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Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R 0 , variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R 0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R 0 and k (95% CrIs: R 0 1.4-12; k 0.04-0.2); however, the upper bound of R 0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon’s relative abundance. In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon’s relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon’s counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis, the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.

The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions.

Crime rate is the number of reported crimes divided by total population. Several factors could contribute the variability of crime rates among areas. This study aims to model the relationship between crime rates among regencies and cities in the East Java Province (Indonesia) and some potentially explanatory variables based on Statistics Indonesia publication in 2020. The crime rate in the East Java Province was consistently at the top three after DKI Jakarta and North Sumatra during 2017 to 2019. Therefore, it is interesting for us to study further about the crime rate in the East Java. Our preliminary analysis indicates that there is an overdispersion in our sample data. To overcome the overdispersion, we fit Generalized Poisson and Negative Binomial regression. The ratio of deviance and degree of freedom based on Negative Binomial is slightly smaller (1.38) than Generalized Poisson (1.99). The results indicate that Negative Binomial and Generalized Poisson regression, compared to standard Poisson regression, are relatively fit to model our crime rate data. Some factors which contribute significantly (α=0.05) for the crime rate in the East Java Province under Negative Binomial as well as Generalized Poisson regression are percentage of poor people, number of households, unemployment rate, and percentage of expenditure.

Rare plant and vertebrate species have been documented to contribute disproportionately to the total morphological structure of species assemblages. These species often possess morphologically extreme traits and occupy the boundaries of morphological space. As rare species are at greater risk of extinction than more widely distributed species, human‐induced disturbances can strongly affect ecosystem functions related to assemblage morphology. Here, we assess to what extent the distributions of ant morphological traits are supported by morphologically extreme species and how they are distributed among habitats in a global biodiversity hotspot, the Brazilian Amazon. We used a morphological database comprising 15 continuous morphological traits and 977 expert‐validated ant species distributed across the Brazilian Amazon. We produced species range estimates using species distribution models or alpha hulls (when few records were available). Next, we conducted a principal components analysis to combine traits into a space with reduced dimensionality (morphospace). Then, we identified morphologically extreme species in this space and quantified their contributions to morphological diversity across different habitat types in the Brazilian Amazon Basin. We identified 114 morphologically extreme ant species across the Amazon ant morphospace. These species also accounted for a large percentage of morphospace filling, exceeding 99% representation in the most disturbed habitats in the Amazon. Our results suggest that a few morphologically extreme species capture most of the variation in ant morphology and, therefore, the spectrum of ecosystem functions performed by ants in the Brazilian Amazon Basin. Further, unlike in many other groups, these extreme morphologies were represented by the set of most common species. These results suggest greater functional redundancy and resilience in Brazilian Amazon ants, but more broadly, they contribute to our understanding of ecological processes that sustain ecosystem functions.

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life face-to-face contact networks. These results suggest that the hardest hit areas, such as New York City, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number , variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of (2-3), the overdispersion parameter of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for and (95% CrIs: 1.4-12; 0.04-0.2); however, the upper bound of was not well informed by the model and data, which did not notably differ from that of the prior distribution. Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Although research on the role of competitive interactions during community assembly began decades ago, a recent revival of interest has led to new discoveries and research opportunities. Using contemporary coexistence theory that emphasizes stabilizing niche differences and relative fitness differences, we evaluate three empirical approaches for studying community assembly. We show that experimental manipulations of the abiotic or biotic environment, assessments of trait-phylogeny-environment relationships, and investigations of frequency-dependent population growth all suggest strong influences of stabilizing niche differences and fitness differences on the outcome of plant community assembly. Nonetheless, due to the limitations of these approaches applied in isolation, we still have a poor understanding of which niche axes and which traits determine the outcome of competition and community structure. Combining current approaches represents our best chance of achieving this goal, which is fundamental to conceptual ecology and to the management of plant communities under global change.

Overdispersion is a common feature of models of biological data, but researchers often fail to model the excess variation driving the overdispersion, resulting in biased parameter estimates and standard errors. Quantifying and modeling overdispersion when it is present is therefore critical for robust biological inference. One means to account for overdispersion is to add an observation-level random effect (OLRE) to a model, where each data point receives a unique level of a random effect that can absorb the extra-parametric variation in the data. Although some studies have investigated the utility of OLRE to model overdispersion in Poisson count data, studies doing so for Binomial proportion data are scarce. Here I use a simulation approach to investigate the ability of both OLRE models and Beta-Binomial models to recover unbiased parameter estimates in mixed effects models of Binomial data under various degrees of overdispersion. In addition, as ecologists often fit random intercept terms to models when the random effect sample size is low (<5 levels), I investigate the performance of both model types under a range of random effect sample sizes when overdispersion is present. Simulation results revealed that the efficacy of OLRE depends on the process that generated the overdispersion; OLRE failed to cope with overdispersion generated from a Beta-Binomial mixture model, leading to biased slope and intercept estimates, but performed well for overdispersion generated by adding random noise to the linear predictor. Comparison of parameter estimates from an OLRE model with those from its corresponding Beta-Binomial model readily identified when OLRE were performing poorly due to disagreement between effect sizes, and this strategy should be employed whenever OLRE are used for Binomial data to assess their reliability. Beta-Binomial models performed well across all contexts, but showed a tendency to underestimate effect sizes when modelling non-Beta-Binomial data. Finally, both OLRE and Beta-Binomial models performed poorly when models contained <5 levels of the random intercept term, especially for estimating variance components, and this effect appeared independent of total sample size. These results suggest that OLRE are a useful tool for modelling overdispersion in Binomial data, but that they do not perform well in all circumstances and researchers should take care to verify the robustness of parameter estimates of OLRE models.

Increasing evidence indicates that superspreading plays a dominant role in COVID-19 transmission. Recent estimates suggest that the dispersion parameter k for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is on the order of 0.1, which corresponds to about 10% of cases being the source of 80% of infections. To investigate how overdispersion might affect the outcome of various mitigation strategies, we developed an agent-based model with a social network that allows transmission through contact in three sectors: “close” (a small, unchanging group of mutual contacts as might be found in a household), “regular” (a larger, unchanging group as might be found in a workplace or school), and “random” (drawn from the entire model population and not repeated regularly). We assigned individual infectivity from a gamma distribution with dispersion parameter k. We found that when k was low (i.e., greater heterogeneity, more superspreading events), reducing random sector contacts had a far greater impact on the epidemic trajectory than did reducing regular contacts; when k was high (i.e., less heterogeneity, no superspreading events), that difference disappeared. These results suggest that overdispersion of COVID-19 transmission gives the virus an Achilles’ heel: Reducing contacts between people who do not regularly meet would substantially reduce the pandemic, while reducing repeated contacts in defined social groups would be less effective.