Anthony W. King

Aggregating Fine‐Scale Ecological Knowledge to Model Coarser‐Scale Attributes of Ecosystems

As regional and global scales become more important to ecologists, methods must be developed for the application of existing fine-scale knowledge to predict coarser-scale ecosystem properties. This generally involves some form of model in which fine-scale components are aggregated. This aggregation is necessary to avoid the cumulative error associated with the estimation of a large number of parameters. However, aggregation can itself produce errors that arise because of the variation among the aggregated components. The statistical expectation operator can be used as a rigorous method for translating fine-scale relationships to coarser scales without aggregation errors. Unfortunately this method is too cumbersome to be applied in most cases, and alternative methods must be used. These alternative methods are typically partial corrections for the variation in only a few of the fine-scale attributes. Therefore, for these methods to be effective, the attributes that are the most severe sources of error must be identified a priori. We present a procedure for making these identifications based on a Monte Carlo sampling of the fine-scale attributes. We then present four methods of translating fine-scale knowledge so it can be applied at coarser scales: (1) partial transformations using the expectation operator, (2) moment expansions, (3) partitioning, and (4) calibration. These methods should make it possible to apply the vast store of fine-scale ecological knowledge to model coarser-scale attributes of ecosystems.

A hierarchical framework for the analysis of scale

Landscapes are complex ecological systems that operate over broad spatiotemporal scales. Hierarchy theory conceptualizes such systems as composed of relatively isolated levels, each operating at a distinct time and space scale. This paper explores some basic properties of scaled systems with a view toward taking advantage of the scaled structure in predicting system dynamics. Three basic properties are explored:(1) hierarchical structuring, (2) disequilibrium, and (3) metastability. These three properties lead to three conclusions about complex ecological systems. First, predictions about landscape dynamics can often be based on constraints that directly result from scaled structure. Biotic potential and environmental limits form a constraint envelope, analogous to a niche hypervolume, within which the landscape system must operate. Second, within the constraint envelope, thermodynamic and other limiting factors may produce attractors toward which individual landscapes will tend to move. Third, because of changes in biotic potential and environmental conditions, both the constraint envelope and the local attractors change through time. Changes in the constraint structure may involve critical thresholds that result in radical changes in the state of the system. An attempt is made to define measurements to predict whether a specific landscape is approaching a critical threshold.

Oak forest carbon and water simulations: model intercomparisons and evaluations against independent data

Models represent our primary method for integration of small-scale, process- level phenomena into a comprehensive description of forest-stand or ecosystem function. They also represent a key method for testing hypotheses about the response of forest ecosystems to multiple changing environmental conditions. This paper describes the eval- uation of 13 stand-level models varying in their spatial, mechanistic, and temporal com- plexity for their ability to capture intra- and interannual components of the water and carbon cycle for an upland, oak-dominated forest of eastern Tennessee. Comparisons between model simulations and observations were conducted for hourly, daily, and annual time steps. Data for the comparisons were obtained from a wide range of methods including: eddy covariance, sapflow, chamber-based soil respiration, biometric estimates of stand-level net primary production and growth, and soil water content by time or frequency domain reflectometry. Response surfaces of carbon and water flux as a function of environmental drivers, and a variety of goodness-of-fit statistics (bias, absolute bias, and model efficiency) were used to judge model performance. A single model did not consistently perform the best at all time steps or for all variables considered. Intermodel comparisons showed good agreement for water cycle fluxes, but considerable disagreement among models for predicted carbon fluxes. The mean of all model outputs, however, was nearly always the best fit to the observations. Not surprisingly, models missing key forest components or processes, such as roots or modeled soil water content, were unable to provide accurate predictions of ecosystem responses to short-term drought phenomenon. Nevertheless, an inability to correctly capture short-term physiolog- ical processes under drought was not necessarily an indicator of poor annual water and carbon budget simulations. This is possible because droughts in the subject ecosystem were of short duration and therefore had a small cumulative impact. Models using hourly time steps and detailed mechanistic processes, and having a realistic spatial representation of the forest ecosystem provided the best predictions of observed data. Predictive ability of all models deteriorated under drought conditions, suggesting that further work is needed to evaluate and improve ecosystem model performance under unusual conditions, such as drought, that are a common focus of environmental change discussions.

