Indices available in Biodiverse
Generated GMT Mon Oct 11 00:00:05 2010 using build_indices_table.pl, Biodiverse version 0.15.
This is a listing of the indices available in Biodiverse, ordered by the calculations used to generate them. It is generated from the system metadata and contains all the information visible in the GUI, plus some addtional details.
Most of the headings are self-explanatory. For the others:
- The Subroutine is the name of the subroutine used to call the function if you are using Biodiverse through a script.
- The Index is the name of the index in the SPATIAL_RESULTS list, or if it is its own list then this will be its name. These lists can contain a variety of values, but are usually lists of labels with some value, for example the weights used in an endemism calculation. The names of such lists typically end in "LIST", "ARRAY", "HASH" or "LABELS".
- Valid cluster metric is whether or not the index can be used as a clustering metric. A blank value means it cannot.
- The Minimum number of neighbour sets dictates whether or not a calculation or index will be run. If you specify only one neighbour set then all those calculations that require two sets will be dropped from the analysis. (This is always the case for calculations applied to cluster nodes as there is only one neighbour set, defined by the set of groups linked to the terminal nodes below a cluster node). Note that many of the calculations lump neighbour sets 1 and 2 together. See the SpatialConditions page for more details on neighbour sets.
Note that calculations can provide different numbers of indices depending on the nature of the BaseData set used. This currently applies to the hierarchically partitioned endemism calculations (both central and whole) and hierarchical labels.
Table of contents:
Endemism
Endemism central
Description: Calculate endemism for labels only in neighbour set 1, but with local ranges calculated using both neighbour sets
Subroutine: calc_endemism_central
Reference: Crisp et al. (2001) J Biogeog. http://dx.doi.org/10.1046/j.1365-2699.2001.00524.x ; Laffan and Crisp (2003) J Biogeog. http://www3.interscience.wiley.com/journal/118882020/abstract
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula | Reference |
| 1 | ENDC_CWE | Corrected weighted endemism | | 1 |  | |
| 2 | ENDC_RICHNESS | Richness used in ENDC_CWE (same as index RICHNESS_SET1) | | 1 | | |
| 3 | ENDC_SINGLE | Endemism unweighted by the number of neighbours. Counts each label only once, regardless of how many groups in the neighbourhood it is found in. Useful if your data have sampling biases and best applied with a small window. | | 1 |  where  is a label (taxon) in the set of labels (taxa)  in neighbour set 1, and  is the global range of label across the data set (the number of groups it is found in, unless the range is specified at import). | Slatyer et al. (2007) J. Biogeog http://dx.doi.org/10.1111/j.1365-2699.2006.01647.x |
| 4 | ENDC_WE | Weighted endemism | | 1 |  where is a label (taxon) in the set of labels (taxa) in neighbour set 1,  is the local range (the number of elements containing label within neighbour sets 1 & 2, this is also its value in list ABC2_LABELS_ALL), and is the global range of label across the data set (the number of groups it is found in, unless the range is specified at import). | |
Endemism central hierarchical partition
Description: Partition the endemism central results based on the taxonomic hierarchy inferred from the label axes. (Level 0 is the highest).
Subroutine: calc_endemism_central_hier_part
Reference: Laffan, Ramp and Roger (in prep)
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 5 | ENDC_HPART_0 | List of the proportional contribution of labels to the endemism central calculations, hierarchical level 0 | | 1 |
| 6 | ENDC_HPART_1 | List of the proportional contribution of labels to the endemism central calculations, hierarchical level 1 | | 1 |
| 7 | ENDC_HPART_C_0 | List of the proportional count of labels to the endemism central calculations (equivalent to richness per hierarchical grouping), hierarchical level 0 | | 1 |
| 8 | ENDC_HPART_C_1 | List of the proportional count of labels to the endemism central calculations (equivalent to richness per hierarchical grouping), hierarchical level 1 | | 1 |
| 9 | ENDC_HPART_E_0 | List of the expected proportional contribution of labels to the endemism central calculations (richness per hierarchical grouping divided by overall richness), hierarchical level 0 | | 1 |
| 10 | ENDC_HPART_E_1 | List of the expected proportional contribution of labels to the endemism central calculations (richness per hierarchical grouping divided by overall richness), hierarchical level 1 | | 1 |
| 11 | ENDC_HPART_OME_0 | List of the observed minus expected proportional contribution of labels to the endemism central calculations , hierarchical level 0 | | 1 |
| 12 | ENDC_HPART_OME_1 | List of the observed minus expected proportional contribution of labels to the endemism central calculations , hierarchical level 1 | | 1 |
Endemism central lists
Description: Lists used in endemism central calculations
Subroutine: calc_endemism_central_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 13 | ENDC_RANGELIST | List of ranges for each label used in the endemism central calculations | | 1 |
| 14 | ENDC_WTLIST | List of weights for each label used in the endemism central calculations | | 1 |
Endemism central normalised
Description: Normalise the WE and CWE scores by the neighbourhood size. (The number of groups used to determine the local ranges).
