## Key Concepts

**MODELING COMPLEX ADAPTIVE SYSTEMS**

It is important to become more conversant with the notion that forest ecosystems, as well as the human communities that depend on them, are complex adaptive systems. Studying and viewing forests as complex systems and managing for ecological resilience and complexity is an explicit objective of the SORTIE-ND research program lead by Dr. David Coates in British Columbia. Many of the concepts about complexity, complex adaptive systems, and modeling approaches presented below are taken from the book "A Critique of Silviculture: Managing for Complexity" by Klaus Puettmann, David Coates and Christian Messier, 2009, Island Press (see book review). You can also refer to the Complexity Science and Global Change Workshop organized by the Bulkley Valley Research Centre for a more in depth discussion of issues around complexity science.

Since ecosystems are fundamentally a network of interacting elements, new models and modeling approaches need to be able to represent the important elements of the system both spatially and temporally. To simulate the intricate functions of a forest, a model will need to represent, in a spatially explicit manner, the most important objects and functions that affect its short- and long-term dynamics at more than one spatial scale. Many hierarchical representations are possible, but in most cases they will encompass some or all of the following levels (individuals< populations< communities< ecosystems< biomes). Complexity theory implies that it is not possible to simulate complex behaviours in stands by using whole stands as modeling agents because no interacting elements are present that can generate emergent properties at the stand scale. In fact, ecosystems structures, functions, and processes emerging from inter-hierarchical interactions. Complex behaviour is always represented using a "bottom-up" approach to modeling. In such an approach, each hierarchical element is modeled as a discrete agent or object state, where each entity has functions that are characterized by relationships described by rules (or equations) and constant values or variables. This is the approach we take in SORTIE-ND.

SORTIE-ND is an individual-based model where the forest is represented by a large collection of interacting trees that are followed both in time (in steps of at least one year) and space. Those trees are currently divided among seedlings, saplings and adult trees. Population-level dynamics are simulated by summing the collective activities of numerous individuals. Each tree is a discrete object that is described with various attributes (size, growth rate, age, crown morphology, etc.). Each tree's (individual) behaviour is modeled with rules that describe the interactions with other individuals (e.g., effect of species and distance of neighbours on growth of individual trees) or its environment (e.g., growth of seedlings in relation to available light levels). Many of the interactions have non-linear relationships and/or have random events associated with them. The non-linearity of many interactions, the stochastic behaviour of some objects and processes, and the large number of objects, rules and stochastic events makes SORTIE-ND a good example of a modeling approach aimed at being able to represent complex behaviour in forests. The basic elements that are required to simulate complex behaviours are : (1) a representation of many hierarchical levels, (2) a representation of both spatial and temporal scales, (3) some stochasticity, (4) some non-linearity, and (5) some representation of discrete entities or elements.

**The science of Complexity:** **Some basic terminology **• A complex system refers to any system that has many parts (components), and whose parts interact.

• The interaction among components of a complex system gives rise to emergent patterns, behaviours or processes that wouldn't occur if the parts did not interact.

• Complexity refers to the amount of emergent or self-organized pattern or behaviour within a system. A highly ordered system (think of a plantation with straight rows of planted pines) has relatively low complexity, but so does a completely chaotic system with no order at all. Thus, complexity can also be defined as the amount of hidden, difficult-to-understand order that lies between complete order and randomness.

• A complex adaptive system is a dynamic system that is able to fix or adjust itself, essentially without outside help, in response to changing circumstances'?in other words, it self-organizes.

**Complex systems have several defining features:**

(1) nonlinear relationships and indeterminate , chaotic and quasi-chaotic behavior make predictions uncertain;

(2) boundaries are difficult to determine and we are never certain what defines the system;

(3) the system is open to outside influences and so is never totally at equilibrium;

(4) relationships contain feedback loops that may cross scales or hierarchies of organization, making the system self-regulated or self-organized;

(5) the system can exhibit behaviors that are emergent - that is , behaviors that cannot be predicted from the individual parts of the system or from understanding the individual components of lower levels of organization; and

(6) the system "remembers" its previous states, as prior states partially influence present ones.

**Any biological system can be classified as complex and adaptive if it displays the following properties:**

(1) it is composed of many parts (trees, insects, soil, and so on) and processes (nutirent cycling, seed dispersion, tree mortality, decay, and so on);

(2) these parts and processes interact with each other and with the external environment in many different ways and over multiple spatial and temporal scales;

(3) these interactions give rise to heterogeneous structures and nonlinear relationships;

(4) these structures and relationships are neither completely random nor entirely deterministic, but instead represent a combination of randomness and order;

(5) they contain both positive and negative feedback mechanisms, stabilizing or destabilizing the system, depending on conditions;

(6) the system is open to the outside world, exchanging energy, materials, and/or information;

(7) it is sensitive to initial conditions following a disturbance and subsequent perturbations; and

(8) it contains many adaptive components and subsystems nested within each other, giving rise to emergent properties.

**MAXIMUM LIKELIHOOD METHODS AND MODEL SELECTION TECHNIQUES**

In the SORTIE-ND research program model selection techniques are often used to test and select scientific models (or behaviours) for use in the model.

The study of forest dynamics and, more specifically, the study of individual tree neighborhood dynamics is particularly well suited to the use of maximum likelihood methods and model selection techniques (Hilborn and Mangel 1997; Burnham and Anderson 2002; Johnson and Omland 2004; Canham and Uriarte 2006; Hobbs and Hilborn 2006). At the heart of the methods is the explicit interplay between data and models, with "model" used in the sense of a mathematical statement of the quantitative relationships that are assumes to have generated the observed data (Canham and Uriarte 2006). Classical hypothesis testing is replaced by the more general process of model selection and comparison, using likelihood and parsimony to compare the strength of evidence for competing hypotheses, repersenting the different possible mathematical models (Johnson and Omland 2004; Canham and Uriarte 2006).

Model selection is a technique that emphasizes evaluation of the weight of evidence for multiple hyotheses by seeking accurate and precise estimates of parameters of interest, for example, factors affecting understory tree growth. Model selection evaluates competing hypotheses against observed data and aids identification of the mechanisms most likely to explain understory tree growth as a function of local neighborhood conditions. Traditionally, models used by silviculture researchers were limited to a relatively small set of linear forms that did not explicitly represent biological states and processes (Hobbs and Hilborn 2006). Model selection has three primary advantages over null hypothesis testing (Johnson and Omland 2004): (1) it is not restricted to a single model, measured against some arbitrary probability threshold; rather, multiple models are assessed by comparing relative support in the observed data; (2) models can be ranked, thus providing a measure of support for each hypothesis; and (3) if competing hypotheses have similar levels of support, model averaging can be used to make robust parameter estimates and predictions. Dramatic increases in computer power have made it far easier to use these techniques than it was in the past.