IndicesDevVersion

Shawn Laffan edited this page Jun 26, 2016 · 4 revisions

Indices available in Biodiverse

Generated GMT Sun Jun 26 05:21:15 2016 using build_indices_table.pl, Biodiverse version 1.99_002.

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 additional 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", "LABELS" or "STATS".
  • Grouping? states whether or not the index can be used to define the grouping for a cluster or region grower analysis. A blank value means it cannot be used for either.
  • 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.

Indices available in Biodiverse:

Element Properties

Group property Gi* statistics

Description: List of Getis-Ord Gi* statistics for each group property across both neighbour sets

Subroutine: calc_gpprop_gistar

Reference: Getis and Ord (1992) Geographical Analysis. http://dx.doi.org/10.1111/j.1538-4632.1992.tb00261.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
1 GPPROP_GISTAR_LIST List of Gi* scores 1

Group property data

Description: Lists of the groups and their property values used in the group properties calculations

Subroutine: calc_gpprop_lists

Index # Index Index description Grouping metric? Minimum number of neighbour sets
2 GPPROP_STATS_GPROP1_DATA List of values for property GPROP1 1
3 GPPROP_STATS_GPROP2_DATA List of values for property GPROP2 1

Group property hashes

Description: Hashes of the groups and their property values used in the group properties calculations. Hash keys are the property values, hash values are the property value frequencies.

Subroutine: calc_gpprop_hashes

Index # Index Index description Grouping metric? Minimum number of neighbour sets
4 GPPROP_STATS_GPROP1_HASH Hash of values for property GPROP1 1
5 GPPROP_STATS_GPROP2_HASH Hash of values for property GPROP2 1

Group property quantiles

Description: Quantiles for each group property across both neighbour sets

Subroutine: calc_gpprop_quantiles

Index # Index Index description Grouping metric? Minimum number of neighbour sets
6 GPPROP_QUANTILE_LIST List of quantiles for the label properties (05 10 20 30 40 50 60 70 80 90 95) 1

Group property summary stats

Description: List of summary statistics for each group property across both neighbour sets

Subroutine: calc_gpprop_stats

Index # Index Index description Grouping metric? Minimum number of neighbour sets
7 GPPROP_STATS_LIST List of summary statistics (count mean min max median sum sd iqr) 1

Label property Gi* statistics

Description: List of Getis-Ord Gi* statistic for each label property across both neighbour sets

Subroutine: calc_lbprop_gistar

Reference: Getis and Ord (1992) Geographical Analysis. http://dx.doi.org/10.1111/j.1538-4632.1992.tb00261.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
8 LBPROP_GISTAR_LIST List of Gi* scores 1

Label property Gi* statistics (local range weighted)

Description: List of Getis-Ord Gi* statistic for each label property across both neighbour sets (local range weighted)

Subroutine: calc_lbprop_gistar_abc2

Reference: Getis and Ord (1992) Geographical Analysis. http://dx.doi.org/10.1111/j.1538-4632.1992.tb00261.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
9 LBPROP_GISTAR_LIST_ABC2 List of Gi* scores 1

Label property data

Description: Lists of the labels and their property values used in the label properties calculations

Subroutine: calc_lbprop_data

Index # Index Index description Grouping metric? Minimum number of neighbour sets
10 LBPROP_STATS_EXPROP1_DATA List of data for property EXPROP1 1
11 LBPROP_STATS_EXPROP2_DATA List of data for property EXPROP2 1

Label property hashes

Description: Hashes of the labels and their property values used in the label properties calculations. Hash keys are the property values, hash values are the property value frequencies.

Subroutine: calc_lbprop_hashes

Index # Index Index description Grouping metric? Minimum number of neighbour sets
12 LBPROP_STATS_EXPROP1_HASH Hash of values for property EXPROP1 1
13 LBPROP_STATS_EXPROP2_HASH Hash of values for property EXPROP2 1

Label property hashes (local range weighted)

Description: Hashes of the labels and their property values used in the local range weighted label properties calculations. Hash keys are the property values, hash values are the property value frequencies.

Subroutine: calc_lbprop_hashes_abc2

Index # Index Index description Grouping metric? Minimum number of neighbour sets
14 LBPROP_STATS_EXPROP1_HASH2 Hash of values for property EXPROP1 1
15 LBPROP_STATS_EXPROP2_HASH2 Hash of values for property EXPROP2 1

Label property lists

Description: Lists of the labels and their property values within the neighbour sets

Subroutine: calc_lbprop_lists

Index # Index Index description Grouping metric? Minimum number of neighbour sets
16 LBPROP_LIST_EXPROP1 List of data for property EXPROP1 1
17 LBPROP_LIST_EXPROP2 List of data for property EXPROP2 1

Label property quantiles

Description: List of quantiles for each label property across both neighbour sets

Subroutine: calc_lbprop_quantiles

Index # Index Index description Grouping metric? Minimum number of neighbour sets
18 LBPROP_QUANTILES List of quantiles for the label properties: (05 10 20 30 40 50 60 70 80 90 95) 1

Label property quantiles (local range weighted)

Description: List of quantiles for each label property across both neighbour sets (local range weighted)

Subroutine: calc_lbprop_quantiles_abc2

Index # Index Index description Grouping metric? Minimum number of neighbour sets
19 LBPROP_QUANTILES_ABC2 List of quantiles for the label properties: (05 10 20 30 40 50 60 70 80 90 95) 1

Label property summary stats

Description: List of summary statistics for each label property across both neighbour sets

Subroutine: calc_lbprop_stats

Index # Index Index description Grouping metric? Minimum number of neighbour sets
20 LBPROP_STATS List of summary statistics (count mean min max median sum skewness kurtosis sd iqr) 1

Label property summary stats (local range weighted)

Description: List of summary statistics for each label property across both neighbour sets, weighted by local ranges

Subroutine: calc_lbprop_stats_abc2

Index # Index Index description Grouping metric? Minimum number of neighbour sets
21 LBPROP_STATS_ABC2 List of summary statistics (count mean min max median sum skewness kurtosis sd iqr) 1

Endemism

Absolute endemism

Description: Absolute endemism scores.

Subroutine: calc_endemism_absolute

Index # Index Index description Grouping metric? Minimum number of neighbour sets
22 END_ABS1 Count of labels entirely endemic to neighbour set 1 region grower 1
23 END_ABS1_P Proportion of labels entirely endemic to neighbour set 1 region grower 1
24 END_ABS2 Count of labels entirely endemic to neighbour set 2 region grower 1
25 END_ABS2_P Proportion of labels entirely endemic to neighbour set 2 region grower 1
26 END_ABS_ALL Count of labels entirely endemic to neighbour sets 1 and 2 combined region grower 1
27 END_ABS_ALL_P Proportion of labels entirely endemic to neighbour sets 1 and 2 combined region grower 1

Absolute endemism lists

Description: Lists underlying the absolute endemism scores.

Subroutine: calc_endemism_absolute_lists

Index # Index Index description Grouping metric? Minimum number of neighbour sets
28 END_ABS1_LIST List of labels entirely endemic to neighbour set 1 1
29 END_ABS2_LIST List of labels entirely endemic to neighbour set 1 1
30 END_ABS_ALL_LIST List of labels entirely endemic to neighbour sets 1 and 2 combined 1

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 Grouping metric? Minimum number of neighbour sets Formula Reference
31 ENDC_CWE Corrected weighted endemism 1 =\frac{ENDC\_WE}{ENDC\_RICHNESS}
32 ENDC_RICHNESS Richness used in ENDC_CWE (same as index RICHNESS_SET1) 1
33 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 ![=\sum_{t \in T} \frac {1} {R_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {1} {R_t}) where t is a label (taxon) in the set of labels (taxa) T in neighbour set 1, and R_t is the global range of label t 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
34 ENDC_WE Weighted endemism 1 ![=\sum_{t \in T} \frac {r_t} {R_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {r_t} {R_t}) where t is a label (taxon) in the set of labels (taxa) T in neighbour set 1, r_t is the local range (the number of elements containing label t within neighbour sets 1 & 2, this is also its value in list ABC2_LABELS_ALL), and R_t is the global range of label t 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 et al. (2013) J Biogeog. http://dx.doi.org/10.1111/jbi.12001

