Overdispersion is common in models of count data in ecology and evolutionary biology, and can occur due to missing covariates, non-independent (aggregated) data, or an excess frequency of zeroes ...(zero-inflation). Accounting for overdispersion in such models is vital, as failing to do so can lead to biased parameter estimates, and false conclusions regarding hypotheses of interest. Observation-level random effects (OLRE), where each data point receives a unique level of a random effect that models the extra-Poisson variation present in the data, are commonly employed to cope with overdispersion in count data. However studies investigating the efficacy of observation-level random effects as a means to deal with overdispersion are scarce. Here I use simulations to show that in cases where overdispersion is caused by random extra-Poisson noise, or aggregation in the count data, observation-level random effects yield more accurate parameter estimates compared to when overdispersion is simply ignored. Conversely, OLRE fail to reduce bias in zero-inflated data, and in some cases increase bias at high levels of overdispersion. There was a positive relationship between the magnitude of overdispersion and the degree of bias in parameter estimates. Critically, the simulations reveal that failing to account for overdispersion in mixed models can erroneously inflate measures of explained variance (r (2)), which may lead to researchers overestimating the predictive power of variables of interest. This work suggests use of observation-level random effects provides a simple and robust means to account for overdispersion in count data, but also that their ability to minimise bias is not uniform across all types of overdispersion and must be applied judiciously.
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.
Recent advances in tagging and biologging technology have yielded unprecedented insights into wild animal physiology. However, time-series data from such wild tracking studies present numerous ...analytical challenges owing to their unique nature, often exhibiting strong autocorrelation within and among samples, low samples sizes and complicated random effect structures. Gleaning robust quantitative estimates from these physiological data, and, therefore, accurate insights into the life histories of the animals they pertain to, requires careful and thoughtful application of existing statistical tools. Using a combination of both simulated and real datasets, I highlight the key pitfalls associated with analysing physiological data from wild monitoring studies, and investigate issues of optimal study design, statistical power, and model precision and accuracy. I also recommend best practice approaches for dealing with their inherent limitations. This work will provide a concise, accessible roadmap for researchers looking to maximize the yield of information from complex and hard-won biologging datasets.
This article is part of the theme issue ‘Measuring physiology in free-living animals (Part II)’.
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.
Host-associated microbes are vital for combatting infections and maintaining health. In amphibians, certain skin-associated bacteria inhibit the fungal pathogen Batrachochytrium dendrobatidis (Bd), ...yet our understanding of host microbial ecology and its role in disease outbreaks is limited. We sampled skin-associated bacteria and Bd from Pyrenean midwife toad populations exhibiting enzootic or epizootic disease dynamics. We demonstrate that bacterial communities differ between life stages with few shared taxa, indicative of restructuring at metamorphosis. We detected a significant effect of infection history on metamorph skin microbiota, with reduced bacterial diversity in epizootic populations and differences in community structure and predicted function. Genome sequencing of Bd isolates supports a single introduction to the Pyrenees and reveals no association between pathogen genetics and epidemiological trends. Our findings provide an ecologically relevant insight into the microbial ecology of amphibian skin and highlight the relative importance of host microbiota and pathogen genetics in predicting disease outcome.
Biological systems, at all scales of organisation from nucleic acids to ecosystems, are inherently complex and variable. Biologists therefore use statistical analyses to detect signal among this ...systemic noise. Statistical models infer trends, find functional relationships and detect differences that exist among groups or are caused by experimental manipulations. They also use statistical relationships to help predict uncertain futures. All branches of the biological sciences now embrace the possibilities of mixed-effects modelling and its flexible toolkit for partitioning noise and signal. The mixed-effects model is not, however, a panacea for poor experimental design, and should be used with caution when inferring or deducing the importance of both fixed and random effects. Here we describe a selection of the perils and pitfalls that are widespread in the biological literature, but can be avoided by careful reflection, modelling and model-checking. We focus on situations where incautious modelling risks exposure to these pitfalls and the drawing of incorrect conclusions. Our stance is that statements of significance, information content or credibility all have their place in biological research, as long as these statements are cautious and well-informed by checks on the validity of assumptions. Our intention is to reveal potential perils and pitfalls in mixed model estimation so that researchers can use these powerful approaches with greater awareness and confidence. Our examples are ecological, but translate easily to all branches of biology.
