s Abstract Biological invasions of marine habitats have been common, and many patterns emerge from the existing literature. In North America, we identify 298 nonindigenous species (NIS) of invertebrates and algae that are established in marine and estuarine waters, generating many "apparent patterns" of invasion: (a) The rate of reported invasions has increased exponentially over the past 200 years; (b) Most NIS are crustaceans and molluscs, while NIS in taxonomic groups dominated by small organisms are rare; (c) Most invasions have resulted from shipping; (d ) More NIS are present along the Pacific coast than the Atlantic and Gulf coasts; (e) Native and source regions of NIS differ among coasts, corresponding to trade patterns. The validity of these apparent patterns remains to be tested, because strong bias exists in the data. Overall, the emergent patterns reflect interactive effects of propagule supply, invasion resistance, and sampling bias. Understanding the relative contribution of each component remains a major challenge for invasion ecology and requires standardized, quantitative measures in space and time that we now lack.

Infectious diseases present ecological and public health challenges that can be addressed with mathematical models. Certain pathogens, however, including the emerging West Nile virus (WN) in North America, exhibit a complex seasonal ecology that is not readily analysed with standard epidemiological methods. We develop a single-season susceptible-infectious-removed (SIR) model of WN cross-infection between birds and mosquitoes, incorporating specific features unique to WN ecology. We obtain the disease reproduction number, R0, and show that mosquito control decreases, but bird control increases, the chance of an outbreak. We provide a simple new analytical and graphical method for determining, from standard public health indicators, necessary mosquito control levels. We extend this method to a seasonally variable mosquito population and outline a multi-year model framework. The model's numerical simulations predict disease levels that are consistent with independent data.

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This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host-vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the hostvector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, R 0 . We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters R 0 and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, R 0 estimates for six common North American bird species indicate that all would be effective outbreak hosts.