Community data

Community data is:

• either a numeric vector containing abundances of species (the numberof individual of each species) or their probabilities (the proportion ofindividuals of each species, summing to 1). This format is convenientwhen a single community is considered.
• or a dataframe whose rows are communities and column are species.Its values are either abundances or probabilities. Special columnscontain the site names, and their weights (e.g. their area or number ofindividuals).

Example data is provided in the datasetparacou_6_abd.Let’s get the abundances of tree species in the 6.25-ha tropical forestplot #6 from Paracou forest station in French Guiana. It is divided into4 equally-sized subplots:

library("divent")

## Le chargement a nécessité le package : Rcpp

paracou_6_abd

## # A tibble: 4 × 337##   site      weight Abarema_jupunba Abarema_mataybifolia Amaioua_guianensis##   <chr>      <dbl>           <int>                <int>              <int>## 1 subplot_1   1.56               2                    2                  1## 2 subplot_2   1.56               2                    0                  1## 3 subplot_3   1.56               2                    2                  0## 4 subplot_4   1.56               4                    0                  0## # ℹ 332 more variables: Amanoa_congesta <int>, Amanoa_guianensis <int>,## #   Ambelania_acida <int>, Amphirrhox_longifolia <int>, Andira_coriacea <int>,## #   Apeiba_glabra <int>, Aspidosperma_album <int>, Aspidosperma_cruentum <int>,## #   Aspidosperma_excelsum <int>, Bocoa_prouacensis <int>,## #   Brosimum_guianense <int>, Brosimum_rubescens <int>, Brosimum_utile <int>,## #   Carapa_surinamensis <int>, Caryocar_glabrum <int>, Casearia_decandra <int>,## #   Casearia_javitensis <int>, Catostemma_fragrans <int>, …

# Number of individuals in each communityabd_sum(paracou_6_abd)

## # A tibble: 4 × 3##   site      weight abundance##   <chr>      <dbl>     <dbl>## 1 subplot_1   1.56       942## 2 subplot_2   1.56       872## 3 subplot_3   1.56       929## 4 subplot_4   1.56       798

The data inparacou_6_abd is an object of classabundances, i.e. a tibble with species as columns and sitesas rows. It can be manipulated as any dataframe and plotted as arank-abundance curve:

autoplot(paracou_6_abd[1, ])

Thercommunity function allows drawing randomcommunities, e.g. a log-normal one(Preston1948):

rc<-rcommunity(1,size =10000,distribution ="lnorm")autoplot(rc,fit_rac =TRUE,distribution ="lnorm")

The Whittaker plot (rank-abundance curve) of a random log-normaldistribution of 10000 individuals simulated with default parameter(\(\sigma = 1\)) is produced.

Diversity estimation

The classical indices of diversity are richness (the number ofspecies), Shannon’s and Simpson’s entropies:

div_richness(paracou_6_abd)

## # A tibble: 4 × 5##   site      weight estimator   order diversity##   <chr>      <dbl> <chr>       <dbl>     <dbl>## 1 subplot_1   1.56 Jackknife 3     0       355## 2 subplot_2   1.56 Jackknife 2     0       348## 3 subplot_3   1.56 Jackknife 2     0       315## 4 subplot_4   1.56 Jackknife 2     0       296

ent_shannon(paracou_6_abd)

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 UnveilJ       1    4.57## 2 subplot_2   1.56 UnveilJ       1    4.73## 3 subplot_3   1.56 UnveilJ       1    4.65## 4 subplot_4   1.56 UnveilJ       1    4.55

ent_simpson(paracou_6_abd)

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 Lande         2   0.976## 2 subplot_2   1.56 Lande         2   0.978## 3 subplot_3   1.56 Lande         2   0.980## 4 subplot_4   1.56 Lande         2   0.972

When applied to probabilities (created withas_probaVector in the following example), noestimation-bias correction is applied: this means that indices are justcalculated by applying their definition function to the probabilities(that is the naive, or plugin estimator).

library("dplyr")

## ## Attachement du package : 'dplyr'

## Les objets suivants sont masqués depuis 'package:stats':## ##     filter, lag

## Les objets suivants sont masqués depuis 'package:base':## ##     intersect, setdiff, setequal, union

paracou_6_abd%>%as_probabilities()%>%ent_shannon()

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 naive         1    4.34## 2 subplot_2   1.56 naive         1    4.48## 3 subplot_3   1.56 naive         1    4.45## 4 subplot_4   1.56 naive         1    4.32

When abundances are available, many estimators can be used(Marcon 2015) to address unobserved species andthe non-linearity of the indices:

ent_shannon(paracou_6_abd)

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 UnveilJ       1    4.57## 2 subplot_2   1.56 UnveilJ       1    4.73## 3 subplot_3   1.56 UnveilJ       1    4.65## 4 subplot_4   1.56 UnveilJ       1    4.55

ent_shannon(paracou_6_abd,estimator ="ChaoJost")

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 ChaoJost      1    4.51## 2 subplot_2   1.56 ChaoJost      1    4.68## 3 subplot_3   1.56 ChaoJost      1    4.62## 4 subplot_4   1.56 ChaoJost      1    4.50

The best available estimator is chosen by default: its name isreturned.

