EcologicalNetwork

Exported

Q(A::Array{Float64, 2}, L::Array{Int64, 1}) ¶

Q -- a measure of modularity

This measures Barber's bipartite modularity based on a matrix and a list of module labels.

source: EcologicalNetwork/src/modularity.jl:29

Q(P::Partition) ¶

Q -- a measure of modularity

This measures Barber's bipartite modularity based on a Partition object, and update the object in the proccess.

source: EcologicalNetwork/src/modularity.jl:47

Qr(A::Array{Float64, 2}, L::Array{Int64, 1}) ¶

Qr -- a measure of realized modularity

Measures Poisot's realized modularity, based on a a matrix and a list of module labels. Realized modularity takes values in the [0;1] interval, and is the proportion of interactions established within modules.

Note that in some situations, Qr can be lower than 0. This reflects a partition in which more links are established between than within modules.

source: EcologicalNetwork/src/modularity.jl:65

Qr(P::Partition) ¶

Qr -- a measure of realized modularity

Measures Poisot's realized modularity, based on a Partition object.

source: EcologicalNetwork/src/modularity.jl:80

a_var(p::Array{Float64, N}) ¶

Variance of a series of additive Bernoulli events

f(p): ∑(p(1-p))

source: EcologicalNetwork/src/proba_utils.jl:65

betadiversity(A::Array{Float64, 2}, B::Array{Float64, 2}) ¶

Measure the expected network similarity

Note that this is only meaningful to apply this function when the two matrices have the same species at the same position! If this is note the case, a BoundsError will be thrown.

This function will return a BetaSet, which is then used by the function to actually measure the beta-diversity. This package uses the approach of Koleff et a. (2003).

References

Koleff, P., Gaston, K. J. and Lennon, J. J. (2003), Measuring beta diversity for presence–absence data. Journal of Animal Ecology, 72: 367–382. doi: 10.1046/j.1365-2656.2003.00710.x

source: EcologicalNetwork/src/betadiversity.jl:41

centrality_katz(A::Array{Float64, 2}) ¶

Measures Katz's centrality for each node in a unipartite network.

Keyword arguments

a (def. 0.1), the weight of each subsequent connection
k (def. 5), the maximal path length considered

source: EcologicalNetwork/src/centrality.jl:11

connectance(A::Array{Float64, 2}) ¶

Expected connectance for a probabilistic matrix, measured as the number of expected links, divided by the size of the matrix.

source: EcologicalNetwork/src/connectance.jl:16

connectance_var(A::Array{Float64, 2}) ¶

Expected variance of the connectance for a probabilistic matrix, measured as the variance of the number of links divided by the squared size of the matrix.

source: EcologicalNetwork/src/connectance.jl:24

count_motifs(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Motif counter

This function will go through all k-permutations of A to measure the probability of each induced subgraph being an instance of the motif given by m (the square adjacency matrix of the motif, with 0 and 1).

source: EcologicalNetwork/src/motifs.jl:38

degree(A::Array{Float64, 2}) ¶

Expected degree

source: EcologicalNetwork/src/degree.jl:15

degree_in(A::Array{Float64, 2}) ¶

Expected number of ingoing degrees

source: EcologicalNetwork/src/degree.jl:9

degree_out(A::Array{Float64, 2}) ¶

Expected number of outgoing degrees

source: EcologicalNetwork/src/degree.jl:3

free_species(A::Array{Float64, 2}) ¶

Expected number of species with no interactions

This function will be applied on the unipartite version of the network. Note that the functions species_ |predecessors will work on bipartite networks, but the unipartite situation is more general.

