No abstract

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.

The life histories of many species depend first on dispersal to local sites and then on establishment. After dispersal, density-independent and density-dependent mortalities modify propagule supply, determining the number of individuals that establish. Because multiple factors influence recruitment, the dichotomy of propagule versus establishment limitation is best viewed as a continuum along which the strength of propagule or establishment limitation changes with propagule input. To evaluate the relative importance of seed and establishment limitation for plants, we (1) describe the shape of the recruitment function and (2) use limitation and elasticity analyses to quantify the sensitivity of recruitment to perturbations in seed limitation and density-independent and density-dependent mortality. Using 36 seed augmentation studies for 18 species, we tested four recruitment functions against one another. Although the linear model (accounting for seed limitation and density-independent mortality) fitted the largest number of studies, the nonlinear Beverton-Holt model (accounting for density-dependent mortality) performed better at high densities of seed augmentation. For the 18 species, seed limitation constrained population size more than other sources of limitation at ambient conditions. Seedling density reached saturation with increasing seed density in many studies, but at such high densities that seedling density was primarily limited by seed availability rather than microsite availability or density dependence.

Previous work on fluctuating asymmetry (FA) has highlighted its controversial relationship with environmental stress and genetic architecture. While size-based measures of FA have been assumed to have half-normal distributions within populations, studies of model developmental mechanisms have suggested other plausible distributions for FA. We investigated the distribution of FA in large empirical data sets of wing shape and wing size asymmetry from three species of insects (cotton aphid Aphis gossipyii Glover, honeybee Apis mellifera, and long-legged fly Chrysosoma crinitus). Regardless of measurement method, FA was best described by a double Pareto-lognormal (DPLN) distribution or one of its limiting functional forms. To investigate convergence of mean sample FA to the population mean at various sample sizes, we sampled repeatedly under a DPLN distribution using parameter values that best fitted our data. Sample variances are much larger, and hence, convergence is slowed considerably with univariate or multivariate size-based measures of FA in contrast to a multivariate shape-based measure of FA. We suggest that much of the past work on FA may be undersampled, and we recommend using multivariate shape-based approaches or collecting larger data sets in future studies. We also discuss the implications of the DPLN distribution for understanding the developmental mechanisms underlying FA.