STEPHEN W. PACALA
Frederick D. Petrie Professor 
Department of Ecology and Evolutionary Biology  Princeton University, Princeton, NJ 08544
S e l e c t e d   P u b l i c a t i o n   A B S T R A C T S  2000 - 2003
2003
Pacala, S.W., J.P. Casperson and M. Hansen. 2003. Forest Inventory Data Falsify Ecosystem Models of CO2 Fertilization. (Manuscript)
We analyze tree growth data from Wisconsin forest inventories completed in 1968, 1983, 1996 and 2002. These show that the rate of forest tree growth decreased steadily over the period, in contrast to the increases predicted by CO2 fertilization models. Measured growth rate changed an average of -0.27% y-1 (95% confidence range: -0.05% to -0.49% y-1), whereas the prediction for CO2 fertilization is 0.16% y-1 (corresponding to a ß of 0.36). The high statistical precision is due both to large sample sizes and positive inter-temporal correlations among the growth rates within the same plot. Decreased growth occurred in stands of all ages, and so our results are not caused by age-related declines in growth.
Data allowing a direct examination of growth rates over several decades are available only for Wisconsin, but Caspersen et al. (2000) introduced an indirect method for detecting past changes in growth rate using only two sequential inventories. This method was criticized by Joos et al. (2002), who claimed that it lacked the statistical power to evaluate state-of–the-art ecosystem models of CO2 fertilization. We explain both the sound points and the critical errors in Joos et al.’s argument, introduce a transparent and analytically tractable version of Caspersen et al.’s method, and use it to re-analyze the Michigan forest inventory data (1977 and 1990) examined in both previous studies. The results show a decrease in Michigan forest growth rates, which corresponds to a mean change of -0.19% y-1 over the period of the Wisconsin study, and a 95% confidence range of 0.00% y-1 to 0.040% y-1 that overlaps the range estimated in Caspersen et al. (2002). Neither the direct analysis of growth rates in Wisconsin, nor the re-analysis of the Michigan inventories is consistent with the CO2 fertilization model in Joos et al. (2002).
State-of-the-art ecosystem models of CO2 fertilization are evidently false for this region over the later third of the 20th century. We discuss the implications of this and other reasons for skepticism about the future magnitude of CO2 fertilization. In particular, the fossil fuel emissions reductions required to stabilize atmospheric CO2 at 500+50 ppm must begin decades sooner if the predictions of the CO2 fertilization models in the IPCC Third Assessment (Prentice et al. 2001) are incorrect. The difference between a terrestrial carbon sink that grows because of CO2 fertilization, and one that shrinks because it is caused by recovery from past land use, is the difference between the luxury of decades of delay and the need to act now.
Purves, D.W., J.P. Casperson, P.R. Moorcroft, G.C. Hurtt, S.W. Pacala. 2003. Human-induced Changes in U.S. Biogenic VOC Emissions: evidence from long-term forest inventory data.
Biogenic volatile organic compounds (BVOC) contribute to tropospheric ozone formation. We estimate changes in BVOC emission rates, under hot bright conditions, for the Eastern U.S. between 1985 and 1992. In most locations, changes in BVOC emissions were much larger than changes in emissions of anthropogenic VOCs. Many locations, particularly in the South, experienced rapid increases in BVOC emissions (>3% per year), but other locations experienced rapid decreases. Changes resulted mainly from logging and ecological succession, which in general increased and decreased emissions respectively.
Purves, D.W. and S.W. Pacala. 2003. Ecological Drift in niche-structured communites: neutral pattern does not imply neutral process. British Ecological Society. (In Press)
Summary
(1) Which is more important in determining the diversity and species composition of communities: niche-packing because species are different; or ecological drift because species are equivalent? This is a vigorous current debate in community ecology, and it has continued apace because there is very good evidence for both sides: countless observations and experiments have demonstrated that coexisting species are not equivalent, because they have different competitive abilities in different situations; and yet in many communities the distributions of the population sizes of different species shows a near perfect match to the predictions of neutral models.
(2) We demonstrate, with a formal proof and model simulations, that these two observations are not contradictory. The inclusion of three different forms of extremely strong niche-structure – successional niches, lottery niches and habitat specialization – into the most important neutral model in the literature (Hubbell’s zero-sum ecological drift) does not affect the predicted distribution of species abundances, except when diversity is low.
(3) The predictions for species abundances given by neutral models are therefore more robust than previously suspected, and this strengthens the case that ecological drift is the dominant factor determining the pattern species abundances in tropical forest communities.
(4) However the result also shows that a fit between observed patterns of species abundances, and the predictions of a neutral model, does not mean that the species are equivalent, or that population dynamics are neutral. The equivalence of species must be tested directly, and these tests have shown repeatedly that species are not equivalent.
(5) In diverse communities, the distribution of species abundances is determined entirely by ecological drift, independent of niche structure; but the biogeochemical functioning is determined entirely by niche structure, independent of drift.
Keith, D.W., J.F. DeCarolis, D.C. Denkenberger, D.H. Lenschow, S.L. Malyshev, S.W. Pacala, and P.J. Rasch. 2003. The Influence of Large-scale Wind-Power on Global Climate Change. (Submitted to Nature Feb. 2004)
Large scale use of wind power can alter local and global climate by extracting kinetic energy and by modifying turbulent transport in the atmospheric boundary layer. We explored the climatic impacts of extracting 3-20 TW of electricity with a suite of numerical experiments using two independent atmospheric GCMs and two parameterizations of the wind-turbine arrays. Wind power has a negligible effect on global-mean surface temperature, but at continental scales, the average magnitude of climatic change due to wind power can be significant when compared to the reduction in climatic change achieved by the substitution of wind for fossil-fuels.

