• Intrinsic Growth Rate: The maximum potential for growth under ideal conditions and with unlimited resources available.

The lemming and the arctic fox have a direct, predator-prey relationship. This means that as the lemming population increases, so does the arctic fox population. Similarly, if the lemming population decreases, so does the arctic fox population.
Because of this, the lemming and the arctic fox have very close intrinsic growth rates. Knowing that the lemming's intrinsic growth rate is 2, we can estimate that the arctic fox's intrinsic growth rate is similar to that. (No data could be found on the exact growth rate).

• Growth Rate Model Curve

The above graph demonstrates the growth rates of both the lemming and the arctic fox. As you can see, there is about a 2 year time period in which the populations react to each other. For example, we can see that in 1993 there was a spike in arctic fox dens with pups. Two years after this spike, there was a dramatic decrease to near zero lemming offspring.

• Logistic Growth Rate

Assuming an intrinsic growth rate of 2 for both the lemming and the arctic fox, and using the formula:  we can calculate the logistic growth rate (assuming an Arctic Fox population of 200,000 total and 60000 reproducing individuals, and a Lemming population of 225000 total and 67500 reproducing individuals)
Arctic Fox Logistic Growth Rate: Nt=60000e2t
Lemming Logistic Growth Rate: Nt=67500e2t

• Population Overshoots and Die-offs

Population Overshoot: When there are more newborns than the environment's carrying capacity can maintain.
Population Die-offs: A rapid decline in population due to a greater number of deaths than births.

The above graph demonstrates the relationship between population die-offs and overshoots in the lemming and arctic fox populations. There is a clear overshoot in the lemming population in 2000, followed by an extreme resulting die-off in 2001. At the same time as the lemming population die-off in 2001, there is a die-off in the arctic fox population. This demonstrates the dependence that each population has on the other.

• Survivorship Curve

In the survivorship curve, the arctic fox is categorized as type 1 and the lemming is categorized as type 3. The arctic fox is type 1 because it is a K-selected species: a somewhat large animal, with successful survival rates in early life, and death in large numbers at old age. The lemming is type 3 because it is a r-selected species: a rather small animal, with unsuccessful survival rates in early life (easy prey at a young age), and delivered in large litters.