M ΩD ∑LC ∆L ∑N D ∆R 2015Our thinking in social-ecological systems research is influenced by many models. This calendar highlights some of these models. It is a result of monthly dinners and model discussions over a year by a group of researchers at the Beijer Institute of Ecological Economics and the Stockholm Resilience Centre.

JANUARY 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Social-ecological system, or cake model (Folke 1990; Perrings et al. 1992)

PURPOSE: The cake model demonstrates that the economy is a part of the social system, which is in its turn part of the biosphere. This makes the economy an intertwined part of system earth.

IMPACT: The model evoked a perspective shift of the traditional economic view of land, labour, capital as factors of production for the economy to the economy as an embedded part of the biosphere. The social-ecological system model represents the core of the Stockholm Resilience Centre and the Beijer Institute of Ecological Economics as well as the key view in coining this era as the Antrophocene. The model has been criticized for placing the economy in the centre, however, being represented in the inner circle refers to economies as a subsystem, explicitly placed into a social-ecological/biosphere perspective.

RELATED MODELS: Opposing, but strongly related earlier model: component parts of price: land-labour-capital (Smith 1776). Inspiration for this model: The Economics of the Coming Spaceship Earth (Boulding 1966); Ecology: A Bridge Between Science and Society (Odum 1975); Ecology and Our Endangered Life-Support Systems (Odum 1989); For The Common Good: Redirecting the Economy toward Community, the Environment, and a Sustainable Future (Daly & Cobb 1989).

No man is an island, Entire of itself; Every man is a piece of the continent, A part of the main. –John Donne

We all are part of the biosphere

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SOCIETY

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FEBRUARY 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Lotka-Volterra

PURPOSE: The model was independently developed by A.J. Lotka (1925) and V. Volterra (1926) to analyse the interaction of a predator and a prey species over time.

IMPACT: The early model highlighted that changes in one population or system might affect a dependent system and vice versa, in what we now call a link or feedback. It also fostered the use of differential equations in describing the dynamics of ecological systems. This method was later transferred to economic systems to analyse the interactions between two industrial sectors.

RELATED MODELS: The 1989 Arditi-Ginzburg model provides a simpler alternative description of observed predator-prey dynamics. Analogous models were developed independently in economics to demonstrate the relationship between wages and employment (Goodwin 1967).

The world is dynamic

The snake which cannot cast its skin has to die. As well the minds which are prevented from changing their opinions; they cease to be mind. –Friedrich Nietzsche

If nothing ever changed, there’d be no butterflies. –Unknown

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MARCH 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Small world network model

PURPOSE: The model shows how everybody is connected to everybody else in the world. We are not connected directly, but rather by the connections of the connections we have with people in our network. This leads to the common saying, “It’s a small world!” when strangers realize they share a common friend.

IMPACT: The interaction between people can be described using a network, which highlights the critical role that the structure of neighborhood interactions has on our society’s function. In general network structure is important in appreciating how complex systems function.

RELATED MODELS: Scale free networks, random networks and planar networks. Also relates to Erdős number, Kevin Bacon game and small world phenomenon (Watts & Strogatz 1998).

The worldis small

El mundo es un pañuelo. –Refrán iberoamericano

It’s a small world after all. –Sherman Brothers 1965

It’s a small world, so be careful what you say. –Jessica Klemann, Forbes

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APRIL 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Fold bifurcation

PURPOSE: It is easy to think that the state of a system changes smoothly with a change in its driver. Fold bifurcations show that the state of a system can, however, change abruptly even after a very small change in its driver. Henri Poincaré, a French mathematician, was the first to introduce and study bifurcations back in 1885, showing that in dynamic systems even a small smooth change in a parameter can cause a sudden qualitative change in the system’s behaviour.

