Carrying Capacity- 4B

4B
Comparing Exponential and Logistic growth
Research question: How to projections of the exponentially and logistic growth models compare?

Population over time as compared to exponential and logistic models

Expected Population up to the year 2020

Darwin’s projection for his Addo elephants can be plotted as a J curve. This is not nearly as conservative as he thought and claimed, although the curve starts out slower, over the finite period of time the population grows at a much faster rate than projected in these exponential curves shown above.

If the Addo elephants do reach carrying capacity, some factors that may limit the further growth of the population would be amount of nutrition available for consumption, availability of drinking water, and space for inhabitation. In order to maintain biodiversity, however, it is much better to keep the population below carrying capacity. An example of this could be compared to practices in Myakka State Park. Invasive wild boars are harmful to the ecosystem health, so a common way to control this population is to catch the boars in traps to be sent elsewhere. While elephants are a much larger size than boars, a similar method could be devised to maintain the humane aspect of controlling the population. Killing the elephants may be a complicated and publicly opposed process. As another important point, it may be very difficult to dispose of the dead elephants other than in natural means.

The carrying capacity for the exercise was presumed at 500 K, however, in order to calculate a more accurate number the space and resources available should be taken into account. This could effectively raise or lower the K for specific areas. Populations of other animals consuming the same resources will also affect this number, as the resources will be limited.

Humans at one time were assumed to follow a similar problem, our growth would continue until we eventually outgrew our food supply. However, we now have scientific advances that allow us to genetically modify food supplies and effectively lower the cost of food, and the problems that come from harvesting it from the wild. Because we do have more access to necessary supplies to keep us alive, there is no longer really an r-selection applicable. Humans live in a fairly stable environment in terms of resources. Thus, K- selection is increased. This stabilizes the population for now, until living spaces no longer are available and the population must decrease.

Thus, for humans, carrying capacity depends on living space available, as we are able to determine effectively the food supply. At this time it is neither effective or possible to determine a human carrying capacity, as we are not sure of the technological advances yet to come.

Experiment K4A on population growth

4A

Research Question:

How rapidly did populations of the Egyptian goose grow in the Netherlands?

Year	Population Size	ln Population Size
1985	259	5.557
1986	277	5.624
1987	501	6.217
1988	626	6.439
1989	897	6.799
1990	1324	7.188
1991	2475	7.814
1992	2955	7.991
1993	5849	8.674
1994	7259	8.890

Time in Years (x axis) vs. ln N(y axis) / with red “fit” line

The slope of the fit line was found to be 0.382 ln N/year. This indicates that each year, the population of the Egyptian goose in the Netherlands grew exponentially by 0.382. In other words, the population flourished.

Questions:

1.     In the exponential population growth equation, Nt = N0 (e^rt), identify what each of the symbols stand for, and explain whether it is a variable or a constant for a given growing population.

A quantity Nt depends exponentially on time t, where the constant N0 is the original population, and the constant r is a positive growth factor.

2.     In 1985, the number of Egyptian geese observed was 259. Starting with this as an initial population size, N0=259, and using the value of r that you calculated in Method A, use the exponential growth equation to project numbers of geese in year 1994. Since that date is nine years later, use t=9 in the equation. Does the calculated number approximate the number actually observed in 1994?

Nt= 259(e^0.382*9)

Nt= 8061.28

The actual value for this year is actually 7259, giving an 11% error for the calculated value. This is a fairly good representation of the population, although the calculated value was higher than the actual value.

3.     To calculate r, ln was plotted as a function of years, and the best straight line was drawn through the points. Two points were used from that line to determine a slope. Why is this method more reliable than simply choosing two points from the data table to determine the slope?

Date from certain years could be considered outliers on a fitted line graph, thus should be excluded from finding the r value (slope). The values used to find r should be the beginning and end points to the fitted line in order to find the best and most accurate r value.

4.     Why do you think Egyptian goose populations are increasing exponentially in the Netherlands, but not in Africa where they originated?

The geese most likely do not have a natural predator in the Netherlands to control their population. In Africa, however, natural predators do exist, controlling the population from growing exponentially.

5.     When species are introduced to a new continent, they often grow so quickly that they out-compete native species. It may be too soon to tell if this is the case for the Egyptian goose, but there are North American examples of introduced species that have become an ecological problem. Name an example and explain why this species is an ecological threat.

Brazilian red pepper is a common plant to Florida. It was introduced from frost-free south American regions, and is now spreading rapidly and replacing native plants such as mangroves. It is suited to grow in nearly any environment, and grows with a vine like quality choking out many plants nearby and absorbing nutrients in the soil.