get_diversity_from_path {triversity}

Compute the diversity associated to a random walk following a path between the levels of a tripartite graph.

Description

get_diversity_from_path computes diversity values of the probability distribution of a random walk following a path between the different levels of the input tripartite graph. It starts at a given level with an initial probability distribution, then randomly follows the links of the graph between the different levels according to the input path, then stops at the last specified level. The implemented diversity measures all belong to the parametrized family of "True Diversity" measures. They can either be specified by their diversity order in [0,Inf[ or by their measure name when it corresponds to classical instances such as the richness, the Shannon entropy, the Herfindahl-Hirschman index, or the Berger-Parker index.

Usage

get_diversity_from_path(tripartite, path, conditional_path = NULL,
  initial_distribution = NULL, initial_node = NULL, order = NULL,
  measure = NULL)

Arguments

tripartite

A tripartite graph obtained by calling the get_tripartite function.

path

A vector of integers in {1, 2, 3} giving the path of the random walk between the different levels of the input tripartite graph. This path can be as long as wanted. Two successive levels should always be adjacent, that is the random walk cannot go from level 1 to level 3 (or conversely) without first going through level 2.

conditional_path

A vector of integers in {1, 2, 3} eventually giving another path to compute conditional diversity values instead of regular diversity values. When specified, this conditional path is first used to initiate the random walk. The resulting probability distribution is then used to weight the individual diversity values obtained on the input path when computing their geometric means (see get_conditional_diversity_from_transition). This path can be as long as wanted. The last level of the conditional path should be the same as the first level of the input path. Moreover, two successive levels should always be adjacent, that is the random walk cannot go from level 1 to level 3 (or conversely) without first going through level 2.

initial_distribution

A vector of floats in [0,1] and summing to 1 giving the probability distribution to start with at the first level of the input path, or at the first level of the input conditional_path if specified. It should hence contain as many values as there are nodes in the corresponding level. If not specified, this distribution is assumed uniform.

initial_node

A string giving the name of a node in the first level of the input path, or at the first level of the input conditional_path if specified. This node is then considered to have probability one, thus being equivalent to specifying an initial_distribution with only zeros except for one node. If not specified, no such node is defined and the initial distribution is assumed uniform.

order

A vector of positive floats (possibly including Inf) giving the orders of the diversity measures to be computed. If neither order nor measure is specified, a predefined list of 8 diversity measures is computed.

measure

A vector of strings giving the names of the diversity measures to compute. Possible values are richness, entropy, herfindahl, and bergerparker.

Value

A vector of positive floats giving the diversity values (or conditional diversity values) of the random walk following the input path.

Examples

data (tripartite_example)
tripartite <- get_tripartite (data=tripartite_example)


# COMPUTING DIFFERENT DIVERSITY VALUES FOR A GIVEN PATH

# Herfindahl-Hirschman index of nodes in level 3 wrt nodes in level 1
get_diversity_from_path (tripartite, path=c(1,2,3), measure='herfindahl')
1 / get_diversity_from_path (tripartite, path=c(1,2,3), order=2)

# Shannon entropy of nodes in level 3 wrt nodes in level 1
get_diversity_from_path (tripartite, path=c(1,2,3), measure='entropy')
log2 (get_diversity_from_path (tripartite, path=c(1,2,3), order=1))

# Some other diversity values of nodes in level 3 wrt nodes in level 1
get_diversity_from_path (tripartite, path=c(1,2,3), order=c(1,2,Inf),
                         measure=c('richness','bergerparker'))

# Eight of the main diversity values of nodes in level 3 wrt nodes in level 1
get_diversity_from_path (tripartite, path=c(1,2,3))


# SPECIFYING THE INITIAL DISTRIBUTION

# Diversity of nodes in level 3 wrt nodes in level 1 (with non-uniform weights)
get_diversity_from_path (tripartite, path=c(1,2,3), initial_distribution=c(0.75,0.25))

# Individual diversity of nodes in level 3 wrt node 'u1' in level 1
get_diversity_from_path (tripartite, path=c(1,2,3), initial_node='u1')
get_diversity_from_path (tripartite, path=c(1,2,3), initial_distribution=c(1,0))


# COMPUTING THE MEAN OF INDIVIDUAL DIVERSITES

# Mean of individual diversities of nodes in level 3 wrt nodes in level 2 (with
# uniform weights)
get_diversity_from_path (tripartite, path=c(2,3), conditional_path=c(2))

# Mean of individual diversities of nodes in level 3 wrt nodes in level 2 (weighted
# according to the path from level 1 to level 2, with a uniform distribution in level 1)
get_diversity_from_path (tripartite, path=c(2,3), conditional_path=c(1,2))

# Mean of individual diversities of nodes in level 3 wrt nodes in level 2 (weighted
# according to the path from level 1 to level 2, with only node 'u1' in level 1)
get_diversity_from_path (tripartite, path=c(2,3), conditional_path=c(1,2),
                         initial_node='u1')