Index # Index Index description Grouping metric? Minimum number of neighbour sets
35 ENDC_HPART_0 List of the proportional contribution of labels to the endemism central calculations, hierarchical level 0 1
36 ENDC_HPART_1 List of the proportional contribution of labels to the endemism central calculations, hierarchical level 1 1
37 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
38 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
39 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
40 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
41 ENDC_HPART_OME_0 List of the observed minus expected proportional contribution of labels to the endemism central calculations , hierarchical level 0 1
42 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 Grouping metric? Minimum number of neighbour sets
43 ENDC_RANGELIST List of ranges for each label used in the endemism central calculations 1
44 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 Grouping metric? Minimum number of neighbour sets Formula
45 ENDC_CWE_NORM Corrected weighted endemism normalised by groups 1 =\frac{ENDC\_CWE}{EL\_COUNT\_ALL}
46 ENDC_WE_NORM Weighted endemism normalised by groups 1 =\frac{ENDC\_WE}{EL\_COUNT\_ALL}

Endemism whole

Description: Calculate endemism using all labels found in both neighbour sets

Subroutine: calc_endemism_whole

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
47 ENDW_CWE Corrected weighted endemism region grower 1 =\frac{ENDW\_WE}{ENDW\_RICHNESS}
48 ENDW_RICHNESS Richness used in ENDW_CWE (same as index RICHNESS_ALL) region grower 1
49 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. region grower 1 ![=\sum_{t \in T} \frac {1} {R_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {1} {R_t}) where t is a label (taxon) in the set of labels (taxa) T across neighbour sets 1 & 2, and R_t is the global range of label t 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
50 ENDW_WE Weighted endemism region grower 1 ![=\sum_{t \in T} \frac {r_t} {R_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {r_t} {R_t}) where t is a label (taxon) in the set of labels (taxa) T across both neighbour sets, r_t is the local range (the number of elements containing label t within neighbour sets 1 & 2, this is also its value in list ABC2_LABELS_ALL), and R_t is the global range of label t 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 et al. (2013) J Biogeog. http://dx.doi.org/10.1111/jbi.12001

Index # Index Index description Grouping metric? Minimum number of neighbour sets
51 ENDW_HPART_0 List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 0 1
52 ENDW_HPART_1 List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 1 1
53 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
54 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
55 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
56 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
57 ENDW_HPART_OME_0 List of the observed minus expected proportional contribution of labels to the endemism whole calculations , hierarchical level 0 1
58 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 Grouping metric? Minimum number of neighbour sets
59 ENDW_RANGELIST List of ranges for each label used in the endemism whole calculations 1
60 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 Grouping metric? Minimum number of neighbour sets Formula
61 ENDW_CWE_NORM Corrected weighted endemism normalised by groups region grower 1 =\frac{ENDW\_CWE}{EL\_COUNT\_ALL}
62 ENDW_WE_NORM Weighted endemism normalised by groups region grower 1 =\frac{ENDW\_WE}{EL\_COUNT\_ALL}

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 Grouping metric? Minimum number of neighbour sets
63 HIER_A0 A score for level 0 1
64 HIER_A1 A score for level 1 1
65 HIER_ARAT1_0 Ratio of A scores, (HIER_A1 / HIER_A0) 1
66 HIER_ASUM0 Sum of shared label sample counts, level 0 1
67 HIER_ASUM1 Sum of shared label sample counts, level 1 1
68 HIER_ASUMRAT1_0 1 - Ratio of shared label sample counts, (HIER_ASUM1 / HIER_ASUM0) cluster metric 1
69 HIER_B0 B score for level 0 1
70 HIER_B1 B score for level 1 1
71 HIER_BRAT1_0 Ratio of B scores, (HIER_B1 / HIER_B0) 1
72 HIER_C0 C score for level 0 1
73 HIER_C1 C score for level 1 1
74 HIER_CRAT1_0 Ratio of C scores, (HIER_C1 / HIER_C0) 1

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 Grouping metric? Minimum number of neighbour sets
75 IEI_CV Coefficient of variation (IEI_SD / IEI_MEAN) region grower 1
76 IEI_GMEAN Geometric mean region grower 1
77 IEI_KURT Kurtosis region grower 1
78 IEI_MAX Maximum value (100th percentile) region grower 1
79 IEI_MEAN Mean cluster metric 1
80 IEI_MIN Minimum value (zero percentile) region grower 1
81 IEI_N Number of samples region grower 1
82 IEI_RANGE Range (max - min) region grower 1
83 IEI_SD Standard deviation region grower 1
84 IEI_SKEW Skewness region grower 1

Inter-event interval statistics data

Description: The underlying data used for the IEI stats.

Subroutine: calc_iei_data

Index # Index Index description Grouping metric? Minimum number of neighbour sets
85 IEI_DATA_ARRAY Interval data in array form. Multiple occurrences are repeated 1
86 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 Grouping metric? Minimum number of neighbour sets
87 EL_COUNT_ALL Count of elements in both neighbour sets region grower 1
88 EL_COUNT_SET1 Count of elements in neighbour set 1 1
89 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 Grouping metric? Minimum number of neighbour sets
90 EL_LIST_ALL List of elements in both neighour sets 2
91 EL_LIST_SET1 List of elements in neighbour set 1 1
92 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 Grouping metric? Minimum number of neighbour sets
93 ABC_A Count of labels common to both neighbour sets region grower 1
94 ABC_ABC Total label count across both neighbour sets (same as RICHNESS_ALL) region grower 1
95 ABC_B Count of labels unique to neighbour set 1 region grower 1
96 ABC_C Count of labels unique to neighbour set 2 region grower 1

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 Grouping metric? Minimum number of neighbour sets
97 ABC_D Count of labels not in either neighbour set (D score) region grower 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 Grouping metric? Minimum number of neighbour sets
98 ABC2_LABELS_ALL List of labels in both neighbour sets 2
99 ABC2_LABELS_SET1 List of labels in neighbour set 1 1
100 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 Grouping metric? Minimum number of neighbour sets
101 ABC2_MEAN_ALL Mean label range in both element sets region grower 1
102 ABC2_MEAN_SET1 Mean label range in neighbour set 1 1
103 ABC2_MEAN_SET2 Mean label range in neighbour set 2 2
104 ABC2_SD_ALL Standard deviation of label ranges in both element sets region grower 2
105 ABC2_SD_SET1 Standard deviation of label ranges in neighbour set 1 1
106 ABC2_SD_SET2 Standard deviation of label ranges in neighbour set 2 2

Non-empty element counts

Description: Counts of non-empty elements in neighbour sets 1 and 2.

Subroutine: calc_nonempty_elements_used

Index # Index Index description Grouping metric? Minimum number of neighbour sets
107 EL_COUNT_NONEMPTY_ALL Count of non-empty elements in both neighbour sets region grower 1
108 EL_COUNT_NONEMPTY_SET1 Count of non-empty elements in neighbour set 1 1
109 EL_COUNT_NONEMPTY_SET2 Count of non-empty elements in neighbour set 2 2

Rank relative sample counts per label

Description: Find the per-group percentile rank of all labels across both neighbour sets, relative to the processing group. An absence is treated as a sample count of zero.

Subroutine: calc_label_count_quantile_position

Index # Index Index description Grouping metric? Minimum number of neighbour sets
110 LABEL_COUNT_RANK_PCT List of percentile ranks for each label's sample count 1

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

Reference: Garcillan et al. (2003) J Veget. Sci. http://dx.doi.org/10.1111/j.1654-1103.2003.tb02174.x

Formula: ![=1 - \frac{richness}{sum\ of\ the\ sample\ counts}](http://latex.codecogs.com/png.latex?=1 - \frac{richness}{sum\ of\ the\ sample\ counts})

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
111 REDUNDANCY_ALL for both neighbour sets region grower 1 ![=1 - \frac{RICHNESS\_ALL}{ABC3\_SUM\_ALL}](http://latex.codecogs.com/png.latex?=1 - \frac{RICHNESS\_ALL}{ABC3\_SUM\_ALL})
112 REDUNDANCY_SET1 for neighour set 1 1 ![=1 - \frac{RICHNESS\_SET1}{ABC3\_SUM\_SET1}](http://latex.codecogs.com/png.latex?=1 - \frac{RICHNESS\_SET1}{ABC3\_SUM\_SET1})
113 REDUNDANCY_SET2 for neighour set 2 2 ![=1 - \frac{RICHNESS\_SET2}{ABC3\_SUM\_SET2}](http://latex.codecogs.com/png.latex?=1 - \frac{RICHNESS\_SET2}{ABC3\_SUM\_SET2})

Richness

Description: Count the number of labels in the neighbour sets

Subroutine: calc_richness

Index # Index Index description Grouping metric? Minimum number of neighbour sets
114 RICHNESS_ALL for both sets of neighbours region grower 1
115 RICHNESS_SET1 for neighbour set 1 1
116 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 Grouping metric? Minimum number of neighbour sets
117 ABC3_LABELS_ALL List of labels in both neighbour sets with their sample counts as the values. 2
118 ABC3_LABELS_SET1 List of labels in neighbour set 1. Values are the sample counts. 1
119 ABC3_LABELS_SET2 List of labels in neighbour set 2. Values are the sample counts. 2

Sample count quantiles

Description: Quantiles of the sample counts across the neighbour sets.

