text:
Can the word phalanx also be used to describe the finger bone plus the soft parts around the bone?
I was talking in an SE chatroom about fingers, and not being a native English speaker, I had to look up the word used for the part of a finger from the tip to the closest knuckle. I came across the word "phalanges", but the Wikipedia article specifically refered to this as phalanx bones, i.e. just the bone and not everything around it. Can this term also be used to describe the bone plus all of the softer parts around it like the muscles, blood vessels, skin and nail? If not, is there a more commonly accepted biological term for the bone plus the soft tissue around it?

It's a great question, and in my humble opinion, the answer is:
Phalanx (plural: phalanges), (also Cambridge and MedicineNet) is the term for one of the bones (only) in the fingers or toes and not for all the "meat" around it. The Google images search for phalanges is quite convincing.
Someone on https://english.stackexchange.com/ might know a word for the whole bone + "meat" part of the finger.

Hmm, are you implying that asking for terminology is off-topic on this stack?

@Nzall,  No, I'm trying to explain anatomy terms. All fine, if you ask me. I was thinking, if you are asking for a term that describes the whole part of the finger asociated with a phalanx, some person on English could serve you better.


text:
Does one parent transmit more DNA to the offspring than the other one?
Does one parent transmit more DNA to the offspring than the other one? Or do both parents always transmit the same amount of genetic material to their offspring?
In other words, can a baby be provided with a gene from the mother without an "opposite gene" from the father?

I completely reformulated the question. Please let me know if you think it changed its meaning.

SHORT ANSWER
The two parents transmit the same amount of genetic material to their offspring ....or almost
LONG ANSWER
Nuclear versus Cytoplasmic DNA
All Eukaryotes (everything that is neither a Bacteria nor an Archeabacteria) have nuclear and cytoplasmic DNA. Most of the DNA is nuclear DNA. As its name indicates, nuclear DNA is found in the nucleus. The cytoplasmic DNA is found in the cytoplasm, that is, outside of the nucleus. More specifically, in all eukaryotes, cytoplasmic DNA can be found in the mitochondrion. In plants (which are eukaryotes), you can find cytoplasmic DNA in the mitochondrion and in the plastids (including the chloroplasts (plastids active in photosynthesis)). See here for more information about the origin of the organelles (≈ organ of a cell) who carry DNA.
Nuclear and cytoplasmic DNA doesn't have the same mode of inheritance.
Inheritance of Nuclear Genes
In the diploid (see ploidy) phase (phase during which each individual carries two copies of each gene), an individual carries one copy from his/her mother and one from his/her father.
The above sentence assumes that a diploid phase exists (which is not the case of all species) and that genders (male vs female) exist which is by far not the case of each species. It also assumes that we are talking about autosomes (non-sexual chromosomes, see below for sexual chromosomes). These assumptions hold for humans for example. Note that the diploid phase is much longer in human than the haploid phase (spermatozoid, ovule). We say that humans are diplontic. Some species are haplontic (longer haploid phase) and some are haplo-diplontic. See life-cycle for more info.
In short: Inheritance of nuclear genes is bi-parental, each offspring necessarily carry one copy of a given gene from his/her father and the other copy from his/her mother.
Note: there are some exceptions to this perfect bi-parental transmission (see segregation distorter and intra-genomic conflict). Also, have a look at the short section on sexual chromosomes below.
Inheritance of Cytoplasmic Genes
There are many exceptions to what I am about to write...
Globally speaking, offspring inherit cytoplasmic DNA for their mothers only. That means that your mitochondrion is those of your mother only. Therefore, mothers transmit slightly more genes than fathers because of the concern of cytoplasmic genes.

To complete the picture...
Inheritance of Sexual Chromosomes (Nuclear DNA)
Not all sexual species have sex chromosomes but some do. In these species, it is not rare that one of the two sexual chromosomes is shorter than the other (In mammals, the $Y$ chromosome is shorter than the $X$ chromosome). In such a case, the male transmits slightly less DNA to their male offspring than to their female offspring. Also, in such case, fathers transmit less DNA to their male offspring than do mothers but males transmit as much DNA to their female offspring than do mothers.
The evolution of sex chromosomes is a very interesting subject as well and you will find tons of information on this website or on different sites.
Non-genetic inheritance
Nutrient in eggs
Not only genes are transmitted. Parents also transmit proteins and nutrients in the egg. Females transmit more nutrients to their offspring than males.
Epigenetic
Not only genes are transmitted. Parents also transmit modifications on the DNA that are not modifications in the DNA sequence per se. These modifications are called "epigenetic modifications". Not all species can produce epigenetic modifications. In species who can transmit epigenetic modifications, both males and females can produce them. It is possible that in some species mother have a higher variance in the modifications that they transmit than males (or vice-versa) but I am not aware of such things.
Environment and Cultural transmission
Not only genes are transmitted. Parents also offer an environment in which the offspring grow. Some species typically feed or protect their offsprings. Depending on the species males or females may have more influence on the environment experienced by the offsprings. Finally, in some species (human, chimps and orca for example) a set of traditions (culture) are transmitted to the offsprings from the parents. And depending on the species the father or the mother may have more influence in the culture transmitted to the offspring.
Length of chromosomes may differ between two randomly sampled individuals
Not all variants between two chromosomes in a population is caused by substitutions of one nucleotide by another. Some variation is due to deletions of nucleotides or insertions of nucleotides. You can even a very long piece of DNA who get inserted, duplicated or deleted. Therefore between two given individuals, the exact amount of DNA that is transmitted may also differ only because they happen to have different variants. However, this is not a systematic difference in the quantity of DNA that is transmitted by one sex or another unlike the other cases presented above.

Certainly in the case of flowering plants a triploid can be created by crossing a diploid by a tetraploid.
In this case the teraploid parent will contribute twice as much DNA to the offspring than the diploid parent. Seedless fruits such as bananas, grapes, and watermelons are produced using such crosses.
There is also the possibility (and it does occur) where 2 diploid parents can produce a viable triploid offspring by one parent contributing an unreduced gamete. Here again one parent would contribute more DNA than the other. Such events are fatal in humans but need not be in some species of fish.
In flowering plants, tetraploid and hexaploids can often mate to produce pentaploid offspring. Again an example of unequal DNA contribution by the 2 parents to produce a viable offspring. Such pentaploids can often be semifertile being able to back cross to either parent.
Pentaploid dog roses actually reproduce normally by having a 4 (female) to 1 (male) contribution from the 2 parents.
Interestingly a diploid and tetraploid parent can in rare instances contribute equal amounts to the resulting tetraploid offspring. This happens when the diploid parent contributes an unreduced gamete.
Amazingly in newly created tetraploid hybrids, tetraploid by diploid can produce a diploid offspring where both parents make an equal contribution.
References
Meiosis in Polyploids by W. C. F. Newton and C. D. Darlington in Journal of Genetics 1929
The history of the garden hyacinths by C D Darlington, J B Hair and R Hurcombe in Heredity 1951
Rules of Engagement: Have Pollen—Will Travel by John Perkins · Sally Perkins in Azalean 2010
Weighing in: Discovering the ploidy of hybrid elepidote rhododendrons by Sally Perkins, John Perkins, José Monteiro de Oliveira, Mariana Castro, Sílvia Castro, João Loureiro in Rhododendrons, Camellias and Magnolias, Royal Horticultural Society, Editors: Simon Maughan, pp.34-48 2012
Untersuchung des Ploidiegrades elepidoter Rhododendron-Hybriden by Sally Perkins, John Perkins, Mariana Castro, José Cerca De Oliveira, Silvia Castro, João Loureiro in Rhododendron und Immergrüne , Deutsche Rhododendron-Gesellschaft e.V. , Seite 21: pages 21-42; 11/2013

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text:
Is Sugar a stimulatant or a weak sedative?
Quite often, I have heard the remark that children become hyperactive when high amounts of sugar are consumed.
But common websites suggest that sugar is a sedative, and the hyperactivity in children is more likely caused by 'artificial dyes and preservatives'. (http://curezone.com/forums/am.asp?i=1444631)
So, is Sugar a stimulant (for adults and children) or is it a sedative? Is there any conclusive research to validate this theory?

Can you tell us which websites do claim this?

better ask at skeptics.SE

@edition Sorry, but this page is not a source to be trusted. As Jeremy already answered, this is pseudoscientific bllsht.

thanks for the clarification, but you wanted a website :)

The idea that 'dyes and preservatives' cause hyperactivity dates back to this '76 paper by one Dr. Feingold. Despite being disproved neatly in 1978, it's still around.
As far as sugar goes, I recommend this review paper covers both the arguments for and against sugar causing hyperactivity, as well as 12 double-blind placebo controlled studies showing sugar has no effect on children's actual behavior.

What about sedative effects? Is there a paper in that context? And what about adults?

I couldn't find anything testing specifically sedative effects. I don't see a plausible mechanism and 'no effect' means no effect, hyperactive or sedative. If you can think of a reason why something would be psychoactive only in adults, let me know, but I feel comfortable generalizing from children to adults here.

Could you provide a summary of these arguments? It's better to have the answer here rather than on another site which is behind a paywall (not everyone has institutional subscriptions)

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Proteins and Blood Acidification
Is there evidence to suggest that excessive consumption of Whey, or similar proteins will lead to acidification of the blood?

Can you provide a source for this claim?

Found a study on cows


text:
How many ion channels on average must there be in one µm2 of neuronal membranes?
If the conductance of a single ion channel is 1pS and its capacitance per cm2 is 1uF and the time constant for a human neuron is 1ms
How many ion channels on average must there be in one µm2 of neuronal membranes?
How is it possible to know how many ion channels with only these information? would you be able to explain it?
Thank you

Is this a homework question?

Suggest you check the given units and use those as a hint... https://en.wikipedia.org/wiki/Siemens_(unit) and
https://en.wikipedia.org/wiki/Farad comeback when you have made a slightly bigger effort.

Hi, so I have found the resistance which is = 1/ conductance = 1/110^-12 so resistance = 110^12 ohms per cm^2. (I converted the pS to S). However, I am confused what does it mean by "how many ion channels" do they actually want the number of ion channels, or is there a formula for that, i tried researching a lot but I did not find anything related. Thank you!

