14.0.3 14.4: A population’s growth is limited by its environment.

Life gets harder for individuals when it’s crowded. Whether you are an insect, a plant, a small mammal, or a human, difficulties arise in conjunction with increasing competition for limited resources. In particular, as population size increases, organisms experience:

Limitations such as these on a population’s growth are a consequence of population density—the number of individuals in a given area—and are called density-dependent factors. They cause more than discomfort: with increased density, a population’s growth is reduced as limited resources slow it down. This ceiling on growth is the carrying capacity, K, of the environment. As a population approaches the carrying capacity, death rate increases, emigration rate increases (as individuals seek more hospitable places to live), and a reduction in birth rate usually occurs, as low food supplies result in poor nutrition, which, in turn, reduces fertility (FIGURE 14-5).

Figure 14.5: Fighting over scarce resources.

Here’s how the carrying capacity of an environment influences a population’s growth. We start with our exponential growth equation:

Population growth = r × N

Then we multiply by a term that can slow down exponential growth:

Population growth = (r × N) × [(KN)/K]

When N, the population size, is small relative to the carrying capacity, K, it means there are plenty of resources to go around. In this situation, the term [(KN) / K] is close to 1. To illustrate this, let’s choose a large number for K, say, 100,000, and a small number for N, say, 1,000. This would mean [(KN) / K] equals [(100,000 − 1,000) / 100,000], or 99,000)/100,000, which equals 0.99.

So in this situation, we are multiplying normal exponential growth by 0.99. This is almost the same as multiplying it by 1, which doesn’t change it. As a consequence, the population is growing exponentially (or very close to exponentially).

On the other hand, if the population size, N, is close to the value of K, it means that the environment is nearly full to capacity, and the term [(KN) / K] is close to 0. Let’s plug in some numbers again. We can use 100,000 again for K. But let’s use 99,000 for N. In this case, [(KN) / K] equals [(100,000 − 99,000) / 100,000], or 1,000/100,000, which equals 0.01. In this situation, we multiply normal exponential growth by 0.01, which reduces it to almost zero. In other words, population growth slows more and more as the population size nears the environment’s carrying capacity.

When a population grows exponentially at first, but then slows as the population size approaches the carrying capacity, the growth is called logistic growth and makes an S-shaped curve (FIGURE 14-6).

Figure 14.6: Lack of resources limits growth. Logistic growth is population growth that has stabilized because of limited resources.

Density-independent factors can also knock a population down, acting like “bad luck” limits to population growth. These forces strike populations without regard for population size, by increasing the death rate or decreasing the number and rate of offspring produced. They are mostly weather- or geology-based, including calamities such as floods, earthquakes, and fires. They also include habitat destruction by other species, such as humans. The population hit by the disaster may be at the environment’s carrying capacity, or it may be in the initial stages of exponential growth, before its growth is slowed by the carrying capacity. In either case, the density-independent force simply knocks down the size. The population then resumes logistic growth.

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In an environment where these “bad luck” events repeatedly occur, a population might never have time to reach the carrying capacity. Instead, as the series of jagged curves in FIGURE 14-7 show, the population might perpetually be in the exponential growth portion of the logistic growth curve, with periodic massive mortality events.

Figure 14.7: Events can limit population growth.

The growth of populations doesn’t always appear as a smooth S-shaped logistic growth curve. For some populations, particularly humans, the carrying capacity of an environment is not set in stone. Consider that, in 1883, an acre of farmland in the United States produced an average of 11.5 bushels of corn. By 1933, this was up to 19.5 bushels per acre. By 1992, it had increased to 95 bushels per acre. And by 2013, it had increased to 159 bushels per acre! How did this happen? The development of agricultural technologies—including the use of vigorous hybrid varieties of corn, rich fertilizers, crop rotation, and effective pest management—has allowed farmers to produce more and more food from the same amount of land (FIGURE 14-8). Of course, over this same time, the carrying capacity has most likely been decreased for many other species trying to live in the same environment as humans and their crops.

Figure 14.8: Efficient crop production. Advances in agriculture make it possible to feed the world’s growing population.

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TAKE-HOME MESSAGE 14.4

A population’s growth can be constrained by density-dependent factors: as density increases, a population reaches the carrying capacity of its environment, and limited resources put a ceiling on growth. It can also be reduced by density-independent factors such as natural or human-caused environmental calamities.

Population “A” is subject to heavy density-dependent factors, including reduced food supplies, but not a lot of density-independent factors, such as earthquakes. On the other hand, population “B” is repeatedly affected by density-independent factors but not many density-dependent factors. Which of these two populations is more likely to be experiencing exponential growth? Why?