Subroutine: calc_local_sample_count_quantiles

Index # Index Index description Grouping metric? Minimum number of neighbour sets
120 ABC3_QUANTILES_ALL List of quantiles for both neighbour sets 2
121 ABC3_QUANTILES_SET1 List of quantiles for neighbour set 1 1
122 ABC3_QUANTILES_SET2 List of quantiles for neighbour set 2 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 Grouping metric? Minimum number of neighbour sets
123 ABC3_MEAN_ALL Mean of label sample counts across both element sets. region grower 2
124 ABC3_MEAN_SET1 Mean of label sample counts in neighbour set1. 1
125 ABC3_MEAN_SET2 Mean of label sample counts in neighbour set 2. 2
126 ABC3_SD_ALL Standard deviation of label sample counts in both element sets. region grower 2
127 ABC3_SD_SET1 Standard deviation of sample counts in neighbour set 1. 1
128 ABC3_SD_SET2 Standard deviation of label sample counts in neighbour set 2. 2
129 ABC3_SUM_ALL Sum of the label sample counts across both neighbour sets. region grower 2
130 ABC3_SUM_SET1 Sum of the label sample counts across both neighbour sets. 1
131 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 Grouping metric? Minimum number of neighbour sets
132 MXD_COUNT Count of comparisons used. region grower 1
133 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. 1
134 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. 1
135 MXD_MEAN Mean dissimilarity of labels in set 1 to those in set 2. cluster metric 1
136 MXD_VARIANCE Variance of the dissimilarity values, set 1 vs set 2. cluster metric 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 Grouping metric? Minimum number of neighbour sets
137 MX_KURT Kurtosis region grower 1
138 MX_LABELS List of the matrix labels in the neighbour sets 1
139 MX_MAXVALUE Maximum value region grower 1
140 MX_MEAN Mean region grower 1
141 MX_MEDIAN Median region grower 1
142 MX_MINVALUE Minimum value region grower 1
143 MX_N Number of samples (matrix elements, not labels) region grower 1
144 MX_PCT05 5th percentile value region grower 1
145 MX_PCT25 First quartile (25th percentile) region grower 1
146 MX_PCT75 Third quartile (75th percentile) region grower 1
147 MX_PCT95 95th percentile value region grower 1
148 MX_RANGE Range (max-min) region grower 1
149 MX_SD Standard deviation region grower 1
150 MX_SKEW Skewness region grower 1
151 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: ![=\sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j](http://latex.codecogs.com/png.latex?=\\sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j) where p_i and p_j are the sample counts for the i'th and j'th labels, d_{ij} is the matrix value for the pair of labels ij and L is the set of labels across both neighbour sets that occur in the matrix.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
152 MX_RAO_QE Matrix weighted quadratic entropy region grower 1
153 MX_RAO_TLABELS List of labels and values used in the MX_RAO_QE calculations 1
154 MX_RAO_TN Count of comparisons used to calculate MX_RAO_QE region grower 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 Grouping metric? Minimum number of neighbour sets
155 NUM_DATA_ARRAY Numeric label data in array form. Multiple occurrences are repeated based on their sample counts. 1

Numeric label dissimilarity

Description: Compare the set of numeric labels in one neighbour set with those in another.

Subroutine: calc_numeric_label_dissimilarity

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
156 NUMD_ABSMEAN Mean absolute dissimilarity of labels in set 1 to those in set 2. cluster metric 1 ![=\frac{\sum_{l_{1i} \in L_1} \sum_{l_{2j} \in L_2} abs (l_{1i} - l_{2j})(w{1i} \times w{2j})}{n_1 \times n_2}](http://latex.codecogs.com/png.latex?=\\frac{\\sum_{l_{1i} \in L_1} \sum{l{2j} \in L_2} abs (l_{1i} - l_{2j})(w_{1i} \times w_{2j})}{n_1 \times n_2})whereL1 and L2 are the labels in neighbour sets 1 and 2 respectively, and n1 and n2 are the sample counts in neighbour sets 1 and 2
157 NUMD_COUNT Count of comparisons used. region grower 1 ![=n1 * n2](http://latex.codecogs.com/png.latex?=n1 * n2)where values are as for NUMD\_ABSMEAN
158 NUMD_VARIANCE Variance of the dissimilarity values (mean squared deviation), set 1 vs set 2. cluster metric 1 ![=\frac{\sum_{l_{1i} \in L_1} \sum_{l_{2j} \in L_2} (l_{1i} - l_{2j})^2(w{1i} \times w{2j})}{n_1 \times n_2}](http://latex.codecogs.com/png.latex?=\\frac{\\sum_{l_{1i} \in L_1} \sum{l{2j} \in L_2} (l_{1i} - l_{2j})^2(w_{1i} \times w_{2j})}{n_1 \times n_2})where values are as for NUMD\_ABSMEAN

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 Grouping metric? Minimum number of neighbour sets
159 NUM_GMEAN Geometric mean region grower 1
160 NUM_HMEAN Harmonic mean region grower 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 Grouping metric? Minimum number of neighbour sets
161 NUM_Q005 5th percentile region grower 1
162 NUM_Q010 10th percentile region grower 1
163 NUM_Q015 15th percentile region grower 1
164 NUM_Q020 20th percentile region grower 1
165 NUM_Q025 25th percentile region grower 1
166 NUM_Q030 30th percentile region grower 1
167 NUM_Q035 35th percentile region grower 1
168 NUM_Q040 40th percentile region grower 1
169 NUM_Q045 45th percentile region grower 1
170 NUM_Q050 50th percentile region grower 1
171 NUM_Q055 55th percentile region grower 1
172 NUM_Q060 60th percentile region grower 1
173 NUM_Q065 65th percentile region grower 1
174 NUM_Q070 70th percentile region grower 1
175 NUM_Q075 75th percentile region grower 1
176 NUM_Q080 80th percentile region grower 1
177 NUM_Q085 85th percentile region grower 1
178 NUM_Q090 90th percentile region grower 1
179 NUM_Q095 95th percentile region grower 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 Grouping metric? Minimum number of neighbour sets
180 NUM_CV Coefficient of variation (NUM_SD / NUM_MEAN) region grower 1
181 NUM_KURT Kurtosis region grower 1
182 NUM_MAX Maximum value (100th quantile) region grower 1
183 NUM_MEAN Mean region grower 1
184 NUM_MIN Minimum value (zero quantile) region grower 1
185 NUM_N Number of samples region grower 1
186 NUM_RANGE Range (max - min) region grower 1
187 NUM_SD Standard deviation region grower 1
188 NUM_SKEW Skewness region grower 1

Numeric labels Gi* statistic

Description: Getis-Ord Gi* statistic for numeric labels across both neighbour sets

Subroutine: calc_num_labels_gistar

Reference: Getis and Ord (1992) Geographical Analysis. http://dx.doi.org/10.1111/j.1538-4632.1992.tb00261.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
189 NUM_GISTAR List of Gi* scores region grower 1

PhyloCom Indices

NRI and NTI expected values

Description: Expected values used in the NRI and NTI calculations. Derived using a null model without resampling where each label has an equal probability of being selected (a null model of even distrbution). The expected mean and SD are the same for each unique number of labels across all neighbour sets. This means if you have three neighbour sets, each with three labels, then the expected values will be identical for each, even if the labels are completely different.

Subroutine: calc_nri_nti_expected_values

Reference: Webb et al. (2008) http://dx.doi.org/10.1093/bioinformatics/btn358

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
190 PHYLO_NRI_NTI_SAMPLE_N Number of random resamples used region grower 1
191 PHYLO_NRI_SAMPLE_MEAN Expected mean of pair-wise distances region grower 1
192 PHYLO_NRI_SAMPLE_SD Expected standard deviation of pair-wise distances region grower 1
193 PHYLO_NTI_SAMPLE_MEAN Expected mean of nearest taxon distances region grower 1
194 PHYLO_NTI_SAMPLE_SD Expected standard deviation of nearest taxon distances region grower 1

NRI and NTI, abundance weighted

Description: NRI and NTI for the set of labels on the tree in the sample. This version is -1* the Phylocom implementation, so values >0 have longer branches than expected. Abundance weighted.