Those indices are special cases of the Tsallis entropy(1988) or order\(q\) (respectively\(q=0,1,2\) for richness, Shannon,Simpson):

ent_tsallis(paracou_6_abd,q =1)

## # A tibble: 4 × 5##   site      weight estimator order entropy##   <chr>      <dbl> <chr>     <dbl>   <dbl>## 1 subplot_1   1.56 UnveilJ       1    4.57## 2 subplot_2   1.56 UnveilJ       1    4.73## 3 subplot_3   1.56 UnveilJ       1    4.65## 4 subplot_4   1.56 UnveilJ       1    4.55

Entropy should be converted to its effective number of species,i.e. the number of species with equal probabilities that would yield theobserved entropy, calledHill (1973)numbers or simply diversity(Jost2006).

div_hill(paracou_6_abd,q =1)

## # A tibble: 4 × 5##   site      weight estimator order diversity##   <chr>      <dbl> <chr>     <dbl>     <dbl>## 1 subplot_1   1.56 UnveilJ       1      96.3## 2 subplot_2   1.56 UnveilJ       1     113. ## 3 subplot_3   1.56 UnveilJ       1     105. ## 4 subplot_4   1.56 UnveilJ       1      94.6

Diversity is the deformed exponential of order\(q\) of entropy, and entropy is the deformedlogarithm of of order\(q\) ofdiversity:

(d2<-div_hill(paracou_6_abd,q =2)$diversity)

## [1] 42.28417 44.58777 48.83999 36.01687

ln_q(d2,q =2)

## [1] 0.9763505 0.9775723 0.9795250 0.9722352

(e2<-ent_tsallis(paracou_6_abd,q =2)$entropy)

## [1] 0.9763505 0.9775723 0.9795250 0.9722352

exp_q(e2,q =2)

## [1] 42.28417 44.58777 48.83999 36.01687

If an ultrametric dendrogram describing species phylogeny (here, amere taxonomy with family, genus and species) is available, phylogeneticentropy and diversity(Marcon and Hérault2015) can be calculated:

div_phylo(paracou_6_abd,tree = paracou_6_taxo,q =1)

## # A tibble: 4 × 4##   site      weight estimator diversity##   <chr>      <dbl> <chr>         <dbl>## 1 subplot_1   1.56 UnveilJ        41.0## 2 subplot_2   1.56 UnveilJ        52.9## 3 subplot_3   1.56 UnveilJ        46.1## 4 subplot_4   1.56 UnveilJ        43.2

Recall that all those functions can be applied to a numeric vectorcontaining abundances, without having to build an object of classabundances.

# Richness of a community of 100 species, each of them with 10 individualsdiv_richness(rep(10,100))

## # A tibble: 1 × 3##   estimator   order diversity##   <chr>       <dbl>     <int>## 1 Jackknife 0     0       100

With a Euclidian distance matrix between species, similarity-baseddiversity(Leinster and Cobbold 2012; Marcon,Zhang, and Hérault 2014) is available:

# Similarity is computed from the functional distance matrix of Paracou speciesZ<-fun_similarity(paracou_6_fundist)# Calculate diversity of order 2div_similarity(paracou_6_abd,similarities = Z,q =2)

## # A tibble: 4 × 5##   site      weight estimator order diversity##   <chr>      <dbl> <chr>     <dbl>     <dbl>## 1 subplot_1   1.56 UnveilJ       2      1.31## 2 subplot_2   1.56 UnveilJ       2      1.33## 3 subplot_3   1.56 UnveilJ       2      1.32## 4 subplot_4   1.56 UnveilJ       2      1.30

Diversity profiles

Diversity can be plotted against its order to provide a diversityprofile. Order 0 corresponds to richness, 1 to Shannon’s and 2 toSimpson’s diversities:

profile_hill(paracou_6_abd)%>% autoplot

Profiles of phylogenetic diversity and similarity-based diversity areobtained the same way.

profile_phylo(paracou_6_abd,tree = paracou_6_taxo)%>% autoplot

# Similarity matrixZ<-fun_similarity(paracou_6_fundist)profile_similarity(paracou_6_abd,similarities = Z)%>% autoplot

Diversity accumulation

Diversity can be interpolated or extrapolated to arbitrary samplinglevels.