Dispersal success on fractal landscapes: a consequence of lacunarity thresholds

Habitat fragmentation is expected to disrupt dispersal, and thus we explored how patch metrics of landscape structure, such as percolation thresholds used to define landscape connectivity, corresponded with dispersal success on neutral landscapes. We simulated dispersal as either a purely random process (random direction and random step lengths) or as an area-limited random walk (random direction, but movement limited to an adjacent cell at each dispersal step) and quantified dispersal success for 1000 individuals on random and fractal landscape maps across a range of habitat abundance and fragmentation. Dispersal success increased with the number of cells a disperser could search (m), but poor dispersers (m<5) searching via area-limited dispersal on fractal landscapes were more successful at locating suitable habitat than random dispersers on either random or fractal landscapes. Dispersal success was enhanced on fractal landscapes relative to random ones because of the greater spatial contagion of habitat. Dispersal success decreased proportionate to habitat loss for poor dispersers (m=1) on random landscapes, but exhibited an abrupt threshold at low levels of habitat abundance (p<0.1) for area-limited dispersers (m<10) on fractal landscapes. Conventional metrics of patch structure, including percolation, did not exhibit threshold behavior in the region of the dispersal threshold. A lacunarity analysis of the gap structure of landscape patterns, however, revealed a strong threshold in the variability of gap sizes at low levels of habitat abundance (p<0.1) in fractal landscapes, the same region in which abrupt declines in dispersal success were observed. The interpatch distances or gaps across which dispersers must move in search of suitable habitat should influence dispersal success, and our results suggest that there is a critical gap-size structure to fractal landscapes that interferes with the ability of dispersers to locate suitable habitat when habitat is rare. We suggest that the gap structure of landscapes is a more important determinant of dispersal than patch structure, although both are ultimately required to predict the ecological consequences of habitat fragmentation.

Dispersal success on spatially structured landscapes: when do spatial pattern and dispersal behavior really matter?

Abstract Dispersal is a fundamental component of many spatial population models. Concerns over the need to incorporate detailed information on dispersal behavior in spatially explicit population models (SEPMs) motivated us to undertake a simulation study in which we explored (1) the conditions under which landscape structure affects dispersal success and (2) the dependency of dispersal success on the choice of dispersal algorithm. We simulated individual dispersal as a random process (the mean-field approximation), a percolation process (PD) or a nearest-neighbor process (NND) on random and fractal neutral landscapes across gradients of habitat fragmentation and abundance (0.1–90%). Both landscape structure and dispersal behavior affected dispersal success in landscapes with

The potential response of terrestrial carbon storage to changes in climate and atmospheric CO2

We use a georeferenced model of ecosystem carbon dynamics to explore the sensitivity of global terrestrial carbon storage to changes in atmospheric CO2 and climate. We model changes in ecosystem carbon density, but we do not model shifts in vegetation type. A model of annual NPP is coupled with a model of carbon allocation in vegetation and a model of decomposition and soil carbon dynamics. NPP is a function of climate and atmospheric CO2 concentration. The CO2 response is derived from a biochemical model of photosynthesis. With no change in climate, a doubling of atmospheric CO2 from 280 ppm to 560 ppm enhances equilibrium global NPP by 16.9%; equilibrium global terrestrial ecosystem carbon (TEC) increases by 14.9%. Simulations with no change in atmospheric CO2 concentration but changes in climate from five atmospheric general circulation models yield increases in global NPP of 10.0–14.8%. The changes in NPP are very nearly balanced by changes in decomposition, and the resulting changes in TEC range from an increase of 1.1% to a decrease of 1.1%. These results are similar to those from analyses using bioclimatic biome models that simulate shifts in ecosystem distribution but do not model changes in carbon density within vegetation types. With changes in both climate and a doubling of atmospheric CO2, our model generates increases in NPP of 30.2–36.5%. The increases in NPP and litter inputs to the soil more than compensate for any climate stimulation of decomposition and lead to increases in global TEC of 15.4–18.2%.

Boreal forest CO2 exchange and evapotranspiration predicted by nine ecosystem process models: Intermodel comparisons and relationships to field measurements

Nine ecosystem process models were used to predict CO2 and water vapor exchanges by a 150-year-old black spruce forest in central Canada during 1994–1996 to evaluate and improve the models. Three models had hourly time steps, five had daily time steps, and one had monthly time steps. Model input included site ecosystem characteristics and meteorology. Model predictions were compared to eddy covariance (EC) measurements of whole-ecosystem CO2 exchange and evapotranspiration, to chamber measurements of nighttime moss-surface CO2 release, and to ground-based estimates of annual gross primary production, net primary production, net ecosystem production (NEP), plant respiration, and decomposition. Model-model differences were apparent for all variables. Model-measurement agreement was good in some cases but poor in others. Modeled annual NEP ranged from −11 g C m−2 (weak CO2 source) to 85 g C m−2 (moderate CO2 sink). The models generally predicted greater annual CO2 sink activity than measured by EC, a discrepancy consistent with the fact that model parameterizations represented the more productive fraction of the EC tower “footprint.” At hourly to monthly timescales, predictions bracketed EC measurements so median predictions were similar to measurements, but there were quantitatively important model-measurement discrepancies found for all models at subannual timescales. For these models and input data, hourly time steps (and greater complexity) compared to daily time steps tended to improve model-measurement agreement for daily scale CO2 exchange and evapotranspiration (as judged by root-mean-squared error). Model time step and complexity played only small roles in monthly to annual predictions.

