Table of calculations and indices

Generated GMT Sat Feb 7 06:48:46 2026, Biodiverse version 5.0.

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

Indices:

Index Description Minimum number of neighbour sets
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. Returns one list for each property, so if your data have properties named ‘GPROP1’ and ‘GPROP2’ then it will return two lists named ‘GPPROP_STATS_GPROP1_DATA’ and ‘GPPROP_STATS_GPROP2_DATA’, respectively.

Subroutine: calc_gpprop_lists

Indices:

  • Data set dependent

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. Returns one list for each property, so if your data have properties named ‘GPROP1’ and ‘GPROP2’ then it will return two lists named ‘GPPROP_STATS_GPROP1_HASH’ and ‘GPPROP_STATS_GPROP2_HASH’, respectively.

Subroutine: calc_gpprop_hashes

Indices:

  • Data set dependent

Group property quantiles

Description: Quantiles for each group property across both neighbour sets

Subroutine: calc_gpprop_quantiles

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
LBPROP_GISTAR_LIST List of Gi* scores 1

Label property Gi* statistics (local range weighted)

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

Subroutine: calc_lbprop_gistar_abc2

Reference: Getis and Ord (1992) Geographical Analysis

Indices:

Index Description Minimum number of neighbour sets
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. Returns one list for each property, so if your data have properties named ‘PROP1’ and ‘PROP2’ then it will return two lists named ‘LBPROP_STATS_PROP1_DATA’ and ‘LBPROP_STATS_PROP1_DATA’, respectively.

Subroutine: calc_lbprop_data

Indices:

  • Data set dependent

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. Returns one hash for each property, so if your data have properties named ‘PROP1’ and ‘PROP2’ then it will return two lists named ‘LBPROP_STATS_PROP1_HASH’ and ‘LBPROP_STATS_PROP2_HASH’, respectively.

Subroutine: calc_lbprop_hashes

Indices:

  • Data set dependent

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. Returns one hash for each property, so if your data have properties named ‘PROP1’ and ‘PROP2’ then it will return two lists named ‘LBPROP_STATS_PROP1_HASH2’ and ‘LBPROP_STATS_PROP2_HASH2’, respectively.

Subroutine: calc_lbprop_hashes_abc2

Indices:

  • Data set dependent

Label property lists

Description: Lists of the labels and their property values within the neighbour sets. Returns one list for each property, so if your data have properties named ‘PROP1’ and ‘PROP2’ then it will return two lists named ‘LBPROP_LIST_PROP1’ and ‘LBPROP_LIST_PROP2’, respectively.

Subroutine: calc_lbprop_lists

Indices:

  • Data set dependent

Label property quantiles

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

Subroutine: calc_lbprop_quantiles

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
END_ABS1 Count of labels entirely endemic to neighbour set 1 1
END_ABS1_P Proportion of labels entirely endemic to neighbour set 1 1
END_ABS2 Count of labels entirely endemic to neighbour set 2 1
END_ABS2_P Proportion of labels entirely endemic to neighbour set 2 1
END_ABS_ALL Count of labels entirely endemic to neighbour sets 1 and 2 combined region grower 1
END_ABS_ALL_P Proportion of labels entirely endemic to neighbour sets 1 and 2 combined 1

Absolute endemism lists

Description: Lists underlying the absolute endemism scores.

Subroutine: calc_endemism_absolute_lists

Indices:

Index Description Minimum number of neighbour sets
END_ABS1_LIST List of labels entirely endemic to neighbour set 1 1
END_ABS2_LIST List of labels entirely endemic to neighbour set 1 1
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; Laffan and Crisp (2003) J Biogeog

Indices:

Index Description Minimum number of neighbour sets Formula Reference
ENDC_CWE Corrected weighted endemism 1 \(= \frac{ENDC\_WE}{ENDC\_RICHNESS}\)
ENDC_RICHNESS Richness used in ENDC_CWE (same as index RICHNESS_SET1) 1
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 \(= \sum_{t \in T} \frac {1} {R_t}\) 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
ENDC_WE Weighted endemism 1 \(= \sum_{t \in T} \frac {r_t} {R_t}\) 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

Indices:

Index Description Minimum number of neighbour sets
ENDC_HPART_0 List of the proportional contribution of labels to the endemism central calculations, hierarchical level 0 1
ENDC_HPART_1 List of the proportional contribution of labels to the endemism central calculations, hierarchical level 1 1
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
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
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
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
ENDC_HPART_OME_0 List of the observed minus expected proportional contribution of labels to the endemism central calculations , hierarchical level 0 1
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

Indices:

Index Description Minimum number of neighbour sets
ENDC_RANGELIST List of ranges for each label used in the endemism central calculations 1
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

Indices:

Index Description Minimum number of neighbour sets Formula
ENDC_CWE_NORM Corrected weighted endemism normalised by groups 1 \(= \frac{ENDC\_CWE}{EL\_COUNT\_ALL}\)
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula Reference
ENDW_CWE Corrected weighted endemism 1 \(= \frac{ENDW\_WE}{ENDW\_RICHNESS}\)
ENDW_RICHNESS Richness used in ENDW_CWE (same as index RICHNESS_ALL) region grower 1
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 \(= \sum_{t \in T} \frac {1} {R_t}\) 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
ENDW_WE Weighted endemism region grower 1 \(= \sum_{t \in T} \frac {r_t} {R_t}\) 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