Subroutine: calc_endemism_central_normalised
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 15 | ENDC_CWE_NORM | Corrected weighted endemism normalised by groups | | 1 |  |
| 16 | ENDC_WE_NORM | Weighted endemism normalised by groups | | 1 |  |
Endemism whole
Description: Calculate endemism using all labels found in both neighbour sets
Subroutine: calc_endemism_whole
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula | Reference |
| 17 | ENDW_CWE | Corrected weighted endemism | | 1 |  | |
| 18 | ENDW_RICHNESS | Richness used in ENDW_CWE (same as index RICHNESS_ALL) | | 1 | | |
| 19 | ENDW_SINGLE | Endemism unweighted by the number of neighbours. Counts each label only once, regardless of how many groups in the neighbourhood it is found in. Useful if your data have sampling biases and best applied with a small window. | | 1 | where is a label (taxon) in the set of labels (taxa) across neighbour sets 1 & 2, and is the global range of label across the data set (the number of groups it is found in, unless the range is specified at import). | Slatyer et al. (2007) J. Biogeog http://dx.doi.org/10.1111/j.1365-2699.2006.01647.x |
| 20 | ENDW_WE | Weighted endemism | | 1 | where is a label (taxon) in the set of labels (taxa) across both neighbour sets, is the local range (the number of elements containing label within neighbour sets 1 & 2, this is also its value in list ABC2_LABELS_ALL), and is the global range of label across the data set (the number of groups it is found in, unless the range is specified at import). | |
Endemism whole hierarchical partition
Description: Partition the endemism whole results based on the taxonomic hierarchy inferred from the label axes. (Level 0 is the highest).
Subroutine: calc_endemism_whole_hier_part
Reference: Laffan, Ramp and Roger (in prep)
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 21 | ENDW_HPART_0 | List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 0 | | 1 |
| 22 | ENDW_HPART_1 | List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 1 | | 1 |
| 23 | ENDW_HPART_C_0 | List of the proportional count of labels to the endemism whole calculations (equivalent to richness per hierarchical grouping), hierarchical level 0 | | 1 |
| 24 | ENDW_HPART_C_1 | List of the proportional count of labels to the endemism whole calculations (equivalent to richness per hierarchical grouping), hierarchical level 1 | | 1 |
| 25 | ENDW_HPART_E_0 | List of the expected proportional contribution of labels to the endemism whole calculations (richness per hierarchical grouping divided by overall richness), hierarchical level 0 | | 1 |
| 26 | ENDW_HPART_E_1 | List of the expected proportional contribution of labels to the endemism whole calculations (richness per hierarchical grouping divided by overall richness), hierarchical level 1 | | 1 |
| 27 | ENDW_HPART_OME_0 | List of the observed minus expected proportional contribution of labels to the endemism whole calculations , hierarchical level 0 | | 1 |
| 28 | ENDW_HPART_OME_1 | List of the observed minus expected proportional contribution of labels to the endemism whole calculations , hierarchical level 1 | | 1 |
Endemism whole lists
Description: Lists used in the endemism whole calculations
Subroutine: calc_endemism_whole_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 29 | ENDW_RANGELIST | List of ranges for each label used in the endemism whole calculations | | 1 |
| 30 | ENDW_WTLIST | List of weights for each label used in the endemism whole calculations | | 1 |
Endemism whole normalised
Description: Normalise the WE and CWE scores by the neighbourhood size. (The number of groups used to determine the local ranges).
Subroutine: calc_endemism_whole_normalised
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 31 | ENDW_CWE_NORM | Corrected weighted endemism normalised by groups | | 1 |  |
| 32 | ENDW_WE_NORM | Weighted endemism normalised by groups | | 1 |  |
Hierarchical Labels
Ratios of hierarchical labels
Description: Analyse the diversity of labels using their hierarchical levels. The A, B and C scores are the same as in the Label Counts analysis (calc_label_counts) but calculated for each hierarchical level, e.g. for three axes one could have A0 as the Family level, A1 for the Family:Genus level, and A2 for the Family:Genus:Species level. The number of indices generated depends on how many axes are used in the labels. In this case there are 2. Axes are numbered from zero as the highest level in the hierarchy, so level 0 is the top level of the hierarchy.
