The Population Growth Equation

My AP Biology ThoughtsUnit 8 Episode #26

Welcome to My AP Biology Thoughts podcast, my name is CJ and I am your host for episode 26 called Unit 8 Ecology, The Population Growth Equation. Today we will be discussing The Population Growth Equation.

Segment 1: Introduction to Human Impact in Ecology

• Let's start us off with a little bit of background knowledge. The population growth equation was founded in the late 18th century by a couple of biologists. The big one was Thomas Malthus. He saw that populations grew in a geometric pattern. He came up with two models. It is important that we distinguish these two models. One is for logistical growth and the other is for exponential growth. Just like in math, exponential growth is just a line on a graph that looks like a “J”. In fact, in biology, they are often called Exponential growth curves “J” curves. Now logistical growth is similar, up until a crucial point of the population. The curve seems to hit an impasse, or a number on the ‘Y'' axis that will never see a point. Instead of the line continuing up like in an exponential graph, it levels out and shoots to the right, as if hitting a limit. Now this limit is not just a number on an axis. This number represents the carrying capacity of an ecosystem. This carrying capacity is the maximum amount of species in a singular environment. This is most likely due to limiting factors, whether it be biotic or abiotic. Now limiting factors are things in an ecosystem that prevent a species from growing in population without a limit. Now biotic limiting factors are living things, such as lack of food or abundance of predation. These all can limit the total population of a species. Abiotic limiting factors are nonliving things, such as a storm or lack of water or pollution. All of which could kill off a population or make them compete for vital resources.

Segment 2: Example of Human Impact in Ecology

• A huge example of exponential growth rates, are any invasive species. Invasive species in the dictionary are defined as having exponential growth in their population. No predators and unlimited resources. Where they go their population is destined to boom and show no signs of slowing. Invasive species we know and hold near and dear to our hearts are stink bugs, the Asian Giant Hornet, Asian Carps, Japanese Beetles, and of course, the Spotted Lantern Flies. All of these came over and had no predators, so naturally, they breed and reproduce unlimitedly. This is a huge problem because their large numbers knock out any other species with the same niche.

Segment 3: Digging Deeper Human Impact in Ecology

• Enough about the qualitative information about Population Growth Curves, and to the quantitative. Exponential growth curves have an equation of dN/dT = rN. Now, dN/dT stands for the rate at which the population grows. R stands for the maximum growth rate per capita. N stands for the population size. There are other ways to find dN/dT however. The easiest is to subtract the total number of births in a year, with the total number of deaths. For the logistical curves, the equation