Population fluctuations are generally attributed to the deterministic consequences of strong non-linear interactions among organisms, or the effects of random stochastic environmental variation superimposed upon the deterministic skeleton describing population change. Analysis of the population dynamics of the mussel Mytilus californianus taken in 16 plots over 18-years found no evidence that t...

The response of a neuronal population to afferent drive can be expected to be sensitive to both the distribution and dynamics of membrane voltages within the population. Voltage fluctuations can be driven by synaptic noise, neuromodulators, or cellular inhomogeneities: processes ranging from millisecond autocorrelation times to effectively static or "frozen" noise. Here we extend previous studi...

This thesis uses spatially distributed models to test the Metapopulation Hypothesis, which asserts that migration between local populations promotes the persistence of a regional “metapopulation” despite short-term local fluctuations, or even temporary local extinctions, on the local scale. A review of relevant models finds that:1. These models found nothing to disagree with the hypothesis. Sub...

Poisson-Dirichlet distribution arises in many different areas. The parameter θ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting procedure of θ approaching infinity is practically motivated and has led to new interesting mathematical structures. Results of law of large numbers, fluctuation theorems and large deviations have been ...