# Contents

## Idea

Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially entire ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem is a complex system exhibiting emergent properties. Systems ecology focuses on interactions and transactions within and between biological and ecological systems, and is especially concerned with the way the functioning of ecosystems can be influenced by human interventions. It uses and extends concepts from thermodynamics and develops other macroscopic descriptions of complex systems.

## Examples

### Howard Odum

The ‘Energy Systems Language’ was developed by Howard T. Odum and his colleagues in the 1950s during studies of the tropical forests funded by the United States Atomic Energy Commission. Odum is the founder of ‘systems ecology’:

Sometimes called ‘Energese’, the Energy Systems Language is a diagrammatic language featuring elements like these:

His most detailed book on diagrams for systems ecology seems to be this:

• Howard T. Odum, Systems Ecology: an Introduction, Wiley-Interscience, New York, 1983.

In this book:

• R. L. Kitching, Systems Ecology: An Introduction to Ecological Modelling, University of Queensland Press, 1983.

the author writes:

Because of its electrical analogy, the Odum system is relatively easy to turn into mathematical equations…. If one is building a model of energy flow then certainly the Odum system should be given serious consideration…

According to the Wikipedia article on Odum, the Energy Systems Language language looks similar to the Systems Modeling Language recently developed by INCOSE, an international Systems Engineering body.

### Climate change impact on forests

Dr. Andreas Fischlin is a Systems Ecology scientist who has contributed to IPCC reports. His work is mainly in modelling ecosystems, in collaboration with field researchers. He focuses on the impact of climate change on ecosystems, especially forest.

There are many types of model. A commonly used type involves ‘patch dynamics’. For example, an old tree dies, leaving a gap, and seedlings compete for light and nutrients. Seedlings vary: some tolerate shadows, others need more light, and so on. The model tracks individual trees and includes environmental variables such as precipitation which shape the competition. Such models are caricatures or cartoons, and do not attempt to match reality, but can nonetheless capture crucial aspects of a real forest. Different models suit different purposes: one would be used for predicting climate change impact, another for deciding how to best fertilise a forest.

These are some of the best models in ecology. They can predict what kind of natural forest you will find at a particular location, given information about the climate and soil. As well as predicting what we find today, they can also match what happened at the end of the last ice age, as determined from pollen data. This gives some confidence that they can predict what kind of forests we will have in the future.

### Food webs

An interesting question in systems ecology is: which factors make a food web stable or unstable? For decades there has been an intense debate on this question, beginning with quite crude models and moving to ever more realistic ones, and also featuring ever more careful experiments. An excellent review article, featuring a large bibliography, is:

Many consider the father of food-web ecology to be Charles Elton, who in the 1920s noted the ‘pyramid of numbers’ and other basic features of food webs. Elton noted that some simple two-species predator-prey models are unstable and argued that complex food webs were more stable. In 1942, R. L. Lindeman focused attention on the flow of energy through food webs. In the early 1970s, R. M. May showed that in some models, food webs became less stable as the number and strength of species interactions increased:

• R. M. May, Stability and Complexity of Model Ecosystems, 2nd edition, Princeton U. Press, Princeton, New Jersey, 1974.

This led to an outburst of work seeking to show that May’s results were based on oversimplifications, e.g. assuming that any given species has an equal probability of interacting with any other. In the later 1970s, J. E. Cohen began investigating the topology of food webs:

• J. E. Cohen, Food Webs and Niche Space, Princeton U. Press, Princeton, New Jersey, 1978.

Here is a more recent article in this line of work:

• Phillip P. A. Staniczenko, Owen T. Lewis, Nick S. Jones and Felix Reed-Tsochas, Structural dynamics and robustness of food webs, Ecology Letters 13 (2010), 891-899.

Abstract: Food web structure plays an important role when determining robustness to cascading secondary extinctions. However, existing food web models do not take into account likely changes in trophic interactions (‘rewiring’) following species loss. We investigated structural dynamics in 12 empirically documented food webs by simulating primary species loss using three realistic removal criteria, and measured robustness in terms of subsequent secondary extinctions. In our model, novel trophic interactions can be established between predators and food items not previously consumed following the loss of competing predator species. By considering the increase in robustness conferred through rewiring, we identify a new category of species–overlap species–which promote robustness as shown by comparing simulations incorporating structural dynamics to those with static topologies. The fraction of overlap species in a food web is highly correlated with this increase in robustness; whereas species richness and connectance are uncorrelated with increased robustness. Our findings underline the importance of compensatory mechanisms that may buffer ecosystems against environmental change, and highlight the likely role of particular species that are expected to facilitate this buffering.

Felix Reed-Tsochas is the head of the Complex Agent-Based Dynamic Networks (or ‘CABDyn’) group at the University of Oxford:

Since the financial crisis of 2008, economists have been trying to use networks similar to food webs to understand ‘systemic risk’, which is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one portion of the system. An example is this paper:

It begins:

In the 1960s, the notion of the ‘balance of nature’ played a significant part as ecologists sought a conceptual foundation for their subject. In particular, Evelyn Hutchinson1, following Elton, suggested that ‘‘oscillations observed in arctic and boreal fauna may be due in part to the communities not being sufficiently complex to dampout oscillations’’. He went on to state, based on a misunderstanding of MacArthur’s paper, that there was now a ‘‘formal proof of the increase in stability of a community as the number of links in its food web increases’’. To the direct contrary, however, a closer examination of model ecosystems showed that a random assembly of N species, each of which had feedback mechanisms that would ensure the population’s stability were it alone, showed a sharp transition from overall stability to instability as the number and strength of interactions among species increased. More explicitly, for $N >> 1$ this transition occurs once $m \alpha^2 > 1$, where $m$ is the average number of links per species, and $\alpha$ their average strength.