Subroutine: calc_hierarchical_label_ratios
Reference: Jones and Laffan (2008) Trans Philol Soc http://dx.doi.org/10.1111/j.1467-968X.2008.00209.x
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 33 | HIER_A0 | A score for level 0 | | 2 |
| 34 | HIER_A1 | A score for level 1 | | 2 |
| 35 | HIER_ARAT1_0 | Ratio of A scores, (HIER_A1 / HIER_A0) | | 2 |
| 36 | HIER_ASUM0 | Sum of shared label sample counts, level 0 | | 2 |
| 37 | HIER_ASUM1 | Sum of shared label sample counts, level 1 | | 2 |
| 38 | HIER_ASUMRAT1_0 | 1 - Ratio of shared label sample counts, (HIER_ASUM1 / HIER_ASUM0) | cluster metric | 2 |
| 39 | HIER_B0 | B score for level 0 | | 2 |
| 40 | HIER_B1 | B score for level 1 | | 2 |
| 41 | HIER_BRAT1_0 | Ratio of B scores, (HIER_B1 / HIER_B0) | | 2 |
| 42 | HIER_C0 | C score for level 0 | | 2 |
| 43 | HIER_C1 | C score for level 1 | | 2 |
| 44 | HIER_CRAT1_0 | Ratio of C scores, (HIER_C1 / HIER_C0) | | 2 |
Inter-event Interval Statistics
Inter-event interval statistics
Description: Calculate summary statistics from a set of numeric labels that represent event times. Event intervals are calculated within groups, then aggregated across the neighbourhoods, and then summary stats are calculated.
Subroutine: calc_iei_stats
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 45 | IEI_CV | Coefficient of variation (IEI_SD / IEI_MEAN) | | 1 |
| 46 | IEI_GMEAN | Geometric mean | | 1 |
| 47 | IEI_KURT | Kurtosis | | 1 |
| 48 | IEI_MAX | Maximum value (100th percentile) | | 1 |
| 49 | IEI_MEAN | Mean | cluster metric | 1 |
| 50 | IEI_MIN | Minimum value (zero percentile) | | 1 |
| 51 | IEI_N | Number of samples | | 1 |
| 52 | IEI_RANGE | Range (max - min) | | 1 |
| 53 | IEI_SD | Standard deviation | | 1 |
| 54 | IEI_SKEW | Skewness | | 1 |
Inter-event interval statistics data
Description: The underlying data used for the IEI stats.
Subroutine: calc_iei_data
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 55 | IEI_DATA_ARRAY | Interval data in array form. Multiple occurrences are repeated | | 1 |
| 56 | IEI_DATA_HASH | Interval data in hash form where the interval is the key and number of occurrences is the value | | 1 |
Lists and Counts
Element counts
Description: Counts of elements used in neighbour sets 1 and 2.
Subroutine: calc_elements_used
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 57 | EL_COUNT_ALL | Count of elements in both neighbour sets | | 2 |
| 58 | EL_COUNT_SET1 | Count of elements in neighbour set 1 | | 1 |
| 59 | EL_COUNT_SET2 | Count of elements in neighbour set 2 | | 2 |
Element lists
Description: Lists of elements used in neighbour sets 1 and 2. These form the basis for all the spatial calculations.
Subroutine: calc_element_lists_used
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 60 | EL_LIST_ALL | List of elements in both neighour sets | | 2 |
| 61 | EL_LIST_SET1 | List of elements in neighbour set 1 | | 1 |
| 62 | EL_LIST_SET2 | List of elements in neighbour set 2 | | 2 |
Label counts
Description: Counts of labels in neighbour sets 1 and 2. These form the basis for the Taxonomic Dissimilarity and Comparison indices.
Subroutine: calc_abc_counts
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 63 | ABC_A | Count of labels common to both neighbour sets | | 2 |
| 64 | ABC_ABC | Total label count across both neighbour sets (same as RICHNESS_ALL) | | 2 |
| 65 | ABC_B | Count of labels unique to neighbour set 1 | | 2 |
| 66 | ABC_C | Count of labels unique to neighbour set 2 | | 2 |
Label counts not in sample
Description: Count of basedata labels not in either neighbour set (shared absence) Used in some of the dissimilarity metrics.
Subroutine: calc_d
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 67 | ABC_D | Count of labels not in either neighbour set (D score) | | 1 |
Local range lists
Description: Lists of labels with their local ranges as values. The local ranges are the number of elements in which each label is found in each neighour set.
Subroutine: calc_local_range_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 68 | ABC2_LABELS_ALL | List of labels in both neighbour sets | | 2 |
| 69 | ABC2_LABELS_SET1 | List of labels in neighbour set 1 | | 1 |
| 70 | ABC2_LABELS_SET2 | List of labels in neighbour set 2 | | 2 |
Local range summary statistics
Description: Summary stats of the local ranges within neighour sets.