Indices:

Index Description Minimum number of neighbour sets
ENDW_HPART_0 List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 0 1
ENDW_HPART_1 List of the proportional contribution of labels to the endemism whole calculations, hierarchical level 1 1
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
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
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
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
ENDW_HPART_OME_0 List of the observed minus expected proportional contribution of labels to the endemism whole calculations , hierarchical level 0 1
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

Indices:

Index Description Minimum number of neighbour sets
ENDW_RANGELIST List of ranges for each label used in the endemism whole calculations 1
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

Indices:

Index Description Minimum number of neighbour sets Formula
ENDW_CWE_NORM Corrected weighted endemism normalised by groups 1 \(= \frac{ENDW\_CWE}{EL\_COUNT\_ALL}\)
ENDW_WE_NORM Weighted endemism normalised by groups 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 list elements generated depends on how many axes are used in the labels. Axes are order from zero as the highest level in the hierarchy, so index 0 is the top level of the hierarchy.

Note that this calculation produces lists since version 4.99_002 so one can no longer use the SUMRAT indices for clustering. This can be re-enabled if there is a need.

Subroutine: calc_hierarchical_label_ratios

Reference: Jones and Laffan (2008) Trans Philol Soc

Indices:

Index Description Minimum number of neighbour sets
HIER_A A score for each level 2
HIER_ARAT Ratio of A scores between adjacent levels 2
HIER_ASUM Sum of shared label sample counts 2
HIER_ASUMRAT 1 - Ratio of shared label sample counts between adjacent levels 2
HIER_B B score for each level 2
HIER_BRAT Ratio of B scores between adjacent levels 2
HIER_C C score for each level 2
HIER_CRAT Ratio of C scores between adjacent levels 2

Lists and Counts

Element arrays

Description: Arrays of elements used in neighbour sets 1 and 2. These form the basis for all the spatial calculations.

Subroutine: calc_element_lists_used_as_arrays

Indices:

Index Description Minimum number of neighbour sets
EL_ARRAY_ALL Array of elements in both neighbour sets 2
EL_ARRAY_SET1 Array of elements in neighbour set 1 1
EL_ARRAY_SET2 Array of elements in neighbour set 2 2

Element counts

Description: Counts of elements used in neighbour sets 1 and 2.

Subroutine: calc_elements_used

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
EL_COUNT_ALL Count of elements in both neighbour sets region grower 1
EL_COUNT_SET1 Count of elements in neighbour set 1 1
EL_COUNT_SET2 Count of elements in neighbour set 2 2

Element lists

Description: [DEPRECATED] Lists of elements used in neighbour sets 1 and 2. These form the basis for all the spatial calculations. The return types are inconsistent. New code should use calc_element_lists_used_as_arrays

Subroutine: calc_element_lists_used

Indices:

Index Description Minimum number of neighbour sets
EL_LIST_ALL List of elements in both neighour sets 2
EL_LIST_SET1 List of elements in neighbour set 1 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
ABC_A Count of labels common to both neighbour sets region grower 2
ABC_ABC Total label count across both neighbour sets (same as RICHNESS_ALL) region grower 2
ABC_B Count of labels unique to neighbour set 1 2
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
ABC2_LABELS_ALL List of labels in both neighbour sets 2
ABC2_LABELS_SET1 List of labels in neighbour set 1 1
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

Indices:

Index Description Minimum number of neighbour sets
ABC2_MEAN_ALL Mean label range in both element sets 1
ABC2_MEAN_SET1 Mean label range in neighbour set 1 1
ABC2_MEAN_SET2 Mean label range in neighbour set 2 2
ABC2_SD_ALL Standard deviation of label ranges in both element sets 2
ABC2_SD_SET1 Standard deviation of label ranges in neighbour set 1 1
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

Indices:

Index Description Minimum number of neighbour sets
EL_COUNT_NONEMPTY_ALL Count of non-empty elements in both neighbour sets 1
EL_COUNT_NONEMPTY_SET1 Count of non-empty elements in neighbour set 1 1
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

Indices:

Index Description Minimum number of neighbour sets
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

Formula: \(= 1 - \frac{richness}{sum\ of\ the\ sample\ counts}\)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
REDUNDANCY_ALL for both neighbour sets region grower 1 \(= 1 - \frac{RICHNESS\_ALL}{ABC3\_SUM\_ALL}\)
REDUNDANCY_SET1 for neighour set 1 1 \(= 1 - \frac{RICHNESS\_SET1}{ABC3\_SUM\_SET1}\)
REDUNDANCY_SET2 for neighour set 2 2 \(= 1 - \frac{RICHNESS\_SET2}{ABC3\_SUM\_SET2}\)