Baidya Roy, S., S.W. Pacala and R.L. Walko. 2003. Can Windfarms Affect Local Meteorology? (Submitted to Journal of Geophysical Research)
A numerical model was used to explore the possible impacts of large windfarms in the Great Plains region on local meteorology over synoptic timescales. A wind turbine was approximated as a sink of energy and source of turbulence. Turbulence generated by rotors can affect atmospheric dynamics and thermodynamics as well as surface fluxes of heat and moisture.
Hurtt, G.C., R. Dubayah, J. Drake, P. Moorcroft, S. Pacala, and M. Fearon. 2003. Beyond Potential Vegetation: Combining Lidar Remote Sensing and a Height Structured Ecosystem Model for Improved Estimates of Carbon Stocks and Fluxes. Ecological Applications. (In Press)
Carbon estimates from terrestrial ecosystem models currently are limited by large uncertainties in the present conditions of the land surface. Natural and anthropogenic disturbance events have a dramatic impact on vegetation dynamics and associated biogeochemical fluxes. Without such data it is difficult to go beyond estimates based on "potential vegetation" to predictions for the current landscape across policy-relevant time scales. Two recent developments, one in remote sensing technology, the other in ecosystem modeling, are combined and evaluated for their potential to improve carbon stock and flux estimates. The first is airborne lidar remote sensing, which measures fine-scale heterogeneity in the vertical structure of vegetation. The second is a new height-structured terrestrial ecosystem model (the Ecosystem Demography model, ED), which is capable of estimating the consequences of this heterogeneity in regional analyses of carbon stocks and fluxes. In this research, we assess the potential for using lidar observations of canopy structure to initialize and validate the ED model at a tropical forest site in Costa Rica. Using canopy height measurements from lidar to initialize the ED model, regional estimates of aboveground biomass are produced to within 1.2% of regression-based approaches. In addition, lidar data are shown to provide substantial constraints on ED model estimates of net carbon fluxes.

