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AbstractA principled approach to understand networks is to formulate generative models and infer their parameters from given network data. Due to the scarcity of data in the form of multiple networks that have evolved from the same process, generative models are typically formulated to learn parameters from a single network observation, hence ignoring the natural variability of the "true" process. In this paper, we highlight the importance of variability in evaluating generative models and present two ways of quantifying the variability for a finite set of networks. The first evaluation scheme compares the statistical properties of networks in a dissimilarity space, while the other relies on data-driven entropy measures to compute variability in network populations. Using these measures, we evaluate the ability of four generative models to synthesize networks that capture the variability of the "true" process. Our empirical analysis suggests that generative models fitted for a single network observation fail to capture the variability in the network population. Our work highlights the need for rethinking the way we evaluate the goodness-of-fit of new and existing network models and devising models that are capable of matching the variability of network populations when available.

Direct quantification of terrestrial biosphere responses to global change is crucial for projections of future climate change in Earth system models. Here, we synthesized ecosystem carbon-cycling data from 1,119 experiments performed over the past four decades concerning changes in temperature, precipitation, CO2 and nitrogen across major terrestrial vegetation types of the world. Most experiments manipulated single rather than multiple global change drivers in temperate ecosystems of the USA, Europe and China. The magnitudes of warming and elevated CO2 treatments were consistent with the ranges of future projections, whereas those of precipitation changes and nitrogen inputs often exceeded the projected ranges. Increases in global change drivers consistently accelerated, but decreased precipitation slowed down carbon-cycle processes. Nonlinear (including synergistic and antagonistic) effects among global change drivers were rare. Belowground carbon allocation responded negatively to increased precipitation and nitrogen addition and positively to decreased precipitation and elevated CO2. The sensitivities of carbon variables to multiple global change drivers depended on the background climate and ecosystem condition, suggesting that Earth system models should be evaluated using site-specific conditions for best uses of this large dataset. Together, this synthesis underscores an urgent need to explore the interactions among multiple global change drivers in under-represented regions such as semi-arid ecosystems, forests in the tropics and subtropics, and Arctic tundra when forecasting future terrestrial carbon-climate feedback. ; National Natural Science Foundation of ChinaNational Natural Science Foundation of China [31430015, 31830012]; US NSFNational Science Foundation (NSF) [DEB-0955771]; ClimMani COST actionEuropean Cooperation in Science and Technology (COST) [ES1308] ; We thank J. Wang (Hebei University), S. Yang (Institute of Botany, Chinese Academy of Sciences), L. Zhou (East China Normal University), C. Qiao (Xinyang Normal University) and H. Li (Henan University) for their help in meta-analyses and interaction analyses, and H. Li, Y. Liu (Institute of Tibetan Plateau Research, Chinese Academy of Sciences) and Y. He (Peking University) for their help in plotting figures. This work was financially supported by the National Natural Science Foundation of China (grant nos. 31430015 and 31830012). This study emerged from the INTERFACE Workshop in Beijing, China (https://www.bio.purdue.edu/INTERFACE/) supported by the US NSF DEB-0955771. We also acknowledge support from the ClimMani COST action (ES1308). ; Public domain authored by a U.S. government employee