deathrate = 1/(average lifespan).
Not in this problem. This problem implies massive dieoffs from such regularly occuring events as predation and/or disease. These other things aren't given to simplify the problem. What was given is the fact of stable population.
There's a predator-prey problem underlying this example. It shows swings about some average population number. The birthrate, populaiton average lifespan and the population average deathrate remains constant. At any particular time though, the deathrate can execede 1/avg lifespan by orders of magnitude.
The predator could even be the DNR and their licensed hunters. In that case, the negative swings are minimized.