Subroutine: calc_local_range_stats
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 71 | ABC2_MEAN_ALL | Mean label range in both element sets | | 1 |
| 72 | ABC2_MEAN_SET1 | Mean label range in neighbour set 1 | | 1 |
| 73 | ABC2_MEAN_SET2 | Mean label range in neighbour set 2 | | 2 |
| 74 | ABC2_SD_ALL | Standard deviation of label ranges in both element sets | | 2 |
| 75 | ABC2_SD_SET1 | Standard deviation of label ranges in neighbour set 1 | | 1 |
| 76 | ABC2_SD_SET2 | Standard deviation of label ranges in neighbour set 2 | | 2 |
Redundancy
Description: Ratio of labels to samples. Values close to 1 are well sampled while zero means there is no redundancy in the sampling
Subroutine: calc_redundancy
Formula:
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 77 | REDUNDANCY_ALL | for both neighbour sets | | 1 |  |
| 78 | REDUNDANCY_SET1 | for neighour set 1 | | 1 |  |
| 79 | REDUNDANCY_SET2 | for neighour set 2 | | 2 |  |
Richness
Description: Count the number of labels in the neighbour sets
Subroutine: calc_richness
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 80 | COMPL | A crude complementarity index for use in clustering. It is actually the same as RICHNESS_ALL and might be disabled in a later release. | cluster metric | 2 |
| 81 | RICHNESS_ALL | for both sets of neighbours | | 1 |
| 82 | RICHNESS_SET1 | for neighbour set 1 | | 1 |
| 83 | RICHNESS_SET2 | for neighbour set 2 | | 2 |
Sample count lists
Description: Lists of sample counts for each label within the neighbour sets. These form the basis of the sample indices.
Subroutine: calc_local_sample_count_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 84 | ABC3_LABELS_ALL | List of labels in both neighbour sets with their sample counts as the values. | | 2 |
| 85 | ABC3_LABELS_SET1 | List of labels in neighbour set 1. Values are the sample counts. | | 1 |
| 86 | ABC3_LABELS_SET2 | List of labels in neighbour set 2. Values are the sample counts. | | 2 |
Sample count summary stats
Description: Summary stats of the sample counts across the neighbour sets.
Subroutine: calc_local_sample_count_stats
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 87 | ABC3_MEAN_ALL | Mean of label sample counts across both element sets. | | 2 |
| 88 | ABC3_MEAN_SET1 | Mean of label sample counts in neighbour set1. | | 1 |
| 89 | ABC3_MEAN_SET2 | Mean of label sample counts in neighbour set 2. | | 2 |
| 90 | ABC3_SD_ALL | Standard deviation of label sample counts in both element sets. | | 2 |
| 91 | ABC3_SD_SET1 | Standard deviation of sample counts in neighbour set 1. | | 1 |
| 92 | ABC3_SD_SET2 | Standard deviation of label sample counts in neighbour set 2. | | 2 |
| 93 | ABC3_SUM_ALL | Sum of the label sample counts in neighbour set2. | | 2 |
| 94 | ABC3_SUM_SET1 | Sum of the label sample counts in neighbour set1. | | 1 |
| 95 | ABC3_SUM_SET2 | Sum of the label sample counts in neighbour set2. | | 2 |
Matrix
Compare dissimilarity matrix values
Description: Compare the set of labels in one neighbour set with those in another using their matrix values. Labels not in the matrix are ignored. This calculation assumes a matrix of dissimilarities and uses 0 as identical, so take care).
Subroutine: calc_compare_dissim_matrix_values
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 96 | MXD_COUNT | Count of comparisons used. | | 2 |
| 97 | MXD_LIST1 | List of the labels used from neighbour set 1 (those in the matrix). The list values are the number of times each label was used in the calculations. This will always be 1 for labels in neighbour set 1. | | 2 |
| 98 | MXD_LIST2 | List of the labels used from neighbour set 2 (those in the matrix). The list values are the number of times each label was used in the calculations. This will equal the number of labels used from neighbour set 1. | | 2 |
| 99 | MXD_MEAN | Mean dissimilarity of labels in set 1 to those in set 2. | cluster metric | 2 |
| 100 | MXD_VARIANCE | Variance of the dissimilarity values, set 1 vs set 2. | cluster metric | 2 |
Matrix overlap
Description: Calculate matrix overlap metrics between the two sets of groups. Many of them measure homogeneity, where 0 = homogeneous. Excludes labels not in the selected matrix, and variances are deviations from zero. It is best to apply these using a small neighbour set 1 relative to a large neighbour set 2
Subroutine: calc_overlap_mx
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 101 | MXO_LABELS | List of labels in neighbour set 1. | | 1 | |
| 102 | MXO_MEAN | Mean of neighbour set 1 | | 1 | |
| 103 | MXO_M_RATIO | Ratio of the set1 mean to the total mean | | 1 |  |
| 104 | MXO_N | Count of labels used in neighbour set 1 | | 1 | |
| 105 | MXO_TLABELS | List of all labels used (across both neighbour sets). | | 1 | |
| 106 | MXO_TMEAN | Mean of both neighbour sets | cluster metric | 1 | |
| 107 | MXO_TN | Count of all labels used | | 1 | |
| 108 | MXO_TVARIANCE | Variance of both neighbour sets (mean squared difference from zero) | | 1 | |
| 109 | MXO_VARIANCE | Variance of neighbour set 1 (mean squared difference from zero) | | 1 | |
| 110 | MXO_V_RATIO | Ratio of the set1 variance to the total variance | | 1 |  |
| 111 | MXO_Z_RATIO | A ratio of the local to total z-scores. | | 1 |  |
| 112 | MXO_Z_SCORE | Z-score of the set1 mean given the total mean and SD | | 1 |  |
Matrix statistics
Description: Calculate summary statistics of matrix elements in the selected matrix for labels found across both neighbour sets. Labels not in the matrix are ignored.