source: EcologicalNetwork/src/free_species.jl:32

gaston(S::BetaSet) ¶

Gaston measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:72

harrison(S::BetaSet) ¶

Harrison measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:97

hartekinzig(S::BetaSet) ¶

Harte-Kinzig measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:92

i_esp(p::Float64) ¶

Expected value of a single Bernoulli event

Simply f(p): p

source: EcologicalNetwork/src/proba_utils.jl:39

i_var(p::Float64) ¶

Variance of a single Bernoulli event

f(p): p(1-p)

source: EcologicalNetwork/src/proba_utils.jl:52

jaccard(S::BetaSet) ¶

Jaccard measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:67

lande(S::BetaSet) ¶

Lande measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:82

links(A::Array{Float64, 2}) ¶

Expected number of links for a probabilistic matrix

source: EcologicalNetwork/src/connectance.jl:3

links_var(A::Array{Float64, 2}) ¶

Expected variance of the number of links for a probabilistic matrix

source: EcologicalNetwork/src/connectance.jl:9

m_var(p::Array{Float64, N}) ¶

Variance of a series of multiplicative Bernoulli events

source: EcologicalNetwork/src/proba_utils.jl:74

make_bernoulli(A::Array{Float64, 2}) ¶

Generate a random 0/1 matrix from probabilities

Returns a matrix B of the same size as A, in which each element B(i,j) is 1 with probability A(i,j).

source: EcologicalNetwork/src/matrix_utils.jl:20

make_binary(A::Array{Float64, 2}) ¶

Returns the adjacency/incidence matrix from a probability matrix

Returns a matrix B of the same size as A, in which each element B(i,j) is 1 if A(i,j) is greater than 0.

source: EcologicalNetwork/src/matrix_utils.jl:71

make_threshold(A::Array{Float64, 2}, k::Float64) ¶

Generate a random 0/1 matrix from probabilities

Returns a matrix B of the same size as A, in which each element B(i,j) is 1 if A(i,j) is > k. This is probably unwise to use this function since this practice is of questionnable relevance, but it is included for the sake of exhaustivity.

k must be in [0;1[.

source: EcologicalNetwork/src/matrix_utils.jl:54

make_unipartite(A::Array{Float64, 2}) ¶

Transforms a bipartite network into a unipartite network

Note that this function returns an asymetric unipartite network.

source: EcologicalNetwork/src/matrix_utils.jl:5

modularity(A::Array{Float64, 2}) ¶

This function is a wrapper for the modularity code. The number of replicates is the number of times the modularity optimization should be run.

Non-keywords arguments:

A, probability matrix

Keywords arguments:

replicates, defaults to 100
kmax, defaults to twice the matrix size, number of propagations to do
smax, maximum number of steps without an increase in modularity before LP stops

Keep in mind that this approach has not been thoroughly tested. The measure of modularity works, but the optimization routine is not guaranteed to give robust/correct results.

source: EcologicalNetwork/src/modularity.jl:155

motif(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Expected number of a given motif

source: EcologicalNetwork/src/motifs.jl:60

motif_p(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Probability that a group of species form a given motif

source: EcologicalNetwork/src/motifs.jl:22

motif_v(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Variance that a group of species form a given motif

source: EcologicalNetwork/src/motifs.jl:27

motif_var(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Expected variance of a given motif

source: EcologicalNetwork/src/motifs.jl:65

nestedness(A::Array{Float64, 2}) ¶

Nestedness of a matrix, using the Bastolla et al. (XXXX) measure

Returns three values:

nestedness of the entire matrix
nestedness of the columns
nestedness of the rows

source: EcologicalNetwork/src/nestedness.jl:33

nestedness_axis(A::Array{Float64, 2}) ¶

Nestedness of a single axis (called internally by nestedness)

source: EcologicalNetwork/src/nestedness.jl:4

nodiag(A::Array{Float64, 2}) ¶

Sets the diagonal to 0

Returns a copy of the matrix A, with the diagonal set to 0. Will fail if the matrix is not square.

source: EcologicalNetwork/src/matrix_utils.jl:36

null1(A::Array{Float64, 2}) ¶

Given a matrix A, null1(A) returns a matrix with the same dimensions, where every interaction happens with a probability equal to the connectance of A.

source: EcologicalNetwork/src/nullmodels.jl:8

null2(A::Array{Float64, 2}) ¶

Given a matrix A, null2(A) returns a matrix with the same dimensions, where every interaction happens with a probability equal to the degree of each species.

