Prey population growth contrained by predators

What if a growing population gets eaten by another population? In a previous post I showed why we might expect a population to grow exponentially when not resource limited. We then extended this to the case where a population reaches some carrying capacity (using a simple and non-mechanistic logistic function). But population growth can also be curtailed through interactions with another species population, such as a predator. In my area of study, we deal with a lot of herbivorous pests of agricultural systems.

Modelling density dependent population growth (logistic growth)

Let’s derive some more population growth functions! The logistic population growth function In a previous post we derived a function for population growth based on the vital rates of reproduction and mortality. We assumed that the growth rate was constant with respect to the number of individuals in the population or (\frac{dt}{dN} = rN). This led to the unrealistic prediction that populations will grow indefinitely. Of course, populations will eventually run into resource problems (e.