I know we have: Resistance, area (um^2), conductance and capacitance but i do not know how to put this information together to find the number of ion channels.

You also have a time constant. That will be key. Look for the relationship between the time constant and the other parameters you have. (note also: you have the conductance of just one channel; you are solving for how many channels you need i.e. how many multiples of that conductance)

does this mean we need to find current?

To notify a user, you should type @ before their name. For e.g. @BryanKrause

OP: I already gave you the hint that you need to use the time constant. Look up equations for the time constant that are in the units of the things you are studying: resistances, capacitances, etc.

I expect your homework was already due, so...
You're supposed to remember what a membrane time constant is. I'll quote from page 12 of my (by now quite old) copy of "Ion channels of excitable membranes", by Hille:

For biological membranes the product, RmCm, of membrane resistance and capacitance is often called the membrane time constant, taum.

Since you know tau and C, your goal is then to determine the membrane resistance. You also need to convert the capacitance to square microns (1e-14F per square micron). In this case: 1ms/1e-14F = 1e11Ohms, or 1e-11S, or 10pS. So on average there are 10 channels per square micron, assuming I didn't make any silly mistakes.


text:
When does meiosis occur in flowering plants?
At what point does meiosis occur during the development of a flower?

Wikipedia says when the plant(anther) is growing for pollen at least, sorry if that is vague though, https://en.wikipedia.org/wiki/Microspore#Angiosperms

In case of male gametophyte (in angiosperms), meiosis ends before the formation of the pollen tetrads which in turn marks the end of cell division in anthers and petals (Li and Johnston, 1999). However, the same study reveals that the relative timing of pollen tetrad formation with respect to floral development (abbreviated as RAFT), varies between different plants. Despite the variation, they seem to form three clusters with mean RAFT at 0.45, 0.62 and 0.73.
In case of the female gametophyte, the megasporogenesis happens inside the ovule (Yadegari and Drews, 2004). Therefore, ovule should have formed before the onset of meiosis. I could not find a detailed study on the timing of the megasporogenesis.


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Has the protein composition (with identification) in honey and other honeybee byproducts been studied?
I am interested in studying honey and other honeybee byproducts.  I have not been able to find sequence or structure records for any of the contents of honey.
In particular, I want to study the protein sequence and structure and the amino acid compositions within honey.
Has any of this data been produced and published in any databases or research papers?

First of all: Honey is not a byproduct of bees - it's their main and most important product which stores energy for the bee hive for the time when no flowers are available.
Honey itself consists (according to the USDA database) to about 99.5% of water and sugars (82.5% sugars, 17% water). The sugars are mostly fructose and glucose, but also some other mono- di and tri-saccherides in traces. See reference 1 for details. It also contains trace amounts of vitamins and minerals, see table from the Wikipedia on Honey:

The protein content varies between honey sample but is somewhere in the range between 0.2 and 0.5% (see also reference 1). The proteins come from flowers (pollen incorporated into the honey) as well as from the bees (see reference 2). Paper 1 lists a number of enzymes as most common bee proteins in the honey, but doesn't go into much more details here. These are invertase, diastase, glucose oxidase and catalase.
You could now go into the sequence databases (Apis mellifera has been complete sequenced) and look up the sequence information of the enzymes. Information can be found here and here.
References:

A review of the analytical methods to determine the geographical and
botanical origin of honey
Source of the honey protein responsible for apple juice
clarification


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Genotype to phenotype map and the G-matrix
Suppose I have a genotype-phenotype map defined by the matrix $\mathbf{Z}$:

The scalars $G,P$ represent the number of genotypes and traits, respectively. The map assigns a set of phenotypic traits (the columns) to a set of genotypes (the rows), where $z_{ij}$ is the quantitative measure of an individual of genotype $i$ with respect to a trait $j$. I want to know how the average value of each of the phenotypic traits changes over time, suggesting I should use quantitative genetics theory and formulate the equation
$\Delta \bar{\boldsymbol{z}} = \mathbf{G}\mathbf{P}^{-1}\mathbf{s}$,
where, $\mathbf{G}$ is the additive genetic variance covariance matrix, $\mathbf{P}$ is the phenotypic variance covariance matrix, and $\mathbf{s}$ is a vector of covariances of each trait with fitness. Assume that I know the frequencies of the different genotypes in the population.
Question 1 Can I formulate the additive genetic variance-covariance matrix from the genotype-phenotype map alone (and pop freq)? Note, I don't know anything about the underlying genetic model - number of loci representing each genotype, dominance structure, epistatic interactions, etc.
Question 2 If I assume the genotypes represent haploid individuals, does this change things? Is the additive genetic variance always equal to the phenotypic variance (assuming no environmental effects) in a haploid model? In other words does $\mathbf{G}\mathbf{P}^{-1} = \mathbf{I}$? What I'm thinking is that epistatic variance might affect things, but it shouldn't affect heritability in a haploid model, which is what $\mathbf{G}\mathbf{P}^{-1}$ is a measure of.

From the pheno-geno map and the genotypes frequencies, you have the whole distribution of phenotypes in your population. The mean of the phenoype $n$, $P_n$ is the
$$\bar P_n = \sum f_{G_i} P_{G_i}$$
, where $f_{G_i}$ is the proportions of individuals having genotype $G_i$ and $P_{G_i}$ is the phenotype of the individuals with genotype $G_i$. Therefore, the variance of $P_n$ is
$$var(P_n) = \sum f_{G_i} (P_{G_i} - \bar P_n)^2$$.
The covariance between the phenotypic traits $n$ and $m$ is
$$cov(P_n,P_m) = \sum f_{G_i} (P_{G_i} - \bar P_n)(P_{G_i} - \bar P_m)$$
The only assumptions you need is that there is no environmental variance. I don't think the above calculations required any other assumption. $G$ can be defined at the haploid or diploid stage, it doesn't change anything.
The above calculations however give you the genetic variance and covariance but not the additive genetic variance covariance. I think (but I might be mistaken) that the additive genetic variance would be equal to
$$\sigma_D^2 = \sum_i f_i^2(1-f_i)^2(2 \cdot P_{n,i,12} - P_{n,i,11} - P_{n,i,22})^2$$
$$\sigma_A^2 = \sum_i 2f_i(1-f_i)(f_iP_{n,i,11}+(1-2f_i)P_{n,i,12} - (1-f_i)P_{n,i,22})^2$$
, where $f_i$ is the frequency of the allele $A$ at the locus $i$ (you should get those data by reformatting your geno-pheno map matrix) and $P_{n,i,11}$, $P_{n,i,12}$ and
$$P_{n,i,22} =\frac{1}{l-1} \sum_j P_{n,i,j,22}$$
is the $n^{th}$ phenotypic trait for the genotype $22$ and locus $i$ averaged over all other genotypes. There are $l$ genotypes in total. Of course, this works only for biallelic loci. I don't know what it would look like for more alleles.


text:
What are the effects on hearing of in ear headphones?
I have been told many times by my teachers and grandparents that using in ear headphones will ruin my hearing, but I was unsure of these claims. So of course I turned to stack exchange to help me.
So really I'd like to know the effect on hearing from frequent earphone use (particularly as I listen to quite a lot of loud rock music)?
Thanks.

The main effect on hearing is the volume of the sound. Both the intensity and duration matter. However, it seems like hearing loss from personal music players is not as prevalent as from other causes like gunfire or occupational noise exposure (see also here).
The specific problem with in-ear headphones is people tend to listen to them louder than other types of headphones, here is an example study that shows this result.
So, in summary, there isn't anything wrong with in-ear headphones if you listen at a low volume, but be wary that peoples' tendency is to listen louder with in-ear headphones, and you already mentioned liking loud music. The volume is going to be your problem.
Be very wary with your hearing though: once you have lost hearing, there is no way to get it back at this time. Hearing aids only temporarily compensate for the loss. You might be okay now but regret a lifetime of noise exposure by the time you are an older adult.
References:
Clark, W. W. (1991). Noise exposure from leisure activities: a review. The Journal of the Acoustical Society of America, 90(1), 175-181.
Hodgetts, W. E., Rieger, J. M., & Szarko, R. A. (2007). The effects of listening environment and earphone style on preferred listening levels of normal hearing adults using an MP3 player. Ear and hearing, 28(3), 290-297.
Mostafapour, S. P., Lahargoue, K., & Gates, G. A. (1998). Noise‐induced hearing loss in young adults: The role of personal listening devices and other sources of leisure noise. The Laryngoscope, 108(12), 1832-1839.

why this answer is not pinned to the billboards, streets, whole internet and TV's? We need to shout out this to all.


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Deliberately choosing one nostril to breathe through
James Nestor, on pp. 41-42 of his book Breath: the New Science of a Lost Art, claims the following.

The right nostril is a gas pedal. When you're inhaling primarily through this channel, circulation speeds up, your body gets hotter, and cortisol levels, blood pressue, and heart rate all increase. This happens because breathing through the right side of the nose activates the sympathetic nervous system, the "fight or flight" mechanism that puts the body in a more elevated state of alertness and readiness. Breathing through the right nostril will also feed more blood to the opposite hemisphere of the brain, specificially to the prefrontal cortex, which has been associated with logical decisions, language, and computing.

Inhaling through the left nostril has the opposite effect: it works as a kind of brake system to the right nostril's accelerator. The left nostril is more deeply connected to the parasympathetic nervous system, the rest-and-relax side that lowers temperature and blood pressue, cools the body, and reduces anxiety.

... Our bodies operate most efficiently in a state of balance, pivoting between action and relaxation, daydreaming and reasoned thought. This balance is influenced by the nasal cycle, and may even be controlled by it. It's a balance that can also be gamed.

A question on this site describes we only breathe out of one nostril at a time: at any given time, one of our nasal cavities will be more open than the other, and this switches back and forth every couple hours. For the most part, we are unaware of this. (At any rate, I was!)
I am very curious about Nestor's claim that the balance can be gamed. It seems that one could prepare effectively for a math exam by practicing right-nostril breathing, or for sleep by practicing left-nostril breathing. Is this the case?

