Ecological Count Data Research Articles

Count Regression and Machine Learning Techniques for Zero-Inflated Overdispersed Count Data: Application to Ecological Data

The aim of this study is to investigate the overdispersion problem that is rampant in ecological count data. In order to explore this problem, we consider the most commonly used count regression models: the Poisson, the negative binomial, the zero-inflated Poisson and the zero-inflated negative binomial models. The performance of these count regression models is compared with the four proposed machine learning (ML) regression techniques: random forests, support vector machines, k-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k-$$\\end{document}nearest neighbors and artificial neural networks. The mean absolute error was used to compare the performance of count regression models and ML regression models. The results suggest that ML regression models perform better compared to count regression models. The performance shown by ML regression techniques is a motivation for further research in improving methods and applications in ecological studies.

EcoCountHelper: an R package and analytical pipeline for the analysis of ecological count data using GLMMs, and a case study of bats in Grand Teton National Park.

Here we detail the use of an R package, 'EcoCountHelper', and an associated analytical pipeline aimed at making generalized linear mixed-effects model (GLMM)-based analysis of ecological count data more accessible. We recommend a GLMM-based analysis workflow that allows the user to (1) employ selection of distributional forms (Poisson vs negative binomial) and zero-inflation (ZIP and ZINB, respectively) using AIC and variance-mean plots, (2) examine models for goodness-of-fit using simulated residual diagnostics, (3) interpret model results via easy to understand outputs of changes in predicted responses, and (4) compare the magnitude of predictor variable effects via effects plots. Our package uses a series of easy-to-use functions that can accept both wide- and long-form multi-taxa count data without the need for programming experience. To demonstrate the utility of this approach, we use our package to model acoustic bat activity data relative to multiple landscape characteristics in a protected area (Grand Teton National Park), which is threatened by encroaching disease-white nose syndrome. Global threats to bat conservation such as disease and deforestation have prompted extensive research to better understand bat ecology. Notwithstanding these efforts, managers operating on lands crucial to the persistence of bat populations are often equipped with too little information regarding local bat activity to make informed land-management decisions. In our case study in the Tetons, we found that an increased prevalence of porous buildings increases activity levels of Eptesicus fuscus and Myotis volans; Myotis lucifugus activity decreases as distance to water increases; and Myotis volans activity increases with the amount of forested area. By using GLMMs in tandem with 'EcoCountHelper', managers without advanced programmatic or statistical expertise can assess the effects of landscape characteristics on wildlife in a statistically-robust framework.

An Overview of Modern Applications of Negative Binomial Modelling in Ecology and Biodiversity

Negative binomial modelling is one of the most commonly used statistical tools for analysing count data in ecology and biodiversity research. This is not surprising given the prevalence of overdispersion (i.e., evidence that the variance is greater than the mean) in many biological and ecological studies. Indeed, overdispersion is often indicative of some form of biological aggregation process (e.g., when species or communities cluster in groups). If overdispersion is ignored, the precision of model parameters can be severely overestimated and can result in misleading statistical inference. In this article, we offer some insight as to why the negative binomial distribution is becoming, and arguably should become, the default starting distribution (as opposed to assuming Poisson counts) for analysing count data in ecology and biodiversity research. We begin with an overview of traditional uses of negative binomial modelling, before examining several modern applications and opportunities in modern ecology/biodiversity where negative binomial modelling is playing a critical role, from generalisations based on exploiting its Poisson-gamma mixture formulation in species distribution models and occurrence data analysis, to estimating animal abundance in negative binomial N-mixture models, and biodiversity measures via rank abundance distributions. Comparisons to other common models for handling overdispersion on real data are provided. We also address the important issue of software, and conclude with a discussion of future directions for analysing ecological and biological data with negative binomial models. In summary, we hope this overview will stimulate the use of negative binomial modelling as a starting point for the analysis of count data in ecology and biodiversity studies.

‘SRS’ R Package and ‘q2-srs’ QIIME 2 Plugin: Normalization of Microbiome Data Using Scaling with Ranked Subsampling (SRS)

Several ecological data types, especially microbiome count data, are commonly sample-wise normalized before analysis to correct for sampling bias and other technical artifacts. Recently, we developed an algorithm for the normalization of ecological count data called ‘scaling with ranked subsampling (SRS)’, which surpasses the widely adopted ‘rarefying’ (random subsampling without replacement) in reproducibility and in safeguarding the original community structure. Here, we describe an implementation of the SRS algorithm in the ‘SRS’ R package and the ‘q2-srs’ QIIME 2 plugin. We also provide accessory functions for dataset exploration to guide the choice of parameters for SRS.

