Comparison of two statistical measures of complexity applied to ecological bipartite networks

HUAYLLA, CLAUDIA A.; KUPERMAN, MARCELO N.; GARIBALDI, LUCAS A.

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2024

0378-4371

Networks are a convenient way to represent many interactions among differententities as they provide an efficient and clear methodology to evaluate andorganize relevant data. While there are many features for characterizingnetworks, a quantity seems rather elusive: Complexity. The quantification ofthe complexity of networks is nowadays a fundamental problem. Here, wepresent a novel tool for identifying the complexity of ecological networks. Wecompare the behavior of two relevant indices of complexity: K-complexity andSingle Value Decomposition (SVD) entropy. For that, we use real data andtwo types of null models. Both null models consist of randomized networksbuilt by swapping a controlled number of links of the original ones. Weanalyze 23 plant-pollinator and 19 host-parasite networks as case studies. Ourresults show that (a) it is necessary to calculate, not only the original networkK-complexity and SVD entropy but also to calculate the correspondingindices of the randomized networks (b) the density and degree distribution areessential in the characterization of a network and the randomized networksare a suitable tool to detect the network complexity, and (c) plant-pollinatornetworks are more complex than host-parasite networks. We found that, for the first null model, K-complexityand SVD did not change with link swapping in both pollinator-plant andhost-parasite networks. For the second null model, K-complexity for pollinator-plantnetworks generally decreased with an increasing number of links swapped(i.e. negative slope), showing that plant-pollinator networks lose complexitywith increasing link swapping. In contrast, there was a positive slope betweenK-complexity and link swapping for host-parasite networks, showing that thesenetworks are less complex than plant-pollinator networks. For both types ofnetworks, in general, the slope between K-complexity and the number of linksswapped became more positive with network density. Overall, SVD entropywas less responsive to link swapping. Our analyses show that althoughSVD entropy has been widely used to characterize network complexity,K-complexity is a more reliable tool. Additionally, they show that degreedistribution and density are important drivers of network complexity andshould be accounted for in future studies.