Exponential Population Growth

Unlike the expansion of the universe, no population of living organisms can go on and on, forever increasing. Living creatures require too many resources and encounter too many confounding factors to expand indefinitely at a constant rate. However, for short periods of time, some organisms can experience very fast and constant growth rates. When this occurs, it is known as exponential growth!

• In the following article, we will:
• discuss how and why some populations may experience exponential growth,
• provide some examples,
• detail the significance of population growth to ecology, and
• provide the formulas and models used to illustrate exponential growth.

What is Population Growth?

In order to understand population growth, we must first understand what a population is and how it relates to ecology.

Population ecology is a field of science (a subfield of synecology, which deals with species groups relative to their ecosystems) interested in how and why certain factors (e.g., birth rates, death rates, immigration, and emigration) influence populations over periods of time.

Birth rates and immigration rates are collectively known as a population's recruitment rates. A population's size refers to the total number of individuals of a certain species in a certain area and a population's density is its size relative to its habitat.

Finally, population growth involves population dynamics, which deal with the variability in a given population's size over time.

What is Exponential Population Growth?

The Relevance of Exponential Population Growth to Population Ecology

Understanding exponential growth is important because it helps us to predict future population sizes, estimate resource consumption, and evaluate the impact of population growth on the environment. Furthermore, exponential population growth can have significant consequences for population dynamics, such as competition for resources, changes in habitat availability, and the potential for population crashes.

Overall, understanding the relevance of exponential population growth to population ecology is crucial to develop a comprehensive understanding of how ecological systems work and how human activities can affect them.

Exponential Population Growth Example

In living organisms, exponential population growth is most frequently observed in bacteria. However, there is another example that you are likely to be much more familiar with.

Thanks to modern medical and technological advances, much of the human population has been temporarily and unnaturally able to mitigate the negative impact that some population-depleting density-dependent factors (e.g., food availability and predation) would have on population growth.

Despite this, these factors still have a major impact on many human populations, particularly in parts of the developing world, where overcrowding, poverty, starvation, and increased pollution are largely fueled by this unsustainable increase in population on a global scale.

Eventually and inevitably, the human population will level off and produce a logistic growth curve, due to the increasing intensity of these limiting factors as the population increases. The problem is, how much damage will be done before we reach that point?

Bacteria more commonly experience exponential population growth than any other kind of organism, particularly when placed into an ideal medium. Bacteria have very fast generation times, allowing them to breed and evolve at a very high rate (this is how some bacteria quickly evolve antibiotic resistance).

Nonliving organisms, such as viruses, can also experience exponential population growth. The coronavirus, COVID-19, for example, experienced exponential growth following the beginning of the pandemic in late 2019/early 2020. This exponential growth of the virus population occurred alongside the exponential increase in the number of people infected.

Mitigation techniques, such as social distancing and the wearing of masks, can substantially reduce the exponential population growth of the virus and the number of people infected with it (Fig. 2).

Finally, let's talk about the formula for the population growth rate.

This formula can be displayed as dN (difference in population size) divided by dT (difference in time), resulting in rN (per capita population growth rate).

\[rN = \frac{dN}{dt}\]

Sometimes, in exponential population growth, "r" is referred to as "r_max", but they both signify the same thing - the growth rate.

The equation for rN is different for exponential and logistic population growth.

• In exponential population growth, no matter how large population growth is, per capita growth rate remains constant. Therefore, the equation is simply rN.

• In logistic population growth, the population size decreases as it grows larger and approaches its carrying capacity. Therefore, in logistic population growth, we must subtract the carrying capacity (K) from the population size (N), and then divide by the carrying capacity (K) and multiply by the population size (N). So, the formula in this case is \(\frac{dN}{dt} = r_{max}(\frac{K-N}{K})N\).

In addition, when plotting a graph for exponential population growth, a J-shaped curve is produced, while logistic population growth produces an S-shaped curve (Fig. 3).

• Exponential population growth produces a J-shaped curve because the population's growth rate remains the same as the population grows in size.

• Logistic population growth results in an S-shaped curve because the population's growth rate tapers off gradually as the population approaches its carrying capacity.

Over a long enough period of time, virtually all populations will have an S-shaped curve, even populations which may have experienced exponential growth for a short period of time previously. Thus, no populations ever experienced permanent exponential growth, as it simply is not possible on a planet with finite resources.