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Ecol Lett. Author manuscript; available in PMC 2010 June 16.
Published in final edited form as:
PMCID: PMC2886595

Changes in a tropical forest support metabolic zero-sum dynamics


Major shifts in many ecosystem-level properties of tropical forests have been observed, but the processes driving these changes are poorly understood. The forest on Barro Colorado Island (BCI) exhibited a 20% decrease in the number of trees and a 10% increase in average diameter. Using a metabolism-based zero-sum framework, we show that increases in per capita resource use at BCI, caused by increased tree size and increased temperature, compensated for the observed declines in abundance. This trade-off between abundance and average resource use resulted in no net change in the rate resources are fluxed by the forest. Observed changes in the forest are not consistent with other hypotheses, including changes in overall resource availability and existing self-thinning models. The framework successfully predicts interrelated changes in size, abundance and temperature, indicating its utility for understanding changes in the structure and dynamics of ecosystems.

Keywords: Community ecology, metabolic ecology, neutral theory, tropical forests, zero-sum dynamics


The assumption that the abundance, distribution and diversity of species are due primarily to resource limitation is a cornerstone of ecological and evolutionary theory (Van Valen 1973; Charnov 1993; Hubbell 2001; Brown et al. 2004). Fundamental to this assumption is the idea that the rate of supply of usable energy or material to an ecosystem limits the carrying capacity, which can be defined as the total resource use or metabolism of the biota. At steady state, when the total rate of resource use by organisms equals the rate of limiting resource supply, an ecosystem is subject to a zero-sum metabolic constraint; any increase in resource use by some organisms must be balanced by decreases in resource use by other organisms (Van Valen 1973; Ernest & Brown 2001; Hubbell 2001). Such zero-sum dynamics impose simple rules on ecosystem-level properties (Enquist et al. 1998, 2003; Ernest & Brown 2001; Hubbell 2001; White et al. 2004; Ernest et al. 2008). For example, changes in the overall rate of resource supply (R) will be reflected in changes in the overall rate of resource use (Utot) by the community of organisms that share requirements for the same limiting resource (i.e. energy and/or materials).

The rate of energy and material use by an individual organism is related to its whole-organism metabolic rate (Bi) and the total rate of resource use of an ecological guild, community or ecosystem will be related to the sum of the resource use of the component individuals (Enquist et al. 1998, 2003; Ernest & Brown 2001; White et al. 2004), so,


where i indexes the individuals constrained by a common resource and the proportionality indicates that the group in question does not have to use all of the available resource, just a constant proportion. In eqn 1, we have made 1NUi1NBi to denote the approximate relationship between metabolic rate and actual organism resource use. Because the metabolic rate of an individual is related to its size (Brown et al. 2004), a given rate of resource supply can support many small individuals or fewer larger individuals. Specifically, under zero-sum dynamics (i.e. if R equals a constant) eqn 1 implies a trade-off between the number of organisms and their average individual metabolic rate (Enquist et al. 1998; White et al. 2004)


and changes in the size distribution of individuals (White et al. 2007) should result in specific, quantifiable, changes in abundance.

Studies of tropical forests have documented a variety of dynamic changes, including shifts in biomass (Phillips et al. 1998; Chave et al. 2008), individual growth rates (Clark et al. 2003; Laurance et al. 2004; Feeley et al. 2007b), abundance (Losos & Leigh 2004; Pitman 2005), size structure (Condit et al. 1996) and species composition (Condit 1998a; Laurance et al. 2004). These shifts could have multiple causes, including climate change (e.g. long-term shifts in temperature, light availability), increased CO2 or other abiotic or biotic effects on population dynamics (Condit et al. 1996; Graham et al. 2003; Laurance et al. 2004; Pitman 2005; Feeley et al. 2007a). Changes in the ecosystem-level properties of tropical forests have been interpreted as implying that climate change has altered overall rates of primary production through changes in light availability and/or CO2 enrichment (Clark et al. 2003; Graham et al. 2003; Laurance et al. 2004; Feeley et al. 2007b). A long-term study of trees on Barro Colorado Island (BCI), Panama (Condit 1998b; Hubbell et al. 1999; Condit et al. 2005) provides an excellent case study for evaluating alternative hypotheses for changes documented in this tropical forest. The BCI 50-ha plot has been repeatedly and intensively censused since 1981. Documented changes include: altered species composition (Condit et al. 1996; Condit 1998a), large decreases in the numbers of small trees (Condit et al. 1996), smaller increases in the numbers of large trees (Condit et al. 1999) and consequently, an overall decrease in the abundance of trees (Condit et al. 1999; Losos & Leigh 2004). Many of these changes are similar to changes documented in other tropical forests (Clark et al. 2003; Losos & Leigh 2004; Feeley et al. 2007b).