Analysis of landscape sources and sinks: the effect of spatial pattern on avian demography

Abstract To develop theoretical insights into the relationship between spatial pattern and demography, we coupled a spatially structured demographic model with neutral landscape models to investigate how landscape structure affected population persistence and the source–sink potential of landscapes for a generalized, territorial migratory songbird. Four species-types, with different sensitivities to habitat area and edge effects, were simulated on replicated landscapes across a range of habitat abundance (1–90%) and fragmentation or spatial contagion (random, fractal with minimal contagion, and fractal with maximum contagion). For each species-type in each landscape, the expected number of female offspring produced per female (fecundity, b) was modeled as an explicit function of habitat area and spatial structure (patch edge-to-area ratio). Fecundity estimates (b) were combined with survivorship in a life-table analysis to estimate the net lifetime reproductive output (R0) for the population of each landscape. Landscapes for which R0 1. As expected, reproductive output (R0) was generally highest on fractal landscapes with maximum clumping (minimum fragmentation) and lowest on random landscapes (maximum fragmentation), especially for species with high edge sensitivity. For species with low edge sensitivity, population persistence was unlikely when the landscape had

Historical variations in terrestrial biospheric carbon storage

Changes in carbon storage in terrestrial ecosystems are a consequence of shifts in the balance between net primary production (NPP) and heterotrophic respiration (RH). Historical climatic variations which favored NPP over RH may have led to increased ecosystem carbon storage and might account for at least part of the “missing” sink required to balance the current centurys global carbon budget. To test this hypothesis, we employed a georeferenced global terrestrial biosphere model of 0.5° spatial resolution. The model was driven from an assumed equilibrium in 1900 using gridded historical time series of monthly temperature and precipitation and the historical record of changes in atmospheric CO2 concentration. Interannual variability in climate induced interannual changes in terrestrial biospheric carbon storage and net carbon exchange with the atmosphere of the order of 1–2 Gt C yr−1. With climate change alone, global biospheric carbon storage declined by 1% (23 Gt C) over the period 1900–1988. With the addition of a moderate CO2 fertilization response, biospheric carbon storage increased by 3% (57 Gt C), primarily as a consequence of changes in NPP and litter inputs to the soil system. With CO2 fertilization, the models cumulative carbon sink for the period 1900–1988 accounts for about 69% of the missing sink derived by deconvolution. For the period 1950–1988, the modeled sink is about 56% of the missing sink. Our results suggest that the temporal evolution of the missing sink over the period 1900–1988 could be a response of the terrestrial biosphere to changes in climate and atmospheric CO2 or perhaps climate change alone. The discrepancy in the magnitudes of the modeled and deconvolved sinks may be due to limitations of the biospheric model or to overestimates of the land-use source flux.

A comparison of geographical information systems-based algorithms for computing the TOPMODEL topographic index

[1] The performance of six geographical information systems (GIS)-based topographic index algorithms is evaluated by computing root-mean-square errors of the computed and the theoretical topographic indices of three idealized hillslopes: planar, convergent, and divergent. In addition to these three idealized cases, two divergent hillslopes with varying slopes, i.e., concave (slopes decrease from top to bottom) and convex (slopes increase from top to bottom) are also tested. The six GIS-based topographic index algorithms are combinations of flow direction and slope algorithms: i.e., single flow direction (SFD), biflow direction (BFD), and multiple flow direction (MFD) plus methods that determine slope values in flat areas, e.g., W-M method [Wolock and McCabe, 1995] and tracking flow direction (TFD) method. Two combinations of horizontal resolution and vertical resolution of the idealized terrain data are used to evaluate those methods. Among those algorithms the MFD algorithm is the most accurate followed by the BFD algorithm and the SFD algorithm. As the vertical resolution increases, the errors in the computed topographic index for all algorithms decrease. We found that the orientation of the contour lines of planar hillslopes significantly influences the SFD’s computed topographic index. If the contour lines are not parallel to one of eight possible flow directions, the errors in the SFD’s computed topographic index are significant. If mean slope is small, TFD becomes more accurate because slope values in flat areas are better estimated. INDEX TERMS: 1899 Hydrology: General or miscellaneous; 1824 Hydrology: Geomorphology (1625); 1832 Hydrology: Groundwater transport; KEYWORDS: GIS, TOPMODEL, topographic index, single flow direction algorithm, biflow direction algorithm, multiple flow direction algorithm