## Generating a metacommunity

Before calculating diversity a `metacommunity` object must be created. This object contains all the information needed to calculate diversity. In the following example, we generate a metacommunity (`partition`) comprising two species (“cows” and “sheep”), and partitioned across three subcommunities (a, b, and c).

    # Load the package into R
    library(rdiversity)

    # Initialise data
    partition <- data.frame(a=c(1,1),b=c(2,0),c=c(3,1))
    row.names(partition) <- c("cows", "sheep")

The `metacommunity()` function takes two arguments, `partition` and `similarity`. When species are considered completely distinct, an identity matrix is required, which is generated automatically if the `similarity` argument is missing, as below:

    # Generate metacommunity object
    meta <- metacommunity(partition = partition)

    ## Metacommunity matrix was normalised to sum to 1.

Note that a warning is displayed when abundances (rather than relative abundances) are entered into the `partition` argument. Both are acceptable inputs.

When species share some similarity and a similarity matrix is available, then a similarity object (and the metacommunity object) is generated in the following way:

    # Initialise similarity matrix
    s <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)
    row.names(s) <- c("cows", "sheep")
    colnames(s) <- c("cows", "sheep")

    # Generate similarity object
    s <- similarity(similarity = s, dat_id = "my_taxonomic")

    # Generate metacommunity object
    meta <- metacommunity(partition = partition, similarity = s)

    ## Metacommunity matrix was normalised to sum to 1.

Alternatively, if a distance matrix is available, then a distance object is generated in the following way:

    # Initialise distance matrix
    d <- matrix(c(0, 0.7, 0.7, 0), nrow = 2)
    row.names(d) <- c("cows", "sheep")
    colnames(d) <- c("cows", "sheep")

    # Generate distance object
    d <- distance(distance = d, dat_id = "my_taxonomic")

    # Convert the distance object to similarity object (by means of a linear or exponential transform)
    s <- dist2sim(dist = d, transform = "linear")

    # Generate metacommunity object
    meta <- metacommunity(partition = partition, similarity = s)

    ## Metacommunity matrix was normalised to sum to 1.

Each `metacommunity` object contains the following slots:

- `@type_abundance` : the abundance of types within a metacommunity,
- `@similarity` : the pair-wise similarity of types within a metacommunity,
- `@ordinariness` : the ordinariness of types within a metacommunity,
- `@subcommunity_weights` : the relative weights of subcommunities within a metacommunity, and
- `@type_weights` : the relative weights of types within a metacommunity.

## Calculating diversity

### Method 1

This method uses a wrapper function to simplify the pipeline and is recommended if only a few measures are being calculated.

A complete list of these functions is shown below:

- `raw_sub_alpha()` : estimate of naive-community metacommunity diversity
- `norm_sub_alpha()` : similarity-sensitive diversity of subcommunity j in isolation
- `raw_sub_rho()` : redundancy of subcommunity j
- `norm_sub_rho()` : representativeness of subcommunity j
- `raw_sub_beta()` : distinctiveness of subcommunity j
- `norm_sub_beta()` : estimate of effective number of distinct subcommunities
- `sub_gamma()` : contribution per individual toward metacommunity diversity
- `raw_meta_alpha()` : naive-community metacommunity diversity
- `norm_meta_alpha()` : average similarity-sensitive diversity of subcommunities
- `raw_meta_rho()` : average redundancy of subcommunities
- `norm_meta_rho()` : average representativeness of subcommunities
- `raw_meta_beta()` : average distinctiveness of subcommunities
- `norm_meta_beta()` : effective number of distinct subcommunities
- `meta_gamma()` : metacommunity similarity-sensitive diversity

Each of these functions take two arguments, `meta` (a `metacommunity` object) and `qs` (a vector of q values), and output results as a `rdiv` object. For example, to calculate normalised subcommunity alpha diversity for q=0, q=1, and q=2:

    # Initialise data
    partition <- data.frame(a=c(1,1),b=c(2,0),c=c(3,1))
    row.names(partition) <- c("cows", "sheep")

    # Generate a metacommunity object
    meta <- metacommunity(partition)

    ## Metacommunity matrix was normalised to sum to 1.

    # Calculate diversity
    norm_sub_alpha(meta, 0:2)

    ##            measure q type_level type_name partition_level partition_name
    ## 1 normalised alpha 0      types              subcommunity              a
    ## 2 normalised alpha 0      types              subcommunity              b
    ## 3 normalised alpha 0      types              subcommunity              c
    ## 4 normalised alpha 1      types              subcommunity              a
    ## 5 normalised alpha 1      types              subcommunity              b
    ## 6 normalised alpha 1      types              subcommunity              c
    ## 7 normalised alpha 2      types              subcommunity              a
    ## 8 normalised alpha 2      types              subcommunity              b
    ## 9 normalised alpha 2      types              subcommunity              c
    ##   diversity dat_id transformation normalised  k max_d
    ## 1  2.000000  naive             NA         NA NA    NA
    ## 2  1.000000  naive             NA         NA NA    NA
    ## 3  2.000000  naive             NA         NA NA    NA
    ## 4  2.000000  naive             NA         NA NA    NA
    ## 5  1.000000  naive             NA         NA NA    NA
    ## 6  1.754765  naive             NA         NA NA    NA
    ## 7  2.000000  naive             NA         NA NA    NA
    ## 8  1.000000  naive             NA         NA NA    NA
    ## 9  1.600000  naive             NA         NA NA    NA

However, if multiple measures are required and computational efficiency is an issue, then the following method is recommended (the same results are obtained).

### Method 2

This method requires that we first calculate the species-level components, by passing a `metacommunity` object to the appropriate function; `raw_alpha()`, `norm_alpha()`, `raw_beta()`, `norm_beta()`, `raw_rho()`, `norm_rho()`, or `raw_gamma()`. Subcommunity- and metacommunity-level diversities are calculated using the functions `subdiv()` and `metadiv()`. Since both subcommunity and metacommunity diversity measures are transformations of the same species-level component, this method is computationally more efficient.

    # Initialise data
    partition <- data.frame(a=c(1,1),b=c(2,0),c=c(3,1))
    row.names(partition) <- c("cows", "sheep")

    # Generate a metacommunity object
    meta <- metacommunity(partition)

    ## Metacommunity matrix was normalised to sum to 1.

    # Calculate the species-level component for normalised alpha
    component <- norm_alpha(meta)

    # Calculate normalised alpha at the subcommunity-level
    subdiv(component, 0:2)

    ##            measure q type_level type_name partition_level partition_name
    ## 1 normalised alpha 0      types              subcommunity              a
    ## 2 normalised alpha 0      types              subcommunity              b
    ## 3 normalised alpha 0      types              subcommunity              c
    ## 4 normalised alpha 1      types              subcommunity              a
    ## 5 normalised alpha 1      types              subcommunity              b
    ## 6 normalised alpha 1      types              subcommunity              c
    ## 7 normalised alpha 2      types              subcommunity              a
    ## 8 normalised alpha 2      types              subcommunity              b
    ## 9 normalised alpha 2      types              subcommunity              c
    ##   diversity dat_id transformation normalised  k max_d
    ## 1  2.000000  naive             NA         NA NA    NA
    ## 2  1.000000  naive             NA         NA NA    NA
    ## 3  2.000000  naive             NA         NA NA    NA
    ## 4  2.000000  naive             NA         NA NA    NA
    ## 5  1.000000  naive             NA         NA NA    NA
    ## 6  1.754765  naive             NA         NA NA    NA
    ## 7  2.000000  naive             NA         NA NA    NA
    ## 8  1.000000  naive             NA         NA NA    NA
    ## 9  1.600000  naive             NA         NA NA    NA

