What are the assumptions underlying the predator-prey model di...

Question

What are the assumptions underlying the predator-prey model discussed in this section?

Accepted Answer

Hello there. Today we're to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In the classical predator prey model, which statement correctly describes the interaction between the two species? Awesome. So it appears for this particular problem we're asked to look at our multiple choice answers and we're asked to determine which of these statements in our multiple choice answers correctly describes the interaction between the two species for the classical predator prey model. So now that we know what we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is prey and predators compete for the same resources. B is predators consume prey at a rate proportional to the product of their populations. C is prey population remains constant regardless of predator presence, and D is the environment limits the prey population through carrying capacity. Awesome. So with that in mind, we need to first recall and note that the model, this classical predator prey model assumes that the predation, so the predator rate is proportional to X multiplied by Y. So let's write that down. X multiplied by Y. Fantastic. So, With that in mind, prey and predators do not compete for the same resources as we should recall. The prey population does not remain constant due to the fact that it is affected by predators. And there is no carrying capacity, as we should recall, so there's no carrying capacity is included in the basic model for this classical predator prey model. So with this information in mind, let us analyze our multiple choice answers individually to see which one is the correct final answer. Starting with multiple choice answer letter A, which once again states that prey and predators compete for the same resources. So this is incorrect because predators and prey do not compete for the same resources. Predators consume prey, so A is incorrect. OK, moving right along here. Multiple choice B states that predators consume prey at a rate proportional to the product of their populations. And this statement is correct, because in the classical Lata Volterra model, the interaction term is, and let's write this down, is Alpha, so alpha multiplied by P multiplied by N, where P is the predator population and N is the prey population. Awesome. So now that we know that the correct answer, without a doubt is multiple choice answer letter B, let's investigate why C and D are incorrect. So C states that the prey population remains constant regardless of predator presence, and this is incorrect because predator presence does indeed affect the prey population through consumption. So that is why it is incorrect. And finally, for D, which states that the environment limits the prey population through carrying capacity, this is incorrect. For the classical model, which does not include a carrying capacity term for prey, it is only present in modified models. And because of that fact, that is why multiple choice answer letter D is incorrect. So once again, without a doubt, our final answer is multiple choice answer letter B, which is predators consume prey at a rate proportional to the product of their populations, and that's it. That's our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

What are the assumptions underlying the predator-prey model discussed in this section?

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