Joint inference for telemetry and spatial survey data.

Data integration, the joint statistical analysis of data from different observation platforms, is pivotal for data-hungry disciplines such as spatial ecology. Pooled data types obtained from the same underlying process, analyzed jointly, can improve both precision and accuracy in models of species distributions and species-habitat associations. However, the integration of telemetry and spatial survey data has proved elusive because of the fundamentally different analytical approaches required by these two data types. Here, "spatial survey" denotes a survey that records spatial locations and has no temporal structure, for example, line or point transects but not capture-recapture or telemetry. Step selection functions (SSFs-the canonical framework for telemetry) and habitat selection functions (HSFs-the default approach to spatial surveys) differ in not only their specifications but also their results. By imposing the constraint that microscopic mechanisms (animal movement) must correctly scale up to macroscopic emergence (population distributions), a relationship can be written between SSFs and HSFs, leading to a joint likelihood using both datasets. We implement this approach using maximum likelihood, explore its estimation precision by systematic simulation, and seek to derive broad guidelines for effort allocation in the field. We find that complementarities in spatial coverage and resolution between telemetry and survey data often lead to marked inferential improvements in joint analyses over those using either data type alone. The optimal allocation of effort between the two methods (or the choice between them, if only one can be selected) depends on the overall effort expended and the pattern of environmental heterogeneity. Examining inferential performance over a broad range of scenarios for the relative cost between the two methods, we find that integrated analysis usually offers higher precision. Our methodological work shows how to integrate the analysis of telemetry and spatial survey data under a novel joint likelihood function, using traditional computational methods. Our simulation experiments suggest that even when the relative costs of the two methods favor the deployment of one field approach over another, their joint use is broadly preferable. Therefore, joint analysis of the two key methods used in spatial ecology is not only possible but also computationally efficient and statistically more powerful.