Subroutine: calc_matrix_stats
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 113 | MX_KURT | Kurtosis | | 1 |
| 114 | MX_MAXVALUE | Maximum value | | 1 |
| 115 | MX_MEAN | Mean | | 1 |
| 116 | MX_MEDIAN | Median | | 1 |
| 117 | MX_MINVALUE | Minimum value | | 1 |
| 118 | MX_N | Number of samples (matrix elements, not labels) | | 1 |
| 119 | MX_PCT05 | 5th percentile value | | 1 |
| 120 | MX_PCT25 | First quartile (25th percentile) | | 1 |
| 121 | MX_PCT75 | Third quartile (75th percentile) | | 1 |
| 122 | MX_PCT95 | 95th percentile value | | 1 |
| 123 | MX_RANGE | Range (max-min) | | 1 |
| 124 | MX_SD | Standard deviation | | 1 |
| 125 | MX_SKEW | Skewness | | 1 |
| 126 | MX_VALUES | List of the matrix values | | 1 |
Rao's quadratic entropy, matrix weighted
Description: Calculate Rao's quadratic entropy for a matrix weights scheme. BaseData labels not in the matrix are ignored
Subroutine: calc_mx_rao_qe
Formula:
where 
and 
are the sample counts for the i'th and j'th labels, 
is the matrix value for the pair of labels 
and 
is the set of labels across both neighbour sets that occur in the matrix.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 127 | MX_RAO_QE | Matrix weighted quadratic entropy | | 1 |
| 128 | MX_RAO_TLABELS | List of labels and values used in the MX_RAO_QE calculations | | 1 |
| 129 | MX_RAO_TN | Count of comparisons used to calculate MX_RAO_QE | | 1 |
Numeric Labels
Numeric label data
Description: The underlying data used for the numeric labels stats, as an array. For the hash form, use the ABC3_LABELS_ALL index from the 'Sample count lists' calculation.
Subroutine: calc_numeric_label_data
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 130 | NUM_DATA_ARRAY | Numeric label data in array form. Multiple occurrences are repeated based on their sample counts. | | 1 |
Numeric label harmonic and geometric means
Description: Calculate geometric and harmonic means for a set of numeric labels.
Subroutine: calc_numeric_label_other_means
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 131 | NUM_GMEAN | Geometric mean | | 1 |
| 132 | NUM_HMEAN | Harmonic mean | | 1 |
Numeric label quantiles
Description: Calculate quantiles from a set of numeric labels. Weights by samples so multiple occurrences are accounted for.
Subroutine: calc_numeric_label_quantiles
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 133 | NUM_Q005 | 5th percentile | | 1 |
| 134 | NUM_Q010 | 10th percentile | | 1 |
| 135 | NUM_Q015 | 15th percentile | | 1 |
| 136 | NUM_Q020 | 20th percentile | | 1 |
| 137 | NUM_Q025 | 25th percentile | | 1 |
| 138 | NUM_Q030 | 30th percentile | | 1 |
| 139 | NUM_Q035 | 35th percentile | | 1 |
| 140 | NUM_Q040 | 40th percentile | | 1 |
| 141 | NUM_Q045 | 45th percentile | | 1 |
| 142 | NUM_Q050 | 50th percentile | | 1 |
| 143 | NUM_Q055 | 55th percentile | | 1 |
| 144 | NUM_Q060 | 60th percentile | | 1 |
| 145 | NUM_Q065 | 65th percentile | | 1 |
| 146 | NUM_Q070 | 70th percentile | | 1 |
| 147 | NUM_Q075 | 75th percentile | | 1 |
| 148 | NUM_Q080 | 80th percentile | | 1 |
| 149 | NUM_Q085 | 85th percentile | | 1 |
| 150 | NUM_Q090 | 90th percentile | | 1 |
| 151 | NUM_Q095 | 95th percentile | | 1 |
Numeric label statistics
Description: Calculate summary statistics from a set of numeric labels. Weights by samples so multiple occurrences are accounted for.
Subroutine: calc_numeric_label_stats
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 152 | NUM_CV | Coefficient of variation (NUM_SD / NUM_MEAN) | | 1 |
| 153 | NUM_KURT | Kurtosis | | 1 |
| 154 | NUM_MAX | Maximum value (100th quantile) | | 1 |
| 155 | NUM_MEAN | Mean | cluster metric | 1 |
| 156 | NUM_MIN | Minimum value (zero quantile) | | 1 |
| 157 | NUM_N | Number of samples | | 1 |
| 158 | NUM_RANGE | Range (max - min) | | 1 |
| 159 | NUM_SD | Standard deviation | | 1 |
| 160 | NUM_SKEW | Skewness | | 1 |
Phylogenetic Indices
Phylogenetic Diversity
Description: Phylogenetic diversity (PD) based on branch lengths back to the root of the tree. Uses labels in both neighbourhoods.
