Complexity, individuation and function in ecology Part II, sec 3 Emergence in ecosystems and ecosystem levels Prof. John Collier (Departamento de Filosofia, Universidade de Kwazulu-Natal, África do Sul. Pesquisador Visitante do Laboratório de Ensino, Filosofia e História das Ciências (LEFHBio), Programa Ciência sem Fronteiras)

Outline Why we should expect emergent properties in ecosystems. Nesting of ecosystems – Do larger ecosystems emerge from smaller ones? – How are boundaries established? Levels of ecosystem properties – Macro and micro, intensive and extensive – Properties, their components and property fusion

Emergence in ecosystems Ecosystems are complexly organized (type IV) systems with flows and constraints. They also have an overhead (if healthy) which is uncommitted information. This permits self-organization incorporaiting some of the information in the overhead through including it in the forces and flows that contribute to system ascendency.

Emergence in networks My previous (Part I) account of emergence works most obviously for purely physical systems in which we can determine from the dynamics that they are radically non-Hamiltonian. Similar conditions in which work is done by the system on its boundary conditions was hypothesized to underlie other forms of self-organization. The problem is finding the correct dynamics for this to happen. Stable networks can be analyzed by traditional methods although they may be emergent and have emergent components. Emergence, necessarily, occurs in networks only when the number of nodes changes. Ulanowicz has developed a general theory of emergence in networks based on his approach to growth and development. However it gives only the conditions in which emergence is possible in a network, not a test for its existence.

Ulanowicz’ approach Ulanowicz uses a modification of MacArthur’s approach to the diversity of flow through a system’s pathways using his idea of total system throughput (for what the kind of throughput is relevant). Q i is T i /T, the probability of the rate of unit flow through the ith component of the system. K is an arbitrary constant. C is then the diversity of throughputs.

Growth and Development C as defined does not take into consideration network growth and development. Scale can be provided by setting K to T, the total system throughput. We also need to include the probability of a given rate of throughput between nodes, f ij : A is just the network ascendency. C > A > 0.

Recall that

Conditions for self-organization A = C – (S+E+R), in other words, the uncommitted capacity, though that can be increased through efficiency increase (-S and/or -E) or a reduction in redundancy (R). A is power if the units are energy. This gives the analogy to the physical case a stronger basis. (Think also about the economic case in which the flow is money.) Emergence can occur via organization within the overhead, which would produce new nodes (routes via which power or some other system product K) flows. This can be non-local (probably will be), but the treatment in terms of information theory avoids that issue. It might be interesting for other reasons, though. Emergence is an increase in system ascendency, typically through either greater T or an increase in some of the f ij.

Interior versus holistic emergence New phenomena can emerge at various scales. This can create sub-ecosystems, for example the invasion of termites that form a new mound with its own microclimate. But new phenomena can also emerge in the whole system, for example the self-sustaining rainfall of the Amazon rain forest. In both cases, however, the new phenomena can be treated as network nodes due to the mathematical magic of information theory.

Termite mounds

Convectional rainfall (Amazon)

Nesting of ecosystems New ecosystems can emerge within existing ones at a smaller spatial scale, but a larger scale than their previous component nodes. An example might be a termite mound (see above). New ecosystems can invade and establish themselves within larger ecosystems. This might be a reducible process, but if it is emergent it is of the previous type. This can occur at any number of levels. However, the boundary conditions of the new system must be compatible with its role as a node in the larger ecosystem. This gives us some way to identify ecosystem levels: some sub ecosystems act as nodes in a larger ecosystem network. We could include all their nodes in the network, but if it is possible not to without changing overall values, then they are somewhat independent. We would expect, then, that they have well-formed boundaries.

Boundary example, community criterion Generally when there are clear ecosystem boundaries only one criterion might be dominant, but this does not necessarily mean that there is only one applicable metamodel. One example is the separation of communities by in river gorges separated by difficult to traverse mountains. This keeps the communities and largely the populations separate physically. Note that cyclic, developmental (succession), physical constraints and evolutionary issues will still be involved in defining the ecosystem. However, the clear community boundary makes this less of an issue.

Intensive and extensive properties Like any other dynamical system, an ecosystem has various intensive (local) and extensive (global) properties. Unlike in classical thermodynamics, these are not measures of static quantities, but of flows and (possibly changing) constraints. Extensive: T, A, C, S, E, R Intensive: the various ij terms. Both can be measured, but measurement of both is required to get accurate diversity measures to put into Ulanowicz’ equations.

Properties and property components; fusion I will talk about this more in the final lecture, but properties also have components, not just objects. In a process oriented approach we just have nodes as objects, but they are defined by their interactions. So property structure becomes important, especially if we want to identify functional properties. When properties act together dynamically the original parts are constrained such the there is a new property that is called the fusion of the properties. Fused properties are real, their dynamical components are abstractions (consider the combination of gravitational and electromagnetic forces, for example).