Statistical measures of complexity applied to ecological networks

TL;DR

This paper introduces a new method to quantify ecological network complexity using K-complexity and SVD entropy, demonstrating that K-complexity is more reliable and highlighting the influence of degree distribution and density.

Contribution

The study compares two complexity indices on ecological networks and establishes K-complexity as a more dependable measure, emphasizing the role of degree distribution and density.

Findings

K-complexity outperforms SVD entropy in reliability.

Differences observed between pollinator-plant and host-parasite networks.

Degree distribution and density significantly influence network complexity.

Abstract

Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks there is a quantity that seems rather elusive: Complexity. The quantification of the complexity of networks is nowadays a fundamental problem. Here, we present a novel tool for identifying the complexity of ecological networks. We compare the behavior of two relevant indices of complexity: K-complexity and Single value decomposition (SVD) entropy. For that, we use real data and null models. Both null models consist of randomized networks built by swapping a controlled number of links of the original ones. We analyze 23 plant-pollinator and 19 host-parasite networks as case studies. Our results show interesting features in the behavior for the K-complexity and SVD entropy with clear differences between pollinator-plant and host-parasite networks, especially when the degree distribution is not preserved. Although SVD entropy has been widely used to characterize network complexity, our analyses show that K-complexity is a more reliable tool. Additionally, we show that degree distribution and density are important drivers of network complexity and should be accounted for in future studies.