A new nestedness estimator in community networks

A recent problem in community ecology lies in defining structures behind matrices of species interactions. The interest in this area is to quantify the nestedness degree of the matrix after its maximal packing. In this work we evaluate nestedness using the sum of all distances of the occupied sites to the vertex of the matrix. We calculate the distance for two artificial matrices with the same size and occupancy: a random matrix and a perfect nested one. Using these two benchmarks we develop a nestedness estimator. The estimator is applied to a set of 23 real networks of insect-plant interactions.

💡 Research Summary

The paper introduces a novel metric for quantifying nestedness in bipartite ecological interaction matrices, addressing shortcomings of the widely used Nestedness Temperature (NT) index. The authors first “pack” the adjacency matrix by ordering rows and columns in descending order of degree (the number of links each species has). This packing concentrates the ones (interactions) toward the top‑left corner, producing a visual representation that highlights nested structure.

Each occupied cell (i, j) is then projected onto the unit square using the coordinates xᵢ = (i‑1)/L₁ + 1/(2L₁) and yⱼ = (j‑1)/L₂ + 1/(2L₂). The Manhattan distance from the origin to each cell, dᵢⱼ = xᵢ + yⱼ, is computed, and the total distance d is the sum over all occupied cells.

Two benchmark matrices with the same dimensions (L₁, L₂) and occupancy ρ are defined: (1) a maximally nested matrix ˜M, constructed by filling cells along diagonals emanating from (1, 1); this yields the minimal possible total distance d_min, and (2) a random matrix M_r, where each cell is independently occupied with probability ρ, giving an expected total distance d_rand = N·μ, where μ = 1 and N is the number of ones.

The new nestedness estimator η is defined as

 η = (d − d_min) / (d_rand − d_min).

By construction, η ∈