# Estimate the diversity of 1000 individualsdiv_hill(paracou_6_abd,q =1,level =1000)

## # A tibble: 4 × 6##   site      weight estimator order level diversity##   <chr>      <dbl> <chr>     <dbl> <dbl>     <dbl>## 1 subplot_1   1.56 Chao2015      1  1000      78.1## 2 subplot_2   1.56 Chao2015      1  1000      91.1## 3 subplot_3   1.56 Chao2015      1  1000      87.2## 4 subplot_4   1.56 Chao2015      1  1000      78.8

The sampling level can be a sample coverage, that is converted to theequivalent number of individuals.

# Estimate the diversity at 80% coveragediv_hill(paracou_6_abd,q =1,level =0.8)

## # A tibble: 4 × 6##   site      weight estimator     order level diversity##   <chr>      <dbl> <chr>         <dbl> <dbl>     <dbl>## 1 subplot_1   1.56 Interpolation     1   304      60.5## 2 subplot_2   1.56 Interpolation     1   347      71.4## 3 subplot_3   1.56 Interpolation     1   333      68.6## 4 subplot_4   1.56 Interpolation     1   303      60.5

Diversity accumulation curves are available.

accum_hill(  paracou_6_abd[1, ],q =1,levels =1:500,n_simulations =100)%>%autoplot()

Phylogenetic diversity can be addressed the same way. Confidenceintervals of the estimation can be computed, taking into accountsampling variability.

accum_div_phylo(  paracou_6_abd[1, ],tree = paracou_6_taxo,q =1,levels =1:2000)%>%autoplot()

Meta-community data

A metacommunity is the assemblage several communities.

The set of communities is described by the abundances of theirspecies and their weight.

Species probabilities in the meta-community are by definition theweighted average of their probabilities in the communities. Abundancesare calculated so that the total abundance of the metacommunity is thesum of all abundances of communities. If weights are equal, then theabundances of the metacommunity are simply the sum of those of thecommunities. If they are not, the abundances of the metacommunity aregenerally not integer values, which complicates the estimation ofdiversity.

Example:

# Abundances of three communities with four species(abd<-matrix(c(10,0,25,10,20,15,10,35,0,10,5,2  ),ncol =4))

##      [,1] [,2] [,3] [,4]## [1,]   10   10   10   10## [2,]    0   20   35    5## [3,]   25   15    0    2

# Community weightsw<-c(1,2,1)

A set of communities is built.

(communities<-as_abundances(abd,weights = w))

## # A tibble: 3 × 6##   site   weight  sp_1  sp_2  sp_3  sp_4##   <chr>   <dbl> <dbl> <dbl> <dbl> <dbl>## 1 site_1      1    10    10    10    10## 2 site_2      2     0    20    35     5## 3 site_3      1    25    15     0     2

The functionmetacommunity() creates a metacommunity. Toplot it, use argumenttype = "Metacommunity when plottingthespecies_distribution.

(mc<-metacommunity(communities))

## # A tibble: 1 × 6##   site          weight  sp_1  sp_2  sp_3  sp_4##   <chr>          <dbl> <dbl> <dbl> <dbl> <dbl>## 1 metacommunity      4  24.6  45.7  56.2  15.5

plot(communities,type ="Metacommunity")

Each shade of grey represents a species. Heights correspond to theprobability of species and the width of each community is itsweight.

Diversity estimation

High level functions allow computing diversity of all communities(\(\alpha\) diversity), of themeta-community (\(\gamma\) diversity),and\(\beta\) diversity, i.e. thenumber of effective communities (the number of communities with equalweights and no common species that would yield the observed\(\beta\) diversity).

Thediv_part function calculates everything at once, fora given order of diversity\(q\):

div_part(paracou_6_abd,q =1)

## # A tibble: 7 × 6##   site          scale     estimator order diversity weight##   <chr>         <chr>     <chr>     <dbl>     <dbl>  <dbl>## 1 Metacommunity gamma     "UnveilJ"     1    111.     6.25## 2 Metacommunity beta      ""            1      1.09  NA   ## 3 Metacommunity alpha     ""            1    102.    NA   ## 4 subplot_1     community "UnveilJ"     1     96.3    1.56## 5 subplot_2     community "UnveilJ"     1    113.     1.56## 6 subplot_3     community "UnveilJ"     1    105.     1.56## 7 subplot_4     community "UnveilJ"     1     94.6    1.56

An alternative is thegamma argument of all diversityestimation function to obtain\(\gamma\) diversity instead of the diversityof each community.

div_hill(paracou_6_abd,q =1,gamma =TRUE)

## # A tibble: 1 × 4##   site          estimator order diversity##   <chr>         <chr>     <dbl>     <dbl>## 1 Metacommunity UnveilJ       1      111.