds on organic matter, typically having specialized sense organs and nervous system and able to respond rapidly to stimuli”

Certain plants such as Venus fly trap would seem to me to fall under this definition.
So, is there a formally accepted definition of an animal in biology? If it is the definition given by Wikipedia, how do we decide which organisms fall into this kingdom? Or is it just that whatever morally feels like an animal (e.g. human, cat, dog, horse, fish, etc.) gets put into this kingdom?

Related Q&A: https://biology.stackexchange.com/questions/113386/what-is-a-fungus-formally/

@virolino From the perspective of biology, reptiles are always animals. Insects are always animals.

@virolino I'm honestly curious: what contexts are you thinking of where reptiles or insects wouldn't be described as animals? I legitimately can't think of any.

The Venus Fly Trap doesn't have a nervous system.

@Idran: In the context of the real world, where jokes like this are funny exactly because of that: "Is a bat an animal or a bird?"

@virolino Huh. I guess I can see that, but to me the humor in jokes like that is specifically from the two options not being mutually exclusive and/or the mixup in wording for one of them (a.k.a., accidentally saying "animal" instead of "mammal" because they sound similar). Like, it wouldn't be funny to me if in the context of the joke birds actually weren't considered a subcategory of animals, because there wouldn't be any twist.

There are two implicit parts to the question:

what animals are as a taxon and
why we call this taxon "animals" (= Animalia = Metazoa).

Organisms are classified mostly based on the understanding of the evolutionary relationships between them. Nowadays, evolutionary relationships for extant organisms are resolved using molecular data, in particular multiple gene sequences which provide many simple characters for phylogenetic reconstructions.
There are many branches on the tree of life (clades), each one has the potential to be treated as a taxon. To understand what clade deserves a name and corresponds to a particular rank, taxonomists search for well-supported clades with easily recognizable derived traits associated with them.
So, animals can be defined as the organisms belonging to the clade that includes organisms from Trichoplax and sponges to humans, or in other words: which includes the last common ancestor of these organisms and all its descendants. It is a well-supported deep clade and we call it Animalia = Metazoa based on the fact that most organisms that have been included in the typological definitions (i.e. definitions based on formal morphological inclusion criteria) of the traditional taxon "Animalia" starting from Linnaeus belong here. The typological taxon "Animalia" in turn is an improvement upon the earlier typological definitions of the word "animals/ζῷα/animalia" starting from Aristotle and both are attempts at formalizing the intuition languages originally have for the word "animals".
Thanks to shared ancestry, animals have a number of synapomorphies (features evolved in their last common ancestor) which include multicellularity, anisogamy, specific developmental signalling pathways, reduced mitochondrial genome and others. Synapomorphies are not inclusion criteria as in typology. Even if some other group developed a similar trait (e.g. multicellularity evolved several times among eukaryotes independently) or even if some animals lose some of these traits (although outside of zoological taxonomy, one extreme case might be transmissible cancers, such as canine transmissible venereal tumour which are essentially unicellular parasites recently derived from multicellular animals) those organisms do not become/stop being animals.
Oxford Dictionary in your citation does not define what an animal is. From the perspective of modern biology, it only mentions some traits found in some animals — not all animals have nervous system and not all rapidly respond to stimuli. Analogously, organisms that independently evolved fast responses do not become animals: they do not share ancestry with them and they lack their synapomorphies. Whatever similarities they might have with animals would be due to plesiomorphies (traits inherited from a more distant ancestors) or convergences/homoplasies (traits evolved independently).

So transmissible cancers fall under kingdom of animalia?

They are self-sustaining cell lines which diverged relatively recently (hundreds to thousands of years ago), so they are outside of zoological taxonomy and nomenclature, although I imagine that if a transmissible cancer is discovered to have survived for longer periods of time over, say, 1my, this would definitively warrant establishment of a separate species. The point here though is that these cell lines do not cease to be animal cells just because they underwent reductive evolution and complete their life-cycle without a multi-cellular stage.

Good answer, +1. But to emphasize a point - which is implicit in your answer - we didn't start from the bottom of the tree of life; we started with what is 'obviously animals', like cows, and then worked our way down, so to speak. Thus, what fundamentally defines what an animal is, derives from this process, and is incidentally somewhat muddled at the bottom level.

While the information shared by @alephreish is fascinating, it does seem to fall short of answering the question "what is the defintion of an animal". It seems a bit circular: an animal is an organism that belongs to the clade Animalia. OK, but why does it belong there? Yes, the evolutionary relationships are mentioned, but where along the trail backwards do life forms become "animal" and upon what basis?

@j4nd3r53n Good point, I'll update my answer

@DaveWelden When you get to the common ancestor of all animals. "Animal" is a label for a branch of the tree of organisms, defined by common descent. A different tree of life from some alien world would not ever have an "Animal" by that definition; you might describe something as animal-like, but there is no generic "Animal" definition the way the term is used in modern biology, and it's a mistake to expect one.

You can come up with characteristics that help you identify something as an animal, but that's not the same as a definition. Something that met all the characteristics but wasn't evolved from animals would not be an animal.

No disagreements, but here is the nub: why at a certain branch did organisms become classified as Animal? Why is that common ancestor of animals THE common ancestor? That seems to be the key unanswered question.

@DaveWelden & j4nd3r53n Pls see my update to the answer, I hope it addresses your points.

@DaveWelden - "Why is that common ancestor of animals THE common ancestor?"  It's not the most recent common ancestor of "all traditional animals" who ended up representing Animalia.  It's an earlier common ancestor on that branch, one selected so as to be easier to define genetically (or phenotypically), but still not needlessly extensive beyond traditional animals.

@DaveWelden That's also fairly arbitrary. If we drew the line somewhere more recent than sponges, then we'd need a separate category for sponges all alone. We didn't, so those are animals, too.

Maybe the common ancestor is not the right way to approach this, but I feel we are getting closer. Let me approach the question this way. What were the factors that indicated branch Animalia as a separate branch/clave from the other branchs/claves? Something identifies Animalia as distinct from the others. Is it some distinctions in the DNA or RNA as mentioned in some commentary? Is it morphology? Is it generating food vs. need to obtain food externally? A combination of these and other factors?

@DaveWelden They are multicellular eukaryotes that consume (rather than produce, as plants) organic material, move, and develop through a blastula. But...that's not a definition, because if you find another multicellular eukaryote that consumes and moves, etc, that wouldn't make it an animal in the taxonomic sense. Rather, those are the hints that the group of organisms sharing those characteristics are possibly related by common descent.

So the best conclusion I can draw at this point is that it is somewhat arbitrary. Animalia includes the organisms that have historically been identified as animals as well as some that perhaps were unknown/not considered historically. But while they are related in terms of descent from a common ancestor, the selection of the ancestor and the factors that led to Animalia as a distinct branch are somewhat arbitrary. We decided to draw the line here and called it Animalia.

@DaveWelden I think that's a good summary, yes. I think it's also worth considering the broader context of the task of organizing the known life on earth, which has been quite a difficult and sometimes controversial task. https://en.wikipedia.org/wiki/Tree_of_life_(biology) might be a good place to start reading. I'd also suggest looking at the history of "protists" to see how organisms that may have some apparent shared characteristics are not treated as a meaningful grouping by modern biology. Conceptually, the same thing could have happened with old ideas of what makes an animal.