“Breathe on me breath of God”. Notice the difference in spelling which reflects the difference in pronunciation.

I ve never heard any citations stating a basis of research on which side nostril causes what mental states, so the research is probably lacking. Wim hoff stuff conversely does have evidence.

A quick search shows that there is evidence that nostril breathing influences the autonomic nervous system, but currently not much evidence that right vs left nostril breathing influence different states.

Any kind of higher awareness of breathing is likely to improve mental abilities, for one it gives free divers the ability to dive a lot longer, and Wim Hof uses it to stay consciou s and submerged in ice water for 112 minutes, which wasn't believed to be humanly possible previously. It must be difficult to tell the difference of a breathing exercise versus an alternate nostrile breathing exercise.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3681046/
Assessment of the Effects of Pranayama/Alternate Nostril Breathing on the Parasympathetic Nervous System in Young Adults
Result and Conclusion: This study showed that the parasympathetic tone was enhanced appreciably in the participants. The observations of this study suggest that the yogic exercise of A.N.B. influences the parasympathetic nervous system significantly.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3978938/
Slow Yogic Breathing Through Right and Left Nostril Influences Sympathovagal Balance, Heart Rate Variability, and Cardiovascular Risks in Young Adults
Short-term practice of LNB improves vagal tone, increases HRV, and promotes cardiovascular health of medical students. Practice of RNB increases sympathetic tone and could jeopardize cardiovascular health.

There seems to be some evidence that this works.

note the sample sizes, n=30 which makes the conclusions of the study very weak at best, the differences are equally miniscule (and swamped by the margins of error). this is just bad applications of statistics in the guise of a preliminary study.

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text:
Does eating beans of a mother cause flatulence on babies?
Is it true that if you eat beans it could cause flatulence on babies (when breastfeeding them)?
I can't find any research or scientific facts about that topic.
I thought the body of the mother would filter "bad" ingedients.

When the mother eat beans, the fiber (oligosaccharides) from them is not digested in the small intestine, so it travels to the large intestine, where normal intestinal bacteria break it down to some absorbable nutrients (like short-chain fatty acids) and gas that is largerly expelled (fao.org). Some gas can be absorbed into the blood and then removed by the lungs (PubMed).
This means that neither the fiber nor the resulting gas ends up in the mothers breast milk, so it cannot give gas to the baby.
Breast milk contains human milk oligosaccharides (HMO). HMO is undigestible, but bacteria in the infant's intestine can break it down and produce gas. However, the amount of HMO in the breast milk is not likely related to the amount of beans or other high-fiber foods the mother consumes, but is genetically determined (PubMed).


text:
How long does it take for a blocked dopamine receptor to be broken down by the body?
Do the blocked dopamine receptors get broken down by the body and if so how often ?
In other words how long does it take for the dopamine receptors blocked by irreversible dopamine antagonists to degrade ?

If you could depersonalize this question to make it about the pharmacology of haldol, we may be able to give you an answer, though it may not be very satisfying. As it is, you're asking a personal medical question (how long do you have to wait for recovery of normal function after stopping haldol), which is off topic for any SE site.

Thank you for rewording. I've retracted my close vote. This is a complicated question that will require some time to carefully answer.

Partial Answer and Suggestions
As @De_Novo says, this is a complicated, albeit very interesting, question. There are various reasons for this, such as the fact that the receptors aren't just internalised but also recycled and the fact that there may be antagonist and dose-dependent changes in receptor internalisation. There's the added complexity that receptors can have their expression changed in the short term (by internalisation) but also in the long term (by varying synthesis). You should then note that there's not a set lifespan of the receptors - there's a statistical distribution for how long they'll last at the membrane.
But I'd quite like to stimulate discussion about it so I'm proposing some smaller questions:

Do irreversible dopamine antagonists change the rates of receptor internalisation, degradation or recycling? This is likely to be the case as internalisation of receptors is often activity-dependent. Also, the shape of the irreversible antagonist could change how the receptor fits into a clathrin-coated pit.
Do the irreversible antagonists change the rate of receptor synthesis?
What mathematical models can describe the dynamics of internalisation? This might be a bit tricky since there are feedback mechanisms here (e.g. recycling --> internalisation --> degradation --> less recycling).
How does the proportion of blocked receptors affect these factors?

By answering these questions (or even by finding an experiment that measures the half life of the receptors with blocking), you could come up with an answer for the half-life of the blocked receptors.


text:
Dominance coefficient
I am trying to understand the meaning of the dominance coefficient. I'll be more specific to what I don't understand, in a moment.
Let $A_{11}$, $A_{12}$ and $A_{22}$ be genotypes with fitnesses $1$, $1-sh$ and $1-s$ respectively. I can understand the meaning of the selection coefficient $s$ as its sign clearly determines which allele is more advantageous.
Though, I cannot figure out the meaning of the dominance coefficient $h$. I understand the following:

if $h>1$ we have underdominance i.e. both homozygotes are more fit than the heterozygote
if $h<0$ we have overdominance i.e. the heterozygote is more fit than the homozygotes
if $0 < h <1$ we have that the heterozygote is only more fit than the deleterious homozygote

The last point is called incomplete dominance as opposed to complete dominance in the cases $h=0$ and $h=1$. Here, I'm having trouble to understand how this is related to dominance. I mean, I can clearly state that $h=0$ implies that the fitnesses of $A_{11}$ and $A_{12}$ are equal, but why does this imply that $A_1$ is dominant and $A_2$ recessive (the situation $h=1$ is symmetrical of course)?
For this terminology, I'm referring to Gillespie's Population Genetics: a concise guide. A table resuming what I'm talking about is also on Wikipedia here.
I'd like to point out that I'm not a biologist, but just a mathematician, so it may be something simple in how dominance works that I'm missing. Also, for the same reason, please, forgive me if I have worded something not appropriately. Thanks to those who will help.
EDIT: I'm not asking what the biological process behind dominance is. I'm just asking how $A_{11}$ and $A_{12}$ having the same fitnesses (which, for me, reads as having the same chance at surviving) relates to $A_1$ being dominant. As it was pointed out in the comments, this is the definition of dominance. Though, I thought that dominance of one allele means only which phenotype will prevail in the heterozygote case and I cannot find the relation between the two definitions.

The answer to I mean, I can clearly state that h=0h=0 implies that the fitnesses of A11A11 and A12A12 are equal, but why does this imply that A1A1 is dominant and A2A2 recessive  is just, because it exactly how dominance is defined.

If your question is about the mechanism behind dominance relationships (which seems to be what your last paragraph is asking for), then you should have a look at Why are some genes dominant over others? What is the mechanism behind it? and eventually Evolution of dominance of alleles.

Possible duplicate of Why are some genes dominant over others? What is the mechanism behind it?

Thanks for your comment. I think I'm just missing the big picture then. I thought dominance was only related to which phenotype will show. If fitnesses of $A_{11}$ and $A_{12}$ are equal, doesn't it mean just that $A_{11}$ and $A_{22}$ have the same chance at surviving? Isn't this what "fitness" measures?

Fitness is indeed some function of survival and reproductive success. The exact definition of this function may slightly vary depending on the model used.One will not that fitness is typically considered as a phenotypic trait. Note that when modelling fitnesses with $s$ and $h$, $s$ is typically positive and $h$ is typically between 0 and 1. For cases of overdominance, authors often prefer to use other 2 variables to express the fitnesses of all three genotypes. I am not sure this comment is of any help though...

Thank you for asking such a well-thought out question, I really enjoyed how hard this made me think about the concept. I think there might be an issue here that's quite common to biology, in my experience- poor definition of terminologies.
I think the core question can be summed up by your comment:

I thought dominance was only related to which phenotype will show. If fitnesses of $A_{11}$ and $A_{22}$ are equal, doesn't it mean just that $A_{11}$ and $A_{22}$ have the same chance at surviving?

In my thinking, the definition of dominant could mean two things:

The expression of a particular characteristic
The fitness associated with the expression of a characteristic

Of course, the second definition depends entirely on the first- if the phenotype of the heterozygote ($A_{12}$) is the same as the homozygote ($A_{11}$ or $A_{22}$), then their fitness must be the same- evolution acts on phenotypes, not genotypes.
Let me break this down using Gillespie's tables. For a given value of $s$ (between 0 and 1), we can imagine the following scenarios for the value of $h$:

$h$
Phenotype
$A_1A_2$ fitness
Dominance scenario

h=0
$A_1A_2$ phenotype = $A_1A_1$ phenotype
$1-s\times 0 = 1 = A_1A_1 fitness$
$A_1$ is dominant allele

h=1
$A_1A_2$ phenotype = $A_2A_2$ phenotype
$1-s\times 1 = 1 - s = A_2A_2 fitness$
$A_2$ is dominant allele

This is assuming the phenotype for $A_1A_2$ is the same as the phenotype of the homozygote, in each scenario. It may be possible that the phenotypes are different, but the fitness is the same- what we are actually measuring with $h$ and $s$ are fitness, not phenotypes. But if the phenotypes are the same, the fitnesses must also be the same- natural selection works on phenotypes, not genotypes.
Where the break between fitness and phenotype becomes complete is when $h$ is a value other than 0 or 1 (not complete dominance).

