Final answer:
The situation described would demonstrate an evolutionary burst where rabbits fill ecological niches left by humans, leading to genetic drift and potential changes in allele frequencies. A logistic model predicts new population equilibrium, with natural selection favoring adaptations to new environmental pressures.
Step-by-step explanation:
If humans were to suddenly die off and rabbits began to flourish and spread across the globe as a dominant species, this scenario would illustrate an instance of evolutionary burst and ecological niche fill due to the absence of human influence leading to genetic drift and change in species dynamics. Before the die-off, humans likely played a significant role in maintaining the ecological balance, possibly keeping rabbit populations in check either directly or indirectly. The sudden lack of human presence would leave a vacuum in various ecological niches that rabbits could then fill. Over time, with the removal of the human-induced checks on their population, rabbits would experience a population increase until reaching a new equilibrium as outlined in the logistic model of population growth.
Examples of what might occur in terms of genetic drift if rabbits were to become dominant include the increased survival and reproduction of rabbits in areas where their natural predators were suppressed by humans, leading to changes in allele frequencies in rabbit populations. Additionally, certain colored rabbits (such as white rabbits) might thrive or struggle depending on their visibility to predators in new environments into which they expand post-human extinction, thus affecting their genetic representation in the population.
It's important to note that such evolutionary processes would also be impacted by other factors, such as natural disasters, which can cause genetic drift by randomly removing individuals and alleles from the population. Diversifying or directional selection might also result, as new environmental conditions would favor certain traits over others, and populations potentially adapt to new types of predation or foraging challenges.