in-animals-the-rate-of-sequence-change-appears-to-vary-as-a-function-of-metabolic-rate-as-well-as--2

Question

In animals, the rate of sequence change appears to vary as a function of metabolic rate as well as generation time. Gillooly and colleagues have recently attempted to unify these data with the original classic neutral model of evolution. According to their model, the molecular clock ticks at one substitution "per unit of mass-specific metabolic energy" rather than per unit time. Here is Gillooly's paper, along with two of the original papers that raised the issue of metabolic rate:

Jacquelyn Trost · Accepted Answer

it&#x27;s problem. We have been given an equation showing the thermic effect of food on a person. And this function is in terms of T where t is the number of hours have elapsed since you&#x27;ve eaten the meal. So we want to know where this function is increasing and where it is decreasing. To do that, we need to start by finding the derivative. So the derivative of this function is going to be 175.9 times the derivative of this piece that&#x27;s in red. So this is a product. So it&#x27;s gonna be the first times the derivative of the second. And I do have to multiply that by the derivative of that, um, exponents. So that&#x27;s gonna be times negative 1/1 0.3 plus the second times, the derivative of the first. Hey, Now they do have something in common so I can pull out. In addition to the 175.9, I can pull out E to the negative t divided by 1.3 and what I have left his negative t over 1.3 plus one. So I&#x27;m gonna box this in green. I don&#x27;t want to lose this. This is the equation of our derivatives. Now to know where our function is increasing and decreasing, we need to find where this derivative equation equals zero. So that will tell us places where I could be switching from pop from increasing the decreasing or from decreasing to increase it. So let&#x27;s set this equal to zero. Well, this piece here e to anything each any exponents will never equal zero. So if I want this function equals zero, the only piece that could possibly equals zero is this factor right here. Negative t divided by 1.3 plus one. I&#x27;m gonna set that equal to zero. I have negative t over 1.3 equals negative one or T equals 1.3. So that is a point at which I could be switching from increasing the decreasing, or vice versa. So if I want to look at my intervals, I&#x27;m going to start it. Zero. That&#x27;s when I eat my meal. I need toe Look where t is 1.3 and then I don&#x27;t have anything else. But I do need to look at what&#x27;s happening in that interval from 1.3 and beyond out toward infinity. So two different intervals and I&#x27;m going to just pick a random point in each one of those and plug it into are derivative equation. So I&#x27;m gonna take one as a representative point of that first interval, and I&#x27;m gonna take two as a representative point of that second interval and let&#x27;s see what the value of the derivative is. Well, the derivative function evaluated it. One gives me a value of 18.809 That is a positive slope. A positive slope means my function is increasing by Plug in to I get a value of negative 20.34 A negative derivative means a negative slope. I am decreasing, so I am increasing on the interval from zero toe 1.3, and I am decreasing on the interval from 1.3 out to infinity. What does this mean? Well, it means that after I eat a meal until about 1.3 hours after the meal is done, the thermic effect of food is increasing after 1.3 hours. Once the meal is over, the thermic effect of food will start to decrease and We&#x27;ll just keep dropping off until eventually it will just peter out. So these are my intervals on which this function is increasing and decreasing.

