In this lecture, we review topics that might be covered on the Spring 2023 final exam of SOS 220 (Systems Thinking). This involves going back to reviewing concepts from resilience thinking about dynamical systems to topics in network science to topics in game-theoretic modeling of social systems. We also review the relationship between the second law of thermodynamics and closed thermodynamic systems as well as some basic terms in the biology of inheritance and natural selection.
In this lecture, we wrap up the course by connecting the networking thinking from the previous unit to the resilience thinking introduced earlier in the course. We first cover scale-free networks as a particular kind of small-world network with a notable (and apparently very natural) degree distribution. This helps motivate that metrics of networks can be informative about the processes that are driving the structure of those networks. This lets us pivot to a relatively new result testing the stress-gradient hypothesis in mixed-species bird flocks in South America. That study shows that with increased stresses, social networks of species within observed bird flocks become more connected (and less modular). We connect this observation to previous units on the adaptive cycle and panarchy as well as the current chapter on using resilience thinking for sustainability problems. In particular, we discuss how diversity is an asset in communities under stresses that reduce competitive structure (i.e., diversity increases the robustness of the communities to stressors); however, when there is low stress, communities tend to be shaped by competitive exclusion (and efficiency maximization).
Comments in this lecture were motivated by Walker and Salt (2006, Chapter 6), which presents 9 hypothetical attributes of resilient (and sustainable) societies which are built around "creating space" in those societies/organizations.
In this lecture, we finish up our discussion of the Hawk–Dove (chicken) model as a game-theoretic exploration of commons/common-pool resources problems (and the tragedy of the commons). We contrast the Hawk–Dove with the stag hunt (public goods problem). Putting them together helps illustrate the idea of "network effects" from economics and motivates why looking at "networks" more formally might lead to understanding other macroscale phenomena. That lets us transition to Stanley Milgram and his experiment with letters that led to the "six degrees of separation" "small-world network" observation about human society. We discuss how network science provides a formal set of tools behind this network thinking and then provide the graph-theoretic ideas necessary to speak this language (nodes, edges, hubs, clusters, degree, degree distribution, etc.). We use Google PageRank as an example of how degree can be a useful tool for differentiating between nodes in a network and then start to discuss a formal definition of small-world networks and, eventually, scale-free networks. We will finish discussing scale-free networks in the next lecture.
This lecture is based on topics from Chapters 15 and 16 from Melanie Mitchell's 2009 Complexity book.
In this lecture, we review the classic "Prisoner's Dilemma" game-theoretic model of the challenges of cooperation in a world of strong temptation to defect, and then we contrast it with two other models that are possibly more realistic (but similarly simple) models of cooperation and competition in the real world -- the stag hunt model and the Hawk–Dove model. The stag hunt is a model of positive externalities, like those that characterize public goods games. We discuss how the stag hunt is like a Prisoner's Dilemma with a stronger reward for cooperation (stronger positive externalities) than a temptation to defect. This lets us introduce coordination games, assurance games, and correlated equilibria. In general, the stag hunt shows us that there are more fundamental issues to cooperation beyond incentives -- there are barriers to the coordination of actions and information limitations that prevent cooperation even when it is favored. We extend the stag hunt to the N-player stag hunt, which is a better model of public goods problems, in order to introduce the idea of a mixed (Nash) equilibrium. We then close with an introduction of the Hawk–Dove game, which is a model of competition and negative externalities that often characterize common-pool resources problems ("tragedies of the commons"). We will continue discussion of the Hawk–Dove next time and explore why it is a better match to tragedy of the commons problems than the Prisoner's Dilemma.