Richness

Description: Count the number of labels in the neighbour sets

Subroutine: calc_richness

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
RICHNESS_ALL for both sets of neighbours region grower 1
RICHNESS_SET1 for neighbour set 1 1
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

Indices:

Index Description Minimum number of neighbour sets
ABC3_LABELS_ALL List of labels in both neighbour sets with their sample counts as the values. 2
ABC3_LABELS_SET1 List of labels in neighbour set 1. Values are the sample counts. 1
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

Indices:

Index Description Minimum number of neighbour sets
ABC3_QUANTILES_ALL List of quantiles for both neighbour sets 2
ABC3_QUANTILES_SET1 List of quantiles for neighbour set 1 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
ABC3_MEAN_ALL Mean of label sample counts across both element sets. 2
ABC3_MEAN_SET1 Mean of label sample counts in neighbour set1. 1
ABC3_MEAN_SET2 Mean of label sample counts in neighbour set 2. 2
ABC3_SD_ALL Standard deviation of label sample counts in both element sets. 2
ABC3_SD_SET1 Standard deviation of sample counts in neighbour set 1. 1
ABC3_SD_SET2 Standard deviation of label sample counts in neighbour set 2. 2
ABC3_SUM_ALL Sum of the label sample counts across both neighbour sets. region grower 2
ABC3_SUM_SET1 Sum of the label sample counts across both neighbour sets. 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
MXD_COUNT Count of comparisons used. 2
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
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
MXD_MEAN Mean dissimilarity of labels in set 1 to those in set 2. 2
MXD_VARIANCE Variance of the dissimilarity values, set 1 vs set 2. cluster metric 2

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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
MX_KURT Kurtosis 1
MX_LABELS List of the matrix labels in the neighbour sets 1
MX_MAXVALUE Maximum value region grower 1
MX_MEAN Mean 1
MX_MEDIAN Median 1
MX_MINVALUE Minimum value 1
MX_N Number of samples (matrix elements, not labels) 1
MX_PCT05 5th percentile value 1
MX_PCT25 First quartile (25th percentile) 1
MX_PCT75 Third quartile (75th percentile) 1
MX_PCT95 95th percentile value 1
MX_RANGE Range (max-min) 1
MX_SD Standard deviation 1
MX_SKEW Skewness 1
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: \(= \sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j\) 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.

Indices:

Index Description Minimum number of neighbour sets
MX_RAO_QE Matrix weighted quadratic entropy 1
MX_RAO_TLABELS List of labels and values used in the MX_RAO_QE calculations 1
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

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
NUMD_ABSMEAN Mean absolute dissimilarity of labels in set 1 to those in set 2. cluster metric 2 \(= \frac{\sum_{l_{1i} \in L_1} \sum_{l_{2j} \in L_2} abs (l_{1i} - l_{2j})(w_{1i} \times w_{2j})}{n_1 \times n_2}\) where \(L1\) 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
NUMD_COUNT Count of comparisons used. 2 \(= n1 * n2\) where values are as for \(NUMD\_ABSMEAN\)
NUMD_VARIANCE Variance of the dissimilarity values (mean squared deviation), set 1 vs set 2. cluster metric 2 \(= \frac{\sum_{l_{1i} \in L_1} \sum_{l_{2j} \in L_2} (l_{1i} - l_{2j})^2(w_{1i} \times w_{2j})}{n_1 \times n_2}\) 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

Indices:

Index Description Minimum number of neighbour sets
NUM_GMEAN Geometric mean 1
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

Indices:

Index Description Minimum number of neighbour sets
NUM_Q005 5th percentile 1
NUM_Q010 10th percentile 1
NUM_Q015 15th percentile 1
NUM_Q020 20th percentile 1
NUM_Q025 25th percentile 1
NUM_Q030 30th percentile 1
NUM_Q035 35th percentile 1
NUM_Q040 40th percentile 1
NUM_Q045 45th percentile 1
NUM_Q050 50th percentile 1
NUM_Q055 55th percentile 1
NUM_Q060 60th percentile 1
NUM_Q065 65th percentile 1
NUM_Q070 70th percentile 1
NUM_Q075 75th percentile 1
NUM_Q080 80th percentile 1
NUM_Q085 85th percentile 1
NUM_Q090 90th percentile 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
NUM_CV Coefficient of variation (NUM_SD / NUM_MEAN) 1
NUM_KURT Kurtosis 1
NUM_MAX Maximum value (100th quantile) region grower 1
NUM_MEAN Mean 1
NUM_MIN Minimum value (zero quantile) 1
NUM_N Number of samples region grower 1
NUM_RANGE Range (max - min) 1
NUM_SD Standard deviation 1
NUM_SKEW Skewness 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

Indices:

Index Description Minimum number of neighbour sets
NUM_GISTAR List of Gi* scores 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) https://doi.org/10.1093/bioinformatics/btn358, Tsirogiannis et al. (2012)

Indices:

Index Description Minimum number of neighbour sets
PHYLO_NRI_NTI_SAMPLE_N Number of random resamples used 1
PHYLO_NRI_SAMPLE_MEAN Expected mean of pair-wise distances 1
PHYLO_NRI_SAMPLE_SD Expected standard deviation of pair-wise distances 1
PHYLO_NTI_SAMPLE_MEAN Expected mean of nearest taxon distances 1
PHYLO_NTI_SAMPLE_SD Expected standard deviation of nearest taxon distances 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

