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Logistic growth takes place when a population's per capita growth rate decreases as population size approaches a maximum imposed by limited resources, the carrying capacity(K ). It's represented by the equation:
Logistic growth is used to measure changes in a population, much in the same way as exponential functions. The model has a characteristic “s” shape, but can best be understood by a comparison to the more familiar exponential growth model.
What are the underlying principles of how populations change over time? Two basic principles are involved, the idea of exponential growth and its ultimate control.
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.
Logistic growth occurs when a population grows exponentially at first, but then slows. As the population’s growth slows, its size begins to level off. Logistic growth usually occurs as resources become scarce and competition increases. Populations that have logistic growth produce an S-shaped curve.
The growth of the population eventually slows nearly to zero as the population reaches the carrying capacity ( K) for the environment. The result is an S-shaped curve of population growth known as the logistic curve. It is determined by the equation.
Populations growing according to logistic growth are observed in laboratory populations (Paramecium and Daphnia) as well as in nature (fur seals).
Jul 18, 2022 · Logistic Growth. If a population is growing in a constrained environment with carrying capacity \(K\), and absent constraint would grow exponentially with growth rate \(r\), then the population behavior can be described by the logistic growth model: \(P_{n}=P_{n-1}+r\left(1-\frac{P_{n-1}}{K}\right) P_{n-1}\)
Oct 31, 2023 · When resources are limited, populations exhibit logistic growth. In logistic growth, population expansion decreases as resources become scarce, leveling off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.
Logistic growth describes a model for population growth that takes into account carrying capacity, and is therefore a more realistic model for population growth. According to the logistic growth model, a population first grows exponentially because there are few individuals and plentiful resources.
