Beta Diversity Functions
Beta diversity is a fundamental concept in ecology that quantifies the variation in species composition between different plots, or over time. In the context of community ecology, beta diversity functions help to assess how community composition changes spatially or temporally.
The beta_diversity functions in MetaCommunityMetrics are adapted from the beta.div.comp function in the R package adespatial. These methods, originally developed by Legendre (2014), are implemented in Julia to provide a more efficient means of computation for large-scale datasets. The functions use indices from the Podani family, Jaccard-based indices, and Ruzicka-based indices to calculate total beta diversity and its components: replacement and richness difference.
Choosing the Right Function
- Use
beta_diversityfor a general, comprehensive measure of beta diversity across your dataset. This function provides an overall assessment of how species composition varies between sites or over time, capturing both replacement (the turnover of species) and richness difference(the difference in species richness). - Use
spatial_beta_divto compare local communities of a metacommunity across different spatial locations with individual species abundance in each site aggregated across all time points. - Use
temporal_beta_divto compare metacommunities over time with individual species abundance aggregated across all sites.
The Functions
MetaCommunityMetrics.beta_diversity — Functionbeta_diversity(mat::Matrix; quant::Bool) -> DataFrameCalculate beta diversity decompositions for a given biodiversity data. This function supports both binary (occurrences) and quantitative (abundance) data.
Arguments
mat::Matrix: A matrix where each row represents a site and each column represents a species. The elements of the matrix should represent the occurrence or abundance of species.quant::Bool: Specifies the data type for analysis. Whenfalse, treats data as occurrences, converting any quantitative values into binary values and applying Jaccard-based indices. Whentrue, treats data as abundance data and applies Ruzicka-based indices.
Returns
DataFrame: A DataFrame with the following columns:BDtotal: Total beta diversity, which captures the overall dissimilarity between local communities.Repl: Replacement component of diversity, which reflects species turnover between sites: how much communities differ due to having different species compositions rather than different species counts.RichDif: Richness difference component of diversity, which captures differences in the number of species between communities.
Details
- Empty sites (empty rows in the matrix) have to be removed before calculation.
- Species that did not occupy any sites in the data (empty columns in the matrix) have to be removed before calculation.
- This function is a translation/adaptation of the
beta.div.compfunction from the R packageadespatial`, licensed under GPL-3. - Original package and documentation available at: https://cran.r-project.org/web/packages/adespatial/index.html
Example
julia> using MetaCommunityMetrics, Pipe, DataFrames
julia> df = load_sample_data()
53352×12 DataFrame
Row │ Year Month Day Sampling_date_order plot Species Abundance Presence Latitude Longitude standardized_temperature standardized_precipitation
│ Int64 Int64 Int64 Int64 Int64 String3 Int64 Int64 Float64 Float64 Float64 Float64
───────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 │ 2010 1 16 1 1 BA 0 0 35.0 -110.0 0.829467 -1.4024
2 │ 2010 1 16 1 2 BA 0 0 35.0 -109.5 -1.12294 -0.0519895
3 │ 2010 1 16 1 4 BA 0 0 35.0 -108.5 -0.409808 -0.803663
4 │ 2010 1 16 1 8 BA 0 0 35.5 -109.5 -1.35913 -0.646369
5 │ 2010 1 16 1 9 BA 0 0 35.5 -109.0 0.0822 1.09485
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
53348 │ 2023 3 21 117 9 SH 0 0 35.5 -109.0 -0.571565 -0.836345
53349 │ 2023 3 21 117 10 SH 0 0 35.5 -108.5 -2.33729 -0.398522
53350 │ 2023 3 21 117 12 SH 1 1 35.5 -107.5 0.547169 1.03257
53351 │ 2023 3 21 117 16 SH 0 0 36.0 -108.5 -0.815015 0.95971
53352 │ 2023 3 21 117 23 SH 0 0 36.5 -108.0 0.48949 -1.59416
53342 rows omitted
julia> matrix_with_abundance = @pipe df |>
select(_, Not(:Year, :Month, :Day, :Longitude, :Latitude, :standardized_temperature, :standardized_precipitation, :Presence)) |>
filter(row -> row[:Sampling_date_order] == 1, _) |>
unstack(_, :Species, :Abundance, fill=0) |>
select(_, Not(:Sampling_date_order, :plot)) |>
Matrix(_) |> #convert the dataframe to a matrix
_[:, sum(_, dims=1)[1, :] .!= 0] |>
_[sum(_, dims=2)[:, 1] .!= 0,:]
15×5 Matrix{Union{Missing, Int64}}:
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
2 0 0 0 0
1 0 0 1 0
4 0 0 1 0
1 0 0 0 0
⋮
0 0 0 2 0
1 0 0 0 0
0 0 0 1 0
0 0 0 0 1
0 0 1 0 0
0 0 0 0 1
julia> matrix_with_presence = @pipe df |>