source: EcologicalNetwork/src/nullmodels.jl:47

null3in(A::Array{Float64, 2}) ¶

Given a matrix A, null3in(A) returns a matrix with the same dimensions, where every interaction happens with a probability equal to the in-degree (number of predecessors) of each species, divided by the total number of possible predecessors.

source: EcologicalNetwork/src/nullmodels.jl:35

null3out(A::Array{Float64, 2}) ¶

Given a matrix A, null3out(A) returns a matrix with the same dimensions, where every interaction happens with a probability equal to the out-degree (number of successors) of each species, divided by the total number of possible successors.

source: EcologicalNetwork/src/nullmodels.jl:21

nullmodel(A::Array{Float64, 2}) ¶

This function is a wrapper to generate replicated binary matrices from a template probability matrix A.

If you use julia on more than one CPU, i.e. if you started it with julia -p k where k is more than 1, this function will distribute each trial to one worker. Which means that it's fast.

Note that you will get a warning if there are less networks created than have been requested. Not also that this function generates networks, but do not check that their distribution is matching what you expect. Simulated annealing routines will be part of a later release.

Keyword arguments

n (def. 1000), number of replicates to generate
max (def. 10000), number of trials to make

source: EcologicalNetwork/src/nullmodels.jl:79

number_of_paths(A::Array{Float64, 2}) ¶

Measures the expected number of paths in a probabilistic network

Keyword arguments

n (def. 2), the path length

source: EcologicalNetwork/src/paths.jl:7

propagate_labels(A::Array{Float64, 2}, kmax::Int64, smax::Int64) ¶

A very experimental label propagation method for probabilistic networks

This function is a take on the usual LP method for community detection. Instead of updating labels by taking the most frequent in the neighbors, this algorithm takes each interaction, and transfers the label across it with a probability equal to the probability of the interaction. It is therefore not generalizable for non-probabilistic networks.

The other pitfall is that there is a need to do a large number of iterations to get to a good partition. This method is also untested.

source: EcologicalNetwork/src/modularity.jl:96

ruggiero(S::BetaSet) ¶

Ruggiero measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:87

sorensen(S::BetaSet) ¶

Sorensen measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:62

species_has_no_predecessors(A::Array{Float64, 2}) ¶

Probability that a species has no predecessors

source: EcologicalNetwork/src/free_species.jl:2

species_has_no_successors(A::Array{Float64, 2}) ¶

Probability that a species has no successors

source: EcologicalNetwork/src/free_species.jl:8

species_is_free(A::Array{Float64, 2}) ¶

Probability that a species has no links

This will return a vector, where the ith element is the probability that species i has no interaction. Note that this is only meaningful for unipartite networks.

source: EcologicalNetwork/src/free_species.jl:20

whittaker(S::BetaSet) ¶

Whittaker measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:57

williams(S::BetaSet) ¶

Williams measure of beta-diversity

source: EcologicalNetwork/src/betadiversity.jl:77

Partition ¶

Type to store a community partition

This type has three elements:

A, the probability matrix
L, the array of (integers) module labels
Q, if needed, the modularity value

source: EcologicalNetwork/src/modularity.jl:14

Internal

motif_internal(A::Array{Float64, 2}, m::Array{Float64, 2}) ¶

Internal motif calculations

The two arguments are A the adjacency matrix (probabilistic) and m the motif adjacency matrix (0.0 or 1.0 only). The two matrices must have the same size. The function returns a vectorized probability of each interaction being in the right state for the motif, i.e. P if m is 1, and 1 - P if m is 0.

source: EcologicalNetwork/src/motifs.jl:9

BetaSet ¶

Partition of network similarity

The sets are, respectively

a, expected number of common interactions
b, expected number of interactions unique to B
c, expected number of interactions unique to A

Note that all values are Float64, since when dealing with probabilistic events, the expected cardinality of each set is not integers.

source: EcologicalNetwork/src/betadiversity.jl:13

@checkprob(p) ¶

Quite crude way of checking that a number is a probability

The two steps are

The number should be of the Float64 type -- if not, will yield a TypeError
The number should belong to [0,1] -- if not, will throw a DomainError

source: EcologicalNetwork/src/proba_utils.jl:17