Summary: Recently, interest in species distribution modelling has increased following the development of new methods for the analysis of presence‐only data and the deployment of these methods in user‐friendly and powerful computer programs. However, reliable inference from these powerful tools requires that several assumptions be met, including the assumptions that observed presences are the consequence of random or representative sampling and that detectability during sampling does not vary with the covariates that determine occurrence probability. Based on our interactions with researchers using these tools, we hypothesized that many presence‐only studies were ignoring important assumptions of presence‐only modelling. We tested this hypothesis by reviewing 108 articles published between 2008 and 2012 that used the MAXENT algorithm to analyse empirical (i.e. not simulated) data. We chose to focus on these articles because MAXENT has been the most popular algorithm in recent years for analysing presence‐only data. Many articles (87%) were based on data that were likely to suffer from sample selection bias; however, methods to control for sample selection bias were rarely used. In addition, many analyses (36%) discarded absence information by analysing presence–absence data in a presence‐only framework, and few articles (14%) mentioned detection probability. We conclude that there are many misconceptions concerning the use of presence‐only models, including the misunderstanding that MAXENT, and other presence‐only methods, relieve users from the constraints of survey design. In the process of our literature review, we became aware of other factors that raised concerns about the validity of study conclusions. In particular, we observed that 83% of articles studies focused exclusively on model output (i.e. maps) without providing readers with any means to critically examine modelled relationships and that MAXENT's logistic output was frequently (54% of articles) and incorrectly interpreted as occurrence probability. We conclude with a series of recommendations foremost that researchers analyse data in a presence–absence framework whenever possible, because fewer assumptions are required and inferences can be made about clearly defined parameters such as occurrence probability.

Summary: 1. Understanding the factors affecting species occurrence is a pre‐eminent focus of applied ecological research. However, direct information about species occurrence is lacking for many species. Instead, researchers sometimes have to rely on so‐called presence‐only data (i.e. when no direct information about absences is available), which often results from opportunistic, unstructured sampling. maxent is a widely used software program designed to model and map species distribution using presence‐only data.2. We provide a critical review of maxent as applied to species distribution modelling and discuss how it can lead to inferential errors. A chief concern is that maxent produces a number of poorly defined indices that are not directly related to the actual parameter of interest – the probability of occurrence (ψ). This focus on an index was motivated by the belief that it is not possible to estimate ψ from presence‐only data; however, we demonstrate that ψ is identifiable using conventional likelihood methods under the assumptions of random sampling and constant probability of species detection.3. The model is implemented in a convenient r package which we use to apply the model to simulated data and data from the North American Breeding Bird Survey. We demonstrate that maxent produces extreme under‐predictions when compared to estimates produced by logistic regression which uses the full (presence/absence) data set. We note that maxent predictions are extremely sensitive to specification of the background prevalence, which is not objectively estimated using the maxent method.4. As with maxent, formal model‐based inference requires a random sample of presence locations. Many presence‐only data sets, such as those based on museum records and herbarium collections, may not satisfy this assumption. However, when sampling is random, we believe that inference should be based on formal methods that facilitate inference about interpretable ecological quantities instead of vaguely defined indices.

The foundational ecosystem processes of gross primary production (GPP) and ecosystem respiration (ER) cannot be measured directly but can be modeled in aquatic ecosystems from subdaily patterns of oxygen (O₂) concentrations. Because rivers and streams constantly exchange O₂ with the atmosphere, models must either use empirical estimates of the gas exchange rate coefficient (K₆₀₀) or solve for all three parameters (GPP, ER, and K₆₀₀) simultaneously. Empirical measurements of K₆₀₀ require substantial field work and can still be inaccurate. Three‐parameter models have suffered from equifinality, where good fits to O₂ data are achieved by many different parameter values, some unrealistic. We developed a new three‐parameter, multiday model that ensures similar values for K₆₀₀ among days with similar physical conditions (e.g., discharge). Our new model overcomes the equifinality problem by (1) flexibly relating K₆₀₀ to discharge while permitting moderate daily deviations and (2) avoiding the oft‐violated assumption that residuals in O₂ predictions are uncorrelated. We implemented this hierarchical state‐space model and several competitor models in an open‐source R package, streamMetabolizer. We then tested the models against both simulated and field data. Our new model reduces error by as much as 70% in daily estimates of K₆₀₀, GPP, and ER. Further, accuracy benefits of multiday data sets require as few as 3 days of data. This approach facilitates more accurate metabolism estimates for more streams and days, enabling researchers to better quantify carbon fluxes, compare streams by their metabolic regimes, and investigate controls on aquatic activity.

Significance: This paper provides a comprehensive analysis of the annual patterns of ecosystem productivity and respiration for more than 200 rivers, comparing the magnitude and phenology of river metabolic regimes with annual estimates from more than 150 terrestrial ecosystems. Although mean annual temperature and mean annual precipitation explain much of the variation in terrestrial productivity and are used to define biomes, for rivers the most important controls are annual light availability and flow stability. Attention to these gradients will substantially improve our ability to scale and model river ecosystem dynamics and may fundamentally change the way rivers are studied.

Ecologists routinely fit complex models with multiple parameters of interest, where hundreds or more competing models are plausible. To limit the number of fitted models, ecologists often define a model selection strategy composed of a series of stages in which certain features of a model are compared while other features are held constant. Defining these multi‐stage strategies requires making a series of decisions, which may potentially impact inferences, but have not been critically evaluated. We begin by identifying key features of strategies, introducing descriptive terms when they did not already exist in the literature. Strategies differ in how they define and order model building stages. Sequential‐by‐sub‐model strategies focus on one sub‐model (parameter) at a time with modeling of subsequent sub‐models dependent on the selected sub‐model structures from the previous stages. Secondary candidate set strategies model sub‐models independently and combine the top set of models from each sub‐model for selection in a final stage. Build‐up approaches define stages across sub‐models and increase in complexity at each stage. Strategies also differ in how the top set of models is selected in each stage and whether they use null or more complex sub‐model structures for non‐target sub‐models. We tested the performance of different model selection strategies using four data sets and three model types. For each data set, we determined the "true" distribution of AIC weights by fitting all plausible models. Then, we calculated the number of models that would have been fitted and the portion of "true" AIC weight we recovered under different model selection strategies. Sequential‐by‐sub‐model strategies often performed poorly. Based on our results, we recommend using a build‐up or secondary candidate sets, which were more reliable and carrying all models within 5–10 AIC of the top model forward to subsequent stages. The structure of non‐target sub‐models was less important. Multi‐stage approaches cannot compensate for a lack of critical thought in selecting covariates and building models to represent competing a priori hypotheses. However, even when competing hypotheses for different sub‐models are limited, thousands or more models may be possible so strategies to explore candidate model space reliably and efficiently will be necessary.