Final answer:
Population models such as exponential and logistic growth help ecologists predict population dynamics. Exponential growth leads to rapid population increase under unlimited resource conditions, while logistic growth accounts for environmental limits. Differential calculus is used to determine instantaneous rates of change in populations.
Step-by-step explanation:
Population ecologists make use of deterministic models, like exponential growth and logistic growth, to describe and predict the dynamics of population change over time. Exponential growth is characterized by a rate of change that is proportional to the current population, leading to a rapid increase in population size, depicted as a 'J-shaped' curve. This could happen when unlimited resources are available. Logistic growth, on the other hand, includes limits to growth as the population nears the carrying capacity of the environment, producing an 'S-shaped' curve.
The birth rate (B) is expressed as a per capita figure, calculated as the birth rate 'b' times the current number of individuals 'N'. The same format is used to calculate the death rate (D). Utilizing differential calculus, ecologists calculate an instantaneous growth rate, summarizing the difference between birth and death rates by the intrinsic rate of increase 'r'. This foundational concept in population dynamics can have profound implications, including potential risks for human populations if exponential growth continues long-term without adequate resources.