Course: BIS 105 Environmental Biology

Unit 4 Learning Module

Population Dynamics

Imagine a huge bowl of your favorite potato salad, ready for a picnic on a beautiful, hot, midsummer day. The cook was careful to prepare it under strictly sanitary conditions, using fresh eggs, clean organic vegetables, and new jars of mayonnaise and mustard. Familiar with food poisoning warnings, s/he was so thorough that only a single bacterium made it into that vast amount of food. While such a scenario is highly unrealistic without authentic canning, it will serve as an example as we begin our investigation of how populations change, or population dynamics. Because potato salad provides an ideal environment for bacterial growth, just as your mother may have warned, we can use this single bacterial cell in the potato salad to ask:

How Do Populations Grow Under Ideal Conditions?

Given food, warm temperatures, moisture, and oxygen, a single aerobic bacterial cell can grow and divide by binary fission to become two cells in about 20 minutes. The two new cells, still under those ideal conditions, can each repeat this performance, so that after 20 more minutes, four cells constitute the population. Given this modest doubling, how many bacteria do you predict will be happily feeding on potato salad after five hours at the picnic? After you’ve thought about this, compare your prediction with the “data” below.

Time (Hours and Minutes) | Population Size (Number of Bacteria)
0 | 1
20 min | 2
40 min | 4
1 hr | 8
1 hr 20 min | 16
1 hr 40 min | 32
2 hr | 64
2 hr 20 min | 128
2 hr 40 min | 256
3 hr | 512
3 hr 20 min | 1024
3 hr 40 min | 2048
4 hr | 4096
4 hr 20 min | 8192
4 hr 40 min | 16,384
5 hr | 32,768

Are you surprised? This phenomenal capacity for growth of living populations was first described by Thomas Robert Malthus in his 1798 Essay on the Principle of Population. Although Malthus focused on human populations, biologists have found that many populations are capable of this explosive reproduction, if provided with ideal conditions. This pattern of growth is exponential, or geometric growth: as the population grows larger, the rate of growth increases. If you have worked compound interest problems in math or played with numbers for estimating the interest in your savings account, you can compare the growth of a population under ideal conditions to the growth of a savings account under a constant rate of compound interest. The graph below, using potato salad bacterial “data,” shows the pattern of exponential growth: the population grows very slowly at first, but more and more rapidly as time passes.

Exponential or geometric growth is very slow at first, but accelerates as the population grows. Because rate of growth depends on population size, growth rate increases as population increases. Most populations have the ability to grow exponentially, but such growth usually occurs only under ideal conditions that are not found in nature. Note the “J” shape of the curve.

The maximum rate that a population can increase under ideal conditions is its biotic potential. Different species have different maximum rates of growth. A species' life history characteristics, such as age of maturity or number of reproductive periods during their lifetime, will determine whether it has a large or small biotic potential.

Of course, if bacterial populations always grew exponentially, they would long ago have covered the Earth many times over. While Thomas Malthus emphasized the importance of exponential growth on population, he also stated that ideal conditions do not often exist in nature. A basic limit for all life is energy. Growth, survival, and reproduction require energy. Because energy supplies are limited, organisms must “spend” them wisely. We will end this lesson with a much more realistic model of population growth and the implications of its limits, but first, let’s look more carefully at the characteristics of populations which allow them to grow.

Births and Deaths: Balancing Costs of Reproduction and Survival

The growth rate of a population is the change in population size per member of the population per unit of time. The symbol r denotes growth rate. Growth rate clearly depends on birth rate b, the number of births per individual within the population per unit of time, as well a death rate d, the number of deaths per individual per unit of time. The following equation calculates growth rate, according to our preliminary understanding:

r = b – d

growth rate = birth rate – death rate

If birth rate exceeds death rate, r is positive and the population grows. If death rate exceeds birth rate, r is negative and the population declines. And if birth rate and death rate are in equilibrium, growth rate is zero, and the population remains stable. In a stable population, each individual, on the average, produces one offspring which survives long enough to reproduce itself. Mere survival is not success in the game of life; natural selection requires that survivors reproduce. As Malthus realized, nearly all species have the potential to grow – to reproduce many more than just a single replacement offspring. However, species vary in the strategies they use to achieve reproductive success, making trade-offs between the energy and time “costs” of survival and those of reproduction. Age at first reproduction, frequency of reproduction, number of offspring, parental care, reproductive lifespan, and offspring death rate are some of the traits which build strategies for successful reproduction.

