Question

Define the concept of overdispersion and discuss how it relates to the regulation of parasites and their hosts.  Be sure to include experimental evidence where appropriate (long answer)

Answer 1

Over dispersion means the presence of higher variability in a data set than can be obtained from a given simple statistical model. It refers to a dataset with higher than the expected variance and finds wide applications in biological sciences. Over dispersion exists when the observed variance is higher than the variance of a theoretical model. The mean reason behind over dispersion is that population is always much more heterogeneous than it is predicted to be. In Poisson distribution, over dispersion is often encountered and the variance cannot be adjusted independent of the mean. Hence, a negative binomial distribution can sometimes be used instead in which the mean itself is a random variable.

Many models of parasitic infections lead to an approximately Poisson distribution of parasites among hosts, in contrast to the highly over-dispersed distributions that are usually encountered in practice. For example, a model is analyzed which, while assuming all individuals to be alike, can still lead to a very heterogeneous distribution of parasites among the host population. The model can be viewed as a very simple mean field interacting particle system, with the particles corresponding to the individual hosts, which behaves like an associated deterministic system when the number of hosts is large. The deterministic system describes the evolution over time of the proportions of the population with different parasite loads, and its equilibria are interpreted as typical distributions of parasites among hosts.