Sandin, S.A. and S.W. Pacala. 2003. Regulation in populations of coral reef fish: an exploration of models and data. Proceedings of the Ninth International Coral Reef Symposium, Bali. (In press)
The study of population regulation in reef fish populations is confounded by large amounts of stochasticity obscuring patterns in the field. We analyze a series of population models, comparing equilibrial solutions under conditions of top-down and bottom-up regulation. We also treat patterns of population variance that will be expected as recruitment variance is propagated through to adult populations. We find that predators affect reef fish populations by absorbing
recruitment variance across space and through time. Food limitation will instead reduce fluctuations of adult fish biomass through time. Our model suggests that the study of regulation cannot be conducted through counting fish alone, but requires measurement of biomass simultaneously. By surveying fish across natural and human-created clines of recruitment and mortality, we can focus fieldwork on testing focused predictions of regulation on coral reefs.

Baidya Roy, S., G. C. Hurtt, C. P. Weaver, and S. W. Pacala, Impact of historical land cover change on the July climate of the United States, J. Geophys. Res., 108(D24), 4793, doi:10.1029/2003JD003565, 2003.
We use the Regional Atmospheric Modeling System (RAMS) model to investigate the possible impact of landcover change on the July climate of the coterminous U.S. over the last 290 years. Vegetation data was estimated using the Ecosystem Demography (ED) model. The observed change in landcover leads to a weak warming along the Atlantic coast and a strong cooling of more than 1K over the mid-west and the Great Plains region. The precipitation signal shows some reduction in the mid-west due to changes in the patterns of large-scale moisture advection.


Kinzig A.P., D. Starrett, K. Arrow, S. Aniyar, B. Bolin, P. Dasgupta, P. Ehrlich, C. Folke, M. Hanemann, G. Heal, M. Hoel, A.M. Janesson, B.O. Janesson, N. Kautsky, S. Levin, J. Lubchenco, K.G. Maler, S.W. Pacala, S.H. Schneider, D. Siniscalco, and B. Walker. 2003. Coping with Uncertainty: A Call for a New Science-Policy Forum. Royal Swedish Academy of Sciences. Ambio Vol. 32. 5.
The scientific and policy worlds have different goals, which can lead to different standards for what constitutes “proof” of a change or phenomena, and different approaches for characterizing and conveying uncertainty and risk. These differences can compromise effective communication among scientists, policymakers, and the public, and constrain the types of socially compelling questions scientists are willing to address. In this paper, we review a set of approaches for dealing with uncertainty, and illustrate some of the errors that arise when science and policy fail to coordinate correctly. We offer a set of recommendations, including restructuring of science curricula and establishment of science-policy forums populated by leaders in both arenas, and specifically constituted to address problems of uncertainty.

Pacala, S. W. 2003. Global Constraints on Reservoir Leakage in Proceedings of the 6th International Greenhouse Gas Control Technologies Conference, 1st-4th October 2002 (Kyoto, Japan).Pp. 267-272. Elsevier Science Unlimited.
 A crucial unresolved problem about geological sequestration is that some receptor reservoirs will leak stored CO2. At local scales, leaks might endanger shallower drinking water supplies or public health. At global scales, leaks might be large enough to make sequestration ineffective. This paper focuses on the global-scale problem and uses models of carbon storage reservoirs and natural carbon sinks to calculate constraints on reservoir leakage. It assumes fossil fuel consumption at a level that would that would lead to an atmospheric CO2 concentration of 750 ppm and then calculates the sequestration and leakage limits that would reduce the maximum concentration to 450 or 550 ppm. The surprising result is that leakage limits are much less severe than expected because of heterogeneity among reservoirs. In some cases, the reduction from 750 to 450 ppm would be possible even with a mean leakage rate of 1% per year or more. The results imply that economic considerations or local risks are likely to constrain allowable leakage rates more tightly than impacts of leakage on global atmospheric CO2.