Subroutine: calc_pd
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula | Reference |
| 161 | PD | Phylogenetic diversity | | 1 |  where  is the set of branches in the minimum spanning path joining the labels in both neighbour sets to the root of the tree, is a branch (a single segment between two nodes) in the spanning path , and  is the length of branch . | Faith (1992) Biol. Cons. http://dx.doi.org/10.1016/0006-3207(92)91201-3 |
| 162 | PD_P | Phylogenetic diversity as a proportion of total tree length | | 1 |  where terms are the same as for PD, but , and are calculated for all nodes in the tree. | |
| 163 | PD_P_per_taxon | Phylogenetic diversity per taxon as a proportion of total tree length | | 1 |  | |
| 164 | PD_per_taxon | Phylogenetic diversity per taxon | | 1 |  | |
Phylogenetic Diversity node list
Description: Phylogenetic diversity (PD) nodes used.
Subroutine: calc_pd_node_list
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 165 | PD_INCLUDED_NODE_LIST | List of tree nodes included in the PD calculations | | 1 |
Phylogenetic Endemism
Description: Phylogenetic endemism (PE).Uses labels in both neighbourhoods and trims the tree to exclude labels not in the BaseData object.
Subroutine: calc_pe
Reference: Rosauer et al (2009) Mol. Ecol. http://dx.doi.org/10.1111/j.1365-294X.2009.04311.x
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 166 | PE_WE | Phylogenetic endemism | | 1 |
| 167 | PE_WE_P | Phylogenetic weighted endemism as a proportion of the total tree length | | 1 |
| 168 | PE_WE_SINGLE | Phylogenetic endemism unweighted by the number of neighbours. Counts each label only once, regardless of how many groups in the neighbourhood it is found in. Useful if your data have sampling biases. Better with small sample windows. | | 1 |
| 169 | PE_WE_SINGLE_P | Phylogenetic endemism unweighted by the number of neighbours as a proportion of the total tree length. Counts each label only once, regardless of how many groups in the neighbourhood it is found. Useful if your data have sampling biases. | | 1 |
Phylogenetic Endemism lists
Description: Lists used in the Phylogenetic endemism (PE) calculations.
Subroutine: calc_pe_lists
Reference: Rosauer et al (2009) Mol. Ecol. http://dx.doi.org/10.1111/j.1365-294X.2009.04311.x
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 170 | PE_RANGELIST | Node ranges used in PE calculations | | 1 |
| 171 | PE_WTLIST | Node weights used in PE calculations | | 1 |
Taxonomic/phylogenetic distinctness
Description: Taxonomic/phylogenetic distinctness and variation. THIS IS A BETA LEVEL IMPLEMENTATION.
Subroutine: calc_taxonomic_distinctness
Reference: Warwick & Clarke (1995) Mar Ecol Progr Ser. http://dx.doi.org/10.3354/meps129301 ; Clarke & Warwick (2001) Mar Ecol Progr Ser. http://dx.doi.org/10.3354/meps216265
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 172 | TD_DENOMINATOR | Denominator from TD_DISTINCTNESS calcs | | 1 |
| 173 | TD_DISTINCTNESS | Taxonomic distinctness | | 1 |
| 174 | TD_NUMERATOR | Numerator from TD_DISTINCTNESS calcs | | 1 |
| 175 | TD_VARIATION | Variation of the taxonomic distinctness | | 1 |
Taxonomic/phylogenetic distinctness, binary weighted
Description: Taxonomic/phylogenetic distinctness and variation using presence/absence weights. THIS IS A BETA LEVEL IMPLEMENTATION.
Subroutine: calc_taxonomic_distinctness_binary
Reference: Warwick & Clarke (1995) Mar Ecol Progr Ser. http://dx.doi.org/10.3354/meps129301 ; Clarke & Warwick (2001) Mar Ecol Progr Ser. http://dx.doi.org/10.3354/meps216265
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 176 | TDB_DENOMINATOR | Denominator from TDB_DISTINCTNESS | | 1 | |
| 177 | TDB_DISTINCTNESS | Taxonomic distinctness, binary weighted | | 1 | )}%.png "= \frac{\sum \sum_{i \neq j} \omega_{ij}}{s(s-1))}") where  is the path length from label  to the ancestor node shared with  |
| 178 | TDB_NUMERATOR | Numerator from TDB_DISTINCTNESS | | 1 | |
| 179 | TDB_VARIATION | Variation of the binary taxonomic distinctness | | 1 | )} - \bar{\omega}^2%.png "= \frac{\sum \sum_{i \neq j} \omega_{ij}^2}{s(s-1))} - \bar{\omega}^2") where )} \equiv TDB\_DISTINCTNESS%.png "\bar{\omega} = \frac{\sum \sum_{i \neq j} \omega_{ij}}{s(s-1))} \equiv TDB\_DISTINCTNESS") |
Rarity
Rarity central
Description: Calculate rarity for species only in neighbour set 1, but with local sample counts calculated from both neighbour sets. Uses the same algorithm as the endemism indices but weights by sample counts instead of by groups occupied.
