Summary 0[ This paper explores the concept of the critical community size for persistence of infection in wildlife populations[ We use as a case study the 0877 epidemic of phocine distemper virus in the North Sea population of harbour seals\ Phoca vitulina[ 1[ We summarize the available data on this epidemic and use it to parameterize a stochastic compartmental model for an infection spreading through a spatial array of patches coupled by nearest!neighbour mixing\ with replacement of susceptibles occurring as a discrete annual event[ 2[ A combination of analytical and simulation techniques is used to show that the high levels of transmission between di}erent seal subpopulations\ combined with the small annual birth cohort\ act to make persistence of infection impossible in this harbour seal population at realistic population levels[ The well known mechanisms by which metapopulation structures may act to promote persistence can be seen to have an e}ect only at weaker levels of spatial coupling\ and higher levels of host recruitment\ than those empirically observed[ We ask which of the variables of this critical meta! Reviewing that mass mortality\ Hall "0884# com! population distribution are central in determining per! mented that {if PDV behaves like other morbilliviruses sistence] for example\ is it more important to know it should have been eliminated from the North Sea\ patch population sizes\ the number of patches\ the because the surviving population of susceptible ani! level of interpatch mixing or the total population size< mals is too small to allow the disease to persist or to Metapopulation theory has been used to estimate the permit the establishment of a new epidemic|[ This minimum amount of suitable habitat Ð MASH "Han! concept of a threshold susceptible population has been ski\ Moilanen + Gyllenberg 0885# Ð necessary for a a central one in ecological epidemiology since the population to persist[ On the other hand\ conservation work of Bartlett on measles 39 years ago "Bartlett biologists have attempted to estimate the minimum size necessary for a population to have a particular 0845# and much theoretical work has been concerned to establish that persistence properties can be strongly probability of persisting for a certain length of time "the minimum viable population\ MVP "Soule 0876dependent on mixing structure[ In this paper we use the PDV example to study how the mixing that arises Bjo Ârge\ Steen + Stenseth 0883##[ The fact that the theoretical relationship between patch size and local from a patchy host population a}ects persistence[ A common theoretical approach to this problem is to extinction is well understood in an epidemiological setting has enabled us to investigate the way in which interpret the host patches as habitat patches of a pathogen metapopulation "Hanski + Gilpin 0880#[ local and total population size interact in determining

An important issue in the dynamics of directly transmitted microparasites is the relationship between infection probability and host density. We use models and extensive spatio‐temporal data for the incidence of measles to examine evidence for spatial heterogeneity in transmission probability, in terms of urban–rural hierarchies in infection rate. Pre‐vaccination measles data for England and Wales show strong evidence for urban–rural heterogeneities in infection rate – the proportion of urban cases rises significantly before major epidemics. The model shows that this effect is consistent with a higher infection rate in large cities, though small towns have epidemic characteristics intermediate between town and country. Surprisingly, urban and rural areas of the same population size have a similar propensity for local extinction of infection. A spatial map of urban–rural correlations reveals complex regional patterns of synchronization of towns and cities. The hierarchical heterogeneities in infection persist into the vaccine era; their implications for disease persistence and control are discussed.

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.

An important issue in the history of ecology has been the study of the relative importance of deterministic forces and processes noise in shaping the dynamics of ecological populations. We address this question by exploring the temporal dynamics of two childhood infections, measles and whooping cough, in England and Wales. We demonstrate that epidemics of whooping cough are strongly influenced by stochasticity; fully deterministic approaches cannot achieve even a qualitative fit to the observed data. In contrast, measles dynamics are extremely well explained by a deterministic model. These differences are shown to be caused by their contrasting responses to dynamical noise due to different infectious periods.

We present and evaluate an approach to analyzing population dynamics data using semimechanistic models. These models incorporate reliable information on population structure and underlying dynamic mechanisms but use nonparametric surface-fitting methods to avoid unsupported assumptions about the precise form of rate equations. Using historical data on measles epidemics as a case study, we show how this approach can lead to better forecasts, better characterizations of the dynamics, and a better understanding of the factors causing complex population dynamics relative to either mechanistic models or purely descriptive statistical time-series models. The semimechanistic models are found to have better forecasting accuracy than either of the model types used in previous analyses when tested on data not used to fit the models. The dynamics are characterized as being both nonlinear and noisy, and the global dynamics are clustered very tightly near the border of stability (dominant Lyapunov exponent lambda approximately 0). However, locally in state space the dynamics oscillate between strong short-term stability and strong short-term chaos (i.e., between negative and positive local Lyapunov exponents). There is statistically significant evidence for short-term chaos in all data sets examined. Thus the nonlinearity in these systems is characterized by the variance over state space in local measures of chaos versus stability rather than a single summary measure of the overall dynamics as either chaotic or nonchaotic.