Okay, Someone 12 is a long one. That's was jump into it. We'll start with part A. And he were given the equation for the number of leaves, like a minimum number of leaves that a tree would have is being equivalent to, uh, to pry times d squared, even the diameter of the tree and the surface area of the leaf. So that's the length and width of the league's. This is the first service area of be a more complicated equation for finding this. Did it involve the full area of the leaf? But this you need They just skip over some of that and just give us the punch line here. So that's why I use and the diameter of tree. Okay, so then we want to find the equation. Ah, for the energy exchange in and with the transpiration rate relationship using D, l and W. And so first we need to add some data. And so it would be great to know, uh, the energy being absorbed, right? So I feel it e v the energy per leaf free energy for relief. But we also need to know Ah, company carbon atoms are fixed. Um bye by the amount of energy, right? This isn't real. Carbon atoms sticks. And we're told we're told sort of in the very beginning that we get 200 funded water molecules really spread carbon. So I'm just gonna hours that at 300 because, um, take it, do this twice and get a range right. Could cut good at the 200 of them at the 400 give yourself a range. So we have 300 water molecules, her carbon for our ah, transpiration rate. Right. So that's her transporation. Okay. And then the relationship, we can get them. We won't want the number of Lee years, and that was given to us as the two ply d squared times. L w okay. And multiply that by the amount of energy per leaf. Right? So it's gonna give us our total sort of intake of energy. Okay. And then that should be roughly equal to our 300. You want a molecule? A superior carbon multiplied multiplied by ex Multiply that by our Carmen. The amount of carbon molecules that are fixed right now give us sort of how much transpiration has occurred in relationship to our free energy. Okay, then we move along here, go to part B and part B. This little story about diversity, Okay. And so what's happening here is, um, on the globe, we have our equator and some further away Mont iTunes and latitudes, right. So closer to the north or South Pole. And this is saying that the equator has a greater diversity. Then in some, these systems, uh, that air cool there. Okay. And in one of the explanations for this is the energy equivalent models. It's the energy equivalent model up. Okay, What does the energy of Cleveland's models say? Well, that says that as free energy increases so as our free energy increases at the population also increases, okay, But then, as as our populations increase will, then our mutations also increase. Okay? And they're saying that evidence evidence for this model are correlated at the family level. The adversity of Eve apple transpiration. So evacuate transporation if we have ah, so the ground here and we have atmospheric water, right? So there's some sort of water in the atmosphere. Some of that water is just gonna come from evaporating off the grounds. That's our evaporation and some of it is going to come from transporation, okay, from the plants and those two things together make up our atmospheric water. And so this process of both transpiration plus evaporation is tthe eee vap o transpiration. Right? So it's not really the most clever name he'd ever heard you the least. It makes it easy to remember. OK, so that's our You've got both transporation. It's the idea of being that if you're at the equator, right for the equator, your evaporation should stay roughly the same, uh, off of the ground. And so the variance you see across the globe but at the same latitude variance in region is going to be then due to transporation by the plants. And so the idea then is that we can use this Eve Apple transpiration too, to find a correlation at family level diversity. Okay. And so So. Part B wants us to explain, uh, this relationship between free energy exchange and latitude, right? And so so the idea here than being that this process of this free energy right being increased at the equator because there is a lot more, uh, like sun energy happening at the equator right. So you get this increase happening at the equator that you don't see as much of intimate ease further away latitudes. Okay? And then So because we have this energy exchange at the increasing the energy of the equator, we get the increase in populations. And you also see Seon rainforest areas, uh, larger sort of populations, right? And then, by following the model, this increase in population leads to the increase in mutation. Okay? And that increase in mutation, then this sort of the basis of of creating the diversity that we see at the equator, right, So it's sort of cyclical here. Um, So the increase in energy gives us this increasing mutation specifically at the equator, okay. And then really move on to part See, which is giving us some information on specific areas. Right. So they are at the same sort of latitude in all area, right? So the getting the same amount of of energy here, uh, but we're given is we have an Asian ecosystem, and at the family level, it had 67 families. Right? Because this is specifically about family level variation. Okay. And then we have in North American Ecosystem and this one had 46 families in it for diversity. Okay, And then we're also given their you've apple tree inspiration, right? And in the Grapple Transporation for North America was 850 plus or minus 200. And for e Asian one, uh, we have 730 plus or minus 1 60 The first thing to note is that they're actually you take the merging of air into the county overlap. Okay, Um, but but their margin of heirs are roughly similar. And so we see here, then, is that this Asian population had larger family diversity and a smaller ive apple transpiration. Okay. And the North American one had a smaller, smaller family diversity in a larger IV apple transpiration. So this told us that, you know, part be suggested, uh, that these things are correlated and it's possible that they are correlated negatively. Right? So this would suggest that a greater family diversity actually leads to a smaller You've apple transpiration quantity eso In a way, this really does not support the idea that ah, larger family diversity would increase your IV apple transporation