IMPACT: Fold bifurcations are a common model of regime shifts, since they can produce large, abrupt changes that are difficult to reverse: in other words, hysteresis (Scheffer et al. 2001; Scheffer & Carpenter 2003). For example, deforestation could trigger an irreversible shift to savanna. Because of hysteresis, it is a rule of thumb from the management perspective that it is easier and cheaper to prevent regime shifts than to restore shifted social-ecological systems, as embodied in the folk saying ‘A stitch in time saves nine’. Regime shifts and their implicit thinking of non-linear surprises are a major foundation of resilience thinking.

RELATED MODELS: Bifurcation theory, Catastrophe theory, Chaos theory

The world changes abruptlyA stich in time saves nine. –Anonymous

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MAY 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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Share your world!Sketch your own model that reflects how the world is seen differently (if you like in the field below). Take a picture of it and share it with the other model calendar owners at our modeling calendar website: modelcalendar.blogspot.se.

How? Send an email to: mymaymodel.2015@blogger.com with the title of your model as subject of the email. Attach your model, i.e. picture or drawing. You can include a description in the body of the email if you like. Have a look here for inspiring examples: modelcalendar.blogspot.se.

The world is seen differently

There are no facts, only interpretations. –Friedrich Nietzsche

We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses. –Abraham Lincoln

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Resources

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JUNE 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: World3 (The Limits to Growth)

PURPOSE: World3 (Meadows et al. 1972) is a system dynamics model which simulates the interactions between population and industrial growth, food production and biophysical limits of the Earth. The purpose of the model was to explore how exponential economic and population growth interacts with finite resources, and to observe how certain key variables (world population, industrialisation, pollution, food production and resource depletion) change once they reach the limits to growth. The model assumes that the world has biophysical limits that are finite, and that there are therefore limits to growth.

IMPACT: The World3 model challenged the status quo of the growth paradigm and had a significant impact on the serious uptake of environmental issues. The book ‘Limits to Growth’, in which the model and its implications was presented, was a milestone for focusing rigorous debate on linkages between natural, economic, and environmental factors. The model, which in some circles was controversial (Cole et al. 1973), countered the basic assumption that growth is always good.

RELATED MODELS: Planetary boundaries, Mesarovic/Pestel model, Bariloche model, MOIRA model, SARU model, FUGI model, UN world model

The original projections of the Limits to Growth model extended to the year 2100 (time scale 1900-2100), modified from Hall and Day (2009).

There are no limits to growth and human progress when men and women are free to follow their dreams. – Ronald Reagan

You may be able to fool the voters but not the atmosphere. –Donella Meadows

http://youtu.be/bqz3R1NpXzM

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JULY 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Conway’s game of life (Gardner 1970)

PURPOSE: The model is a successful representation of a hypothetical machine that can build copies of itself (a problem posed by the mathematician John von Neumann in the 1940’s). Four rules applied iteratively to each cell on a grid can produce recurrent structures.

IMPACT: The ‘Game of life’ is famous as it shows how complex patterns can emerge from simple rules. It is one example of ‘cellular automata’ (CA: grid cells follow rules that depend on the states of their neighbors). CA are applied to a range of real life phenomena, such as the rise and fall of societies and patterns on seashells, and serve as an example of emergence and self-organisation. The fact that simple rules can result in complex patterns relates to ‘more is different’ by indicating that interactions between one kind of unit (micro-level/individuals) may result in unforeseen patterns at another level (macro/group) without any obvious causal explanation.

RELATED MODELS: Schelling’s model of spatial segregation (Schelling 1969), MayaSim (Heckbert 2013), Flocking, herds and schools - movement models (Reynolds 1987)

*Anderson (1972)

More is different*The whole is more than the sum of its parts. –Aristotle

Illustration: Calendar creators

AUGUST 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Lorenz Attractor

PURPOSE: In 1963, Edward Lorenz developed a simple mathematical model for atmospheric convection. The output of his model turned out to be extremely sensitive to initial conditions. A tiny change in the fourth decimal place led to a huge change in predictions about the future state of the atmosphere in the model. The Lorenz attractor is a plot of the system’s long-term dynamics.

