Data analysis

4.5.1 Tree Density

The distance measurements were used to establish absolute density o f all species combined and the density o f individual plant species (Mueller-Dombois & Ellenberg, 1974). Distance from the point to the plant centre was initially calculated as the sum o f the radius (calculated from the girth measurement) and the distance to the trunk.

The absolute density for all species, D, may be calculated from these distance

measures as described in Box 4-2 (Mueller-Dombois & Ellenberg, 1974 p p ll3 - l 14).

Box 4-2 Calculating density from distance measures

Y d

Mean distance ( ) for each transect = ---

where

d

= distance to the centre o f an individual tree, n= number o f trees o f all species

Absolute density, (D) = Area

10000 E.g. where distance measures are in metres, absolute density/ha = —^

The density (Da) for an individual tree species “a” can also be calculated: _ Number o f species" a" ^ ,

Da = ---X Absolute density

These estimates o f density are useful for description, but cannot readily be statistically compared (Greig-Smith, 1982) in the absence o f any measure o f variance. For

statistical comparison between transects within the same strata, the distance data were used. For comparison between strata, mean values for the transects were used to avoid pseudo replication which tends to increase the likelihood o f rejecting a null hypothesis incorrectly by over-inflating the sample size (Crawley, 1993).

The density data for individual species were used in direct ordination to establish patterns o f species density across the 23 transects.

4.5.2 Seedling density

Seedling density was calculated per hectare for each transect (by multiplying the number counted within each plot by 125 (10,000/(4x20)) and the averages for all transects compared across the three blocks, for all species combined and individually, using a simple analysis o f variance (using SPSS 6.1, Norusis, 1994) and multivariate ordination techniques.

4.5.3 Stand structure

For the analysis o f the stand structure, the number o f individuals within defined basal diameter size classes (each class had a width o f 5cm) was calculated per hectare for each transect using equation 5 shown above. These calculations were made for individual species and for all species combined.

The efficiency o f the power function model (Box 4-1 above), to describe the relationship between density (the independent variable) and the mean o f each size class linearly was tested by regressing log density against the log o f the mean o f each size class. Linear relationships within different populations can be compared using analysis o f covariance. Given a linear relationship, it was possible to compare the stand structure within the three grazing strata statistically by analysis o f covariance using GLIM4 (Crawley, 1993, see appendix four).

4.5.4 Species diversity

4.5.4.1 Diversity indices

The above measures all describe the physical attributes o f the forest in the different strata without taking differences in species diversity into account.

A number o f indices have been developed which encapsulate species diversity data in one parameter. These are by definition simplistic but can provide a rapid means o f

comparison (Magurran, 1988). The three indices used in this study are the Sorensen coefficient o f similarity, the Shannon-Wiener index and Pielous’s J.

The Sorensen coefficient o f similarity (S J is used to determine the degree to which the species composition o f the transects is alike. This looks only at the

presence/absence o f species and gives no weight to relative density or dominance. Species diversity was probably underestimated since a number o f vernacular names included more than one species. The formula for the Sorensen coefficient o f similarity (Ss) is shown in Box 4-3.

Box 4-3 Calculating the Sorensen coefficient of similarity ( S s )

l a

Sc — xlOO

(b + c)

where a = number o f species common to both samples b = number o f species in sample 1

c = number o f species in sample 2

The greater the similarity the closer Ss is to 100 When Ss = 0 there is zero similarity.

A direct count o f species provides a simple and objective measure o f species richness, however it is highly dependent on the sample size (Peet, 1974) and does not take heterogeneity into account. The Shannon-Wiener index is used to express the diversity o f a transect in a single parameter, combining species richness (the number o f species) with relative abundance or equitability (Magurran, 1988; Kent & Coker,

1993; Greig-Smith, 1983; Peet, 1974). The index measures the “average degree o f uncertainty of predicting the species o f a given individual picked at random from a community” (Hair, 1980). There are other indices o f diversity, however, the Shannon- Wiener index is most sensitive to differences in the rarest species and therefore

Equitability defines the evenness with which individuals are divided among the species present (Hair 1980). This may be measured from the Shannon diversity index using Pielous’s J. The formula for the Shannon diversity index and Pielou’s J is shown in Box 4-4.

Box 4-4 Calculating the Shannon diversity index (H') and Pielou’s J

Diversity H' = - ]^ p d n p i

where s = the number o f species

P i = the proportion o f the total number o f individuals

In document People and cattle: Agents of ecological change in a dry montane forest, Samburu District, Kenya (Page 134-137)