Naturally occurring populations of bacteria and archaea are vital to life on the earth and are of enormous practical significance in medicine, engineering and agriculture. However, the rules governing the formation of such communities are still poorly understood, and there is a need for a usable mathematical description of this process. Typically, microbial community structure is thought to be shaped mainly by deterministic factors such as competition and niche differentiation. Here we show, for a wide range of prokaryotic communities, that the relative abundance and frequency with which different taxa are observed in samples can be explained by a neutral community model (NCM). The NCM, which is a stochastic, birth-death immigration process, does not explicitly represent the deterministic factors and therefore cannot be a complete or literal description of community assembly. However, its success suggests that chance and immigration are important forces in shaping the patterns seen in prokaryotic communities.

Vaccines rarely provide full protection from disease. Nevertheless, partially effective (imperfect) vaccines may be used to protect both individuals and whole populations. We studied the potential impact of different types of imperfect vaccines on the evolution of pathogen virulence (induced host mortality) and the consequences for public health. Here we show that vaccines designed to reduce pathogen growth rate and/or toxicity diminish selection against virulent pathogens. The subsequent evolution leads to higher levels of intrinsic virulence and hence to more severe disease in unvaccinated individuals. This evolution can erode any population-wide benefits such that overall mortality rates are unaffected, or even increase, with the level of vaccination coverage. In contrast, infection-blocking vaccines induce no such effects, and can even select for lower virulence. These findings have policy implications for the development and use of vaccines that are not expected to provide full immunity, such as candidate vaccines for malaria.

We use a general additive quantitative genetic model to study the evolution of costly female mate choice by the "handicap" principle. Two necessary conditions must be satisfied for costly preference to evolve. The conditions are (i) biased mutation pressure on viability and (ii) a direct relationship between the degree of expression of the male mating character and viability. These two conditions explain the success and failure of previous models of the "handicap" principle. Our model also applies to other sources of fitness variation like migration and host-parasite coevolution, which cause effects equivalent to biased mutation.

The analysis of the tempo and mode of evolution has a strong tradition in paleontology. Recent advances in molecular phylogenetic reconstruction make it possible to complement this work by using data from extant species.Cladogenesis is the division of one evolutionary lineage into two. How often do lineages undergo cladogenesis to give daughter lineages that will survive for long periods of evolutionary time? And what characteristics of species determine rates of successful cladogenesis? Such questions are tackled traditionally by using the fossil record (1-8), the quality of which limits the accuracy of the answers obtained (9). However, paleontological data could be usefully complemented with information from extant species if the dates when pairs of species last shared a common ancestor were known (10). Fig. 1 line A is a semilogarithmic plot of the number of lineages against time since the first bifurcation. As there is uncertainty about the calibration of the molecular clock pertaining to these data (15, 16), we measure time in arbitrary units since the time of the first bifurcation. The slope of this curve reflects the per-lineage rate of effective cladogenesis and, so, would appear to be a straight line, with stochastic wiggling, if the rate were constant through time. Instead, the rate appears to decrease quite smoothly over time. As the legend of Fig. 1 describes, the data are incompatible with a constant-rate model.Following the failure of the one-parameter constant-rate model, we fitted a two-parameter density-dependent model, in which the per-lineage rate of cladogenesis is a function of the form p/Na, where N is the number of lineages and a is a constant. The compatibility of this model with the data is good (Fig. 1), not only because there is an extra parameter to fit but also because of its qualitative form (the possession of a positive second derivative). This contrasts with the relatively poor performance of the two-parameter logistic model ofdensity dependence, p(l -N/K), which is commonly used in population biology.It has been suggested that the degree of molecular divergence between taxa is not related to time since divergence in a linear fashion, as we have assumed here, but that the genetic divergence between taxa was more rapid early in the history of an adaptive radiation (17). If this controversial (18,19) suggestion is true, the deceleration in cladogenesis was even more rapid than we have estimated (i.e., a larger a). The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

1. We take a previously studied model for two species -one of which is competitively inferior -coexisting in a patchy environment, and examine the effects of removing patches (that is, of decreasing the amount of available habitat). Habitat destruction or patch removal reduces the number (and proportion) ofpatches occupied by the superior competitor, but can result in an increase in the total number of patches occupied by the inferior competitor (even though there are fewer patches in total).3. It has long been appreciated that disturbance and destruction of habitat can create edge effects and other ecological changes favouring 'weedy' species. The present study suggests that patch removal can by itself favour such species, even in the absence of other, concomitant changes.4. An implication relevant to conservation biology is that habitat loss can bring about changes in community composition in remaining patches, even if such patches themselves undergo no intrinsic changes whatsoever.

We use a general additive quantitative genetic model to study the evolution of costly female mate choice by the "handicap" principle. Two necessary conditions must be satisfied for costly preference to evolve. The conditions are (i) biased mutation pressure on viability and (ii) a direct relationship between the degree of expression of the male mating character and viability. These two conditions explain the success and failure of previous models of the "handicap" principle. Our model also applies to other sources of fitness variation like migration and host-parasite coevolution, which cause effects equivalent to biased mutation.

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Phylogenies reconstructed from contemporary taxa do not contain information about lineages that have gone extinct. We derive probability models for such phylogenies, allowing real data to be compared with specified null models of evolution, and lineage birth and death rates to be estimated.