# Complex socio-ecological systems/Networks

Facilitators: Sam and Renato
Required readings:
Watts Duncan J. and Steven H. Strogatz. 1997. Collective dynamics of ‘small-world’ networks. Nature. 393: 440-442. Illustrates "six degrees of separation," the popular notion that all humans are separated by a maximum of 5 chains in a network. While this has become kind of an "urban legend," it is based on an actual experiment that is described and analyzed in the Linked book, below.
Lijeros, et al. 2001. The Web of Human Sexual Contacts. Nature 407-408. This brief communication describes the scale-free nature of networks of human sexual partners, and the implication that the way to "attack" the disease transmission properties of this network is by attacking the hubs of the network.
Bascompte, J and Pedro Jordano. 2007. Plant-animal mutualistic networks: The architecture of biodiversity. Annual Reviews of Ecology, Evolution and Systematics. 38:567-593. Reviews network structures in ecosystems. Reviews complex network concepts, describes the structure of mutualisms in plant-animal communities, looks at ecological and evolutionary processes that could create these networks, and the implications of network structure for co-evolution, robustness and conservation.
Palla, Barabasi and Vicsek. 2007. Quantifying Social Group Evolution. Nature 446: 664-667. Compares the dynamics of small versus large social groups over time, using 2 network cases: scientific co-authorship and mobile phone calling. Has cool graphs.
Supplementary Readings:
Barabasi, Albert-Laszlo and Reka Albert. 1999. Emergence of Scaling in Random Networks. Science 286: 509-512 This technical paper provides a mathematical (or logical) explanation of how scale-free networks can emerge by following a simple rule. Remember that "scale-free" networks are those that have the same structure at any scale. Mathematically, such networks follow a power function of the probability of "k", where "k" is the number of connections for a given node. The power function expresses mathematically the distribution of k, such that many nodes have low k or few connections, and few nodes have high k or many connections. [Incidentally, fractals are also "scale-free", i.e. the structure repeats at multiple scales, from the minute to the grandiose -- fractals can also be described by the same mathematical power law function.]
In this paper, Barabasi demonstrates mathematically a simple but elegant rule which results in such a distribution. The rule is that if you start with a small network and gradually add nodes/connections, such that the probability of an existing node receiving a new connection is proportional to the number of existing connections, the power law distribution naturally arises. In other words, "the rich get richer." This creates the hub and spoke structure of scale-free networks, because new nodes are more likely to connect to existing hubs than to a random node.
Barabasi, Albert-Laszlo. 2003. Linked: How Everything Is Connected to Everything Else and What It Means
This is a popular overview of network theory and it's application to daily life. It discusses the implications of "scale-free networks" and "small-world" networks.
Hahn, T.; L. Schultz; C. Folke; and P. Olsson. 2008. Social Networks as Sources of Resilience in Social-Ecological Systems. In: J. Norberg and G. S. Cumming (eds.). Complexity theory for a sustainable future. New York: Columbia University Press. 119-148 p. This chapter of the book "Complexity theory for a sustainable future", the authors relate the study and management of social networks in processes of adaptive co-management of SES, and in building resilience at both the ecosystem and the social system dimensions. Using a case study from southern Sweden (Kristiantads Vattenrike), the authors show the role of multileveled social networks for generating visions and ecological knowledge and connecting this to management and governance of SES. They focus on three main topics that connect stakeholders in different scales: motivations, values and vision; investing in local context adaptive co-management of ecosystems; and navigating the larger environment. Extreme reliance on one or few key persons (nodes) may indicate vulnerability in a process or project for ecosystem management. Therefore, there is need to invest in social capital in the weak ties to bridge the interests of diverse stakeholder groups. Also, the formalization and institutionalization of some actions in the co-management process may reduce vulnerability in case key persons leave the network. The authors conclude that social network studies for resilience of SES are important tools in knowledge generation, mobilizing people, identifying common interests, staring projects and providing feedback.
Christakis NA, Fowler JH (2009) Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives (Little Brown, New York). Christakis, a physician, and Fowler, a political scientist, are well known for their academic articles showing that obesity, smoking, and happiness can spread through social networks like contagions or epidemics. In Connected, the authors describe the powerful ways in which social networks shape society and individual human livelihoods. The authors discuss a wide assortment of phenomena, including the physical properties of human waves at sporting events, why emotions and suicides are contagious, and how social groups influence the spread of financial scams, voting behavior, and romantic relationships. This book makes use of a large set of longitudinal data to establish its claims that Millgram’s six degrees of separation can actually be understood in terms of three degrees of influence, an idea that is very controversial in the scholarly world.
Summary of discussion Seminar was opened with a reading from Christakis and Fowler (2009) on bucket brigades, and how the metaphor of a superogranism might help us to understand the concept of the emergent properties and nested hierarchies. UCINET, perhaps the most common software used for analyzing whole social networks, was then introduced to the class to best explain some of the concepts in the readings and in previous discussions. There were many questions from the group relating to what exactly the visualizations in NetDraw, a offshoot of UCINET, depict. We then dove into the readings, and there were a number of questions relating to how useful SNA is to understanding ecological networks and vice-versa. The Palla et al. (2007) article was pointed to as perhaps the best bridge for the two, but much of the seminar was devoted to deciphering Bascompte, and indeed how ecological networks operate differently. A back and forth ensued over how resilience thinking might be used to bridge the social and ecological networks, and the Hahn et al. (2008) chapter was cited as an example, though not without its own problems. Many questions abounded about the scale, weight, and initial energy of networks, and how best to bound these. Segue into next week’s dicussion: adaptive management.