1. Carry-over effects occur when processes in one season influence the success of an individual in the following season. This phenomenon has the potential to explain a large amount of variation in ...individual fitness, but so far has only been described in a limited number of species. This is largely due to difficulties associated with tracking individuals between periods of the annual cycle, but also because of a lack of research specifically designed to examine hypotheses related to carry-over effects. 2. We review the known mechanisms that drive carry-over effects, most notably macronutrient supply, and highlight the types of life histories and ecological situations where we would expect them to most often occur. We also identify a number of other potential mechanisms that require investigation, including micronutrients such as antioxidants. 3. We propose a series of experiments designed to estimate the relative contributions of extrinsic and intrinsic quality effects in the pre-breeding season, which in turn will allow an accurate estimation of the magnitude of carry-over effects. To date this has proven immensely difficult, and we hope that the experimental frameworks described here will stimulate new avenues of research vital to advancing our understanding of how carry-over effects can shape animal life histories. 4. We also explore the potential of state-dependent modelling as a tool for investigating carry-over effects, most notably for its ability to calculate optimal rates of acquisition of a multitude of resources over the course of the annual cycle, and also because it allows us to vary the strength of density-dependent relationships which can alter the magnitude of carry-over effects in either a synergistic or agonistic fashion. 5. In conclusion carry-over effects are likely to be far more widespread than currently indicated, and they are likely to be driven by a multitude of factors including both macro- and micronutrients. For this reason they could feasibly be responsible for a large amount of the observed variation in performance among individuals, and consequently warrant a wealth of new research designed specifically to decompose components of variation in fitness attributes related to processes across and within seasons.
Increasingly, researchers are interested in quantifying temporal dynamics of host-associated microbiomes, yet an individual-host approach is still rare in the literature.Detailed longitudinal data ...from wild individual hosts are key to understanding the fitness implications of temporal microbiome stability and dynamics.Whether stability or flexibility of host-associated microbiomes is beneficial to a host will depend on the ecological context, and so incorporating knowledge of host ecology to these individual-level approaches is vital.Recent advances in analytical approaches may provide helpful tools in testing hypotheses of individual variation in microbiome temporal stability and the consequences of this for host fitness.
Ignoring the dynamic nature of microbial communities risks underestimating the power of microbes to impact the health of their hosts. Microbiomes are thought to be important for host fitness, yet the coarse temporal scale and population-level focus of many studies precludes the ability to investigate the importance of among-individual variation in stability and identify the ecological contexts in which this variation matters. Here we briefly summarise current knowledge of temporal dynamics in wild host-associated microbial communities. We then discuss the implications of among-individual variation in microbiota stability and suggest analytical approaches for understanding these patterns. One major requirement is for future studies to conduct individual-level longitudinal analyses, with some systems already well set up for answering these questions.
Ignoring the dynamic nature of microbial communities risks underestimating the power of microbes to impact the health of their hosts. Microbiomes are thought to be important for host fitness, yet the coarse temporal scale and population-level focus of many studies precludes the ability to investigate the importance of among-individual variation in stability and identify the ecological contexts in which this variation matters. Here we briefly summarise current knowledge of temporal dynamics in wild host-associated microbial communities. We then discuss the implications of among-individual variation in microbiota stability and suggest analytical approaches for understanding these patterns. One major requirement is for future studies to conduct individual-level longitudinal analyses, with some systems already well set up for answering these questions.
Symbiotic bacterial communities can protect their hosts from infection by pathogens. Treatment of wild individuals with protective bacteria (probiotics) isolated from hosts can combat the spread of ...emerging infectious diseases. However, it is unclear whether candidate probiotic bacteria can offer consistent protection across multiple isolates of globally distributed pathogens. Here, we use the lethal amphibian fungal pathogen Batrachochytrium dendrobatidis to investigate whether probiotic richness (number of bacteria) or genetic distance among consortia members influences broad‐scale in vitro inhibitory capabilities of probiotics across multiple isolates of the pathogen. We show that inhibition of multiple pathogen isolates by individual bacteria is rare, with no systematic pattern among bacterial genera in ability to inhibit multiple B. dendrobatidis isolates. Bacterial consortia can offer stronger protection against B. dendrobatidis compared to single strains, and this tended to be more pronounced for consortia containing multiple genera compared with those consisting of bacteria from a single genus (i.e., with lower genetic distance), but critically, this effect was not uniform across all B. dendrobatidis isolates. These novel insights have important implications for the effective design of bacterial probiotics to mitigate emerging infectious diseases.
Variation among animals in their host-associated microbial communities is increasingly recognized as a key determinant of important life history traits including growth, metabolism, and resistance to ...disease. Quantitative estimates of the factors shaping the stability of host microbiomes over time at the individual level in non-model organisms are scarce. Addressing this gap in our knowledge is important, as variation among individuals in microbiome stability may represent temporal gain or loss of key microbial species and functions linked to host health and/or fitness. Here we use controlled experiments to investigate how both heterogeneity in microbial species richness of the environment and exposure to the emerging pathogen
influence the structure and temporal dynamics of the skin microbiome in a vertebrate host, the European common frog (
). Our evidence suggests that altering the bacterial species richness of the environment drives divergent temporal microbiome dynamics of the amphibian skin. Exposure to ranavirus effects changes in skin microbiome structure irrespective of total microbial diversity, but individuals with higher pre-exposure skin microbiome diversity appeared to exhibit higher survival. Higher diversity skin microbiomes also appear less stable over time compared to lower diversity microbiomes, but stability of the 100 most abundant ("core") community members was similar irrespective of microbiome richness. Our study highlights the importance of extrinsic factors in determining the stability of host microbiomes over time, which may in turn have important consequences for the stability of host-microbe interactions and microbiome-fitness correlations.
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