Problem ER6

The Grünwald Park hosts a relict population of woolly bears (Ursus laniger). A team of German ecologists has been studying the demography of this rare species and finally has proposed the following discrete-time model:

$$N_{t+1} = L\left(N_t\right) N_t$$

where $N$ is the bear number and $L(N)$ is the finite rate of increase which depends on N via the following relationship

$$L(N) =\frac{6N}{480 + 0.8 N + 0.01N^2}.$$

You are required to

• qualitatively draw the Moran diagram for the population of U. laniger Grünwald Park ;
• calculate the bear densities at equilibrium and assess their stability;
• assess the long-term fate of the population, given that the last count evaluated the bear population size to be 80 individuals.