Pacala, S. W., E. Bulte, J. A. List and S. A. Levin. 2003. False Alarm over Environmental False Alarms. Science Vol. 301: 1187-1188.
A series of books, culminating most recently in B. Lomborg's The Skeptical Environmentalist, conclude that environmental scientists issue too many warnings that subsequently turn out to be exaggerated or false. We evaluate this claim in the framework of a cost-benefit analysis of evidentiary standards in the environmental sciences. Is the sensitivity of our environmental alarm set too high? We conclude that marginal benefits currently far outweigh marginal costs, indicating that evidentiary standards for reporting hazards are too conservative, not too liberal.

Bolker, Benjamin M., Stephen W. Pacala, and Claudia Neuhauser. 2003. Spatial dynamics in model plant communities: what do we really know? American Naturalist Vol. 162:2
A variety of models have shown that spatial dynamics and small-scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch models. Studies using all three frameworks agree that spatial dynamics need not enhance coexistence nor slow down dynamics; their effects depend on the underlying competitive interactions in the community. When similar species would coexist in a nonspatial habitat, endogenous spatial structure inhibits coexistence and slows dynamics. When a dominant species disperses poorly and the weaker species has higher fecundity or better dispersal, competition-colonization trade-offs enhance coexistence. Even when species have equal dispersal and per-generation fecundity, spatial successional niches where the weaker and faster-growing species can rapidly exploit ephemeral local resources can enhance coexistence. When interspecific competition is strong, spatial dynamics reduce founder control at large scales and short dispersal becomes advantageous. We describe a series of empirical tests to detect and distinguish among the suggested scenarios.
Levin, S.A. and S.W. Pacala. 2003. Ecosystem Dynamics. In: (K.-G. Mäler andJ. Vincent, eds) Handbook of Environmental Economics. Elsevier/North Holland, Amsterdam. Vol. 1: 61-95.
Ecological communities—the biotic essence of ecosystems—are comprised of many species, which are in turn made up of large numbers of individuals, each with their own separate ecological and evolutionary agendas. The dynamics of ecosystems emerge from the collective dynamics of huge numbers of individual parts, and in turn feed back to influence those parts. To understand how to preserve the services that ecosystems provide it is essential to understand how communities are organized, and which are the most relevant ways to measure biodiversity. Not all species were created equal as regards their role in maintaining functioning of ecosystems, or their resiliency in the face of stress. Thus it is essential to develop ways to relate processes at the level of individual organisms to the populations of which they are members, and to the communities and ecosystems in which they reside. We must learn to scale from the small to the large, from the individual to the collective to the community, from the leaf to the plant to the biosphere. We need, in effect, to build a statistical mechanics of ecological communities, founded upon a combination of observation, controlled experimentation and simulation, and mathematical theory.
The problems we face will be familiar to economists, who well recognize the need to integrate micro- and macro- perspectives, and to relate the dynamics of societies to the way individuals make decisions. They will also recognize the context dependence of decision-making, and that in consequence the dynamics of systems are highly nonlinear, hence constrained by the accidents of history. It is these issues, and how to deal with them, that will form the core of this paper.
2002
Hixon, M.A., S.W. Pacala, and S.A. Sandin. 2002. Population regulation: historical context and contemporary challenges of open vs. closed systems. Ecology 83(6): 1490-1508.
By definition, a population is regulated if it persists for many generations with fluctuations bounded above zero with high probability. Regulation thus requires density-dependent negative feedback whereby the population has a propensity to increase when small and decrease when large. Ultimately, extinction occurs due to regulating mechanisms becoming weaker than various disruptive events and stochastic variation. Population regulation is one of the foundational concepts of ecology, yet this paradigm has often been challenged, during the first half of the 20th century when the concept was not clearly defined, and more recently by some who study demographically open populations.
The history of ecology reveals that earlier manifestations of the concept focused mostly on competition as the mechanism of population regulation. Because competition is often not evident in nature, it was sometimes concluded that population regulation was therefore also absent. However, predation in the broadest sense can also cause density dependence. By the 1950s, the idea that demographic density dependence was essential (but not sufficient) for population regulation was well established, and since then, challenges to the general concept have been short lived. However, some now believe that metapopulations composed of demographically open local populations can persist without density dependence. In particular, some recent manifestations of the Recruitment Limitation Hypothesis all but preclude the possibility of regulation.
The theory of locally open populations indicates that persistence always relies on direct demographic density dependence at some spatial and temporal scale, even in models reportedly demonstrating the contrary. There is also increasing empirical evidence, especially in marine systems where competition for space is not self evident, that local density dependence is more pervasive than previously assumed and is often caused by predation. However, there are currently insufficient data to test unequivocally whether or not any persistent metapopulation is regulated. The challenge for more complete understanding of regulation of metapopulations lies in combined empirical and theoretical studies that bridge the gap between smaller scale field experiments and larger scale phenomena that can presently be explored solely by theory.

