Biomedical subjects

Michelle Girvan

Publications and source records attributed to Michelle Girvan.

4 recordsLinked to original sources

PubMed2006

Policing stabilizes construction of social niches in primates.

All organisms interact with their environment, and in doing so shape it, modifying resource availability. Termed niche construction, this process has been studied primarily at the ecological level with an emphasis on the consequences of construction across generations. We focus on the behavioural process of construction within a single generation, identifying the role a robustness mechanism--conflict management--has in promoting interactions that build social resource networks or social niches. Using 'knockout' experiments on a large, captive group of pigtailed macaques (Macaca nemestrina), we show that a policing function, performed infrequently by a small subset of individuals, significantly contributes to maintaining stable resource networks in the face of chronic perturbations that arise through conflict. When policing is absent, social niches destabilize, with group members building smaller, less diverse, and less integrated grooming, play, proximity and contact-sitting networks. Instability is quantified in terms of reduced mean degree, increased clustering, reduced reach, and increased assortativity. Policing not only controls conflict, we find it significantly influences the structure of networks that constitute essential social resources in gregarious primate societies. The structure of such networks plays a critical role in infant survivorship, emergence and spread of cooperative behaviour, social learning and cultural traditions.

Animals↗

PubMed2006

The size of the sync basin.

We suggest a new line of research that we hope will appeal to the nonlinear dynamics community, especially the readers of this Focus Issue. Consider a network of identical oscillators. Suppose the synchronous state is locally stable but not globally stable; it competes with other attractors for the available phase space. How likely is the system to synchronize, starting from a random initial condition? And how does the probability of synchronization depend on the way the network is connected? On the one hand, such questions are inherently difficult because they require calculation of a global geometric quantity, the size of the "sync basin" (or, more formally, the measure of the basin of attraction for the synchronous state). On the other hand, these questions are wide open, important in many real-world settings, and approachable by numerical experiments on various combinations of dynamical systems and network topologies. To give a case study in this direction, we report results on the sync basin for a ring of n >> 1 identical phase oscillators with sinusoidal coupling. Each oscillator interacts equally with its k nearest neighbors on either side. For k/n greater than a critical value (approximately 0.34, obtained analytically), we show that the sync basin is the whole phase space, except for a set of measure zero. As k/n passes below this critical value, coexisting attractors are born in a well-defined sequence. These take the form of uniformly twisted waves, each characterized by an integer winding number q, the number of complete phase twists in one circuit around the ring. The maximum stable twist is proportional to n/k; the constant of proportionality is also obtained analytically. For large values of n/k, corresponding to large rings or short-range coupling, many different twisted states compete for their share of phase space. Our simulations reveal that their basin sizes obey a tantalizingly simple statistical law: the probability that the final state has q twists follows a Gaussian distribution with respect to q. Furthermore, as n/k increases, the standard deviation of this distribution grows linearly with square root of n/k. We have been unable to explain either of these last two results by anything beyond a hand-waving argument.

Journal Article↗

PubMed2002

Optimal design, robustness, and risk aversion.

Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin of the power laws. We also generalize the model to incorporate risk aversion, which results in truncation of the tails of the power law so that the probability of catastrophically large events is dramatically lowered, giving the system more robustness.

Journal Article↗

PubMed2002

Simple model of epidemics with pathogen mutation.

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals; (2) endemic infection; (3) periodic epidemic outbreaks; and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.

Disease Outbreaks↗