Pairwise Hill-number dissimilarity

For every pair of sites, beta_hill_pair() computes gamma, alpha and beta diversity of order q from the observed abundances. It also gives the four normalised dissimilarities of Chao, Chiu and Jost (2014) for two assemblages, with the same names as in beta_hill(): dis_sorensen (\(1 - C_{qN}\)), dis_jaccard (\(1 - U_{qN}\)), dis_turnover_sorensen (\(1 - V_{qN}\)) and dis_turnover_jaccard (\(1 - S_{qN}\)). Classic indices are special cases:

Usage

beta_hill_pair(
  data,
  site = site,
  species = species,
  abundance = NULL,
  q = c(0, 1, 2),
  weight = c("equal", "size"),
  .by = NULL
)

Arguments

data

A data frame in long format, with one row per record.

site, species

<tidy-select> The column holding site identifiers and the column holding species names.

abundance

<tidy-select> The column holding counts. If NULL (the default), a column called abundance is used when present, otherwise every row counts as one individual.

q

Orders of diversity, between 0 and 3 (non-negative numbers).

weight

"equal" or "size", as described above.

.by

<tidy-select> Optional grouping columns, kept in the output. Grouped data frames are also respected.

Value

A td_beta_hill_pair tibble with the grouping columns, site_1, site_2, q, gamma, alpha, beta and the four dis_ columns. beta_dist() turns one order into a distance matrix, and ggplot2::autoplot() draws it as a heatmap.

Details

Order	dis_sorensen	dis_jaccard
q = 0	Sorensen	Jaccard
q = 1	Horn	Horn
q = 2	Morisita-Horn	Regional overlap

With weight = "equal" (the default) each site's abundances are turned into relative abundances before pooling, so a heavily sampled site does not dominate the pair, and q = 2 gives Morisita-Horn exactly. With weight = "size" raw abundances are pooled, as in beta_hill() and iNEXT.beta3D. At q = 0 the weighting makes no difference.

These are empirical values. Use beta_hill() to compare whole sets of sites at a standardised sample coverage.

References

Chao, A., Chiu, C.-H. and Jost, L. (2014). Unifying species diversity, phylogenetic diversity, functional diversity, and related similarity and differentiation measures through Hill numbers. Annual Review of Ecology, Evolution, and Systematics, 45, 297-324. doi:10.1146/annurev-ecolsys-120213-091540

Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427-2439. doi:10.1890/06-1736.1

Examples

beta_hill_pair(png_ants, abundance = workers, .by = season)
#> # A tibble: 60 x 11
#>    season site_1 site_2     q gamma alpha  beta dis_sorensen dis_jaccard
#>    <chr>  <chr>  <chr>  <dbl> <dbl> <dbl> <dbl>        <dbl>       <dbl>
#>  1 dry    MW0200 MW0700     0    26  15.5  1.68        0.677       0.808
#>  2 dry    MW0200 MW1200     0    26  14.5  1.79        0.793       0.885
#>  3 dry    MW0200 MW1700     0    20  10.5  1.90        0.905       0.95 
#>  4 dry    MW0200 MW2200     0    22  11    2           1           1    
#>  5 dry    MW0700 MW1200     0    23  14    1.64        0.643       0.783
#>  6 dry    MW0700 MW1700     0    19  10    1.9         0.9         0.947
#>  7 dry    MW0700 MW2200     0    20  10.5  1.90        0.905       0.95 
#>  8 dry    MW1200 MW1700     0    18   9    2           1           1    
#>  9 dry    MW1200 MW2200     0    18   9.5  1.89        0.895       0.944
#> 10 dry    MW1700 MW2200     0    11   5.5  2           1           1    
#> # i 50 more rows
#> # i 2 more variables: dis_turnover_sorensen <dbl>, dis_turnover_jaccard <dbl>