$h$
Dominance Type
Scenario

0<h<1
Incomplete dominance
The heterozygote ($A_1A_2$) more fit than $A_2A_2$ and less fit than $A_1A_1$

h<0
Overdominance
The heterozygote ($A_1A_2$) more fit than homozygotes ($A_1A_1$ and $A_2A_2$)

h>1
Underdominance
The heterozygote ($A_1A_2$) less fit than  homozygotes ($A_1A_1$ and $A_2A_2$)

In each of these cases, the phenotype of the heterozygote is something different than either of the homozygotes (hence the term incomplete dominance). What the value $h$ is measuring here is not the difference in phenotypes, it's the effect it has on fitness- which might be different in different contexts.
Let's think about the classic example of overdominance, sickle cell disease. In terms of fitness, individuals with one copy of the sickle cell allele have the sickle cell trait. The sickle cell trait offers resistance to malaria, and therefore higher fitness in regions with endemic malaria. An individual with two copies of the sickle cell allele are less fit because they have sickle cell disease. An individual with no copies of the sickle cell allele is less fit because they don't have resistance to malaria infection.
But this measure of dominance, where we define dominance as the fitness associated with a the expression of a characteristic, is context-dependent- individuals with the sickle cell trait are prone to other diseases, and in the absence of endemic malaria it might be they have lower fitness than an individual with no copies of the sickle cell allele ($0<h<1$).
If we think about dominance as simply the expression of a characteristic, we would actually describe the sickle cell heterozygote as co-dominant- when you look at the blood of individuals with sickle cell trait (heterozygotes), they have a mix of normal-shaped red blood cells and sickle-shaped red blood cells.
So to conclude:

Dominance sometimes refers to the expression of a trait in relation to an allele, and sometimes refers to the fitness associated with the expression of a trait in relation to an allele.
Differences in fitness imply differences in phenotype (because natural selection acts on phenotypes, not genotypes)
Differences in phenotype do not necessarily imply differences in fitness

I wrote also some notes on the following, but as they're not directly relevant to the question (but might be useful for Googlers later on) I will put them here below the cut:
Table of relative fitness measures with dominance coefficient $h$ and selection coefficient $s$

Genotype
$A_1A_1$
$A_1A_2$
$A_2A2$

Relative fitness
$1$
$1-hs$
$1-s$

The choice of alleles assigned to $A_1$ and $A_2$ are arbitrary- in reality these are As, Ts, Cs, and Gs. By convention the first allele is the dominant one, but if you're not sure which is dominant before you test it may be the second!
Similarly, by convention we assume the individual with $A_2A_2$ is not more fit than individual with $A_1A_1$ (in other words, $0<s<1$). But you might have it backwards!

More often than not selection acts at the phenotypic level, and dominance refers to the phenotype. However, when we talk about genotypic fitness ($W$), without any information about the phenotype that each genotype produce, we disregard phenotypic quantity and look at phenotypic quality (fitness). By saying that $W_{A_{11}}=W_{A_{12}}>W_{A_{22}}$, we assume that the phenotypic quality of $A_1$ dominates over the phenotypic quality of $A_2$ because $W_{A_{12}}=W_{A_{11}}$, and not $W_{A_{12}}=W_{A_{22}}$. But this is not always the case.
We cannot say that $A_1$ is dominant over $A_2$ because we don't have the information about the phenotype. Let's look at two scenarios. In scenario 1, we have a population in which the following genotypes produce the following phenotypes:
$$A_1A_1 \rightarrow GREEN \\
A_1A_2 \rightarrow YELLOW \\
A_2A_2 \rightarrow RED \\$$
Let's assume that this species cannot distinguish $GREEN$ from $YELLOW$ and these are also the colors that have the highest reproductive success, which means that the following fitness values can apply:
$$W_{A_1A_1} \rightarrow 1.0 \\
W_{A_1A_2} \rightarrow 1.0 \\
W_{A_2A_2} \rightarrow 0.9 \\$$
If we don't have the information about the phenotypes described above, one could mistakenly assume that $A_1$ is dominant over $A_2$ based on the fitness values only.
In scenario 2, assume the following phenotypes and fitness values:
$$A_1A_1 \rightarrow GREEN \rightarrow 1.0\\
A_1A_2 \rightarrow GREEN \rightarrow 1.0\\
A_2A_2 \rightarrow RED \rightarrow 0.9\\$$
In this case, assuming that $A_1$ is dominant over $A_2$ is correct, but one cannot be certain of that, unless we have the information about the phenotypes.


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Drinking soda triggers tingling on a tiny spot on my upper back... but how?
The title pretty much says it all.  Yes, I know it doesn't make sense. That's why I'm baffled.
For the past week or two, I've noticed that drinking soda seems to cause a tingling/stinging sensation on a very tiny spot on the skin of my upper-left back. It happens within a second or two after I swallow. This has been happening pretty consistently since I first noticed it. (I've noticed it at least a dozen times; I'm pretty sure I'm not hallucinating...) I think it also happened once or twice when I was drinking plain water, but not enough for me to be sure whether or not I actually felt it or if I was just imagining things...
I've been otherwise healthy and there's nothing particularly special about that spot on my back, so I'm pretty baffled at the moment. How/why could this possibly be happening?

The skin is a very richly innervated organ, and minor strange sensory phenomena are not exceedingly uncommon.
The thing about sensory nerves is that they can misfire and you seem to feel something when there's nothing there. This actually happens all over our bodies all the time (mostly our brain blocks them out, like it blocks out background noises after a while): an itch for no reason whatsoever (no bug, no bite, no reason) is the most common manifestation of this phenomenon.
Sensory nerves start their journey out of the central nervous system as relatively large bundles coming off the spinal cord, and keep on branching becoming finer and finer as they reach the periphery.

since there's a lot of muscle under the skin, most of these sensory nerves have to come up through muscle.

Sometimes an inflamed bundle of muscle fibers (aka a "knot") will entrap a small branch of a sensory nerve, and the pressure on the nerve will cause it to "misfire", causing a sensory illusion, if you will. If this is the case (if it's in the exact same spot every time) and a slender nerve branch is being squeezed by a muscle knot in your back, you can do a little test on yourself: have someone run a fine sharp object (say the end of a toothpick) softly over an area starting away from the spot going through it. If the sensation changes right on that spot - going from sharp to dull, for example - and does so consistently, that's what's going on. If you have the person map the change of sensation with a pen, the spot will be about the size of a quarter or smaller.
If, however, the sensation is only associated with swallowing, and there's no change to light touch, I have no idea what's going on.
Anyone reading this should know, though, that strange neurological symptoms can be an early sign of MS.

+1 thanks for the answer. I suspect it's just associated with swallowing, but I'll try to have someone do what you wrote just to see what happens. I'll have to wait until I get more soda though, so I can figure out the exact spot again first...


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What is the minimum air pressure the human body can tolerate if oxygen supply is not an issue?
Disregarding hypoxia, what is the minimum air pressure that the human body can tolerate?
(i.e. at what air pressure would the blood start to boil, or skin start to burst, or whatever else might happen that would kill you but isn't related to oxygen?)

Can you separate lack of oxygen from low pressure?

@kmm: I don't see why not. Just because there's not enough oxygen reaching the brain doesn't mean your blood would start boiling or your skin would start bursting...

I think one cannot really separate the lack of oxygen from air pressure. Because the inside pressure balance the outside pressure, if the pressure is low outside, one cannot inhale lots of air without lung injury. Similarly, a scuba diver always inhale air at the pressure associated with its depth. (In consequence divers absorb much more oxygen (and consume more air) in deep water than in shallow water). You may eventually separate air pressure from oxygen if you consider someone who put a single arm or leg in a artificially very low pressure environment.

@Remi.b: I don't see what's so hard about separating the two. Let me reword the question for you. Let's pretend the human body did not need oxygen/respiration at all, i.e. whatever you breathed in was exactly equal to whatever was breathed out (with no O2 or CO2 or anything else added or removed). What would be the minimum pressure it could survive in in that case? (If you're saying this has never been measured because, perhaps, it is impossible to measure, then please post that as an answer.)

You might be interested to know what happen to our body in a vacuum. It does not tell you "the minimum pressure under which we can survive if we were to assume we don't need oxygen" but it might give you some sense of what you're looking for.

@Remi.b: Thanks for the link, that's very enlightening -- definitely not what I expected! I guess for the purposes of my question, we can consider the minimum air pressure for a longer term (say, a few hours), not just for a few seconds. (Still reading the link.)

Last link seems to have broken; new link is this.

The lowest pressure a human can survive is time dependant. https://www.scientificamerican.com/article/survival-in-space-unprotected-possible
Up to 15 seconds before loss of consciousness and a minute or more before death. Can’t post an answer here as I don’t have enough reputation

@Slarty: I think for this question I was looking for pressures that allow survival indefinitely, not merely for a few seconds or minutes. Still, good to know, thanks!

@user541686 I suspect that you may be right, but indefinitely is a long time and I doubt very much that anyone could survive at the Armstrong limit for a very long period.

@Slarty: Yeah, quite possible. I just don't have better information unfortunately.

Disregarding hypoxia, the lowest atmospheric pressure the human body can withstand is around 6 percent sea level pressure, or 61.8 millibars, below that pressure the water and blood in your body starts to boil. Harry George Armstrong, a physician, and an airman, was the first to recognise this limit, which on Earth occurs at an altitude of roughly 63,000 feet, beyond which humans absolutely cannot survive in an unpressurised environment. The limit was named in his honour and so is called the Armstrong Limit. The lowest atmospheric pressure humans can breathe in, with a pure oxygen supply on hand, is roughly around 12.2 percent sea level air pressure or 121.7 millibars, the pressure found at 49,000 feet. Or, as a slightly madder alternative example, in a terraforming Mars situation, which might arise one day; a fit person could in theory walk around outside without a spacesuit on, but breathing from an oxygen tank, only when the atmospheric pressure got above about 120 millibars, and hope to survive for long.

For reference the natural atmospheric pressure on Mars is around 6 millibars.

At sea level, where atmospheric pressure is 1 atm and oxygen is about 21% the partial pressure of oxygen is enough to saturate hemoglobin.
The lowest tolerable pressure of air is about 0.47 atm (475 millibars of atmospheric pressure) - recorded at 5950m altitude.
At about 0.35 atm (less than 356 millibars at around 8000m) life is impossible. Pulmonary and cerebral edema lead to death.
Source: Wikipedia, Effects of high altitude on humans

You've got at least one number wrong. The "Death zone" at Mt Everest is considered to start at about 8000 meters, and the pressure there is about 0.75 atm. See http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html

Just to clarify, I didn't mean that the "Death zone" altitude is the answer to the question, just that your altitude and pressure numbers don't match. Also, I couldn't find those numbers in the linked article.

@jarlemag In the article Death zone pressure was in milibars. I converted it to atm.

