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Faced with limitations in data availability, funding, and time constraints, ecologists are often tasked with making predictions beyond the range of their data. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We propose using the trace or determinant of the predictive variance matrix to obtain a scalar value measure that, when paired with a selected cutoff value, allows for delineation between prediction and extrapolation. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we outline novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees. The use of our Multivariate Predictive Variance (MVPV) measures and multiple cutoff values when exploring the validity of predictions made from multivariate statistical models can help guide ecological inferences. [ABSTRACT FROM AUTHOR]

Scientific research—especially high-impact research—is increasingly being performed in teams that are interdisciplinary and demographically diverse. Nevertheless, very little research has investigated how the climate on these diverse science teams affects data sharing or the experiences of their members. To address these gaps, we conducted a quantitative study of 266 scientists from 105 NSF-funded interdisciplinary environmental science teams. We examined how team climate mediates the associations between team diversity and three outcomes: satisfaction with the team, satisfaction with authorship practices, and perceptions of the frequency of data sharing. Using path analyses, we found that individuals from underrepresented groups perceived team climate more negatively, which was associated with lower satisfaction with the team and more negative perceptions of authorship practices and data sharing on the team. However, individuals on teams with more demographic diversity reported a more positive climate than those on teams with less demographic diversity. These results highlight the importance of team climate, the value of diverse teams for team climate, and barriers to the full inclusion and support of individuals from underrepresented groups in interdisciplinary science teams. [ABSTRACT FROM AUTHOR]

The nutrient-water color paradigm is a framework to characterize lake trophic status by relating lake primary productivity to both nutrients and water color, the colored component of dissolved organic carbon. Total phosphorus (TP), a limiting nutrient, and water color, a strong light attenuator, influence lake chlorophyll a concentrations (CHL). But, these relationships have been shown in previous studies to be highly variable, which may be related to differences in lake and catchment geomorphology, the forms of nutrients and carbon entering the system, and lake community composition. Because many of these factors vary across space it is likely that lake nutrient and water color relationships with CHL exhibit spatial autocorrelation, such that lakes near one another have similar relationships compared to lakes further away. Including this spatial dependency in models may improve CHL predictions and clarify how well the nutrient-water color paradigm applies to lakes distributed across diverse landscape settings. However, few studies have explicitly examined spatial heterogeneity in the effects of TP and water color together on lake CHL. In this study, we examined spatial variation in TP and water color relationships with CHL in over 800 north temperate lakes using spatially-varying coefficient models (SVC), a robust statistical method that applies a Bayesian framework to explore space-varying and scale-dependent relationships. We found that TP and water color relationships were spatially autocorrelated and that allowing for these relationships to vary by individual lakes over space improved the model fit and predictive performance as compared to models that did not vary over space. The magnitudes of TP effects on CHL differed across lakes such that a 1 μg/L increase in TP resulted in increased CHL ranging from 2–24 μg/L across lake locations. Water color was not related to CHL for the majority of lakes, but there were some locations where water color had a positive effect such that a unit increase in water color resulted in a 2 μg/L increase in CHL and other locations where it had a negative effect such that a unit increase in water color resulted in a 2 μg/L decrease in CHL. In addition, the spatial scales that captured variation in TP and water color effects were different for our study lakes. Variation in TP–CHL relationships was observed at intermediate distances (~20 km) compared to variation in water color–CHL relationships that was observed at regional distances (~200 km). These results demonstrate that there are lake-to-lake differences in the effects of TP and water color on lake CHL and that this variation is spatially structured. Quantifying spatial structure in these relationships furthers our understanding of the variability in these relationships at macroscales and would improve model prediction of chlorophyll a to better meet lake management goals. [ABSTRACT FROM AUTHOR]

Catchment land uses, particularly agriculture and urban uses, have long been recognized as major drivers of nutrient concentrations in surface waters. However, few simple models have been developed that relate the amount of catchment land use to downstream freshwater nutrients. Nor are existing models applicable to large numbers of freshwaters across broad spatial extents such as regions or continents. This research aims to increase model performance by exploring three factors that affect the relationship between land use and downstream nutrients in freshwater: the spatial extent for measuring land use, hydrologic connectivity, and the regional differences in both the amount of nutrients and effects of land use on them. We quantified the effects of these three factors that relate land use to lake total phosphorus (TP) and total nitrogen (TN) in 346 north temperate lakes in 7 regions in Michigan, USA. We used a linear mixed modeling framework to examine the importance of spatial extent, lake hydrologic class, and region on models with individual lake nutrients as the response variable, and individual land use types as the predictor variables. Our modeling approach was chosen to avoid problems of multi-collinearity among predictor variables and a lack of independence of lakes within regions, both of which are common problems in broad-scale analyses of freshwaters. We found that all three factors influence land use-lake nutrient relationships. The strongest evidence was for the effect of lake hydrologic connectivity, followed by region, and finally, the spatial extent of land use measurements. Incorporating these three factors into relatively simple models of land use effects on lake nutrients should help to improve predictions and understanding of land use-lake nutrient interactions at broad scales. [ABSTRACT FROM AUTHOR]

Agent-based models (ABMs) have been widely used to study socioecological systems. They are useful for studying such systems because of their ability to incorporate micro-level behaviors among interacting agents, and to understand emergent phenomena due to these interactions. However, ABMs are inherently stochastic and require proper handling of uncertainty. We propose a simulation framework based on quantitative uncertainty and sensitivity analyses to build parsimonious ABMs that serve two purposes: exploration of the outcome space to simulate low-probability but high-consequence events that may have significant policy implications, and explanation of model behavior to describe the system with higher accuracy. The proposed framework is applied to the problem of modeling farmland conservation resulting in land use change. We employ output variance decomposition based on quasi-random sampling of the input space and perform three computational experiments. First, we perform uncertainty analysis to improve model legitimacy, where the distribution of results informs us about the expected value that can be validated against independent data, and provides information on the variance around this mean as well as the extreme results. In our last two computational experiments, we employ sensitivity analysis to produce two simpler versions of the ABM. First, input space is reduced only to inputs that produced the variance of the initial ABM, resulting in a model with output distribution similar to the initial model. Second, we refine the value of the most influential input, producing a model that maintains the mean of the output of initial ABM but with less spread. These simplifications can be used to 1) efficiently explore model outcomes, including outliers that may be important considerations in the design of robust policies, and 2) conduct explanatory analysis that exposes the smallest number of inputs influencing the steady state of the modeled system. [ABSTRACT FROM AUTHOR]