In this lecture, we review the key results from the computational tournaments run by Robert Axelrod on the iterated/repeated Prisoner's dilemma game. We re-introduce the Prisoner's dilemma and the puzzle of how cooperation can evolve, identifying the difference between the Nash equilibrium and a socially efficient solution that is not a Nash equilibrium as being the key problem. This lets us talk about resolutions to the problem – including relatedness and compensation. We then discuss how iterating the Prisoner's Dilemma introduces temporal relatedness, and how placing the Prisoner's Dilemma on a grid introduces network relatedness. After mentioning how punishment can also be used to maintain cooperation in Prisoner's Dilemma games, we open the topic of how the Prisoner's Dilemma may be unrealistic and other games might be better/more useful models, particularly when it comes to natural resources and sustainability. We close with a brief introduction to the Stag Hunt coordination game, which we will pick up on next time (as well as introduce the Hawk–Dove game, which is a better model for the tragedy of the commons than the Prisoner's Dilemma).
In this lecture, we discuss topics related to "Prospects of Computer Modeling" by Mitchell (2009, Chapter 14). We start with a discussion of what it means for complex systems science to be a science. We follow that with a re-introduction to the scientific process, where we make things like causal questions, hypotheses, experiments, models, predictions, and theories explicit. We focus a lot on how hypotheses are answers to causal how/why questions and are NOT if–then statements (which are predictions). After going through the scientific process, we introduce the computational social simulation of the evolution of cooperation (starting with Robert Axelrod's popular efforts) and the prisoner's dilemma model. We do not quite get to the main computational results from Axelrod's study, which we will touch on at the start of the next lecture. We do discuss the requirements for a game to be a prisoner's dilemma and how the Nash equilibrium of the prisoner's dilemma is not Pareto efficient, which makes it a good model for such traps as the tragedy of the commons.
In this lecture, we continue to discuss the different ways to search for and process information from the environment in distributed architectures in nature. Whereas the last lecture focused on nonlinear recruitment strategies (and more generally strategies focused on trail laying and external memory), this lecture focusses on linear recruitment strategies such as the honeybee waggle dance (and piping transition in the case of nest-site selection) and the ant tandem run (and transition to transport in the case of nest-site selection). After demonstrating the waggle dance, the tandem run, and the differences between individual and group performance in decision-making tasks, the lecture closes discussing different mechanistic models for how individual ants decide when to transition from tandem run to transport.
DUE TO TECHNICAL ISSUES IN THE ROOM, there are small parts of this lecture where the audio or video will drop out.
This lecture focuses on the diverse ways that ants (and slime mold) process information from their environment. We start with some basic background on ants (including their evolution from solitary wasps) and then discuss mass recruitment (one of the three main ways that ants recruit to food or candidate nest sites). We contrast the dynamic performance of Lasius niger with Pheidole megacephala and explore the suggestion that "errors" make P. megacephala better at tracking changes (using fire ants as an example that confirms this idea). We then discuss how trails are used in slime mold for enhancing exploration (instead of the exploitation case in ants) and show how slime mold can spread itself out to make decisions that compare different options in the environment. That brings us to ants that similarly spread themselves out (using linear recruitment strategies instead of the nonlinear pheromone-trail-based mass recruitment strategies) so that they can make similar deliberative decisions. We will pick up with this case in the next lecture.
In this lecture, we discuss topics related to the chapter, "Information Processing in Living Systems," by Mitchell (2009, Chapter 12). The beginning of the lecture discusses the first use of information theory for a non-human application -- an analysis of the honeybee waggle dance. That requires a description of the waggle dance/waggle run. We then move on to examples brought up by Mitchell -- the adaptive immune system (lymphocytes, B cells, T cells, antibodies) and ants (primarily the use of pheromone trails for recruiting to discovered foods during foraging). Our discussion of the vertebrate adaptive/acquired immune system also gives us an opportunity to briefly discuss the innate immune system (which has a much deeper phylogenetic history). We discuss natural selection within the adaptive immune system, both in terms of negative selection (central tolerance and autoimmune disorders) and positive selection. We close with a brief description of basic trail laying behavior, which we will pick up in our next lecture that will discuss more sophisticated communication cases in ants and other non-human organisms.