Certainly the task is immense and the classification schemes have evolved over time. There has been controversy and new categories have been created as knowledge has expanded. I was hoping that where the lines were drawn to say this organism is Plant, that one is Animal, the other is Fungi, etc., would be more easily explained, but perhaps it oversimplifies the reality.

@DaveWelden welcome to biology, nature does not care about our human need to group organsims in boxes. Any line we draw between organsms is at some level arbitrary.


text:
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 very simple model. I welcome any explanation of some other classic model of the evolution of quantitative traits.
Scenario
Consider a haploid population of constant size $N$. The fitness of the individuals is determined exclusively by a single quantitative trait $z$. $l$ loci codes for this trait. The genetic value at each locus adds up to give the quantitative trait $z$. The mutation rate at each locus is $\mu$. A mutation changes the genetic value at any given locus by $+ \Delta z$ with probability $\frac{1}{2}$ and by $- \Delta z$ with probability $\frac{1}{2}$. If you prefer to consider the effects of a mutation to be drawn from a normal distribution with mean $=0$ and variance $= \sigma^2$, please feel free to do so. The fitness $w(z)$ of an individual is given as a gaussian function of its quantitative trait $z$
$$w(z)=\exp\bigl(-Vz^2\bigr),$$
where $V$ is the strength of selection. The optimal phenotype is $0$, that is $w(0)=1$. The larger is $V$, the more severe it is to be at a given distance to the optimal phenotype. If you want to assume that the fitness $w(z)$ is some other function of the trait $z$, such as the even more simple $w(z)=z$, please feel free to do so. For simplicity, we assume no environmental variance on the quantitative trait.
Questions
What is the equilibrium mean fitness $\bar w$ of the population?
What is the equilibrium genetic variance (=phenotypic variance) for fitness $w$ and for phenotype $z$?

What have you gotten, so far? This reads like a homework question.

I would have love receiving this kind of homework. It is not a homework question. Because I was trained in Europe, the last homework I had to do was probably during the first year of my bachelor degree or even in High school. For the moment, I pretty much developed the basis of a model (presented in the post) to think the evolution of quantitative trait but this is it, I fail to bring it any further to answer my question(s).

@dd3 This is a little complicated than a usual homework.

Trait z is represented by k genes: z1....zk (I am using k instead of l because the former is visually differentiable from 1 ).
For simplicity let's assume that there is only one mutable site in a gene. So a mutation can impart a change of $\pm \Delta z$. Starting from initial state of z at zero, the system will proceed to equilibrium where the rate of forward mutation would be same as that of backward mutation; since the rates are same the deterministic steady state of z should be zero.
A mutation event can also be considered a binomially distributed RV. After n events, the mean number of forward mutations would be 0.5×n.   Mean fitness = mean forward mutation — mean backward mutations = 0
You can also model the mutation events as a simple random walk. The mean of that is 0 and the variance is n. But what about large n; I am not sure. You should read about random walks or ask in CrossValidated. With $t\to \infty$, you would get a lot of variants but variants would be filtered out by selection (as the optimum is at 0). I think selection can be incorporated in the random walk with death rate being proportional to the distance from 0. But again I do not have much experience with such hybrid models.
I tried a simulation with n=10000000 (using Monte Carlo); different colours denote different runs (or in another words different loci). Y-axis denotes the value of z.

This is interesting, I didn't think about modelling this with a diffusion process. A diffusion equation contains 2 terms, "diffusion" (equivalent of genetic drift) and "drift" (equivalent of selection). An issue with this methodology though is that we can only track the mean trait and the variance in mean trait (the RV mean trait is normally distribution if the process is a random walk) of the population and not the variance in the trait within a population. +1


text:
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 remember the methods that exists and what are their assumptions.
For example some use $P=2s$, this obviously cannot be right for be values of s, neither for deleterious mutations, and therefore, this approximation seems to make sens only for big population size. Haldane developed a method to calculate the probability of fixation based on the assumption that the fecundity follows a binomial distribution. Kimura used diffusion equation to approximate the probability to fixation. There might exist other solutions. I don't think I ever seen an equation that allows for varying dominance effect $h$.
Can you make a summary of the methods you know for calculating the probability of fixation? Don't forget to highlight the assumptions. A comparison between the accuracy of the different methods would be great as well.


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Why are animal mitochondrial genomes so conserved and small in comparison to those of plants?
Background
Levings and Brown (1989):

Higher plant mitochondrial genomes are much larger and
  more complex than those of other organisms. They vary
  in size from about 200 kb in Brassica species to 2500 kb
  in watermelon, which is substantially larger and more variable
  than mammalian (15-18 kb) or fungal (18-78 kb) mitochondrial
  (mt) DNAs

Boore (1999):

Animal mitochondrial DNA is a small, extrachromosomal genome, typically ∼16 kb in size. With few exceptions, all animal mitochondrial genomes contain the same 37 genes: two for rRNAs, 13 for proteins and 22 for tRNAs.

Question
Why are animal mitochondrial genomes so conserved and so small in comparison to those of plants?

Interesting question. Do you have access to this paper? I don't, but the abstract seems promising.

Here's another.


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Why can't other electron acceptors produce as much ATP as oxygen?
I have been wondering about life using a different "Final" electron acceptor(replacing oxygen), but every thing I can find in my research say that oxygen produces more ATP because of its higher affinity for electrons.
But as far as I know, in the electron transport chain, the ATP produced is because of protons going through the ATP synthase because of an imbalance in protons(the protons being generated by the electrons moving through the ETC). But since all the protons are generated by the time the electrons have made it through and are ready to be accepted by oxygen, then shouldn't the number of protons generated be the same regardless of that final electron acceptor? And if the number of protons produced is the same, then shouldn't the same amount of ATP be produced?
Why, despite the same number of protons being generated by electrons in the ETC, do other "Final" electron acceptors (such as Fe3+) besides oxygen produce less ATP?

Welcome to Biology StackExchange! Can you please include some references for your statements, that is: which sources did you use in research that has these claims?

Short answer: The "worse" final electron acceptor will just not accept the electron, and electrons will just get back up in the electron transport chain, shutting down oxidative phosphorylation.
Long answer: This is related to a deceptively dissimilar question: "Why do cells throw away perfectly good organics in fermentation?"
To really explain this, you'll have to know some quantum mechanics.

Every nucleus, atom, molecule and ion has orbitals (MO theory) , little "slots" for electrons to exist in (shown as horizontal lines). Orbitals have distinct "energy levels", thanks to the electromagnetic interaction between the electron, the nucleus (nuclei) and other electrons. Typically, electrons will exist in the lowest energy level not occupied by another pair of electrons. Electrons release energy when they move down and absorb energy when they move up. A free electron ($n= \infty $) will release more energy moving to the lowest energy level ($n=1$) when that lowest energy level is more negative, and will have to absorb more energy to become free again. This is what is meant when we say an electron acceptor has "higher affinity for electrons".

The ENTIRE gimmick of the electron transport chain is that the electron moves to progressively higher affinity acceptors, releasing energy in the process. By the time the electron reaches the penultimate of the electron transport chain, its energy level is so low/the acceptor affinity is so high (equivalent) that it takes another acceptor with even higher affinity to attract that electron.
But what if the cell just... throw the electron away? Well, that would completely defeat the point. For the electron to become free it needs to be provided with energy. More energy than what the electron transport chain has extracted for sure, because the electron in the food molecule isn't even free to begin with.
Ok, but WHAT IF the cell use the electron to build organics instead? Every cell requires an energy source, a carbon source and an electron source. Unfortunately, that won't work in this case. Organics in biology usually requires electrons with energy equivalent to that of NADH. Since that is the very beginning of the electron transport chain here, it won't work.
The ONLY productive way to throw an electron away is to give it an acceptor and then throw that away too.
So that's why Fe3+ etc cannot accept an electron from the penultimate of the aerobic electron transport chain. Because you'd need to provide energy to the electron to do so.
Back to the question I proposed in the beginning. "Why do cells throw away perfectly good organics in fermentation?". By definition, fermentation means using an organic terminal electron acceptor. What usually happens is that cells do this clever maneuver where they rip the electron from an high energy position in the molecule and puts it in another position with lower energy.

