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The following questions are linked + A native species of earthworm (species has maximum of 0.5,and carrying capacity of 50 worms per square meter of soil. An invasi...

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The following questions are linked + A native species of earthworm (species has maximum of 0.5,and carrying capacity of 50 worms per square meter of soil. An invasive introduced earthworm species (species 2) has an r of 0.6 and carrying capacity of 100 (per square meter): The niches of these two earthworms overlap to some degree such that a - 0.8 and p-0.6.What would the outcome of competition be after long period of competition between these two species? The native would win, and the invasive w

The following questions are linked + A native species of earthworm (species has maximum of 0.5,and carrying capacity of 50 worms per square meter of soil. An invasive introduced earthworm species (species 2) has an r of 0.6 and carrying capacity of 100 (per square meter): The niches of these two earthworms overlap to some degree such that a - 0.8 and p-0.6. What would the outcome of competition be after long period of competition between these two species? The native would win, and the invasive would be excluded: The invasive would win and the native would be excluded The two species would coexist: The outcome would depend on the initial starting N'$ of each The outcome cannot be predicted with the information given. In the absence of the invasive what would the long-term equilibrium population size be for the native species? [0O 166 (E) 183



Answers

Biologists have wondered how introduced species that would probably have limited genetic variation (due to the founder effect) survive and adapt so successfully that they become invasive. Part of the answer may be that invasive species are the result of multiple introductions instead of a single one. Explain how multiple introductions from a species' native area to an introduced area could increase that species' invasion success.

Okay, so the continual reintroduction of new species make them able to breed with the species that survived the last introduction. So each time more and more species survived. Then eventually the last group of reintroduced species will just be breeding with this, their own species that were left over from the last introduction. So this makes the introduced species more likely to become invasive because they have an increased rate of success due to being continually introduced the same area.

Hey, everybody, my name's Colin and let's go ahead and jump right into this problem where we look at predator and prey over a variety of experiments and we're looking for whether or not we meet the conditions for performing inference about their aggression model so real quick. I just want to go through with those five conditions are and then we'll test for them individually. They are. I've got him written up here. We've got linearity, independence, equal variants, normality and randomness of the data. And in order to meet the conditions for performing in France, we have to have all five of these conditions met. If any one of them is not met him, we cannot perform Inference. We are given here a residual plot in a hist a gram, the residuals to help us in our journey to figure out whether or not we can in fact perform inference. So let's jump in right into it with linearity. If we have these scatter plots for the original data, we would be looking for some sort of pattern. Maybe you like this, you know where you've got a linear pattern or maybe something. Also, you could have something like this. We're looking for a linear pattern, but since we don't have that, we have to in fact, rely on that residual plot. And what we're looking for is whether or not the residuals are roughly centered on that residual equal zero line each x value, meaning that you know there's the same above and below or ah, there roughly at the same spot above and below each individual x value. Since we only have 4 10 2040 and 60 with residuals, we can look at those when we actually do see that they're fairly symmetrical. Fairly, ah, centered on each individual line, we don't see many. We don't really see a curved pattern amongst the residuals in that plot, so we can go ahead and say that we do in fact meet the condition for performing inference that is linearity. Now if we look at independence of the data, how we're looking at how the data were produced, so it's whether it's random sampling, random assignment, seeing whether each individual observation is independent and you know, we do see from the problem that the researchers selects the purchase random, and we do also know that the results from the pen with tan did not impact the results with 20 and vice versa. And so we can go ahead and say that this day, this independent as well. Now we look for equal variants. What we're really asking is whether or not for a singular y value it has thesafeside standard deviation across all values of X. And so to determine this, we're actually going to look at that residual plot and we're gonna look at above and below that residual equal zero line, and we're gonna and the amount of scatter should be roughly the same from the smallest to largest X value meaning there should be roughly the same amount of residuals above and below that residual equal zero line, uh, for each value of X. And when we see when we look at this, we do in fact, see that this is the case most residual. Most of those X values have you no one above and one below or two above and two below others. You know, there is that one with X equal 10. But since the other three very much meat, this case and that one with X equal 10 is very close. We can actually go ahead and say that because this is roughly, uh, the same from smallest to largest weekend. We can go ahead and say that we do meet that condition as well Now for normality. This we're having that hissed a gram plot of the residuals comes in handy. So if you'll recall, you'll remember that the normal probability plot looks something like this. Your your standard bell curve. And we're looking at that hissed a gram there to see whether or not there is any SK eunice or any other major departures from normality eso we'd be looking for, You know, maybe whether or not the data was skewed to one side, it would look maybe something like this. Um, And when we look at that history, ma'am, you know, you do see that's that slight dip in the middle. But overall, we've got ah fewer results on the outside that we've got a higher amount of residuals, cram their more or less into the inside. And so what we see is actually ah, a history and plot that does look very similar to that normal probability plot here that I've got drawn. And so we can go ahead and say that we do actually meet that normality of the residuals as well. And lastly, all we have to do is check and see if the data were produced by random sampling or a randomized experiment on it does again saying the problem that he selected are the researchers selected deficient random hey, selected the predators at random. And so we do actually have the best. We have the word random right there in the problem, which is the best indicator that this data is in fact random. And since we meet all five of these conditions for performing inference, we can say that for this problem, yes, we can, in fact, perform inference.

