The structure and diversity of all open microbial communities are shaped by individual births, deaths, speciation and immigration events; the precise timings of these events are unknowable and unpredictable. This randomness is manifest as ecological drift in the population dynamics, the importance of which has been a source of debate for decades. There are theoretical reasons to suppose that drift would be imperceptible in large microbial communities, but this is at odds with circumstantial evidence that effects can be seen even in huge, complex communities. To resolve this dichotomy we need to observe dynamics in simple systems where key parameters, like migration, birth and death rates can be directly measured. We monitored the dynamics in the abundance of two genetically modified strains of Escherichia coli, with tuneable growth characteristics, that were mixed and continually fed into 10 identical chemostats. We demonstrated that the effects of demographic (non-environmental) stochasticity are very apparent in the dynamics. However, they do not conform to the most parsimonious and commonly applied mathematical models, where each stochastic event is independent. For these simple models to reproduce the observed dynamics we need to invoke an 'effective community size', which is smaller than the census community size.

In all but the most sterile environments bacteria will reside in fluid being transported through conduits and some of these will attach and grow as biofilms on the conduit walls. The concentration and diversity of bacteria in the fluid at the point of delivery will be a mix of those when it entered the conduit and those that have become entrained into the flow due to seeding from biofilms. Examples include fluids through conduits such as drinking water pipe networks, endotracheal tubes, catheters and ventilation systems. Here we present two probabilistic models to describe changes in the composition of bulk fluid microbial communities as they are transported through a conduit whilst exposed to biofilm communities. The first (discrete) model simulates absolute numbers of individual cells, whereas the other (continuous) model simulates the relative abundance of taxa in the bulk fluid. The discrete model is founded on a birth-death process whereby the community changes one individual at a time and the numbers of cells in the system can vary. The continuous model is a stochastic differential equation derived from the discrete model and can also accommodate changes in the carrying capacity of the bulk fluid. These models provide a novel Lagrangian framework to investigate and predict the dynamics of migrating microbial communities. In this paper we compare the two models, discuss their merits, possible applications and present simulation results in the context of drinking water distribution systems. Our results provide novel insight into the effects of stochastic dynamics on the composition of non-stationary microbial communities that are exposed to biofilms and provides a new avenue for modelling microbial dynamics in systems where fluids are being transported.

ABSTRACT 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. IMPORTANCE Safe and regulation-compliant drinking water may contain up to millions of microorganisms per liter, representing phylogenetically diverse groups of bacteria, archaea, and eukarya that affect public health, water infrastructure, and the aesthetic quality of water. The ability to predict the dynamics of the drinking water microbiome will ensure that microbial contamination risks can be better managed. Through a spatial-temporal survey of drinking water bacterial communities, we present novel insights into their spatial and temporal community dynamics and recommend steps to link these insights in a predictive framework for microbial management of drinking water systems. Such a predictive framework will not only help to eliminate microbial risks but also help to modify existing water quality monitoring efforts and make them more resource efficient. Further, a predictive framework for microbial management will be critical if we are to fully anticipate the risks and benefits of the beneficial manipulation of the drinking water microbiome.

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.

a Faculty of Psychology and Educational Sciences, University of Geneva, Boulevard du Pont d'Arve 40, 1211 Geneva, Switzerland b Distance Learning University, Switzerland c Department of Experimental Psychology, University of Oxford, 9 South Parks Road, Oxford, OX1 3UD, U.K. d University of Western Australia, Perth, Australia e Department of Statistics and St. Hughs' College, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, U.K. f Center for Lifespan Development, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany

OBJECTIVES:To test whether different terminal pathologies are associated with different rates of age-related decline in fluid and crystallized mental abilities and whether pathology-associated declines are accelerated by age.METHODS:During a 20-year longitudinal study, 6203 participants were quadrennially assessed on the Heim's (Heim, A 1970) The AH4 series of intelligence tests Slough, U.K.: NEP) AH4-1 and AH4-2 tests of fluid intelligence and on the Raven's (Raven, J. C. 1965) The Mill Hill Vocabulary Scale London: H.K. Lewis) Mill Hill A and B tests of recognition and production vocabulary. Dates and proximate causes of death were logged for 2499 participants. Multilevel modelling compared rates of decline after effects of sex, demographics, and practice were taken into consideration.RESULTS:Rates of cognitive decline markedly differed across pathologies, being most rapid for dementias and infections, slower for malignancies, and most prolonged for cardiovascular conditions. Pathologies were associated with faster declines in older individuals.DISCUSSION:After sex, age, and demographics have also been considered, different terminal pathologies are associated with markedly different rates of decline. Age accelerates pathology-related decline. This raises the further question as to whether any, or how much of, age-related cognitive decline is brought about by other causes than an increasing burden of pathologies.

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.

A sample of 4,314 volunteers who, when first recruited, were aged from 41 to 93 years were quadrennially tested from 2 to 4 occasions during the next 4 to 20 years on the Cattell Culture Fair intelligence test, 2 tests of information-processing speed, the Wechsler Adult Intelligence Scale (WAIS) vocabulary test, and 3 memory tests. After significant effects of practice, sex, demographics, socio-economic advantage, and recruitment cohort had been identified and considered, performance on all tests declined with age. These age-related declines accelerated for the Cattell and WAIS, 2 tests of information speed, and 2 of the memory tests. For all tests individuals' trajectories of age-related change diverged with increasing age but, unexpectedly, were not affected by demographic factors. Practice gains from an initial experience of the cognitive tests remained undiminished as the interval before the second experience increased from 4 to 8 + years.