April Townson · Answer

In order to answer this question, we have to first understand what a molecular clock is. So let&#x27;s just review the definition real quick. A molecular clock is defined as the average rate. A gene or an amino acid or basically a section of a genetic code mutates over generational time. For instance, we might have these two genes or gene segments. It could even be like individual bases along each path that mutates, say, five times each generation. And these mutations could be silence of just substitution. Zor they could be non synonymous. Substitution. So, yeah, there&#x27;s no real way of knowing exactly just yet. This is just a general example. In comparison, though, we might have these other genes or gene components that mutate 15 times each generation. And so there&#x27;s. That&#x27;s why we&#x27;re only looking at certain proteins or certain genetic code, not the GM as a whole, because different sections might mutate a different rates, depending on different factors. And I know you might now be thinking OK, well, now that we have this down, what are those factors? Well, as we can see, sometimes there are internal factors or inherent factors that just means certain sections of a Gino mutate more certain proteins or more tended to certain mutations or changes, perhaps based on certain biochemical interactions or the type of DNA, polymerase cetera. But there are also a lot of external factors, and by external factors. I&#x27;m talking about things beyond the biochemical, genome and proteins themselves. And this question in particular, mentions two important things. It mentions population size and generation time. So now that we have two examples of factors that might affect molecular clocks and why we might not be able to, you know, use this data in order to make certain assumptions about, uh, how often genetic changes happen over time and how we can use that to make file a genetic trees, we first have to address these things that can cause differences in the rates and why they might not be comparable in certain circumstances. And so, first, let&#x27;s address the most a parent factor, which is generation time and note how on the first flight, I mentioned that this is the average rate a gene or me too acid or protein mutates over generations. This is because genetic mutations can be passed down through a population not just as a function of time like year to year, but as a function of how often those genes will get passed down, which is a measure of the generation time, or how often a new generation arises. And this changes depending on the organism. So some species like humans. We live an average of 70 to 80 years, and because of our longer development time, usually about every 20 to 30 years, we might have a new generation of. And so every 20 to 30 years. That means that this is the time line of when these mutations might take hold in a population when we can actually see changes in the molecular clock. Basically, in comparison, some species of Drosophila can have 10 to 20 generations per year. And so dress awful. Uh, species obviously live on a much shorter timeline than humans do, and so they have to reproduce ah lot more often in order to maintain their population sides. And so because of this, if we were to compare, say, let&#x27;s say we wanted to compare genes that were shared incoming between humans and just awful oh, flies. This might be important developmental genes or something that&#x27;s been in our lineages for a very long time and can be traced back to a common ancestor. If we were to do that, then we would have to note that the amount of time that this particular original ancestral green might have mutated along our lineage would be much less often then, along the just awful a lineage, because every year there would be 10 or 20 times that this gene or this protein might have mutated, whereas for the humans every 20 or 30 years it would mutate. And so that&#x27;s why we have to consider these differences and generation time. If we wanted to compare the molecular clocks of these two genes and trace it back to AnAnd Cess, Tral gene or a most recent common ancestor and so that takes care of generation time. But how much population size? Uh, excuse me. Not population time. Population size effect. Uh, these genes are these military clocks. Excuse me. So let&#x27;s take an example where we have a large population and a dill. It eerie ISS gene mutation springs up in some members of the opposition in one generation. And this is this event Asians, to this population. And so, over the course of many generations, let&#x27;s say 10. It is completely wiped out. It&#x27;s removed from the population. Maybe it springs up again in, like, one or two, just because mutations are goingto happen anyway. But they will again be bread out of the population because it&#x27;s large enough that these organisms won&#x27;t find mates usually and are. They&#x27;re much less likely to be able to reproduce and spread that mutation. And so you&#x27;re less likely to see fixation of certain genes. And as a result, you&#x27;re more likely to see a lot of mutations happening in this particular section of the Gina, where this military issue Haitian occur. So let&#x27;s compare what would happen in a small population. We would. We have a much smaller population size and but the same number of organisms that become affected with this deal. It eeriest vacation over the same amount of generations because there are much fewer organisms to make with. It&#x27;s much more likely that these organisms here are going to spread this rotation, and you would expect to see this gene proliferate among larger and larger segments of the population, and maybe over time it would become fixated. And in that case, if every or most of the organisms in this population have this bad copy of this gene, yes, it is likely to mutate, but you&#x27;re not going to see as many variations in it at all. And there are also from just outside, like a pure numbers perspective. You&#x27;re not going to have as many chances for it to mutate because there were fewer organisms in the first place. Like, let&#x27;s say, let&#x27;s return to our human and fly example in a case where we&#x27;re looking at the same gene or a homologous gene between the two. If a human population on Lee has 10 people would say it&#x27;s on a remote island off somewhere, far from the rest of like people and on the same island you have, I don&#x27;t know, maybe 50 or something just awful. A species get very hypothetical. Um, in this case, you would have many more copies of the just awful lodging than the human gene. In order to that, would a be able to be mutated and be be present at all for data collection. And so this is how population size can effect molecular clocks and why we also need to take a look at