Hurtt, G.C., S.W. Pacala, P.R. Moorcroft, J. Caspersen, E. Shevliakova, R.A. Houghton and B. Moore III. 2002. Projecting the Future of the U.S. Carbon Sink. Proceedings of the National Academy of Sciences. 99 (3), 1389-1394.
Atmospheric and ground-based methods agree on the presence of a carbon sink in the coterminous United States (the United States minus Alaska and Hawaii), and the primary causes for the sink recently have been identified. Projecting the future behavior of the sink is necessary for projecting future net emissions. Here we use two models, the Ecosystem Demography model and a second simpler empirically based model (Miami Land Use History), to estimate the spatio-temporal patterns of ecosystem carbon stocks and fluxes resulting from land-use changes and fire suppression from 1700 to 2100. Our results are compared with other historical reconstructions of ecosystem carbon fluxes and to a detailed carbon budget for the 1980s. Our projections indicate that the ecosystem recovery processes that are primarily responsible for the contemporary U.S. carbon sink will slow over the next century, resulting in a significant reduction of the sink. The projected rate of decrease depends strongly on scenarios of future land use and the long-term effectiveness of fire suppression.

Kinzig, A.P. S.W. Pacala and G.D. Tilman (Eds.) 2002. The Functional Consequences of Biodiversity: Experimental Progress and Theoretical Extensions. Princeton University Press, Princeton, NJ.

  Kinzig, A.P. and S.W. Pacala. 2002. Successional Biodiversity and Ecosystem Functioning. Pp. 175-212.
  Pacala, S.W. and G.D. Tilman. 2002. The Transition from Sampling to Complementarity. Pp. 151-166.
  Pacala, S.W. and A.P. Kinzig. 2002. Introduction to Theory and the Common Ecosystem Model. Pp. 169-174.
  Chesson, P., S.W. Pacala and C. Neuhauser. 2002. Environmental Niches and Ecosystem Functioning. Pp. 213-245.
  Kinzig, A.P., S.W. Pacala and G.D. Tilman. 2002. Looking Back, Peering Forward. Pp. 314-329.
This volume synthesizes empirical studies on the relationship between biodiversity and ecosystem functioning and extends that knowledge using a novel and coordinated set of models and theoretical approaches. These experimental and theoretical analyses demonstrate that functioning usually increases with biodiversity, but also reveals when and under what circumstances other relationships between biodiversity and ecosystem functioning might occur. It also accounts for apparent changes in diversity-functioning relationships that emerge over time in disturbed ecosystems, thereby addressing a major controversy in the field. The volume concludes with a blueprint for moving beyond small-scale studies to regional ones--a move of enormous significance for policy and conservation but one that will entail tackling some of the most fundamental challenges in ecology.

