# Biodiversity indices

Hill N2 index 1:  This index represents a weighted average of the proportional abundances of each species (pi). For each species (i), the number of individuals of that species in the sample (ni) is divided by the total number of individuals in the sample (N =  ni). In order to ….. the final index is calculated from the reciprocal of the sum of the square of the different pi’s.

Hill Index = 1/  (pi)2

Modified Hill Index calculated from relative abundance values: In this study, plant abundances were estimated using relative abundance estimates rather than plant counts. Absolute abundances are corrected to relative abundances by multiplying the absolute abundance estimates by the absolute to relative coverage factor. % absolute abundances were used directly as the pi values in the Hill index calculation.

Modified Hill Index = 1/   ( %abundance)2

The variation of determining the percent coverage was found, using a one way ANOVA, to be not statistically different from random error variations in the determination of abundance at the different tesserae. (needs link to show supporting evidence)

The relative abundances of specific plants at the different tesserae were found to be significantly different from randomness (F=5.019; 86 degrees of freedom, P<0.001);  (needs link  to show supporting evidence)

Jaccard’s Dissimilarity Metric. This metric was used to assess the dissimilarity between postulated tesserae based on  presence absence data. The total number of species present in two different tesserae is given by a and b, c represents the number of species in common.

Ji,j = a + b / (a+ b +c)

A Monte Carlo simulation was used to  test the validity of the Jaccard dissimilarity results. Jaccard dissimilarity values between 0 and .63 and between .85 and 1  had less than 5% probability and did not support the null hypothesis of the metrics been the result of random absence-presence processes. Metrics between .65 and .83 can not be distinguished from being due to the random distribution of species. (needs link to show supporting evidence)

# Floristic Indices

Ecosite Wetness Biodiversity Indices (WE) were calculated separately for grasses (WEg) and forbs (WEf). This indices are based on the relative contributions of each species to the overall wetness index of each ecosection. Average Wetness index for each site, based only on the presence-absence of species, was inadequate to represent, through the wetness index, the moisture regime prevalent in the ecosection under study. Ecosite Wetness Biodiversity Indices were calculated by adding the product of the species wetness index with its %absolute abundances.

WE =   ( wi x %abundance)

Ecosite Index of Conservatism (CE), Ecosite Index of Nitrogen fixation (NE), Ecosite Protein Potential (PPE), ….  were similarly calculated from the sum of the product of the appropriate  index for each species with its %abundance.

CE =    ( ci x  %abundance)

NE =    ( ni  x  %abundance)

PPE =   ( ppi  x  %abundance)

Exotics or invasives: Information regarding the origin of plants was obtained from NHIS14 data base. The data was summarized as % exotics/invasives  for each tessera

# Faunistic Indices

Index of Arthropod Encounter (EA) was developed to show the differences in arthropod richness among the tesserae studied. It is based on the number of different species encountered within a given tessera and the time spent surveying the site. It is based on two metrics, Frequency  of Encounter  Metric (TE), and Density of Encounter Metric (SE)

In this study all surveys were documented using pictures to record the species encountered. The time was assessed from the time signature of the pictures from the start of a shoot to the end of the series for each tessera. Subsequent visits were added to the total time spent in a section (the approach proved very effective and further refinement using a timer and a timing protocol should make it a practical approach to further surveys). The  Frequency of Encounter Metric (TE) was calculated in terms of the total number of species of each tessera per total survey time; it carries the units (h-1).

The relative area occupied by each of the tesserae was determined from a 1:xxxxxx map in terms of two measurements: longest axis (Lmax) and the largest perpendicular axis to the longest axis (L) measured in metres. The Density of Encounter Metric (SE) is determined by the total number of species in each ecotrope divided by the square root of the product of Lmax and L; it carries the units (m-1)

The Index of Arthropod Encounter (EA) is obtained by the square root of the product of the Frequency  of Encounter  Metric (TE), with the Density of Encounter Metric (SE); it carries the units (h m)½

For the sake of a first approximation, the probabilities of encountering any given species is assumed to follow a Poisson probability distribution. Based on this assumption it is possible to calculate an estimate of the total number of individuals expected for each species based on the number of specimens encountered during the survey walks.  For each species, the 100% cumulative probability (P100)  number of observations is calculated assuming that the average number of specimens observed corresponds to the λ metric of the Poisson distribution. The total number of individuals is then calculated from the product of the P100 value with the total number of sites where the species has been detected. The results of this calculation seem to fall within logical values for many species with restricted mobility ranges during the observation season, however it might greatly overestimate those species with extensive  mobility such as some Odonata, Hymenoptera and Lepidoptera .  Results for this calculation have been restricted to their order of magnitude in base 2, rather than an actual value.