IMPACT: The Lorenz attractor was a major trigger for the development of chaos theory and the collapse in the Newtonian belief of a predictable clockwork universe. Even if the rules of a system are completely known, the system’s future can be effectively unpredictable, because accurate prediction would require input information of infinite accuracy.

RELATED MODELS: The butterfly effect, Chaos theory

The worldcan be unpredictablePrediction is very difficult, especially about the future. –Attributed to various, including Niels Bohr and Mark Twain

Illustration: E Wikander/Azote. Funded by Beijer and SRC.

SEPTEMBER 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Panarchy (inspired by the adaptive cycle). The adaptive cycle is a model of adaptive change. Panarchy captures the adaptive and evolutionary nature of nested adaptive cycles.

PURPOSE: Panarchy (Gunderson & Holling 2001) helps us understand interactions across scales of space and time in complex adaptive systems. The model is used to describe transitions in system behaviour and captures how the system is sustained as well as how the system evolves. The adaptive cycle is composed of four distinct phases: the r-phase (exploitation) slowly accumulates capital and connectedness to the K-phase (conservation), which eventually leads to the Ω phase (creative destruction) and quickly reorganizes in the α-phase (engine of variety). It is also possible to think of interconnected adaptive cycles across space and time (as seen in the figure).

IMPACT: Panarchy challenges traditional hierarchy theory in ecology and has been used as a heuristic aid in social-ecological systems analysis. The cyclical behavior exemplified in panarchy provides an alternative to linear conceptions of system behavior.

RELATED MODELS: Adaptive management (Holling 1978; Walters 1986), The adaptive cycle (Gunderson & Holling 2001)

The world is adaptingIt is not the strongest or the most intelligent who will survive but those who can best manage change. – Charles Darwin

Illustration: E Wikander/Azote. Funded by Beijer and SRC.

OCTOBER 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Prisoner’s dilemma

PURPOSE: The Prisoner’s Dilemma (PD) is a game that is designed to show that individuals may not cooperate even if it is in their best interests to do so. Both participating individuals choose the strategy that helps them to avoid their least preferred outcome. This strategy cannot, however, lead to an optimal outcome for both individuals simultaneously.

IMPACT: PD was used to explain how cooperation evolves in human society. Competition and cooperation arise from the combination of strategies chosen by individuals. Repeating the PD game can lead to outcomes in which individuals achieve cooperation. Furthermore, it helps to identify mechanisms (agreements/institutions or trust) that are crucial for having individuals choose strategies that lead to a group optimum. These mechanisms were explored in the tragedy of the commons situation, expressed as prisoner’s dilemma games (Ostrom 1990).

RELATED MODELS: Tragedy of the commons (Hardin 1968); Iterated prisoner’s dilemma (Axelrod 1984); Spatial prisoner’s dilemma (Novak & May 1992)

People cooperate, sometimesThe most powerful force ever known on this planet is human cooperation – a force for construction and destruction. –Jonathan Haidt

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NOVEMBER 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Pathways (Leach et al. 2010)

PURPOSE: Pathways map out future trajectories. They are conceptual models of the directions in which interconnected social, technological and environmental systems could co-evolve over time. The pathways approach emphasises the complex, non-linear interactions that occur in these systems, including the dependence of future pathways on past history.

IMPACT: The pathways approach has encouraged a focus on how different actors in a system can value the same pathways dramatically differently, and can even imagine fundamentally new possible pathways. The pathways approach asks us to recognise sustainability as a political term.

RELATED MODELS: Historical institutionalism, Waddington’s epigenetic landscapes, Development trajectories, Scenario thinking (MA, IPCC), Regime shifts, Critical transitions, Ball and cup diagram

The world has many possible futures If you ride to the left, you will lose your horse; if you ride to the right, you will lose your head. –Russian folk tales

When you come to a fork in the road, take it. –Yogi Berra

Inspired by Stirling (2012) Illustration: Calendar creators

DECEMBER 2015MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

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MODEL: Homo economicus

PURPOSE: The Homo economicus model aims to describe economic decisions. The characteristics of Homo economicus are:

1. complete knowledge: knowing all there is to know about a task’s environment; 2. being a maximiser: a drive to obtain the highest possible utility for oneself; 3. being self-interested: caring only for personal consumption, work and leisure.