In this lecture, we wrap up our introduction to The Modern Synthesis by describing how population genetics connected particulate inheritance (genes with discrete alleles) to quantitative traits and natural selection. After reviewing the initial conflict between Mendelism and Darwinism, we use a simple additive effect example to show how discrete alleles can produce approximately continuous features (that are even more continuous when considering the effect of the environment on gene expression). We then discuss the contributions of Haldane and Wright to population genetics, summarize the key components of population genetics, and hold up population genetics as a foundational core to The Modern Synthesis which also include the primacy of natural selection in evolution. This gives us an opportunity to discuss Stephen Jay Gould's objections, punctuated equilibria, biological constraints (including the "spandrels of evolution"), and historical contingency. We conclude with a brief introduction to the central dogma of molecular biology, which helps to explain how genes lead to the expression of phenotypic traits that confer fitness on alleles. We end this discussion a little early (due to starting a little late).
In this lecture, we review the history of thought about biological evolution, as surveyed by Mitchell (2009, Chapter 5). We start with Lamarck's ideas and discuss their appeal to Darwin. We then move to Darwin and note the influence of Lyell, Lamarck, Mathus, and (Adam) Smith on Darwin's theory of evolution by natural selection. We describe Darwin's finches on the Galapagos Island chain as evidence for natural selection. We then pivot to Mendel to discuss particulate inheritance and point out the difficulties with integrating this with natural selection. We close with an introduction to population genetics (Fisher, Haldane, and Wright) that resolves the conflict between Darwinism and Mendelism, providing the foundations for The Modern Synthesis.
In this lecture, we review the conceptual dimensions of resilience (latitude, resistance, precariousness, and panarchy) and the adaptive cycles that pass information and influence from systems at one scale to systems at other scales. Ultimately, this lecture is about how to manage resilience in systems. We define terms like adaptability and transformability, and we discuss tradeoffs between resilience and short-term profits as well as different forms of resilience (as in specified/targeted/local resilience and generic/global resilience). We finish with a discussion of three properties that help increase generic resilience – diversity, modularity (connectedness), and tightness of feedbacks.
This lecture is based upon content from Walker and Salt (2006, Chapter 5) and Walker et al. (2004).
In this lecture, we review the processes in natural systems that cause diversity to grow initially and then collapse as systems get more mature (and this collapse in diversity can lead to the release and reorganization, as in the Adaptive Cycle). We use a Pareto-based multi-objective framework to conceptualize what is going on in ecological communities. In this framework, Pareto improvements correspond to expansion of diversity (virtuous cycle) that ends up slowing down as the community approaches the Pareto frontier (limits to growth). Once on the frontier, competitive exclusion and genetic drift lead to sparsification of the community (success to the successful). In other words, the initial process generates a diverse set of niches, but the later processes collapse each niche to a very small set of individuals that dominate that niche. We explain how genetic drift causes diversity to collapse even when diverse individuals have equal fitness. We also talk about how we can measure diversity using the Shannon index, which measures both richness as well as evenness. This whole explanation sets up for an introduction of the Adaptive Cycle (r/growth phase, K/conservation phase, omega/release phase, and alpha/reorganization phase). Overall, the adaptive cycle links topics from earlier in the semester (systems archetypes) with more recent topics (chaotic dynamics) and helps provide a framework for understanding how exogenous/slow variables change over time (and thus how stability regimes change over time). Change is inevitable, and sustainability is about surviving change; sustainability is not about preventing change.
In this lecture, we focus on how to estimate the health or general status of large complex systems. This is motivated by the concern that systems that appear, at a macroscale, to be stable might actually be undergoing changes from within that affect their resilience. We provide one example from social welfare economics, which starts with an introduction to the Lorenz curve for wealth distributions and the related Gini coefficient/index used to measure the distance in a distribution from the equal-wealth distribution. We show how the Gini index has changed over time for different countries based on their political decisions, which allows us to talk about Pareto optimality as a framework for thinking about social-welfare policy decisions. We introduce things like the Pareto improvement and the Pareto frontier. We then pivot to community ecology and use the Pareto framework as a lens for thinking about how evolution (and natural selection, in particular) is a sequence of Pareto improvements that moves communities toward a Pareto frontier. Although they diversify in getting to the frontier, that diversification can be limited in later movements along the frontier (which will affect resilience). We begin to talk about how to use Shannon entropy as an index for biodiversity, helping to estimate the "health" of a given ecological community.