select(_, Not(:Year, :Month, :Day, :Longitude, :Latitude, :standardized_temperature, :standardized_precipitation, :Abundance)) |>
filter(row -> row[:Sampling_date_order] == 1, _) |>
unstack(_, :Species, :Presence, fill=0) |>
select(_, Not(:Sampling_date_order, :plot)) |>
Matrix(_) |> #convert the dataframe to a matrix
_[:, sum(_, dims=1)[1, :] .!= 0] |>
_[sum(_, dims=2)[:, 1] .!= 0,:]
15×5 Matrix{Int64}:
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
1 0 0 1 0
1 0 0 1 0
1 0 0 0 0
⋮
0 0 0 1 0
1 0 0 0 0
0 0 0 1 0
0 0 0 0 1
0 0 1 0 0
0 0 0 0 1
julia> result_using_abanduce_data_1 = beta_diversity(matrix_with_abundance; quant=true)
1×3 DataFrame
Row │ BDtotal Repl RichDif
│ Float64 Float64 Float64
─────┼─────────────────────────────
1 │ 0.390317 0.2678 0.122517
julia> result_using_abanduce_data_2 = beta_diversity(matrix_with_abundance; quant=false)
1×3 DataFrame
Row │ BDtotal Repl RichDif
│ Float64 Float64 Float64
─────┼───────────────────────────────
1 │ 0.357143 0.284127 0.0730159
julia> result_using_binary_data = beta_diversity(matrix_with_presence; quant=false)
1×3 DataFrame
Row │ BDtotal Repl RichDif
│ Float64 Float64 Float64
─────┼───────────────────────────────
1 │ 0.357143 0.284127 0.0730159MetaCommunityMetrics.spatial_beta_div — Functionspatial_beta_div(abundance::AbstractVector, time::AbstractVector, site::AbstractVector, species::AbstractVector; quant::Bool) -> DataFrameCalculate the beta diversity decompositions in space based on species abundances or occurrences.
Arguments
abundance::AbstractVector: Vector representing the abundance or occurrence of species.time::AbstractVector: Vector representing sampling dates.site::AbstractVector: Vector representing site names or IDs.species::AbstractVector: Vector representing species names or IDs.quant::Bool: Specifies the data type for analysis. Whenfalse, treats data as binary presence/absence, converting any quantitative values and applying Jaccard-based indices. Whentrue, treats data as abundance data and applies Ruzicka-based indices.
Returns
DataFrame: A DataFrame containing the values of total beta diversity, replacement, and richness difference components in space. Columns arespatial_BDtotal,spatial_Repl, andspatial_RichDif.
Details
- This function uses the
beta_diversityfunction to calculate beta diversity decompositions after aggregating individual species abundances/occurrences across time. - For binary data, the function calculates Podani family, Jaccard-based indices.
- For quantitative data, the function calculates Podani family, Ruzicka-based indices.
Example
julia> using MetaCommunityMetrics, Pipe, DataFrames
julia> df = load_sample_data()
53352×12 DataFrame
Row │ Year Month Day Sampling_date_order plot Species Abundance Presence Latitude Longitude standardized_temperature standardized_precipitation
│ Int64 Int64 Int64 Int64 Int64 String3 Int64 Int64 Float64 Float64 Float64 Float64
───────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 │ 2010 1 16 1 1 BA 0 0 35.0 -110.0 0.829467 -1.4024
2 │ 2010 1 16 1 2 BA 0 0 35.0 -109.5 -1.12294 -0.0519895
3 │ 2010 1 16 1 4 BA 0 0 35.0 -108.5 -0.409808 -0.803663
4 │ 2010 1 16 1 8 BA 0 0 35.5 -109.5 -1.35913 -0.646369
5 │ 2010 1 16 1 9 BA 0 0 35.5 -109.0 0.0822 1.09485
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
53348 │ 2023 3 21 117 9 SH 0 0 35.5 -109.0 -0.571565 -0.836345
53349 │ 2023 3 21 117 10 SH 0 0 35.5 -108.5 -2.33729 -0.398522
53350 │ 2023 3 21 117 12 SH 1 1 35.5 -107.5 0.547169 1.03257
53351 │ 2023 3 21 117 16 SH 0 0 36.0 -108.5 -0.815015 0.95971
53352 │ 2023 3 21 117 23 SH 0 0 36.5 -108.0 0.48949 -1.59416
53342 rows omitted
julia> result_using_abanduce_data_1 = spatial_beta_div(df.Abundance, df.Sampling_date_order, df.plot, df.Species; quant=true)
1×3 DataFrame
Row │ spatial_BDtotal spatial_Repl spatial_RichDif
│ Float64 Float64 Float64
─────┼────────────────────────────────────────────────
1 │ 0.264822 0.121882 0.142939
julia> result_using_abanduce_data_2 = spatial_beta_div(df.Abundance, df.Sampling_date_order, df.plot, df.Species; quant=false)
1×3 DataFrame
Row │ spatial_BDtotal spatial_Repl spatial_RichDif
│ Float64 Float64 Float64
─────┼────────────────────────────────────────────────
1 │ 0.133035 0.05976 0.0732746
julia> result_using_binary_data = spatial_beta_div(df.Presence, df.Sampling_date_order, df.plot, df.Species; quant=false)
1×3 DataFrame
Row │ spatial_BDtotal spatial_Repl spatial_RichDif
│ Float64 Float64 Float64
─────┼────────────────────────────────────────────────
1 │ 0.133035 0.05976 0.0732746MetaCommunityMetrics.temporal_beta_div — Functiontemporal_beta_div(abundance::AbstractVector, time::AbstractVector, site::AbstractVector, species::AbstractVector;quant::Bool) -> DataFrameCalculate the beta diversity decompositions in time based on species abundances or occurrences.