2001
Schimel, D.S., J.I. House, K.A. Hibbard, P. Bousquet, P. Ciais, P. Peylin, B.H. Braswell, M.J. Apps, D. Baker, A. Bondeau, J. Canadell, G. Churkina, W. Cramer, A.S. Denning, C.B. Field, P. Friedlingstein, C. Goodale, M. Heimann, R.A. Houghton, J.M. Melillo, B. Moore III, D. Murdiyarso, I. Noble, S.W. Pacala, I.C. Prentice, M.R. Raupach, P.J. Rayner, R.J. Scholes, W.L. Steffen, C. Wirth. 2001. Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems. Nature 414, 169 – 172.
Knowledge of carbon exchange between the atmosphere, land and the oceans is important, given that the terrestrial and marine environments are currently absorbing about half of the carbon dioxide that is emitted by fossil-fuel combustion. This carbon uptake is therefore limiting the extent of atmospheric and climatic change, but its long-term nature remains uncertain. Here we provide an overview of the current state of knowledge of global and regional patterns of carbon exchange by terrestrial ecosystems. Atmospheric carbon dioxide and oxygen data confirm that the terrestrial biosphere was largely neutral with respect to net carbon exchange during the 1980s, but became a net carbon sink in the 1990s. This recent sink can be largely attributed to northern extratropical areas, and is roughly split between North America and Eurasia. Tropical land areas, however, were approximately in balance with respect to carbon exchange, implying a carbon sink that offset emissions due to tropical deforestation. The evolution of the terrestrial carbon sink is largely the result of changes in land use over time, such as regrowth on abandoned agricultural land and fire prevention, in addition to responses to environmental changes, such as longer growing seasons, and fertilization by carbon dioxide and nitrogen. Nevertheless, there remain considerable uncertainties as to the magnitude of the sink in different regions and the contribution of different processes.

Wilson, H.B., M.J. Keeling and S.W. Pacala. 2001. Deterministic limits to stochastic, spatial models of natural enemies. American Naturalist. 159, 57-80.
Stochastic spatial models are becoming an increasingly popular tool for understanding ecological and epidemiological problems. However, due to the complexities inherent in such models, it has been difficult to obtain any analytical insights. Here, we consider individual-based, stochastic models of both the continuous-time Lotka-Volterra system and the discrete-time Nicholson-Bailey model. The stability of these two stochastic models of natural enemies is assessed by constructing moment equations. The inclusion of these moments, which mimic the effects of spatial aggregation, can produce either stabilizing or destabilizing influences on the population dynamics. Throughout, the theoretical results are compared to numerical models for the full distribution of populations, as well as stochastic simulations.

Moorcroft, P.R., G.C. Hurtt and S.W. Pacala. 2001. A Method for Scaling Vegetation Dynamics: the Ecosystem Demography Model (ED). Ecological Monographs, 71(4), 557-586.
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° N to 15° 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.

Rees, M., R. Condit, M. Crawley, S.W. Pacala and D. Tilman. 2001. Vegetation Dynamics (9315). Science 293 (5530): 650-655.
By integrating a wide range of experimental, comparative, and theoretical approaches, ecologists are starting to gain a detailed understanding of the long-term dynamics of vegetation. We explore how patterns of variation in demographic traits among species have provided insight into the processes that structure plant communities. We find a common set of mechanisms, derived from ecological and evolutionary principles, that underlie the main forces shaping systems as diverse as annual plant communities and tropical forests. Trait variation between species maintains diversity and has important implications for ecosystem processes. Hence, greater understanding of how Earth's vegetation functions will likely require integration of ecosystem science with ideas from plant evolutionary, population, and community ecology.