Notice the cycling of the electron carrier NADH.

The items of information assembled in your answer may be individually correct, but imho they miss the wood for trees, and they do not address the actual question. The wood is that the potential to obtain energy from oxidation depends on the negative magnitude of ΔG, and the question is not why no energy is produced if Fe(III) replaces O2 — dissimilatory oxidation of NADH by Fe(III) exists (https://ecampusontario.pressbooks.pub/bioc2580/chapter/redox-reactions-review/) — but why it is less than with O2 This is not obvious as the ΔG is not significantly different, despite the assertion in the Q.

I highly doubt that the ΔG°' is "not significantly different". ΔE˚' is. However, oxygen accepts 2 electron per water, while ferric iron accepts 1 per iron. Using ΔG°' = -nFΔE°', where n is the number of electrons transfered... Yeah you can see where this is going.

Ok. Point taken. But nevertheless, the fact remains that the overall ΔG is sufficient to reduce Fe(III) in dissimilatory oxidation, and your answer does not acknowledge this fact or address the energetics of this process. I have not answered myself because I have not yet tracked down sources for the details of the components of the ETC in dissimilatory iron-reducing bacteria. If you wish to apply your chemical knowledge to the actual situation it will  save me the effort.


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What are the $2^{23}$ combinations in gamete fusion?
According to my textbook, when two human gametes fuse, there's $2^{23}$ different combinations of chromosomes, but I don't see how that is. The chromosomes are homologous, so they don't have any choice to make, and if they did have a choice to make, there'd be a different formula. Are there two oocytes perhaps, and each chromosome in the sperm can chose either one of the homologous chromosomes that exists in the respective oocytes, a choice available to each of the 23 chromosomes, thus yielding $2^{23}$ possibilities?
EDIT:
My textbook made the above claim as a sidenote to its explanation of meiosis. See my translated quotation under (bold made by me):

Therefore, four possible gametes can be formed (BR, Br, bR and br). If we take all 23 chromosome pairs into account, it will be almost 8.4 million ($2^{23}$) combination possibilities. And when two gametes are finally to fuse, the number of combination possibilities increase to almost 70 000 billion ($2^{23} \cdot 2^{23}$).

As you can see, my textbook says the fusion of gametes can happen with $2^{23}$ different combinations of chromosomes. Since I think I've read somewhere that the (pre?)fetus is triploid at some point, it makes sense to me that these combinations come from the fact that each chromosome from the sperm can pick a homolog from either of the two homologs available from the two oocytes. That's $2^{23}$ possibilities (assuming the sperm comes with only Xs).
My textbook is Naturfag Påbygging, by Aschehoug.

The book says when gametes are formed, not fused, is when there are 2^23 combinations. Where are you getting this triploid idea?

@BryanKrause No, the book says there are $2^{23}$ combinations when a gamete are formed and then another $2^{23}$ possibilities when they are later fused. Also, I got the triploid idea from double-fertilization, so nevermind that, I didn't read it properly the first time.

I think it is difficult to judge the original text on the basis of a translation, but it seems to me to be, at the best ambiguous, and, at the worst, wrong. I think that this ambiguous explanation is widespread and a source of confusion that is not easily remedied by "homework". I think that the question is useful in focussing on this and the downvotes should be reversed. Considering the nonsense we have to put up with from drive-by members of other SE sites, we should consider this question from a genuine student of biology. I have edited the title to fit the situation better.

The calculation is actually quite simple. Each gamete can contribute one of two sister chromatids for each chromosome, so that in humans (with 23 distinct chromosomes) the number of possible combinations in the progeny cell resulting from fusion of the male and female gametes is:

423 (aka approx. 64 trillion  — actually approx 70 trillion)

The number 223 (aka approx. 8 million — hence the erroneous 64 trillion in the source cited below), much loved by various sources including the poster’s text book, is the number of possible combinations of sister chromatids for each individual male or female gamete before fusion.
This is explained with illustration in Biolibre texts in the section entitled “Independent Assortment and Random Fertilization”.
I have no idea why there is an obsession with the number of pre-fusion combinations when the interest of the reader is surely the number of possible outcomes. As a non-biologist the difficulty for me in understanding the explanations I have read is the way that the genetics and cell biology are dealt with together. I admit that the cell biology is important, but if I had to lecture on this topic I would do the genetics first, and then the cell biology.
This explanation is hinted at in the comment from @BryanKrause, but I think that the textbook is at fault, and the poster’s confusion is justified.

The 2^23 number is useful in describing the meiosis process of gamete formation, which occurs before any interaction with any other gamete is relevant. With crossover it's of course also wrong, but still a useful starting point.

Shouldn't it be that there are 2^23 different types of gametes possible from a single individual with 23 chromosomes? The math behind it is as follows:
Case 1: Only one chromosome.
Let's say, from the diploid precursor with 2 homologs of chromosome 1. Half of the gametes would be with the 1A homolog, the other half with the 1b homolog. So, 2^1 types of gametes.
Further cases: More chromosomes.
Consider two chromosomes, 1 and 2, each with 2 homologs (1A, 1B and 2A, 2B). Because each chromosome assorts independent of every other, 2^2 (= 4) possible combinations are possible. 1A-2A, 1A-2B, 1B-2A, and 1B-2B.
Extending the math, this would amount to 2^23 combinations for 23 chromosomes, leading to these many (~8.3 million) gametes from a single human.
Each of these haploid gametes from a male, would combine with a gamete from a female. In each successful fertilization event, the resulting cell would have 46 chromosomes, restoring the diploidy.
I think your textbooks arrives at the 2^23⋅2^23 (= 70,000 billion) by taking into account all the combinations. Since each of the 2^23 male gametes can combine with each of the 2^23 female gametes, the overall combinations come out to be just that. I don't know where you got that fetus is ever triploid (will be happy if you share the source). I still cannot relate this to two oocytes. I'm saying this because your textbook also doesn't mention anything about 2 oocytes (I'm assuming). It just states a combinatorial fact.

This is not what I am wondering about, but it is related. See my edit. My textbook claimed what it did as side note to exactly this.

I think your textbooks arrives at the 2^23⋅2^23 (= 70,000 billion) by taking into account all the combinations. Since each of the 2^23 male gametes can combine with each of the 2^23 female gametes, the overall combinations come out to be just that. I don't know where you got that fetus is ever triploid (will be happy if you share the source). I still cannot relate this to two oocytes. I'm saying this because your textbook also doesn't mention anything about 2 oocytes (I'm assuming). It just states a combinatorial fact.

Ah yes of course, that makes sense. It is the only interpretation that makes sense thus far, so I will accept it if you make that into your answer :)


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Information regarding gastroenterology?
Where, online (preferably free) can learn medical topics in depth, specifically gastroenterology?
I'll try to be concise and to the point:

I have an Associate of Science degree where I actually specialized in Biology
I am asking for online classes, texts, videos, or other resources
My specific interest is in gastroenterology
My need is to understand the subject in depth I imagine several months of research will be required for me to find the answers I need.
Free or nearly free / very cheap sources are the only sources that interest me as I'm rather poor.

