The use of species distribution models (SDMs) has rapidly increased over the last decade, driven largely by increasing observational evidence of distributional shifts of terrestrial and aquatic populations. These models permit, for example, the quantification of range shifts, the estimation of species co-occurrence, and the association of habitat to species distribution and abundance. The increasing complexity of contemporary SDMs presents new challenges—as the choices among modeling options increase, it is essential to understand how these choices affect model outcomes. Using a combination of original analysis and literature review, we synthesize the effects of three common model choices in semi-parametric predictive process species distribution modeling: model structure, spatial extent of the data, and spatial scale of predictions. To illustrate the effects of these choices, we develop a case study centered around sablefish (

Human-induced global climate change and other anthropogenic activities are transforming ecosystems (

Species distribution models (hereafter SDMs, but also known by their special cases as ecological niche models, occupancy models, or climate envelope models) in conjunction with climate and ocean models are the primary tools for describing past and current species distributions, determining the drivers of these patterns, and forecasting distribution shifts. There are a wide range of SDM approaches, including maximum entropy (

The use of SDMs in scientific literature has greatly increased in the past few decades (

While a number of papers have explored key challenges relating to the SDM process (including

For very large datasets, the Gaussian predictive process model may still lead to undesirable results, because while using a smaller number of knots may be computationally efficient, reducing the dimensionality too much will over smooth predictions of the spatial field. An alternative framework for high dimensional spatiotemporal models includes the Integrated Nested Laplace Approximation (INLA,

Given the rise of spatially explicit predictive process models in marine sciences and ecology over the last decade, there is a great need to understand how specific model choices affect inference. In addition to inference about parameters used to describe the spatial field, inference about derived quantities can be important for natural resource management. Within the context of fisheries for example, generating abundance indices that are accurate and precise is critical because these are a key fishery-independent data source for population assessment models used to determine conservation status and set exploitation rates (

The objective of this paper is to quantify the impact of three common decision points in these types of models (

Species distribution models require spatially referenced data, but the way in which space is represented varies among modeling approaches (data may consist of observations in spatial blocks, or observations may be associated with continuous locations in one or more dimensions). Here we focus on models that take geostatistical data as input. Geostatistical data may be collected during a single point in time, providing a snapshot of distributions, or they may be repeated at some regular interval (

As an example case study to illustrate the effect of model choices throughout this paper, we analyze a publicly available dataset of sablefish catch rates from scientific surveys in the Northeast Pacific Ocean. We chose sablefish as a representative of the commercially important groundfish community in the region because it is common and broadly distributed throughout the region (United States and Canadian waters) but also exhibits interannual variability, as well as a prominent environmental gradient in population density (with depth). The association with depth is largely ontogenetic; sablefish are long-lived predators that gradually move deeper with age and are most common along the continental slope (reviewed in

To develop a spatiotemporal model of sablefish, we constructed a model that can be seen as an extension of generalized linear mixed-effects models (GLMM), allowing for inclusion of both fixed and random effects. To ease in interpretation, we decompose total spatial variation into two components: a spatial field (a spatial process that is constant over time) and spatiotemporal fields (spatial variation that is unique to each time step). This approach has been widely used, especially in the context of estimating species’ densities, and has been shown to increase precision of estimated trends (

The generic spatiotemporal GLMM can be written as:

where

For the application of SDMs to sablefish throughout this paper, we decided

Several recent advances have allowed for maximum likelihood estimation to be done using Template Model Builder (

A common goal of predictive process SDMs, like any other statistical model, is to identify model features that improve predictive ability. Widely used model selection tools, like AIC, are computationally convenient—but not wholly appropriate for mixed effects models (

Given the spatiotemporal GLMM described above, we focused on the following three model choices that contribute to inference on parameters and derived quantities: (1) structure of the model, including covariate selection and treatment of spatiotemporal components, (2) spatial extent of data used for fitting, and (3) spatial resolution of predictions. To demonstrate the sensitivity to model resolution, we highlight how such a choice influences trends and scale of total population biomass estimates, derived from model predictions. We focus on biomass estimates (calculated as the sum of the local population densities extrapolated to the resolution of the prediction surface) here because this is a commonly used output of SDMs for population management (

