Month: May 2021

Dynamical systems modelling is a mathematical approach to studying the behaviour of systems that change over time. These systems can be physical, biological, economic, or social in nature, and they are typically characterized by a set of variables that evolve according to certain rules or equations.

CAS (Complex Adaptive Systems) models are a specific type of dynamical systems model that are used to study systems that are complex, adaptive, and composed of many interconnected parts. These systems are often found in natural and social systems, and they are characterized by a high degree of uncertainty, nonlinearity, and emergence.

To build a dynamical systems model, one typically starts by identifying the variables that are relevant to the system being studied and the relationships between them. These relationships are usually represented by a set of equations or rules that describe how the variables change over time. The model is then simulated or analysed to understand the system’s behaviour under different conditions and to make predictions about its future evolution.

CAS models are often used to study systems that exhibit emergent behaviour, where the behaviour of the system as a whole is more than the sum of its parts. These models can help us understand how complex systems self-organize, adapt, and evolve over time, and they have applications in fields such as biology, economics, social science, and computer science.

Whatever the approach, a model is intended to represent the real system, but there are limits to the application of models. The reliability of any model often falls short when attempting to operate within and apply the parameter boundaries of the model to any real life context.

 The previous article outlined some basic characteristics of complex adaptive systems (CAS). The CAS approach to modelling real world phenomena requires a different approach to the more conventional predictive modelling paradigm. Complex adaptive systems such as ecosystems, biological systems, or social systems require looking at interacting elements and observing the patterns that arise, creating boundary conditions from these patterns, running experiments or simulations, and responding to the outcomes in an adaptive way.

To further delineate the complex systems domain in practical terms we can use the Cynefin framework developed by David Snowden et al. to contrast the Simple, Complicated, Complex and Chaotic domains. For the purpose of this article the Chaotic domain will be ignored.

Enabling constraints of CAS models

In contrast to complex domain is the “known” or “simple” domain represented by ordered systems such as a surgical operating theatre or clinical trials framework. These ordered systems are rigidly constrained and can be planned and designed in advance based upon prior knowledge. In this context best practice can be applied because an optimal way of doing things is pre-determined.

The intermediary between the simple and complex domains is the “knowable” or ” complicated” domain. An example of such is the biostatistical analysis of basic clinical data. Within a complicated system there is a right answer that we can discover and design for. In this domain we can apply good practice based on expert advice (not best practice) as a right and wrong way of doing things can be determined with analysis.

Complex domain represents a system that is in flux and not predictable in the linear sense. A complex adaptive system can be operating in a state that is anywhere from equilibrium to the edge of chaos. In order to understand the system state one should perform experiments that probe relationships between entities. Due to the lack of linearity, multiple simultaneous experimental probes should occur in parallel, not in sequence, with the goal of better understanding processes. Emergent practice is determined in line with observed, evolving patterns. Ideally, decentralised Interpretation of data should be distributed to system users themselves rather than determined by a single expert in a centralised fashion.

As opposed to operating from a pre-supposed framework, the CAS structure should be allowed to emerge from the data under investigation. This avoids the confirmation bias that occurs when data are fitted to a predefined framework regardless of whether this framework best represents the data being modelled. Following on from this, model boundaries should also be allowed to emerge from the data itself.

Determining unarticulated needs from clusters of agent anecdotes or data points is a method of determining where improvement needs to occur in service provision systems. Yet this method forms an analogy that is mimicked in biological systems as well if an ABM was to be applied in a biomolecular context.

In understanding CAS, dispositionality of system states rather than linear causality should be the focus . Rather than presuming an inherent certainty as to “if I do A, B will result”, instead dispositional states arise as a result of A, which may result in B, but the evolution of which cannot be truly predicted.

“The longer you hold things in a state of transition the more options you’ve got” linear iterations based on a defined requirement with a degree of ambiguity which should be explored rather than eliminated. The opposite of standard statistical approach.

CAS modelling should include real-time feedback loops over multiple agents to avoid cognitive bias. In CAS modelling, every behaviour or interaction will produce unintended consequences, for this reason, David Snowden suggests, Small, fast experiments should be run in parallel, so that any bad, unintended consequences can be mitigated and the good ones amplified.

Modes of analysis and modelling:

System dynamics models (SDM)

• A SDM simulates the movements of entities within the system and can be used to investigate macro behaviour of the system.
• Changes to system state variables over time are modelled using differential equations.

• SDMs are multi-dimentional, non-linear and include feedback mechanisms.

• Visual representations of the model can be produced using stock and flow diagrams to summarise interdependencies between key system variables.

• Dynamic hypotheses of the system model can be represented in a causal loop diagram
• SDM is appropriate for modelling aggregate flows, trends, sub-system behaviour.

