Ecologists do not simply measure the absolute growth of a population. Doing this would yield a silly, incoherent number. Think about it. What would you make of the statement "The population of penguins has a growth of 2000," or "The population of dodo birds had a growth of -480 before they became extinct"?
These statements do not make sense to us because we have no idea how to interpret a growth of 2000 or -480. First of all, these statements lack any concept of time. Secondly, they do not give us any clue about the total sizes of the penguin or dodo populations. However, if we include time and size, then we can calculate a number that makes a lot more sense. This number is called a growth rate and is denoted by the symbol r.
To calculate growth rate, we need to know two other characteristic rates of a population:
These two rates are fairly simple to figure if, of course, you have a time period and know the population size. Let’s work out an example. Imagine a population of 10,000 emperor penguins in Antarctica. If you cannot imagine this, take a break and go watch Happy Feet or March of the Penguins; then, get back to us. Penguins produce offspring once per year so a good period to use in our calculation of birth and death rates is 1 year. If, over the course of the year, 3000 chicks are born and survive, then the birth rate is 3,000 divided by 10,000, or 0.3 births per individual penguin, per year.
If, over the same year, 1,000 penguins die, then the death rate is 1,000 divided by 10,000, or 0.1 deaths per individual, per year. To calculate the growth rate, you simply subtract the death rate from the birth rate. In this case, the growth rate (r) of the emperor penguin population in Antarctica is 0.3 – 0.1 = 0.2 new individuals per existing individual, per year. Since the growth rate is positive, we also know that the population growth is positive. In other words, the penguin population is growing in the familiar sense of the word. Hooray! Penguins for everyone!
In all this, 0.2 is still a pretty uninteresting number. It would be much more informative to know how much the population grew in terms of number of penguins. To determine this, simply multiply the growth rate (r) by the size of the population. In our example, that would be 0.2 × 10,000 = 2,000. Then, add the product to the population size: 2,000 + 10,000 = 12,000. In one year, the emperor penguin population grew by 2000 individuals, at a rate of 0.2 individuals per individual. This statement is a LOT more informative and useful than what we started with, which was "The population of penguins has a growth of 2000."
With all of this mathematical wizardry under your belt, let’s look more closely at the growth of the emperor penguin population. If we assume that the population will continue to grow at a rate of 0.2 during the next year, we can calculate the size of the population for year 2. That would be 0.2 × 12,000 = 2,400, leading to 2,400 + 12,000 = 14,400 penguins! Using this same technique, and assuming a constant rate of growth, we could easily determine the size of the penguin population in 10, 30, or even 100 years.
For your convenience, we did the calculations for you. In 10 years, the penguin population would reach 61,917. In 30 years, it would top 2 million! And in 100 years, Earth would be overrun with more than 800 billion—yup, with a "b"—penguins. This type of growth, where a population grows in proportion to its size—that is, the bigger it gets, the more rapidly it grows—is called exponential growth.
As you have probably already surmised, the penguin population has not yet reached 800 billion. Nor will it. Bummer, right? Even though exponential population growth is possible, if it occurs, it rarely lasts long in nature. There are many factors that limit population growth, including
Each of these limitations can cause a reduction in birth rate, an increase in death rate, or both. Consider the penguin example again. The birth rate was 0.3, and the death rate was 0.1, leading to a growth rate of 0.2. As the population grows and becomes quite large, it is likely that the amount of resources, or fish, available to an individual penguin will decrease. This will result in malnourishment and less reproductive success. Those are bad things.
Eventually, it will lead to death in the weakest or unluckiest penguins. Unhappy feet. Fairly quickly, the birth rate will equal the death rate, and the population will stop growing. It is even possible for the death rate to go above the birth rate, resulting in a negative growth rate and a reduction in penguin population size from year to year.
Limitations to population growth that are influenced by the size of a population in a given area, called population density, are called density-dependent factors (DDF).
The penguin example above is a good one for understanding DDFs. When the population is small, there are more than enough fish for each penguin, so resource supply does not affect birth or death rates. As the population grows, however, and the amount of fish available to each penguin diminishes, resource supply can begin to affect birth and death rates. The less fish per penguin, or, the more penguins per fish, the greater the impact of resource supply on the birth and death rates (hence, the growth rate) and of the penguin population.
Our penguin example is specific. Emperor penguins can live in few places on Earth. The size of penguin populations is not only limited by resource supply, but also by the amount of space they have, the number of sea lions, or predators, that feed on them, and other factors.
When taken together, all of the density-dependent factors that influence a population’s growth contribute to an environment’s carrying capacity for the population, or the maximum size a population can reach in that environment.
When a population grows exponentially at first, and then levels off to a stable number near the carrying capacity, it is called logistic growth. This density-dependent growth is likely much more common in nature than long-term exponential growth. It is also the reason why emperor penguins, or elk, elephants, mice, or even grass, have not yet overrun the Earth.
We should point out (so we will) that population growth is also limited by factors that couldn’t care less about population density. These aptly named density-independent factors (DIF) affect population birth and death rates randomly, and include such things as
Therefore, the take-home message is that the earth is not swarming with emperor penguins because their population growth is kept in check by both density-dependent and density-independent factors. This is a good thing, because as cute as penguins can appear on the big screen, we have it on good word that penguins in large numbers are awfully loud and stinky.
In terms of individual growth rate, the fastest growing animal in the world is a blue whale calf. The fastest growing plant is bamboo.