Bayesian regression models for ecological count data in PyMC3

Ecological inferences need structurally flexible statistical models to accommodate complex ecological phenomena. PyMC3 is a Probabilistic Programming Language (PPL) and allows for custom statistical distributions to build complex statistical models. This study used PyMC3 to implement Bayesian generalized Poisson (GP), zero-inflated GP, and hurdle GP regression models for over- and under-dispersed counts. The Bayesian GP regression models were fitted to simulated counts and real-world counts of over- and under-dispersion, respectively. Coefficient estimates of the Bayesian regression models were consistent with the known values used in the simulations and those of published work or models. Simulations demonstrated that Bayesian GP regression models with the NUTS sampler worked correctly for under-dispersed counts if the number of non-zero frequency classes was five or more. PyMC3 is not only flexible for building complex statistical models using custom likelihood functions, but also syntactically concise. The programming flexibility of PyMC3 can provide ecologists and environmental scientists with flexible, robust Bayesian computational platforms.

Improved normalization of species count data in ecology by scaling with ranked subsampling (SRS): application to microbial communities.

BackgroundAnalysis of species count data in ecology often requires normalization to an identical sample size. Rarefying (random subsampling without replacement), which is the current standard method for normalization, has been widely criticized for its poor reproducibility and potential distortion of the community structure. In the context of microbiome count data, researchers explicitly advised against the use of rarefying. Here we introduce a normalization method for species count data called scaling with ranked subsampling (SRS) and demonstrate its suitability for the analysis of microbial communities.MethodsSRS consists of two steps. In the scaling step, the counts for all species or operational taxonomic units (OTUs) are divided by a scaling factor chosen in such a way that the sum of scaled counts equals the selected total number of counts Cmin. The relative frequencies of all OTUs remain unchanged. In the subsequent ranked subsampling step, non-integer count values are converted into integers by an algorithm that minimizes subsampling error with regard to the population structure (relative frequencies of species or OTUs) while keeping the total number of counts equal Cmin. SRS and rarefying were compared by normalizing a test library representing a soil bacterial community. Common parameters of biodiversity and population structure (Shannon index H’, species richness, species composition, and relative abundances of OTUs) were determined for libraries normalized to different size by rarefying as well as SRS with 10,000 replications each. An implementation of SRS in R is available for download (https://doi.org/10.20387/BONARES-2657-1NP3).ResultsSRS showed greater reproducibility and preserved OTU frequencies and alpha diversity better than rarefying. The variance in Shannon diversity increased with the reduction of the library size after rarefying but remained zero for SRS. Relative abundances of OTUs strongly varied among libraries generated by rarefying, whereas libraries normalized by SRS showed only negligible variation. Bray–Curtis index of dissimilarity among replicates of the same library normalized by rarefying revealed a large variation in species composition, which reached complete dissimilarity (not a single OTU shared) among some libraries rarefied to a small size. The dissimilarity among replicated libraries normalized by SRS remained negligibly low at each library size. The variance in dissimilarity increased with the decreasing library size after rarefying, whereas it remained either zero or negligibly low after SRS.ConclusionsNormalization of OTU or species counts by scaling with ranked subsampling preserves the original community structure by minimizing subsampling errors. We therefore propose SRS for the normalization of biological count data.

Dirichlet‐multinomial modelling outperforms alternatives for analysis of microbiome and other ecological count data

Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue). The sampling process that generates these data can be modelled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichlet-multinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficacy of three computational methods to implement DMM-Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology.

Higher Density of Primary Care Facilities Is Inversely Associated with Ischemic Heart Disease Mortality, but Not with Stroke Mortality: A Japanese Secondary Medical Service Area Level Ecological Count Data.

