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By Thompson Hobbs (Colorado State University)

The use of models to gain insight in ecology has followed three largely disparate traditions. Empiricists have relied on statistical models, predominantly linear ones, to make quantitative statements about relationships in data. In the empirical tradition, model parameters have no definition apart from the data the models describe. A quite different type of model has characterized the theoretical tradition; unlike empirical models, those used by theorists represent ecological processes symbolically. In the theoretical tradition, model parameters represent biological quantities. To achieve generality, analysis of theoretical models use mathematical techniques that do not require data for insight, for example, the analysis of stability properties. A third tradition, originating with the International Biological Program during the 1970s, focused on development of detailed systems models of communities and ecosystems. The high dimension of these models defied symbolic, mathematical analysis, forcing simulation as the sole route to insight. Simulation, in turn, required estimates of parameters, and these estimates required data. However, in the systems tradition, parameter estimation was accomplished separately from model construction and numerical simulation. Evidence for the distinctness of these traditions can be found in the table of contents of textbooks on ecological modeling and the analysis of ecological data. Texts from the different traditions have virtually no topics in common.

The insights from all three traditions depend in a way that is truly fundamental on characterizing uncertainty. By definition, all models are abstractions. It follows that uncertainties in model predictions must arise because models, as abstractions, deliberately misspecify nature. Moreover, measurements by ecologists are often made with error, which gives rise to additional uncertainties that differ from those arising from model misspecification. Finally, it is clear that there are uncertainties resulting from variation among individuals, locations, and time periods. The core questions of ecology seek to understand this variation. Until recently, it was not widely recognized that these sources of uncertainty could not be lumped into a single “error term” without putting at risk the reliability of the statements we make based on models and data.

Manipulative experiments have offered a sturdy tool for inquiry in ecology, an approach that enjoys wide sanction by the peer-review community. However, it is becoming evident that investigations that depend on traditional, agronomic-style designs cannot address a broad range of critical problems. As the number of variables influencing processes of interest increases and the scale of inquiry expands, other approaches to insight are required. A classic illustration of this requirement is found in the highly engaging paper of Fridley and colleagues (Fridley, D. J., J. J. Stachowicz, S. Naeem, D. F. Sax, E. W. Seabloom, M. D. Smith, T. J. Stohlgren, D. Tilman, and B. Von Holle. 2007. The invasion paradox: Reconciling pattern and process in species invasions. Ecology 88:3–17), who showed that increasing spatial scale and differences in inferential approach caused diametrically opposing conclusions about the relationship between species richness and invasiblity of communities. Problems unsuited to classical experimentation require a flexible approach to fusing models with data, an approach that can accommodate uncertainties in the way ecological processes operate and the way we observe them.

In the focal paper for this Forum, Cressie et al. introduce a statistical framework that holds promise for merging the strengths of the different traditions in ecological modeling: the process orientation of theorists, the reliance on hard-won data by experimentalists, and the embrace of complexity by systems ecologists. This framework provides a flexible way to cope with uncertainty in ecological models. The potentially large impact of these ideas on the way ecologists analyze models and data motivated this Forum.

I invited responses to Cressie et al. from a broad representation of the community of ecological researchers, but I particularly sought ideas from early and mid-career ecologists and statisticians because they will likely participate in the evolution of the approaches described in the featured article. I invited them to expand on key ideas in the paper and to address how an ecologist might get up in the morning and make progress toward applying these methods in his/her own work. Thus, the responses here cluster into two groups: one group adding to key points in the paper, the other discussing how to go about learning to use hierarchical models.

Several responses add value to the Cressie et al. article. Yiqi Luo and colleagues elaborate on a key point made by Cressie et al., that the ability to identify parameters remains a key challenge in designing and implementing hierarchical models. Expanding on a parallel theme, Jennifer Hoeting discusses spatial and temporal correlation in ecological data, and the benefits and pitfalls of accounting for it in ecological models. Kiona Ogle emphasizes the value of hierarchical approaches to estimating parameters for process models. There is a distinctly Bayesian slant to the featured article, but hierarchical models need not be Bayesian. Responses of Subhash Lele and Brian Dennis, as well as Perry De Valpine, describe hierarchical methods that do not require a Bayesian foundation.

With respect to the second group of responses, the methods proposed by Cressie et al. require substantial intellectual investment to master, and there is nothing like success with your own research problems to motivate sustained investment in learning new techniques. Ben Bolker provides valuable advice on how to get started using hierarchical approaches to data modeling, advice that will allow ecologists to gain initial success with simple, hierarchical models. Maria Uriarte and Charles Yackulic rightly identify training in modern statistical methods as vital to the successful use of the emerging National Ecological Observatory Network. They proceed to give useful ideas about how students and working ecologists can learn hierarchical methods. Kiona Ogle also provides valuable resources for self-teaching.

A decade ago I began learning and teaching likelihood-based methods for estimating parameters in dynamic models of ecological processes. My students were particularly attracted to this material. However, they found it was deeply unsatisfying to recognize the importance of accounting for different sources of uncertainty in ecological models while failing to know how to accomplish that accounting in any practical way. Hierarchical models described in this Forum provide a much needed solution to this problem: an accessible, coherent, and intellectually satisfying approach to gaining insight from models using data.

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