Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

Parasites are important determinants of ecological dynamics. Despite the widespread perception that parasites (in the broad sense, including microbial pathogens) threaten species with extinction, the simplest deterministic models of parasite dynamics (i.e. of specialist parasites with density-dependent transmission) predict that parasites will always go extinct before their hosts. We review the primary theoretical mechanisms that allow disease-induced extinction and compare them with the empirical literature on parasitic threats to populations to assess the importance of different mechanisms in threatening natural populations. Small pre-epidemic population size and the presence of reservoirs are the most commonly cited factors for disease-induced extinction in empirical studies. ; MacNeil et al. 2003). In conservation biology, disease is presented as a threat to population viability and a contributing factor to disease extinction (McCallum & Dobson 1995). However, the simplest disease models -which have formed the theoretical foundation for the field of disease ecologysuggest that disease alone cannot drive host populations extinct (Anderson & May 1992). More specifically, deterministic models of directly transmitted specialist parasites with density-dependent transmission predict that disease will always die out when the host population falls below a (nonzero) threshold density, before the host population can go extinct (Swinton et al. 1998;McCallum et al. 2001); stochastic models suggest that disease will often go extinct by so-called Ôfade-outÕ even above this threshold (Bartlett 1960;Black 1966;Keeling & Grenfell 1997). The first part of this paper reviews the important exceptions to these simple conclusions -the qualitative mechanisms that drive disease-induced extinction in theoretical models. The second reviews the existing empirical literature on disease-induced extinction, and makes a first attempt to assess the relative importance of the different mechanisms in natural systems.The literature search was performed in the ISI Web of Science, selecting any article containing the words [Ôextinct*Õ AND (ÔdiseaseÕ OR Ôparasit*Õ OR ÔpathogenÕ)] in the title, abstract or keywords. In total, 336 references were found. References to the coefficient of extinction of some substance (typically in the context of human physiology and medicine), articles that only vaguely mentioned disease as a possible threat for populations, and those referring to the extinction of parasites (rather than hosts) were dropped (260 in total). The remaining articles (76), which are the base of this review, were classified as either theoretical (33) or empirical (43) (some quantitative simulation models of specific hostparasite systems were included in the empirical rather than the theoretical section). We are aware that the so-called Ôgray literatureÕ, not covered by the Web of Science, contains many references on conservation subjects, but we feel confident that our reference base is representative. We have not included cases of...

Trait-mediated interactions (TMIs), in which trophic and competitive interactions depend on individual traits as well as on overall population densities, have inspired large amounts of research, but theoretical and empirical studies have not been well connected. To help mitigate this problem, we review and synthesize the theoretical literature on TMIs and, in particular, on trait-mediated indirect interactions, TMIIs, in which the presence of one species mediates the interaction between a second and third species. (1) In models, TMIs tend to stabilize simple communities; adding further biological detail often reduces stability in models, but populations may persist even if their dynamics become mathematically unstable.(2) Short-and long-term changes in population density caused by TMIs depend even more on details, such as the curvature of functional responses and trade-offs, which have rarely been measured. (3) The effects of TMIs in multipredator communities depend in a straightforward way on the specificity of prey defenses. (4) Tritrophic and more complex communities are theoretically difficult; few general conclusions have emerged. Theory needs new kinds of experiments as a guide. The most critical needs are experiments that measure curvatures of trade-offs and responses, and experiments that (combined with theory) allow us to scale from short-to long-term responses of communities. Anecdotal evidence from long-term and large-scale studies suggests that TMIs may affect community dynamics at practical management scales; community models incorporating TMIs are necessary and require closer collaborations between theory and experiment.

Ecological phenomena are often measured in the form of count data. These data can be analyzed using generalized linear mixed models (GLMMs) 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 standard error distributions used in GLMMs, e.g., parasite counts may be exactly zero for hosts with effective immune defenses but vary according to a negative binomial distribution for non-resistant hosts.We present a new R package, glmmTMB, that increases the range of models that can easily be fitted to count data using maximum likelihood estimation.The interface was developed to be familiar to users of the lme4 R package, a common tool for fitting GLMMs. To maximize speed and flexibility, estimation is done using Template Model Builder (TMB), utilizing automatic differentiation to estimate model gradients and the Laplace approximation for handling random effects. We demonstrate glmmTMB and compare it to other available methods using two ecological case studies.In general, glmmTMB is more flexible than other packages available for esti- . CC-BY-NC 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/132753 doi: bioRxiv preprint first posted online May. 1, 2017; mating zero-inflated models via maximum likelihood estimation and is faster than packages that use Markov chain Monte Carlo sampling for estimation; it is also more flexible for zero-inflated modelling than INLA, but speed comparisons vary with model and data structure. Our package can be used to fit GLMs and GLMMs with or without zero-inflation as well as hurdle models. By allowing ecologists to quickly estimate a wide variety of models using a single package, glmmTMB makes it easier to find appropriate models and test hypotheses to describe ecological processes.

Although spatial patterns of seed distribution are thought to vary greatly among plant species dispersed by different vectors, few studies have directly examined this assumption. We compared patterns of seed rain of nine species of trees disseminated by large birds, monkeys, and wind in a closed canopy forest in Cameroon. We used maximum‐likelihood methods to fit seed rain data to four dispersal functions: inverse power, negative exponential, Gaussian, and Student t. We then tested for differences in dispersal characteristics (1) among individuals within species, and (2) among species dispersed by the same vector. In general, an inverse power function best described animal‐dispersed species and the Gaussian and Student t functions best described wind‐dispersed species. Animal‐dispersed species had longer mean dispersal distances than wind‐dispersed species, but lower fecundities. In addition to these distinct differences in average dispersal distance and functional form of the seed shadow between animal‐ and wind‐dispersed species, seed shadows varied markedly within species and vector, with conspecifics and species within vector varying in their dispersal scale, fecundity, and clumping parameters. Dispersal vectors determine a significant amount of variation in seed distribution, but much variation remains to be explained. Finally, we demonstrate that most seeds, regardless of vector, fall directly under the parent canopy. Long‐distance dispersal events (>60 m) account for a small proportion of the seed crop but may still be important in terms of the absolute numbers of dispersed seeds and effects on population and community dynamics.