IMPACT: The Homo economicus model had and still has a huge impact by being both useful and wrong. Useful because the simplicity of the model allowed people to think, reason, design policies and anticipate economic behaviour. The influence of neoclassical economics shows how good an initial approximation this model is of economic behaviour. The wrongness relates to the inability of this model to describe decision-making outside of market settings. The (ab)use of this model/reasoning outside its original scope evoked and continues to evoke big discussions in science, because it can lead to serious misleading consequences (Gintis 2000).

RELATED MODELS: (Bounded) Rational actor model (Simon 1955), Model Social Agent (Carley & Newell 1994), Homo reciprocans, Homo psychologicus.

All models are wrongbut some are useful*Data without models are just numbers. –Unknown

Remember, always, that everything you know, and everything everyone knows, is only a model. Get your model out there where it can be viewed. Invite others to challenge your assumptions and add their own. –Donella Meadows

It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. –Adam Smith

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*Box & Draper (1987)

If you are wondering what a model is…

A MODEL IS A SIMPLIFIED REPRESENTATION OF A REAL-

WORLD PHENOMENON.

REFERENCESAnderson, P.W., 1972. More is different. Science, 177(4047), pp.393–396.

Arditi, R. & Ginzburg, L.R., 1989. Coupling in Predator-Prey Dynamics: Ratio-Dependence. J.Theor.Biol., 139, pp.311–326.

Axelrod, R., 1984. The Evolution of Cooperation. New York: Basic Books.

Boulding, K.E., 1966. The Economics of the Coming Spaceship Earth. In H. Jarrett, ed. Environmental Quality in a Growing Economy. Baltimore, MD: Resources for the Future/Johns Hopkins University Press.

Box, G.E.P. & Draper, N.R., 1987. Empirical Model-Building and Response Surfaces. Hoboken: Wiley.

Carley, K. & Newell, A., 1994. The nature of the social agent. The Journal of Mathematical Sociology, 19(4), pp.221–262.

Cole, H.S.D. et al., 1973. Models of Doom: A Critique of the Limits to Growth. New York: Universe Publishing.

Daly, H. & Cobb, J.B.J., 1989. For the Common Good: Redirecting the Economy Toward Community, the Environment and a Sustainable Future. Boston: Beacon Press.

Folke, C., 1990. Evaluation of ecosystem life-support in relation to salmon and wetland exploitation. Stockholm University.

Gardner, M., 1970. Mathematical games: The fantastic combinations of John Conway’s new solitaire game “Life.” Scientific American, 223(4), pp.120–124.

Gintis, H., 2000. Beyond Homo economicus: evidence from experimental economics. Ecological Economics, 35(3), pp.311–322.

Goodwin, R.M., 1967. A growth cycle. In C. H. Feinstein, ed. Socialism, Capitalism and Economic Growth. Cambridge University Press.

Gunderson, L.H. & Holling, C.S., 2001. Panarchy: Understanding Transformations in Human and Natural Systems. Wahsington, D.C.: Island Press.

Hall, C.A.S. & Day, J.W., 2009. Revisiting the Limits to Growth After Peak Oil. American Scientist, 97(3), p.230.

Hardin, G., 1968. The Tragedy of the Commons. Science, 162(3859), pp.1243–1248.

Heckbert, S., 2013. MayaSim: An Agent-Based Model of the Ancient Maya Social-Ecological System. Journal of Artificial Societies and Social Simulation, 16(4), p.11.

Holling, C.S., 1978. Adaptive environmental assessment and management. Chichester: John Wiley & Sons.