In this lecture, we review topics from SOS 220 (Systems Thinking) that have been presented before the midterm. This includes topics related to introductory systems thinking, causal loop diagrams (CLD's), systems archetypes, resilience thinking, complexity, complex adaptive systems, bifurcation diagrams, tipping points, chaos, basic thermodynamics, Boltzmann entropy, and Shannon information. In the classroom exercise, we mainly answer questions from the students and walk through examples, such as a sample ball-in-a-basin model of a nonlinear system with two alternative stable states (as in a lake that can switch from a clear state to a murky state).
In this lecture, we revisit the fundamentals of the stochastic modeling at the heart of statistical mechanics (microstates, macrostates, multiplicity, and the second law of thermodynamics). We use those fundamentals to motivate the formula for Boltzmann entropy (i.e., why it is a logarithm) and then discuss how systems with relatively low entropy tend to have high "free energy." That is, they have a high ability to do work on another system. When we consider the whole system, the work done by the low-entropy system ends up producing a lot more entropy, causing the entropy of the whole system to increase. This motivates our discussion of the emergence of "dissipative structures" (like life itself) when there are high amounts of free energy (and we use a ball-in-a-basin conceptual model to justify this). We pivot to discussing a combination of economics and physics – econophysics – and how we can think of wealth distributions as macrostates where equal wealth has the lowest entropy and exponentially distributed wealth has the highest entropy. Tidbits of information references are peppered throughout, but we do not get to a specific discussion about Shannon entropy and its relationship to Boltzmann entropy.
This lecture reviews topics from the "Information" chapter by Mitchell (2009, Chapter 3). This chapter reviews the history and fundamentals of thermodynamics and statistical mechanics and how they led to modern information theory. We review topics as in the second law of thermodynamics, Boltzmann entropy, multi-scale modeling, microstates and macrostates (and coarse graining), temperature and other functions of state, Maxwell's demon, and erasure and the Landaurer limit. This lecture discussion sets up a more formal discussion of information, entropy, and free energy in the next lecture period.
In this lecture, we discuss how predictability and repeatability in dynamical systems models cannot be taken for granted, particularly when there is nonlinear feedback combined with either delay or more than 2 state variables. The lecture uses delay in a simple feedback system to motivate how dynamical systems can have SET-based attractors (e.g., oscillations, "omega limit sets"). With set attractors, aspects of the steady-state pattern can depend upon the initial condition. We then discuss how in systems like the Mackey–Glass system (a physiological model), there are ranges of exogenous variables (parameters) that causes the nonlinear dynamics and delay to generate so-called "chaos," an extreme sensitivity to initial conditions where patterns over time do not repeat, and each initial condition is associated with a different pattern. This phenomenon cannot occur in systems of two endogenous/state variables or less unless there is a delay, but it can occur in systems with three endogenous/state variables without delay. We show this for the Lorenz system, a simple model of atmospheric convection. We visualize the "strange attractor" for the Lorenz system using a parametric plot to reveal that the apparently random trajectories of the system truly are structured, and this structure can be revealed by time-series analysis if the right tools are used. Nevertheless, these models show us that for some systems, accurate prediction beyond a short time horizon may always be impossible (even without worrying about stochasticity or bounded rationality) as we will never be able to measure all endogenous-variable initial conditions perfectly.
We begin by rehashing how descriptions of dynamical systems can turn into "ball-in-a-basin" physical models (potential field models) that give us intuition about the behavior over time (BOT) of systems from different initial conditions. This lets us introduce the term "attractor" for the region of a stability regime that "attracts" trajectories from any initial condition within the regime. We use the ball-in-a-basin perspective to compare local resilience (two deep potential wells with a sharp threshold between them) to global resilience (one shallow potential well). The focus on regime shifts lets us discuss both endogenous regime shifts (gentle pushes over thresholds) to exogenous regime shifts (very rare endogenous shocks as well as bifurcations). We refer to the "exogenous regime shifts" as "tipping" and describe bifurcation points as a type of "tipping point." Bifurcation points are thresholds of EXOGENOUS variables that separate regions with different numbers or types of stability regimes. All of these conceptual frameworks then allow us to introduce systems that challenge them -- as in systems with significant delays. Systems with delay are one of the types of systems that exhibit chaos, a term that we will define in more detail in the next lecture.