Subroutine: calc_nri_nti3

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
195 PHYLO_NRI3 Net Relatedness Index, abundance weighted region grower 1
196 PHYLO_NTI3 Nearest Taxon Index, abundance weighted region grower 1

NRI and NTI, local range weighted

Description: NRI and NTI for the set of labels on the tree in the sample. This version is -1* the Phylocom implementation, so values >0 have longer branches than expected. Local range weighted.

Subroutine: calc_nri_nti2

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
197 PHYLO_NRI2 Net Relatedness Index, local range weighted region grower 1
198 PHYLO_NTI2 Nearest Taxon Index, local range weighted region grower 1

NRI and NTI, unweighted

Description: NRI and NTI for the set of labels on the tree in the sample. This version is -1* the Phylocom implementation, so values >0 have longer branches than expected. Not weighted by sample counts, so each label counts once only.

Subroutine: calc_nri_nti1

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
199 PHYLO_NRI1 Net Relatedness Index, unweighted region grower 1 ![NRI = \frac{MPD_{obs} - mean(MPD_{rand})}{sd(MPD_{rand})}](http://latex.codecogs.com/png.latex?NRI = \frac{MPD_{obs} - mean(MPD_{rand})}{sd(MPD_{rand})})
200 PHYLO_NTI1 Nearest Taxon Index, unweighted region grower 1 ![NTI = \frac{MNTD_{obs} - mean(MNTD_{rand})}{sd(MNTD_{rand})}](http://latex.codecogs.com/png.latex?NTI = \frac{MNTD_{obs} - mean(MNTD_{rand})}{sd(MNTD_{rand})})

Phylogenetic and Nearest taxon distances, abundance weighted

Description: Distance stats from each label to the nearest label along the tree. Compares with all other labels across both neighbour sets. Weighted by sample counts (which currently must be integers)

Subroutine: calc_phylo_mpd_mntd3

Reference: Webb et al. (2008) http://dx.doi.org/10.1093/bioinformatics/btn358

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
201 PMPD3_MAX Maximum of pairwise phylogenetic distances region grower 1
202 PMPD3_MEAN Mean of pairwise phylogenetic distances region grower 1 ![MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j](http://latex.codecogs.com/png.latex?MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j)where ![d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b](http://latex.codecogs.com/png.latex?d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b)is the sum of the branch lengths along the path connecting t_iandt_jsuch that L_bis the length of each branch in the set of branchesB
203 PMPD3_MIN Minimum of pairwise phylogenetic distances region grower 1
204 PMPD3_N Count of pairwise phylogenetic distances region grower 1
205 PMPD3_RMSD Root mean squared pairwise phylogenetic distances region grower 1
206 PNTD3_MAX Maximum of nearest taxon distances region grower 1
207 PNTD3_MEAN Mean of nearest taxon distances region grower 1
208 PNTD3_MIN Minimum of nearest taxon distances region grower 1
209 PNTD3_N Count of nearest taxon distances region grower 1
210 PNTD3_RMSD Root mean squared nearest taxon distances region grower 1

Phylogenetic and Nearest taxon distances, local range weighted

Description: Distance stats from each label to the nearest label along the tree. Compares with all other labels across both neighbour sets. Weighted by sample counts

Subroutine: calc_phylo_mpd_mntd2

Reference: Webb et al. (2008) http://dx.doi.org/10.1093/bioinformatics/btn358

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
211 PMPD2_MAX Maximum of pairwise phylogenetic distances region grower 1
212 PMPD2_MEAN Mean of pairwise phylogenetic distances region grower 1 ![MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j](http://latex.codecogs.com/png.latex?MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j)where ![d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b](http://latex.codecogs.com/png.latex?d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b)is the sum of the branch lengths along the path connecting t_iandt_jsuch that L_bis the length of each branch in the set of branchesB
213 PMPD2_MIN Minimum of pairwise phylogenetic distances region grower 1
214 PMPD2_N Count of pairwise phylogenetic distances region grower 1
215 PMPD2_RMSD Root mean squared pairwise phylogenetic distances region grower 1
216 PNTD2_MAX Maximum of nearest taxon distances region grower 1
217 PNTD2_MEAN Mean of nearest taxon distances region grower 1
218 PNTD2_MIN Minimum of nearest taxon distances region grower 1
219 PNTD2_N Count of nearest taxon distances region grower 1
220 PNTD2_RMSD Root mean squared nearest taxon distances region grower 1

Phylogenetic and Nearest taxon distances, unweighted

Description: Distance stats from each label to the nearest label along the tree. Compares with all other labels across both neighbour sets.

Subroutine: calc_phylo_mpd_mntd1

Reference: Webb et al. (2008) http://dx.doi.org/10.1093/bioinformatics/btn358

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
221 PMPD1_MAX Maximum of pairwise phylogenetic distances region grower 1
222 PMPD1_MEAN Mean of pairwise phylogenetic distances region grower 1 ![MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j](http://latex.codecogs.com/png.latex?MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j)where ![d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b](http://latex.codecogs.com/png.latex?d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b)is the sum of the branch lengths along the path connecting t_iandt_jsuch that L_bis the length of each branch in the set of branchesB
223 PMPD1_MIN Minimum of pairwise phylogenetic distances region grower 1
224 PMPD1_N Count of pairwise phylogenetic distances region grower 1
225 PMPD1_RMSD Root mean squared pairwise phylogenetic distances region grower 1
226 PNTD1_MAX Maximum of nearest taxon distances region grower 1
227 PNTD1_MEAN Mean of nearest taxon distances region grower 1
228 PNTD1_MIN Minimum of nearest taxon distances region grower 1
229 PNTD1_N Count of nearest taxon distances region grower 1
230 PNTD1_RMSD Root mean squared nearest taxon distances region grower 1

Phylogenetic Endemism Indices

Corrected weighted phylogenetic endemism

Description: What proportion of the PD is range-restricted to this neighbour set?

Subroutine: calc_phylo_corrected_weighted_endemism

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
231 PE_CWE Corrected weighted endemism. This is the phylogenetic analogue of corrected weighted endemism. region grower 1 ![PE\_WE / PD](http://latex.codecogs.com/png.latex?PE\\_WE / PD)

Corrected weighted phylogenetic endemism, central variant

Description: What proportion of the PD in neighbour set 1 is range-restricted to neighbour sets 1 and 2?

Subroutine: calc_pe_central_cwe

Index # Index Index description Grouping metric? Minimum number of neighbour sets
232 PEC_CWE Corrected weighted phylogenetic endemism, central variant region grower 1
233 PEC_CWE_PD PD used in the PEC_CWE index. region grower 1

Corrected weighted phylogenetic rarity

Description: What proportion of the PD is abundance-restricted to this neighbour set?

Subroutine: calc_phylo_corrected_weighted_rarity

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
234 PHYLO_RARITY_CWR Corrected weighted phylogenetic rarity. This is the phylogenetic rarity analogue of corrected weighted endemism. region grower 1 ![AED_T / PD](http://latex.codecogs.com/png.latex?AED_T / PD)

PD-Endemism

Description: Absolute endemism analogue of PE. It is the sum of the branch lengths restricted to the neighbour sets.

Subroutine: calc_pd_endemism

Reference: See Faith (2004) Cons Biol. http://dx.doi.org/10.1111/j.1523-1739.2004.00330.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
235 PD_ENDEMISM Phylogenetic Diversity Endemism region grower 1
236 PD_ENDEMISM_P Phylogenetic Diversity Endemism, as a proportion of the whole tree region grower 1
237 PD_ENDEMISM_WTS Phylogenetic Diversity Endemism weights per node found only in the neighbour set 1

PE clade contributions

Description: Contribution of each node and its descendents to the Phylogenetic endemism (PE) calculation.

Subroutine: calc_pe_clade_contributions

Index # Index Index description Grouping metric? Minimum number of neighbour sets
238 PE_CLADE_CONTR List of node (clade) contributions to the PE calculation 1
239 PE_CLADE_CONTR_P List of node (clade) contributions to the PE calculation, proportional to the entire tree 1
240 PE_CLADE_SCORE List of PE scores for each node (clade), being the sum of all descendent PE weights 1

PE clade loss

Description: How much of the PE would be lost if a clade were to be removed? Calculates the clade PE below the last ancestral node in the neighbour set which would still be in the neighbour set.