Agent based models (ABM)

• ABMs can be used to investigate micro behaviour of the system from more of a bottom-up perspective through Intricate flows of individual based activity.
• State changes of individual agents are simulated by ABMs rather than the broader entites captured by SDM
• Multiple types of agent are operating within the same complex adaptive system modelled
• Data within the ABM can be aggregated to infer more macro or top-down system behaviour.

Agents within the ABM can make decisions, engage in behaviour defined by simple rules and attributes, learn from experience and from feedback from interactions with other agents or the modelled environment. This is as true in models of human systems as it is with molecular scale systems. In both examples agents can par take in communication on a one to one, one to many and one to location basis. Previously popular models such as discrete event simulation (DES) was implemented to model passive agents at a finite time rather than active “decision makers” over dynamic periods that are a feature of ABMs.

Hybrid Models

• Both ABM and SDM are complimentary techniques for simulating micro and macro level behaviour of complex adaptive systems and therefore engaging in exploratory style analysis of such systems.
• Hybrid models emulate individual agent variability as well as variability in the the behaviour of aggregate entities they compose.
• Simulate macro and micro level system behaviour in many areas of investigation such as health service provision, biomedical science.

Hybrid models have the ability to combine two or more types of simulation within the same model. These models can combine SDMs and ABMs, or other techniques, to address both top-down and bottom-up micro and macro dynamics in a single model that more closely captures whole system behaviour. This has the potential to elevate many of the necessary trade-offs of using one of the simulation types alone.

As software capability develops we are seeing an increased application of hybrid modelling techquiques. Previously wide-spread techniques such as DES and Markov models, which are one-dimentional, uni-directional, linear, are now proving inadequate in the task of modelling the complex adaptive and dynamic world we inhabit.

Model Validation Techniques

SDMs and ABMs are not fitted to observed data but instead use both qualitative and quantitative real world data to inform and develop the model and it’s parameters as a simulation of real world phenomena. For this reason model validation of SDMs and ABMs should be even more rigorous than for more traditional models such as maximum likelihood or least squares methods. Sensitivity analysis and validation tests such as behavioural validity tests can be used to compare model output against real-world data from organisations or experiments, relevant to the scale of the model being validated.

Structure of the model such as

• Checking how the model behaves when subject to extreme parameter values.
• Things like dimensional consistency, boundary adequacy, mass balance
• Sensitivity analysis – how sensitive is the model to changes in key parameters.

Network Analysis

Data accrual from diverse data sources challenges and limitations

While complex systems theory has origins in the mathematics chaos theory, there are many examples contemporaneously where complex systems theory has been divorced form the mathematics and statistical modelling and applied in diverse fields such as business and healthcare or social services provision. Mathematical modelling adds validity to complex systems analysis. The problem with completing solely qualitative analysis without the empiricism of mathematical modelling, simulation and checking against a variety of real world data sets, the results

While a majority of biomedical and public health research still maintains a linear reductive approach to arrive at empiric insight, reality is in most cases neither of these things. A complex adaptive systems approach, like reality, is non-linear and high dimensional. There are many benefits from taking a linear cause-effect reductivist approach in that the complex problem and it’s solution becomes simplified into terms that can be understood and predicted.  Where this falls short is that predictions don’t often hold up in real world examples in which the outcomes tend to seem unpredictable.

Genomics, proteomics, transcriptomics and other “omics” techniques have generated an unprecedented amount of molecular genetics data. This data can be combined with larger scale data, from cell processes to environmental influences in disease states, to produce highly sophisticated multi-level models of contributing factors in human health and disease.

An area that is currently seeing an evolution into a more personalised nuanced approach, albeit still linear, is clinical trials. By introducing a biomarker component to clinical trials, for example to evaluate drug efficacy, the number of dimensions to the problem is slightly increased in order to arrive at more targeted and accurate solutions. More specifically, the number of patient sub-categories in the clinical trials increases to accommodate various biomarker groups which may respond more of less well to a different pharmacological approach to the same disease. Increasing the dimensions of the problem beyond this would, for now not be feasible or even helpful. On the other hand, understanding the interplay between biomolecular processes and environmental interactions in order to gain insight into disease processes themselves and thereby, which biochemical pathways for oncology drugs to target, is something that clearly benefits from a non-linear approach.

Another example of a system that benefits from a non-linear approach is public health service provision and the desire to garner insights into changes that increase prevention, early intervention and treatment effectiveness as well as reduce service cost for the government and patient. Both of the above examples require attention to both macro and micro processes.

Whether modelling clinical health services networks or biological processes, complex adaptive systems consist of several common characteristics.