I'm sorry to hear that your health is failing. In short, you can't become an expert just like that, it takes several years of full-time training to become expert. However, there is much publically available information for many topics on the NCBI if you search. The latest research is published in journal articles, but these require specialist knowledge to interpret.

@MattDMo Thank you I am aware that asking for personal medical advice is considered off-topic. I am asking for education advice on the topic of biology. The context section was simply provided to help people understand what context I'm asking from, as to be as complete as I can in my query.

@bob1 Thank you for the link to the NCBI, I regularly read research (not just research articles) I figure I have about 2-10 to acquire enough knowledge. Simply reading the latest research, while fun, will not help me much as the research when it leads to treatments nearly always leads to treatments for people with significant money or charity cases, and I just don't make a compelling charity case.
I am seeking to spend the time and effort (not money) that is required to learn the topic of gastroenterology.

Check out https://clinicaltrials.gov for information on ongoing and upcoming... you guessed it! Clinical trials! You don't have to be independently wealthy or a charity case to join a trial, you just need to be (relatively) close to a participating hospital. Many patients are often eligible for trials, and don't participate simply through lack of knowledge of their existence, either their own or their doctor's. If you live near a research hospital, they often have many trials ongoing.

Also, upon rereading your question, I've decided to retract my close vote. I suggest editing out the "context" part at the bottom. We have to be very careful treading around questions like these, because askers can potentially take the first reference off the list of 10 someone provides, skim it and decide that's their answer, then treat themselves accordingly without involving a medical professional or understanding that a single datum of research does not necessarily indicate the way things truly are.

@MattDMo - I wouldn't do that. There's a lot going on here.

Although I voted to close this question, my advice is too long for a comment.
The short answer is, you can't. You can't read enough to learn "gastroenterology". You can go to med school (my oldest classmate was 44), or PA school (much less time). You need to know most of the basics of medicine/biology to understand one organ system, because they are interconnected. Gastroenterologists (off the top of my head) must also understand immunology, endocrinology, neurology, and anatomy (not to mention more basic basics like molecular biology and biochemistry.) Yet, there you are, without an answer. What can you do?
You can pore over the literature, but you won't understand it. You won't know relevant search terms, and whether what you read is reliable. But it doesn't hurt to try. Use Google Scholar instead of Google.
You can write in to various publications (free) where difficult cases are discussed and ask for physicians to help solve the problem or that print difficult cases that were eventually solved to see if they've seen a case like yours or can help you with your problem (The Washington Post and the New York Times are two of the many publications that highlight difficult cases.)
You can "hire" a good patient advocate (not all patient advocates are created equal.) Some people, even physicians, do this work pro bono. A good, empathetic physician who does patient advocacy work would be best. They will review all your medical records with a fresh eye, accompany you on your doctor visits, ask the doctor any questions you might not know to ask, and explain to you what your doctor said (patients don't "hear"/retain about 75% of what doctors tell them, and why they are recommending x, y, or z.) They will also give you an opinion (you need to see someone else/this doctor is competent and trustworthy/other).
Sometimes doctors don't know the answers, but since they can't find anything abnormal, they can tell you whatever is going on isn't going to end your life. Sometimes doctors think they know the answers when what they think is incorrect. The problem is that you don't trust your doctors so far, so the only option is to keep seeing specialists until the issue is diagnosed or resolved. It's expensive, and optimally, get an appointment at a medical center especially well known for excellence, and where cases are reviewed by a board comprised of various specialists.
But what you cannot do is "learn gastroenterology".
I know this doesn't answer the question as asked. But the answer to the question as asked is "nowhere".

Thank you so very, very much for your well-written and informative response! I genuinely do appreciate the thought, the effort, and the insight you have shared with me. You have provided me with some new avenues I had not understood existed! I am very tempted to mark this as the answer to my question, and after an additional month of continuing my search, I will!

I would like to ask, though, who is being helped by "closing" the question? And what can I do to prevent said closing?

Closing a question is a site-specific cultural thing, and it doesn't really "hurt" anyone. It does help to keep off-topic questions off the site. I only answered because I'm a physician who did pro bono patient advocacy work, and because I understand all too well from personal experience what it's like to know something isn't right, yet be unable to find a physician who is capable of making the correct diagnosis. In one case, the ninth doctor I saw immediately diagnosed me correctly, and I had the needed palliative surgery and medications. ...

...I also know how helpless non-medical people can feel in navigating the system. I cared about all my patients, but had a particular soft spot for all patients with difficult diagnoses. That's the reason I provided the answer even though it's off topic.


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Why do some proteins "use" a beta barrel structure instead of alpha helices in transmembrane space?
Most proteins are fixed in the membrane by alpha helices. But some use beta barrels.
Wikipedia describes beta barrels as used for porins, preprotein translocases, and lipocalins. To me, a coiled coil alpha helix structure could surely perform the same functions and given the vast number of proteins using alpha helices there might be some out there.
So my question is twofold:

Are these functions exclusive to beta barrels?
If so, what about alpha helices makes them unsuitable for those functions?

As you can see on the wikipedia page you linked yourself that beta barrels have far larger diameters (in some cases up to 40 angstroms as stated in this paper) depending on the numbers of beta sheets that make up the barrel, compared to the diameter of an alpha helix (that is fixed) of 6 angstroms. (source http://www.chem.uwec.edu/Modeling/GGProteinStructures/Pages/alpha_helix/helix.html). Alpha helices are good to anchor proteins into the membrane, or forming small holes that is suitable for compounds like ions, while with beta barrels larger compounds such as sugars, or various drugs can be transported.
There's a good list of proteins with different functions for both types on wikipedia


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When might an inhibitor of bacterial transformation be useful?
I am part of a project elucidating some structures that are required for bacterial transformation. We have the opportunity to screen inhibitors of the system to stop it from functioning. I am not a microbiologist and have never worked with transformation, and this research process would be time and resource intensive. I am weighing up the pros and cons, however am struggling with how the inhibitors could be practically applied.
How useful would stopping transformation be? My thoughts so far boil down to:
Could it enhance controls by allowing two separate strains to grow on the same plate without any genetic conference?
Could it be applied to stop contamination of genetic information from otherwise insignificant contaminants?
Are there any other problems that transformation is causing in laboratory experiments?

In the research lab? I thought about it for a while and found no usage. But it could be interesting for clinical applications to prevent bacteria spreading their resistance genes (which are usually organized on extra chromosomal plasmids) and thus preventing multi-resistant bacteria.

I did explore this avenue briefly, but although multi resistance may have started by competence (Yeh, 2002: Association of metronidazole resistance and natural competence in Helicobacter pylori. Antimicrobial agents and chemotherapy), I have found no evidence that transformation occurs in patients. It seems that multi resistant bacteria infects a patient, then grows into an established multi-resistant infection.

So you have bacteria coming from outside which make the problem and they are not spreading this ability? Thats interesting.

Well I'm sure they are causing the problem in the body too, but it hasn't been observed or measured. I don't see how a drug would stop reduce multi-resistant bacterial infections since there is so much transformation of these genes externally.