In this lecture, we start by reviewing resilience concepts in complex systems and how some complex systems can suffer from large regime shifts from one discrete stable state to another. We do an analysis of the equilibria in a simple harvested fishery to motivate the "ball-in-a-basin" potential field perspective on stable states. This discussion allows us to introduce the "bifurcation diagram", which concisely summarizes the relationship between exogenous "slow" variables and the stable states of endogenous "fast" variables; this also allows us to define a "tipping point" as a bifurcation point where the equilibrium structure of the system fundamentally changes.
In this lecture, we introduce the topic of "resilience" as applied to social-ecological systems, and related terms such as (resilience) thresholds and vulnerability. This allows us to introduce the notions of "complex adaptive systems" (CAS) in contrast with "simple" systems or even "complicated" systems. Complex adaptive systems sometimes admit multiple steady states and "stability regimes", which we demonstrate with an example from fisheries management. This example motivates the "ball-in-a-basin" dynamical systems conceptual model that we will use as we move on to discuss critical slowing down next time. Next time, we will also define adaptability and transformability, two other important concepts in resilience thinking.
In this lecture, we define the term "bounded rationality" as a sort of higher-level modeling trap that often leads to policy choices that can be described in terms of some of the problematic "systems traps" (systems archetypes) described in earlier lectures. We spend most of the lecture providing concrete examples of several of the archetypes, either from history or from general phenomena that frequently occur in human systems. This lets us describe "policy resistance" and how something like the abortion policy decisions in Romania in the 1960's can be viewed with multiple system archetype "lenses" (borrowing an idea from Kim and Lannon, 1997) that each highlight a different aspect of solutions tried and the problems associated with each of them. This lecture is meant to be a library of examples of applications of systems archetypes. The only major new thing introduced in this lecture is "bounded rationality" (and "policy resistance"). The lecture also helps differentiate between "fixes that fail" and "shifting the burden", which are two very related archetypes that lead to focusing on different aspects of the same system.
In this lecture, we finish discussing causal loop diagrams (CLD's), picking up with a discussion of negative- and positive-feedback loops. We discuss how to identify these loops in a CLD and some common traps related to these two loops. We then move on to briefly discuss "Applying Systems Archetypes" by Kim and Lannon (1997) and "Using the Archetype Family Tree as a Diagnostic Tool" by Goodman and Kleiner (1993).
In this lecture, we review the basic concept of a system as a group of interrelated components, and then we move on to describe dynamical models that represent systems and help to answer "What If" questions. "Variables" in these models can be endogenous, exogenous, or excluded entirely for model simplicity and research-question relevance. We then go into re-introducing the causal loop diagram (CLD), which is itself a kind of qualitative model that captures the systemic structures in a system of interest. We give the rules for naming variables in a CLD, we discuss the formation of causal links, and then we save feedback loops (and their polarities and related traps) for the next lecture.
In this lecture, we review "Introduction to Systems Thinking" by Kim (1999), which defines a "system" and motivates the "feedback-loop worldview" (in contrast with an "event-oriented worldview"). We start by contrasting "systems" and simple "collections." We then move on to talking about events, patterns, and systemic structures, and how finding systemic structures (which are cryptic although events are observable) can lead to finding "leverage points" that allow for choosing small actions that have big changes in system behavior. We start to introduce causal loop diagrams (CLD's) and behavior over time (BOT) graphs (BOTG). We will continue our discussion of CLD's in the next lecture.
In this lecture, we introduce SOS 220 (Systems Thinking) for the Spring 2023 semester. The lecture mainly consists of a syllabus overview and then a few brief comments about systems thinking.