Pacala S.W., Hurtt G.C., Moorcroft P.R., Caspersen J.P. 2001 Carbon storage in the US caused by land use change. Pp. 145-172. In The Present and Future of Modeling Global Environmental Change. Terra Scientific Publishing. Toyko, Japan.
Here we examine the cause, size and future of the U.S. carbon sink. To estimate the size of the U.S. carbon sink we review a comprehensive landbased analysis of the carbon sink in the coterminous U.S. For the 1980s, the sink is between 1/3 and 2/3 PgC y–1, and is split approximately evenly between forest and non-forest sectors. The nonforest sink is caused by fire suppression on non-forested lands, sediment burial in resevoirs, alluvium and colluvium, and agriculturual practices.
The forest sink has been attributed to changes in land use and the enhancement of plant growth by CO2 fertilization, N deposition and climate change. To estimate the relative contribution of land use and growth enhancement in forest ecosystems, we use forest inventory data from five states spanning a latitudinal gradient in the eastern U.S. Land use is the dominant factor governing the rate of carbon accumulation in forests in these states, with growth enhancement contributing far less than previously reported. The
estimated fraction of aboveground net ecosystem production due to growth enhancement is 2.0 +/– 4.4%, with the remainder due to land use.
To forecast the future of the U.S. carbon sink, we used the Ecosystem Demography Model (ED). We first modeled carbon sources and sinks from 1700–1990, and then projected patterns to 2100. Our projections indicate that the land-use portion of the U.S. carbon sink will decrease in the future, with a half-life of approximately 50 years, as U.S. ecosystems gradually equilibrate with current patterns of natural and anthropogenic disturbance.

Pacala, S.W., G.C. Hurtt, R.A. Houghton, R.A. Birdsey, L. Heath, E.T. Sundquist, R.F. Stallard, D. Baker, P. Peylin, P. Moorcroft, J. Caspersen, E. Shevliakova, M.E. Harmon, S.-M. Fan, J.L. Sarmiento, C. Goodale, C.B. Field, M. Gloor and D. Schimel. 2001. Consistent Land- and Atmosphere-Based U.S. Carbon Sink Estimates. Science 292 (5525): 2316-2320. (Designated as top-ten paper of 2001 by Science.)
For the period from 1980-1990, we estimate a sink in the coterminous U.S. between 0.30 and 0.58 PgC y-1 (PgC = 1015 g of carbon). The net flux from the atmosphere to the land is higher: 0.37-0.71 PgC y-1, because a net of 0.07-0.13 PgC y-1 is exported by rivers and commerce and returns to the atmosphere elsewhere. These bounds are considerably larger than those from previous studies (0.08-0.35 PgC y-1). The large estimates reflect the inclusion of additional processes and revised estimates of some. Although component estimates are uncertain, approximately one half the total is outside the forest sector. We also estimated the sink using atmospheric models and the atmospheric concentration of CO2 (the tracer transport inversion method). The inversion results contain the land-based estimates, but span a much larger range. Although estimates from atmospheric and terrestrial data are not inconsistent, the ranges from both methods are currently large.


2000
Lewis, M.A. and S. Pacala. 2000. Modeling and analysis of stochastic invasion processes. Journal of Mathematical Biology 41: 387-429.
In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyze two basic properties of the invasion. The first property is ‘permanence of form’ in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, f which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population.

Keeling, M.J., H.B. Wilson and S.W. Pacala. 2000. Re-interpreting Space, Time-lags, and Functional Responses to Ecological Models. Science. 290:1758-1761.
Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.

Caspersen, J.P., S.W. Pacala, J.C. Jenkins, G.C. Hurtt, P.R. Moorcroft, and R.A. Birdsey. 2000. Contributions of land-use history to carbon accumulation in US forests. Science 290: 1148-1151.
Carbon accumulation forest has been attributed to historical changes in land use and the enhancement of tree growth by CO2 fertilization, N deposition, and climate change. The relative contribution of land use and growth enhancement is estimated by using inventory data from five states spanning a latitudinal gradient in the eastern United States. Land use is the dominant factor governing the rate of carbon accumulation in these states, with growth enhancement contributing far less than previously reported. The estimated fraction of aboveground net ecosystem production due to growth enhancement is 2.0 ± 4.4%, with the remainder due to land use.

