That you can imagine a world where you can This is often known as the predator-prey cycle. They can kind of form this cyclic interaction with each other. Happen to the prey? Well, then, there's gonnaīe less predators around, so they might be able to, their population might start to increase. Where if the population of the prey gets low enough, the predators are gonna have, they're gonna start having trouble finding food again,Īnd so that their population might start to decrease,Īnd as their population decreases, what's gonna Going to start decreasing all the way to a point Of their hunters around, more of their predators around. Likely that they're gonna, they prey is gonna get caught. But what's going to happen is their population is increasing. Imagine their population starting to increase. It's easier for the predators to find a meal, you can Going to happen here? Well, at this point, withĪ low density of predators, it's gonna be much easierįor them for find a meal, and it's gonna be much easierįor the prey to get caught. Let's say we're right there in time, and let's say for whatever reason, our predator population is relatively low. And so let's just, in our starting point, let's say that our prey is starting out at a relatively high point. So the time, the horizontal axis is time. Here that you're probably familiar with by now where we show how a population can change over time. So let's just think about how these populations could interact. I'm doing the prey in I guessĪ somewhat bloody color, I guess 'cause, well, So you have the predatorĪnd prey interactions. And so you have the predator population that likes to eat the prey. And there's many cases of this, but the most cited general example is the case when one population wants to eat another population. Though we will not go through the derivations here, you can try them out on your own by replacing these terms with 0 then solving for N prey and N pred, respectively.Wanna do in this video is think about how different populations that share the same ecosystem can interact with each other and actually provide a feedback loop on each other. In other words, we want to solve for dN pred/dt = 0 and dN prey/dt = 0. For the prey population, we want to find values of predator and prey population sizes at which the prey population remains stable. We will examine these questions by seeking equilibrium solutions to the coupled predator and prey equations we introduced above. Under what conditions will predator and prey populations both persist indefinitely? What will be their population dynamics while they coexist? In other words, will one or both populations stabilize, or will they continue to change over time?.Under what conditions will the predator population die off, leaving the prey population to expand unhindered?.Under what conditions (i.e., parameter values) will the predator population drive the prey to extinction?.
We can ask several questions about the interaction between predators and their prey using these equations: Specifically, these equations lead to oscillations between the populations of predators and their prey. In other words, the equation for prey includes a term for N pred and the equation for predators includes the term N prey and changes in one population will always impact the other population.
It’s important to note that the prey and predator equations above are coupled equations.
R prey = prey per capita rate of increase P = attack rate efficiency (a slope: the change in prey consumed per predator per time as a function of the number of prey) higher search or handling time leads to a lower p In words, the predator population grows according to the attack rate, conversion efficiency, and prey population, minus losses to starvation.ĭN prey/dt = rate of change in prey population (change in number over change in time)ĭN pred/dt = rate of change in predator population (change in number over change in time)Ĭ = rate at which prey are converted into offspring (a slope: predators produced per predator per time as a function of prey consumed per unit time)