With regard to its rate of growth, a population that is...

Key Concepts

Intrinsic Rate of Increase

The intrinsic rate of increase is the maximum potential growth rate of a population under ideal conditions, without density-dependent limitations. In logistic growth, this rate is modified by the population’s proximity to carrying capacity.

Density-Dependent Regulation

Density-dependent regulation refers to factors that affect the growth rate of a population based on its current density. In logistic growth, as a population becomes denser, the growth rate decreases because of increased competition for resources, leading to a peak in growth at an intermediate density.

Carrying Capacity

Carrying capacity is the maximum number of individuals in a population that an environment can sustain indefinitely. It represents the point at which growth rates slow down and eventually stabilize due to competition for limited resources.

Logistic Growth

Logistic growth is a model of population growth that begins exponentially but levels off as the population reaches the carrying capacity of the environment. This results in a sigmoidal or S-shaped curve where growth is initially unrestricted but slows down due to factors such as resource limitations.

Transcript

00:01 For this question we see with regard to its rate of growth, a population that is growing logistically will blank.

00:07 Okay, so we have grows fastest when density is lowest, has a high intrinsic rate of increase, grows fastest at an intermediate population density, or grows fastest at as it approaches carrying capacity.

00:20 Okay.

00:21 So once again, we are asked about the logistic model.

00:25 And remember, what we did here was we increase until we, reach a constant rate of increase and then we start decreasing and we reach an asymptote here or a maximum carrying capacity right because it never goes above this where if it does then it immediately falls back down below carrying capacity okay so knowing that let's look at our choices one more time grows fastest when density is the lowest okay that is not necessarily true because remember when is the rate of growth the greatest for a logistic curve so remember this is logistic when is the rate of growth greatest well we can see that the rate of growth is greatest right about there and when is that that is at one half the carrying capacity remember this is the carrying capacity here and so one half of k is when we have the greatest um rate of growth okay so that's one half carrying capacity all right now that means that it is not growing fastest when density is lowest because density is lowest right down here so a is not true then we have b has a high intrinsic rate of increase well as you can see the rate of increase is actually changing right because first yeah the rate of increase is growing it's increasing but then the rate of increase is decreasing all right and that's kind of hard to picture but we know that the population is still increasing itself but just the speed at which it increases is going to eventually decrease and level off then we see no increase in population okay and it becomes stagnant so we know that the answer is not b and then we have grows fastest at an intermediate population density and that's 100 % true right because at halfway so intermediate we see that at half the carrying capacity at halfway through the curve we see that we have the fastest rate of growth so that is why we would choose c and just to go over d grows fastest that approaches carrying capacity will know in fact d like we said it stagnates so the growth rate approaches zero here.

02:36 So we have, let's just say growth rate equals zero, right at the carrying capacity here...

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