UC San Diego

Nature is hard to predict. Rules and relationships you discover about a system today may be totally different tomorrow. These relationships do not change randomly over time; rather, they change as the state of the system evolves. In a deterministic view of the world, similar states lead to similar outcomes. In this thesis, I leverage this principle to better understand and ultimately predict, complex systems. In chapter 1, I work closely with the National Parks Service to understand variables that influence flow target values through the Everglades National Park. The Tamiami Trail Flow Formula, a linear (not state-dependent) was previously developed to predict such values. In this chapter I show that with only minor adjustments to their linear approach, a non-linear (state-dependent) predictor can be made with significant prediction improvement. Chapter 2 focuses on the role of scale in understand ecosystem relationships. Using both models and real world examples I show that not one scale can capture all of the dynamics of a real world system: for example, some relationships are better resolved at an annual timescale while others are best resolved monthly. In chapter 3 I develop a new method for classifying systems based on the delay in their dynamic relationships. This method is applied to study the behavioral states of the nematode Caenorhabditis elegans. By analyzing the causal relationships between eigenvectors that represent the worm's posture (“eigenworms”), I am able to classify the behavioral state of the worm (foraging or reacting to a harmful stimulus). Additionally, I demonstrate that this technique can identify genetic mutations in these worms solely through analysis of their bodily movements. This work demonstrates the that powerful models and non-linear relationships can be extrapolated directly from data without the need for assumptions or fixed equations.