Subroutine: calc_rarity_central
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 180 | RAREC_CWE | Corrected weighted rarity | | 1 |  |
| 181 | RAREC_RICHNESS | Richness used in RAREC_CWE (same as index RICHNESS_SET1). | | 1 | |
| 182 | RAREC_WE | Weighted rarity | | 1 |  where is a label (taxon) in the set of labels (taxa) across neighbour set 1,  is sum of the sample counts for across the elements in neighbour sets 1 & 2 (its value in list ABC3_LABELS_ALL), and  is the total number of samples across the data set for label (unless the total sample count is specified at import). |
Rarity central lists
Description: Lists used in rarity central calculations
Subroutine: calc_rarity_central_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 183 | RAREC_RANGELIST | List of ranges for each label used in the rarity central calculations | | 1 |
| 184 | RAREC_WTLIST | List of weights for each label used in therarity central calculations | | 1 |
Rarity whole
Description: Calculate rarity using all species in both neighbour sets. Uses the same algorithm as the endemism indices but weights by sample counts instead of by groups occupied.
Subroutine: calc_rarity_whole
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 185 | RAREW_CWE | Corrected weighted rarity | | 1 |  |
| 186 | RAREW_RICHNESS | Richness used in RAREW_CWE (same as index RICHNESS_ALL). | | 1 | |
| 187 | RAREW_WE | Weighted rarity | | 1 | where is a label (taxon) in the set of labels (taxa) across both neighbour sets, is sum of the sample counts for across the elements in neighbour sets 1 & 2 (its value in list ABC3_LABELS_ALL), and is the total number of samples across the data set for label (unless the total sample count is specified at import). |
Rarity whole lists
Description: Lists used in rarity whole calculations
Subroutine: calc_rarity_whole_lists
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 188 | RAREW_RANGELIST | List of ranges for each label used in the rarity whole calculations | | 1 |
| 189 | RAREW_WTLIST | List of weights for each label used in therarity whole calculations | | 1 |
Taxonomic Dissimilarity and Comparison
Beta diversity
Description: Beta diversity between neighbour sets 1 and 2.
Subroutine: calc_beta_diversity
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 190 | BETA_2 | The other beta | cluster metric | 2 | , (A+C))} - 1%.png "= \frac{A + B + C}{max((A+B), (A+C))} - 1") where  is the count of labels found in both neighbour sets,  is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly. |
| 191 | BETA_W | Whittaker's beta (Note that this is numerically the same as the Sorenson index.) | cluster metric | 2 |  + (A+C)}{2})} - 1%.png "= \frac{A + B + C}{(\frac{(A+B) + (A+C)}{2})} - 1") where is the count of labels found in both neighbour sets, is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly. |
Bray-Curtis non-metric
Description: Bray-Curtis dissimilarity between two sets of labels. Reduces to the Sorenson metric for binary data (where sample counts are 1 or 0).
Subroutine: calc_bray_curtis
Formula:
where is the sum of the sample counts in neighbour set 1, is the sum of sample counts in neighbour set 2, and %.png "W=\sum^n_{i=1} min(sample\_count\_label_{i_{set1}},sample\_count\_label_{i_{set2}})")
(meaning it sums the minimum of the sample counts for each of the 
labels across the two neighbour sets),
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 192 | BC_A | The A factor used in calculations (see formula) | | 2 |
| 193 | BC_B | The B factor used in calculations (see formula) | | 2 |
| 194 | BC_W | The W factor used in calculations (see formula) | | 2 |
| 195 | BRAY_CURTIS | Bray Curtis dissimilarity | cluster metric | 2 |
Bray-Curtis non-metric, group count normalised
Description: Bray-Curtis dissimilarity between two neighbourhoods, where the counts in each neighbourhood are divided by the number of groups in each neighbourhood to correct for unbalanced sizes.
Subroutine: calc_bray_curtis_norm_by_gp_counts
Formula:
where is the sum of the sample counts in neighbour set 1 normalised (divided) by the number of groups, is the sum of the sample counts in neighbour set 2 normalised by the number of groups, and %.png "W = \sum^n_{i=1} min(sample\_count\_label_{i_{set1}},sample\_count\_label_{i_{set2}})")
(meaning it sums the minimum of the normalised sample counts for each of the labels across the two neighbour sets),
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 196 | BCN_A | The A factor used in calculations (see formula) | | 2 |
| 197 | BCN_B | The B factor used in calculations (see formula) | | 2 |
| 198 | BCN_W | The W factor used in calculations (see formula) | | 2 |
| 199 | BRAY_CURTIS_NORM | Bray Curtis dissimilarity normalised by groups | cluster metric | 2 |
Jaccard
Description: Jaccard dissimilarity between the labels in neighbour sets 1 and 2.
