Ecosystems are often made up of interactions between large numbers of species. They are considered complex systems because the behaviour of the system as a whole is not always obvious from the properties of the individual parts. A complex system can be represented by a network: a set of interconnected objects. In the case of ecological networks and food webs, the objects are species and the connections are interactions between species. Many complex systems are dynamic and exhibit intricate time series. Time series analysis has been developed to understand a wide range of natural phenomena.
This thesis deals with the structure, dynamics, and robustness of ecological networks, the spatial dynamics of fluctuations in a social system, and the analysis of cardiac time series. Biodiversity on Earth is decreasing largely due to human-induced causes. My work looks at the effect of anthropogenic change on ecological networks. In Chapter Two, I investigate predator adaptation on food-web robustness following species extinctions. I identify a new theoretical category of species that may buffer ecosystems against environmental change. In Chapter Three, I study changes in parasitoid-host (consumer-resource) interaction frequencies between complex and simple environments.
I show that the feeding preferences of parasitoid species actively change in response to habitat modification. Ecological networks are embedded in spatially-heterogeneous landscapes. In Chapter Four, I assess the role of geography on population fluctuations in an analogous social system. I demonstrate that fluctuations in the number of venture capital firms registered in cities in the United States of America are consistent with spatial and temporal contagion.
Understanding how physiological signals vary through time is of interest to medical practitioners. In Chapter Five, I present a technique for quickly quantifying disorder in high frequency event series. Applying the algorithm to patient cardiac time series provides a rapid way to detect the onset of heart arrhythmia. Increasingly, answers to scientific questions lie at the intersection of traditional disciplines. This thesis applies techniques developed in physics and mathematics to problems in ecology and medicine.
2. Structural dynamics and robustness of food webs
2.2. Materials and Methods
3. Active reallocation of food-web interactions under environmental change
3.2. Materials and Methods
4. Spatial contagion of fluctuations in social systems
4.2. Model and methods
4.5.1. Empirical data
4.5.2. Results for 7 additional regions
5. Rapidly detecting disorder in rhythmic biological signals
5.2. Data Analysis
5.2.1. Symbolizing cardiac data
5.2.2. Spectral entropy
5.2.3. Parameter selection
5.2.4. Cardiac disorder map
5.3.1. Arrhythmia detection algorithm
5.3.2. Algorithm results
5.4.1. Disagreements with annotations
5.4.2. Other rhythms
5.4.3. Comparison to other methods
5.4.4. Systematic error
5.5. Further Work
5.7.1. Disagreements with annotations
5.7.2. Other rhythms
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