Sampling and analysis frameworks for inference in ecology

Reliable statistical inference is central to ecological research, much of which seeks to estimate population attributes and their interactions. The issue of sampling design and its relationship to inference has become increasingly important due to rapid proliferation of modelling methodology (line transect modelling, capture-recapture, estimation of occurrence, model selection procedures, hierarchical modelling) and new sampling approaches (adaptive sampling, other specialized designs). It is important for ecologists using these advanced methods to be aware of how the linkages between sample selection and data analysis can potentially affect inference. We examine design-based and model-based inference frameworks for ecological data collected randomly, purposively or opportunistically. We elucidate differences in the probability structures for data arising from these frameworks, clarify the assumptions that underlie them, and demonstrate their differences. Design based inference builds on a probability structure inherited from randomized data collection, whereas model-based inference relies on an assumed stochastic model of the data. By itself, a design-based approach is of limited value for inferences about causal hypotheses. In contrast, model-based inference is dependent on a conditionality principle that can seldom be shown to be met for an ecological system. We describe the conditions under which one can safely ignore sampling design in model-based analysis, along with inferential implications if these conditions are not met. The special case of opportunistic sampling is discussed. We present a combined framework that takes advantage of both approaches to inference, and provides a robust methodology that can deal with the modelling of sampling problems such as non-detection and misclassification, as well as the exploration of causal hypotheses. The combined framework can be useful for identifying optimal sampling strategies. Each approach to inference has its strengths and weaknesses, and practitioners should be aware of these in order to tailor designs and analyses to specific questions. We use the approaches and their underlying rationales to provide guidelines for choosing designs and estimators for reliable inference.