Luuk Verhoeven · Answer

so in this related rates question. They&#x27;re trying to throw you off by talking about elks and weasels. But that is completely relevant, as the first part of profession actually points out, because there is only one relation that holds for all these mammals off different sizes. And that is that the are ways represents the metabolic rate. I think, yes, vegetable that grates our equals 100 and 40 points, two times the body mass to the power off 0.75 And that&#x27;s all we need to know, because then part ay asks us to find the rt ti in terms of the N v t for a weasel. But that doesn&#x27;t better. So basically, they are. Beauty equals what&#x27;s well, we different shades the equation and find that we are U T equals 100 40.2 more supplies by 0.75 and two negative 0.25 times the m dp. So this is your classic related rates differential. You have emptied some power. The derivative is spiral chain rule that power times and the power minus one multiplied by the entity. And this is your answer to a nothing else needs to be done. Um, so it&#x27;s a bit miss meeting and asked you to find the rt t in terms of the M d t. And they&#x27;re still in Ah, loose M in here. But that is really not something that can be solved. Uh, there&#x27;s no way to Seoul this end are to eliminate this mm from the equation. So, um, we can simplify this little bit by mostly at Constance. So 100 and 40 um, most flight by 0.75 will net us 100 and 5.15. Um, times one over mm to the 0 to 5 GM beauty. So that&#x27;s part a Barbie. They again trick the throws off by talking about elk. But it doesn&#x27;t matter, because the relation between metabolic great mass is always the same. On the only important things is that they tell us the massively elk, which is 250 kilos. Um s well, Essie Reed changing the math. So this is Elka skirt gaining waits, uh, other eight off two kilograms for a day. So its metabolic rates the r Petey equals 100 and 5.15 times. One over 250 to 0 to five times two. And if you throw this into your health later, supporting this into your calculator you find that this is about 53 something today. Um, so the metabolic right of this big elk is changing at a rate of 53 something&#x27;s per day. Um, I think the book issued four digits. That, of course, doesn&#x27;t matter. Um, technically, I believe that you should if your answer in one significant digit s so that would be about six b, uh, five times tend to the first whatever, units. Because the smallest significance we get misty two kilograms a day rate of change. So you&#x27;re fine, as you shouldn&#x27;t have more significant digits than that one. Um, but that this usually not a problem. In a math course, you just give, um, a sufficiently precise answer. But again, it&#x27;s a related rates question. Find a relation differential. Substitute sould

Shumayal N · Answer

Okay, so this is a composite function of the form You were the tea whenever we have looking cause it functionally oclock chain rule. So in this case, uh, you TV is given as 64. You teaching because I&#x27;m not a 64. So you replace that where I&#x27;m not is and are B m t is 0.4 t. So you climb of tea, We&#x27;ll also being 60 40 18 and we put him on TV. We&#x27;ll be 0 20004 now, according to the chain will on time of tea, it was given us you climb. Do you have to multiplied with the prime with tea? So our V a t here is 0.0 14 and the right to arrest it is so now. So are you crying off? 0.0 40 is going to be cool. 64 e And here, in place of tea, we&#x27;re gonna put V T, which is your 0.0 40 is your point is you multiply would be primal t which we found a 0.4 If we multiply used to together we get 0.256 The point. Use your four T Now when t is equal to 65 which is what is given in the question. We just substitute that into you Equation for in prime of tea that we just found is your 0.256 e your points You lose you for to 60. Fire gives us 0.332 And this means that when t is equal to 65 the instantaneous girl threat is going to do 650.332 grams per day.

Suman Saurav Thakur · Answer

Well, the number 69. We have been given the temperature function as that did minus to a point fire cause. But I was six de a minus three man. The role at any protein lived in equal to 24. But do you that? I&#x27;m pretending It&#x27;s indeed a small today of the time in our okay. No, We need to return this in sign function, so we will use co function identity, identity. We just ate that well, because cost eater equal to Stein 90 degree minus he here. Utah represents this whole argument. OK, No longer you&#x27;re left with Could be minus. Will point fight sign 92 degree, not 90 degree. You should write it. Bye bye to because all things are in What? Okay, we should right here. Also by two. I went to minus data. That is. You totally be by six. T minus 30. No, just We will open the bracket. 38 minus opened. Fire fine by two minus. It will be by where 60 and u minus. Bye bye. There&#x27;s opening there in a Beckett. Okay, No opening the whole bracket. Do you want to fire? You sign by way. Toe minus by over 60. Blessed by right to it&#x27;s bye bye to win by little Mix it by I am 30 minus to appoint fi sign by minus by over six de If you did by Wessex Common we get sign You could take by Wessex Common You could be having six minus t It should be dollars Answer. Internal sign Thank you so much.

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