Linear Population Growth - Online Tutor, Practice Problems & Exam Prep

The linear population growth model is a simplified framework for understanding population dynamics, characterized by a constant growth rate regardless of population size. This model, represented by the equation $n=rt+n₀$, is useful for short-term projections and initial growth analysis, despite its limitations in real-world applications. It serves as a foundational concept before exploring more complex models like exponential and logistic growth.

Linear Population Growth

This video, we're going to talk about the very first population growth model in our lesson, which is the linear population growth model. The linear population growth model is a very simplified model, especially in comparison to the other two population growth models that we'll talk about moving forward in our course, which are the exponential and logistic growth models. It's so simplified that it's often an oversimplification for most real-world scenarios. However, this linear population growth model is still very helpful as it can provide a basic framework for understanding population growth in the absence of complicating factors, making it a perfect starting place for beginners. The key to this linear population growth model is that unlike the other two population growth models, the population growth rate in this linear model is constant and always going to be the same regardless of the current population size, which makes it very simple and easy, but not realistic to most situations as you might expect that a larger population size would have more individuals that can contribute to the population growth.

Now, although the linear population growth is often an oversimplification, it's not totally useless as it can be helpful and used for analyzing the initial stages of population growth. It can be helpful for short-term projections of population growth and can be applicable in controlled experimental settings. Notice down below, we're showing you the equation for a line, which you should already be familiar with, which is y=mx+b. We're showing you this because it turns out that the linear population growth equation is exactly the same, except that it substitutes the variables with population growth model variables. And so nt=r(t)+n0, where r is the absolute population growth rate, which is just delta n over delta t, where 'absolute' just implies that it is constant and does not change, and that's going to be multiplied by t, which is the amount of elapsed time, plus the, n₀, which is the initial population size.

On a graph like this one that you can see over here, where we have the time on the x-axis and population size on the y-axis, for the linear population growth, it's no surprise that the data will form a straight line, where you started at some non-zero population size and the population growth rate will be constant, creating a straight line in the data. This here concludes our lesson on the linear population growth model. We'll be able to apply these concepts and problems, and then we'll shift over to the other growth models. So, I'll see you in our next video.

Linear Population Growth Example 1

So here we have a pretty straightforward example problem that says, a proliferating stem cell whose progeny does not reproduce would grow via the linear population growth model. Which of the following best explains why this is the case? And we've got these 4 potential answer options down below. Now option a says, the progeny continue to reproduce leading to exponential growth, but this completely contradicts what the problem initially told us, which is that the progeny does not reproduce. And, also, even if the progeny did continue to reproduce and it did lead to exponential growth, that would not be linear population growth.

And so for that reason, we can eliminate answer option a. Now option b says the progeny only reproduce during certain seasons causing cyclical growth patterns. But cyclical growth patterns are not going to be linear growth patterns, and so for that reason, we can eliminate answer option b. Now, option c says, the progeny exhibit high rates of reproduction, but the growth is offset by a greater rate of cell death. Now, once again, this is contradicting what the problem told us initially, which is that the progeny does not reproduce.

So to say that the progeny exhibit high rates of reproduction is not going to be correct. So we can eliminate option c, and this leaves answer option d as the only option and it is the correct answer, which says that the progeny do not contribute to further population growth resulting in constant addition of cells over time, regardless of the current population size. And, ultimately, this is what makes it grow via the linear population growth model. So we can indicate that option d is the correct answer. That concludes this problem, and I'll see you all in our next video.

In a small, isolated island, a population that initially consists of 50 birds is observed to grow by a constant number of 5 birds per month. What is the population size after 2 years?

• A. 110 birds.
• B. 170 birds.
• C. 250 birds.
• D. 60 birds.