Subroutine: calc_pe_clade_loss

Index # Index Index description Grouping metric? Minimum number of neighbour sets
241 PE_CLADE_LOSS_CONTR List of the proportion of the PE score which would be lost if each clade were removed. 1
242 PE_CLADE_LOSS_CONTR_P As per PE_CLADE_LOSS but proportional to the entire tree 1
243 PE_CLADE_LOSS_SCORE List of how much PE would be lost if each clade were removed. 1

PE clade loss (ancestral component)

Description: How much of the PE clade loss is due to the ancestral branches? The score is zero when there is no ancestral loss.

Subroutine: calc_pe_clade_loss_ancestral

Index # Index Index description Grouping metric? Minimum number of neighbour sets
244 PE_CLADE_LOSS_ANC List of how much ancestral PE would be lost if each clade were removed. The value is 0 when no ancestral PE is lost. 1
245 PE_CLADE_LOSS_ANC_P List of the proportion of the clade's PE loss that is due to the ancestral branches. 1

Phylogenetic Endemism

Description: Phylogenetic endemism (PE). Uses labels across 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; Laity et al. (2015) http://dx.doi.org/10.1016/j.scitotenv.2015.04.113; Laffan et al. (2016) http://dx.doi.org/10.1111/2041-210X.12513

Formula: ![PE = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}](http://latex.codecogs.com/png.latex?PE = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}) where \Lambda is the set of branches found across neighbour sets 1 and 2, L_\lambda is the length of branch \lambda , r_\lambda is the local range of branch \lambda (the number of groups in neighbour sets 1 and 2 containing it), and R_\lambda is the global range of branch \lambda (the number of groups across the entire data set containing it).

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
246 PE_WE Phylogenetic endemism region grower 1
247 PE_WE_P Phylogenetic weighted endemism as a proportion of the total tree length region grower 1 ![PE\_WE / L](http://latex.codecogs.com/png.latex?PE\\_WE / L) where L is the sum of all branch lengths in the trimmed tree

Phylogenetic Endemism central

Description: A variant of Phylogenetic endemism (PE) that uses labels from neighbour set 1 but local ranges from across both neighbour sets 1 and 2. Identical to PE if only one neighbour set is specified.

Subroutine: calc_pe_central

Reference: Rosauer et al (2009) Mol. Ecol. http://dx.doi.org/10.1111/j.1365-294X.2009.04311.x

Formula: ![PEC = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}](http://latex.codecogs.com/png.latex?PEC = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}) where \Lambda is the set of branches found across neighbour set 1 only, L_\lambda is the length of branch \lambda , r_\lambda is the local range of branch \lambda (the number of groups in neighbour sets 1 and 2 containing it), and R_\lambda is the global range of branch \lambda (the number of groups across the entire data set containing it).

Index # Index Index description Grouping metric? Minimum number of neighbour sets
248 PEC_WE Phylogenetic endemism, central variant region grower 1
249 PEC_WE_P Phylogenetic weighted endemism as a proportion of the total tree length, central variant region grower 1

Phylogenetic Endemism central lists

Description: Lists underlying the phylogenetic endemism central indices. Uses labels from neighbour set one but local ranges from across both neighbour sets.

Subroutine: calc_pe_central_lists

Reference: Rosauer et al (2009) Mol. Ecol. http://dx.doi.org/10.1111/j.1365-294X.2009.04311.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
250 PEC_LOCAL_RANGELIST Phylogenetic endemism local range lists, central variant 1
251 PEC_RANGELIST Phylogenetic endemism global range lists, central variant 1
252 PEC_WTLIST Phylogenetic endemism weights, central variant 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 Grouping metric? Minimum number of neighbour sets
253 PE_LOCAL_RANGELIST Local node ranges used in PE calculations (number of groups in which a node is found) 1
254 PE_RANGELIST Node ranges used in PE calculations 1
255 PE_WTLIST Node weights used in PE calculations 1

Phylogenetic Endemism single

Description: PE scores, but not weighted by local ranges. This is the strict interpretation of the formula given in Rosauer et al. (2009), although the approach has always been implemented as the fraction of each branch's geographic range that is found in the sample window (see formula for PE_WE).

Subroutine: calc_pe_single

Reference: Rosauer et al (2009) Mol. Ecol. http://dx.doi.org/10.1111/j.1365-294X.2009.04311.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets
256 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. region grower 1
257 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. region grower 1

Phylogenetic Indices

Count labels on tree

Description: Count the number of labels that are on the tree

Subroutine: calc_count_labels_on_tree

Index # Index Index description Grouping metric? Minimum number of neighbour sets
258 PHYLO_LABELS_ON_TREE_COUNT The number of labels that are found on the tree, across both neighbour sets region grower 1

Evolutionary distinctiveness

Description: Evolutionary distinctiveness metrics (AED, ED, ES) Label values are constant for all neighbourhoods in which each label is found.

Subroutine: calc_phylo_aed

Reference: Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets Reference
259 PHYLO_AED_LIST Abundance weighted ED per terminal label 1 Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x
260 PHYLO_ED_LIST "Fair proportion" partitioning of PD per terminal label 1 Isaac et al. (2007) http://dx.doi.org/10.1371/journal.pone.0000296
261 PHYLO_ES_LIST Equal splits partitioning of PD per terminal label 1 Redding & Mooers (2006) http://dx.doi.org/10.1111%2Fj.1523-1739.2006.00555.x

Evolutionary distinctiveness per site

Description: Site level evolutionary distinctiveness

Subroutine: calc_phylo_aed_t

Reference: Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets Reference
262 PHYLO_AED_T Abundance weighted ED_t (sum of values in PHYLO_AED_LIST times their abundances). This is equivalent to a phylogenetic rarity score (see phylogenetic endemism) region grower 1 Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x

Evolutionary distinctiveness per terminal taxon per site

Description: Site level evolutionary distinctiveness per terminal taxon

Subroutine: calc_phylo_aed_t_wtlists

Reference: Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x

Index # Index Index description Grouping metric? Minimum number of neighbour sets Reference
263 PHYLO_AED_T_WTLIST Abundance weighted ED per terminal taxon (the AED score of each taxon multiplied by its abundance in the sample) 1 Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x
264 PHYLO_AED_T_WTLIST_P Proportional contribution of each terminal taxon to the AED_T score 1 Cadotte & Davies (2010) http://dx.doi.org/10.1111/j.1472-4642.2010.00650.x

Labels not on tree

Description: Create a hash of the labels that are not on the tree

Subroutine: calc_labels_not_on_tree

Index # Index Index description Grouping metric? Minimum number of neighbour sets
265 PHYLO_LABELS_NOT_ON_TREE A hash of labels that are not found on the tree, across both neighbour sets 1
266 PHYLO_LABELS_NOT_ON_TREE_N Number of labels not on the tree region grower 1
267 PHYLO_LABELS_NOT_ON_TREE_P Proportion of labels not on the tree region grower 1

Labels on tree

Description: Create a hash of the labels that are on the tree

Subroutine: calc_labels_on_tree

Index # Index Index description Grouping metric? Minimum number of neighbour sets
268 PHYLO_LABELS_ON_TREE A hash of labels that are found on the tree, across both neighbour sets 1

PD clade contributions

Description: Contribution of each node and its descendents to the Phylogenetic diversity (PD) calculation.

Subroutine: calc_pd_clade_contributions

Index # Index Index description Grouping metric? Minimum number of neighbour sets
269 PD_CLADE_CONTR List of node (clade) contributions to the PD calculation 1
270 PD_CLADE_CONTR_P List of node (clade) contributions to the PD calculation, proportional to the entire tree 1
271 PD_CLADE_SCORE List of PD scores for each node (clade), being the sum of all descendent branch lengths 1

PD clade loss

Description: How much of the PD would be lost if a clade were to be removed? Calculates the clade PD below the last ancestral node in the neighbour set which would still be in the neighbour set.

Subroutine: calc_pd_clade_loss

Index # Index Index description Grouping metric? Minimum number of neighbour sets
272 PD_CLADE_LOSS_CONTR List of the proportion of the PD score which would be lost if each clade were removed. 1
273 PD_CLADE_LOSS_CONTR_P As per PD_CLADE_LOSS but proportional to the entire tree 1
274 PD_CLADE_LOSS_SCORE List of how much PD would be lost if each clade were removed. 1

PD clade loss (ancestral component)

Description: How much of the PD clade loss is due to the ancestral branches? The score is zero when there is no ancestral loss.

