# Counting motifs

In this use case, we will count the number of motifs in a food web. Specifically, we will count how many times there is a linear food chain (A→B→C) between three species.

using EcologicalNetwork

N = stony();

# List of motifs
m = unipartitemotifs();

Dict{Symbol,EcologicalNetwork.UnipartiteNetwork} with 13 entries:
:D4 => EcologicalNetwork.UnipartiteNetwork(Bool[false true false; false false…
:S1 => EcologicalNetwork.UnipartiteNetwork(Bool[false true false; false false…
:D1 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; false false …
:D6 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; true false t…
:D3 => EcologicalNetwork.UnipartiteNetwork(Bool[false false true; false false…
:D5 => EcologicalNetwork.UnipartiteNetwork(Bool[false true false; false false…
:S4 => EcologicalNetwork.UnipartiteNetwork(Bool[false true false; false false…
:S3 => EcologicalNetwork.UnipartiteNetwork(Bool[false true false; false false…
:D8 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; true false f…
:S2 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; false false …
:D2 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; false false …
:D7 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; true false f…
:S5 => EcologicalNetwork.UnipartiteNetwork(Bool[false true true; false false …


The m object has 13 different motifs, named as in Stouffer et al. (2007). The function unipartitemotifs will generate them when needed.

The function to count motifs is called motif, and returns a count: how many triplets of species are in a given conformation. For example:

s1 = motif(N, m[:S1])

1035.0


We may be interested in knowing whether this motif is over or under-represented in the empirical network, compared to a random expectation. To determine this, we will shuffle interactions around in a way that preserves the number of interactionsand the degree distribution of all species, using swaps. We will create 100 replicated networks to test.

permutations = swaps(N, 100, constraint=:degree)

ms1 = map(x -> motif(x, m[:S1]), permutations)

100-element Array{Float64,1}:
600.0
609.0
657.0
537.0
616.0
549.0
492.0
641.0
504.0
573.0
⋮
579.0
535.0
581.0
512.0
548.0
672.0
555.0
581.0
599.0