Similar to choosing a response distribution for non-spatial models (^{2} swept by the sampling gear) since it has been shown to perform well in previous applications to such data (

The choice of response type and model structure should be informed by the data properties (

Evaluating the fit of predictive process SDMs and validating assumptions about structure involves considerations that are shared among many statistical models, but also includes others that are specific to—or particularly important for—spatial or spatiotemporal modeling. Examples of diagnostics for SDMs include the analysis of temporal or spatial autocorrelation in residuals (

As a demonstration of evaluating model structure in the sablefish case study, we performed a model comparison among four predictive process SDMs with different spatiotemporal processes. These models included (1) a model with only a spatial component and a covariate of depth, (2) spatiotemporal components that were independent and identically distributed over time

How far to extend the geographic domain of the model or range of predictions relative to the extent of observations is highly dependent on the application (

In addition to making choices about the prediction grid, some applications of SDM predictive process models may also filter observations or restrict data prior to fitting. Filtering data may be needed in situations where the spatial domain of survey sampling varies year to year, but inference is about population change through time (using a subset of observations with a shared domain may be more appropriate). In other cases, it may be prudent to exclude observations that are thought to be beyond the species’ range (

A number of factors may affect the spatial resolution of predictions (

Beyond accuracy, another critical part of the predictive surface resolution decision point is consideration of the research objective. For example, in a study by

For our case study of sablefish, we constrained the prediction grid to the same spatial resolution as the survey sampling frame (

Our evaluation of whether spatiotemporal effects are supported for modeling sablefish, and what form they should take if included, demonstrated that the model with the depth covariate and without any spatiotemporal components (model 1) had the highest predictive ability (

All models include year as a fixed effect and spatial random effects. Five-fold cross validation was used to estimate the out-of-sample predictive density for each fold.

Model | Spatiotemporal effects | Covariates | Log density |
---|---|---|---|

1 | – | depth, year | −68,301.36 |

2 | IID | depth, year | −76,008.62 |

3 | AR(1) | depth, year | −76,061.14 |

4 | – | year | −82,156.34 |

Estimates of total population biomass and mean distribution (measured as the center of gravity or COG) differed between models with the best and worst out-of-sample predictive skill. Biomass estimates from the best model (model 1, including a spatial field and fixed effects of year and depth) were generally lower than estimates from the worst model (model 4, with the same structure as model 1 but without the depth covariate), with the exception of the first year of the time series where they were approximately equal (

Points are COG and lines are 95% confidence intervals of Northings and Eastings (km).

Biomass estimates were somewhat sensitive to the spatial extent of the data included in the model fit, with the greatest contrast in estimates being between model fits using data from the full domain as opposed to any level of truncation at the northern and southern domain limits (

Estimates of the mean spatial distribution (indicated by the COG) were more sensitive to the spatial extent of data included than were biomass estimates. Greater extents of data filtering at the domain edge led to COG estimates that were much less precise and located further southeast compared to those with lesser extents of filtering (

Points are COG and lines are 95% confidence intervals of Northings and Eastings (km).

The scale of the prediction surface produced nuanced effects on predicted population densities in space. Comparing the SDM predictions in each grid cell from the fine scale prediction surface resolution (made at the same resolution as observed data) and coarse prediction surface (4× resolution) in space revealed the largest sensitivity to prediction scale occurred along the continental shelf and shelf break (~50–200 m depth), whereas deeper locations along the continental slope were less sensitive to prediction resolution (

Positive values (red) indicate higher predicted population density by the fine-resolution model and negative values (blue) indicate higher predicted density by the coarse-resolution model. Contour lines denote the 200 m isobath, which approximates the boundary between the continental shelf and slope.

