The combined advantages of graphical modeling and Bayesian inference are transforming environmental science. Ecological processes are highly scale and setting-dependent, and only indirectly related to observations. Ecological data are remarkably heterogeneous, ranging from photosynthetic rate estimates on leaves to remote sensing of subcontinents. By starting with a joint distribution of unknowns, graphs and Bayes provide the capacity to combine diverse sources of information, admit partially known relationships, and allow for hidden variables. Among the trends we can expect in coming decades are i) a breakdown of the traditional dichotomy between 'statistical' or 'empirical' models vs 'theoretical' models, ii) a shift from models that input parameter estimates and output 'data' to those that input data and output parameter estimates, and iii) a shift from the current overemphasis on model selection (and averaging) to 'synthetic modeling' where processes more often 'interact', than 'compete'.

I illustrate these modeling issues with application to the long-standing effort to understand controls on forest diversity, described a half century ago as an paradox represented observations vs implications of models. 'Theoretical' models tell us that species must differ in specific ways in order to coexist as stable ecological communities. These differences must involve tradeoffs among species to insure that the best competitors do not drive all others to extinction. But many species that live together do not appear to possess such differences. The lack of tradeoffs presents a paradox when taken in light of the fact that dynamics involving the same species combinations are not 'neutral'; abundances of many species do not 'drift'. There are strong stabilizing forces that result in coherent spatio-temporal patterns with respect to soils, climate, and disturbance. Those forces must not be ones ecologists have typically measured. The contrast between strict requirements for tradeoffs suggested by 'theoretical' models, dynamic patterns that implicate stabilizing forces, and the difficulty finding them in nature-using 'statistical' models-suggests that we should look more deeply at how species interactions might be stabilized.

In this talk I discuss why the inconsistent assumptions of 'theoretical' and 'statistical' models lead to the paradox. I suggest that coexistence is best understood in terms of population heterogeneity, which may occur along many axes, and is missed by current modeling approaches. First, so-called neutral models contain tradeoffs, incorporated in assumptions about the timing of recruitment. I show that stochastic terms in models represent tradeoffs that are simply hidden from view. The high diversity that can be achieved in lottery models is an example of this phenomenon. Second, I suggest that species differences that are responsible for coexistence are 'high-dimensional', and can be captured in data and in models by admitting an appropriate structure for unknowns. Much of the unexplained variation in data results from differences among individuals. Allowing for this population heterogeneity, or random individual and temporal effects (RITES), indicates broad species 'overlap'. This overlap is stabilizing. It is not neutral (species differences are real), but it occurs across a large number of axes, most of which will be hard to capture in simple experiments and observational data sets. By providing a consistent treatment of information from many scales and complex, interacting processes, graphs and Bayes allow us to estimate each of these influences.