    # Likewise, calculate normalised alpha at the metacommunity-level
    metadiv(component, 0:2)

    ##            measure q type_level type_name partition_level partition_name
    ## 1 normalised alpha 0      types             metacommunity
    ## 2 normalised alpha 1      types             metacommunity
    ## 3 normalised alpha 2      types             metacommunity
    ##   diversity dat_id transformation normalised  k max_d
    ## 1  1.750000  naive             NA         NA NA    NA
    ## 2  1.575314  naive             NA         NA NA    NA
    ## 3  1.454545  naive             NA         NA NA    NA

In some instances, it may be useful to calculate all subcommunity (or metacommunity) measures. In which case, a `metacommunity` object may be passed directly to `subdiv()` or `metadiv()`:

    # Calculate all subcommunity diversity measures
    subdiv(meta, 0:2)

    ##             measure q type_level type_name partition_level partition_name
    ## 1         raw alpha 0      types              subcommunity              a
    ## 2         raw alpha 0      types              subcommunity              b
    ## 3         raw alpha 0      types              subcommunity              c
    ## 4         raw alpha 1      types              subcommunity              a
    ## 5         raw alpha 1      types              subcommunity              b
    ## 6         raw alpha 1      types              subcommunity              c
    ## 7         raw alpha 2      types              subcommunity              a
    ## 8         raw alpha 2      types              subcommunity              b
    ## 9         raw alpha 2      types              subcommunity              c
    ## 10 normalised alpha 0      types              subcommunity              a
    ## 11 normalised alpha 0      types              subcommunity              b
    ## 12 normalised alpha 0      types              subcommunity              c
    ## 13 normalised alpha 1      types              subcommunity              a
    ## 14 normalised alpha 1      types              subcommunity              b
    ## 15 normalised alpha 1      types              subcommunity              c
    ## 16 normalised alpha 2      types              subcommunity              a
    ## 17 normalised alpha 2      types              subcommunity              b
    ## 18 normalised alpha 2      types              subcommunity              c
    ## 19         raw beta 0      types              subcommunity              a
    ## 20         raw beta 0      types              subcommunity              b
    ## 21         raw beta 0      types              subcommunity              c
    ## 22         raw beta 1      types              subcommunity              a
    ## 23         raw beta 1      types              subcommunity              b
    ## 24         raw beta 1      types              subcommunity              c
    ## 25         raw beta 2      types              subcommunity              a
    ## 26         raw beta 2      types              subcommunity              b
    ## 27         raw beta 2      types              subcommunity              c
    ## 28  normalised beta 0      types              subcommunity              a
    ## 29  normalised beta 0      types              subcommunity              b
    ## 30  normalised beta 0      types              subcommunity              c
    ## 31  normalised beta 1      types              subcommunity              a
    ## 32  normalised beta 1      types              subcommunity              b
    ## 33  normalised beta 1      types              subcommunity              c
    ## 34  normalised beta 2      types              subcommunity              a
    ## 35  normalised beta 2      types              subcommunity              b
    ## 36  normalised beta 2      types              subcommunity              c
    ## 37          raw rho 0      types              subcommunity              a
    ## 38          raw rho 0      types              subcommunity              b
    ## 39          raw rho 0      types              subcommunity              c
    ## 40          raw rho 1      types              subcommunity              a
    ## 41          raw rho 1      types              subcommunity              b
    ## 42          raw rho 1      types              subcommunity              c
    ## 43          raw rho 2      types              subcommunity              a
    ## 44          raw rho 2      types              subcommunity              b
    ## 45          raw rho 2      types              subcommunity              c
    ## 46   normalised rho 0      types              subcommunity              a
    ## 47   normalised rho 0      types              subcommunity              b
    ## 48   normalised rho 0      types              subcommunity              c
    ## 49   normalised rho 1      types              subcommunity              a
    ## 50   normalised rho 1      types              subcommunity              b