Sorry, my mistake. I mistook feet and meters in the table. There's still one mistake though: The lowest tolerable pressure (inhabited for two years) and 475 millibar figure is at the height of 5950 m. 5100 m is the height of the highest permanent settlement.

Humans can tolerate huge pressure changes with only a little oxygen  in their lungs and blood system . IE: deep sea divers that dive down hundreds of feet into a huge pressure zone with out air tanks  but just one big breath. Therefore,  we should  be able to live for a short while as well in the very low pressure area that is in the vacum of space. If placed in space suddenly, we would surely get the bends if we lived long enough. If still inside our damaged space craft the heated air would surely be sucked  out,  but the radiant heat of the mass of the whole area should still keep us warm enough for a short while. Outside the capsule in the direct radiation of the sun should not kill us suddenly either. Earth bond fire victims can tolerate over 70% damage and still live a short while. If forced outside into the shade of the damaged space craft, I believe it would be very cold but still very livable until we ran out of oxygen in our blood.  Therefore I think we should have time left to think and  do something physical to save ourselves from the very quick on set of asphyxiation before anything else takes it turn.  IE: like do something like reach for the pressurized oxygen mask hanging on the wall like they have in airliners. If possible then we should freeze to death suffering from the bends.

Add some references to your claim.


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Human body reaction to gamma rays
I attended a meeting where the speaker claimed that a human body reacts to the exposition to gamma rays reducing the amount of acetylcholine. Is this thing scientifically proven? I cannot find any source that confirm this thesis.
- Update -
The source from which the speaker based his theory is this paper. Excluding the fact that here gamma rays seem not to be mentioned, is this a reliable source?


text:
Is this plant lantana camara? If not what is it?
I was in a botanical garden recently and wasn't able to find the tag on this plant. The diameter of the entire flower tended to be around 5cm.
Google seems to suggest its lantana camara but I'm not 100% convinced yet.

When rubbed, its leaves produced a minty aroma

It does seem very similar. Why do you doubt?

It is Lantana camara you are correct.  There are many hybrids out there as well.

It is Lantana camara, you can check here: https://en.wikipedia.org/wiki/Lantana_camara

Someone (not me), downvoted your answer. If this can be helpful for you, the reason might be that you do not give enough details in the answer itself. You should probably give more information such as key criteria that allow the confirmation of the identification of this plant.


text:
Does the leaves of papaya plant help in increasing platelets in a case of dengue?
In Kolkata and nearby regions, due to sudden and huge amounts of rainfall, there has been an outbreak of dengue, a disease spread by female Aedes mosquitoes. The outbreak has been so dangerous that dozens have already died in the villages.
A problem of this disease is that, the platelets in blood are decreasing abnormally. For example, a patient had 120 thousand platelets when checked at night, but when checked on the morning, it drastically reduced to about 20 thousand. This particular patient could not be saved.
Many people say that the juice of papaya leaves (leaves of Carica papaya) helps in increasing the platelets in blood. Some doctors say it's wrong, while others say that it does effectively help. Even tablets and powders have been made, but the confusion persists as to whether they are effective or not.
I could not find any good information on the net. Can anyone, with scientific arguments, answer this question?

Dengue isnt usually fatal with good medical care. I suggest sending them to the nearest hospital immediately

@user35897 a good advice from your side, but hard to follow from our side. Hospitals are full, so much so that patients are lying on the floor, with saline bottles attached to the door handles! Such is the condition. Otherwise way will so many die every day?

I'm really sorry to hear that :( hope this pandemic end soon:(

So With some digging, I found some articles/presentations that provide evidence that fresh papaya leaf extract does increase platelet counts. The first link tested this in a rodent model and found that in the test group treated with the leaf extract, there were significant increase in platelet count and red blood cells (RBCs) from the control group. Here is the summary of their results trend from the paper:

Additionally, I found a Multi-centric, Double-blind, Placebo-controlled, Randomized, Prospective Study and a meta-analyses that supports the observation that papaya leaf extract does in fact show statistically significant increase in platelet count than that of the control groups. (Dengue fever causes platelet counts to plummet). [#2-3]
Below is the image of platelet counts from the Multi-centric, Double-blind, Placebo-controlled, Randomized, Prospective Study (2):
Fig. 1: Comparison of platelet count between two groups during different
timepoint

A good criticism of the meta-analyses on Papaya leaf extract is that something being statistically significant does not equate to clinically significant. But, the placebo-controlled, double-blind prospective clinical trial provides some evidence that in this case, it is actually clinically significant.
However, the mechanism by which this occurs is not well understood. According to the 4th article, "The secondary metabolite of plants origin makes up a vast repository of compounds with a wide range of biological activities". The presentation (5) states some possible mechanisms by which the extract can inhibit the Dengue virus/vector.

Does Carica papaya leaf-extract increase the platelet count? An experimental study in a murine model
Efficacy and safety of Carica papaya leaf extract in the dengue: A systematic review and meta-analysis
A Multi-centric, Double-blind, Placebo-controlled, Randomized, Prospective Study to Evaluate the Efficacy and Safety of Carica papaya Leaf Extract, as Empirical Therapy for Thrombocytopenia associated with Dengue Fever.
Dengue fever treatment with Carica papaya leaves extracts
Role of Papaya in Dengue fever, an evidence based Answer


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Circadian Clock During a Flight
I am interested in knowing how our Circadian Clock responds (and if there are resultant changes) when we travel across Time Zones?
UPDATE 24th April
I am reopening this question as the statement in the answer "When you travel to different time zones, your circadian clock will be off" has further confused me. If it's the case, then I am looking to get a better explanation than that (with solid references). Thanks

Welcome to Biology S.E.! From what I understand, the actual time zone shouldn't cause too much of an issue. However, flying from light into darkness or the other way around seems it could confuse your internal clock. And if you crossed several time zones and then tried to sleep at your normal time and it was still light out... That could be confusing as well.

Just removed some irrelevant tags.

When you travel to different time zones, your circadian clock will be off (incorrect). The reason your circadian clock will be off is because your body has adapted to the time zone you are from. When you enter a new time zone, your circadian clock will still be functioning on the old the time zone. If the time zone difference is $\pm 12$ hours, this is a huge adjustment.
However, your body takes inputs from the environment. That is, you may see it is day light when your body is under the impression it is evening. Your circadian clock is controlled by your master clock located in the hypothalamus. As you take in these external inputs that counter your circadian clock, a group of nerve cells called the suprachiasmagic nucleus will slowly make the master clock adjustment [1]. This resetting can take a few days.

NIH Jet Lag Prevention Guideline

Additionally, there has been a bit of research on exercise reducing jet lag. In a study, researchers test outdoor exercise with flight crew members and found that the group that exercised outdoors had a hastened re synchronization of their circadian clock [2].
Another interesting article is Jet Lag in Athletes.

Thank you! May I have reference for "When you travel to different time zones, your circadian clock will be off."

@dustin - that sentence confused me too; as it stands, it reads like "when you travel to different time zones your circadian clock will be [switched] off". I had a raised eye brow and had to re-read it too.

@AliceD you can edit if you want. It makes sense to me, so I don't see the issue.

@dustin - up to you, it may just be a language barrier making me to mis-read your sentence. It's not critique, just an attempt at analyzing POs question on the reference :)


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Lengthening muscles not good from evolutional perspective? Why do we do it with explicit stretching?
Stretching has many advantages, among other things it helps us to be flexible in our movement (which is an advantage?!).
But why do we need to actively stretch, it seems that the body wants to shorten the muscles by evolution (e.g. when training often in fitness studio). This is the opposite of what we do when stretching.
It seems to be that there are advantages of being not stretched. So what are these advantages / what is the evolutional rationale?
Edit: Why this question is different from this question:
That question asks, why we automatically stretch sometimes after e.g. sleep. The answer is that we stretch the soft tissues because of transitions of high and low activities (especially after sleep, in which we ease the tension in our muscles [muscular antonia]).
This question asks something different. It asks about explicit stretching in sports and not about automatically stretching behavior. The aim is different. In sports we stretch because, we want to lengthen our muscular. The question is why lengthening doesn't seem to be a good thing from an evolutional perspective.
Edit 2: I'm not sure, if it is clear for everybody, what I mean, so I add a succinct example: Why would it be bad (evolutional rationale), if everybody could do a split (gymnastics) by nature (disadvantages?)? In our reality, the ability to do this is almost always an result of stretching. This is only one extreme example, mostly people don't strech to such extremes. Maybe this now  helps to understand, for what this question heads.

@GerardoFurtado Thanks, shall I edit the title to "Lengthening the muscles not good from evolutional perspective? Why do we do it with explicit stretching?"?

I don't know enough about this to make an answer but I wonder if you might find some answers in looking up "hypermobility" or "hyperflexibility", and why it can be bad. There may be a tradeoff between mobility and strength; sometimes you want to bend, but sometimes you want to have a limb "locked in place", and if the muscles/ligaments can stretch too far then you need to spend energy keeping them contracted where you might otherwise not need to.

Muscles only ever work by shortening, as you say, but muscles in the human body tend to be found in antagonistic pairs.  These pairs of muscles act in opposite directions, one example being the biceps and triceps muscles - the biceps bends the arm (a flexor muscle) while the triceps straightens the arm (an extensor muscle), another example is the quadriceps-hamstring muscle pair in the upper leg.
If our muscles remained shortened, our mobility would be impaired.  If the biceps muscle remained too short, it would be impossible to extend our arms, for example.  Muscles do work by shortening, yes, but it's important for them to be able to stretch as well, and remain long enough for antagonistic muscles to have their full movement be possible as well.

Welcome to Biology.SE. Your answer seems good enough to me but please add references (peer-reviewed articles are best, Wikipedia articles or blogs are also okay for common knowledge) to back up your claims and give people starting points for further reading. Thanks!

This doesn't answer my question, or at least what I meant. I edited the question. This question heads for streching in the meaning of lengthening the muscle at its maximum resting length (and maybe to shorten the completely contracted length of the antagonistic muscle partner).

