Diversity.Ecology

In the Diversity.Ecology submodule, we replicate old ecological diversity measures and generalised versions of them that relate to our general measures of alpha, beta and gamma diversity at subcommunity and ecosystem measures. The generalisations of the richness, Shannon and Simpson are the only standard measures we are aware of whose subcommunity components sum directly to the corresponding ecosystem measure (although note that Simpson's index decreases for increased diversity, so small components are more diverse).

Usage

Accessing the functionality in the package is simple:

julia> using Diversity.Ecology, LinearAlgebra

julia> community = [10, 20, 20];

julia> community = community ./ sum(community); # Convert counts to proportions

julia> diversity = simpson(community)
1×7 DataFrame
 Row │ div_type  measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String    String   String      String     String           String          Float64   
─────┼──────────────────────────────────────────────────────────────────────────────────────
   1 │ Unique    Simpson  types                  subcommunity     1                    0.36

julia> ecosystem = [2 2 0; 0 2 2]';

julia> ecosystem = ecosystem ./ sum(ecosystem);

julia> jaccard(ecosystem)
1×8 DataFrame
 Row │ div_type  measure  q      type_level  type_name  partition_level  partition_name  diversity 
     │ String    String   Int64  String      String     String           String          Float64   
─────┼─────────────────────────────────────────────────────────────────────────────────────────────
   1 │ Unique    Jaccard      0  types                  metacommunity                     0.333333

julia> generalisedjaccard(Metacommunity(ecosystem))
1×7 DataFrame
 Row │ div_type  measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String    String   String      String     String           String          Float64   
─────┼──────────────────────────────────────────────────────────────────────────────────────
   1 │ Unique    Jaccard  types                  metacommunity                     0.333333

julia> generalisedjaccard(ecosystem, Matrix(1.0I, 3, 3))
1×7 DataFrame
 Row │ div_type     measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String       String   String      String     String           String          Float64   
─────┼─────────────────────────────────────────────────────────────────────────────────────────
   1 │ Arbitrary Z  Jaccard  types                  metacommunity                     0.333333

julia> community = [0.7, 0.2, 0.1];

julia> pielou(community)
1×7 DataFrame
 Row │ div_type  measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String    String   String      String     String           String          Float64   
─────┼──────────────────────────────────────────────────────────────────────────────────────
   1 │ Unique    Pielou   types                  subcommunity     1                0.729847

julia> communitymat = [10 20 30 20 0; #5 sites/subcommunities (columns) and 6 species (rows)
                       10 0 50 80 10;
                       60 10 90 0 0; 
                       10 10 10 10 10;
                       70 70 70 70 70;
                       10 0 0 90 0];

julia> generalisedpielou(subcommunityDiversity, communitymat)
5×7 DataFrame
 Row │ div_type     measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String       String   String      String     String           String          Float64   
─────┼─────────────────────────────────────────────────────────────────────────────────────────
   1 │ Arbitrary Z  Pielou   types                  subcommunity     1                0.781115
   2 │ Arbitrary Z  Pielou   types                  subcommunity     2                0.745557
   3 │ Arbitrary Z  Pielou   types                  subcommunity     3                0.888073
   4 │ Arbitrary Z  Pielou   types                  subcommunity     4                0.864562
   5 │ Arbitrary Z  Pielou   types                  subcommunity     5                0.622366

julia> generalisedpielou(metacommunityDiversity, communitymat)
1×7 DataFrame
 Row │ div_type     measure  type_level  type_name  partition_level  partition_name  diversity 
     │ String       String   String      String     String           String          Float64   
─────┼─────────────────────────────────────────────────────────────────────────────────────────
   1 │ Arbitrary Z  Pielou   types                  metacommunity                     0.510146

Diversity.Ecology — Module

Diversity.Ecology submodule

The Diversity.Ecology module replicates old ecological diversity measures and generalised versions of them that relate to our general measures of alpha, beta and gamma diversity at subcommunity and metacommunity levels. The generalisations of the richness, Shannon and Simpson are the only standard measures we are aware of whose subcommunity components sum directly to the corresponding ecosystem measure (although note that Simpson's index decreases for increased diversity, so small components are more diverse).

source

Diversity.Ecology.generalisedjaccard — Function

generalisedjaccard(proportions::AbstractArray, qs, Z::AbstractMatrix)
generalisedjaccard(proportions::AbstractArray, qs, sim::AbstractTypes)
generalisedjaccard(meta::AbstractAssemblage, qs)

Calculates a generalisation of the Jaccard similarity of two columns representing the counts of two subcommunities. This evaluates to raw alpha / gamma - 1 for a series of orders, repesented as a vector of qs (or a single number). It also includes an optional similarity matrix for the species. This gives a measure of the distinctness of the subcommunities, though we believe that beta and normalised beta have better properties.

