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.

Two methods are given for the joint estimation of parameters in models for competing risks in survival analysis. In both cases Cox's proportional hazards regression model is fitted using a data duplication method. In principle either method can be used for any number of different failure types, assuming independent risks. Advantages of the augmented data approach are that it limits over-parametrisation and it runs immediately on existing software. The methods are used to reanalyse data from two well-known published studies, providing new insights.

It has long been assumed that differences in the relative abundance of taxa in microbial communities reflect differences in environmental conditions. Here we show that in the economically and environmentally important microbial communities in a wastewater treatment plant, the population dynamics are consistent with neutral community assembly, where chance and random immigration play an important and predictable role in shaping the communities. Using dynamic observations, we demonstrate a straightforward calibration of a purely neutral model and a parsimonious method to incorporate environmental influence on the reproduction (or birth) rate of individual taxa. The calibrated model parameters are biologically plausible, with the population turnover and diversity in the heterotrophic community being higher than for the ammonia oxidizing bacteria (AOB) and immigration into AOB community being relatively higher. When environmental factors were incorporated more of the variance in the observations could be explained but immigration and random reproduction and deaths remained the dominant driver in determining the relative abundance of the common taxa. Consequently we suggest that neutral community models should be the foundation of any description of an open biological system. microbial community assembly

Bacterial communities migrate continuously from the drinking water treatment plant through the drinking water distribution system and into our built environment. Understanding bacterial dynamics in the distribution system is critical to ensuring that safe drinking water is being supplied to customers. We present a 15-month survey of bacterial community dynamics in the drinking water system of Ann Arbor, MI. By sampling the water leaving the treatment plant and at nine points in the distribution system, we show that the bacterial community spatial dynamics of distance decay and dispersivity conform to the layout of the drinking water distribution system. However, the patterns in spatial dynamics were weaker than those for the temporal trends, which exhibited seasonal cycling correlating with temperature and source water use patterns and also demonstrated reproducibility on an annual time scale. The temporal trends were driven by two seasonal bacterial clusters consisting of multiple taxa with different networks of association within the larger drinking water bacterial community. Finally, we show that the Ann Arbor data set robustly conforms to previously described interspecific occupancy abundance models that link the relative abundance of a taxon to the frequency of its detection. Relying on these insights, we propose a predictive framework for microbial management in drinking water systems. Further, we recommend that long-term microbial observatories that collect high-resolution, spatially distributed, multiyear time series of community composition and environmental variables be established to enable the development and testing of the predictive framework.

We show that inferring the taxa-abundance distribution of a microbial community from small environmental samples alone is difficult. The difficulty stems from the disparity in scale between the number of genetic sequences that can be characterized and the number of individuals in communities that microbial ecologists aspire to describe. One solution is to calibrate and validate a mathematical model of microbial community assembly using the small samples and use the model to extrapolate to the taxa-abundance distribution for the population that is deemed to constitute a community. We demonstrate this approach by using a simple neutral community assembly model in which random immigrations, births, and deaths determine the relative abundance of taxa in a community. In doing so, we further develop a neutral theory to produce a taxa-abundance distribution for large communities that are typical of microbial communities. In addition, we highlight that the sampling uncertainties conspire to make the immigration rate calibrated on the basis of small samples very much higher than the true immigration rate. This scale dependence of model parameters is not unique to neutral theories; it is a generic problem in ecology that is particularly acute in microbial ecology. We argue that to overcome this, so that microbial ecologists can characterize large microbial communities from small samples, mathematical models that encapsulate sampling effects are required.

Two recent, independent advances in ecology have generated interest and controversy: the development of neutral community models (NCMs) and the extension of biogeographical relationships into the microbial world. Here these two advances are linked by predicting an observed microbial taxa-volume relationship using an NCM and provide the strongest evidence so far for neutral community assembly in any group of organisms, macro or micro. Previously, NCMs have only ever been fitted using species-abundance distributions of macroorganisms at a single site or at one scale and parameter values have been calibrated on a case-by-case basis. Because NCMs predict a malleable two-parameter taxa-abundance distribution, this is a weak test of neutral community assembly and, hence, of the predictive power of NCMs. Here the two parameters of an NCM are calibrated using the taxa-abundance distribution observed in a small waterborne bacterial community housed in a bark-lined tree-hole in a beech tree. Using these parameters, unchanged, the taxa-abundance distributions and taxa-volume relationship observed in 26 other beech tree communities whose sizes span three orders of magnitude could be predicted. In doing so, a simple quantitative ecological mechanism to explain observations in microbial ecology is simultaneously offered and the predictive power of NCMs is demonstrated.

The recent observation of a power-law relationship, S proportional A(z), between number of taxa, S, and area, A, for microbial eukaryotes and bacteria suggests that this is one of the few generic relationships in ecology, applicable to plants, animals and microbes. However, the rate of increase in the number of species with area varies from approximately the fourth (z = 0.26) to as little as the 50th root (z = 0.0019) in microbes. This is an enormous range for which no quantitative explanation has been proffered. We show by sampling from synthetic populations that the disparity between sample and community sizes in microbial community surveys means z can be considerably underestimated and accrual of rare taxa with increasing area will not be detectable. Significant microbial taxa-area relationships will only be observed when changes in community structure within samples correlate with area. Thus, the very low z values observed recently cannot be used as the sole evidence in support of any particular community theory of community assembly. More generally, this suggests that our search for patterns and laws in the microbial world will be profoundly influenced and, potentially distorted by the sample sizes that are typical of microbial community surveys.

Many aspects of cognition decline from middle to late adulthood, but the dimensionality and generality of this decline have rarely been examined. We analyzed 20-year longitudinal data of 6203 middle-aged to very old adults from Greater Manchester and Newcastle-upon-Tyne, UK. Participants were assessed up to eight times on 20 tasks of fluid intelligence, perceptual speed, memory, and vocabulary. We controlled for potential effects due to retest, city, sex, and socio-economic class. Average performance in all tasks declined with age, and individual differences in decline were present for all but one memory and two vocabulary tasks. Half of the variance in level of performance was shared across tasks. This proportion increased to 66% for individual differences in change. General level of performance and change therein correlated positively. We conclude that cognitive decline is heterogeneous across individuals and rather general at the within-individual level.