Explain why a decrease in population growth rate is expected as a nonhuman population approaches carrying capacity.

Verified step by step guidance

1. Understand the concept of carrying capacity: Carrying capacity, denoted as 'K', is the maximum population size of a species that an environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment.
2. Recognize the role of resources: As the population size increases and approaches the carrying capacity, the availability of resources (such as food and water) begins to decline due to higher consumption rates.
3. Consider the impact of resource limitation: With fewer resources available per individual, the growth rate of the population begins to slow down. This is because competition for limited resources increases, which can lead to higher mortality rates and lower birth rates.
4. Apply the logistic growth model: The logistic growth equation, which models population growth, shows this trend mathematically. It is represented as \( \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right) \), where \(N\) is the population size, \(r\) is the intrinsic rate of increase, and \(K\) is the carrying capacity. As \(N\) approaches \(K\), the term \(\left(1 - \frac{N}{K}\right)\) approaches zero, which in turn causes the growth rate \(\frac{dN}{dt}\) to approach zero.
5. Acknowledge density-dependent factors: Factors such as predation, disease, and territoriality become more significant as populations grow denser. These density-dependent factors further contribute to the slowing of population growth as it nears the carrying capacity.

Key Concepts

Carrying Capacity

Carrying capacity refers to the maximum number of individuals of a particular species that an environment can sustainably support. It is determined by the availability of resources such as food, water, and habitat space. As a population approaches this limit, the growth rate typically slows due to increased competition for these limited resources.

Population Growth Rate

Population growth rate is the rate at which the number of individuals in a population increases over a specific period. It is influenced by factors such as birth rates, death rates, immigration, and emigration. As a population nears its carrying capacity, the growth rate declines due to resource limitations and increased mortality, leading to a more stable population size.

Density-Dependent Factors

Density-dependent factors are environmental influences that affect a population's growth in relation to its density. These include competition for resources, predation, disease, and waste accumulation. As population density increases, these factors become more pronounced, contributing to a decrease in the growth rate as the population approaches carrying capacity.