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What controls Fructose regulation in plants?
Sugars are found ubiquitously in plants and are regulated.
For sucrose it's pretty straightforward - it's basically kept at a low ish level, and put into storage or other intermediate compounds. These act to inhibit or promote other parts of the calvin cycle of sugar production (fructose 2,6 bisphosphate especially iirc).
Fructose is a bit more obscure. What are the regulatory feedback loops involved?

Preamble
In short, fructose kinases (like Fru6P,2-kinase) and fructose phosphotases (such as Fru2,6bisP) regulate and are in turn regulated by fructose (specifically Fru6P)  levels in plants. There are also several metabolites that regulate the rate at which those fructose enzymes function creating quite a complex fructose regulatory network. This phosphorylation can make fructose unavailable or available to proteins as well as providing energy in the process (and aparently the rate of this can be controlled effectively in vivo (Stitt, 1990)).
I haven't come across any cell uptake regulation, but remember plants are physiologically very different to humans and there may not be a like for like system in this case. Although I suspect there will be since in plants fructose can be concencentrated in fruiting bodies. Perhaps another answer, or a major edit to this answer can explain that.
Fructose is often referred to as a regulatory metabolite in plants i.e levels of fructose affect other pathways due to its phosphorylated state. However, there are lots of sugar regulating systems in plants. Although this article focuses more on glucose and galactose, it emphasises the idea of a regulatory web rather than a cycle when it comes to plants and sugar regulation. Below the studies are based on plants such as spinach and other leafy vegetation, not fruiting plants I'm afraid!
Kinase Control
3PGA, 2PGA, PEP, dihydroxyacetone P, and the 2-carbon intermediate glycollate-2-P are all metabolites that control phosphorylation that inhibit the kinase, whilst Pi activates the kinase. Interestingly PPi also inhibits the kinase by competing with ATP. As one can imagine, this causes sigmoidal ATP saturation kinetics and is clearly indicative of regulation.
Phosphorylation
Fru6P and Pi both inhibit Fru2,6bisP hydrolysis by FRU2,6PASE.
This article from 1996 has a figure showing just how complex sugar pathways can be. To expand on your question, we can see how fructose phosphorylation plays a role in regulating in Sucrose and Starch glycolysis (Plaxton, 1996).
Disclaimer: I haven't studied this since undergraduate level, so constructive comments are welcome and I encourage people to edit this answer to improve it and help it more aptly answer the question!


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Is there a stem cell dye for education purposes?
I need a dye that will stain stem cells (for this purpose the stem cells will proquired from chicken bone marrow).
This will be an educational hands on activity for young teenagers so ideally the dye should be:

Safe
Easy to handle
Stain quickly
Be relatively cheap
Present an obvious colour change under a low zoom microscope or the naked eye

I vaguely remember using a dye years ago that fits this bill, but cannot recall the name or company.

There is no specific dye for stem cells. You would have to do an immuno-histochemical staining for stem cell markers such as Sox2/Oct4 etc.
Usually stem cells have a distinct morphology (round and clustered). You can use Leishman's (or Romanowsky-Giemsa) stain.

How about Brdu...? Normally, stem cells have active proliferation, their dividing are fast, thus they could uptake Brdu, and this is one of basic stem cell test in papers. I think it isn't too expensive, comparing with antibodies.... but you may need UV-light, and don't let children play Brdu. It is carcinogen, however, I think it only a very high dose can cause a cancer...


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Is there a difference in cytoplasmic pH between prokaryotes and eukaryotes?
The cytosolic pH in human cells is around 7.4, but fluctuates as the cell is replicating. Prokaryotes and eukaryotes are vastly different in many ways. One thing they share is cytoplasm. Is there any general difference in the pH between these two cytosolic spaces? Any pointers to a previous investigation into this would be hugely appreciated. Ideally I'm after a quantified numerical comparison from a peer reviewed reference, but given the obscurity of the question that might be a tall order!
Googling was to no avail. It's swamped with pH survival data.

In the article "pH of the Cytoplasm and Periplasm of Escherichia coli: Rapid Measurement by Green Fluorescent Protein Fluorimetry", by Jessica C. Wilks and Joan L. Slonczewski, the pH of E.coli cytoplasm was mentioned as 7.2 - 7.8. I just took E.coli's pH range as a common example of prokaryotes.
Reference link: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1951819/


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Inductance in cell
In an animal cell, especially neuron and in particular its axon, while there is electrical resistance and capacitance mechanism in the cell, which play essential roles in the cable theory model of neuronal action potential transmission, is there a prominent self inductance mechanism in the sense of electromagnetism?

i don't think there are any magnetic effects in a typical animal body. I can't think of any inductive effects.

@WYSIWYG: Magnetism is a by product of electricity. Is it not strange that animal does not or produce magnetic field while use electricity extensively?  I can think of one instance of magnetic field use in animal, their perception of orientation based on the earth magnetic field. See this NOVA article http://www.pbs.org/wgbh/nova/nature/magnetic-impact-on-animals.html.

Well moving charge does produce magnetic field but if you do the calculations you would need quite some current to generate a significant magnetic field. Yes animals can sense magnetic field but it is limited to some. Nonetheless, I still cannot think of any inductive effects in the cell (where is a coil?)

@WYSIWYG: I am not quite sure how you define "significant" magnetic field. Two parallel lines of current exerts forces on each other in close proximity. Circuit has to be designed carefully to eliminate the unintended inductive effect. Coils are to make the geometry better generate the inductance, but they are not necessary, since other shapes can generate inductance as well. Of course I do not know what structure in a cell would be able to generate sufficient inductance, hence the question.

What one thinks, no matter how intuitive it may appear is not particularly relevant in science.  The inductance associated with a neural axon has been well documented since Cole (1966).  Its role in the propagation of neural signals is developed extensively in http://neuronresearch.net/hearing/pdf/7Projection.pdf#page=39 .  The actual development begins earlier in Section 7.4 on page 322 of that document.
Failure to consider the inductance associated with any alternating electrical signal passed along a coaxial cable leads to disaster.  The first undersea cable based on the ideas of William Thompson,Lord Kelvin, and described as an RC cable by Hermann (page 322 in the above document) was a technical and financial disaster.  Two years later, a more sophisticated RLC cable based on Maxwell's Equations for a coaxial structure was laid with great success.  No RC cable has ever been used in practice since that time.  For unknown reasons, the biological community keeps trying to ignore the inductance of the coaxial myelinated axon (leading to ridiculous modeling data).  This appears to be the result of introductory courses in electricity for non-engineers trying to avoid the necessary mathematics to understand electromagnetic signal propagation through space and along various types of cables and waveguides.

So you are saying there is indeed inductance in myelinated axon. So should the correct equation for action potential be the telegrapher's equation http://en.wikipedia.org/wiki/Telegraph_equation rather than the cable equation http://en.wikipedia.org/wiki/Cable_equation? Is this the main difference between the myelinated and unmyelinated axon other than the insulation provided by the myelin?

There surely is inductance in neurons. This inductance is introduced by two different mechanisms.
1. The coil structure of myelin sheaths can introduce a real electrical inductance. The solid evidence for this is the opposite spiraling directions between the adjacent myelin sheaths.
Here I quote the description on Wikipedia:At the junction of two Schwann cells along an axon, the directions of the lamellar overhang of the myelin endings are of opposite sense. You can also check the details in this paper:  Uzmman B. G.; Nogueira-Graf G. (1957). "Electron microscope studies of the formation of nodes of Ranvier in mouse sciatic nerves". Journal of Biophysical and Biochemical Cytology. 3 (4): 589–597. doi:10.1083/jcb.3.4.589
The opposite spiraling directions can introduce a positive mutual inductance between adjacent myelin sheaths then further enhance the propagation speed of the neural signal. Meanwhile, it is easy to predict that the myelinated nerve can be stimulated by a magnetic field because of this coil inductor. Because of this opposite spiraling direction, the stimulation result is determined by the spatial gradient of the magnetic field. This phenomenon was validated by years and can be easily understood now.