Subroutine: calc_pd_clade_loss_ancestral

Index # Index Index description Grouping metric? Minimum number of neighbour sets
275 PD_CLADE_LOSS_ANC List of how much ancestral PE would be lost if each clade were removed. The value is 0 when no ancestral PD is lost. 1
276 PD_CLADE_LOSS_ANC_P List of the proportion of the clade's PD loss that is due to the ancestral branches. 1

Phylogenetic Abundance

Description: Phylogenetic abundance based on branch lengths back to the root of the tree. Uses labels in both neighbourhoods.

Subroutine: calc_phylo_abundance

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
277 PHYLO_ABUNDANCE Phylogenetic abundance region grower 1 ![=\sum_{c \in C} A \times L_c](http://latex.codecogs.com/png.latex?=\\sum_{c \in C} A \times L_c) where Cis the set of branches in the minimum spanning path joining the labels in both neighbour sets to the root of the tree,c is a branch (a single segment between two nodes) in the spanning path C, and L_c is the length of branch c, and A is the abundance of that branch (the sum of its descendant label abundances).
278 PHYLO_ABUNDANCE_BRANCH_HASH Phylogenetic abundance per branch 1

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 Grouping metric? Minimum number of neighbour sets Formula Reference
279 PD Phylogenetic diversity region grower 1 ![=\sum_{c \in C} L_c](http://latex.codecogs.com/png.latex?=\\sum_{c \in C} L_c) where Cis the set of branches in the minimum spanning path joining the labels in both neighbour sets to the root of the tree,c is a branch (a single segment between two nodes) in the spanning path C, and L_c is the length of branch c. Faith (1992) Biol. Cons. http://dx.doi.org/10.1016/0006-3207(92)91201-3
280 PD_P Phylogenetic diversity as a proportion of total tree length region grower 1 ![=\frac { PD }{ \sum_{c \in C} L_c }](http://latex.codecogs.com/png.latex?=\\frac { PD }{ \sum_{c \in C} L_c }) where terms are the same as for PD, but c, C and L_c are calculated for all nodes in the tree.
281 PD_P_per_taxon Phylogenetic diversity per taxon as a proportion of total tree length region grower 1 ![=\frac { PD\_P }{ RICHNESS\_ALL }](http://latex.codecogs.com/png.latex?=\\frac { PD\_P }{ RICHNESS\_ALL })
282 PD_per_taxon Phylogenetic diversity per taxon region grower 1 ![=\frac { PD }{ RICHNESS\_ALL }](http://latex.codecogs.com/png.latex?=\\frac { PD }{ RICHNESS\_ALL })

Phylogenetic Diversity node list

Description: Phylogenetic diversity (PD) nodes used.

Subroutine: calc_pd_node_list

Index # Index Index description Grouping metric? Minimum number of neighbour sets
283 PD_INCLUDED_NODE_LIST List of tree nodes included in the PD calculations 1

Phylogenetic Diversity terminal node count

Description: Number of terminal nodes in neighbour sets 1 and 2.

Subroutine: calc_pd_terminal_node_count

Index # Index Index description Grouping metric? Minimum number of neighbour sets
284 PD_INCLUDED_TERMINAL_NODE_COUNT Count of tree terminal nodes included in the PD calculations region grower 1

Phylogenetic Diversity terminal node list

Description: Phylogenetic diversity (PD) terminal nodes used.

Subroutine: calc_pd_terminal_node_list

Index # Index Index description Grouping metric? Minimum number of neighbour sets
285 PD_INCLUDED_TERMINAL_NODE_LIST List of tree terminal nodes included in the PD 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 Grouping metric? Minimum number of neighbour sets
286 TD_DENOMINATOR Denominator from TD_DISTINCTNESS calcs region grower 1
287 TD_DISTINCTNESS Taxonomic distinctness region grower 1
288 TD_NUMERATOR Numerator from TD_DISTINCTNESS calcs region grower 1
289 TD_VARIATION Variation of the taxonomic distinctness region grower 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 Grouping metric? Minimum number of neighbour sets Formula
290 TDB_DENOMINATOR Denominator from TDB_DISTINCTNESS region grower 1
291 TDB_DISTINCTNESS Taxonomic distinctness, binary weighted region grower 1 ![=\frac{\sum \sum_{i \neq j} \omega_{ij}}{s(s-1)}](http://latex.codecogs.com/png.latex?=\\frac{\\sum \sum_{i \neq j} \omega_{ij}}{s(s-1)})where \omega_{ij}is the path length from label ito the ancestor node shared with j
292 TDB_NUMERATOR Numerator from TDB_DISTINCTNESS region grower 1
293 TDB_VARIATION Variation of the binary taxonomic distinctness region grower 1 ![=\frac{\sum \sum_{i \neq j} \omega_{ij}^2}{s(s-1)} - \bar{\omega}^2](http://latex.codecogs.com/png.latex?=\\frac{\\sum \sum_{i \neq j} \omega_{ij}^2}{s(s-1)} - \bar{\omega}^2)where ![\bar{\omega} = \frac{\sum \sum_{i \neq j} \omega_{ij}}{s(s-1)} \equiv TDB\DISTINCTNESS](http://latex.codecogs.com/png.latex?\\bar{\\omega} = \frac{\sum \sum{i \neq j} \omega_{ij}}{s(s-1)} \equiv TDB\_DISTINCTNESS)

Phylogenetic Indices (relative)

Labels not on trimmed tree

Description: Create a hash of the labels that are not on the trimmed tree

Subroutine: calc_labels_not_on_trimmed_tree

Index # Index Index description Grouping metric? Minimum number of neighbour sets
294 PHYLO_LABELS_NOT_ON_TRIMMED_TREE A hash of labels that are not found on the tree after it has been trimmed to the basedata, across both neighbour sets 1
295 PHYLO_LABELS_NOT_ON_TRIMMED_TREE_N Number of labels not on the trimmed tree region grower 1
296 PHYLO_LABELS_NOT_ON_TRIMMED_TREE_P Proportion of labels not on the trimmed tree region grower 1

Labels on trimmed tree

Description: Create a hash of the labels that are on the trimmed tree

Subroutine: calc_labels_on_trimmed_tree

Index # Index Index description Grouping metric? Minimum number of neighbour sets
297 PHYLO_LABELS_ON_TRIMMED_TREE A hash of labels that are found on the tree after it has been trimmed to match the basedata, across both neighbour sets 1

Relative Phylogenetic Diversity, type 1

Description: Relative Phylogenetic Diversity (RPD). The ratio of the tree's PD to a null model of PD evenly distributed across terminals and where ancestral nodes are collapsed to zero length.

Subroutine: calc_phylo_rpd1

Reference: Mishler et al. (2014) http://dx.doi.org/10.1038/ncomms5473

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
298 PHYLO_RPD1 RPD1 region grower 1
299 PHYLO_RPD_DIFF1 How much more or less PD is there than expected, in original tree units. region grower 1 ![=tree\_length \times (PD\_P - PHYLO\_RPD\_NULL1)](http://latex.codecogs.com/png.latex?=tree\\_length \times (PD\_P - PHYLO\_RPD\_NULL1))
300 PHYLO_RPD_NULL1 Null model score used as the denominator in the RPD1 calculations region grower 1

Relative Phylogenetic Diversity, type 2

Description: Relative Phylogenetic Diversity (RPD), type 2. The ratio of the tree's PD to a null model of PD evenly distributed across all nodes (all branches are of equal length).

Subroutine: calc_phylo_rpd2

Reference: Mishler et al. (2014) http://dx.doi.org/10.1038/ncomms5473

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
301 PHYLO_RPD2 RPD2 region grower 1
302 PHYLO_RPD_DIFF2 How much more or less PD is there than expected, in original tree units. region grower 1 ![=tree\_length \times (PD\_P - PHYLO\_RPD\_NULL2)](http://latex.codecogs.com/png.latex?=tree\\_length \times (PD\_P - PHYLO\_RPD\_NULL2))
303 PHYLO_RPD_NULL2 Null model score used as the denominator in the RPD2 calculations region grower 1

Relative Phylogenetic Endemism, central

Description: Relative Phylogenetic Endemism (RPE). The ratio of the tree's PE to a null model where PE is calculated using a tree where all branches are of equal length. Same as RPE2 except it only uses the branches in the first neighbour set when more than one is set.