Well, the first part. We can't inform the original question here into these equation, which is easier to manipulate. If we're the section, we can see that for this problem we're taking. Okay, Ben and Capital M greater than zero. And for the first part, we shall. This inequality Which means that capital m my nose he is greater than zero. You're positive on B. Mine is lower. Case him. It's positive. That means that here we have each term in the product is positive. Which means that the derivative is also positive. And when the derivative is positive, we have that the population have to be increasing. Four be less than Lord Kishan. Ah, we have here some positive constants. Things lower case M is listen Capital M he's also positive and this is negative. So the whole brother is negative under the relative has to be negative which means that the population is decreasing now for Barbie. If we take b, you wantto either capital M or lower case him. We get that the derivative Sarah zero, which means that the solution is constant. That gives us two and it could even solutions. And now we can start emulating the direction who so for the direction field we have await for B equal toe one hundred, two hundred No. On in steps off one hundred, we we have a light here and obtain, for example here my nose seven point two. So we draw a segment with that is lope on. We obtained these direction field. Now, given the direction field, we can draw the solutions. So here we get solutions like long this And here. If the population is greater than capital m this ocean opportunites a synthetically to Capitol Hill And if the population is less than lower, kiss him. Then it started the king. So either mentally reaches syrup. We will see that later. We have the constant soldiers here. No, in this case is a little hard to draw the solutions given that the slopes are very high. So I drew an example for K equals to zero point zero one. And here the solutions are like more easy to drop. And that's part B for party. We can see that we're working with inseparable difference. Your equation. So now we have to take the integral in both sides with respect to time. Here we go, we separate the differential question, and we're going to integrate here. So to avoid that intro, we have to solve the partial fractions problem which starts here. And we get the solution. So you compose a video and check each step, and then we get this. We get the original question, we do this a problem. Then we integrate each site. We use the change of arable touring, huh? Change of variable. And then we we used the separable, the partial fractions, the composition. We're with you. And we need to have a decent girls. So we we take this and this and we know that they're revelation. Is is this? And here it's easy, because it's just constant. And we get that glossy here does. He gets more fired when we multiplied equation by something. But we just keep up Flossie here. It's a common practice. Um, we do a few manipulations and were after these equation. Yeah, And in this equation, it's easier to Appalachia. T equals zero, and we get peace here, here. So we obtain a about you foresee, and we can't do a substitution here. No. So we got the constant and now we do a substitution here on. We obtained this equation from this equation. We just do a few manipulations, standard manipulations. And we get the general solution here. On with that, we have the answer to party. Now we want to solve part the so it does. If the zero this is the only working lower kiss him then the population becomes seemed so. That means these population because to Syria. But that means that the denominator here it has to be equal to zero. So we have a like that. We make it equal to Syria. We possum We moved by on we have here is a product bond. Each of these terms are positive here, here and here. They're positive, but this is negative. We have a minus sign, which means that the whole thing it's positive this whole thing so we can apply the natural hovering in both sides. And we obtained this equation the second one. So then we are right here. We got t equal to this with him. Whether this hero k greater than zero and my nose Same greater than zero. And we want to show that this is positive. Then after a lot of love. So we want to see that these here inside the library is greater than one. We can check it here. Yeah, each of these are equivalent. And we are right here. Toby's inequality, which is true. Which means this is true. Which means that this is the inner organs hero on, which means that the whole thing is rather concerned. And we have a positive time for which P ofthe team is equal to zero. Which means that there's a moment, a positive moment which makes the population go extinct. And we used that zero has to be listening. That was it. The problem ist

