Concept 13 - Concept 52.4 The logistic growth model...

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Concept 52.4 The logistic growth model includes the concept of carrying capacity Typically, resources are limited. As population density increases, each individual has access to an increasingly smaller share  of available resources. Ultimately, there is a limit to the number of individuals that can occupy a habitat. Ecologists define  carrying capacity  (K) as the maximum stable population size that a  particular environment can support. Carrying capacity is not fixed but varies over space and time with the abundance of  limiting resources. Energy limitation often determines carrying capacity, although other factors, such as  shelters, refuges from predators, soil nutrients, water, and suitable nesting sites can be  limiting. If individuals cannot obtain sufficient resources to reproduce, the per capita birth rate b  will decline. If they cannot find and consume enough energy to maintain themselves, the per capita  death rate m may increase. A decrease in b or an increase in m results in a lower per capita rate of increase r. We can modify our mathematical model to incorporate changes in growth rate as the  population size nears the carrying capacity. In the  logistic population growth  model, the per capita rate of increase declines as  carrying capacity is reached. Mathematically, we start with the equation for exponential growth, adding an expression  that reduces the rate of increase as N increases. If the maximum sustainable population size (carrying capacity) is K, then K − N is the 
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Concept 13 - Concept 52.4 The logistic growth model...

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