The piezoelectric effect of the plasma membrane. If you check the molecular structure of the lipid bilayer of the plasma membrane, you will find that it is naturally a piezoelectric layer. The definition of the piezoelectric layer is a layer consists of two crystal layer with opposite polarities, which is exactly the same as the lipid bilayer. The equivalent circuit of this piezoelectric layer will be a RLC circuit, which contains an equivalent inductor. Since the inductor is not a real one, the value is only used to match with the mechanical resonance frequency. When the mechanical resonance frequency is very low, which is the case for a soft and thin plasma membrane, this inductance will be huge. This is why in Cole's paper for measurement of the squid axon, this inductance is 0.2H. Then as a direct prediction, there should be a mechanical wave accompany with the electric signal of the action potential.
This mechanical wave has been measured in this paper: Gonzalez-Perez, A., Mosgaard, L.D., Budvytyte, R., Villagran-Vargas, E., Jackson, A.D. and Heimburg, T., 2016. Solitary electromechanical pulses in lobster neurons. Biophysical chemistry, 216, pp.51-59.

I think here I already give a comprehensive answer to this question. You can check all the details in this paper on bioRix:https://www.biorxiv.org/content/early/2018/10/22/343905
Here I may talk something more, but these things will make most of the people in neuroscience unhappy.
If this inductance introduced by the coil structure of myelin and the piezoelectric effect is true, then the whole neuroscience is wrong from the Day 1. The H-H model is built based on a RC circuit and so many people have developed their theories and models based on this H-H model. But ridiculously, everyone claims his model or theory is correct and can explain the data when tha basis is wrong. I have seen so many absurd explanations to bypass this inductance, such as the frequency-dependent capacitor, virtual cathode, negative resistor, and even negative capacitor.
And indeed, more and more people begin to realize the so-called neuroscience is a complete failure. You can see in the homepage of Neuralink(https://neuralink.com/), they officially claim that they do not need any neuroscience experience, quote here:No neuroscience experience is required
Also, there are many groups now only use deep learning or machine learning to study neurons.

Well I might just be falling into your prediction as someone unhappy in neuroscience, but "the whole neuroscience is wrong from the Day 1" sounds like a gross exaggeration. The inductive effects you are describing are not all that important for understanding neuroscience.

I also have no idea why Neuralink has anything on-topic to do with this question and I feel like a good part of your answer is just a rant.


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Can Two Opposite Running Action Potential Cross Each Other without Annihilation in One Axon
Can two opposite travelling action potential cross each other annihilation in an axon?
My answer would be affirmative. If the propagation mechanism is linear as described by https://en.wikipedia.org/wiki/Cable_theory or even https://en.wikipedia.org/wiki/Telegrapher%27s_equations with approximately constant coefficients, the waves are then linearly additive and each signal should propagate unperturbed. The refractory period on each end of the axon can not possibly prevent the other end from being excited at the same time since the signal has not arrived yet.
This question is inspired by the question Can a single axon propagate multiple simultaneous action potentials?

When the waves collide they should extinguish each other since the membrane each encounters is depolarized (because of the other's propagation).

@mgkrebbs: How does depolarization lead to extinction of both waves? The equations contradict this claim since the electric (action) potential is additive.

@Hans the waves would extinguish each other because both will lead to depolarization of the membrane. The AP cannot proceed further. AFAIK, the amplitude of the AP would be the same for a certain type of neuron. If they are different then the dynamics may be different. Using a model you may be able to predict the behaviour but I am not sure if anyone has checked this experimentally.

@WYSIWYG: Your first sentences are stated without reason, just like the statement from mgkrebbs. It seems you are making the same analogy for AP to domino as Superbest does in his answer judging from your concern with the amplitude of the opposing AP's. However, if you switch to the wave analogy then the two should cross each other without interference. It sounds very much like speculation with different analogies leading to completely different conclusions with one no more convincing than the other. But please do derive the proposition if you think otherwise and are certain of its validity.

@Hans No it is not like a usual wave. You have to understand the physiology behind that. AP leads to membrane depolarization. An already depolarized section of the membrane cannot conduct AP. Of course it is not as simple as two waves clashing and annihilating each other. That's why I said that a simulation would be useful (there may be non-intuitive behaviour as these are non-linear systems). I would do the derivations if I had the time. I am a bit occupied and can tell you only what I know right now.

@WYSIWYG: Your proposition is "an already depolarized section of the membrane cannot conduct AP". You have not stated why it is the case. Maybe you have not stated your claim in the most rigorous form. As it stands, this can not be true as it leads to contradiction due to the continuum of value of potential a channel can assume. When a channel is depolarized,  Following the front of the AP, when the first channel, is depolarized to a small potential, your claim would have lead to the AP wold have stopped there and propagate no further because that first channel has already been depolarized.

@WYSIWYG: In my latest edition to my answer below, I added a reference on FitzHugh-Nagumo model showing colliding wave crossing, coalescing as well as annihilating behaviors all depending on the parameters chose of the model. Just as I suspected, annihilation is not the necessary outcome.

I completely fail to see the need to propose complicated models without having evidence for the phenomenon in the first place. Since a membrane that was recently depolarised cannot trigger another action potential due to the refractory period effect, I completely agree with WYSIWYG that the recently depolarised membranes would stop the AP from proceeding along the axon. In the absence of evidence for your hypothetical occurrence, I see no reason to assume the APs will in fact cross each other.

@MarchHo: Are you saying FitzHugh-Nagumo model, a special case of Hodgkin-Huxley model is a newly proposed model? On the contrary it is a classical and widely accepted model for action potential. I have been saying "recently depolarised cannot trigger another action potential due to the refractory period effect" is a vague statement in need of logical derivation to deduce the annihilation of colliding waves. WYSIWYG claims he has a derivation but only has no time to write down. I am skeptical. That means at least he acknowledges that statement is not a sufficient reasoning for annihilation.

@MarchHo: WYSIWYG proposed simulation. And simulation here is. This shows precisely that the "recently depolarised" is NOT sufficient to obtain annihilation. There may be other reason for not observing wave crossing experimentally, say, the parameters that do produce depolarization but wave crossing are not present in most experimental settings. The effect of model and mathematical reasoning is to test your hypothesis. In this case, the simulation shows the hypothesis "recently depolarised membrane cannot trigger another action potential" is false (insufficient).

