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When does the growth rate of a population following the logistic model equal zero? The logistic model is given as dN/dt = rN(1-N/K)
A)When N/K is exactly one
B)When N nears the carrying capacity of the habitat
C)When N/K equals zero
D)When death rate is greater than birth rate

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Last updated date: 13th Jun 2024
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Answer
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Hint: In logistical expansion, as population size reaches a maximum imposed by finite environmental resources, known as carrying capacity, the per capita growth rate of a population becomes smaller and smaller (K). A J-shaped curve is formed by exponential growth, while an S-shaped curve is created by logistic growth.

Complete answer:
When resources are scarce, logistical construction of a population scale occurs. In order to quantify logistic growth, the formula we use adds carrying capacity to the growth rate as a moderating power. The logistic model is given as dN/dt = rN(1-N/K). When the N/K value is one, then,
dN/dt = rN(1-N/K)
dN/dt = rN(1-1)
dN/dt = rN(0)
dN/dt = 0 (zero)
So since the value of N/K is equal to
zero, the population growth rate would be equal to zero.

A kind of resource that is crucial to a species' existence will act as a constraint. Water, light, nutrients, and habitat for growth are all key tools for plants. Significant services for animals include food, water, shelter, and nesting space. Limited quantities of such resources result from rivalry between members of the same population or intra-specific competition (intra- = within; -specific = species).

Hence, the correct answer is option (A)

Note: Every kind of resource needed for a species to live can act as a limit. For plants, water, sunlight, nutrients, and space to grow are some of the key resources. Significant animal resources provide food, water, shelter and space for nesting. Limited quantities of these resources arise from rivalry between members of the same group or intraspecific competition (intra- = inside; -specific = species).