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There is still much uncertainty about ecological controls on the rate and direction of net C[O.sub.2] exchange by tropical rain forests, in spite of their importance to global C cycling. These controls are thought to arise from hydrologic and nutrient constraints to C[O.sub.2] fixation caused by seasonality of precipitation and adverse chemical properties of some major tropical soil types. Using the ecosystem model ecosys, we show that water uptake to a depth of 8 m avoids constraints to C[O.sub.2] and energy exchange from soil drying during five-month dry seasons typical for eastern Amazonian forests. This avoidance in the model was tested with eddy covariance (EC) measurements of C[O.sub.2] and energy fluxes during 2003 and 2004 over an old-growth forest on an acidic, nutrient-poor oxisol in the Tapajds National Forest (TNF) in Para, Brazil. Modeled C[O.sub.2] fixation was strongly constrained by slow phosphorus (P) uptake caused by low soil pH. Daytime C[O.sub.2] influxes in the model were in close agreement with EC measurements ([R.sup.2] > 0.8) during both wet and dry seasons. Both modeled and measured fluxes indicated that seasonality of precipitation affected C[O.sub.2] and energy exchange more through its effect on radiation and air temperature than on soil water content. When aggregated to a yearly scale, modeled and gap-filled EC C[O.sub.2] fluxes indicated that old-growth forest stands in the TNF remained within 100 g C*[m.sup.-2]*[yr.sup.-1] of C neutrality in the absence of major disturbance. Annual C transformations in ecosys were further corroborated by extensive biometric measurements taken in the TNF and elsewhere in the Amazon basin, which also indicated that old-growth forests were either small C sources or small C sinks. Long-term model runs suggested that rain forests could be substantial C sinks for several decades while regenerating after stand-replacing disturbances, but would gradually decline toward C neutrality thereafter. The time course of net ecosystem productivity (NEP) in the model depended upon annual rates of herbivory and tree mortality, which were based on site observations as affected by weather (e.g., El Nino Southern Oscillation [ENSO] events). This dependence suggests that rain forest NEP is strongly controlled by disturbance as well as by weather. Key words: Brazil; C[O.sub.2] exchange; disturbance; ecosys; ecosystem modeling; Her ecosystem productivity; rain forest.

We evaluate a method for fitting models to time series of population abundances that incorporates both process noise and observation error in a likelihood framework. The method follows the probability logic of the Kalman filter, but whereas the Kalman filter applies to linear, Gaussian systems, we implement the full probability calculations numerically so that any nonlinear, non-Gaussian model can be used. We refer to the method as the 'numerically integrated state-space (NISS) method' and compare it to two common methods used to analyze nonlinear time series in ecology: least squares with only process noise (LSPN) and least squares with only observation error (LSOE). We compare all three methods by fitting Beverton-Holt and Ricker models to many replicate model-generated time series of length 20 with several parameter choices. For the Ricker model we chose parameters for which the deterministic part of the model produces a stable equilibrium, a two-cycle, or a four-cycle. For each set of parameters we used three process-noise and observation-error scenarios: large standard deviation (0.2) for both, and large for one but small (0.05) for the other. The NISS method had lower estimator bias and variance than the other methods in nearly all cases. The only exceptions were for the Ricker model with stable-equilibrium parameters, in which case the LSPN and LSOE methods has lower bias when noise variances most closely met their assumptions. For the Beverton-Holt model, the NISS method was much less biased and more precise than the other methods. We also evaluated the utility of each method for model selection by fitting simulated data to both models and using information criteria for selection. The NISS and LSOE methods showed a strong bias toward selecting the Ricker over the Beverton-Holt, even when data were generated with the Beverton-Holt. It remains unclear whether the LSPN method is generally superior for model selection or has fortuitously better biases in this particular case. These results suggest that information criteria are best used with caution for nonlinear population models with short time series. Finally we evaluated the convergence of likelihood ratios to theoretical asymptotic distributions. Agreement with asymptotic distributions was very good for stable-point Ricker. parameters, less accurate for two-cycle and four-cycle Ricker parameters, and least accurate for the Beverton-Holt model. The numerically integrated state-space method has a number of advantages over least squares methods and offers a useful tool for connecting models and data and ecology. Key words: Beverton-Holt model; Kalman filter; least-squares cf. state-space models; model-fitting; observation error; parameter estimation; population models; process noise; Ricker model; time series.

The problem of scale has been a critical impediment to incorporating important fine-scale processes into global ecosystem models. Our knowledge of fine-scale physiological and ecological processes comes from a variety of measurements, ranging from forest plot inventories to remote sensing, made at spatial resolutions considerably smaller than the large scale at which global ecosystem models are defined. In this paper, we describe a new individual-based, terrestrial biosphere model, which we label the ecosystem demography model (ED). We then introduce a general method for scaling stochastic individual-based models of ecosystem dynamics (gap models) such as ED to large scales. The method accounts for the fine-scale spatial heterogeneity within an ecosystem caused by stochastic disturbance events, operating at scales down to individual canopy-tree-sized gaps. By conditioning appropriately on the occurrence of these events, we derive a size-and age-structured (SAS) approximation for the first moment of the stochastic ecosystem model. With this approximation, it is possible to make predictions about the large scales of interest from a description of the fine-scale physiological and population-dynamic processes without simulating the fate of every plant individually. We use the SAS approximation to implement our individual-based biosphere model over South America from 15 [degrees] N to 15 [degrees] S, showing that the SAS equations are accurate across a range of environmental conditions and resulting ecosystem types. We then compare the predictions of the biosphere model to regional data and to intensive data at specific sites. Analysis of the model at these sites illustrates the importance of fine-scale heterogeneity in governing large-scale ecosystem function, showing how population and community-level processes influence ecosystem composition and structure, patterns of aboveground carbon accumulation, and net ecosystem production. Key words: biogeochemical dynamics; ecosystem dynamics; ecosystem model, terrestrial; individual-based model; moment approximation; plant community dynamics; scaling; size- and age-structured; South America; sub-grid scale heterogeneity; terrestrial biosphere model; vegetation dynamics.

Models are useful when they are compared with data. Whether this comparison should be qualitative or quantitative depends on circumstances, but in many cases some statistical comparison of model and data is useful and enhances objectivity. Unfortunately, ecological dynamic models tend to contain assumptions and simplifications that enhance tractability, promote insight, but spoil model fit, and this can cause difficulties when adopting a statistical approach. Furthermore, the arcane numerical analysis required to fit dynamic models reliably presents an impediment to objective model testing by fitting. This paper presents methods for formulating and fitting partially specified models, which aim to achieve a measure of generality by avoiding some of the irrelevant incidental assumptions that are inevitable in more traditional approaches. This is done by allowing delay differential equation models, difference equation models, and differential equation models to be constructed with part of their structure represented by unknown functions, while part of the structure may contain conventional model elements that contain only unknown parameters. An integrated practical methodology for using such models is presented along with several examples, which include use of models formulated using delay differential equations, discrete difference equations/matrix models, ordinary differential equations, and partial differential equations. The methods also allow better estimation from ecological data by model fitting, since models can be formulated to include fewer unjustified assumptions than would usually be the case if more traditional models were used, while still including as much structure as the modeler believes can be justified by biological knowledge: model structure improves precision, while fewer extraneous assumptions reduce unquantifiable bias. Key words: delay differential equation: ecological dynamic model fitting; multiple smoothing parameter; nonlinear spline model; partially specified model; population dynamic model fitting; semi-mechanistic model; semiparametric model.