Combining the lecture notes on the interchannel and channel  electric potential leads to a description of the propagation of the action potential $V$. Specifically, substituting in $I_{\text{ion}}=I_{\text{ext}}$ of equation (6) of cable theory by equation (1) of Hodgkin-Huxley model gives the full propagation equation. A linearization of the Hodgkin-Huxley model leads to a system of linear partial differential equations. I will write out the full formulation and the linear approximation later. That allows complete superposition of action potential. The original non-linear system of partial differential equations under a set of functions/parameterizations at least close to the linear version should permit two opposing wave to cross each other though with interference. So it is not true that all parameterizations of the Hodgkin-Huxley model prohibit two-wave-crossing.
It would of course be intriguing to investigate the existence of a particular form/parameterization where the model does extinguish two opposing waves with its initial condition being two pulses close to a dirac delta function at each end of the axon.
Here is a paper M. Argentina, P. Coullet and V. Krinsky, Head-on Collisions of Waves in an Excitable FitzHugh-Nagumo System: a Transition from Wave Annihilation to Classical Wave Behavior a special case of the Hodgkin-Huxley model. Just as I expected, the waves do not always annihilate each other, but rather may cross, annihilate or even coalesce or even coalesce then re-emit, all depending on the particular values of the parameters of the model. Another paper Oleg Aslanidi, O. A. Mornev, Can Colliding Nerve Pulses Be Reflected? on the numerical simulation of a full-blown Hodgkin-Huxley model reporting crossing of colliding waves. This paper Follman et al, Dynamics of Signal Propagation and Collision in Axons reports under their particular set of parameterization of Hodgkin-Huxley model, two colliding waves annihilate. This paper by Alfredo Gonzalez-Perez et al demonstrates Penetration of Action Potentials During Collision in the Median
and Lateral Giant Axons of Invertebrates based on the soliton theory of nervous signal propation as described in On soliton propagation in biomembranes and nerves by Thomas Heimburg and Andrew D. Jackson.
The wikipedia page on autowave has some interesting information including references for propagation and collision of nonlinear waves in excitable media.

This answer is theoretical, and it doesn't convince me that the model is a perfect representation of reality. It would be greatly improved if you linked to experimental results showing this phenomenon.

@MarchHo: The theoretical answer shows the model allows for wave crossing and annihilation, and that the depolarization is NOT sufficient to prevent wave crossing. No model is a perfect representation of reality. This model and numerical simulation precisely refutes the hypothesis "recently polarized membrane" would prevent wave crossing --- as insufficient.

@MarchHo Although I wouldn't personally accept the answer, it's definitely valuable to know that some models permit the phenomenon. It's an answer in case experimental data does not exist.


text:
Example of a virus becoming symbiotic with an organism
The human gut has an indispensably beneficial ecosystem of bacteria. What are the examples of a virus that becomes symbiotic with an organism, or even incorporates beneficially into the genome of the organism?

@Jan Symbiotic?

very relevant article https://www.nature.com/articles/nrmicro2491

In humans, endogenous retroviruses (HERVs) comprise a substantial fraction of the genome, as much as 8%.1  While many historical viral incorporation events into the primate genome were likely neutral or detrimental (and therefore selected against), some were co-opted and are now functional elements in humans.  An example: human syncytin is the envelope gene of a defective HERV, and the protein has been co-opted for fusion during human placentation.2  A good primer on the genetics and functions of HERVs can be found in The Pharmaceutical Journal.3  The Feschotte Lab at Cornell studies the evolution of HERVs and other mobile elements in mammalian genomes, and their lab site provides more resources.
In bacteria, prophage (integrated bacteriophage) can be co-opted by their hosts for niche-specific transcriptional control.  A cool example is the pathogen Listeria monocytogenes, which utilizes prophage excision during intracellular growth to activate its Com system and escape from phagosomes.4

References

Lander ES et al. Initial sequencing and analysis of the human genome. Nature. 2001 Feb 15;409(6822):860-921.
Mi S, Lee X, Li X, Veldman GM, Finnerty H, Racie L, LaVallie E, Tang XY, Edouard P, Howes S, Keith JC Jr, McCoy JM. Syncytin is a captive retroviral envelope protein involved in human placental morphogenesis. Nature. 2000 Feb 17;403(6771):785-9.
Dodou K, Whiteley P. We are all part virus — the role of human endogenous retroviruses. The Pharmaceutical Journal, PJ, 1 March 2014, Vol 292, No 7799;292(7799).
Rabinovich L, Sigal N, Borovok I, Nir-Paz R, Herskovits AA. Prophage excision activates Listeria competence genes that promote phagosomal escape and virulence. Cell. 2012 Aug 17;150(4):792-802.

In certain species of parasitic wasp, contained within the wasp genome is the genome for a so-called "polydnavirus". The female wasp somehow creates instances of these polydnaviruses inside its ovaries.
When the wasp injects an egg into a member of the host species (likely a caterpillar), several instances of the polydnavirus are also injected along with it. Although the viruses do not harm the wasp in any way, they do have an immunosuppressant effect on the caterpillar, protecting the wasp egg against the caterpillar's immune system.
I've seen an article in "The Atlantic" which claims the viruses can also manipulate the caterpillar's metabolism in a way beneficial to the parasitic larva, but the article did not provide a source for this.
The polydnaviruses, counterintuitively, cannot actually replicate themselves, and are only "reproduced" when the wasp's cells manufacture them! They do not reproduce inside the caterpillar, serving only to protect the wasp egg/larva and copies of the virus genome encoded in the larva's DNA.
(Actually, for some wasp-species/virus pairings, the viruses may exist and reproduce inside the wasp ovaries instead of being "manufactured" by the wasp.)
If you found this interesting, you may also want to look up "virus-like particles", which are created and used by the wasp in the same way, but do not contain any nucleic acid. Regrettably, I don't know enough about these to elaborate further.
So there you have it! A virus which is very beneficial to its wasp host - or at least to that host's offspring - although certainly not to its later caterpillar host.
Sources:

Hunter P. (2010). The missing link. Viruses revise evolutionary theory. EMBO reports, 11(1), 28–31. doi:10.1038/embor.2009.267
Drezen JM et al. (2017). Endogenous viruses of parasitic wasps: variations on a common theme. Curr Opin Virol. 2017 Aug;25:41-48. doi: 10.1016/j.coviro.2017.07.002. Epub 2017 Jul 17.
Ryan, FP. (2016). Viral symbiosis and the holobiontic nature of the human genome. APMIS 2016; 124: 11– 19.
Drezen JM et al. (2009). Polydnavirus hidden face: the genes producing virus particles of parasitic wasps. J Invertebr Pathol. 2009 Jul;101(3):194-203. doi: 10.1016/j.jip.2009.04.006. Epub 2009 May 19.

See also:
https://www.theatlantic.com/science/archive/2015/09/parasitic-wasps-genetically-engineer-caterpillars-domesticated-viruses/405874/


text:
Inbreeding of selfing and outcrossing plant
I am reading John H. Gillespie's Population Genetics A Concise Guide Section 4.3 Inbreeding. I do not understand these two paragraphs quoted below concerning selfing and outcrossing.

The first paragraph states that an outcrosser individual leaves behind on average two gametes one in an ovule and the other in a pollen.

The second paragraph states that a mutant selfer will leave behind three gametes for every two of the outcrossing plants, with two in its selfed offspring and one in its outcrossed offspring.

What are the effect of the ovules and pollen here? How are these two statistical conclusions drawn? I would like to have a very detailed explanation.

Some interesting evolutionary questions arise with species that are capable
of both selfing and outcrossing. For example, in many plant species there is
an intrinsic advantage to selfing, which leads to the evolutionary conundrum:
Why don't all plant species self? The situation is illustrated in Figure 4.4. The
outcrossing pedigree on the right represents a typical individual in an outcrossing population of constant size. This individual leaves behind, on average, two gametes, one carried in an ovule and the other in a pollen grain. These gametes appear as filled circles in the figure.