Subroutine: calc_jaccard
Formula:
where is the count of labels found in both neighbour sets, is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 200 | JACCARD | Jaccard value, 0 is identical, 1 is completely dissimilar | cluster metric | 2 |
Nestedness-resultant
Description: Nestedness-resultant dissimilarity between the labels in neighbour sets 1 and 2.
Subroutine: calc_nestedness_resultant
Reference: Baselga (2010) Glob Ecol Biogeog. http://dx.doi.org/10.1111/j.1466-8238.2009.00490.x
Formula:
 }%.png "=\frac{ \left | B - C \right | }{ 2A + B + C } \times \frac { A }{ A + min (B, C) }")
where is the count of labels found in both neighbour sets, is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 201 | NEST_RESULTANT | Nestedness-resultant value, 0 is identical, 1 is completely dissimilar | cluster metric | 2 |
Rao's quadratic entropy, taxonomically weighted
Description: Calculate Rao's quadratic entropy for a taxonomic weights scheme. Should collapse to be the Simpson index for presence/absence data.
Subroutine: calc_tx_rao_qe
Formula:
where and are the sample counts for the i'th and j'th labels, is a value of zero if 
, and a value of 1 otherwise. is the set of labels across both neighbour sets.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 202 | TX_RAO_QE | Taxonomically weighted quadratic entropy | | 1 |
| 203 | TX_RAO_TLABELS | List of labels and values used in the TX_RAO_QE calculations | | 1 |
| 204 | TX_RAO_TN | Count of comparisons used to calculate TX_RAO_QE | | 1 |
S2
Description: S2 dissimilarity between two sets of labels
Subroutine: calc_s2
Reference: Lennon et al. (2001) J Animal Ecol. http://dx.doi.org/10.1046/j.0021-8790.2001.00563.x
Formula:
}%.png "= 1 - \frac{A}{A + min(B, C)}")
where is the count of labels found in both neighbour sets, is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 205 | S2 | S2 dissimilarity index | cluster metric | 2 |
Simpson and Shannon
Description: Simpson and Shannon diversity metrics using samples from all neighbourhoods.
Subroutine: calc_simpson_shannon
Formula:
For each index formula, is the number of samples of the i'th label as a proportion of the total number of samples in the neighbourhoods.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 206 | SHANNON_E | Shannon's evenness (H / HMAX) | | 1 |  |
| 207 | SHANNON_H | Shannon's H | | 1 | )%.png "H = - \sum^n_{i=1} (p_i \cdot ln (p_i))") |
| 208 | SHANNON_HMAX | maximum possible value of Shannon's H | | 1 | %.png "HMAX = ln(richness)") |
| 209 | SIMPSON_D | Simpson's D. A score of zero is more similar. | cluster metric | 1 |  |
Sorenson
Description: Sorenson dissimilarity between two sets of labels. It is the complement of the (unimplemented) Czechanowski index, and numerically the same as Whittaker's beta.
Subroutine: calc_sorenson
Formula:
where is the count of labels found in both neighbour sets, is the count unique to neighbour set 1, and is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets |
| 210 | SORENSON | Sorenson index | cluster metric | 2 |
Taxonomic overlap
Description: Calculate taxonomic overlap metrics between the two sets of elements. Uses deviation from zero for variances. In most cases the means and variances will be the same. Bears some relation to Rao's quadratic entropy if this calculation were modified to weight by sample counts. It is best to apply these indices using a small neighbour set 1 relative to a large neighbour set 2. METADATA NEEDS MORE FORMULAE.
Subroutine: calc_overlap_tx
| Index # | Index | Index description | Valid cluster metric? | Minimum number of neighbour sets | Formula |
| 211 | TXO_LABELS | List of labels in neighbour set 1. | | 1 | |
| 212 | TXO_MEAN | Mean of neighbour set 1. | | 1 | |
| 213 | TXO_M_RATIO | Ratio of the set1 mean to the mean of the combined neighbour sets | | 1 |  |
| 214 | TXO_N | Count of labels used in neighbour set 1. | | 1 | |
| 215 | TXO_TLABELS | List of all labels used (across both neighbour sets). | | 1 | |
| 216 | TXO_TMEAN | Mean of both neighbour sets. | | 1 | |
| 217 | TXO_TN | Count of all labels used in the conbined neighbour sets. | | 1 | |
| 218 | TXO_TVARIANCE | Variance of the combined neighbour sets (mean squared difference from zero). | | 1 | |
| 219 | TXO_VARIANCE | Variance of neighbour set 1 (mean squared difference from zero). | | 1 | |
| 220 | TXO_V_RATIO | Ratio of the set1 variance to the variance of the combined neighbour sets. | | 1 |  |
| 221 | TXO_Z_RATIO | (TXO_MEAN / TXO_VARIANCE) / (TXO_TMEAN / TXO_TVARIANCE) | | 1 |  |
| 222 | TXO_Z_SCORE | Z-score of the set1 mean given the mean and SD of the combined neighbour sets | | 1 |  |