Links, degree, connectance

sum(N::AbstractEcologicalNetwork; dims=nothing)

This function will return the sum of all interactions in the network. For quantitative networks, this is the sum of interaction strengths. For binary networks, this is the number of interactions. For probabilistic networks, this is the expected number of realized interactions.

Optionally, one can give the argument dims, simular to the native sum, which computes the sum of the interactions for the lower (dims=2) or higher (dims=1) level.

References

• Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

• Dunne, J.A., 2006. The Network Structure of Food Webs, in: Dunne, J.A., Pascual, M. (Eds.), Ecological Networks: Linking Structure and Dynamics. Oxford University Press, pp. 27–86.

• Martinez, N.D., 1992. Constant Connectance in Community Food Webs. The American Naturalist 139, 1208–1218.

links(N::BinaryNetwork)

Number of non-zero interactions in a deterministic network.

References

• Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

• Dunne, J.A., 2006. The Network Structure of Food Webs, in: Dunne, J.A., Pascual, M. (Eds.), Ecological Networks: Linking Structure and Dynamics. Oxford University Press, pp. 27–86.

• Martinez, N.D., 1992. Constant Connectance in Community Food Webs. The American Naturalist 139, 1208–1218.

links(N::QuantitativeNetwork)

Number of non-zero interactions in a quantitative network (use sum to get the sum of interaction strengths).

References

• Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

• Dunne, J.A., 2006. The Network Structure of Food Webs, in: Dunne, J.A., Pascual, M. (Eds.), Ecological Networks: Linking Structure and Dynamics. Oxford University Press, pp. 27–86.

• Martinez, N.D., 1992. Constant Connectance in Community Food Webs. The American Naturalist 139, 1208–1218.

links(N::ProbabilisticNetwork)

Expected number of interactions in a probabilistic network. To get the number of interactions that have a non-zero probability, use e.g. links(N>0.0).

References

• Poisot, T., Cirtwill, A.R., Cazelles, K., Gravel, D., Fortin, M.-J., Stouffer, D.B., 2016. The structure of probabilistic networks. Methods in Ecology and Evolution 7, 303–312. https://doi.org/10.1111/2041-210X.12468

connectance(N::AbstractEcologicalNetwork)

Number of links divided by the number of possible interactions. In unipartite networks, this is $L/S^2$. In bipartite networks, this is $L/(T × B)$. It is worth noting that while the maximal connectance is always 1 (i.e. the graph is complete), the minimum value (assuming that the network is not degenerate) is not 0. Instead, the minimum number of interactions in a unipartite network is S-1, and in a bipartite network it is max(T,B).

Connectance can therefore be transformed between 0 and 1, using the following approach: let m be the minimum number of interactions, and Co be the measured connectance, then the corrected value is (Co-m)/(1-m). To our best knowledge, this is not standard practice, and therefore is not suggested as a function in the package.

References

• Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

• Dunne, J.A., 2006. The Network Structure of Food Webs, in: Dunne, J.A., Pascual, M. (Eds.), Ecological Networks: Linking Structure and Dynamics. Oxford University Press, pp. 27–86.

• Martinez, N.D., 1992. Constant Connectance in Community Food Webs. The American Naturalist 139, 1208–1218.

linkage_density(N::AbstractEcologicalNetwork)

Number of links divided by species richness.

References

• Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

• Dunne, J.A., 2006. The Network Structure of Food Webs, in: Dunne, J.A., Pascual, M. (Eds.), Ecological Networks: Linking Structure and Dynamics. Oxford University Press, pp. 27–86.

degree(N::AbstractEcologicalNetwork; dims::Union{Nothing,Integer}=nothing)

Returns the degrees of nodes in a network; dims can be 1 for out degree, or 2 for in degree.

References

Delmas, E., Besson, M., Brice, M.-H., Burkle, L.A., Dalla Riva, G.V., Fortin, M.-J., Gravel, D., Guimarães, P.R., Hembry, D.H., Newman, E.A., Olesen, J.M., Pires, M.M., Yeakel, J.D., Poisot, T., 2018. Analysing ecological networks of species interactions. Biological Reviews 112540. https://doi.org/10.1111/brv.12433

Poisot, T., Cirtwill, A.R., Cazelles, K., Gravel, D., Fortin, M.-J., Stouffer, D.B., 2016. The structure of probabilistic networks. Methods in Ecology and Evolution 7, 303–312. https://doi.org/10.1111/2041-210X.12468

Williams, R.J., 2011. Biology, Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks. PLoS One 6, e17645. https://doi.org/10.1371/journal.pone.0017645

degree_var(N::ProbabilisticNetwork; dims::Union{Nothing,Integer}=nothing)

Variance in the degree of species in a probabilistic network.

isdegenerate(N::AbstractEcologicalNetwork)

Networks are called degenerate if some species have no interactions, either at all, or with any species other than themselves. This is particularly useful to decide the networks to keep when generating samples for null models.

simplify!{T<:BipartiteNetwork}(N::T)

Returns a new network in which species with no interactions have been removed.

simplify!{T<:BipartiteNetwork}(N::T)

Returns a new network in which species with no interactions have been removed.

simplify!{T<:BipartiteNetwork}(N::T)

Returns a new network in which species with no interactions have been removed.

simplify!(N::UnipartiteNetwork)

Modifies the network to drop all species without an interaction.

simplify!(N::UnipartiteNetwork)

Modifies the network to drop all species without an interaction.

simplify!(N::UnipartiteNetwork)

Modifies the network to drop all species without an interaction.

simplify(N::T) where {T<:AbstractEcoloigcalNetwork}

Returns a new network in which species with no interactions have been removed.

specificity(N::DeterministicNetwork)

Measure of specificity in a deterministic network. This returns a value between 0 and 1, where 1 indicates maximal specificity.

References

• Poisot, T., Bever, J.D., Nemri, A., Thrall, P.H., Hochberg, M.E., 2011. A conceptual framework for the evolution of ecological specialisation. Ecol. Lett. 14, 841–851. https://doi.org/10.1111/j.1461-0248.2011.01645.x

• Poisot, T., Canard, E., Mouquet, N., Hochberg, M.E., 2012. A comparative study of ecological specialization estimators. Methods in Ecology and Evolution 3, 537–544. https://doi.org/10.1111/j.2041-210X.2011.00174.x