    ## 51   normalised rho 1      types              subcommunity              c
    ## 52   normalised rho 2      types              subcommunity              a
    ## 53   normalised rho 2      types              subcommunity              b
    ## 54   normalised rho 2      types              subcommunity              c
    ## 55            gamma 0      types              subcommunity              a
    ## 56            gamma 0      types              subcommunity              b
    ## 57            gamma 0      types              subcommunity              c
    ## 58            gamma 1      types              subcommunity              a
    ## 59            gamma 1      types              subcommunity              b
    ## 60            gamma 1      types              subcommunity              c
    ## 61            gamma 2      types              subcommunity              a
    ## 62            gamma 2      types              subcommunity              b
    ## 63            gamma 2      types              subcommunity              c
    ##    diversity dat_id transformation normalised  k max_d
    ## 1  8.0000000  naive             NA         NA NA    NA
    ## 2  4.0000000  naive             NA         NA NA    NA
    ## 3  4.0000000  naive             NA         NA NA    NA
    ## 4  8.0000000  naive             NA         NA NA    NA
    ## 5  4.0000000  naive             NA         NA NA    NA
    ## 6  3.5095307  naive             NA         NA NA    NA
    ## 7  8.0000000  naive             NA         NA NA    NA
    ## 8  4.0000000  naive             NA         NA NA    NA
    ## 9  3.2000000  naive             NA         NA NA    NA
    ## 10 2.0000000  naive             NA         NA NA    NA
    ## 11 1.0000000  naive             NA         NA NA    NA
    ## 12 2.0000000  naive             NA         NA NA    NA
    ## 13 2.0000000  naive             NA         NA NA    NA
    ## 14 1.0000000  naive             NA         NA NA    NA
    ## 15 1.7547654  naive             NA         NA NA    NA
    ## 16 2.0000000  naive             NA         NA NA    NA
    ## 17 1.0000000  naive             NA         NA NA    NA
    ## 18 1.6000000  naive             NA         NA NA    NA
    ## 19 0.2500000  naive             NA         NA NA    NA
    ## 20 0.3333333  naive             NA         NA NA    NA
    ## 21 0.5000000  naive             NA         NA NA    NA
    ## 22 0.2886751  naive             NA         NA NA    NA
    ## 23 0.3333333  naive             NA         NA NA    NA
    ## 24 0.5000000  naive             NA         NA NA    NA
    ## 25 0.3333333  naive             NA         NA NA    NA
    ## 26 0.3333333  naive             NA         NA NA    NA
    ## 27 0.5000000  naive             NA         NA NA    NA
    ## 28 1.0000000  naive             NA         NA NA    NA
    ## 29 1.3333333  naive             NA         NA NA    NA
    ## 30 1.0000000  naive             NA         NA NA    NA
    ## 31 1.1547005  naive             NA         NA NA    NA
    ## 32 1.3333333  naive             NA         NA NA    NA
    ## 33 1.0000000  naive             NA         NA NA    NA
    ## 34 1.3333333  naive             NA         NA NA    NA
    ## 35 1.3333333  naive             NA         NA NA    NA
    ## 36 1.0000000  naive             NA         NA NA    NA
    ## 37 4.0000000  naive             NA         NA NA    NA
    ## 38 3.0000000  naive             NA         NA NA    NA
    ## 39 2.0000000  naive             NA         NA NA    NA
    ## 40 3.4641016  naive             NA         NA NA    NA
    ## 41 3.0000000  naive             NA         NA NA    NA
    ## 42 2.0000000  naive             NA         NA NA    NA
    ## 43 3.0000000  naive             NA         NA NA    NA
    ## 44 3.0000000  naive             NA         NA NA    NA
    ## 45 2.0000000  naive             NA         NA NA    NA
    ## 46 1.0000000  naive             NA         NA NA    NA
    ## 47 0.7500000  naive             NA         NA NA    NA
    ## 48 1.0000000  naive             NA         NA NA    NA
    ## 49 0.8660254  naive             NA         NA NA    NA
    ## 50 0.7500000  naive             NA         NA NA    NA
    ## 51 1.0000000  naive             NA         NA NA    NA
    ## 52 0.7500000  naive             NA         NA NA    NA
    ## 53 0.7500000  naive             NA         NA NA    NA
    ## 54 1.0000000  naive             NA         NA NA    NA
    ## 55 2.6666667  naive             NA         NA NA    NA
    ## 56 1.3333333  naive             NA         NA NA    NA
    ## 57 2.0000000  naive             NA         NA NA    NA
    ## 58 2.3094011  naive             NA         NA NA    NA
    ## 59 1.3333333  naive             NA         NA NA    NA
    ## 60 1.7547654  naive             NA         NA NA    NA
    ## 61 2.0000000  naive             NA         NA NA    NA
    ## 62 1.3333333  naive             NA         NA NA    NA
    ## 63 1.6000000  naive             NA         NA NA    NA

