# Lotka-Volterra model ~ intro

**mind of a Markov chain » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

So many know about the Lotka-Volterra model (*i.e.* the predator-prey model) in ecology. This model portrays two species, the predator (y) and the prey (x), interacting each other in limited space.

The prey grows at a linear rate () and gets eaten by the predator at the rate of (). The predator gains a certain amount vitality by eating the prey at a rate (), while dying off at another rate ().

Given this base, we can ask questions like, what parameterizations can we expect to find a coexistence between the fox and the hare (for example)?

Let’s choose some values for the model: . These values assume a weaker growth of the rabbits relative to the strength of the death of foxes. Below, I simulated these values in R.

And we get coexistence, they live happily forever after. With this simple model, we can play around by generalizing (logistic growth of prey, etc.). I will put up some posts doing so.

The way to do this in R is as follows (just use the deSolve package, which will supersede the odesolve package):

library(deSolve) LotVmod <- function (Time, State, Pars) { with(as.list(c(State, Pars)), { dx = x*(alpha - beta*y) dy = -y*(gamma - delta*x) return(list(c(dx, dy))) }) } Pars <- c(alpha = 2, beta = .5, gamma = .2, delta = .6) State <- c(x = 10, y = 10) Time <- seq(0, 100, by = 1) out <- as.data.frame(ode(func = LotVmod, y = State, parms = Pars, times = Time)) matplot(out[,-1], type = "l", xlab = "time", ylab = "population") legend("topright", c("Cute bunnies", "Rabid foxes"), lty = c(1,2), col = c(1,2), box.lwd = 0)

Filed under: deSolve, Food Web, ODEs, R

**leave a comment**for the author, please follow the link and comment on their blog:

**mind of a Markov chain » R**.

R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.