Complexity A more recent conceptualization of how to look at nature and our interaction with it Originated in general systems theory, a way of looking at the world in which phenomena interact as sets of systems 1968

Complex adaptive systems

Characteristics of complex adaptive systems The economy, ecosystems, ant colonies, the brain, our immune systems, traffic flow, crowd or swarm behavior Have path dependence Exhibit emergence Are dynamic and adaptive Control is distributed rather than centralized

The Newtonian world…. Mechanistic and deterministic, predictable

The Newtonian World

Laplace’s demon If a demon (or some all-knowing entity) had knowledge of the positions and direction of all particles in the universe at a single instant, Newtonian equations could be invoked to explain all future events and hindcast all of history

However, Newtonian concepts are not capable of explaining ecological change, which is also strongly coupled to human systems

We live in a world in which Newtonian mechanics has limits The shear number of species and their interactions limits prediction of change using Newtonian concepts alone Contingencies, historical events, ongoing evolution limit prediction into the future. Interactions can develop which we often cannot anticipate, and these in turn guide the expression of other interactions and outcomes. We live in a world in which Newtonian mechanics has limits This is only a static representation of the many players and interactions found in the food web. In actual fact, the food web is a ‘living' dynamic system that responds to variation in time and space. The incredibly flexible food-web architecture actually expands and contracts, like an accordion.

Complex adaptive systems dynamics Can be simulated in Cellular automata Agent-based modeling

Cellular automata Originated in 1940’s

Cellular automata Global patterns can emerge from simple local rules Cellular automata can be used to model real-world socio-ecological phenomena Examples: Game of life Schelling’s segration model Wildfire modeling

In the Game of Life, simple rules are assigned to cells, and then the cellular automata is allowed to play out over time. Each individual cell is sensitive to the neighborhood around it and responds to it according to the rules that define it. Often, how the game plays out is sensitive to initial conditions. The original configuration of black and white grid cells will determine how the system evolves. Game of Life because the basis for studying artificial life.

In the cellular automata devised to study segregation by Schelling, each cell can be assigned a tolerance value. For example, a tolerance value of 25% implies that a person will move if one quarter of their neighbors is not of the same race/ethnicity. What is unique about Schelling’s segregation model is that even when someone is tolerant (i.e., a tolerance value of 50%), neighborhoods will still become segregated if people are allowed to move to a new home. Despite a willingness to have half of their neighbors of a different race or ethnic identity, the environment can become segregated.

http://wildfireanalyst.com/ An example of cellular automata modeling to predict and understand the dynamics of wildfire. There are several software packages to model fire, this is just one of them. The fire burns according to pixel rules that define its flammability, wind direction, temperature, and slope of the terrain. The cellular automata can be adjusted to allow fires to spot – for small embers to float out from the main fire and initiate new fires.

Agent-based modeling Agents are programmed to interact with other agents Agents have local instead of global knowledge Agents can exhibit adaptation Agent-based modeling can be used to simulate real-world ecological phenomena

In an agent-based model, individual agents have local rules and a much more mobile capacity than with cellular automata. They can ‘see’ their local environment and respond accordingly. With many agents, their individual behaviors can scale up to create emergent patterns. In this agent-based model, the agents are kids in different neighborhoods. They interact with each other and their neighbors in how they buy and talk about candy sold by three companies. Agent-based models are ways to simulate the dynamics of the world that are not readily done with Newtonian equations.

Many video games, like Minecraft, are designed around an agent-based framework.

NetLogo is a very popular modeling platform for creating agent-based models

How to describe a complex adaptive system They reflect an interaction of determinism and contingency, of order and disorder

How to describe a CAS As a system having path dependency – the events that have unfolded in the past constrain the immediate future Microsoft staff, Albuquerque, Dec 7, 1978 Querty

How to describe a CAS They have global properties emerge from interactions among many individual components, which then may feed back to influence the subsequent development of these interactions.

How to describe a CAS They exhibit self-organization Process where some form of order arises from local interactions and feedbacks between parts of an initially disordered system. The process is spontaneous, and is not controlled by an external agent. Promotes stability of the system so that it and the feedbacks within it persist

How to describe a CAS As an open-ended system exhibiting self organization and adaptation Daisyworld

Gaia theory (Lovelock and Margulis, 1974) The Earth is a complex adaptive system Biotic and abiotic components of the Earth have co-evolved through feedbacks Cumulative global effects can arise through essentially local phenomena. Feedback loops can become established that support life Adaptation is open-ended and path dependent Daisyworld illustrates the complex adaptive systems dynamics of Gaia theory Lovelock and Margulis, 1974

How complexity is used in ecology Convergence (Clementsian) Whatever the starting points or variations in initial conditions, system self-organizes toward same particular end state Divergence (Gleasonian) System becomes more diverse over time. Initial differences and disturbances tend to persist and grow.

How complexity is used in ecology Provides a more nuanced way to understand how nature changes and how it exihibits stability

How complexity is used in ecology Stability in complex adaptive systems is different from how we typically think of it Ecological systems can exhibit more than one stable state (you on the other hand, as shown at right, have one)

The working vocabulary of complex adaptive systems Vocabulary varies depending upon intellectual tradition, but in general these phenomena are recognized Stability domains Critical transitions Tipping points Hysteresis Bistability

Stability domains Fire-reinforcing longleaf pine stability domain Fire-resisting longleaf pine stability domain 30

Stability domains

Examples (drawn in class) Fire-dependent forests Grasslands Semi-arid rangelands Shallow lakes Rocky nearshore marine communities

Critical transitions A system may change, or transition, from one stable state or stability domain to another Systems can transition gradually, or sharply when a threshold is crossed Tipping implies a sudden and sometimes irreversible change

Gradual and developmental transition Threshold transition without hysteresis Threshold transition with pronounced tipping and hysteresis

Hysteresis and bistability Multiple states may persist under equal environmental conditions with hysteresis.