Subroutine: calc_phylo_rpe_central

Reference: Mishler et al. (2014) http://dx.doi.org/10.1038/ncomms5473

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
304 PHYLO_RPEC Relative Phylogenetic Endemism score, central region grower 1
305 PHYLO_RPE_DIFFC How much more or less PE is there than expected, in original tree units. region grower 1 ![=tree\_length \times (PE\_WEC\_P - PHYLO\_RPE\_NULLC)](http://latex.codecogs.com/png.latex?=tree\\_length \times (PE\_WEC\_P - PHYLO\_RPE\_NULLC))
306 PHYLO_RPE_NULLC Null score used as the denominator in the PHYLO_RPEC calculations region grower 1

Relative Phylogenetic Endemism, type 1

Description: Relative Phylogenetic Endemism (RPE). The ratio of the tree's PE to a null model of PD evenly distributed across terminals, but with the same range per terminal and where ancestral nodes are of zero length (as per RPD1).

Subroutine: calc_phylo_rpe1

Reference: Mishler et al. (2014) http://dx.doi.org/10.1038/ncomms5473

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
307 PHYLO_RPE1 Relative Phylogenetic Endemism score region grower 1
308 PHYLO_RPE_DIFF1 How much more or less PE is there than expected, in original tree units. region grower 1 ![=tree\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL1)](http://latex.codecogs.com/png.latex?=tree\\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL1))
309 PHYLO_RPE_NULL1 Null score used as the denominator in the RPE calculations region grower 1

Relative Phylogenetic Endemism, type 2

Description: Relative Phylogenetic Endemism (RPE). The ratio of the tree's PE to a null model where PE is calculated using a tree where all branches are of equal length.

Subroutine: calc_phylo_rpe2

Reference: Mishler et al. (2014) http://dx.doi.org/10.1038/ncomms5473

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
310 PHYLO_RPE2 Relative Phylogenetic Endemism score, type 2 region grower 1
311 PHYLO_RPE_DIFF2 How much more or less PE is there than expected, in original tree units. region grower 1 ![=tree\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL2)](http://latex.codecogs.com/png.latex?=tree\\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL2))
312 PHYLO_RPE_NULL2 Null score used as the denominator in the RPE2 calculations region grower 1

Phylogenetic Turnover

Phylo Jaccard

Description: Jaccard phylogenetic dissimilarity between two sets of taxa, represented by spanning sets of branches

Subroutine: calc_phylo_jaccard

Reference: Lozupone and Knight (2005) http://dx.doi.org/10.1128/AEM.71.12.8228-8235.2005

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
313 PHYLO_JACCARD Phylo Jaccard score cluster metric 1 ![=1 - (A / (A + B + C))](http://latex.codecogs.com/png.latex?=1 - (A / (A + B + C))) where A is the length of shared branches, and B and C are the length of branches found only in neighbour sets 1 and 2

Phylo Range weighted Turnover

Description: Phylo Range weighted Turnover

Subroutine: calc_phylo_rw_turnover

Reference: TBA

Index # Index Index description Grouping metric? Minimum number of neighbour sets
314 PHYLO_RW_TURNOVER Range weighted turnover cluster metric 1
315 PHYLO_RW_TURNOVER_A Range weighted turnover, shared component region grower 1
316 PHYLO_RW_TURNOVER_B Range weighted turnover, component found only in nbr set 1 region grower 1
317 PHYLO_RW_TURNOVER_C Range weighted turnover, component found only in nbr set 2 region grower 1

Phylo S2

Description: S2 phylogenetic dissimilarity between two sets of taxa, represented by spanning sets of branches

Subroutine: calc_phylo_s2

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
318 PHYLO_S2 Phylo S2 score cluster metric 1 ![=1 - (A / (A + min (B, C)))](http://latex.codecogs.com/png.latex?=1 - (A / (A + min (B, C)))) where A is the length of shared branches, and B and C are the length of branches found only in neighbour sets 1 and 2

Phylo Sorenson

Description: Sorenson phylogenetic dissimilarity between two sets of taxa, represented by spanning sets of branches

Subroutine: calc_phylo_sorenson

Reference: Bryant et al. (2008) http://dx.doi.org/10.1073/pnas.0801920105

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
319 PHYLO_SORENSON Phylo Sorenson score cluster metric 1 ![1 - (2A / (2A + B + C))](http://latex.codecogs.com/png.latex?1 - (2A / (2A + B + C))) where A is the length of shared branches, and B and C are the length of branches found only in neighbour sets 1 and 2

Phylogenetic ABC

Description: Calculate the shared and not shared branch lengths between two sets of labels

Subroutine: calc_phylo_abc

Index # Index Index description Grouping metric? Minimum number of neighbour sets
320 PHYLO_A Length of branches shared by labels in nbr sets 1 and 2 region grower 1
321 PHYLO_ABC Length of all branches associated with labels in nbr sets 1 and 2 region grower 1
322 PHYLO_B Length of branches unique to labels in nbr set 1 1
323 PHYLO_C Length of branches unique to labels in nbr set 2 1

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 Grouping metric? Minimum number of neighbour sets Formula
324 RAREC_CWE Corrected weighted rarity 1 =\frac{RAREC\_WE}{RAREC\_RICHNESS}
325 RAREC_RICHNESS Richness used in RAREC_CWE (same as index RICHNESS_SET1). 1
326 RAREC_WE Weighted rarity 1 ![=\sum_{t \in T} \frac {s_t} {S_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {s_t} {S_t}) where t is a label (taxon) in the set of labels (taxa) T across neighbour set 1, s_t is sum of the sample counts for t across the elements in neighbour sets 1 & 2 (its value in list ABC3_LABELS_ALL), and S_t is the total number of samples across the data set for label t (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 Grouping metric? Minimum number of neighbour sets
327 RAREC_RANGELIST List of ranges for each label used in the rarity central calculations 1
328 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 Grouping metric? Minimum number of neighbour sets Formula
329 RAREW_CWE Corrected weighted rarity region grower 1 =\frac{RAREW\_WE}{RAREW\_RICHNESS}
330 RAREW_RICHNESS Richness used in RAREW_CWE (same as index RICHNESS_ALL). region grower 1
331 RAREW_WE Weighted rarity region grower 1 ![=\sum_{t \in T} \frac {s_t} {S_t}](http://latex.codecogs.com/png.latex?=\\sum_{t \in T} \frac {s_t} {S_t}) where t is a label (taxon) in the set of labels (taxa) T across both neighbour sets, s_t is sum of the sample counts for t across the elements in neighbour sets 1 & 2 (its value in list ABC3_LABELS_ALL), and S_t is the total number of samples across the data set for label t (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 Grouping metric? Minimum number of neighbour sets
332 RAREW_RANGELIST List of ranges for each label used in the rarity whole calculations 1
333 RAREW_WTLIST List of weights for each label used in therarity whole calculations 1

Richness estimators

ACE

Description: Abundance Coverage-based Estimator os species richness

Subroutine: calc_ace

Reference: needed

Index # Index Index description Grouping metric? Minimum number of neighbour sets
334 ACE_CI_LOWER ACE lower confidence interval estimate region grower 1
335 ACE_CI_UPPER ACE upper confidence interval estimate region grower 1
336 ACE_ESTIMATE ACE score region grower 1
337 ACE_ESTIMATE_USED_CHAO Set to 1 when ACE cannot be calculated and so Chao1 estimate is used region grower 1
338 ACE_INFREQUENT_COUNT Count of infrequent species region grower 1
339 ACE_SE ACE standard error region grower 1
340 ACE_UNDETECTED Estimated number of undetected species region grower 1
341 ACE_VARIANCE ACE variance region grower 1

Chao1

Description: Chao1 species richness estimator (abundance based)

Subroutine: calc_chao1

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
342 CHAO1_CI_LOWER Lower confidence interval for the Chao1 estimate region grower 1
343 CHAO1_CI_UPPER Upper confidence interval for the Chao1 estimate region grower 1
344 CHAO1_ESTIMATE Chao1 index region grower 1 NEEDED
345 CHAO1_F1_COUNT Number of singletons in the sample region grower 1
346 CHAO1_F2_COUNT Number of doubletons in the sample region grower 1
347 CHAO1_META Metadata indicating which formulae were used in the calculations. Numbers refer to EstimateS equations at http://viceroy.eeb.uconn.edu/EstimateS/EstimateSPages/EstSUsersGuide/EstimateSUsersGuide.htm 1
348 CHAO1_SE Standard error of the Chao1 estimator [= sqrt(variance)] region grower 1
349 CHAO1_UNDETECTED Estimated number of undetected species region grower 1
350 CHAO1_VARIANCE Variance of the Chao1 estimator region grower 1

