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Ecology

In the Diversity.Ecology package, 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

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

julia> community /= sum(community);

julia> diversity = simpson(community)
1×7 DataFrames.DataFrame
│ Row │ measure   │ q │ type_level │ type_name │ partition_level │
├─────┼───────────┼───┼────────────┼───────────┼─────────────────┤
│ 1   │ "Simpson" │ 2 │ "types"    │ ""        │ "subcommunity"  │

│ Row │ partition_name │ diversity │
├─────┼────────────────┼───────────┤
│ 1   │ "1"            │ 0.36      │

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

julia> ecosystem /= sum(ecosystem);

julia> jaccard(ecosystem)
1×7 DataFrames.DataFrame
│ Row │ measure   │ q │ type_level │ type_name │ partition_level │
├─────┼───────────┼───┼────────────┼───────────┼─────────────────┤
│ 1   │ "Jaccard" │ 0 │ "types"    │ ""        │ "metacommunity" │

│ Row │ partition_name │ diversity │
├─────┼────────────────┼───────────┤
│ 1   │ ""             │ 0.333333  │

julia> generalisedjaccard(ecosystem, [0, 1, 2])
3×7 DataFrames.DataFrame
│ Row │ measure   │ q │ type_level │ type_name │ partition_level │
├─────┼───────────┼───┼────────────┼───────────┼─────────────────┤
│ 1   │ "Jaccard" │ 0 │ "types"    │ ""        │ "metacommunity" │
│ 2   │ "Jaccard" │ 1 │ "types"    │ ""        │ "metacommunity" │
│ 3   │ "Jaccard" │ 2 │ "types"    │ ""        │ "metacommunity" │

│ Row │ partition_name │ diversity │
├─────┼────────────────┼───────────┤
│ 1   │ ""             │ 0.333333  │
│ 2   │ ""             │ 0.414214  │
│ 3   │ ""             │ 0.5       │

julia> generalisedjaccard(ecosystem, [0, 1, 2], eye(3))
3×7 DataFrames.DataFrame
│ Row │ measure   │ q │ type_level │ type_name │ partition_level │
├─────┼───────────┼───┼────────────┼───────────┼─────────────────┤
│ 1   │ "Jaccard" │ 0 │ "types"    │ ""        │ "metacommunity" │
│ 2   │ "Jaccard" │ 1 │ "types"    │ ""        │ "metacommunity" │
│ 3   │ "Jaccard" │ 2 │ "types"    │ ""        │ "metacommunity" │

│ Row │ partition_name │ diversity │
├─────┼────────────────┼───────────┤
│ 1   │ ""             │ 0.333333  │
│ 2   │ ""             │ 0.414214  │
│ 3   │ ""             │ 0.5       │

Diversity.jl

# Diversity.Ecology — Module.

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)

Calculates a generalisation of the Jaccard index 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
qs: single number or vector of values of parameter q
Z: similarity matrix

Returns:

Jaccard-related distinctivess measures

source

# Diversity.Ecology.generalisedrichness — Function.

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

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

Returns:

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

source

# Diversity.Ecology.generalisedshannon — Function.

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

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

Returns:

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

source

# Diversity.Ecology.generalisedsimpson — Function.

Calculate a generalised version of Simpson's index

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

Returns:

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

source

# Diversity.Ecology.jaccard — Method.

jaccard(proportions::AbstractMatrix)

Calculates Jaccard index (Jaccard similarity coefficient) of two columns representing independent subcommunity counts, which is normmetaalpha(proportions, 0) / metagamma(proportions, 0) - 1

Arguments:

proportions: population proportions

Returns:

the Jaccard index

source

# Diversity.Ecology.richness — Method.

richness(proportions::AbstractMatrix)

Calculates species richness (diversity at q = 0) of a series of columns representing independent subcommunity counts.

Arguments:

proportions: population proportions

Returns:

diversities of subcommunities

source

# Diversity.Ecology.shannon — Method.

Calculate Shannon entropy of populations

Calculates shannon entropy (log of diversity at q = 1) of a series of columns representing independent subcommunity counts.

Arguments:

proportions: population proportions

Returns:

entropies of subcommunities

source

# Diversity.Ecology.simpson — Method.

simpson(proportions::AbstractMatrix)

Calculates Simpson's index (1 / diversity at q = 2) of a series of columns representing independent subcommunity counts.

Arguments:

proportions: population proportions

Returns:

concentrations of subcommunities

source