Mevin B. Hooten

A guide to Bayesian model selection for ecologists

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

On the use of log‐transformation vs. nonlinear regression for analyzing biological power laws

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.

Clonal dynamics in western North American aspen (Populus tremuloides)

Clonality is a common phenomenon in plants, allowing genets to persist asexually for much longer periods of time than ramets. The relative frequency of sexual vs. asexual reproduction determines long‐term dominance and persistence of clonal plants at the landscape scale. One of the most familiar and valued clonal plants in North America is aspen (Populus tremuloides). Previous researchers have suggested that aspen in xeric landscapes of the intermountain west represent genets of great chronological age, maintained via clonal expansion in the near absence of sexual reproduction. We synthesized microsatellite data from 1371 ramets in two large sampling grids in Utah. We found a surprisingly large number of distinct genets, some covering large spatial areas, but most represented by only one to a few individual ramets at a sampling scale of 50 m. In general, multi‐ramet genets were spatially cohesive, although some genets appear to be fragmented remnants of much larger clones. We conclude that recent sexual reproduction in these landscapes is a stronger contributor to standing genetic variation at the population level than the accumulation of somatic mutations, and that even some of the spatially large clones may not be as ancient as previously supposed. Further, a striking majority of the largest genets in both study areas had three alleles at one or more loci, suggesting triploidy or aneuploidy. These genets tended to be spatially clustered but not closely related. Together, these findings substantially advance our understanding of clonal dynamics in western North American aspen, and set the stage for a broad range of future studies.

Practical guidance on characterizing availability in resource selection functions under a use-availability design

Habitat selection is a fundamental aspect of animal ecology, the understanding of which is critical to management and conservation. Global positioning system data from animals allow fine-scale assessments of habitat selection and typically are analyzed in a use availability framework, whereby animal locations are contrasted with random locations (the availability sample). Although most use-availability methods are in fact spatial point process models, they often are fit using logistic regression. This framework offers numerous methodological challenges, for which the literature provides little guidance. Specifically, the size and spatial extent of the availability sample influences coefficient estimates potentially causing interpretational bias. We examined the influence of availability on statistical inference through simulations and analysis of serially correlated mule deer GPS data. Bias in estimates arose from incorrectly assessing and sampling the spatial extent of availability. Spatial autocorrelation in covariates, which is common for landscape characteristics, exacerbated the error in availability sampling leading to increased bias. These results have strong implications for habitat selection analyses using GPS data, which are increasingly prevalent in the literature. We recommend that researchers assess the sensitivity of their results to their availability sample and, where bias is likely, take care with interpretations and use cross validation to assess robustness.

Spatial occupancy models for large data sets

Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence–absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Com...

Climate influences the demography of three dominant sagebrush steppe plants

Climate change could alter the population growth of dominant species, leading to profound effects on community structure and ecosystem dynamics. Understanding the links between historical variation in climate and population vital rates (survival, growth, recruitment) is one way to predict the impact of future climate change. Using a unique, long-term data set from eastern Idaho, USA, we parameterized integral projection models (IPMs) for Pseudoroegneria spicata, Hesperostipa comata, and Artemisia tripartita to identify the demographic rates and climate variables most important for population growth. We described survival, growth, and recruitment as a function of genet size using mixed-effect regression models that incorporated climate variables. Elasticites for the survival + growth portion of the kernel were larger than the recruitment portion for all three species, with survival + growth accounting for 87-95% of the total elasticity. The genet sizes with the highest elasticity values in each species were very close to the genet size threshold where survival approached 100%. We found strong effects of climate on the population growth rate of two of our three species. In H. comata, a 1% decrease in previous years precipitation would lead to a 0.6% decrease in population growth. In A. tripartita, a 1% increase in summer temperature would result in a 1.3% increase in population growth. In both H. comata and A. tripartita, climate influenced population growth by affecting genet growth more than survival or recruitment. Late-winter snow was the most important climate variable for P. spicata, but its effect on population growth was smaller than the climate effects we found in H. comata or A. tripartita. For all three species, demographic responses lagged climate by at least one year. Our analysis indicates that understanding climate effects on genet growth may be crucial for anticipating future changes in the structure and function of sagebrush steppe vegetation.

Predicting the spatial distribution of ground flora on large domains using a hierarchical Bayesian model

Accomodation of important sources of uncertainty in ecological models is essential to realistically predicting ecological processes. The purpose of this project is to develop a robust methodology for modeling natural processes on a landscape while accounting for the variability in a process by utilizing environmental and spatial random effects. A hierarchical Bayesian framework has allowed the simultaneous integration of these effects. This framework naturally assumes variables to be random and the posterior distribution of the model provides probabilistic information about the process. Two species in the genus Desmodium were used as examples to illustrate the utility of the model in Southeast Missouri, USA. In addition, two validation techniques were applied to evaluate the qualitative and quantitative characteristics of the predictions.

Statistical Agent-Based Models for Discrete Spatio-Temporal Systems

Agent-based models have been used to mimic natural processes in a variety of fields, from biology to social science. By specifying mechanistic models that describe how small-scale processes function and then scaling them up, agent-based approaches can result in very complicated large-scale behavior while often relying on only a small set of initial conditions and intuitive rules. Although many agent-based models are used strictly in a simulation context, statistical implementations are less common. To characterize complex dynamic processes, such as the spread of epidemics, we present a hierarchical Bayesian framework for formal statistical agent-based modeling using spatiotemporal binary data. Our approach is based on an intuitive parameterization of the system dynamics and can explicitly accommodate directionally varying dispersal, long distance dispersal, and spatial heterogeneity.

Velocity-Based Movement Modeling for Individual and Population Level Inference

Understanding animal movement and resource selection provides important information about the ecology of the animal, but an animals movement and behavior are not typically constant in time. We present a velocity-based approach for modeling animal movement in space and time that allows for temporal heterogeneity in an animals response to the environment, allows for temporal irregularity in telemetry data, and accounts for the uncertainty in the location information. Population-level inference on movement patterns and resource selection can then be made through cluster analysis of the parameters related to movement and behavior. We illustrate this approach through a study of northern fur seal (Callorhinus ursinus) movement in the Bering Sea, Alaska, USA. Results show sex differentiation, with female northern fur seals exhibiting stronger response to environmental variables.

When to be discrete: the importance of time formulation in understanding animal movement

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.