    # Calculate all metacommunity diversity measures
    metadiv(meta, 0:2)

    ##             measure q type_level type_name partition_level partition_name
    ## 1         raw alpha 0      types             metacommunity
    ## 2         raw alpha 1      types             metacommunity
    ## 3         raw alpha 2      types             metacommunity
    ## 4  normalised alpha 0      types             metacommunity
    ## 5  normalised alpha 1      types             metacommunity
    ## 6  normalised alpha 2      types             metacommunity
    ## 7          raw beta 0      types             metacommunity
    ## 8          raw beta 1      types             metacommunity
    ## 9          raw beta 2      types             metacommunity
    ## 10  normalised beta 0      types             metacommunity
    ## 11  normalised beta 1      types             metacommunity
    ## 12  normalised beta 2      types             metacommunity
    ## 13          raw rho 0      types             metacommunity
    ## 14          raw rho 1      types             metacommunity
    ## 15          raw rho 2      types             metacommunity
    ## 16   normalised rho 0      types             metacommunity
    ## 17   normalised rho 1      types             metacommunity
    ## 18   normalised rho 2      types             metacommunity
    ## 19            gamma 0      types             metacommunity
    ## 20            gamma 1      types             metacommunity
    ## 21            gamma 2      types             metacommunity
    ##    diversity dat_id transformation normalised  k max_d
    ## 1  5.0000000  naive             NA         NA NA    NA
    ## 2  4.4556597  naive             NA         NA NA    NA
    ## 3  4.0000000  naive             NA         NA NA    NA
    ## 4  1.7500000  naive             NA         NA NA    NA
    ## 5  1.5753136  naive             NA         NA NA    NA
    ## 6  1.4545455  naive             NA         NA NA    NA
    ## 7  0.3958333  naive             NA         NA NA    NA
    ## 8  0.3938284  naive             NA         NA NA    NA
    ## 9  0.4000000  naive             NA         NA NA    NA
    ## 10 1.0833333  naive             NA         NA NA    NA
    ## 11 1.1139149  naive             NA         NA NA    NA
    ## 12 1.1428571  naive             NA         NA NA    NA
    ## 13 2.7500000  naive             NA         NA NA    NA
    ## 14 2.5391770  naive             NA         NA NA    NA
    ## 15 2.4000000  naive             NA         NA NA    NA
    ## 16 0.9375000  naive             NA         NA NA    NA
    ## 17 0.8977346  naive             NA         NA NA    NA
    ## 18 0.8571429  naive             NA         NA NA    NA
    ## 19 2.0000000  naive             NA         NA NA    NA
    ## 20 1.7547654  naive             NA         NA NA    NA
    ## 21 1.6000000  naive             NA         NA NA    NA

## Taxonomic diversity

1. Initialise data:

    # Taxonomic lookup table
    Species <- c("tenuifolium", "asterolepis", "simplex var.grandiflora", "simplex var.ochnacea")
    Genus <- c("Protium", "Quararibea", "Swartzia", "Swartzia")
    Family <- c("Burseraceae", "Bombacaceae", "Fabaceae", "Fabaceae")
    Subclass <- c("Sapindales", "Malvales", "Fabales", "Fabales")
    lookup <- cbind.data.frame(Species, Genus, Family, Subclass)