Despite the apparent differences in local population densities, estimates of biomass and COG derived from these predictions had low sensitivity to the choice of prediction scale. Biomass estimates were not sensitive to the choice of prediction scale, as relative biomass estimates and their uncertainty were similar among prediction resolutions (

Points are COG and lines are 95% confidence intervals of Northings and Eastings (km).

In light of theoretical considerations, lessons learned from the literature, and illustrations through a worked example, we show how certain steps in the SDM process are key decision points influencing results and interpretation of SDMs. Though our focus is on spatial semi-parametric models, these choices are applicable to a variety of other SDM models:

Model family and structure: It is important to choose the appropriate model family and structure to be well-suited for the study species and the hypothesized underlying mechanisms that explain the species’ spatiotemporal patterns. Appropriate model structure need not involve throwing everything at the problem (

Spatial extent of data and predictions: The spatial extent of data and predictions is highly dependent on the application of the SDM, but it is important to be mindful of the potential impact of data filtering and extrapolation of predictions on model outputs.

Spatial resolution of predictions: The spatial resolution of predictions should align with the research objective, but also typically be no finer than the scale of the sampling unit of the survey design.

Our case study application to sablefish illustrates that two of the three sensitivities (model structure and spatial domain of data used for the estimation) impact estimates of biomass trends and mean spatial distribution. While other studies have noted that the choice of prediction surface resolution is a critical decision that can affect precision and accuracy of predictions (

Seemingly minor decisions in the development of SDMs can influence the interpretation of model outputs used to inform conservation and management of fish and wildlife. From our sablefish example, filtering the observations in the model based on their spatial extent or use of an incorrect model structure could lead to the conclusion that the stock is more abundant than it truly is in many years, which could lead to catch recommendations that are too high. In addition, such oversights could lead to the inference that the population is distributed further southeast than it actually is. The potential influence of such deviations on expected management performance depends on the type of natural resource decision. For example, while fisheries management is becoming more spatial over time, spatial information or shifts are still rarely incorporated into stock assessment models (

Species distribution modeling decisions affecting abundance index scale (

In the context of wildlife management and conservation, the reliability of predicted species distributions is perhaps just as critical to management performance as abundance estimates, thus modeling choices affecting indicators of change in core and limits of distributions can be highly influential. For example, erroneous estimates of the distribution of habitat suitability or population density could lead to failure by misrepresenting the benefits of habitat restoration or managed relocation by overestimating the carrying capacity of restored areas relative to current population densities (

There are a number of frontiers in SDM development and exploration that warrant further examination:

Spatiotemporal scales: We urge further development of methods for determining appropriate spatial and temporal scales at which to model relationships between responses and predictors, building on studies aimed at evaluating non-local or landscape effects on species distributions (

Computational: An ongoing frontier in SDM development is computational speed and efficiency. Further development of methods, such as Bayesian sampling approaches (

Data assimilation: Exploring methods for combining multiple data sources (

Improving projections and quantifying predictive performance: Because of the impacts of climate change, the importance of predicting population responses to novel environments and conditions will only increase. Therefore, further exploration of this topic (

Tailoring approaches to specific management applications: Finer-scale analyses of population density like those in this study can help detect or predict local depletion that may otherwise be obscured by coarse-scale or non-spatial resource assessment methods. This is becoming particularly important for managers performing scenario planning of socio-ecological impacts of climate-driven species distribution shifts, as such issues are often lost in the mismatch between scales of climate prediction, regional management, and ecological processes (

Multi-species distribution models: Species distribution models typically do not explicitly model species interactions, but these relationships greatly shape species distributions (

We acknowledge the NOAA NWFSC FRAM Fisheries Research Survey Team and commercial captains and crew on the US West Coast Groundfish Bottom Trawl Survey for collecting the data used in our case study. We also thank the members of the NOAA Fisheries and the Environment (FATE) Spatial Indicator Working Group for discussions that helped conceive the project, and we thank Kristin Marshall and two anonymous reviewers for feedback on an earlier version of this manuscript.

The authors declare that they have no competing interests.

The following information was supplied regarding data availability:

Additional modeling details and code to replicate analyses are available at GitHub: