Population Growth Dynamics and Snow Goose Case Study

Exponential vs. Logistic Growth Patterns

Population growth generally occurs in five major phases: the lag phase, the exponential phase, the stationary phase, the overshoot phase, and the death phase. The change in the size of the snow goose population over the years is a perfect demonstration of how growth flows through these five phases. This paper discusses the specific events that occur in each phase and applies those concepts to the lesser snow goose as a real-world case study.

Exponential growth is said to exist when the rate of growth is proportional or equal to the existing amount, such that the larger the existing amount, the greater the growth rate (Gilewski & Norton, 2008). In terms of population growth, this refers to a situation where the birth rate is constant and is not restricted by disease or scarcity of resources — in other words, there are sufficient resources to support the continuous doubling of the population. If, however, the growth of a population is restricted by factors such as disease or resource scarcity, the growth pattern ceases to be exponential and is instead referred to as logistic growth. Logistic growth exists when growth is restricted by scarcity of resources.

Both logistic and exponential growth patterns are characterized by increases proportional to existing amounts; however, whereas logistic growth includes competition and resource limitations, exponential growth is characterized by an abundance of resources and a lack of competition. Another fundamental difference between the two is that in logistic growth, the growth rate is faster at the beginning and then slows down in progressive periods as resources become scarce and competition increases; in exponential growth, the rate is slow at first but increases as the population grows larger.

The Five Phases of Population Growth

a) Lag Phase: In this phase, there is very little or no growth at all, as organisms are still synthesizing biochemicals and adjusting to the new environment. The only noticeable change at this stage is growth in the size of individual cells. How long this phase lasts depends on the conditions of the environment and the health status of the organisms. During this phase, members of the population are still adjusting, synthesizing enzymes and RNA, and storing nutrients. Cells are not yet mature and are therefore unable to divide to form new cells, so the birth rate is essentially nil and no population growth is experienced.

b) Exponential Phase: In this phase, organisms are well-accustomed to the environment, and rapid growth is characterized by the doubling of cells within every specified length of time. Resources are available in abundance, providing ample opportunity for cells to divide extensively. The birth rate is highest at this stage, as competition is still very low.

c) Stationary Phase / Carrying Capacity: Carrying capacity refers to the maximum population size that an environment can support without imposing a strain on resources. In this stage, growth levels off and the rate of cell division becomes proportional to that of cell death. Owing to the massive growth experienced in the exponential phase, competition for resources intensifies and available resources become scarce. This reduction in resource availability causes the death rate to rise (through the process of natural selection) as the birth rate falls, continuing until the birth rate equals the death rate and no further growth is experienced.

d) Population Overshoot: At this stage, the population has surpassed the environment's carrying capacity, and the rate of cell death is slightly greater than that of cell division. Following the rapid division of cells in the exponential phase, competition increases and toxic byproducts are released at a high rate. The birth rate falls below the death rate, resulting in negative growth. Growth slows as it becomes harder to survive the toxins or find food.

e) Population Crash: At this stage, the death rate is extremely high, causing a steady decline in population size. Toxicity in the environment increases as more cells die. Cells are no longer dividing but mutating to better survive environmental changes. The birth rate falls to extremely low levels — sometimes to near zero — such that the population size decreases until the carrying capacity is reached, at which point it levels off.

Environmental Conditions and Growth Sustainability

Exponential growth can only exist if natural resources are infinitely available. For plants, this would include sufficient space, nutrients, sunlight, and water; for animals, it would include mates, nesting space, shelter, food, and water. In order for exponential growth to be sustained, these resources must increase at the same rate as the population; otherwise, competition would develop and the growth rate would level off, producing logistic growth. Logistic growth, however, can be sustained indefinitely at carrying capacity if death rates and birth rates are balanced such that the carrying capacity is maintained.

Of the two models, the logistic one is more realistic for two major reasons. First, resources will always be limited — land, for instance, will never increase along with the population in reality as the exponential model suggests. It would be unreasonable to assume that resources could grow proportionally with the population. Second, we cannot assume that growth occurs continuously — growth will only occur when conditions are favorable. Fish, for instance, typically show higher rates of growth during summer than in winter, meaning the rate of growth cannot be constant across both favorable and unfavorable seasons.

Carrying Capacity: Biotic and Abiotic Influences

Biotic factors are the living things that indirectly or directly affect an organism's ability to reproduce or survive in a particular environment. They include factors such as predation, disease, and parasitism. Abiotic factors, on the other hand, are the chemical and non-living physical factors that influence an organism's ability to thrive in a particular environment. They include pollutants, dissolved gases, pH level, temperature range, light intensity, and similar variables. Both biotic and abiotic factors work to restrict the size of a population to ensure that carrying capacity is not surpassed.

Abiotic factors such as oxygen shortages and water pollutants, for instance, limit the size of aquatic species by causing intolerant individuals to die until the remaining numbers can be sufficiently supported by the existing oxygen levels (Williams, 2000). Moreover, plants need light of the correct duration, intensity, and wavelength to survive — inappropriate light conditions could cause intolerant species to die until the carrying capacity for that environment under the prevailing conditions is reached. Biotic factors work in a similar way: predators can limit the numbers of a prey species such that fewer animals compete for space and resources when those resources are scarce. Furthermore, the greater the size of a population, the greater the likelihood of a disease spreading and reducing numbers until they can be sufficiently supported by existing resources.

Carrying capacity is therefore a function of existing resources, and since the level of resources is constantly changing, the carrying capacity of a particular environment also changes over time. It would be inaccurate to describe carrying capacity as a parameter that stays constant. A practical example is that of a grazing field: if one begins with ten heads of cattle on a sizeable piece of land, resources will be abundant, and the land's carrying capacity might be estimated at ten; however, as pasture becomes less available, competition develops, and the land may no longer be able to support ten animals — the carrying capacity might then fall to five, because resources are less readily available.

References

Batt, B. D. (Ed.). (1998). The Greater Snow Goose: Report of the Arctic Goose Habitat Working Group. U.S. Fish and Wildlife Service.

EPA. (2015). Future climate change. The U.S. Environmental Protection Agency.

Gilewski, T. A., & Norton, A. (2008). Norton-Simon hypothesis. In M. Perry (Ed.), The Chemotherapy Sourcebook (4th ed., pp. 7–20). Lippincott Williams and Wilkins.

U.S. Fish and Wildlife Service. (2015). Factors contributing to high populations of white geese. U.S. Fish and Wildlife Service.

Williams, G. (2000). Advanced Biology for You. Stanley Thornes Publishers.