Thanks for your comments, both.  Apologies that I don't have any references, it was purely reasoning that lead me to my answer so please take it with a pinch of salt, obviously!

Sorry I haven't been able to answer your question entirely. Perhaps it's just the case that stretching to such extremes aren't that frequently used in a natural setting.  It may not be detrimental, but it may not be advantageous enough for it to have been selected for over the course of evolution.  This article has some suggestions too: http://www.ideafit.com/fitness-library/does-stretching-reduce-injury-risk-0


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Correct/complete representation of RTPCR statistics
In papers reporting a relative quantification of gene expression by RTPCR, I often see a bar chart with mean ± standard error or deviation, with the deviation belonging to biological replicates. This ignores all the previous layers of technical replicates. In the regular $2^{\Delta(\Delta Ct)}$ estimation with 3 reactions per primer/template, we have the standard deviation (SD) from each technical replicate, then the SD from normalization, end finally the SD from quantification. If the end results are fold changes, add one more layer to this. I'm not even including normalization with the geometric mean of 3 housekeeping genes (the better method)  How can I  correctly calculate / depict the statistical variations in this case?

Maybe these articles show relative expression changes between time points? In my institute we do these as well and the SD comes from the biological replicates in these cases. Also it might only be a data representation issue.

I think you can follow this method:

Test the statistical significance of a single experiment by comparing technical replicates (lets say Tests: T1, T2, T3 and Controls: C1, C2, C3). This will tell you if the instrument can reliably detect difference or not. Note that you should compare the relative expression (i.e. wrt your reference gene) and not the CT values. The ΔΔCt method is fine but you should note that it is not necessarily a power of 2; 2 denotes perfect PCR efficiency. See these posts:

Real time PCR normalization algorithm
Real time PCR standard curve

If the difference is found significant in all technical replicates then test the difference between biological replicates by using the means of the technical replicates in each experiment; for example mean of T1, T2 and T3 in biological replicate-a ($\bar{T_a}$) used as the sample value for that replicate. You can proceed with t-test for computing statistical significance which will tell you if the difference in expression is because of a random cellular behaviour or not. You can also do an ANOVA to compare the variance between technical replicates (within an experiment) and biological replicates (mean of the technical replicates between experiments). ANOVA lets you know some aspects of reproducibility of a measurement technique.
Fold changes (FC) are a problematic issue because many biologists seem to mess up with the interpretation of the data. First of all a t-test cannot be applied to FC directly (especially if FC is calculated pairwise for each replicate). Now all you have is a single random variable i.e fold change that you cannot statistically compare with anything. Fold changes are not really bad but I would recommend that a t-test be done between the control and the test samples and if the difference is found statistically relevant then report the FC. I personally know many people who do the other way round and set variance of the control sample as zero (because pairwise FC would be = 1 in all cases): This is a blunder.


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How can a heart of human work if one of its valve is not working?
Yesterday I went to a hospital and heard a doctor say that one of the heart valves of a patient is not working. However, the patient was still alive and was healthy; the patient could walk and talk too. I could not understand it because I have read that all valves of heart are extremely important. I have tried searching on google but all I could find was heart attack problems.

See the following articles on wikipedia to get your head around that topic: aortic insufficiency and aortic stenosis. You can also look for stenosis or insufficiency of the mitral, tricuspid, or pulmonary valves, all on wikipedia.

It is not possible that one of the valve is completely closed and the person is still alive without being in ICU. I think what the doctor was trying to communicate to the patient was that one of the valves is in the process of complete closure. There are three main types of diseases associated with heart valves :-
1- Blood flows backwards
2- Heart valve opening becomes narrow
3- upper condition may lead to complete closure
For details see the following link:-
http://www.nhlbi.nih.gov/health/health-topics/topics/hvd
http://en.wikipedia.org/wiki/Pulmonary_atresia
Hope you understand. :)

"Not working" can also mean that the valve cannot close, instead of being permanently closed.

@MarchHo Even if the valve cannot close properly, will there not be problem in blood supply. If what I am saying is right then patient should be in ICU. But as I said before patient was looking fine.

@NigHterz If the insufficiency or stenosis of the heart valve becomes severe, it will lead to death even with extensive care in the ICU. The only treatment is valve replacement, either by surgery or interventional cardiology. However, people do just fine with a minor defect. For example, a minor degree of mitral insufficiency can be found in almost 30% (depending on sources) of people, and they often never even learn about it in their lifetime. They live normally and practice sports.

@NigHterz 'But as I said before patient was looking fine', These problems often develop gradually and the impact gradually increases. The patient you saw may be fine as along as they are sitting, but they may be unable to climb a flight of stairs or walk more then a few dozen yards, without feeling short of breath.


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While in motion, why do closer objects appear to move faster?
When I look outside the window while travelling by a car, why do closer things seem to be moving faster and appear unclear but the farther ones seem to be moving slower and appear clear?

@BagiM no answers in the comments please

@AliceD Sorry i thaught the question is going to be moved/deleted since it is not biology so i just left a comment. I can repost the comment as an answer.

@BagiM: the 2nd half of the question/answer clearly involves some biology.

@BagiM this is all about perception. Ontopic as can be. Only problemis that OP hasn't gone through any prior effrt, so that would, for me, be a valid reason to put it on hold.

@Fizz you are probably right. I didn't think of it that way since the same effect of motion blurr would happen for a camera and I thaught of it in terms of physics. But now I see you are right.

Why do closer things seem to be moving faster?

This is due to parallax. A very simple phenomenon exhaustively explained on wikipedia.

Why do faster moving things appear unclear?

This is primarily due to retinal persistence also well detailed on wikipedia.
It takes time for the retina to detect a change in light at a given position on the retina. Things that move quickly across your visual field (i.e. retina), or that reflect very low amounts of light tend to blur or simply be invisible. Car headlights moving close to you will blur because it takes time for photoreceptors to 'switch off' and the headlights would appear as a streak or trail of light for you. And similarly, if a car were to move at an incredibly large speed, the car wouldn't reflect enough light to trigger a response in the retina, so it would be unseen by you. Remember that what matters here is how much range of your visual field an object crosses, not the speed of the object itself. For example, a fast car in the distance does not blur since it's crossing a tiny fraction of your visual field, but a slow car right in front of your nose will be crossing your entire visual space very quickly.
These are properties of the retina. It is also possible the encoding of visual information in the brain also plays a role in how your perceive something. However, the illusion you describe is entirely explained by these retinal phenomena due to sensory neuron biology.

It also works the other way around.  Flying in a passenger jet at 30K ft seems excruciatingly slow, even though you're moving at ~600 kts, while a single-engine plane doing ~100 kts at treetop level seems quite fast :-)


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Why does the DSC peak have a bell shape?
I am studying Differential Scanning Calorimetry (DSC) and am not quite understanding why most proteins have a bell shape when the heat capacity is plotted against the temperature.
Also, I would appreciate if you could provide good sources on this topic (books, articles, etc).

This is just a guess, but it's probably because the heat measurement is actually measuring the sum of many, many molecules reactions. It is a fact of mathematics, rather than natural science, that forces such phenomena to approximately follow bell curves (i.e., Gaussian functions). Basically, the central limit theorem states that if you have many instances of the same (random) variables and average them together, then the result will look like a bell curve. Here, the local thermodynamic change induced by a single individual protein molecule, as a function of the temperature, is presumably that random variable, since the thermodynamic behaviour of each protein is roughly similarly distributed. The randomness comes from the essentially chaotic random movements of the molecules.
See here or here for more.

I guess the symmetry can be explained by the cumulative states of the ensemble. However, I can't think of a no reason for this peak to be Gaussian. People often confuse most symmetric shapes (including the bell shape) as Gaussian.

@WYSIWYG True, the CLT is not always appropriate. I am not familiar enough withe subject to comment definitively, but from looking up a few curves, they are decidedly non-Gaussian far from the peak point. I had merely guessed that each molecule's "peak" (denaturation/unfolding) could be viewed as an RV (so the solution is an IID sample), and the observation was composed of the avg over molecules. This formulation, of course, only says that there should be near-Gaussianity close to that point! But even this may well be physically inaccurate. Hopefully someone more knowledgeable can jump in. :)


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Can all animals of the same species crossbreed?
For example, take Canis lupus, the species of dog and wolf. Within their species, can all dog and wolf types crossbreed? We can forget the logistics and assume this is all done through artificial insemination or in vitro methods (let's assume that the in vitro methods would be feasible).
If yes to the main question, does cross-breeding stop at the species class, or does cross-breeding extend across other taxonomic classes? From what I gathered, the taxonomic classes seem somewhat loose in their definitions. Perhaps I should ask, is there a rule "in general" to cross-breeding?
Let me know if this question ought to be refined in any way.

To clarify; you are mainly asking if all individuals within the same species can interbreed?

Whether dogs (Canis familliaris or Canis lupus familliaris) and wolves (Canis lupus) are the same species is debatable. I believe the modern consensus tends towards considering them different subspecies of the same species but as far as I know, the details are not entirely clear. Remember that the line between species is blurry at best.

@fileunderwater Yes, for the most part. The choice of species was a bit arbitrary. I'm wondering if there is a general rule as to what individuals can interbreed with others. Within a species just makes the question a bit more specific.

Can and do is a big difference a lot of things we consider different species can breed if we force them.

Species definitions are a somewhat contentious part of biology. There are no hard boundaries in nature that mean "this group here is one species, this group here is another species". Some people don't even believe that species truly exist and there are only gradations of relatedness. That being said, the Biological Species Concept is one of the more popular species definitions.
From the linked website: "The biological species concept defines a species as members of populations that actually or potentially interbreed in nature". Thus, by definition, all animals of the same species can and do interbreed in nature. If two individuals breed in nature, they are considered the same species (under this definition).
Of course, you can already see some problems with this definition. Under the BSC, are a dog and a wolf the same species? Do dogs and wolves breed "in nature"? Of course, fertile half-dog half-wolf animals exist, but does it even make sense to ask whether a domestic species breeds "in nature". I suppose you can say they can "potentially" breed in nature. But how do you define "potentially" breeding? Asking questions about species can lead to many exciting debates.

breed and give rise to fertile offspring will be more precise definition?

