Q.(a) What is the carrying capacity of a species in a habitat ?
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Start your 14-day free trial to unlock the full solution →Carrying capacity is the maximum population size a habitat can sustain indefinitely; the logistic growth curve models how populations grow rapidly at first, then slow as they approach this limit.
Carrying capacity: the habitat's ceiling
Every habitat—whether a forest, a pond, or a grassland—has finite resources: food, water, shelter, nesting sites, and so on. The carrying capacity (denoted K) is the maximum number of individuals of a species that the environment can support indefinitely without degrading. It represents a dynamic equilibrium where births roughly equal deaths, and the population stabilizes because resources are fully utilized but not exhausted.
Think of it this way: a small pond might support fifty frogs comfortably, but if a hundred frogs tried to live there, competition for insects and breeding sites would intensify, starvation or disease would increase, and the population would crash back down. Carrying capacity isn't a rigid number—it can fluctuate with seasons, rainfall, or changes in the ecosystem—but it sets a realistic upper boundary for population size.
The logistic growth curve: reality checks exponential dreams
When a few individuals of a species colonize a new habitat with abundant resources and no competitors, the population can grow exponentially. Each generation produces more offspring than the last, and the growth accelerates without limit—at least in theory. This exponential growth follows a J-shaped curve and is described by the equation
dN/dt = rN
where N is population size, t is time, and r is the intrinsic rate of natural increase. It's growth without brakes.
But nature always applies brakes. As the population grows, resources become scarce, competition intensifies, waste accumulates, predators may increase, and diseases spread more easily in crowded conditions. Growth slows. The logistic growth model captures this reality by incorporating carrying capacity into the equation:
dN/dt = rN × (K − N)/K
The term (K − N)/K is the key. When the population N is very small compared to K, this fraction is close to 1, and growth is nearly exponential. As N approaches K, the fraction shrinks toward zero, and growth slows to a crawl. When N = K, growth stops altogether. …
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