Gloor, M., S.-M. Fan, S.W. Pacala, and J.L. Sarmiento. 2000. Optimal sampling of the atmosphere for purpose of inverse modelling - a model study. Global Biogeochem. Cycles 14(1): 407-428.
The 66 stations of the GLOBALVIEW-CO2 sampling network (GLOBALVIEW- CO2: Cooperative Atmospheric Data Integration Project – Carbon Dioxide, (1997)) are located primarily remotely from continents where signals of fossil fuel consumption and biospheric exchange are diluted. It is thus not surprising that inversion studies are able to estimate terrestrial sources and sinks only to a very limited extent. The poor constraint on terrestrial fluxes propagates to the oceans and strongly limits estimates of oceanic fluxes as well, at least if no use is made of other information such as isotopic ratios. We analyze here the resolving power of the GLOBALVIEW- CO2 network, compare the efficiency of different measurement strategies, and determine optimal extensions to the present network. We find the following: (1) GLOBALVIEW- CO2 is well suited to characterize the meridional distribution of sources and sinks but is poorly suited to separate terrestrial from oceanic sinks at the same latitude. The most poorly constrained regions are South America, Africa, and southern hemispheric oceans. (2) To improve the network, observing stations need to be positioned on the continents near to the largest biospheric signals despite the large diurnal and seasonal fluctuations associated with biological activity and the dynamics of the PBL. The mixing in the atmosphere is too strong to allow positioning of stations remote from large fluxes. Our optimization results prove to be fairly insensitive to the details of model transport and the inversion model with the addition of ~ 10 optimally positioned stations. (3) The best measurement strategy among surface observations, N-S airplane transects, and vertical profiles proves to be vertical profiles. (4) Approximately 12 optimally positioned vertical profiles or 30 surface stations in addition to GLOBALVIEW- CO2 would reduce estimate uncertainties cause by insufficient data coverage from ~ 1 Pg C yr-1 per region to ~ 0.2 Pg C yr-1 per region.

Bolker, B.M., S.W. Pacala, S.A. Levin. 2000. Moment methods for stochastic processes in continuous space and time. Pp. 388-411. In: U. Dieckmann, R. Law and J. Metz (eds.) The geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge University Press, Cambridge.
Spatial dynamics of populations have long been of interest to ecologists, but recent advances in data collection and in computational power have put theses ideas within reach of many ecologists for the first time. Computational models suggest important and previously unexplored effects of space and discrete individuals on population dynamics. Analytic approaches that capture these effects are starting to emerge, building on methods developed in other contexts. This chapter presents a general method for deriving approximate equations for spatial dynamics in continuous space and time that has advantages over classical and many modern approaches.

Gloor, M., S-M. Fan, S.W. Pacala, J.L. Sarmiento, and M. Ramonet. 2000. A model-based evaluation of 3-D GCM inversions, using annual mean mixing ratios, as a tool to monitor CO2 surface fluxes J. Geophys. Res-Atmos 104(D12): 14245-14260.
The inversion of atmospheric transport of CO2 may potentially be a means for monitoring compliance with emission treaties in the future. There are two types of errors, though, which may cause errors in inversions: (1) amplification of high-frequency data variability given the information loss in the atmosphere by mixing and (2) systematic errors in the CO2 flux estimates caused by various approximations used to formulate the inversions. In this study we use simulations with atmospheric transport models and a time independent inverse scheme to estimate these errors as a function of network size and the number of flux regions solved for. Our main results are as follows. (1) When solving for 10-20 source regions, the average uncertainty of flux estimates caused by amplification of high-frequency data variability alone decreases strongly with increasing number of stations for up to 150 randomly positioned stations and then levels off (for 150 stations of the order of 0.2 Pg C yr -1). As a rule of thumb, about 10 observing stations are needed per region to be estimated. (2) Of all the sources of systematic errors, modeling error is the largest. Our estimates of SF6 emissions from five continental regions simulated with 12 different AGCMs differ by up to a factor of 2. The number of observations needed to overcome the information loss due to atmospheric mixing is hence small enough to permit monitoring of fluxes with inversions on a continental scale in principle. Nevertheless errors in transport modeling are still too large for inversions to be a quantitatively reliable option for flux monitoring.
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