Figure 4.4: The gametes produced by a selfer and an outcrosser. The p to the right of
an arrow indicates that the parent’s contribution came from pollen; an o indicates it
came from an ovule. The filled circles represent gametes from the illustrated parents;
the open circles represent gametes chosen at random from the gamete pool.
Suppose a mutant appears that self-fertilizes all of its ovules, M illustrated
on the left side of the figure. Suppose also that there is enough pollen in each
individual of this species that the few grains needed for self-pollination by the
mutant represent a small fraction of the total pollen. As a consequence, the
selfing mutant has essentially the same quantity of pollen available for outcrossing as does a nonselfing individual. All else being equal, the selfing mutant will leave behind three gametes for every two of the outcrossing plants, as indicated by the three filled circles in the figure. Two of the gametes are in its selfed offspring; one is in its outcrossed offspring. Thus, the mutant should increase in frequency, perhaps leading to the establishment of selfing as the usual mode of reproduction.

I don't think it's a terribly rigorous statistical argument, so much as a toy model arguing that there can be a reproductive advantage to selfing in an outcrossing population. Here is the logic as I see it:

Ovule and pollen represent the female and the male reproductive gametes in a monoecious plant (monoecious means that it has both male and female reproductive organs in the same individual).
In sexual organisms that do standard sex (i.e. not a complicated variety of sex), both ovule and pollen (gametes) are necessary to generate a fertilized offspring (zygote).
In outcrossing individuals, pollen is broadcast to fertilize other individuals (1 pollen gamete) and ovules receive pollen from other individuals (1 ovule gamete). Total: 2 gametes
In selfing individuals in an outcrossing population, selfing individuals guarantee that they fertilize their own ovules. Thus, they replace the pollen of other individuals (1 pollen gamete + 1 ovule gamete).
Selfing individuals still broadcast pollen to fertilize other outcrossing individuals (+1 pollen gamete). Total: 3 gametes

The key is in looking at the figure and understanding what it's arguing.
Again, these are not really rigorous ratios, details will be determined by exact biology of any case in real life. As far as I can tell from the text, the argument is not "these are the exact ratios in all organisms", but rather that "selfing gives the advantage that a selfer contributes all of the same gametes as the outcrosser, plus the male gametes to fertilize its own male gametes".
Secondary note: this model is only true when the proportion of selfers in the outcrossing population is very small. Note that as the proportion of selfers increases, everyone is just fertilizing their own ovules, and the net contribution goes back down to 2 gametes per generation. So this does not describe an equilibrium case for population composition. [As noted in comments, it is likely the case that it is equilibrium for population size, e.g. number of individuals.]
For more theory about this, you can read about the evolution of self-(in)compatibility. Here is a somewhat recent review. Evolution of self-compatibility in plants is extremely dynamic, as you might expect from the arms-race aspect.
Update:
Pulling up some notes from the comments on the assumptions of the model:

I think that this example works when population number is at equilibrium, but population composition (e.g. selfers vs. outcrossers) might not be at equilibrium.
I think that for the amount of pollen, we have to assume that all organisms contribute an equal, infinite amount of pollen. So selfers fertilize their own, and then also dump pollen into a pool into which outcrossers also dump infinite pollen.
However, there are only a few ovules; every individual contributes one. That is, outcrossers and selfers contribute one ovule per individual.
On average, everyone's pollen will be sampled roughly once (actually a little less) if every non-selfed ovule takes one pollen from an infinite pollen pool of uniform composition.
As number of selfers in the population increases, less and less of the common pool of pollen will be sampled.
If everyone in the population is a selfer, there will obviously be no outcrossing, because everyone just fertilizes their own ovule. This is the equilibrium state, if selfing is heritable and this stated advantage to selfing holds.

It is not very clear. Each plant has one ovule and multiple pollen. What prevents a selfer outcrosser from contributing more than one pollen and a outcrosser more than two pollen? It seems to me each plant can contribute as many pollen to it offsprings as it has. I suspect it is an argument for when the population is in some kind of equilibrium. But it is not clearly stated what equilibrium this is and how it is achieved. But you say it is not an equilibrium. So it is even less clear.

@Hans I think that this example works when population number is at equilibrium, but population composition (e.g. selfers vs. outcrossers) might not be at equilibrium. I think that for the amount of pollen, we have to assume that all organisms contribute an equal, infinite amount of pollen. So selfers fertilize their own, and then also dump pollen into a pool into which outcrossers also dump infinite pollen. However, there are only a few ovules. On average, everyone's pollen will be sampled roughly once if everyone takes one pollen from an infinite pollen pool of uniform composition.

I think the key is that a selfer preserves its phenotype while an outcrosser does not. The selfers' pollen "invade" the offsprings of outcrossers. The specific numbers in gametes 2 and 3 are misleading. Also it needs further constraints to make the argument stand. I suppose we need to assume that each plant produces the same number of ovules and, as you say, the same large number of pollen. The proportion of ovules from the outcrossers pollinated by the selfers is proportional to the proportion of the selfers amongst the whole population in the last generation.

+1 for your informative answer. In case you have not noticed, I have pasted text of the quotation from the textbook to my question instead of the screenshot.

Ok, appreciated. I don't use a screen reader but it is supposed to be very helpful in general. I'll edit the answer.


text:
How much Open Access Data is there in genetics?
Type of data of interest
I would like to consider

Genetics data (SNP, microsatelites, whole genome sequencing, RFLP, ...)
Genetic - phenotype data (disease-related data, QTL, etc...)
Sequence annotation and function
Transcriptomic data

I would like to include data on any living thing (including data from fossils) and not only human data. To avoid issues of semantic I would leave out epigenetic data.
Question
How much (in bytes) of such data is available in Open Access online?
Difficulties
I realize getting to such estimate might be hard and the estimate may be very inaccurate. Also, the format used for storing these data will definitely affect the relationship between information content and storage usage. But if someone can give just a rough order of magnitude, a vague intuition, it would already help. Is it a few terabytes or a few petabyte or even more?
I would welcome as well a detail of how you got to this estimate. I am particularly interested in what fraction of it is human data (if you happen to get to such fine detail).

Despite all your tags, I rather think this is off-topic for biology. Regardless, I would imagine that if you checked how much NCBI has in GenBank that would give you the order of magnitude you need.

Functional annotations etc will be negligible, as the size of largest databases (e.g.: Interpro, or EBI GTX) only is 100GB. For sequences, it depends, if you save difference to references. Otherwise you can extrapolate from NCBI statistics - as also noted by David -, that - depending on sequence complexity - you'd be in double digit petabytes ( https://www.ncbi.nlm.nih.gov/genbank/statistics/ ) ; note that sequencing information is small compared to image-based biological data, and the - open / not licensed - image information contained in old books and texts could easily exceed petabyte

Can you clarify which type of data you are looking for and what for?
There are lots of public databases with all sorts of information. And obviously most of it is redundant.
Coming back to you question I'd say there is much more data publically available that not even the most powerful supercomputer would be able to handle. But as I said, it depens on what you want to do with it.

@aLbAc I don't intend to do anything with these data right now. My question comes out of curiosity mainly. I was just trying to get an appreciation of how much data we are producing and storing in genetics.

The answer is "huge amounts" and increasing exponentially with the new generation of high througput sequencers.

It is difficult to answer this if we include all NGS and microarray data on the genome and gene expression. In addition to reference sequences, databases with expression  data are growing exponentially as well. Separate projects such as TCGA, ENCODE, FANTOM, HapMap, and various biobanks also have massive data repositories. As such, any answer would be outdated very quickly.

I'm voting to close this question as off-topic because the answer to this question will change over time.