Detecting population-environmental interactions with mismatched time series data

The relative influence of sea surface temperature anomalies on the benthic composition of an Indo-Pacific and Caribbean coral reef over the last decade

Rising ocean temperatures are the primary driver of coral reef declines throughout the tropics. Such declines include reductions in coral cover that facilitate the monopolization of the benthos by other taxa such as macroalgae, resulting in reduced habitat complexity and biodiversity. Long-term monitoring projects present rare opportunities to assess how sea surface temperature anomalies (SSTAs) influence changes in the benthic composition of coral reefs across distinct locations. Here, using extensively monitored coral reef sites from Honduras (in the Caribbean Sea), and from the Wakatobi National Park located in the center of the coral triangle of Indonesia, we assess the impact of global warming on coral reef benthic compositions over the period 2012-2019. Bayesian generalized linear mixed effect models revealed increases in the sponge, and hard coral coverage through time, while rubble coverage decreased at the Indonesia location. Conversely, the effect of SSTAs did not predict any changes in benthic coverage. At the Honduras location, algae and soft coral coverage increased through time, while hard coral and rock coverage were decreasing. The effects of SSTA at the Honduras location included increased rock coverage, but reduced sponge coverage, indicating disparate responses between both systems under SSTAs. However, redundancy analyses showed intralocation site variability explained the majority of variance in benthic composition over the course of the study period. Our findings show that SSTAs have differentially influenced the benthic composition between the Honduras and the Indonesian coral reefs surveyed in this study. However, the large intralocation variance that explains the benthic composition at both locations indicates that localized processes have a predominant role in explaining benthic composition over the last decade. The sustained monitoring effort is critical for understanding how these reefs will change in their composition as global temperatures continue to rise through the Anthropocene.

Temporal scope influences ecosystem driver-response relationships: A case study of Lake Erie with implications for ecosystem-based management

Understanding environmental driver-response relationships is critical to the implementation of effective ecosystem-based management. Ecosystems are often influenced by multiple drivers that operate on different timescales and may be nonstationary. In turn, contrasting views of ecosystem state and structure could arise depending on the temporal perspective of analysis. Further, assessment of multiple ecosystem components (e.g., biological indicators) may serve to identify different key drivers and connections. To explore how the timescale of analysis and data richness can influence the identification of driver-response relationships within a large, dynamic ecosystem, this study analyzed long-term (1969-2018) data from Lake Erie (USA-Canada). Data were compiled on multiple biological, physical, chemical, and socioeconomic components of the ecosystem to quantify trends and identify potential key drivers during multiple time intervals (20 to 50 years duration), using zooplankton, bird, and fish community metrics as indicators of ecosystem change. Concurrent temporal shifts of many variables occurred during the 1980s, but asynchronous dynamics were evident among indicator taxa. The strengths and rank orders of predictive drivers shifted among intervals and were sometimes taxon-specific. Drivers related to nutrient loading and lake trophic status were consistently strong predictors of temporal patterns for all indicators; however, within the longer intervals, measures of agricultural land use were the strongest predictors, whereas within shorter intervals, the stronger predictors were measures of tributary or in-lake nutrient concentrations. Physical drivers also tended to increase in predictive ability within shorter intervals. The results highlight how the time interval examined can filter influences of lower-frequency, slower drivers and higher-frequency, faster drivers. Understanding ecosystem change in support of ecosystem-based management requires consideration of both the temporal perspective of analysis and the chosen indicators, as both can influence which drivers are identified as most predictive of ecosystem trends at that timescale.

A practical guide to selecting models for exploration, inference, and prediction in ecology

Selecting among competing statistical models is a core challenge in science. However, the many possible approaches and techniques for model selection, and the conflicting recommendations for their use, can be confusing. We contend that much confusion surrounding statistical model selection results from failing to first clearly specify the purpose of the analysis. We argue that there are three distinct goals for statistical modeling in ecology: data exploration, inference, and prediction. Once the modeling goal is clearly articulated, an appropriate model selection procedure is easier to identify. We review model selection approaches and highlight their strengths and weaknesses relative to each of the three modeling goals. We then present examples of modeling for exploration, inference, and prediction using a time series of butterfly population counts. These show how a model selection approach flows naturally from the modeling goal, leading to different models selected for different purposes, even with exactly the same data set. This review illustrates best practices for ecologists and should serve as a reminder that statistical recipes cannot substitute for critical thinking or for the use of independent data to test hypotheses and validate predictions.

Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities

Over the past two decades, there have been numerous calls to make ecology a more predictive science through direct empirical assessments of ecological models and predictions. While the widespread use of model selection using information criteria has pushed ecology toward placing a higher emphasis on prediction, few attempts have been made to validate the ability of information criteria to correctly identify the most parsimonious model with the greatest predictive accuracy. Here, we used an ecological forecasting framework to test the ability of information criteria to accurately predict the relative contribution of density dependence and density-independent factors (forage availability, harvest, weather, wolf [Canis lupus] density) on inter-annual fluctuations in beaver (Castor canadensis) colony densities. We modeled changes in colony densities using a discrete-time Gompertz model, and assessed the performance of four models using information criteria values: density-independent models with (1) and without (2) environmental covariates; and density-dependent models with (3) and without (4) environmental covariates. We then evaluated the forecasting accuracy of each model by withholding the final one-third of observations from each population and compared observed vs. predicted densities. Information criteria and our forecasting accuracy metrics both provided strong evidence of compensatory density dependence in the annual dynamics of beaver colony densities. However, despite strong within-sample performance by the most complex model (density-dependent with covariates) as determined using information criteria, hindcasts of colony densities revealed that the much simpler density-dependent model without covariates performed nearly as well predicting out-of-sample colony densities. The hindcast results indicated that the complex model over-fit our data, suggesting that parameters identified by information criteria as important predictor variables are only marginally valuable for predicting landscape-scale beaver colony dynamics. Our study demonstrates the importance of evaluating ecological models and predictions with long-term data and revealed how a known limitation of information criteria (over-fitting of complex models) can affect our interpretation of ecological dynamics. While incorporating knowledge of the factors that influence animal population dynamics can improve population forecasts, we suggest that comparing forecast performance metrics can likewise improve our knowledge of the factors driving population dynamics.

Improving inference for nonlinear state-space models of animal population dynamics given biased sequential life stage data

State‐space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage‐structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage‐structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near‐zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (a) the need for relevant process covariates and (b) the benefits of using externally estimated observation variances for inference about nonlinear stage‐structured SSMs.

Cumulative weather effects can impact across the whole life cycle

Predicting how species will be affected by future climatic change requires the underlying environmental drivers to be identified. As vital rates vary over the lifecycle, structured population models derived from statistical environment-demography relationships are often used to inform such predictions. Environmental drivers are typically identified independently for different vital rates and demographic classes. However, these rates often exhibit positive temporal covariance, suggesting that vital rates respond to common environmental drivers. Additionally, models often only incorporate average weather conditions during a single, a priori chosen time window (e.g. monthly means). Mismatches between these windows and the period when the vital rates are sensitive to variation in climate decrease the predictive performance of such approaches. We used a demographic structural equation model (SEM) to demonstrate that a single axis of environmental variation drives the majority of the (co)variation in survival, reproduction, and twinning across six age-sex classes in a Soay sheep population. This axis provides a simple target for the complex task of identifying the drivers of vital rate variation. We used functional linear models (FLMs) to determine the critical windows of three local climatic drivers, allowing the magnitude and direction of the climate effects to differ over time. Previously unidentified lagged climatic effects were detected in this well-studied population. The FLMs had a better predictive performance than selecting a critical window a priori, but not than a large-scale climate index. Positive covariance amongst vital rates and temporal variation in the effects of environmental drivers are common, suggesting our SEM-FLM approach is a widely applicable tool for exploring the joint responses of vital rates to environmental change.

Surviving drought: a framework for understanding animal responses to small rain events in the arid zone

Large rain events drive dramatic resource pulses and the complex pulse-reserve dynamics of arid ecosystems change between high-rain years and drought. However, arid-zone animal responses to short-term changes in climate are unknown, particularly smaller rain events that briefly interrupt longer-term drought. Using arthropods as model animals, we determined the effects of a small rain event on arthropod abundance in western New South Wales, Australia during a longer-term shift toward drought. Arthropod abundance decreased over 2 yr, but captures of 10 out of 15 ordinal taxa increased dramatically after the small rain event (<40 mm). The magnitude of increases ranged from 10.4 million% (collembolans) to 81% (spiders). After 3 months, most taxa returned to prerain abundance. However, small soil-dwelling beetles, mites, spiders, and collembolans retained high abundances despite the onset of winter temperatures and lack of subsequent rain. As predicted by pulse-reserve models, most arid-zone arthropod populations declined during drought. However, small rain events may play a role in buffering some taxa from declines during longer-term drought or other xenobiotic influences. We outline the framework for a new model of animal responses to environmental conditions in the arid zone, as some species clearly benefit from rain inputs that do not dramatically influence primary productivity.

Filling in the gaps in survival analysis: using field data to infer plant responses to environmental stressors

Elucidating how organismal survival depends on the environment is a core component of ecological and evolutionary research. To reconcile high-frequency covariates with lower-frequency demographic censuses, many statistical tools involve aggregating environmental conditions over long periods, potentially obscuring the importance of fluctuating conditions in driving mortality. Here, we introduce a flexible model designed to infer how survival probabilities depend on changing environmental covariates. Specifically, the model (1) quantifies effects of environmental covariates at a higher frequency than the census intervals, and (2) allows partitioning of environmental drivers of individual survival into acute (short-term) and chronic (accumulated) effects. By applying our method to a long-term observational data set of eight annual plant species, we show we can accurately infer daily survival probabilities as temperature and moisture levels change. Next, we show that a species' water use efficiency, known to mediate annual plant population dynamics, is positively correlated with the importance of "chronic stress" inferred by the model. This suggests that model parameters can reflect underlying physiological mechanisms. This method is also applicable to other binary responses (hatching, phenology) or systems (insects, nestlings). Once known, environmental sensitivities can be used for ecological forecasting even when the frequency or variability of environments are changing.