The characterization of the dispersal of populations of non-identical individuals is relevant to most ecological and epidemiological processes. In practice, the movement is quantified by observing relatively few individuals, and averaging to estimate the rate of dispersal of the population as a whole. Here, we show that this can lead to serious errors in the predicted movement of the population if the individuals disperse at different rates. We develop a stochastic model for the diffusion of heterogeneous populations, inspired by the movement of the parasitic nematode Phasmarhabditis hermaphrodita. Direct observations of this nematode in homogeneous and heterogeneous environments reveal a large variation in individual behaviour within the population as reflected initially in the speed of the movement. Further statistical analysis shows that the movement is characterized by temporal correlations and in a heterogeneously structured environment the correlations that occur are of shorter range compared with those in a homogeneous environment. Therefore, by using the first-order correlated random walk techniques, we derive an effective diffusion coefficient for each individual, and show that there is a significant variation in this parameter among the population that follows a gamma distribution. Based on these findings, we build a new dispersal model in which we maintain the classical assumption that individual movement can be described by normal diffusion, but due to the variability in individual dispersal rates, the diffusion coefficient is not constant at the population level and follows a continuous distribution. The conclusions and methodology presented are relevant to any heterogeneous population of individuals with widely different diffusion rates.

Over the last 60 years, soil microbiologists have accumulated a wealth of experimental data showing that the bulk, macroscopic parameters (e.g., granulometry, pH, soil organic matter, and biomass contents) commonly used to characterize soils provide insufficient information to describe quantitatively the activity of soil microorganisms and some of its outcomes, like the emission of greenhouse gasses. Clearly, new, more appropriate macroscopic parameters are needed, which reflect better the spatial heterogeneity of soils at the microscale (i.e., the pore scale) that is commensurate with the habitat of many microorganisms. For a long time, spectroscopic and microscopic tools were lacking to quantify processes at that scale, but major technological advances over the last 15 years have made suitable equipment available to researchers. In this context, the objective of the present article is to review progress achieved to date in the significant research program that has ensued. This program can be rationalized as a sequence of steps, namely the quantification and modeling of the physical-, (bio)chemical-, and microbiological properties of soils, the integration of these different perspectives into a unified theory, its upscaling to the macroscopic scale, and, eventually, the development of new approaches to measure macroscopic soil characteristics. At this stage, significant progress has been achieved on the physical front, and to a lesser extent on the (bio)chemical one as well, both in terms of experiments and modeling. With regard to the microbial aspects, although a lot of work has been devoted to the modeling of bacterial and fungal activity in soils at the pore scale, the appropriateness of model assumptions cannot be readily assessed because of the scarcity of relevant experimental data. For significant progress to be made, it is crucial to make sure that research on the microbial components of soil systems does not keep lagging behind the work on the physical and (bio)chemical characteristics. Concerning the subsequent steps in the program, very little integration of the various disciplinary perspectives has occurred so far, and, as a result, researchers have not yet been able to tackle the scaling up to the macroscopic level. Many challenges, some of them daunting, remain on the path ahead. Fortunately, a number of these challenges may be resolved by brand new measuring equipment that will become commercially available in the very near future.

BackgroundCognitive impairment of various kinds is common in older people admitted to hospital, but previous research has usually focused on single conditions in highly-selected groups and has rarely examined associations with outcomes. This study examined prevalence and outcomes of cognitive impairment in a large unselected cohort of people aged 65+ with an emergency medical admission.MethodsBetween January 1, 2012, and June 30, 2013, admissions to a single general hospital acute medical unit aged 65+ underwent a structured specialist nurse assessment (n = 10,014). We defined ‘cognitive spectrum disorder’ (CSD) as any combination of delirium, known dementia, or Abbreviated Mental Test (AMT) score < 8/10. Routine data for length of stay (LOS), mortality, and readmission were linked to examine associations with outcomes.ResultsA CSD was present in 38.5% of all patients admitted aged over 65, and in more than half of those aged over 85. Overall, 16.7% of older people admitted had delirium alone, 7.9% delirium superimposed on known dementia, 9.4% known dementia alone, and 4.5% unspecified cognitive impairment (AMT score < 8/10, no delirium, no known dementia). Of those with known dementia, 45.8% had delirium superimposed. Outcomes were worse in those with CSD compared to those without – LOS 25.0 vs. 11.8 days, 30-day mortality 13.6% vs. 9.0%, 1-year mortality 40.0% vs. 26.0%, 1-year death or readmission 62.4% vs. 51.5% (all P < 0.01). There was relatively little difference by CSD type, although people with delirium superimposed on dementia had the longest LOS, and people with dementia the worst mortality at 1 year.ConclusionsCSD is common in older inpatients and associated with considerably worse outcomes, with little variation between different types of CSD. Healthcare systems should systematically identify and develop care pathways for older people with CSD admitted as medical emergencies, and avoid only focusing on condition-specific pathways such as those for dementia or delirium alone.Electronic supplementary materialThe online version of this article (doi:10.1186/s12916-017-0899-0) contains supplementary material, which is available to authorized users.

Objective: To investigate the association between visit-to-visit HbA1c variability and cardiovascular events and microvascular complications in patients with newly diagnosed type 2 diabetes. Research Design and Methods: This retrospective cohort study analyzed patients from Tayside and Fife in the Scottish Care Information-Diabetes Collaboration (SCI-DC), who were observable from the diagnosis of diabetes and had at least five HbA1c measurements before the outcomes being evaluated. We used the previously reported HbA1c variability score (HVS) calculated as the percentage of the number of changes in HbA1c over 0.5% (5.5 mmol/mol) among all HbA1c measurement within an individual. The association between HVS and ten outcomes was assessed using Cox proportional-hazards models. Results: We included 13,111 to 19,883 patients in the analyses of each outcome. The patients with HVS over 60% were associated with elevated risks of all outcomes compared with the lowest quintile (for example, hazard ratios and 95% confidence intervals [HVS >80 to ≤100 vs. HVS ≥0 to ≤20]: 2.38 [1.61~3.53] for major adverse cardiovascular events [MACE]; 2.4 [1.72~3.33] for all-cause mortality; 2.4 [1.13~5.11] for atherosclerotic cardiovascular [ASCV] death; 2.63 [1.81~3.84] for coronary artery disease; 2.04 [1.12~3.73] for ischemic stroke; 3.23 [1.76~5.93] for heart failure; 7.4 [3.84~14.27] for diabetic retinopathy; 3.07 [2.23~4.22] for diabetic peripheral neuropathy; 5.24 [2.61~10.49] for diabetic foot ulcer; 3.49 [2.47~4.95] for the newonset chronic kidney disease). Four sensitivity analyses, including adjustment for timeweighted average HbA1c confirmed the robustness of the results. Conclusions: Our study shows that higher HbA1c variability is associated with increased risks of all-cause mortality, cardiovascular events and microvascular complication of diabetes independently of high HbA1c.