Arguments:

proportions: population proportions
meta: metacommunity / assemblage
Z: similarity matrix or
sim: instance of AbstractTypes

Returns:

Jaccard-related distinctivess measures

source

Diversity.Ecology.generalisedrichness — Function

generalisedrichness(level::DiversityLevel, proportions::AbstractArray,
                    Z::AbstractMatrix)
generalisedrichness(level::DiversityLevel, proportions::AbstractArray,
                    sim::AbstractTypes)

Calculates species richness (diversity at q = 0) of a series of columns representing subcommunity counts, allowing a similarity matrix for the types / species.

Arguments:

level: DiversityLevel to calculate at (e.g. subcommunityDiversity)
proportions: population proportions
Z: similarity matrix or
sim: instance of AbstractTypes

Returns:

diversity (at ecosystem level) or diversities (of subcommunities)

source

Diversity.Ecology.generalisedshannon — Function

generalisedshannon(level::DiversityLevel, proportions::AbstractArray,
                   Z::AbstractMatrix)
generalisedshannon(level::DiversityLevel, proportions::AbstractArray,
                   sim::AbstractTypes)

Calculates Shannon entropy (log of diversity at q = 1) of a series of columns representing independent subcommunity counts, allowing a similarity matrix for the types / species.

Arguments:

level: DiversityLevel to calculate at (e.g. subcommunityDiversity)
proportions: population proportions
Z: similarity matrix or
sim: instance of AbstractTypes

Returns:

entropy (at metacommunity level) or entropies (of subcommunities)

source

Diversity.Ecology.generalisedsimpson — Function

generalisedsimpson(level::DiversityLevel, proportions::AbstractArray,
                   Z::AbstractMatrix)
generalisedsimpson(level::DiversityLevel, proportions::AbstractArray,
                   sim::AbstractTypes)

Calculates Simpson's index (1 / diversity at q = 2) of a series of columns representing independent subcommunity counts, allowing a similarity matrix for the types / species.

Arguments:

level: DiversityLevel to calculate at (e.g. subcommunityDiversity)
proportions: population proportions
Z: similarity matrix or
sim: instance of AbstractTypes

Returns:

concentration (at ecosystem level) or concentrations (of subcommunities)

source

Diversity.Ecology.gower — Function

gower(proportions::AbstractMatrix; countzeros::Bool = false, logscale::Bool = true)
gower(asm::AbstractAssemblage; countzeros::Bool = false, logscale::Bool = true)

Calculates Gower's dissimarity of up to two columns representing independent subcommunity counts.

Arguments:

proportions: population proportions; or
count: population counts; or
asm: Abstract Assemblage
``

Returns:

Gower dissimilarity of the subcommunities

source

Diversity.Ecology.jaccard — Method

jaccard(proportions::AbstractMatrix)
jaccard(asm::AbstractAssemblage)

Calculates Jaccard similarity coefficient of two columns representing independent subcommunity counts

Arguments:

proportions: population proportions
asm: assemblage / metacommunity

Returns:

the Jaccard index

source

Diversity.Ecology.pielou — Method

pielou(proportions::AbstractMatrix)
pielou(asm::AbstractAssemblage)

Calculates Pielou's evenness of a series of columns representing independent subcommunity counts.

Arguments:

proportions: population proportions

Returns:

evenness of subcommunities

Example:

communitymat = [10 20 30 20 0;
                10 0 50 80 10;
                60 10 90 0 0; 
                10 10 10 10 10;
                70 70 70 70 70;
                10 0 0 90 0];

pielou(communitymat)

source

Diversity.Ecology.richness — Method