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Population Ecology: Exponential vs. Logistic Growth Models

Population Ecology: Exponential vs. Logistic Growth Models

Author: Jensen Morgan

Differentiate between exponential and logistic population growth models.

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Source: Earth PD, Graphs created by Jensen Morgan

Video Transcription

Hi. I'm Jensen Morgan. We're going to talk about some great concepts in environmental science. Today's topic is population ecology. So let's get started.

We're going to talk about population ecology and different types of population growth. Population is the group of a given species in a specific time and area. Population ecology is the study of those populations, their characteristics, population growth, and what influences that growth. Important characteristics are as follows-- abundance, or the number of organisms in a population; density, or the number of individuals in the population in a given area; patterns of dispersion, or the geographical spread of species; age structure, or the relative number of different ages of a species in a population; sex ratio, or the relative number of males versus females in a species; and variability, or the differences between organisms in a species.

Population growth is the rate of growth of a species over a period of time. Population growth is usually understood through modeling or the simple equation n equals b minus d. n is population change for whatever interval of time is being measured. b is the number of births. It is also sometimes referred to as fecundity. d is the number of deaths within the population. Therefore, births minus deaths equals the population change for that time interval. Positive growth rate occurs when there are more births than deaths. Negative growth occurs when there are more deaths than births, and zero change occurs when the two are equal.

For example, let's calculate the fictional population growth of rabbits in Cottonwood. The initial population was 50. The first year, there were 20 births and five deaths. 20 minus 5 equals 15. So the population change was plus 15. You can see that the total population increased to 65 in 2001. This process was continued until 2004. The end for 2002 was 25. And 2003, it was zero. And in 2004, it was 25 again.

Within the study population growth, there are two main types-- exponential and logistic. We're going to talk about exponential first. Exponential growth assumes unlimited resources in an idealized situation without limiting factors. Because of this assumption, population can grow in an exponential manner based on birth and death rates. However, in the real world, exponential growth cannot be sustained for long in any population. An exponential growth curve when time is the x-axis and population is the y-axis is a lot like a J shape if extended over enough intervals of time. The slope of an exponential population graph at any given interval is determined by the rate of change of births and deaths.

Let's look at two examples of exponential graphs. This first one is a shallower growth curve, because the population has a lower birth rate. However, if that birth rate increases, the curve of the graph will get steeper. Let's look at the second graph. In this graph, it is all the same data except that the birth rate is higher. See-- the curve of the graph has gotten steeper. Even though infinite exponential growth is unrealistic, it gives scientists the ability to understand maximum potential population growth in ideal conditions of a species.

On the other, more realistic side of things is a logistic population growth graph which takes into account limited available resources. Limiting resources might be both biotic and abiotic factors, such as food availability or the amount of precipitation. Due to limiting factors, all populations in a certain area have what's called a carrying capacity, also referred to as k. This is the maximum sustainable population that an area can support. If a population exceeds this benchmark, it will inevitably decrease and fall below this line, because the ecosystem cannot support anything above that line.

Let's look at a graphical example. This here is the carrying capacity, or k. Logistics graphs tend to create an S curve as the population's growth rate increases and then decreases as it nears k. In ecosystems, species populations are generally below the carrying capacity for that species in that location. Another important tool for population ecologists are life tables. Life tables like this one here summarise age-specific birth and death rates for a species population.

This table here shows the number of fictional insects of a particular species at various ages. At one month, it has dropped down to 722 individuals. Its birth rate at three months is 430 offspring. Life tables like these are used for population management and conservation. It allows humans to identify which parts of species populations at which times are needing protection and which can be harvested.

Now let's have a recap. We talked about population ecology and the two types of population growth graphs-- exponential and logistic. Well, that's all for this tutorial. I look forward to next time. Bye.