@aaaaaa Yes, that is correct

I'd say it's "in nature" if the male wolf or coyote comes from the wild to your domestic bitch who happens to be in heat.

even this definition runs into problems things like ring species A can breed with B and B with C but A can't breed with C,, it is also completely useless for asexual organisms or extinct organisms. that is why there are more than a dozen working definitions of species.

Even under the Biological Species Concept, there is no requirement for universality of interbreeding. It is a population level definition, not an individual ones. Genetic incompatibilities that prevent successful reproduction are extremely common.

No, definitely not. Even under the Biological Species Concept (BSC) the requirement for interbreeding applies at the population level not at the individual level.
The most common example of how the mechanism breaks down are Ring Species. In the simplest case there are three populations - call them A, B, and C - where A can breed with B, B can breed with C, but A and C cannot directly breed. Because there continues to be genetic flow across the whole collective they are considered to be a single species under the BSC. Two real world examples of ring species are Larus gulls and the Greenish Warbler.
However, the biggest example is simply the majority of species which are asexual and thus cannot cross-breed at all. This, and a host of other problems, are why many biologists reject the BSC as a functional definition of the species concept.

Try breeding a Chihuahua female with a Great Dane male. Both are dogs.


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Does level of bats activity differs from day to day?
Say we measure bats activity as number of passes through given area. Can it differ significantly depending from day to day or it stays on average roughly the same? I am wondering whether the following might have an effect:

Weather conditions (wind or rain). I do not mean here heavy conditions (strong wind or rain), those understandably will affect bats eagerness to fly
Moon cycle
Mating
For insect-easting bats: the prey not being active every night

I would welcome some good reading on the subject.
My question stems from the following problem. Say I have one detector and want to measure activity in three locations. If I rotate it between them, will I get unbiased result?


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Do molecular motors have a life time?
Most of the enzymes have a certain lifetime. I want to know that do molecular motors have a certain lifetime after which they degenerate? Any reference will be appreciated.
Basically, I just want to model a molecular motor with a finite lifetime for that I need a certain numerical age span that they follow or maybe some exponential decay model.
Furthermore, as suggested by WYSIWYG I have got a particular term for the protein lifetime with which I can search. I will try to find the answer myself and post it.

All proteins have turnover. Even if they are not actively degraded they are at least reduced by half because of cell division. Can you please elaborate so that we can understand the rationale of your question better?

@WYSIWYG I just want to model a molecular motor with a finite lifetime for that I need a certain numerical age span that they follow or maybe some exponential decay model.

You should [edit] your question to add all the details instead of replying in comments. Comments are not searchable and even otherwise not easily noticed. Moreover, posts should be self sufficient. Anyway, your question is still very broad. There are several molecular motors in different cell types and there are different ways to model biochemical reactions. Did you try to search the literature (just Google "turnover rate of xxx")?


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Why do genetic testing companies (FTDNA,AncestryDNA,23andme) express DNA shared in centimorgans (cM) instead of in number of base pairs or in percent?
Expressing DNA shared in number of base pairs or in percent of total genome would be so much simpler and easier to understand for the customers.
.

What kind of data / reports are you referring to? Also not that these comapies do not perform DNA sequencing, they do DNAchip based SNP characterisation; therefore any actual basepair positions they could give would come from a refernece genome, which has to have a specific version and is not easy to use/understand for customers.

@Nicolai You could probably make an answer out of your comment.


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In men, why do over 80% of sperm have abnormal form?
Here is the percentage of normal forms among fertile mens according to the centile (Source: Cooper et al. 2010):

2.5: 3%
5 (below this is Teratozoospermia): 4%
10: 5.5%
25: 9%
50 (median): 15%
75: 24.5%
90: 36%
95: 44%
97.5: 48%

Men who have less than 4% of their sperm that have normal morphology are diagnosticated with Teratozoospermia (also called Teratospermia) and are likely to be infertile, though technically 5% of fertile men have Teratozoospermia.
I read on the internet that abnormally-shaped sperms are bad and useless because their abnormal shape prevents transport through the cervix and/or prevents them from adhering to the ovum.
But I think that if they were really that bad, Mother Nature would not have engineered the average men with 85% of their sperm abnormally-shaped.
And I also heard that even animals have a big fraction of their sperm that are abnormally-shaped.
So, in men, why do over 80% of sperm have abnormal form?

Why do you think it has an adaptive purpose? Not all traits have been selected for. For example, forming abnormal sperm might be a high probability event, and so ejaculating a large number of sperm may have been selected for to counter that. Of course I do not know if that is what happened, but I am illustrating how not all traits are adaptive.

How is a 'normal morphological form' defined? For most other medical reference values one would take exactly a distribution like that to have 'normal values' in the first place.

@NatWH: True this is a possibility, but I think it's unlikely because more than 80% of failed creations is really high, it's so high that this cause a significant fraction of men to be infertile.

@James: This question is a general question, it's answers are just general possibilities. My question is a precise question about a precise topic and needs a precise answer. E.g. answering "maybe there is a tradeoff" would not be an acceptable answer, but answering "there is a tradeoff which is that the abnormal sperm have the advantageous function that ... something" could be a correct answer.

@Nicolai: A normal morphological form is a form which can reach and penetrate an egg. An abnormal form is a form which cannot. Normal sperm have an oval head with a long tail. Abnormal sperm have head or tail defects, such as a large or misshapen head or a crooked or double tail.

@Aero that was the purpose of my hypothetical example - if the proportion of malformed sperm is high, then one way to deal with that is to produce huge numbers of sperm, and hope that the 20% still represents a large enough fraction to fertilize the egg.

@Aero: "normal morphological form is a form which can reach and penetrate an egg" sounds more like what you wish Cooper 2010 was reporting about rather than what they actually were able to report about. As Nicolai shows below, they are actually compiling data about lab microscopy about sperm appearance, not about whether sperm actually reached and penetrated ova.  So you shouldn't assume that the median man has semen with only 15% of the sperm present capable of fertilizing an egg just because of that report.

The way the winds are blowing, this question is about to get closed as a duplicate of a question that doesn't talk about sperm at all.  This might be able to be headed off by changing the headline to drop the evolution/purpose aspect, as e.g. "Why do over 80% of sperm have abnormal form?".

@mgkrebbs: Done.

@NatWH: 1% of men have 100% abnormal forms, so even producing huge numbers of sperm won't increase the number of normal forms. Based on the many articles I just read, it seems that abnormal forms can in some men still possibly fertilize the egg but that it's just much less likely for an abnormal form to succeed compare to a normal form.

What do you mean with 'why'? These edits take out the evolution aspect,but replacing it with 'why' makes it unclear. Why, as in, what are the underlying mechanisms? Or why in terms of the evolutionary benefits? The latter makes it a dupe.

So I've dug a bit into how a 'normal morphological' form is defined and characterised, since assessing morphology into 'normal' and 'not normal' is always a very tricky thing.
Looking into the method section of the source you cited, we get:

All laboratories generating the data analysed here used standardized
  methods for semen analysis [...] The various editions of the manual provided similar
  methods for assessing sperm concentration, motility and morphology but
  provided different criteria for categorising morphology.

So the  problem begins already with the fact that there is not one, but multiple different recommended practices.
(For anyone interested the different staining methods used were: Bryan–Leishman [B], DiffQuik [D], Haematoxylin and Eosin [H], Papanicolaou [P], Quickdip [Q] and Shorr [S]. Of thses H, S and P were used for generation of the 'normal morphology' reference set).
Clearly this problem was also obvious to the authors, so they tried to restrict the data they used:

Although all centres reported using WHO procedures, the recommended
  methodologies have changed over time, and many centres have
  experienced difficulties with the subjective assessments of
  morphology. Data on normal sperm morphology were only included if
  results were reported as determined according to the so-called
  ‘strict’ (Tygerberg) method (WHO, 1992, 1999).

Fortunately these WHO guidelines are available on Google Books and they require the following points to met (most of which were defined by 95% confidence intervals of control samples):

head length 4.0-5.0µm
head width 2.5-3.5µm
head length-to-width ratio 1.5-1.75
well defined microsomal region compromising 40-70% of the head area
mid piece should be slender, <1µm
[mid piece should be] 1.5x size of the head
[mid piece should be] axially attached to the head
Cytoplasmic droplets should be less than half size of the head
Tail should be [...] approximately 45µm long

Plus one very important sentence:

This classification scheme requires that all 'borderline' forms be considered abnormal

This sentence is important, because it means that each criterion stated has to be fulfilled for a single sperm to classified as morphological normal.
If we take only the numeric requirements (which should cover ~95% of the normal value distribution for a healthy population) and assume that they are not correlated, this means that for any given single healthy sperm we have a $0.95^9 = 0.63 = 63\%$ chance that it is within the 95% interval of all defined parameters.
This means that applying this strict categorisation scheme should even for a 100% healthy population only result around 63% sperm cells categorised as morphologically normal (ignoring that the parameters are probably not interdependent which would make it a bit better).
If we now take into account that the analysed samples were probably not 100% healthy cells and remember that the (reported) difficulties of assessing morphology, I think that the reported values for 'morphological normal' are not as quite as unexpected as they might seem.
Note: all bold highlighting in the quote blocks was added by me.

Biological evolution occurs when there is a change in gene frequencies over time (as I recall).  There are two components, or elements, required for this process:

genetic variation, which provides the raw material
natural selection, which results in the genes from the most successful reproducers being transferred to subsequent generations

The data you present support the hypothesis that “normal” sperm morphology in human males is not a strongly selected trait (because otherwise “normal” sperm would be more prevalent). Period. Full stop.
Any attempt to answer the “Why” part of this would have to be a conjecture, and ultimately untestable on an evolutionary scale.


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Which part of human body sustains most pressure when standing up straight?
Let's suppose a healthy fit barefoot young adult standing comfortably on a flat solid surface.
A reasonable guess is somewhere around the foot.
But is it the ankle, the heel, or the Metatarsus?

ankle seems reasonable. pressure is force/area, but higher you climb, less mass you have to support (neck vs lumbar vertebrae)

the graph here shows that peak pressure is higher at the Metatarsus compared to the heel. however I cannot find a convincing comparison between ankel and Metatarsus.