Leach, M., Scoones, I. & Stirling, A., 2010. Dynamic sustainabilities: technology, environment, social justice. London: Earthscan.

Lorenz, E.N., 1963. Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), pp.130–141.

Lotka, A.J., 1925. Elements of physical biology. Williams and Wilkins Company.

Meadows, D.H. et al., 1972. The Limits to Growth. New York: Universe Books.

Nowak, M.A. & May, R.M., 1992. Evolutionary games and spatial chaos. Nature, 359, pp.826–829.

Odum, E.P., 1975. Ecology: A Bridge Between Science and Society. Sunderland: Sinauer Associates Inc.

Odum, E.P., 1989. Ecology and Our Endangered Life-Support Systems. Sunderland: Sinauer Associates Inc.

Ostrom, E., 1990. Governing the commons: The evolution of institutions for collective action. Cambridge University Press.

Perrings, C., Folke, C. & Mäler, K.-G., 1992. The Ecology and Economics of Biodiversity Loss: The Research Agenda. Ambio, 21(3), pp.201–211.

Reynolds, C.W., 1987. Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Computer Graphics, 21(4), pp.25–34.

Scheffer, M. et al., 2001. Catastrophic shifts in ecosystems. Nature, 413(6856), pp.591–596.

Scheffer, M. & Carpenter, S.R., 2003. Catastrophic regime shifts in ecosystems: linking theory to observation. Trends in Ecology & Evolution, 18(12), pp.648–656.

Schelling, T.C., 1969. Models of Segregation. The American Economic Review, 59(2), pp.488–493.

Simon, H.A., 1955. A Behavioral Model of Rational Choice Author. The Quarterly Journal of Economics, 69(1), pp.99–118.

Smith, A., 1776. An Inquiry into the Nature and Causes of the Wealth of Nations. London: W. Strahan and T. Cadell.

Stirling, A., 2012. Pathways to Sustainable Energy: issues of power, diversity and transformation. Available at: http://www.slideshare.net/Stepscentre/andy-stirling.

Volterra, V., 1926. Fluctuations in the Abundance of a Species considered Mathematically. Nature, 118, pp.558–560.

Walters, C.J., 1986. Adaptive management of natural resources. New York, NY: Mc Graw Hill.

Watts, D.J. & Strogatz, S.H., 1998. Collective dynamics of “small-world” networks. Nature, 393, pp.440–442.

THANK YOU!Early team members: Johan Enqvist, Daniel Ospina-Medina and Emma Sundström. Thanks for your initial momentum, any project needs early believers. Movie actors: Timothy Karpouzoglou and Olivia Murzabekov, for the realistic performance of the hilarious misunderstandings modellers can encounter. Catwalkers: Jonathan Donges, Miriam Huitric, Jean-Baptiste Jouffray, Johan Enqvist, Ingo Fetzer, Vanessa Masterson, Andrew Merrie and Lan Wang thanks for expressing every month in ways that only you can. And thank you, Carl Folke for your SES insights (January), and Miriam, you are simply the best catwalk commentator!

Lastly, a special thanks to our colleagues at Beijer and SRC for all their support, feedback and enthusiasm.

Curious about the making of? www.modelcalendar.blogspot.se

CALENDAR CREATORS

INSTITUTIONAL SUPPORTThe realisation of this calendar would not have been possible without the financial support of the Stockholm Resilience Centre (SRC) and the Beijer Institute of Ecological Economics (Beijer). We are grateful for the support to design the majority of the illustrations (Beijer & SRC) as well as the layout (SRC) of the calendar, which are designed by Elsa Wikander and Jerker Lokrantz at Azote.

Caroline Schill

Kirill Orach

Patrick Keys

Maja Schlüter

Nanda Wijerman

sJamila Haid

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Stuart Kininmonth

Romina Martin

Emilie Lindkvist

Juan-Carlos Rocha

Ste

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Diego Galafas

si

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Lindahl Anne-Sophie Crépin