Final answer:
The population of a species surviving a mass extinction event would likely experience rapid initial growth due to less competition and newly available niches, then enter a phase of logistic growth, and finally reach a new equilibrium that might differ from pre-extinction levels.
Step-by-step explanation:
After a mass extinction event, the population of a surviving species would likely exhibit a rapid initial growth due to the sudden availability of ecological niches and reduced competition. This is followed by logistic growth as described by the S-shaped curve, where the population growth rate slows as it approaches the carrying capacity of the environment. Once the resources begin to become scarce, the population's growth will level off and may even decline slightly due to resource limitations. Over time, survivors may also evolve and adapt to exploit new ecological niches created by the extinction event, potentially leading to an overall gradual increase in diversity.
It's important to note that these changes are not linear and can be subject to various factors such as predation, changes in climate, and resource scarcity. The population dynamics will stabilize eventually, but the new equilibrium would likely differ from pre-extinction levels due to the changed environmental conditions and the possibility of the species evolving to adapt to their new surroundings.