Indices:

Index Description Minimum number of neighbour sets
PHYLO_NRI3 Net Relatedness Index, abundance weighted 1
PHYLO_NTI3 Nearest Taxon Index, abundance weighted 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

Indices:

Index Description Minimum number of neighbour sets
PHYLO_NRI2 Net Relatedness Index, local range weighted 1
PHYLO_NTI2 Nearest Taxon Index, local range weighted 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

Indices:

Index Description Minimum number of neighbour sets Formula
PHYLO_NRI1 Net Relatedness Index, unweighted 1 \(NRI = \frac{MPD_{obs} - mean(MPD_{rand})}{sd(MPD_{rand})}\)
PHYLO_NTI1 Nearest Taxon Index, unweighted 1 \(NTI = \frac{MNTD_{obs} - mean(MNTD_{rand})}{sd(MNTD_{rand})}\)

Net VPD expected values

Description: Expected values for VPD, analogous to the NRI/NTI results

Subroutine: calc_vpd_expected_values

Reference: Warwick & Clarke (2001)

Indices:

Index Description Minimum number of neighbour sets
PHYLO_NET_VPD_SAMPLE_MEAN Expected mean of pair-wise variance (VPD) 1
PHYLO_NET_VPD_SAMPLE_N Number of random resamples used to calculate expected pair-wise variance scores(will equal PHYLO_NRI_NTI_SAMPLE_N for non-ultrametric trees) 1
PHYLO_NET_VPD_SAMPLE_SD Expected standard deviation of pair-wise variance (VPD) 1

Net variance of pair-wise phylogenetic distances, unweighted

Description: Z-score of VPD calculated using NRI/NTI resampling Not weighted by sample counts, so each label counts once only.

Subroutine: calc_net_vpd

Indices:

Index Description Minimum number of neighbour sets
PHYLO_NET_VPD Net variance of pair-wise phylogenetic distances, unweighted 1

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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PMPD3_MAX Maximum of pairwise phylogenetic distances 1
PMPD3_MEAN Mean of pairwise phylogenetic distances 1 \(MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j\) where \(d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b\) is the sum of the branch lengths along the path connecting \(t_i\) and \(t_j\) such that \(L_b\) is the length of each branch in the set of branches \(B\)
PMPD3_MIN Minimum of pairwise phylogenetic distances 1
PMPD3_N Count of pairwise phylogenetic distances 1
PMPD3_RMSD Root mean squared pairwise phylogenetic distances 1
PMPD3_VARIANCE Variance of pairwise phylogenetic distances, similar to Clarke and Warwick (2001; http://dx.doi.org/10.3354/meps216265) but uses tip-to-tip distances instead of tip to most recent common ancestor. 1
PNTD3_MAX Maximum of nearest taxon distances region grower 1
PNTD3_MEAN Mean of nearest taxon distances 1
PNTD3_MIN Minimum of nearest taxon distances 1
PNTD3_N Count of nearest taxon distances 1
PNTD3_RMSD Root mean squared nearest taxon distances 1
PNTD3_VARIANCE Variance of nearest taxon distances 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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PMPD2_MAX Maximum of pairwise phylogenetic distances 1
PMPD2_MEAN Mean of pairwise phylogenetic distances 1 \(MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j\) where \(d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b\) is the sum of the branch lengths along the path connecting \(t_i\) and \(t_j\) such that \(L_b\) is the length of each branch in the set of branches \(B\)
PMPD2_MIN Minimum of pairwise phylogenetic distances 1
PMPD2_N Count of pairwise phylogenetic distances 1
PMPD2_RMSD Root mean squared pairwise phylogenetic distances 1
PMPD2_VARIANCE Variance of pairwise phylogenetic distances, similar to Clarke and Warwick (2001; http://dx.doi.org/10.3354/meps216265) but uses tip-to-tip distances instead of tip to most recent common ancestor. 1
PNTD2_MAX Maximum of nearest taxon distances region grower 1
PNTD2_MEAN Mean of nearest taxon distances 1
PNTD2_MIN Minimum of nearest taxon distances 1
PNTD2_N Count of nearest taxon distances 1
PNTD2_RMSD Root mean squared nearest taxon distances 1
PNTD2_VARIANCE Variance of nearest taxon distances 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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PMPD1_MAX Maximum of pairwise phylogenetic distances 1
PMPD1_MEAN Mean of pairwise phylogenetic distances 1 \(MPD = \frac {\sum_{t_i = 1}^{n_t-1} \sum_{t_j = 1}^{n_t} d_{t_i \leftrightarrow t_j}}{(n_t-1)^2}, i \neq j\) where \(d_{t_i \leftrightarrow t_j} = \sum_{b \in B_{t_i \leftrightarrow t_j}} L_b\) is the sum of the branch lengths along the path connecting \(t_i\) and \(t_j\) such that \(L_b\) is the length of each branch in the set of branches \(B\)
PMPD1_MIN Minimum of pairwise phylogenetic distances 1
PMPD1_N Count of pairwise phylogenetic distances 1
PMPD1_RMSD Root mean squared pairwise phylogenetic distances 1
PMPD1_VARIANCE Variance of pairwise phylogenetic distances, similar to Clarke and Warwick (2001; http://dx.doi.org/10.3354/meps216265) but uses tip-to-tip distances instead of tip to most recent common ancestor. 1
PNTD1_MAX Maximum of nearest taxon distances region grower 1
PNTD1_MEAN Mean of nearest taxon distances 1
PNTD1_MIN Minimum of nearest taxon distances 1
PNTD1_N Count of nearest taxon distances 1
PNTD1_RMSD Root mean squared nearest taxon distances 1
PNTD1_VARIANCE Variance of nearest taxon distances 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

