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Due to the high dimensional integration over latent variables, computing marginal likelihood and posterior distributions for the parameters of a general hierarchical model is a difficult task. The Markov Chain Monte Carlo (MCMC) algorithms are commonly used to approximate the posterior distributions. These algorithms, though effective, are computationally intensive and can be slow for large, complex models. As an alternative to the MCMC approach, the Laplace approximation (LA) has been successfully used to obtain fast and accurate approximations to the posterior mean and other derived quantities related to the posterior distribution. In the last couple of decades, LA has also been used to approximate the marginal likelihood function and the posterior distribution. In this paper, we show that the bias in the Laplace approximation to the marginal likelihood has substantial practical consequences. 

Understanding how populations respond to increasingly variable conditions is a major objective for natural resource managers forecasting extinction risk. The lesson from current modelling is clear: increasing environmental variability increases population abundance variability. We show that this paradigm fails to describe a broad class of empirically observed dynamics, namely endogenously driven population cycles. In contrast to the dominant paradigm, these populations can exhibit reduced long-run population variance under increasing environmental variability. We provide evidence for a mechanistic explanation of this phenomenon that relies on how stochasticity interacts with long transient dynamics present in the deterministic cycling model. This interaction stands in contrast to the often assumed additivity of stochastic and deterministic drivers of population fluctuations. We show evidence for the phenomenon in two cyclical populations: flour beetles and Canadian lynx. We quantify the impact of the phenomenon with new theory that partitions the effects of nonlinear dynamics and stochastic variation on dynamical systems. In both empirical examples, the partitioning shows that the interaction between deterministic and stochastic dynamics reduces the variance in population size. Our results highlight that previous predictions about extinction under environmental variability may prove inadequate to understand the effects of climate change in some populations. 

A substantial body of literature reports that ctenophores exhibit an apparently unique life history characterized by biphasic sexual reproduction, the first phase of which is called larval reproduction or dissogeny. Whether this strategy is plastically deployed or a typical part of these species’ life history was unknown. In contrast to previous reports, we show that the ctenophore Mnemiopsis leidyi does not have separate phases of early and adult reproduction, regardless of the morphological transition to what has been considered the adult form. Rather, these ctenophores begin to reproduce at a small body size and spawn continuously from this point onward under adequate environmental conditions. They do not display a gap in productivity for metamorphosis or other physiological transition at a certain body size. Furthermore, nutritional and environmental constraints on fecundity are similar in both small and large animals. Our results provide critical parameters for understanding resource partitioning between growth and reproduction in this taxon, with implications for management of this species in its invaded range. Finally, we report an observation of similarly small-size spawning in a beroid ctenophore, which is morphologically, ecologically, and phylogenetically distinct from other ctenophores reported to spawn at small sizes. We conclude that spawning at small body size should be considered as the default, on-time developmental trajectory rather than as precocious, stress-induced, or otherwise unusual for ctenophores. The ancestral ctenophore was likely a direct developer, consistent with the hypothesis that multiphasic life cycles were introduced after the divergence of the ctenophore lineage. 

Moss-associated N2 fixation provides a substantial but heterogeneous input of new N to nutrient-limited ecosystems at high latitudes. In spite of the broad diversity of mosses found in boreal and Arctic ecosystems, the extent to which host moss identity drives variation in N2 fixation rates remains largely undetermined. We used 15N2 incubations to quantify the fixation rates associated with 34 moss species from 24 sites ranging from 60° to 68° N in Alaska, USA. Remarkably, all sampled moss genera fixed N2, including well-studied feather and peat mosses and genera such as Tomentypnum, Dicranum, and Polytrichum. The total moss-associated N2 fixation rates ranged from almost zero to 3.2 mg N m−2 d−1, with an average of 0.8 mg N m−2 d−1, based on abundance-weighted averages of all mosses summed for each site. Random forest models indicated that moss taxonomic family was a better predictor of rate variation across Alaska than any of the measured environmental factors, including site, pH, tree density, and mean annual precipitation and temperature. Consistent with this finding, mixed models showed that trends in N2 fixation rates among moss genera were consistent across biomes. We also found “hotspots” of high fixation rates in one-fourth of sampled sites. Our results demonstrated the importance of moss identity in influencing N2 fixation rates. This in turn indicates the potential utility of moss identity when making ecosystem N input predictions and exploring other sources of process rate variation. 

Bacillus anthracis , the etiological agent of anthrax, is a well-established model organism. For B. anthracis and most other infectious diseases, knowledge regarding transmission and infection parameters in natural systems, in large part, comprises data gathered from closely controlled laboratory experiments. Fatal, natural anthrax infections transmit the bacterium through new host−pathogen contacts at carcass sites, which can occur years after death of the previous host. For the period between contact and death, all of our knowledge is based upon experimental data from domestic livestock and laboratory animals. Here we use a noninvasive method to explore the dynamics of anthrax infections, by evaluating the terminal diversity of B. anthracis in anthrax carcasses. We present an application of population genetics theory, specifically, coalescence modeling, to intrainfection populations of B. anthracis to derive estimates for the duration of the acute phase of the infection and effective population size converted to the number of colony-forming units establishing infection in wild plains zebra ( Equus quagga ). Founding populations are small, a few colony-forming units, and infections are rapid, lasting roughly between 1 d and 3 d in the wild. Our results closely reflect experimental data, showing that small founding populations progress acutely, killing the host within days. We believe this method is amendable to other bacterial diseases from wild, domestic, and human systems.