    # Partition matrix
    partition <- matrix(rep(1, 8), nrow = 4)
    colnames(partition) <- LETTERS[1:2]
    rownames(partition) <- lookup$Species

and assign values for each taxonomic level:

    values <- c(Species = 0, Genus = 1, Family = 2, Subclass = 3, Other = 4)

1. Generate a distance object from a lookup table using the `tax2dist()` function:

    d <- tax2dist(lookup, values)

By default the `tax2dist()` argument `precompute_dist` is TRUE, such that a pairwise distance matrix is calculated automatically and is stored in `d@distance`. If the taxonomy is too large, `precompute_dist` can be set to FALSE, which enables pairwise taxonomic similarity to be calculated on the fly, in step 4.

1. Convert the distance object to similarity object (by means of a linear or exponential transform) using the `dist2sim()` function:

    s <- dist2sim(d, "linear")

1. Generate a metacommunity object using the `metacommunity()` function:

    meta <- metacommunity(partition, s)

    ## Metacommunity matrix was normalised to sum to 1.

1. Calculate diversity:

    meta_gamma(meta, 0:2)

    ##   measure q type_level type_name partition_level partition_name diversity
    ## 1   gamma 0      types             metacommunity                 3.142857
    ## 2   gamma 1      types             metacommunity                 3.023716
    ## 3   gamma 2      types             metacommunity                 2.909091
    ##      dat_id transformation normalised k max_d
    ## 1 taxonomic         linear       TRUE 1     4
    ## 2 taxonomic         linear       TRUE 1     4
    ## 3 taxonomic         linear       TRUE 1     4

## Phylogenetic diversity

Phylogenetic diversity measures can be broadly split into two categories – those that look at the phylogeny as a whole, such as Faith’s (1992) phylogenetic diversity (Faith’s PD), and those that look at pairwise tip distances, such as mean pairwise distance (MPD; Webb, 2000). The framework of measures presented in this package is able to quantify phylogenetic diversity using both of these methods.

### Distance-based phylogenetic diversity

1. Initialise data:

    # Example data
    tree <- ape::rtree(4)
    partition <- matrix(1:12, ncol=3)
    partition <- partition/sum(partition)

1. Generate a distance matrix using the `phy2dist()` function:

    d <- phy2dist(tree)

By default the `phy2dist()` argument `precompute_dist` is TRUE, such that a pairwise distance matrix is calculated automatically and is stored in `d@distance`. If the taxonomy is too large, `precompute_dist` can be set to FALSE, which enables pairwise taxonomic similarity to be calculated on the fly, in step 4.

1. Convert the distance object to similarity object (by means of a linear or exponential transform) using the `dist2sim()` function:

    s <- dist2sim(d, "linear")

1. Generate a metacommunity object using the `metacommunity()` function

    meta <- metacommunity(partition, s)

1. Calculate diversity

    meta_gamma(meta, 0:2)

    ##   measure q type_level type_name partition_level partition_name diversity
    ## 1   gamma 0      types             metacommunity                 2.506940
    ## 2   gamma 1      types             metacommunity                 2.459285
    ## 3   gamma 2      types             metacommunity                 2.414723
    ##         dat_id transformation normalised k    max_d
    ## 1 phylogenetic         linear       TRUE 1 1.796924
    ## 2 phylogenetic         linear       TRUE 1 1.796924
    ## 3 phylogenetic         linear       TRUE 1 1.796924

### Branch-based phylogenetic diversity

1. Initialise data:

    tree <- ape::rtree(4)
    partition <- matrix(1:12, ncol=3)
    partition <- partition/sum(partition)
    colnames(partition) <- letters[1:3]
    row.names(partition) <- paste0("sp",1:4)
    tree$tip.label <- row.names(partition)

1. Generate a similarity object using the `phy2branch()` function

    s <- phy2branch(tree, partition)

1. Generate a metacommunity object using the `metacommunity()` function

    meta <- metacommunity(partition, s)

1. Calculate diversity

    meta_gamma(meta, 0:2)

