Madingley and questions of abstraction and scale

Madingley is a global computational model. To a broad approximation, the Madingley model represents all (most) forms of life. It achieves this by using what’s called a functional-type representation. Species are aggregated in to broad categories that describe a select number of their properties, rather than everything about them. For some, this conceptual leap is too much. Why take a step towards representing all life, but miss the explicit inclusion of species? The answer lies in making the best of human knowledge, and balancing computational expense.

Another essential feature of Madingley is its individual- or agent-based representation. I’ll come back to why that’s interesting in a moment. For now, let me point out that model individuals carry all the information about their current state, and potentially even a record of their entire life history. These pieces of information take up space in computer memory, and require time to process. When summed over thousands or even millions of interacting agents, individual-based models can become very expensive. Computational power has only recently become accessible enough that it’s feasible to explicitly represent millions of agents in a model. For this reason, it’s necessary to exclude as much irrelevant information as possible. In this way, individual-based modelling and functional-type representations go hand-in-hand. So what is the benefit of this approach? Why diverge from well-established methods?

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Ecosystem modelling has its roots in mathematical models where differential equations describe changes to the level of a population like a physical property or chemical abundance. Models of this type are often heavily informed by data, painstakingly collected from the real world, with equations parameterised to fit them. Their history, and explicit use of data can make them seem well grounded. The approach can work very well for a small number of species, but it can struggle for many species interacting in a temporally varying environment. Like in nature. Because of this, mathematical models will generally fail when applied to a completely, or even a vaguely novel context. Why?

The simple fact is, while it is possible to represent a natural system using mathematics, nature will not represent the mathematics. Rigid equations won’t respond in the same way that life does to a novel situation. Rigidity in nature is a question of scale and statistical likelihood. For example, there are certain chemical ‘laws’ on which life relies. Yet, if we were able to look closely at each molecular interaction, we would see some that defy those laws. From a much higher perspective we see things operating under the overwhelming weight of statistical likelihood. Similarly, plasticity or adaptability in nature is apparent when some smaller-scale alternative is selected. Representation of those alternatives, or others, therefore becomes important for model plasticity.

Mathematicians often talk of ‘discovering’ mathematics. As though it’s been there all along, to be mined from the face of knowledge. Arguably that’s true, but it’s irrelevant while it’s also true that we lack the mathematics required to accurately describe the complexity of nature. Until we do, it’s useful to see any and all model approaches as abstract. Regardless of how much data is used. If anything, it can be argued that mathematical models require so much data precisely because they are so abstract. Many of the functions within a computational model are based on well accepted theories, each with decades of research, data collection, and experimentation to support them. It happens that linking them together with computer code is a convenient way to test them in unison.

Life is the function of a massive set of interleaved and overlapping physical and chemical processes taking place simultaneously across an incredible range of scales. It’s true that Madingley doesn’t go so far as to capture this complexity, but it takes a bold step in that direction. Lowering the level of description to that of the individual or group of individuals permits an explicit representation of processes operating on different scales. Local-scale interactions producing net, global-scale results. It’s a test-bed for the inclusion of well understood mechanisms, and the exploration of speculative hypotheses. In this way, it may evolve in to a model that can adapt in a similar way to the real-world subject. The Madingley Model is not an end. It is a beginning. It embodies an approach and philosophy to modelling life that sheds the bias of human perception and views life as it really is: as a global phenomenon.

Written by Phil Underwood @phlndrwd. Phil Underwood is a Senior Nereus Fellow at the United Nations Environment Programme World Conservation Monitoring Centre.

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