When determining the spatial structure of a population, ecologists look at three properties: distribution, density, and dispersion. Distribution is how the population is spread out over a landscape, or a population’s range. Density refers to the number of individuals in a given unit of area or volume. Lastly, dispersion is the arrangement of individuals of the population within their area relative to one another. Dispersion hints at different abiotic and biotic factors that could be affecting the population.
There are three main patterns of dispersion. The first, random dispersion, occurs when individuals arrange themselves independently of one another. This arrangement usually suggests that neither abiotic nor biotic factors are acting on the population’s dispersion pattern. The second, clumped dispersion, occurs when individuals arrange themselves in clumps or communities. Often, this is a result of social behavior, like mating, or the clumped availability of resources. Lastly, there is uniform dispersion, in which individuals are arranged evenly. This sometimes happens due to competition for territory, like in plants.
Ecology students sampled dallisgrass (Paspalum dilatatum) in the Confederate Cemetery at the corner of UTC’s campus in the previous week. Now, they aim to determine the dispersion pattern of that plant in this area. In the wild, the null hypothesis is that all populations exhibit random dispersion. In this case, students have created an alternative hypothesis: when the data is applied to the Poisson distribution and chi-square analysis, it will be found that the dallisgrass species exhibits a uniform distribution due to competition for resources like root space.
To test the alternative hypothesis, students used random sampling of the dallisgrass at the Confederate Cemetery. The cemetery is the site for hundreds of individual graves, so it is maintained, and UTC students sometime walk through it. Students began in their groups with four to five individuals. One member of the group generated a random number, and another walked that many steps in one direction. Another random number was generated, and the student walked that many steps in a different direction. A 1m2 quadrat was placed at their feet, and the group counted the number of dallisgrass individuals within the quadrat. The group repeated this to sample a total of ten quadrats. With four groups in the class, this came out to be forty quadrats total for the entire class.
Students then analyzed the data. To determine the number of plants per quadrat for a random dispersion pattern, they used the Poisson distribution and graphed a histogram with the results. Poisson distribution is as follows:
P(x)=(axe-a)/ x!
In this formula, a represents the mean density of individuals per subplot and x is the number of individuals in the subplot. P(x), then, is the probability of finding a given number of individuals in any given subplot.
Students also created a histogram for the observed results to compare the two. If the histograms were found to be different, students determined if the observed results suggested clumping or uniform dispersion. To prove that the results were not random, students performed a Chi-square analysis test and compared the calculated p-value to the critical value at the alpha, or probability, level of 0.05. The Chi-square analysis formula is as follows:
X2=∑ [(Observed-Expected)2 / Expected]
In one group, students analyzed 9 plots, as they had the outlier. They counted 37 individuals total, had an average of 4.33 individuals per plot, and found a maximum of eight individuals within a single plot. The expected and observed histograms are shown in Figures 1 and 2.
Figure 1. The group’s expected dispersion histogram based on Poisson’s test.
Figure 2. The group’s observed dispersion pattern as a histogram.
The group had a total sample size of nine plots (N). The calculated Chi-square value was 6.83. The critical chi-square value was 15.507, as the group had eight degrees of freedom and an alpha level of 0.05.
Students found that there was an outlier in their data, so they disregarded it in their results and analyzed data from 39 plots instead of 40. As a class, they counted a total of 191 individuals, had a mean of 4.9 individuals per plot, and found a maximum of 16 individuals within one plot. The expected and observed histograms are shown in Figures 3 and 4.
Figure 3. The expected class histogram based on Poisson’s test.
Figure 4. The observed histogram of the class.
The class had a total sample size of 39 quadrants (N), making for 38 degrees of freedom. The critical value was 53.384, and the calculated Chi-square value was 668.17. The alpha level for the critical value was 0.05.
According to the group dataset, the species is found to have a random dispersion. Though the observed histogram, Figure 2, differs from the expected, Figure 1, the null hypothesis was accepted because the calculated P-value fell below the critical value. This means that there was a probability greater than 5% that the results were due to chance, leading to acceptance of the null hypothesis that the species had random dispersion. In such a case, no abiotic or biotic factors would play into the population’s dispersion.
However, the opposite can be said for the class dataset. The observed histogram, Figure 4, differs visually from the expected, Figure 3. Figure 4 holds the appearance of a clumped dispersion histogram. Additionally, the calculated P-value was well above the critical value, which means the null hypothesis was rejected. Thus, it can be concluded that the dallisgrass exhibits a clumped dispersion pattern, rejecting the alternate hypothesis that the population is uniform in dispersion. This is likely due to the clumping of resources, like sunlight.
It is important to keep two things in mind when considering the results. For one, environmental factors may have impacted the results. Students may have failed to count some individuals of dallisgrass due to lack of familiarity with the species. Additionally, it hadn’t rained for days at the time of collection, so the grasses had wilted, and the blades curled in. This may have caused students to misidentify the individuals. Also, it must be noted that the sampling sizes between the group dataset and class dataset were extremely different. Sampling nine plots does not allow a whole picture of the entire community. Sampling thirty-nine plots, on the other hand, provides a greater scope of the community. Thus, the class data analysis is likely to be more accurate for both expected and observed results of the sampling.
Exploring Ecology 