Arguments
abundance::AbstractVector: Vector representing the abundance or occurrence of species.time::AbstractVector: Vector representing sampling dates.site::AbstractVector: Vector representing site names or IDs.species::AbstractVector: Vector representing species names or IDs.quant::Bool: Specifies the data type for analysis. Whenfalse, treats data as occurrences, converting any quantitative values into binary values and applying Jaccard-based indices. Whentrue, treats data as abundance data and applies Ruzicka-based indices.
Returns
DataFrame: A DataFrame containing the values of total beta diversity, replacement, and richness difference components in time. Columns aretemporal_BDtotal,temporal_Repl, andtemporal_RichDif.
Details
- This function uses the
beta_diversityfunction to calculate beta diversity decompositions after aggregating individual species abundances/occurrences across sites. - For binary data, the function calculates Podani family, Jaccard-based indices.
- For quantitative data, the function calculates Podani family, Ruzicka-based indices.
Example
julia> using MetaCommunityMetrics, Pipe, DataFrames
julia> df = load_sample_data()
53352×12 DataFrame
Row │ Year Month Day Sampling_date_order plot Species Abundance Presence Latitude Longitude standardized_temperature standardized_precipitation
│ Int64 Int64 Int64 Int64 Int64 String3 Int64 Int64 Float64 Float64 Float64 Float64
───────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 │ 2010 1 16 1 1 BA 0 0 35.0 -110.0 0.829467 -1.4024
2 │ 2010 1 16 1 2 BA 0 0 35.0 -109.5 -1.12294 -0.0519895
3 │ 2010 1 16 1 4 BA 0 0 35.0 -108.5 -0.409808 -0.803663
4 │ 2010 1 16 1 8 BA 0 0 35.5 -109.5 -1.35913 -0.646369
5 │ 2010 1 16 1 9 BA 0 0 35.5 -109.0 0.0822 1.09485
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
53348 │ 2023 3 21 117 9 SH 0 0 35.5 -109.0 -0.571565 -0.836345
53349 │ 2023 3 21 117 10 SH 0 0 35.5 -108.5 -2.33729 -0.398522
53350 │ 2023 3 21 117 12 SH 1 1 35.5 -107.5 0.547169 1.03257
53351 │ 2023 3 21 117 16 SH 0 0 36.0 -108.5 -0.815015 0.95971
53352 │ 2023 3 21 117 23 SH 0 0 36.5 -108.0 0.48949 -1.59416
53342 rows omitted
julia> result_using_abanduce_data_1 = temporal_beta_div(df.Abundance, df.Sampling_date_order, df.plot, df.Species; quant=true)
1×3 DataFrame
Row │ temporal_BDtotal temporal_Repl temporal_RichDif
│ Float64 Float64 Float64
─────┼───────────────────────────────────────────────────
1 │ 0.311222 0.0995483 0.211674
julia> result_using_abanduce_data_2 = temporal_beta_div(df.Abundance, df.Sampling_date_order, df.plot, df.Species; quant=false)
1×3 DataFrame
Row │ temporal_BDtotal temporal_Repl temporal_RichDif
│ Float64 Float64 Float64
─────┼───────────────────────────────────────────────────
1 │ 0.206262 0.0693664 0.136895
julia> result_using_binary_data = temporal_beta_div(df.Presence, df.Sampling_date_order, df.plot, df.Species; quant=false)
1×3 DataFrame
Row │ temporal_BDtotal temporal_Repl temporal_RichDif
│ Float64 Float64 Float64
─────┼───────────────────────────────────────────────────
1 │ 0.206262 0.0693664 0.136895References
- Legendre, P. (2014). Interpreting the replacement and richness difference components of beta diversity. Global Ecology and Biogeography, 23(11), 1324-1334. https://doi.org:https://doi.org/10.1111/geb.12207