Indices:

Index Description Minimum number of neighbour sets Formula Reference
PE_CWE Corrected weighted endemism. This is the phylogenetic analogue of corrected weighted endemism. 1 \(PE\_WE / PD\)

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

Indices:

Index Description Minimum number of neighbour sets
PEC_CWE Corrected weighted phylogenetic endemism, central variant 1
PEC_CWE_PD PD used in the PEC_CWE index. 1

Corrected weighted phylogenetic rarity

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

Subroutine: calc_phylo_corrected_weighted_rarity

Indices:

Index Description Minimum number of neighbour sets Formula Reference
PHYLO_RARITY_CWR Corrected weighted phylogenetic rarity. This is the phylogenetic rarity analogue of corrected weighted endemism. 1 \(AED_T / PD\)

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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
PD_ENDEMISM Phylogenetic Diversity Endemism region grower 1
PD_ENDEMISM_P Phylogenetic Diversity Endemism, as a proportion of the whole tree region grower 1
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

Indices:

Index Description Minimum number of neighbour sets
PE_CLADE_CONTR List of node (clade) contributions to the PE calculation 1
PE_CLADE_CONTR_P List of node (clade) contributions to the PE calculation, proportional to the entire tree 1
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

Indices:

Index Description Minimum number of neighbour sets
PE_CLADE_LOSS_CONTR List of the proportion of the PE score which would be lost if each clade were removed. 1
PE_CLADE_LOSS_CONTR_P As per PE_CLADE_LOSS but proportional to the entire tree 1
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

Indices:

Index Description Minimum number of neighbour sets
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
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; Laity et al. (2015); Laffan et al. (2016)

Formula: \(PE = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}\) 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).

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PE_WE Phylogenetic endemism region grower 1
PE_WE_P Phylogenetic weighted endemism as a proportion of the total tree length region grower 1 \(PE\_WE / L\) 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

Formula: \(PEC = \sum_{\lambda \in \Lambda } L_{\lambda}\frac{r_\lambda}{R_\lambda}\) 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).

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
PEC_WE Phylogenetic endemism, central variant region grower 1
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

Indices:

Index Description Minimum number of neighbour sets
PEC_LOCAL_RANGELIST Phylogenetic endemism local range lists, central variant 1
PEC_RANGELIST Phylogenetic endemism global range lists, central variant 1
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

Indices:

Index Description Minimum number of neighbour sets
PE_LOCAL_RANGELIST Local node ranges used in PE calculations (number of groups in which a node is found) 1
PE_RANGELIST Node ranges used in PE calculations 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
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
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

RWiBaLD

Description: Range weighted branch length differences. Values are spatially constant, only the subsets change

Subroutine: calc_rwibald

Reference: Mishler et al. (in review)

Indices:

Index Description Minimum number of neighbour sets
RWIBALD_CODES RWiBaLD codes, 1=palaeo, 2=neo, 3=meso 1
RWIBALD_CODE_COUNTS Counts of branches in each RWiBaLD category 1
RWIBALD_DIFFS RWiBaLD scores (continuous differences) 1
RWIBALD_METADATA General metadata for the RWiBaLD calculations 1
RWIBALD_RR_DIFFS RWiBaLD scores for the range restricted subset (continuous differences) 1

Phylogenetic Indices

Count labels on tree

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

Subroutine: calc_count_labels_on_tree

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
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)

Indices:

Index Description Minimum number of neighbour sets Reference
PHYLO_AED_LIST Abundance weighted ED per terminal label 1 Cadotte & Davies (2010)
PHYLO_ED_LIST “Fair proportion” partitioning of PD per terminal label 1 Isaac et al. (2007)
PHYLO_ES_LIST Equal splits partitioning of PD per terminal label 1 Redding & Mooers (2006)

Evolutionary distinctiveness per site

Description: Site level evolutionary distinctiveness

Subroutine: calc_phylo_aed_t

Reference: Cadotte & Davies (2010)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Reference
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)

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)

Indices:

Index Description Minimum number of neighbour sets Reference
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)
PHYLO_AED_T_WTLIST_P Proportional contribution of each terminal taxon to the AED_T score 1 Cadotte & Davies (2010)

Labels not on tree

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

Subroutine: calc_labels_not_on_tree

Indices:

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

Labels on tree

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

Subroutine: calc_labels_on_tree

Indices:

Index Description Minimum number of neighbour sets
PHYLO_LABELS_ON_TREE A hash of labels that are found on the tree, across both neighbour sets 1

Last shared ancestor properties

Description: Properties of the last shared ancestor of an assemblage. Uses labels in both neighbourhoods.