Components of complex adaptive systems

Massive interdependencies and elaborate connectivity

The complex adaptive systems approach shifts emphasis away from studying individual parts (such as seen in conventional medical science which produces notably fragmented results) to characterising the organisation of these parts in terms of their inherently dynamic interactions. CAS are open rather than closed systems because it is exogenous elements impacting on the system that cause the disruption required for growth.

Complex adaptive systems can be understood by relations and networks. System processes occur in networks that link component entities or agents. This approach emphasises that structures are dynamic and it is the process of becoming rather than the being itself that is of empirical interest.

Necessarily transdisciplinary or multi-disciplinary

A complex adaptive systems approach requires a transdisciplinary approach. The collaboration of numerous disparate experts is required in the combining of myriad biological, physical and societal based sciences into a holistic model. This model should aim to represent pertinent simultaneous top-down and bottom up processes that reveal contexts and relationships within the observed system dynamics.

Self-organising, emergent behaviour

Complex adaptive systems are selt-organising in the sense that observed patterns are open ended, potentially unfinished and cannot be predicted by the conventional definition. Rules of cause and effect are context dependent and can’t be applied in a rigid sense.

A self organising dynamic structure, which can be identified as a pattern, emerges as a result of individual spontaneous interactions between individual agents or elements. This pattern then impacts the interactions of individuals in a continual top down, bottom up symbiosis.

While linear models represent a reductionist, closed conceptualisation of the phenomena under analysis, a complex systems approach embraces high dimensionality true to the myriad real world phenomena composing a system. This requires that the system be treated as open and of uncertain ontology and thus lacking predictive capacity with regards to the outcomes of system dynamics.

As an emergent phenomena, the complex adaptive system can be understood by interacting with it rather than through analysis or static modelling. This approach is concerned with “state change” or to evaluate “how things are becoming”, rather than “how thing are”. How did today’s state emerge from yesterday’s trajectories and process dynamics?

Fractal engagement. Fractal engagement entails that the system as a whole orientates through multiple actions. The same data can produce frameworks at the level of responsibility of every individual agent. Using public health intervention as an example, Individual agents make decisions, based on the data, as to what changes they can make tomorrow within their own sphere of competence, rather than overarching changes being dictated and determined in a top down way, or by others.

Feedback loops

Feedback loops link individual parts into an overaching dynamic structure. Feedback loops are self-reinforcing and can be positive or negative.

Negative feedback loops are stabalising in that they have a dampening effect on oscillations that causes the system or component to move closer to equilibrium. Positive feedback loops are morphogenic and increase the frequency and amplitude of oscillations driving the system away from homeostasis and leading to changes in the underlying structure or the system.

Positive feedback loops, while facilitating growth and adaptation, tend towards chaos and decay and are thus crucially counterbalanced by simultaneously operating negative feedback loops. Evolution is supposed to occur as a series of phase transitions, back and forth, from ordered to disordered states.

Both top-down and bottom-up “causality”

While CAS models describe elements in terms of possibilities and probabilities, rather than cause and effect in the linear sense, there is a clear interplay between top down and bottom up causality and influence on the dynamic flows and trajectories of any system. This is very much a mirror of real world systems. One example of this is the human body where both conscious thought (top down) and biomolecular processes such as hormonal and neurochemical fluctuations (bottom up) effect mood, which in turn has a lot of flow on effects down stream that cause changes that shirt the system back and forth from health to disease. One such manifestation of this is stress induced illness of various kinds. As a social example, we can of course find many examples of top down and bottom up causation in a public heath or epidemiological setting.

This has been a non-exhaustive description of just some key components of complex adaptive systems. The main purpose is to differentiate the CAS paradigm from the more mainstream biomedical research paradigm and approach. For a deeper dive into the concepts mentioned see the references below.

References:

https://core-cms.prod.aop.cambridge.org/core/services/aop-cambridge core/content/view/F6F59CA8879515E3178770111717455A/9781108498692c7_100-118.pdf/role_of_the_complex_adaptive_systems_approach.pdf

Carmichael T., Hadžikadić M. (2019) The Fundamentals of Complex Adaptive Systems. In: Carmichael T., Collins A., Hadžikadić M. (eds) Complex Adaptive Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-20309-2_1

https://www.health.org.uk/sites/default/files/ComplexAdaptiveSystems.pdf

Milanesi, L., Romano, P., Castellani, G., Remondini, D., & Liò, P. (2009). Trends in modeling Biomedical Complex Systems. BMC bioinformatics, 10 Suppl 12(Suppl 12), I1. https://doi.org/10.1186/1471-2105-10-S12-I1

Sturmberg J. P. (2021). Health and Disease Are Dynamic Complex-Adaptive States Implications for Practice and Research. Frontiers in psychiatry, 12, 595124. https://doi.org/10.3389/fpsyt.2021.595124