4.7 Calculation of community parameters
Butterfly diversity was analysed using EstimateS 5 (Colwell 1997). As comprehensive sampling of species richness is difficult in rich tropical communities, statistical methods have been established to estimate total species richness from single samples and randomisation of species turnover between them (see Colwell and Coddington 1994, 1995). For a research program on the arthropods of the La Selva forest, Costa Rica (Project ALAS), the calculation software EstimateS was developed by Colwell (1997). The program allows to compute richness estimators (as well as indexes of diversity and species similarity, if requested) based on the successive pooling of data from single samples. Using data (number of individuals per species) of one trap installed for an equal number of trap days as single samples, the following estimators were computed: Fisher’s alpha (alpha), Shannon and Simpson (1/D) diversity index (Magurran 1988), Evenness (E=Simpson/total species number S), as well as the size of the local species pools, as Abundance-Based (ACE) and Incidence-Based (ICE) Coverage Estimators of species richness (Colwell 1997). Sample order randomization with EstimateS (Colwell 1997) was set at 50 randomizations. Furthermore, differences in species richness and α-diversity were tested between the communities at each trap location for control, thinned and plantation comparing number of species (S), Simpson (1/D) diversity index and Evenness (E) with Mann-Whitney U-statistics.
Some information to the applied diversity indices is given in the following and principally derived from Magurran (1988).
A first group of diversity measures is called the diversity statistic indices. They are based on the idea that natural diversity can be measured as information contained in a theoretic code or message. Based on this rationale, theoretic diversity functions have been described. A frequently used diversity measure is the Shannon or Shannon-Weaver index.
The Shannon or Shannon-Weaver index is calculated as:
H
sp ln p
ii=1 S
= − ∑
iand pi = ni / N
and considers the proportion of individuals found in the ith species, pi . This value is estimated as ni / N (number of individuals in the ith species divided by the total number of individuals).
Compared to other indices, the Shannon index is sensitive to changes in abundance of rare or intermediate abundant species. It appeared to have an only moderate discriminant ability and, since it is strongly influenced by changes in rare species, is sensitive to sample size. The index assumes that sampling is random and allows you to include all species present in the community.
The ratio of observed to maximum diversity can be taken as a measure of Evenness.
Evenness is calculated as
E = H´/ ln S
with Hmax the „maximum diversity“ (all species equally abundant). Evenness E is constrained between 0 and 1.0, providing better opportunities for comparisons.
A second group of diversity measures are referred to as dominance measures since they particularly consider the abundances of the most common species rather than providing a measure of species richness. One of the most used dominance measures is Simpson’s index, which calculates the probability that any two individuals drawn at random from an infinitely large community belong to different species. It is calculated as:
D = Σp²i (reciprocal) 1/D = 1/Σp²i
and p²i = ni(ni-1) / N(N-1)
In the formula, pi is the proportion of individuals in the ith species and is estimated from the relation of the number of individuals in the ith species to the total number of individuals.
Simpson’s index especially takes into account the abundance of the most common species, and is less sensitive to species richness. It has a moderate discriminant ability and a low
sensitivity to sample size, since it does not stress on changes in abundance of rare species, but of the commonest species. Since diversity decreases when D increases, mostly the reciprocal form of the index is used (1/D).
Another index which is very frequently used is Fisher’s alpha diversity. It is calculated as:
α = N (1 - x) / x
S/N = (1-x) / x- ln (1/x)
and principally considers the total number of individuals N and x which is estimated from the iterative solution of S/N = (1-x)/x - ln(1/x) . It does not take into account the relative abundance of the species. This means, in situations were the total number of species and individuals stay constant but the eveness of the community changes, alpha will not indicate a difference. However, the index appeared to have a very good discriminant ability between different samples and is not so sensitive to sample size. This attribute of alpha is a result of its dependence on the numbers of species of intermediate abundance, it is relatively unaffected by either rare or common species abundance changes. The index is based on the log-series species abundance model developed by Fisher, and is strictly speaking only appropriate when the community shows a log-series distribution. However, in practice it appeared to be a good diversity measure independent of the underlying abundance pattern.
To describe species abundance distributions of samples, species-abundance models were fitted to expected distributions (log-normal, log-series) by chi-square Goodness of fit tests.
Expected distributions were calculated with the software LOGSERIE and LOGNORM, inserted in Krebs (1989). The majority of natural communities display a log-normal distribution which is believed to indicate a large, mature and varied community (Magurran 1988). A log-normal distribution of relative abundance implies a concave (logarithmic) abundance-rank diagram for the „lower“-ranking species (i.e. the most common ones) and a a convex curve for the „higher“ ranking species. An extreme abundance form is the broken-stick abundance model, which reflects an even more equitable state being the biological correspondent of a uniform distribution. If a broken-stick distribution is found, there is incidence that an important ecological factor is shared more or less evenly between the species. The log-series distribution is often visible in immature or stressed communities, dominated by one or a few ecological factors, but can also be due to small sample sizes. In a (logarithmic) abundance-rank diagram, a logarithmic series distribution implies a straight line except for the „lower“ ranking species.
The main estimator of total species richness used was the abundance-based coverage richness estimator ACE (Chao et al. 1993), based on functions of singletons and doubletons in the
sample. For reference, the respective formulas are added (Colwell 1997). ACE is based on the fact