Hey there. So today we're kind of talking about food webs and using that and word problems combined with math problems sounds a little daunting. Looks a little daunting, but it's really not that bad. So, um, let's start out with explaining what a food web is basically out of food web. You have the bottom part being the part that feeds the top eventually, right? So energy has to come from somewhere All animals have to eat. Figuring out what they eat is important. Um, and basically, whatever the bottom eats is essential distill feeding the top even though, like coyotes don't eat grass, they are eating grass through the deer and the rabbit. This is important in a lot of different situations, especially like if you have. If you are feeding predators, you should keep in mind about what they're pray eight and make sure that the prey that you feed them also eat that because those air actually essential parts of their nutrients as well. Okay, um, so food webs as a recap from the bottom, uh, bottom being, what feeds the thing that feeds the predator Or, you know, there could be some steps in between there, and the top is the predators. So on these predators, we have coyotes and hawks. Um, now looks like more directly deal with what we're doing. So you kind of just have to dissect your word problem. So it talks about your food web, and it tells you how big your food web. I mean, how big the meadow habitat is, which is the bottom part of your food web, which is 25.6 square kilometers. Um, I wrote that down here, As you can see, 25.6, and then I multiplied it by 1500 kilograms. And so together that equals 38,400. So I kind of put that down for meadow grasses. Um, next up were given some more information in the problem. Talking about basically what we're trying to figure out the end solution is, is if they approve this, let's think of it like an apartment complex and like a field or something like that. It'll reduce the producers biomass by 50% so that be like the bottom part, which is the meadow grasses. So if you think about it like an apartment complex, it's pretty easy Thio figure out why it would take up that like it's destroying grasses. There's people around yada yada. Next up, it says that it will remove all rabbits and deer. And that's important to note because, well, we'll get to that, actually. So these air basically the constraints that are put on that. Okay, so from that, we can figure out a few things. So through this math, we know that it's uniformly distributed, right? So we can figure out that the coyote and the Hawk are getting the same amount of stuff because the deer, the rabbit and the vole are getting the same resource is so, um, they are getting in this situation. It would be 10% of this, right? And so we're gonna put hope. Sorry. Working through these word problems is difficult, Which I'm sure is why you're reading this or watching this. Yes. So this is gonna be 1200 kg. This is also going to be 1200 kg. This is going to be 1200 kg, and then we kind of look at this and we say, Okay, so the vole is only going to the hawk. So if we multiply that by 10%. We get 120 13, and then over here, we should get 100 and 20 kg, and you're tempted just to put 120. 120. That's not the case, because this is being split. So it should be half of 122 64 kg, 64 kg. And this leads us, right? We add this up and we figure out these are 192 kg and 192 um, biomass of a hawk 192. That's what I wrote down there. This is, uh and you should kind of write this out. I would always suggest writing out these graphs and stuff that they're pretty simple because of AIDS in your visual understanding. Eso That's why I kind of wrote those. Like where the arrows go. Um, but now we know that we're reducing our metal grasses by 50%. Cross that out. We're gonna put 190. This is sad. Right? Um but also, the rabbit is removed and the deer is removed, so basically the vole is getting 10% which now equals 1920 kg. Um, from that we can figure out it's hard to do these word problems for everybody. Not just young. So, um 100. Okay, 1000 920 kilograms. So because of that, you kind of use your brain, right? And you go. Okay, So the coyote was Onley eating the deer and the rabbit. It's just preferential food because it's uniformly distributed. That means that the vole, it was only going to the Hawk. And now the bowl is out competing, Um, everything to the hawk. And now 192 kg are available to the hot because there is not, like any reason that the coyote can't eat the bowl. This means that the coyote will change its preference to feed on the Volt. See, there's no longer these resource is available to the coyote. And now the hawk is getting more food from than anybody. So we know that the coyote is going to have to change its reference. Um, that means that the answer is C. Yeah, maybe we figured it out. This is like a really complicated question. But even if you didn't do any of the math, right, you're a smart biology student and you can figure this out pretty pretty quickly, So if you go through Option A, it talks about the biomass of coyotes you know will be really small, and the biomass of Hawks will be really smaller than that. But that doesn't make any sense, right? Because we look at our food web even without any of the numbers. We know that thought that it's uniformly distributed. That's why I wrote that in the corner right there. So we know that that can't be true, because why would a hawk get less when it's the one? With Maurer of the resource available right and option B, the biomass of coyotes will be drastically reduced. Um, this is true. I mean, they did, but they're not just going to starve their opportunistic and so they're gonna figure things out so we can figure out that it's gonna be see just by that, right? Because that's the only one that could be true. But and then D let's look a D. It's 50% of your bowls and a lot less hawks. That doesn't make any sense. Just looking at the food web. The coyote is the one with left Resource is and now the bull has more resource is which I don't know if that's, like, plainly apparent. You kind of have to look at the food Web and do the math toe like see why that's the case, because it's kind of confusing just to look at. But you can figure it out. That's not true. Um, they're not getting 50% less. Resource is because all their competitors are gone. And so why would also, why would it be 90% fewer hawks? That doesn't even make any sense. So it has to be seat anyway. There you go. And I hope that helped you and your understanding of food webs and coyotes and how all this works. Have a great day. Bye bye.


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