Diversity

A package for measuring and partitioning diversity

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Summary

Diversity is a Julia package that provides functionality for measuring alpha, beta and gamma diversity of metacommunities (e.g. ecosystems) and their constituent subcommunities. It uses the diversity measures described in the arXiv paper arXiv:1404.6520 (q-bio.QM), How to partition diversity. It also provides a series of other older diversity measures through sub-modules. Currently these are all ecological diversity measures, but this will be expanded through interfacing to EcoJulia and BioJulia.

This package is in beta now, but is cross-validated against our R package boydorr/rdiversity, which is developed independently, so please raise an issue if you find any problems. We now use a DataFrame as the common output format for all of the diversity calculations to provide consistency with our R package rdiversity. The code is not optimised for speed at the moment due to the substantial changes that have happened to it under the hood, and the Phylogenetics submodule is also recently revised, and may need further improvements.

Installation

The package is registered in the General registry on v1.x and so can be installed with add. For example on Julia v1.10:

``julia (@v1.10) pkg> add Diversity Resolving package versions... Updating~/.julia/environments/v1.10/Project.toml [d3d5718d] + Diversity v0.5.15 Updating~/.julia/environments/v1.10/Manifest.toml` [d3d5718d] + Diversity v0.5.15

(@v1.10) pkg> ```

Project Status

The package is confirmed to build and work against Julia v1.9 and the current release and the latest release on Linux, macOS, and Windows. It is also tested against nightly.

Contributing and Questions

Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems or would just like to ask a question.

Usage

Diversity Measures

The main 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 arXiv:1404.6520 (q-bio.QM)). 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 ascii names (e.g. NormalisedAlpha()), which are. We also provide a general function for extract any diversity measure for a series of subcommunity relative abundances.

Getting started

Before calculating diversity a Metacommunity object must be created. This object contains all the information needed to calculate diversity.

```julia

Load the package into Julia

using Diversity

Example population

pop = [1 1 0; 2 0 0; 3 1 4] pop = pop / sum(pop)

Create Metacommunity object

meta = Metacommunity(pop) ```

Calculating diversity

First we need to calculate the low-level diversity component seperately, by passing a metacommunity object to the appropriate function; RawAlpha(), NormalisedAlpha(), RawBeta(), NormalisedBeta(), RawRho(), NormalisedRho(), or Gamma().

```julia

First, calculate the normalised alpha component

component = NormalisedAlpha(meta) ```

Afterwhich, subdiv() or metadiv() are used to calculate subcommunity or metacommunity diversity, respectively (since both subcommunity and metacommunity diversity measures are transformations of the same low-level components, this is computationally more efficient).

```julia

Then, calculate species richness of the subcommunities

subdiv(component, 0)

or the average (alpha) species richness across the whole population

metadiv(component, 0)

We can also generate a diversity profile by calculating multiple q-values simultaneously

df = subdiv(component, 0:30) ```

In some instances, it may be useful to calculate all subcommunity (or metacommunity) measures. In which case, a Metacommunity object may be passed directly to subdiv() or metadiv():

```julia

To calculate all subcommunity diversity measures

subdiv(meta, 0:2)

To calculate all metacommunity diversity measures

metadiv(meta, 0:2) ```

Alternatively, if computational efficiency is not an issue, a single measure of diversity may be calculated directly by calling a wrapper function:

julia norm_sub_alpha(meta, 0:2)

A complete list of these functions is shown below:

• raw_sub_alpha() : per-subcommunity estimate of naive-community metacommunity diversity
• norm_sub_alpha() : similarity-sensitive diversity of each subcommunity in isolation
• raw_sub_rho() : redundancy of individual subcommunities
• norm_sub_rho() : representativeness of individual subcommunities
• raw_sub_beta() : distinctiveness of individual subcommunities
• norm_sub_beta() : per-subcommunity estimate of effective number of distinct subcommunities
• sub_gamma() : contribution per individual in a subcommunity toward metacommunity diversity
• raw_meta_alpha() : naive-community metacommunity diversity
• norm_meta_alpha() : average similarity-sensitive diversity of subcommunities
• raw_meta_rho() : average redundancy of subcommunities
• norm_meta_rho() : average representativeness of subcommunities
• raw_meta_beta() : average distinctiveness of subcommunities
• norm_meta_beta() : effective number of distinct subcommunities
• meta_gamma() : metacommunity similarity-sensitive diversity

Phylogenetic diversity

Phylogenetic diversity (described here) is automatically included in the Diversity module when the Phylo package is loaded. Documentation for these diversity measures can be found here. The phylogenetics code relies on the Phylo package to generate trees to incorporate into the diversity code, and the ppropriate code will be created when both main packages are loaded:

```julia-repl julia> using Diversity, Phylo

julia> communities = [4 1; 3 2; 1 0; 0 1] / 12;

julia> nt = rand(Nonultrametric(4)) RootedTree with 4 tips, 7 nodes and 6 branches. Leaf names are tip 1, tip 2, tip 4 and tip 3

julia> metaphylo = Metacommunity(communities, PhyloBranches(nt));

julia> rawmetarho(metaphylo, [1, 2]) 2×8 DataFrame │ Row │ divtype │ measure │ q │ typelevel │ typename │ partitionlevel │ partition_name │ diversity │ │ │ String │ String │ Int64 │ String │ String │ String │ String │ Float64 │ ├─────┼─────────────────────┼─────────┼───────┼────────────┼───────────┼─────────────────┼────────────────┼───────────┤ │ 1 │ Phylogenetic Branch │ RawRho │ 1 │ types │ │ metacommunity │ │ 1.7787 │ │ 2 │ Phylogenetic Branch │ RawRho │ 2 │ types │ │ metacommunity │ │ 1.66749 │ ```

The package also provides some other sub-modules for related measures:

Diversity.Ecology

Many existing ecological diversity measures can be derived from our diversity measures, and so we provide them in the Diversity.Ecology submodule along with generalised versions of them that relate to our general measures of alpha, beta and gamma diversity at subcommunity and metacommunity levels. The generalisations of species richness, Shannon entropy and Simpson's index are the only standard measures we are aware of whose subcommunity components sum directly to the corresponding metacommunity measure (although note that Simpson's index decreases for increased diversity, so small components are more diverse). Documentation for these diversity measures can be found here.

Diversity.Hill

Hill numbers are found in the Diversity.Hill sub-module. Documentation for these diversity measures can be found here.

Diversity.Jost

Lou Jost's diversity measures are found in the Diversity.Jost sub-module. Documentation for these diversity measures is here.

Documentation

Documentation is generated by the Base documentation in Julia and online via the Documenter package.

Using the docs

Accessing the documentation in Julia is easy:

```julia using Diversity

Returns any documentation for the subdiv() function

?subdiv ```

The documentation is also available online.

Latest release

The online documentation for the current stable release is here.

Development branch

The online documentation for the latest dev (unreleased) branch is here.