Subroutine: calc_last_shared_ancestor_props

Indices:

Index Description Minimum number of neighbour sets
LAST_SHARED_ANCESTOR_DEPTH Depth of last shared ancestor from the root. The root has a depth of zero. 1
LAST_SHARED_ANCESTOR_DIST_TO_ROOT Distance along the tree from the last shared ancestor to the root. Includes the shared ancestor’s length. 1
LAST_SHARED_ANCESTOR_DIST_TO_TIP Distance along the tree from the last shared ancestor to the furthest tip in the sample. This is calculated from the point at which the lineages merge, which is the branch end further from the root 1
LAST_SHARED_ANCESTOR_LENGTH Branch length of last shared ancestor 1
LAST_SHARED_ANCESTOR_POS_REL Relative position of the last shared ancestor. Value is the fraction of the distance from the root to the furthest terminal.This uses the point at which the lineages merge, and is the branch end further from the root 1

PD clade contributions

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

Subroutine: calc_pd_clade_contributions

Indices:

Index Description Minimum number of neighbour sets
PD_CLADE_CONTR List of node (clade) contributions to the PD calculation 1
PD_CLADE_CONTR_P List of node (clade) contributions to the PD calculation, proportional to the entire tree 1
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

Indices:

Index Description Minimum number of neighbour sets
PD_CLADE_LOSS_CONTR List of the proportion of the PD score which would be lost if each clade were removed. 1
PD_CLADE_LOSS_CONTR_P As per PD_CLADE_LOSS but proportional to the entire tree 1
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

Indices:

Index Description Minimum number of neighbour sets
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
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula Reference
PHYLO_ABUNDANCE Phylogenetic abundance region grower 1 \(= \sum_{c \in C} A \times L_c\) where \(C\) is 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).
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula Reference
PD Phylogenetic diversity region grower 1 \(= \sum_{c \in C} L_c\) where \(C\) is 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
PD_P Phylogenetic diversity as a proportion of total tree length region grower 1 \(= \frac { PD }{ \sum_{c \in C} L_c }\) where terms are the same as for PD, but \(c\) , \(C\) and \(L_c\) are calculated for all nodes in the tree.
PD_P_per_taxon Phylogenetic diversity per taxon as a proportion of total tree length 1 \(= \frac { PD\_P }{ RICHNESS\_ALL }\)
PD_per_taxon Phylogenetic diversity per taxon 1 \(= \frac { PD }{ RICHNESS\_ALL }\)

Phylogenetic Diversity (local)

Description: Phylogenetic diversity (PD) based on branch lengths back to the last shared ancestor. Uses labels in both neighbourhoods.

Subroutine: calc_pd_local

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PD_LOCAL Phylogenetic diversity calculated to last shared ancestor region grower 1 \(= \sum_{c \in C} L_c\) where \(C\) is the set of branches in the minimum spanning path joining the labels in both neighbour sets to the last shared ancestor, \(c\) is a branch (a single segment between two nodes) in the spanning path \(C\) , and \(L_c\) is the length of branch \(c\) .
PD_LOCAL_P Phylogenetic diversity as a proportion of total tree length region grower 1 \(= \frac { PD }{ \sum_{c \in C} L_c }\) where terms are the same as for PD, but \(c\) , \(C\) and \(L_c\) are calculated for all nodes in the tree.

Phylogenetic Diversity node list

Description: Phylogenetic diversity (PD) nodes used.

Subroutine: calc_pd_node_list

Indices:

Index Description Minimum number of neighbour sets
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

Indices:

Index Description Minimum number of neighbour sets
PD_INCLUDED_TERMINAL_NODE_COUNT Count of tree terminal nodes included in the PD calculations 1

Phylogenetic Diversity terminal node list

Description: Phylogenetic diversity (PD) terminal nodes used.

Subroutine: calc_pd_terminal_node_list

Indices:

Index Description Minimum number of neighbour sets
PD_INCLUDED_TERMINAL_NODE_LIST List of tree terminal nodes included in the PD calculations 1

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

Indices:

Index Description Minimum number of neighbour sets
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
PHYLO_LABELS_NOT_ON_TRIMMED_TREE_N Number of labels not on the trimmed tree 1
PHYLO_LABELS_NOT_ON_TRIMMED_TREE_P Proportion of labels not on the trimmed tree 1

Labels on trimmed tree

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

Subroutine: calc_labels_on_trimmed_tree

Indices:

Index Description Minimum number of neighbour sets
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 type 1 (RPD1). 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.You probably want to use RPD2 instead as it uses the tree’s topology.

