Count data can be analyzed using generalized linear mixed models when observations are correlated in ways that require random effects. However, count data are often zero-inflated, containing more zeros than would be expected from the typical error distributions. We present a new package, glmmTMB, and compare it to other R packages that fit zero-inflated mixed models. The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here we focus on count responses. glmmTMB is faster than glmmADMB, MCMCglmm, and brms, and more flexible than INLA and mgcv for zero-inflated modeling. One unique feature of glmmTMB (among packages that fit zero-inflated mixed models) is its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean. Overall, its most appealing features for new users may be the combination of speed, flexibility, and its interface's similarity to lme4.

Summary1 Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise. 2 We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters. 3 As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA. 4 Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species' traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.

Identifying the existence and magnitude of density dependence is one of the oldest concerns in ecology. Ecologists have aimed to estimate density dependence in population and community data by fitting a simple autoregressive (Gompertz) model for density dependence to time series of abundance for an entire population. However, it is increasingly recognized that spatial heterogeneity in population densities has implications for population and community dynamics. We therefore adapt the Gompertz model to approximate, local densities over continuous space instead of population-wide abundance, and allow productivity to vary spatially using Gaussian random fields. We then show that the conventional (nonspatial) Gompertz model can result in biased estimates of density dependence (e.g., identifying oscillatory dynamics when not present) if densities vary spatially. By contrast, the spatial Gompertz model provides accurate and precise estimates of density dependence for a variety of simulation scenarios and data availabilities. These results are corroborated when comparing spatial and nonspatial models for data from 10 years and -100 sampling stations for three long-lived rockfishes (Sebastes spp.) off the California, USA coast. In this case, the nonspatial model estimates implausible oscillatory dynamics on an annual time scale, while the spatial model estimates strong autocorrelation and is supported by model selection tools. We conclude by discussing the importance of improved data archiving techniques, so that spatial models can be used to reexamine classic questions regarding the existence and magnitude of density. dependence in wild populations.

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Reproduction by individuals is typically recorded as count data (e.g., number of fledglings from a nest or inflorescences on a plant) and commonly modeled using Poisson or negative binomial distributions, which assume that variance is greater than or equal to the mean. However, distributions of reproductive effort are often underdispersed (i.e., variance < mean). When used in hypothesis tests, models that ignore underdispersion will be overly conservative and may fail to detect significant patterns. Here we show that generalized Poisson (GP) and Conway‐Maxwell‐Poisson (CMP) distributions are better choices for modeling reproductive effort because they can handle both overdispersion and underdispersion; we provide examples of how ecologists can use GP and CMP distributions in generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to quantify patterns in reproduction. Using a new R package, glmmTMB, we construct GLMMs to investigate how rainfall and population density influence the number of fledglings in the warbler Oreothlypis celata and how flowering rate of Heliconia acuminata differs between fragmented and continuous forest. We also demonstrate how to deal with zero‐inflation, which occurs when there are more zeros than expected in the distribution, e.g., due to complete reproductive failure by some individuals.