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(adapted from lab exercise, BIO 490/590, Fishery Techniques & Fish Identification)
Biological systems are organized on many different levels: molecules, cells, organisms, populations, communities and ecosystems. Species diversity is a characteristic unique to the community level of biological organization. Higher species diversity is generally thought to indicate a more complex and healthier community because a greater variety of species allows for more species interactions, hence greater system stability, and indicates good environmental conditions. A variety of diversity indices can be calculated to compare ecological communities. In addition, pairs of communities can be compared using community similarity indices.
Species diversity has two parts. Richness refers to the number of species found in a community and evenness refers to the relative abundance of each species. A community is said to have high species diversity if many nearly equally abundant species are present. If a community has only a few species or if only a few species are very abundant, then species diversity is low. Consider a community with 100 individuals distributed among 10 species. It should make sense that if there are 10 individuals in each of the 10 species in the community it is more diverse than if there are 91 individuals in one species and one individual in each of the other nine species.
You will enter the data for the fish collected in Northrup Creek into a spreadsheet, create formulas and calculate indices to compare the fish communities above and below the WTP, and reach conclusions about the similarity and diversities of the two communities.
Exercise 1: Calculating the Proportional Index of Community Similarity
A good way to compare communities in different places or at different times is to examine community similarity. You will use a simple measure, called Proportional Similarity, to compare fish communities in Northrup Creek. Table 1 gives an example of this method.
Table 1. The percent of fish sampled in each species in community 1 and community 2 (e.g., 50 = # of species 1 captured in community 1; 93 = total # of fish captured in community 1).
Species Community 1 Community 2
1 50/93 = 54% 0/112 = 0%
2 25/93 = 27% 7/112 = 6%
3 12/93 = 13% 15/112 = 13%
4 6/93 = 6% 30/112 = 27%
5 0/93 = 0% 60/112 = 54%
Total 93 fish sampled 112 fish sampled
PS (Percent Similarity) = (lowest percent value of a species between communities), in this case:
PS = 0% + 6% + 13% + 6% + 0% = 25% (Equation 1)
Calculate PS for the fish communities above/below the WTP discharge to Northrup Creek.
Exercise 2: Simpson's Index of Diversity
Simpson's Index calculates the probability that two organisms sampled from a community of will belong to different species (the more even the abundance of individuals across species, the higher the probability that the two individuals sampled will belong to different species). Simpson's Index values range from 0 to 1, with 1 representing perfect evenness (all species present in equal numbers). The formula for Simpson's Index is:
Ds = 1  Sum1i [ni*(ni1)]/[N*(N1)] (Equation 2)
where = add all ni*(ni1) values together, ni = the number of individuals in the ith species collected, and N = the total number of organisms in the sample. For example, suppose you collected 3 species with 40, 25 and 15 individuals, respectively.
Ds = 1  40(39) + 25(24) + 15(14)
80(79)
= 1  2370
6320
= 1  0.375
= 0.625
2. Calculate SI for the fish communities above/below the WTP discharge to Northrup Creek.
Exercise 3: Determining Statistically Significant Differences in Simpson's Diversity
Inevitably, the Ds values you calculate for each community you sample will be different. How can you tell if the communities have significantly different Ds values or not? To answer this question requires using statistics, a branch of mathematics that allows you to determine with a known degree of reliability how likely it is that two or more groups are the same or not. To make this kind of comparison, you need to calculate the variability in the data you collected (the more variable the data, the greater the difference in the diversity values has to be to show a significant difference between any two Ds values). The formula to calculate the variance (s2) of Simpson's Index is:
s2 = 4[pi3  (pi2)2]/N (Equation 3)
where pi is the proportion of the number of organisms in the ith species (ni ) to the total number of organisms in the sample (N).
Therefore, pi = ni/N (these are the same values you used to calculate Simpson's Diversity). Using the data from the example from Equation 2, you can calculate s2.
s2 = 4{[(40/80)3 + (25/80)3 + (15/80)3]  [(40/80)2 + (25/80)2 + (15/80)2]2}/80
= 4{[0.125 + 0.031 + 0.007]  [0.250 + 0.098 + 0.035]2}/80
= 4{[0.163]  [0.383]2}/80
= 4(0.160)/80
= 0.0008
You will use a ttest to determine whether or not Simpson's diversity values are different for the fish communities above and below the WTP.
t = (Equation 4)
For example, suppose that diversities in two hypothetical communities are 0.8 and 0.3, respectively, and that the variances of the two diversity estimates are 0.03 (s21) and 0.01 (s22), respectively.
t = 0.8  0.3
= 0.5/0.2
= 2.5
For this example, if the degrees of freedom ( # taxa in community 1 + # taxa in community 2  2 = n1 + n2  2) are 8, the ttable value is 2.306 (see last page). For any calculated value of "t" greater than the number you find in the table, the difference in diversity between the two communities is considered to be significant. For any calculated value of "t" less than the number you find in the table, the difference in diversity between the two communities is not considered to be significant. For these calculations, statistical significance means there is 1 chance in 20 (5%) that the data show a difference in community diversity values when in reality there is no difference.
3. Use a spreadsheet to calculate s2 for the fish communities above and below the WTP discharge to Northrup Creek and do a ttest. Is there a statistically significant difference in diversity between the two communities? Explain.
References
Brower, J.E., and J.H. Zar. 1984. Field and Laboratory Methods for General Ecology (2nd Ed.). Wm. C. Brown Publishers. Dubuque, IA.
Powell, F.C. 1982. Statistical Tables for the Social, Biological and Physical Sciences. Cambridge University Press. London.
NSF/DUE/CCLIND Regional Workshop Exercise Rev. 7/01
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