Subroutine: calc_phylo_rpd1

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_RPD1 RPD1 1
PHYLO_RPD_DIFF1 How much more or less PD is there than expected, in original tree units. 1 \(= tree\_length \times (PD\_P - PHYLO\_RPD\_NULL1)\)
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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_RPD2 RPD2 1
PHYLO_RPD_DIFF2 How much more or less PD is there than expected, in original tree units. 1 \(= tree\_length \times (PD\_P - PHYLO\_RPD\_NULL2)\)
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)

Indices:

Index Description Minimum number of neighbour sets Formula
PHYLO_RPEC Relative Phylogenetic Endemism score, central 1
PHYLO_RPE_DIFFC How much more or less PE is there than expected, in original tree units. 1 \(= tree\_length \times (PE\_WEC\_P - PHYLO\_RPE\_NULLC)\)
PHYLO_RPE_NULLC Null score used as the denominator in the PHYLO_RPEC calculations 1

Relative Phylogenetic Endemism, type 1

Description: Relative Phylogenetic Endemism, type 1 (RPE1). 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).You probably want to use RPE2 instead as it uses the tree’s topology.

Subroutine: calc_phylo_rpe1

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_RPE1 Relative Phylogenetic Endemism score 1
PHYLO_RPE_DIFF1 How much more or less PE is there than expected, in original tree units. 1 \(= tree\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL1)\)
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 non-zero branches are of equal length.

Subroutine: calc_phylo_rpe2

Reference: Mishler et al. (2014)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_RPE2 Relative Phylogenetic Endemism score, type 2 1
PHYLO_RPE_DIFF2 How much more or less PE is there than expected, in original tree units. 1 \(= tree\_length \times (PE\_WE\_P - PHYLO\_RPE\_NULL2)\)
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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_JACCARD Phylo Jaccard score cluster metric 2 \(= 1 - (A / (A + B + C))\) 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: Laffan et al. (2016)

Indices:

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

Phylo S2

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

Subroutine: calc_phylo_s2

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_S2 Phylo S2 score cluster metric 2 \(= 1 - (A / (A + min (B, C)))\) where A is the sum of shared branch lengths, and B and C are the sum of branch lengths foundonly 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)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
PHYLO_SORENSON Phylo Sorenson score cluster metric 2 \(1 - (2A / (2A + B + C))\) 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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
PHYLO_A Sum of branch lengths shared by labels in nbr sets 1 and 2 region grower 2
PHYLO_ABC Sum of branch lengths associated with labels in nbr sets 1 and 2 region grower 2
PHYLO_B Sum of branch lengths unique to labels in nbr set 1 2
PHYLO_C Sum of branch lengths unique to labels in nbr set 2 2

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

Indices:

Index Description Minimum number of neighbour sets Formula
RAREC_CWE Corrected weighted rarity 1 \(= \frac{RAREC\_WE}{RAREC\_RICHNESS}\)
RAREC_RICHNESS Richness used in RAREC_CWE (same as index RICHNESS_SET1). 1
RAREC_WE Weighted rarity 1 \(= \sum_{t \in T} \frac {s_t} {S_t}\) 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

Indices:

Index Description Minimum number of neighbour sets
RAREC_RANGELIST List of ranges for each label used in the rarity central calculations 1
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

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
RAREW_CWE Corrected weighted rarity 1 \(= \frac{RAREW\_WE}{RAREW\_RICHNESS}\)
RAREW_RICHNESS Richness used in RAREW_CWE (same as index RICHNESS_ALL). region grower 1
RAREW_WE Weighted rarity region grower 1 \(= \sum_{t \in T} \frac {s_t} {S_t}\) 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

Indices:

Index Description Minimum number of neighbour sets
RAREW_RANGELIST List of ranges for each label used in the rarity whole calculations 1
RAREW_WTLIST List of weights for each label used in therarity whole calculations 1

Richness estimators

ACE

Description: Abundance Coverage-based Estimator of species richness

Subroutine: calc_ace

Reference: Chao and Lee (1992)

Indices:

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

Chao1

Description: Chao1 species richness estimator (abundance based)

Subroutine: calc_chao1

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Reference
CHAO1_CI_LOWER Lower confidence interval for the Chao1 estimate region grower 1
CHAO1_CI_UPPER Upper confidence interval for the Chao1 estimate region grower 1
CHAO1_ESTIMATE Chao1 index region grower 1 NEEDED
CHAO1_F1_COUNT Number of singletons in the sample region grower 1
CHAO1_F2_COUNT Number of doubletons in the sample region grower 1
CHAO1_META Metadata indicating which formulae were used in the calculations. Numbers refer to EstimateS equations at https://www.robertkcolwell.org/media_files/63 1
CHAO1_SE Standard error of the Chao1 estimator [= sqrt(variance)] region grower 1
CHAO1_UNDETECTED Estimated number of undetected species region grower 1
CHAO1_VARIANCE Variance of the Chao1 estimator region grower 1

Chao2

Description: Chao2 species richness estimator (incidence based)

