Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

In this synthesis, we hope to accomplish two things: 1) reflect on how the analysis of the new archaeological cases presented in this special feature adds to previous case studies by revisiting a set of propositions reported in a 2006 special feature, and 2) reflect on four main ideas that are more specific to the archaeological cases: i) societal choices are influenced by robustness–vulnerability trade-offs, ii) there is interplay between robustness–vulnerability trade-offs and robustness–performance trade-offs, iii) societies often get locked in to particular strategies, and iv) multiple positive feedbacks escalate the perceived cost of societal change. We then discuss whether these lock-in traps can be prevented or whether the risks associated with them can be mitigated. We conclude by highlighting how these long-term historical studies can help us to understand current society, societal practices, and the nexus between ecology and society.

What relationships can be understood between resilience and vulnerability in social-ecological systems? In particular, what vulnerabilities are exacerbated or ameliorated by different sets of social practices associated with water management? These questions have been examined primarily through the study of contemporary or recent historic cases. Archaeology extends scientific observation beyond all social memory and can thus illuminate interactions occurring over centuries or millennia. We examined trade-offs of resilience and vulnerability in the changing social, technological, and environmental contexts of three long-term, pre-Hispanic sequences in the U.S. Southwest: the Mimbres area in southwestern New Mexico (AD 650–1450), the Zuni area in northern New Mexico (AD 850–1540), and the Hohokam area in central Arizona (AD 700–1450). In all three arid landscapes, people relied on agricultural systems that depended on physical and social infrastructure that diverted adequate water to agricultural soils. However, investments in infrastructure varied across the cases, as did local environmental conditions. Zuni farming employed a variety of small-scale water control strategies, including centuries of reliance on small runoff agricultural systems; Mimbres fields were primarily watered by small-scale canals feeding floodplain fields; and the Hohokam area had the largest canal system in pre-Hispanic North America. The cases also vary in their historical trajectories: at Zuni, population and resource use remained comparatively stable over centuries, extending into the historic period; in the Mimbres and Hohokam areas, there were major demographic and environmental transformations. Comparisons across these cases thus allow an understanding of factors that promote vulnerability and influence resilience in specific contexts.

The context in which many self-governed commons systems operate will likely be significantly altered as globalization processes play out over the next few decades. Such dramatic changes will induce some systems to fail and subsequently to be transformed, rather than merely adapt. Despite this possibility, research on globalization-induced transformations of social-ecological systems (SESs) is still underdeveloped. We seek to help fill this gap by exploring some patterns of transformation in SESs and the question of what factors help explain the persistence of cooperation in the use of common-pool resources through transformative change. Through the analysis of 89 forest commons in South Korea that experienced such transformations, we found that there are two broad types of transformation, cooperative and noncooperative. We also found that two system-level properties, transaction costs associated group size and network diversity, may affect the direction of transformation. SESs with smaller group sizes and higher network diversity may better organize cooperative transformations when the existing system becomes untenable.

We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiple-relation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.