Diversity.jl

A package for measuring and partitioning diversity

The main Diversity package measures the alpha, beta and gamma diversity of a metacommunity and of each of its subcommunities, for any notion of similarity between the individuals in it — taxonomic, phylogenetic, genetic, functional or phenotypic.

It provides numbers-equivalent diversity measures (Hill numbers), similarity-sensitive diversity measures generalising them, and the alpha, beta and gamma measures that partition those across subcommunities. The framework explains what each measure means and where it came from; start there if the names below are unfamiliar.

The diversity functions exist both with unicode names (e.g. ᾱ()), which are not automatically exported (as we feel they are too short) and with matching longer ASCII names (e.g. NormalisedAlpha()), which are. We also provide functions to calculate appropriate subdiv() and metadiv() values for each measure, and a general diversity() function to extract any diversity measure at a series of scales.

Accessing the main functionality in the package is simple:

julia> using Diversity
julia> pop = [1 1 0; 2 0 0; 3 1 4]3×3 Matrix{Int64}:
 1  1  0
 2  0  0
 3  1  4
julia> pop = pop ./ sum(pop)3×3 Matrix{Float64}:
 0.0833333  0.0833333  0.0
 0.166667   0.0        0.0
 0.25       0.0833333  0.333333
julia> meta = Metacommunity(pop)Metacommunity{Float64, Matrix{Float64}, Matrix{Float64}, UniqueTypes, Subcommunities} with 3 species in 3 subcommunities measuring Unique diversity.

Species names:
1, 2, 3

Subcommunity names:
1, 2, 3
julia> norm_meta_alpha(meta, [0, 1, 2, Inf])4×8 DataFrame
 Row │ div_type  measure          q        type_level  type_name  partition_le ⋯
     │ String    String           Float64  String      String     String       ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ Unique    NormalisedAlpha      0.0  types                  metacommunit ⋯
   2 │ Unique    NormalisedAlpha      1.0  types                  metacommunit
   3 │ Unique    NormalisedAlpha      2.0  types                  metacommunit
   4 │ Unique    NormalisedAlpha    Inf    types                  metacommunit
                                                               3 columns omitted

Every measure returns a DataFrame in the same format, whatever the measure and whatever the scale, so results can be compared and concatenated directly. The diversity column holds the answer; the rest say what was calculated and for what.

Adding a similarity matrix makes the measures similarity-sensitive — two types that resemble each other now contribute less diversity between them than two that do not:

julia> Z = [1.0 0 0; 0 1 1; 1 1 1]3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  1.0
 1.0  1.0  1.0
julia> meta_z = Metacommunity(pop, Z)Metacommunity{Float64, Matrix{Float64}, Matrix{Float64}, GeneralTypes{Float64, Matrix{Float64}, Vector{Int64}}, Subcommunities} with 3 species in 3 subcommunities measuring Arbitrary Z diversity.

Species names:
1, 2, 3

Subcommunity names:
1, 2, 3
julia> subdiv(RawRho(meta_z), 2)3×8 DataFrame
 Row │ div_type     measure  q      type_level  type_name  partition_level  pa ⋯
     │ String       String   Int64  String      String     String           St ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ Arbitrary Z  RawRho       2  types                  subcommunity     1  ⋯
   2 │ Arbitrary Z  RawRho       2  types                  subcommunity     2
   3 │ Arbitrary Z  RawRho       2  types                  subcommunity     3
                                                               2 columns omitted

Note that the abundances are relative to the whole metacommunity and must sum to one across it — not one per subcommunity. Counts are normalised for you, and floating point abundances that do not sum to one are corrected with a warning.

Diversity.Diversity — Module

Diversity package

The main Diversity package provides basic numbers-equivalent diversity measures (described in Hill, 1973), similarity-sensitive diversity measures (generalised from Hill, and described in Leinster and Cobbold, 2012), and related alpha, beta and gamma diversity measures at the level of the metacommunity and its component subcommunities (generalised in turn from Leinster and Cobbold, and described in Reeve et al, 2014). The diversity functions exist both with unicode names (e.g. ᾱ()), which are not automatically exported (as we feel they are too short) and with matching longer ASCII names (e.g. NormalisedAlpha()), which are. We also provide functions to calculate appropriate subcommunityDiversity() and metacommunityDiversity() values for each measure, and a general diversity() function to extract any diversity measure at a series of scales.