Subroutine: calc_chao2

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Reference
CHAO2_CI_LOWER Lower confidence interval for the Chao2 estimate region grower 1
CHAO2_CI_UPPER Upper confidence interval for the Chao2 estimate region grower 1
CHAO2_ESTIMATE Chao2 index region grower 1 NEEDED
CHAO2_META Metadata indicating which formulae were used in the calculations. Numbers refer to EstimateS equations at https://www.robertkcolwell.org/media_files/63 1
CHAO2_Q1_COUNT Number of uniques in the sample region grower 1
CHAO2_Q2_COUNT Number of duplicates in the sample region grower 1
CHAO2_SE Standard error of the Chao2 estimator [= sqrt (variance)] region grower 1
CHAO2_UNDETECTED Estimated number of undetected species region grower 1
CHAO2_VARIANCE Variance of the Chao2 estimator region grower 1

Hurlbert richness estimation

Description: Hurlbert estimated species richness scores for given number of samples.

Subroutine: calc_hurlbert_es

Reference: Hurlbert, S.H. (1971)

Indices:

Index Description Minimum number of neighbour sets
HURLBERT_ES List of Hurlbert estimated species richness scores for given number of samples 1

ICE

Description: Incidence Coverage-based Estimator of species richness

Subroutine: calc_ice

Reference: Gotelli and Chao (2013)

Indices:

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

Taxonomic Dissimilarity and Comparison

Beta diversity

Description: Beta diversity between neighbour sets 1 and 2.

Subroutine: calc_beta_diversity

Indices:

Index Description Grouping metric? Minimum number of neighbour sets Formula
BETA_2 The other beta cluster metric 2 \(= \frac{A + B + C}{max((A+B), (A+C))} - 1\) 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.

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: \(= 1 - \frac{2W}{A + B}\) 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 \(W=\sum^n_{i=1} min(sample\_count\_label_{i_{set1}},sample\_count\_label_{i_{set2}})\) (meaning it sums the minimum of the sample counts for each of the \(n\) labels across the two neighbour sets),

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
BC_A The A factor used in calculations (see formula) 2
BC_B The B factor used in calculations (see formula) 2
BC_W The W factor used in calculations (see formula) region grower 2
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: \(= 1 - \frac{2W}{A + B}\) 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 \(W = \sum^n_{i=1} min(sample\_count\_label_{i_{set1}},sample\_count\_label_{i_{set2}})\) (meaning it sums the minimum of the normalised sample counts for each of the \(n\) labels across the two neighbour sets),

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
BCN_A The A factor used in calculations (see formula) 2
BCN_B The B factor used in calculations (see formula) 2
BCN_W The W factor used in calculations (see formula) region grower 2
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: \(= 1 - \frac{A}{A + B + C}\) 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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
JACCARD Jaccard value, 0 is identical, 1 is completely dissimilar cluster metric 2

Kulczynski 2

Description: Kulczynski 2 dissimilarity between two sets of labels.

Subroutine: calc_kulczynski2

Formula: \(= 1 - 0.5 \times (\frac{A}{A + B} + \frac{A}{A + C})\) 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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
KULCZYNSKI2 Kulczynski 2 index cluster metric 2

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.

Formula: \(=\frac{ \left | B - C \right | }{ 2A + B + C } \times \frac { A }{ A + min (B, C) }= SORENSON - S2\) 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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
NEST_RESULTANT Nestedness-resultant index cluster metric 2

Range weighted Sorenson

Description: Range weighted Sorenson

Subroutine: calc_rw_turnover

Reference: Laffan et al. (2016)

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
RW_TURNOVER Range weighted turnover cluster metric 2
RW_TURNOVER_A Range weighted turnover, shared component 2
RW_TURNOVER_B Range weighted turnover, component found only in nbr set 1 2
RW_TURNOVER_C Range weighted turnover, component found only in nbr set 2 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: \(= \sum_{i \in L} \sum_{j \in L} d_{ij} p_i p_j\) 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 \(i = j\) , and a value of 1 otherwise. \(L\) is the set of labels across both neighbour sets.

Indices:

Index Description Minimum number of neighbour sets
TX_RAO_QE Taxonomically weighted quadratic entropy 1
TX_RAO_TLABELS List of labels and values used in the TX_RAO_QE calculations 1
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.

Formula: \(= 1 - \frac{A}{A + min(B, C)}\) 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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
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, \(p_i\) is the number of samples of the i’th label as a proportion of the total number of samples \(n\) in the neighbourhoods.

Indices:

Index Description Minimum number of neighbour sets Formula
SHANNON_E Shannon’s evenness (H / HMAX) 1 \(Evenness = \frac{H}{HMAX}\)
SHANNON_H Shannon’s H 1 \(H = - \sum^n_{i=1} (p_i \cdot ln (p_i))\)
SHANNON_HMAX maximum possible value of Shannon’s H 1 \(HMAX = ln(richness)\)
SIMPSON_D Simpson’s D. A score of zero is more similar. 1 \(D = 1 - \sum^n_{i=1} p_i^2\)

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: \(= 1 - \frac{2A}{2A + B + C}\) 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.

Indices:

Index Description Grouping metric? Minimum number of neighbour sets
SORENSON Sorenson index cluster metric 2