Poor accessibility to physicians might be linked to the inadequate control of cardiovascular risk factors. The aim of this study was to investigate whether the accessibility of primary care physicians was related to a lower incidence of ischemic heart disease and stroke mortality via ecological data analyses of both primary care facility density and internal physician density. The unit of observation was the Japanese secondary medical service area, the basic unit for healthcare planning and administration. A primary care facility was defined as a clinic or medical institution with less than 200 inpatient beds, whose specialty included internal medicine. The number of primary care facilities per 10,000 population and the number of internal physicians per 10,000 population were used as explanatory variables. Bayesian hierarchical models were used to analyze the relative risks (RR) of primary care facility density and internal physician density using the socioeconomic confounders of designated emergency hospitals, natural log-transformed population density, birth rate, secondary and tertiary industrial workers, and taxable income. In multivariate models for ischemic heart disease mortality, primary care facility density was significantly related to the total population (RR = 0.986, 95% credible interval [CrI]: 0.979-0.993), men (RR = 0.988, 95% CrI: 0.981-0.996), and women (RR = 0.986, 95% CrI: 0.979-0.993). No significant results were obtained for internal physician density. In the multivariate models for stroke mortality, neither primary care facility density nor internal physician density showed any significant effects. Increasing primary care facility density may reduce ischemic heart disease mortality.

Soil Chemical Properties Barely Perturb the Abundance of Entomopathogenic Fusarium oxysporum: A Case Study Using a Generalized Linear Mixed Model for Microbial Pathogen Occurrence Count Data.

Fusarium oxysporum exhibits insect pathogenicity—however, generalized concerns of releasing phytopathogens within agroecosystems marred its entomopathogenicity-related investigations. In a previous study, soils were sampled from Douro vineyards and adjacent hedgerows. In this study, 80 of those soils were analyzed for their chemical properties and were subsequently co-related with the abundance of entomopathogenic F. oxysporum, after insect baiting of soils with Galleria mellonella and Tenebrio molitor larvae. The soil chemical properties studied were organic matter content; total organic carbon; total nitrogen; available potassium; available phosphorus; exchangeable cations, such as K+, Na+, Ca2+, and Mg2+; pH; total acidity; degree of base saturation; and effective cation exchange capacity. Entomopathogenic F. oxysporum was found in 48 soils, i.e., 60% ± 5.47%, of the total soil samples. Out of the 1280 insect larvae used, 93, i.e., 7.26% ± 0.72%, were found dead by entomopathogenic F. oxysporum. Stepwise deletion of non-significant variables using a generalized linear model was followed by a generalized linear mixed model (GLMM). A higher C:N (logarithmized) (p < 0.001) and lower exchangeable K+ (logarithmized) (p = 0.008) were found significant for higher fungal abundance. Overall, this study suggests that entomopathogenic F. oxysporum is robust with regard to agricultural changes, and GLMM is a useful statistical tool for count data in ecology.

Relationships between road‐distance to primary care facilities and ischemic heart disease and stroke mortality in Hokkaido, Japan: A Bayesian hierarchical approach to ecological count data

ObjectivePoor access to a primary care physician may lead to poor control of risk factors for disease. This study investigated whether geographic access to a primary care physician was related to ischemic heart disease and stroke mortality.MethodsRoad‐distances from the centroids of the basic unit blocks of the 2010 Japanese Census to the nearest primary care facilities in Hokkaido, northern Japan, were measured using geographic information system (GIS) software. Next, block population‐weighted mean road‐distances to primary care facilities in all municipalities were calculated. The numbers of deaths from ischemic heart disease and stroke were obtained from the Vital Statistics Bureau. A Bayesian spatial conditional autoregressive (CAR) model was used to analyze relative risk (RR) by road‐distance with the numbers of physicians in the municipality included as a covariate.ResultsRelative risk (per 1 kilometer increased) of death from ischemic heart disease to road‐distance to the nearest primary care facility was not significantly higher in men (1.108: 95% credible interval [CI] 0.999‐1.037) and women (1.023: 95% CI 1.000‐1.046). However, RR of death from stroke was significantly higher in men (1.019: 95% CI 1.005‐1.032) and women (1.019: 95% CI 1.006‐1.033).ConclusionLonger road‐distance to a primary care facility may increase the risk of stroke mortality.

Modelling of fire count data: fire disaster risk in Ghana.