Chao2

Description: Chao2 species richness estimator (incidence based)

Subroutine: calc_chao2

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula Reference
351 CHAO2_CI_LOWER Lower confidence interval for the Chao2 estimate region grower 1
352 CHAO2_CI_UPPER Upper confidence interval for the Chao2 estimate region grower 1
353 CHAO2_ESTIMATE Chao2 index region grower 1 NEEDED
354 CHAO2_META Metadata indicating which formulae were used in the calculations. Numbers refer to EstimateS equations at http://viceroy.eeb.uconn.edu/EstimateS/EstimateSPages/EstSUsersGuide/EstimateSUsersGuide.htm 1
355 CHAO2_Q1_COUNT Number of uniques in the sample region grower 1
356 CHAO2_Q2_COUNT Number of duplicates in the sample region grower 1
357 CHAO2_SE Standard error of the Chao2 estimator [= sqrt (variance)] region grower 1
358 CHAO2_UNDETECTED Estimated number of undetected species region grower 1
359 CHAO2_VARIANCE Variance of the Chao2 estimator region grower 1

ICE

Description: Incidence Coverage-based Estimator of species richness

Subroutine: calc_ice

Index # Index Index description Grouping metric? Minimum number of neighbour sets
360 ICE_CI_LOWER ICE lower confidence interval estimate region grower 1
361 ICE_CI_UPPER ICE upper confidence interval estimate region grower 1
362 ICE_ESTIMATE ICE score region grower 1
363 ICE_ESTIMATE_USED_CHAO Set to 1 when ICE cannot be calculated and so Chao2 estimate is used region grower 1
364 ICE_INFREQUENT_COUNT Count of infrequent species region grower 1
365 ICE_SE ICE standard error region grower 1
366 ICE_UNDETECTED Estimated number of undetected species region grower 1
367 ICE_VARIANCE ICE variance region grower 1

Taxonomic Dissimilarity and Comparison

Beta diversity

Description: Beta diversity between neighbour sets 1 and 2.

Subroutine: calc_beta_diversity

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
368 BETA_2 The other beta cluster metric 1 ![=\frac{A + B + C}{max((A+B), (A+C))} - 1](http://latex.codecogs.com/png.latex?=\\frac{A + B + C}{max((A+B), (A+C))} - 1) where Ais the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C 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: ![=1 - \frac{2W}{A + B}](http://latex.codecogs.com/png.latex?=1 - \frac{2W}{A + B}) where A is the sum of the sample counts in neighbour set 1, B is the sum of sample counts in neighbour set 2, and ![W=\sum^n_{i=1} min(sample\count\label{i{set1}},sample\count\label{i{set2}})](http://latex.codecogs.com/png.latex?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 n labels across the two neighbour sets),

Index # Index Index description Grouping metric? Minimum number of neighbour sets
369 BC_A The A factor used in calculations (see formula) 1
370 BC_B The B factor used in calculations (see formula) 1
371 BC_W The W factor used in calculations (see formula) region grower 1
372 BRAY_CURTIS Bray Curtis dissimilarity cluster metric 1

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: ![=1 - \frac{2W}{A + B}](http://latex.codecogs.com/png.latex?=1 - \frac{2W}{A + B}) where A is the sum of the sample counts in neighbour set 1 normalised (divided) by the number of groups, B is the sum of the sample counts in neighbour set 2 normalised by the number of groups, and ![W = \sum^n_{i=1} min(sample\count\label{i{set1}},sample\count\label{i{set2}})](http://latex.codecogs.com/png.latex?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 n labels across the two neighbour sets),

Index # Index Index description Grouping metric? Minimum number of neighbour sets
373 BCN_A The A factor used in calculations (see formula) 1
374 BCN_B The B factor used in calculations (see formula) 1
375 BCN_W The W factor used in calculations (see formula) region grower 1
376 BRAY_CURTIS_NORM Bray Curtis dissimilarity normalised by groups cluster metric 1

Jaccard

Description: Jaccard dissimilarity between the labels in neighbour sets 1 and 2.

Subroutine: calc_jaccard

Formula: ![=1 - \frac{A}{A + B + C}](http://latex.codecogs.com/png.latex?=1 - \frac{A}{A + B + C}) where A is the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
377 JACCARD Jaccard value, 0 is identical, 1 is completely dissimilar cluster metric 1

Kulczynski 2

Description: Kulczynski 2 dissimilarity between two sets of labels.

Subroutine: calc_kulczynski2

Formula: ![=1 - 0.5 * (\frac{A}{A + B} + \frac{A}{A + C})](http://latex.codecogs.com/png.latex?=1 - 0.5 * (\frac{A}{A + B} + \frac{A}{A + C})) where A is the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
378 KULCZYNSKI2 Kulczynski 2 index cluster metric 1

Nestedness-resultant

Description: Nestedness-resultant index 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: ![=\frac{ \left | B - C \right | }{ 2A + B + C } \times \frac { A }{ A + min (B, C) }= SORENSON - S2](http://latex.codecogs.com/png.latex?=\\frac{ \left | B - C \right | }{ 2A + B + C } \times \frac { A }{ A + min (B, C) }= SORENSON - S2) where A is the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
379 NEST_RESULTANT Nestedness-resultant index cluster metric 1

Range weighted Sorenson

Description: Range weighted Sorenson

Subroutine: calc_rw_turnover

Reference: TBA

Index # Index Index description Grouping metric? Minimum number of neighbour sets
380 RW_TURNOVER Range weighted turnover cluster metric 1
381 RW_TURNOVER_A Range weighted turnover, shared component region grower 1
382 RW_TURNOVER_B Range weighted turnover, component found only in nbr set 1 region grower 1
383 RW_TURNOVER_C Range weighted turnover, component found only in nbr set 2 region grower 1

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: ![=\sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j](http://latex.codecogs.com/png.latex?=\\sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j) where p_i and p_j are the sample counts for the i'th and j'th labels, d_{ij} is a value of zero if ![i = j](http://latex.codecogs.com/png.latex?i = j) , and a value of 1 otherwise. L is the set of labels across both neighbour sets.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
384 TX_RAO_QE Taxonomically weighted quadratic entropy region grower 1
385 TX_RAO_TLABELS List of labels and values used in the TX_RAO_QE calculations 1
386 TX_RAO_TN Count of comparisons used to calculate TX_RAO_QE region grower 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: ![=1 - \frac{A}{A + min(B, C)}](http://latex.codecogs.com/png.latex?=1 - \frac{A}{A + min(B, C)}) where A is the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
387 S2 S2 dissimilarity index cluster metric 1

Simpson and Shannon

Description: Simpson and Shannon diversity metrics using samples from all neighbourhoods.

Subroutine: calc_simpson_shannon

Formula: For each index formula, p_i is the number of samples of the i'th label as a proportion of the total number of samples n in the neighbourhoods.

Index # Index Index description Grouping metric? Minimum number of neighbour sets Formula
388 SHANNON_E Shannon's evenness (H / HMAX) region grower 1 ![Evenness = \frac{H}{HMAX}](http://latex.codecogs.com/png.latex?Evenness = \frac{H}{HMAX})
389 SHANNON_H Shannon's H region grower 1 ![H = - \sum^n_{i=1} (p_i \cdot ln (p_i))](http://latex.codecogs.com/png.latex?H = - \sum^n_{i=1} (p_i \cdot ln (p_i)))
390 SHANNON_HMAX maximum possible value of Shannon's H region grower 1 ![HMAX = ln(richness)](http://latex.codecogs.com/png.latex?HMAX = ln(richness))
391 SIMPSON_D Simpson's D. A score of zero is more similar. region grower 1 ![D = 1 - \sum^n_{i=1} p_i^2](http://latex.codecogs.com/png.latex?D = 1 - \sum^n_{i=1} p_i^2)

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: ![=1 - \frac{2A}{2A + B + C}](http://latex.codecogs.com/png.latex?=1 - \frac{2A}{2A + B + C}) where A is the count of labels found in both neighbour sets, B is the count unique to neighbour set 1, and C is the count unique to neighbour set 2. Use the Label counts calculation to derive these directly.

Index # Index Index description Grouping metric? Minimum number of neighbour sets
392 SORENSON Sorenson index cluster metric 1
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