What about the base of the spinal column? Very small surface area compared to the two feet, bearing a huge fraction of the load of the upper body. I'm not sure at all about this one, just speculating.

It is logically clear that the ankle could only partly be analyzed in the group of joints that are below its height. There is no direct way to measure the pressure on ankle joint (on talus bone), but from the logic it is clear that it should be the point of highest pressure in the group of points lister in the question, however the pressure is distributed through the other joints of the foot.
Below are the graphs of pressure distribution according to surfaces (not joints). From the graph we can conclude that part of the pressure experienced by ankle joint distributed tangentially to metatarsal region and other surfaces.

Indeed the highest pressure in standing person in on feets. The term you are asking about is foot pressure distribution (FPD).
In we assess the FPD dynamically, in younger persons the FPD is nearly equivalent between calcaneus region and metatarsal region, while in older persons the FDT in calcaneus region is higher than metatarsal pressure.
During stance:

Foot pressure distribution. A. Maximum pressure distribution on all sensors during stance for one subject. B. The nine anatomical masks superimposed on the insole (MC = medial calcaneus, LC = lateral calcaneus, MA = medial arch, LA = lateral arch, MT1 = first metatarse, 3 = second and third metatarse, 4 = fourth and fifth metatarse, H = hallux, and T = toes).

Pressure distribution by anatomical region. Normalized maximum pressure distribution for the young (white bar) and elderly (black bar) group for each anatomical region (medial calcalneus mask p = 0.0001, lateral calcaneus mask p = 0.03):

source article, you can find much more using FPD as a keyword.

Thanks for your answer. It is clear and informaitive. Maybe someone can run a simulator of human foot on computer and get a 3D pressure map? It'll be fantastic.

@GrigoriSun I'd say this simulator is a good candidate for PhD for someone... %)

@Ilan cheers mate!

Note that estimations in this answer are very very crude. I can speak with confidence that the mean pressure of ankel joint is greater than the heel and the metatarsus. However I do not trust that it can pin down the point with most pressure.

@Ilan gave a very good synopsis on foot pressure distribution. However, pressure in ankles was not analyzed in his answer.
Kimizuka et. al. measured contact area of human ankle joints under various load-force configurations. The main results were shown in the graph below.

For a $70kg$ human, the contact area of each ankle is about $3cm^2$, whereas of each foot with ground surface is approximately $37 cm^2$. Please note that we include only the heel ($4cm\times4cm$) and the metatarsus ($7cm\times 3cm$) in above calculation, which sustain most pressure.
We can safely ignore the mass of both feet compared to the whole body. So it seems that ankle pressure is the clear winner here.


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Can someone identify the species of this frog/ toad?
Location: Tirupati, Andhra Pradesh, India
I found it at night time near a lake
It was quite small in size ( 5-6 cm Approx.) having dark brown spots all over its body and three prominent green stripes running along the length of its body and 2 stripes running across its upper body ( one crossing over its eyes).

Looks to me like an Indus Valley bullfrog (Hoplobatrachus tigerinus).
Your specimen would be a bit small, but the species is nocturnal, the area fits and the patterning looks like a decent match as well:

(taken from the Wikipedia page)


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Can we use differential equations for population that is discrete?
Population dynamics is often modeled using ODE. For example one common model is logistic growth model:
$$\frac{dx}{dt} = k.x.\left(1-\frac{x}{C}\right)$$
where x is population size, k is rate constant for growth, C is carrying capacity.
But population is a discrete variable. It is not continuous. It always takes whole numbers. You can have a population of 3000 fish, but not 3001.2 fish.
Then how can one use population as a dependent variable in a differential equation?
Integration of the ODE, given above, will give me a function to calculate size of population, x(t), at time t, when size of the population at t = 0, was x0. We can specify a whole number for x0. Here, x(t) can be a real number with fraction, but a population size is always a whole number.
How does one tackle this anomaly?

You can make the continuous approximation when the population size is large. As mentioned by arboviral, there are algorithms that allow you to perform stochastic simulations with discrete variables. However, these are computationally much more intensive than integration of ODEs. Moreover, analytical solutions for the master-equations (time evolution of probabilities) are very difficult to calculate. Therefore, whenever possible, people go for ODE-based continuous models.
These models would give incorrect representation of the dynamics for small populations and fail to explain phenomena such as extinction. However, they can explain the dynamics of large populations fairly well. So the choice of the modelling approach depends on the questions you want to ask and the complexity/computational cost of the model.

+1 To cite a famous example of continuous approximations, there are the diffusion equation approach to markov models such as those used by Kimura.

@Remi.b yes. And diffusion equations are also used for migration models.

Isn't this the basis of calculcus, that you can approximate things by computing the limits of smaller and smaller divisions?  And aren't many differential equations applied to things like fluid flows that are fundamentally discrete (being made of atoms), but can be approximated very closely by assuming they're continuous?

I'd hardly call myself an expert on this topic by any stretch of the imagination, but you can actually come up with good approximations based on ODE-based models by rounding off to the nearest whole number (assuming that your populations are sufficiently large). The key word is "approximation" - it's not actually all that big of a deal to have to round your number when you realize that 3001.2 is just an approximation to begin with. You're not predicting that there will be exactly 3001.2 fish, you're predicting that there'll be approximately that many. In fact, predicting that there will be 3001.2 fish when there were actually 3000 a superb approximation: that's an error of only approximately 0.0003% once when you round down to 3001.
The important thing to keep in mind about mathematical models is that answers tend to be less "cut-and-dry" than you may be used to from other fields of mathematics. Most people think mathematics is all about having one correct way to come to "the" correct answer, but that mentality doesn't really apply to mathematical models. Try to think of models more in terms of "better vs. worse" as opposed to "right vs. wrong."
The other factor, of course, is that it can be difficult (or impossible) to know the exact value of all of the variables. For example, I was recently working on a mathematical model of urban pigeon populations. As shown in this question, it's not all that easy to get accurate population data on pigeons, and it's certainly extremely difficult to know what the exact carrying capacity is for a given area. (Quick - what's London's total carrying capacity for pigeons?)
This doesn't apply to this particular differential equation, but there are plenty of cases (both in differential equations in particular and in mathematical modeling in general) where it's either impractical or impossible to come up with an exact numerical solution. (You can often use various approximation techniques like Euler's Method, for example, to come up with good approximations; you can also use graphical techniques like direction fields to get a sense of general trends). This kind of a situation actually comes up a lot in practical cases that we'd like to be able to come up with a good model.
TL;DR Your model's an approximation to begin with, so I wouldn't worry too much about having to round.

Yes, you can. For example, the Gillespie algorithm (Gillespie-Doob algorithm) generates a statistically correct trajectory of a discrete population from a system of differential equations. This is computationally more intensive than treating a discrete population size as continuous, so is only normally used for relatively small populations.


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Clonality of tumour cells
Does all cancer cells come from a single clone of cells or are there evidences of polyclonal cancer cells too?

Both. There exist homogeneous and heterogeneous tumors. Just depends on the type, its site and cell type of origin, and other factors.

Most tumors are probably not strictly clonal; all cancer cells in a tumor seldom have the exact same set of mutations. Tumors tend to be subclonal, with all cancer cells having a single common ancestor but with later evolution resulting in some mutations shared among all cancer cells but others restricted to sub-populations of cancer cells. This fact and its implications for therapy were noted 40 years ago by Nowell (Science 194:23-28, 1976), and verified by much recent work as reviewed for example by McGranahan and Swanton (Cancer Cell 27:15-26, 2015).
A tumor might need to have a billion ($10^9$) or so cancer cells to be clinically detectable. Thus many years and many cell divisions have passed since the time that a single cell developed the set of mutations originally needed to produce the invasive tumor. With a probability of some uncorrected mutation at each cell division, particularly in cancer cells that often have defects in DNA replication and repair and in chromosome separation, it is essentially impossible for all of the billion cancer cells in the tumor to have identical sets of mutations. See, for example, the work of Bozic et al (eLife 2: e000747,2013). So although there is a clonal origin of the tumor, the tumor is typically a collection of related but genetically distinct populations best considered to be subclones.
Differences among subclones present a major barrier to traditional cytotoxic therapies, to more modern targeted therapies, and to the immunotherapies that presently receive so much attention. Even if most of the tumor is sensitive and responds, a subclone whose mutations somehow provide resistance to the therapy will be able to repopulate the tumor thereafter. Bozic and Nowak (PNAS 111:15964-8, 2014) estimated that a clinically detectable tumor may have 10 or more subclones resistant to any targeted therapy, due to mutations accumulated during the subclinical growth of the tumor.
As examples from immunotherapy for cancer, McGranahan et al recently showed (Science 351:1463-1469, 2016) that responses to immune checkpoint inhibition in melanoma and non-small cell lung cancer were best in patients with clonal rather than subclonal tumor neoantigens for the immune system to attack. Zaretzky et al (New Engl J Med 2016, epub ahead of print) identified subclonal mutations in interferon-receptor signaling and antigen presentation in some patients, mutations enriched in the recurrent tumors following immune checkpoint inhibition and thus likely accounting for relapse following that therapy.
It is possible in principle for a single physical tumor to have multiple cells of origin. Tumors often develop from a region of tissue that has been subject to field cancerization, where carcinogenic challenges have produced many cells with mutations that lead to dysregulated but not invasive behavior. This can lead to multiple independent cancers arising from the same general location, as individual cells later develop the full complement of mutations needed for an invasive tumor. In principle, such multiple cancers might coalesce into a single tumor mass so that the tumor is polyclonal, but I'm not aware of any well documented cases. So it seems that tumors are seldom truly polyclonal with multiple independent cells of origin.

Can you provide some peer-reviewed citations for your claims in the first 3 paragraphs?

@MattDMo I've reorganized a bit and provided some references. Many more available in the McGranahan and Swanton review.

Looks much better. +1