Stochastic dynamics involved in ecological count data require distribution fitting procedures to model and make informed judgments. The study provides empirical research, focused on the provision of an early warning system and a spatial graph that can detect societal fire risks. It offers an opportunity for communities, organizations, risk managers, actuaries and governments to be aware of, and understand fire risks, so that they will increase the direct tackling of the threats posed by fire. Statistical distribution fitting method that best helps identify the stochastic dynamics of fire count data is used. The aim is to provide a fire-prediction model and fire spatial graph for observed fire count data. An empirical probability distribution model is fitted to the fire count data and compared to the theoretical probability distribution of the stochastic process of fire count data. The distribution fitted to the fire frequency count data helps identify the class of models that are exhibited by the fire and provides time leading decisions. The research suggests that fire frequency and loss (fire fatalities) count data in Ghana are best modelled with a Negative Binomial Distribution. The spatial map of observed fire frequency and fatality measured over 5 years (2007–2011) offers in this study a first regional assessment of fire frequency and fire fatality in Ghana.

Using observation-level random effects to model overdispersion in count data in ecology and evolution.

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 (r2), 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.

A Hierarchical Bayesian Approach to Ecological Count Data: A Flexible Tool for Ecologists

Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical Bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy.

Using the negative binomial distribution to model overdispersion in ecological count data

A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.

Spatial analyses of ecological count data: A density map comparison approach

Analysing spatial patterns of population distributions may help to infer the decisive underlying ecological processes. Here we propose a method adapted to the spatial analysis of count data. Named MAPCOMP (MAP COMParison), it is based on the calculation of a formal distance, the Hellinger distance, between the density map of counts and the density map of sampling effort. Statistical tests of spatial homogeneity are based on count permutations across sampling sites and on valuable properties of the Hellinger distance. We assessed the efficiency of MAPCOMP by simulating different types and locations of clusters of individuals and compared its performance to the classical red–blue SADIE method, used as a reference. The two methods were also compared with respect to counts of codling moth larvae in orchards. Thanks to its better theoretical properties than SADIE, MAPCOMP was efficient in detecting spatial inhomogeneity when clusters were located on square or elongated spatial domains and more or less close to the edges, even for small sample sizes. It also appeared not very sensitive to edge effects. Another advantage of MAPCOMP is a bandwidth parameter that allows assessing the spatial extent of heterogeneity, if any.

A unified approach to model selection using the likelihood ratio test

Summary1. Ecological count data typically exhibit complexities such as overdispersion and zero‐inflation, and are often weakly associated with a relatively large number of correlated covariates. The use of an appropriate statistical model for inference is therefore essential. A common selection criteria for choosing between nested models is the likelihood ratio test (LRT). Widely used alternatives to the LRT are based on information‐theoretic metrics such as the Akaike Information Criterion.2. It is widely believed that the LRT can only be used to compare the performance of nested models – i.e. in situations where one model is a special case of another. There are many situations in which it is important to compare non‐nested models, so, if true, this would be a substantial drawback of using LRTs for model comparison. In reality, however, it is actually possible to use the LRT for comparing both nested and non‐nested models. This fact is well‐established in the statistical literature, but not widely used in ecological studies.3. The main obstacle to the use of the LRT with non‐nested models has, until relatively recently, been the fact that it is difficult to explicitly write down a formula for the distribution of the LRT statistic under the null hypothesis that one of the models is true. With modern computing power it is possible to overcome this difficulty by using a simulation‐based approach.4. To demonstrate the practical application of the LRT to both nested and non‐nested model comparisons, a case study involving data on questing tick (Ixodes ricinus) abundance is presented. These data contain complexities typical in ecological analyses, such as zero‐inflation and overdispersion, for which comparison between models of differing structure – e.g. non‐nested models – is of particular importance.5. Choosing between competing statistical models is an essential part of any applied ecological analysis. The LRT is a standard statistical test for comparing nested models. By use of simulation the LRT can also be used in an analogous fashion to compare non‐nested models, thereby providing a unified approach for model comparison within the null hypothesis testing paradigm. A simple practical guide is provided in how to apply this approach to the key models required in the analyses of count data.

Do not log‐transform count data

Summary 1. Ecological count data (e.g. number of individuals or species) are often log‐transformed to satisfy parametric test assumptions. 2. Apart from the fact that generalized linear models are better suited in dealing with count data, a log‐transformation of counts has the additional quandary in how to deal with zero observations. With just one zero observation (if this observation represents a sampling unit), the whole data set needs to be fudged by adding a value (usually 1) before transformation. 3. Simulating data from a negative binomial distribution, we compared the outcome of fitting models that were transformed in various ways (log, square root) with results from fitting models using quasi‐Poisson and negative binomial models to untransformed count data. 4. We found that the transformations performed poorly, except when the dispersion was small and the mean counts were large. The quasi‐Poisson and negative binomial models consistently performed well, with little bias. 5. We recommend that count data should not be analysed by log‐transforming it, but instead models based on Poisson and negative binomial distributions should be used.

