Causal Dynamics for Complex Systems

A course in structural causal dynamics

0.1 Preface

Status: In Progress

v0.5

Causal Dynamics for Complex Systems joins causal reasoning with dynamical systems modelling. The object is a complex system (organism, ecosystem, clinical cohort, coupled socio-technical process) under intervention: how the process unfolds through time, what feedback sustains it, which equilibria (“attractor states”) it can settle into as its environment shifts, and what remains learnable when observation is partial and noisy.

Put another way: can we predict how a process evolves under different interventions from imperfect data? What would it take for such a system to settle into a new equilibrium if conditions or treatments change? Those questions arise wherever feedback, latent structure, and limited measurement meet (ecology, epidemiology, medicine, climate, and engineered systems among them).

The book organises that problem so that complex dynamical systems are described carefully enough, and their mechanisms understood deeply enough, that the observable effects of interventions become predictable in principle. The framing is general; the worked examples often draw on biology because that is where I work, not because the logic fails elsewhere.

The material is organised in three strata: Structural (causal structure and invariance), Dynamical (latent states unfolding through time), and Observable (noisy measurement). Pearl’s three levels of Reason (association, intervention, and counterfactual) cut across those strata: co-occurrence, setting a variable’s value, and asking what would have been.

Computation in these pages uses a Julia stack (CausalDynamics.jl, CausalTargeted.jl, and DAGMakie.jl) to identify structure, estimate effects under intervention, and draw graphs. This book is not the documentation for that software; the packages implement the challenges the book describes. The concepts remain usable in another language or toolkit. For why Julia is the working language here (one-language workflow, maths-like syntax, multiple dispatch, composability), see Why Julia in the Introduction.

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0.2 Chapter Progress

Introduction

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0.2.1 Part I – Structural

The Causal Hierarchy and Three Strata

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The Primary Unit: The Dyad

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Graph Theory and Causal Patterns

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Structural Causal Models as Executable Mechanisms

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Identification: When Can We Learn from Data?

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Causal Discovery

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Do-Calculus: Rules for Interventions

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Counterfactuals: Alternative Concrescences at Structural Level

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Transportability: Generalising Structural Claims

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From Structure to Time: FEP and Attractors

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Cyclic Causal Structures

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0.2.2 Part II – Dynamical

Deterministic Dynamics: ODEs as Causal Processes

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Stochastic Dynamics: SDEs and Random Processes

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State-Space Models: Inferring Structure from Observations

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Intervening in Deterministic Systems

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Intervening in Stochastic Systems

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Advanced Dynamics: Regimes, Networks, and Resilience

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Multi-Scale Causal Dynamics

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Counterfactual Dynamics: Alternative Trajectories

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Sensitivity Analysis and Robustness in Dynamics

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From Dynamical to Observable: Measurement and Actualisation

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0.2.3 Part III – Observable

Observational Methods: Learning from Data

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TMLE and Doubly Robust Estimation

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Model Validation with Observable Data

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Interventional Reasoning: Forecasting Under Interventions

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Policy Evaluation and Dynamic Treatment Strategies

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Causal Decision-Making

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Counterfactual Reasoning: Unit-Level Alternatives

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Hypothesis Generation from Counterfactuals

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Experimental Design: Optimal Measurements

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0.2.4 Part IV – Synthesis

CDMs: The Unified Framework

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Biological Case Studies

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0.2.5 Appendices

Concept Reference Tables

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Reporting Standards

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Software Patterns

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