Analyzing extreme examples can help you understand the trade-offs species must make between survival and reproductive success. Let’s compare two groups of birds. Somewhat like precocious children who mature early, precocial birds run around to find their own food soon after hatching. Geese, ducks, and chickens use this strategy for raising their young. Often living and nesting on the ground, precocial species are subject to high predation rates, so few survive long enough to reproduce. Therefore, those who do reproduce lay many eggs at once, and these eggs are large. The young emerge well-developed, ready to feed and escape predators soon after hatching. Precocial species invest a great deal of energy in a large number of offspring but do not spend much energy on parental care, because even though some offspring are likely to die, others will survive long enough to reproduce.

Geese and ducks use a precocial strategy to ensure reproductive success. They invest a great deal of energy in a large number of large eggs, so that young are born well-developed and ready to fend for themselves almost immediately after hatching. Predation on goslings and ducklings is high, but this death rate is offset by a high birthrate. Overall, the population remains stable.

Contrast this precocial strategy with the opposite, altricial strategy used by hummingbirds. These birds hatch helpless and naked, completely unprepared for independent life. Parents invest little energy in just a few, small eggs; hummingbirds’ eggs are the smallest in the bird world, and average two per nest. However, survival of these offspring matters a great deal, because there are so few. So, parents build elaborate nests safely hidden in trees and invest a great deal of energy hunting for food around-the-clock until the young have developed enough to fledge and find food on their own.

Hummingbirds illustrate an altricial reproductive strategy. Very little energy is spent to produce two tiny eggs, but they are enclosed in a secluded nest, usually hidden in a tree. Survival of the offspring is critical because there are only two, so parents invest tremendous amounts of energy finding food for themselves and their young for nearly three weeks. This energy investment allows the offspring to develop to nearly adult size before they fledge into the world of predators and competition.

Precocial and altricial birds play by the rules of costs and benefits, each group using a different strategy. Cowbirds, however, make up their own rules, earning them the title of “parasites” in the bird world. How can a bird be a parasite? Cowbirds are altricial, but they parasitize by laying their eggs in other birds’ nests, thereby escaping the high costs of parental care. Cowbird eggs are usually slightly larger and hatch a little sooner than the host eggs affording cowbird parents a bit of extra energy. “Early bird” hatchlings do indeed “get the worm,” easily out-competing their smaller host siblings for parental food deliveries. Sometimes, they are strong enough to ungratefully oust their “sibs” from the nest. On the other hand, host parents occasionally recognize and eject the foreign egg before it hatches. Yellow warblers simply block off the offending egg (along with their own eggs) by building a new nest bottom. They then lay a new clutch of their own eggs (The eggs are not their primary energy investment). A five-“story” nest holds the record for yellow warbler (and cowbird?) determination!

A brown-headed cowbird egg in a red-winged blackbird's nest illustrates yet another strategy for reproductive success: invest all of your energy in a single egg, just large enough to out-compete your altricial host’s eggs, and let the host parents feed your offspring! The right photo shows a male individual of this parasitic species.

Many species fall in between the extremes of precocial and altricial strategies, but all must make trade-offs between the costs of reproduction and those of surviving predation, competition, and disease, in order to ensure that at least one offspring per adult survives long enough to reproduce. It’s worth reprising the survivorship curves introduced in the previous lesson to illustrate these trade-offs (see figure below). Which curve illustrates the precocial strategy used by ducks, chickens, and grouse? Which curve demonstrates the altricial strategy of hummingbirds? What shape do you think a cowbird’s survivorship curve might take?

Survivorship curves show the various strategies for achieving population growth by adjustments in birth rate and death rate. Recall that r = b – d. Hummingbirds have low birth rates (b), but through time and energy spent on parental care and feeding, ensure high survival rates for their altricial offspring (low d). Geese, however, invest energy in many large eggs (high b) to offset high death rates from predation (d) among their precocial offspring.

One more strategy, introduced in the last lesson, involves variation of age at maturity. All other factors being equal (number and size of offspring, survival rates, and more), delayed reproduction lowers population growth rate. Bald eagles require five years of growth before they are able to reproduce. If they were to lay the same number of eggs during their first year, those first-year offspring and several generations of their offspring, as well as the parents, would be able to reproduce during that time, tremendously increasing the overall population. By delaying reproduction, bald eagles not only ensure good energy supplies for reproduction at maturity, but also limit population density to suit their large bodied, long-lived life history.