Do not log-transform count data

Abstract1. Ecological count data (e.g., number of individuals or species) are often log-transformed to satisfy parametric test assumptions.2. Apart from the fact that generalized linear models are better suited in dealing with count data, a log-transformation of counts has the additional quandary in how to deal with zero observations. With just one zero observation (if this observation represents a sampling unit), the whole dataset needs to be fudged by adding a value (usually 1) before transformation. 3. Simulating data from a negative binomial distribution, we compared the outcome of fitting models that were transformed in various ways (log, square-root) with results from fitting models using Poisson and negative binomial models to untransformed count data. 4. We found that the transformations performed poorly, except when the dispersion was small and the mean counts were large. The Poisson and negative binomial models consistently performed well, with little bias.

Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data

Traditional occupancy–abundance and abundance–variance–occupancy models do not take into account zero-inflation, which occurs when sampling rare species or in correlated counts arising from repeated measures. In this paper we propose a novel approach extending occupancy–abundance relationships to zero-inflated count data. This approach involves three steps: (1) selecting distributional assumptions and parsimonious models for the count data, (2) estimating abundance, occupancy and variance parameters as functions of site- and/or time-specific covariates, and (3) modelling the occupancy–abundance relationship using the parameters estimated in step 2. Five count datasets were used for comparing standard Poisson and negative binomial distribution (NBD) occupancy–abundance models. Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) occupancy–abundance models were introduced for the first time, and these were compared with the Poisson, NBD, He and Gaston's and Wilson and Room's abundance–variance–occupancy models. The percentage of zero counts ranged from 45 to 80% in the datasets analysed. For most of the datasets, the ZINB occupancy–abundance model performed better than the traditional Poisson, NBD and Wilson and Room's model. He and Gaston's model performed better than the ZINB in two out of the five datasets. However, the occupancy predicted by all models increased faster than the observed as density increased resulting in significant mismatch at the highest densities. Limitations of the various models are discussed, and the need for careful choice of count distributions and predictors in estimating abundance and occupancy parameter are indicated.

Dealing with overdispersed count data in applied ecology

Summary The ability to identify key ecological processes is important when solving applied problems. Increasingly, ecologists are adopting Akaike's information criterion (AIC) as a metric to help them assess and select among multiple process‐based ecological models. Surprisingly, however, it is still unclear how best to incorporate AIC into the selection process in order to address the trade‐off between maximizing the probability of retaining the most parsimonious model while minimizing the number of models retained. Ecological count data are often observed to be overdispersed with respect to best‐fitting models. Overdispersion is problematic when performing an AIC analysis, as it can result in selection of overly complex models which can lead to poor ecological inference. This paper describes and illustrates two approaches that deal effectively with overdispersion. The first approach involves modelling the causes of overdispersion implicitly using compound probability distributions. The second approach ignores the causes of overdispersion and uses quasi‐AIC (QAIC) as a metric for model parsimony. Simulations and a novel method that identifies the most parsimonious model are used to demonstrate the utility of the two overdispersion approaches within the context of two ecological examples. The first example addresses binomial data obtained from a study of fish survival (as related to habitat structure) and the second example addresses Poisson data obtained from a study of flower visitation by nectarivores. Applying either overdispersion approach reduces the chance of selecting overly complex models, and both approaches result in very similar ecological inference. In addition, inference can be made more reliable by incorporating model nesting into the selection process (i.e. identifying which models are special cases of others), as it reduces the number of models selected without significantly reducing the probability of retaining the most parsimonious models. Synthesis and applications. When data are overdispersed, inference can be improved by either modelling the causes of overdispersion or applying QAIC as a metric for model parsimony. Inference can also be improved by adopting a model filtering procedure based on how models are nested. The general simulation approach presented in this paper for identifying the most parsimonious model, as defined by information theory, should help to improve our understanding of the reliability of model selection when using AIC, and help the development of better selection rules.