In this paper, we extended a parallel system survival model based on the bivariate exponential to incorporate a time varying covariate. We calculated the bias, standard error and rmse of the parameter estimates of this model at different censoring levels using simulated data. We then compared the difference in the total error when a fixed covariate model was used instead of the true time varying covariate model. Following that, we studied three methods of constructing confidence intervals for such models and conclusions were drawn based on the results of the coverage probability study. Finally, the results obtained by fitting the diabetic retinopathy study data to the model were analysed.

Absolute differences in global brain volume predict differences in cognitive ability among healthy older adults. However, absolute differences confound lifelong differences in brain size with amounts of age-related shrinkage. Measurements of cerebrospinal fluid (CSF) volume were made to estimate age-related shrinkage in 93 healthy volunteers aged 63 to 86 years. Their current levels of brain shrinkage predicted their amounts of decline over the previous 8 to 20 years on repeated assessments during a longitudinal study on the Cattell "Culture Fair" Intelligence Test, on two tests of information processing speed, and marginally on the Wechsler Adult Intelligence Scale (D. Wechsler, 1981), but not on three memory tests. Loss of brain volume is an effective marker both for current cognitive status and for amounts and rates of previous age-related cognitive losses.

During a 20-year longitudinal study of cognitive change in old age 2,342 of 5,842 participants died and 3,204 dropped out. To study cognitive change as death approaches, we grouped participants by survival, death, dropout, or dropout followed by death. Linear mixed-effects pattern-mixture models compared rates of cognitive change before death and dropout from four quadrennial administrations of tests of fluid intelligence, vocabulary, and verbal learning. After we took into account the significant effects of age, gender, demographics, and recruitment cohorts, we found that approach to death and dropout caused strikingly similar reductions in mean test scores and amounts of practice gains between successive quadrennial testing sessions. Participants who neither dropped out nor died showed significant but slight cognitive declines. These analyses illustrate how neglect of dropout miscalculates effects of death, of worsening health, and of all other factors affecting rates of cognitive change.

During a 20-year longitudinal study, 5,842 participants aged 49 to 93 years significantly improved over two to four successive experiences of the Heim AH4-1 intelligence test (first published in 1970), even with between-test intervals of 4 years and longer. After we considered significant attrition by death and dropout and the effects of gender, socioeconomic advantage, and recruitment cohort, we found that participants with high intelligence test scores showed greater improvement than did those with lower intelligence test scores. Practice gains also reduced with age, even after we took into consideration the individual differences in intelligence test scores. This emphasizes the methodological point that neglect of individual differences in improvement during longitudinal studies underestimates age-related changes in younger and more able participants and the theoretical point that, like all experiences during everyday life, participation in longitudinal studies alters the ability of aging humans to cope with cognitive demands to different extents according to their baseline abilities.

BACKGROUND:therapeutic use of cytokines can induce delirium, and delirium often occurs during infections associated with elevated levels of cytokines. This study examined the association of demographic, clinical and biological factors (IL-1alpha, IL-1beta, IL-1RA, IL-6, TNF-alpha, IFN-gamma, LIF, IGF-I, APOE genotype) with the presence and severity of delirium.METHODS:in an observational prospective longitudinal study, patients aged 70+ were recruited from an elderly medical unit and assessed every 3-4 days (maximum assessments 4). At each time, the scales MMSE, DRS, CAM, APACHEII were administered and blood was withdrawn to estimate the above biological factors. Mixed effects (PQL) and GEE were used to analyse the repeated measurements and investigate the associations at the individual and population average levels.RESULTS:a total of 205 observations on 67 individuals were analysed. Lower levels of IGF-I, and lower levels of circulating IL-1RA, are significantly (P < 0.05) associated with delirium, while the remaining of cytokines, severity of illness and possession of epsilon 4 allele had a non-significant effect. This has been shown by both statistical methods. Similarly lower levels of IGF-I, and high levels of IFN-gamma, are statistically significantly (P < 0.05) associated with higher DRS scores (more severe delirium).CONCLUSIONS:this study finds that (i) low levels of both neuroprotective factors (IGF-I, IL-1RA) are associated with delirium, (ii) high IFN-gamma and low IGF-I have significant effects on delirium severity and (iii) otherwise the pro-inflammatory cytokines studied, APOE genotype and severity of illness do not appear to be associated, in older medically ill patients, with either delirium or severity of it.

This paper investigates several alternative methods of constructing confidence interval estimates based on the bootstrap and jackknife techniques for the parameters of a parallel two-component system model with dependent failure and a time varying covariate, when data is censored. This model is an extension of the bivariate exponential model. Bootstrap confidence interval techniques, the bootstrap-t, bootstrap-percentile and BCa methods are compared with the confidence interval based on the jackknife via coverage probability study using simulated data. The results clearly indicate that the jackknife technique works far better than any of the bootstrap techniques when dealing with censored data.

It is well known that approaching death accelerates cognitive decline. The converse issue, that is, the question of whether rapid declines in cognitive ability are risk factors for imminent death, has not been investigated. Every 4 years between 1983 and 2003, we gave 1,414 healthy community residents who were aged between 49 and 93 years the Heim AH4-1 test of fluid intelligence. A modified Andersen-Gill model evaluated AH4-1 scores at entry to the study and changes in scores between successive quadrennial test sessions as risk factors for death and dropout. Deaths, dropouts, age, gender, occupational categories, and recruitment cohorts were also taken into account. Participants with lower AH4-1 scores on entry were significantly more likely to die or to drop out. At all ages and levels of baseline intelligence, the risks of deaths and dropouts further increased if test scores fell by 10%, and again increased if they fell by 20% during 4-year intervals between successive assessments.