Students explore predator and prey relationships in ecosystems. example from the Elaborate section of lesson (i.e. Canadian Lynx and Snowshoe Hare). 2. snowshoe hare and lynx The hare cycle is mainly driven by excess predation by the lynx, but other Lessons to Be Learned About Predator-Prey Balance. the predator-prey population cycle of the snowshoe hare and the Canada lynx. The Going Further section is more extensive than for other lesson plans on.
But what's going to happen is their population is increasing. Well, it's gonna be more likely that they're gonna, they prey is gonna get caught.
There's gonna be more of their hunters around, more of their predators around. So that population is going to start decreasing all the way to a point where if the population of the prey gets low enough, the predators are gonna have, they're gonna start having trouble finding food again, and so that their population might start to decrease, and as their population decreases, what's gonna happen to the prey? Well, then, there's gonna be less predators around, so they might be able to, their population might start to increase.
And so I think you see what's happening.
The predator and prey, they can kind of form this cyclic interaction with each other. And what I've just drawn, this is often known as the predator-prey cycle. And I just reasoned through that you can imagine a world where you can have the cycle between predator and prey populations.
But you can also run computer simulations that will show this, and even observational data out in the field also shows this. One of the often cited examples is interactions between, between the snowshoe hare, which would be the prey in this situation, and the Canadian lynx, which would be the predator, the predator in this situation. And you see a very similar cycle to what I just drew, kind of just reasoning through it, and this, right here, is actual data.
You see the passage of time here, and this is a long passage of time. We're starting in the early 's going all the way to the early-mid 's. What about an underpopulation? Students conduct a Rally Robbin discussion of these questions.
A Rally Robin is a cooperative learning strategy. In pairs, students alternate generating responses. Teacher poses a question to which there are multiple possible responses. In pairs, students take turns stating responses or solutions orally. This activity uses a model of the Virtual Ecosystem with three species: This limited model allows students to explore the effect of predation on the prey population.
But there is a food supply: And what's bad for hares is good for lynx.
Exploring Predator and Prey Relationships
That is, the energy to support growth of the predator population is proportional to deaths of prey, so. The Lotka-Volterra model consists of a system of linked differential equations that cannot be separated from each other and that cannot be solved in closed form. Nevertheless, there are a few things we can learn from their symbolic form. Show that there is a pair of nonzero equilibrium populations. That is, if andthen neither population ever changes.
Express and in terms of a, b, c, and p. This is a general result in calculus -- not particular to this setting. Give a justification for this result. Use the preceding step to write a single differential equation for y as a function of x, with the time variable t eliminated from the problem.
Seventh grade Lesson Exploring Predator and Prey Relationships
The solutions of this differential equation are called trajectories of the system. Separate the variables and integrate to find an equation that defines the trajectories. Different values of the constant of integration give different trajectories. What do you learn about trajectories from the solution equation?