    ##   measure q type_level type_name partition_level partition_name diversity
    ## 1   gamma 0      types             metacommunity                 2.483452
    ## 2   gamma 1      types             metacommunity                 2.286031
    ## 3   gamma 2      types             metacommunity                 2.118287
    ##      dat_id transformation normalised  k max_d
    ## 1 phybranch             NA         NA NA    NA
    ## 2 phybranch             NA         NA NA    NA
    ## 3 phybranch             NA         NA NA    NA

Note that: a metacommunity that was generated using this approach will contain three additional slots:

- `@raw_abundance` : the relative abundance of terminal species (where types are then considered to be historical species),
- `@raw_structure` : the length of evolutionary history of each historical species
- `@parameters` : parameters associated with historical species

## Genetic diversity

1. Initialise data: Note: the package `pinfsc50` must be installed for this example to work.

    library(rdiversity)
    vcf_file <- system.file("extdata", "pinf_sc50.vcf.gz", package = "pinfsc50")
    #read in twice: first for the column names then for the data
    tmp_vcf <- readLines(vcf_file)
    vcf_data <- read.table(vcf_file, stringsAsFactors = FALSE)
    # filter for the columns names
    vcf_names <- unlist(strsplit(tmp_vcf[grep("#CHROM",tmp_vcf)],"\t"))
    names(vcf_data) <- vcf_names
    partition <- cbind.data.frame(A = c(rep(1, 9), rep(0, 9)), B = c(rep(0, 9), rep(1, 9)))
    partition <- partition/sum(partition)

1. Generate a distance matrix using the `gen2dist()` function:

    d <- gen2dist(vcf)

1. Convert the distance object to a similarity object (by means of a linear or exponential transform) using the `dist2sim()` function:

    s <- dist2sim(d, transform = 'l')

Note: the `dist2sim()` function contains an optional argument, `max_d`, which defines the distance at which pairs of individuals have similarity zero. If not supplied this is set to the maximum distance observed in the distance matrix. If comparing different windows on a genome, for example, it is necessary to ensure `max_d` is the same for each analysis.

1. Generate a metacommunity object using the `metacommunity()` function:

    rownames(partition) <- rownames(s@similarity)
    meta <- metacommunity(partition, s)

1. Calculate diversity, for example beta diversity measures are used to identify trends such as differentiation:

    norm_meta_beta(meta, 0:2)

### User defined distance

    partition <- matrix(sample(6), nrow = 3)
    rownames(partition) <- paste0("sp", 1:3)
    partition <- partition / sum(partition)

    d <- matrix(c(0,.75,1,.75,0,.3,1,.3,0), nrow = 3)
    rownames(d) <- paste0("sp", 1:3)
    colnames(d) <- paste0("sp", 1:3)
    d <- distance(d, "my_taxonomy")
    s <- dist2sim(d, "linear")

    meta <- metacommunity(partition, s)

### User defined similarity

    partition <- matrix(sample(6), nrow = 3)
    rownames(partition) <- paste0("sp", 1:3)
    partition <- partition / sum(partition)

    s <- matrix(c(1,.8,0,.8,1,.1,0,.1,1), nrow = 3)
    rownames(s) <- paste0("sp", 1:3)
    colnames(s) <- paste0("sp", 1:3)
    s <- similarity(s, "my_functional")

    meta <- metacommunity(partition, s)

## Additional tools

### `repartition()`

    tree <- ape::rtree(5)
    tree$tip.label <- paste0("sp", 1:5)

    partition <- matrix(rep(1,10), nrow = 5)
    row.names(partition) <- paste0("sp", 1:5)
    partition <- partition / sum(partition)
    s <- phy2branch(tree, partition)
    meta <- metacommunity(partition, s)

    new_partition <- matrix(sample(10), nrow = 5)
    row.names(new_partition) <- paste0("sp", 1:5)
    new_partition <- new_partition / sum(new_partition)

    new_meta <- repartition(meta, new_partition)