In ecology this has, since the 1970s, prompted a search for special food-web structures that may help reconcile complexity with persistence or stability. Along these lines there is, for example, tentative evidence for modularity (particularly in plant–pollinator associations, where linkages tend to be overdispersed or disassociative), and more generally for nested hierarchies in food webs. The fact that some features of the network structure of interactions (such as predator/prey ratios) inferred from the Burgess Shale communities are similar to those in present day ones reinforces hopes that this is a meaningful area of research.

In the wake of the global financial crisis that began in 2007, there is increasing recognition of the need to address risk at the systemic level, as distinct from focusing on individual banks. This quest to understand the network dynamics of what might be called ‘financial ecosystems’ has interesting parallels with ecology in the 1970s. Implicit in much economic thinking in general, and financial mathematics in particular, is the notion of a ‘general equilibrium’. Elements of this belief underpin, for example, the pricing of complex derivatives. But, as shown below, deeper analysis of such systems reveals explicit analogies with the concept that too much complexity implies instability, which was found earlier in model ecosystems.

There are, of course, major differences between ecosystems and financial systems…

### GUMBO

A very ambitious systems ecology model is GUMBO, a “global unified metamodel of the biosphere”. The network diagrams in this paper are intimidatingly complicated, though doubtless very simplified compared to the reality:

Abstract: A global unified metamodel of the biosphere (GUMBO) was developed to simulate the integrated earth system and assess the dynamics and values of ecosystem services. It is a ‘metamodel’ in that it represents a synthesis and a simplification of several existing dynamic global models in both the natural and social sciences at an intermediate level of complexity. The current version of the model contains 234 state variables, 930 variables total, and 1715 parameters. GUMBO is the first global model to include the dynamic feedbacks among human technology, economic production and welfare, and ecosystem goods and services within the dynamic earth system. GUMBO includes modules to simulate carbon, water, and nutrient fluxes through the Atmosphere, Lithosphere, Hydrosphere, and Biosphere of the global system. Social and economic dynamics are simulated within the Anthroposphere. GUMBO links these five spheres across eleven biomes, which together encompass the entire surface of the planet. The dynamics of eleven major ecosystem goods and services for each of the biomes are simulated and evaluated. Historical calibrations from 1900 to 2000 for 14 key variables for which quantitative time-series data was available produced an average $R^2$ of 0.922. A range of future scenarios representing different assumptions about future technological change, investment strategies and other factors have been simulated. The relative value of ecosystem services in terms of their contribution to supporting both conventional economic production and human well-being more broadly defined were estimated under each scenario, and preliminary conclusions drawn. The value of global ecosystem services was estimated to be about 4.5 times the value of Gross World Product (GWP) in the year 2000 using this approach. The model can be downloaded and run on the average PC to allow users to explore for themselves the complex dynamics of the system and the full range of policy assumptions and scenarios.

The authors claim that GUMBO is unique in three ways:

1. “Ecosystem services are a focus of GUMBO and explicitly affect both economic production and social welfare. This allows the model to calculate dynamically changing values for ecosystem services based on their marginal contributions relative to other inputs into the production and welfare functions.”

2. “Both ecological and socioeconomic changes are endogenous to the model, with a pronounced emphasis on interactions and feedbacks between the two. All other global models to date limit either ecological or socioeconomic change to exogenously determined scenarios (c.f. Meadows et al., 1992; Rotmans and de Vries, 1997; IPCC, 2001).”

3. “The model includes natural capital, human capital, social capital and built capital as state variables and factors of production, and distinguishes between material factors and factors of transformation (material cause and efficient cause, in Aristotelian terms). Thus, the model allows limited substitution between factors of production at the margin, but also imposes strong sustainability constraints for the system as a whole.”

## References

Here is a good place to start:

This is a collection of classic papers from 1963 to 1979:

• H. H. Shugart and R. V. O’Neill, Systems Ecology, Dowden, Hutchinson and Ross, Stroudsburg, Pennsylvania, 1979.

Among other things it includes some classic papers on the stability of food webs:

• M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: critical values for stability, Nature 228 (1970), 784.

• M. L. Rosenzweig, Paradox of enrichment: destabilization of exploitation ecosystems in ecological time, Science 171 (1971), 385-387.

• R. M. May, Will a large complex system be stable?, Nature 238 (1972), 413-414.

• D. L. Angelides, Stability and connectance in food webs, Ecology 56 (1975), 238-243.

Odum’s book:

• Howard T. Odum, Systems Ecology: an Introduction, Wiley-Interscience, New York, 1983.

is a classic reference. Our section on Odum is taken from

• John Baez and Jacob Biamonte, Diagrams.

For a broad overview of biological networks, see this collection of papers:

• Francois Képès, ed. Biological Networks, World Scientific, Singapore, 2007.

This contains Louis-Félix Bersier’s A history of the study of ecological networks, mentioned above, but also many other interesting papers.