Here, we use a metabolic zero-sum framework to evaluate whether changes observed at BCI reflect (i) the reallocation of resources due to the trade-off between individual resource use and abundance; (ii) self-thinning processes caused by geometric packing constraints as trees grow larger or (iii) whether they result from a reduced carrying capacity due to decreased resource supply. These alternative hypotheses make clear predictions: (i) zero-sum dynamics – if overall resource supply rate has remained effectively constant, and the changes in forest structure reflect a metabolic trade-off between the number of individuals and the metabolic rates of those individuals, we should observe no directional change in total forest-level energy flux, and N and B should be inversely related, so NB1; (ii) self-thinning – as a forest recovers from disturbance, large numbers of young, small trees grow larger creating packing constraints, which lead to increased mortality and decreases in tree abundance. Different models for self-thinning suggest a variety of relationships between N and diameter (D), with the extremes represented by the 3/2 and the 4/3 thinning models (Enquist et al. 1998; Pretzsch 2006) which, properly accounting for Jensen's inequality (see Supplementary material), result in the predictions: ND21 or ND1691, respectively; (iii) reduced carrying capacity – if the decrease in the total number of trees reflects a decrease in the overall carrying capacity of the environment for trees, then the estimated rate of energy flux should have decreased over the 20-year period and the slope of the relationship between abundance and average metabolic rate should differ from −1. Furthermore, a potentially limiting resource would need to exhibit a significant decline over the period of the study.


Research site

Data for this study come exclusively from the Smithsonian Tropical Research Institute's research station at BCI. BCI is an artificial island formed when the Panama Canal was flooded and has been part of a protected biodiversity reserve since 1923. The 1500 ha island contains a moist lowland tropical forest community. This forest was disturbed by human activities – by both pre- and post-Columbian societies – through forestry and clearing for agricultural land until 1923 (Leigh et al. 1996).

Forest data

All data on trees were obtained from the online database for the 50 ha Forest Dynamic Plot on BCI. This forest plot has been completely censused approximately every 5 years since 1980. Detailed methods for the census are available at Here, we only discuss census methodology relevant for this study.

For each forest census, all stems greater than or equal to 10 mm were identified and diameter at breast height (DBH) was measured. Because there is no data for individuals < 10 mm, our forest-level estimates and subsequent analyses are only valid for that component of the forest ≥ 10 mm DBH. DBH is defined as diameter at 1.3 m unless the tree contained buttresses or stilts in which case DBH was taken immediately above these structural components. Each individual in the census was given a unique tag number. If an individual had multiple stems, a DBH was taken for all stems ≥ 10 mm. Methodology is consistent across censuses except that in the 1980 and 1985 census the DBH for all trees < 50 mm was rounded down to the lowest 5 mm increment. Because of the importance for this study of having comparable size estimates across all censuses, we follow Muller-Landau et al. (2006) and do not use the data from the first two censuses.

Because theoretical models linking the diameter of a tree with its metabolic rate are based on the diameter of the basal stem (West et al. 1999), basal stem diameter had to be estimated for individuals with multiple stems at breast height. We used the pipe model, an area preserving model used since Leonardo da Vinci, to back calculate the basal diameter from the number of stems at breast height (n) and the diameter of each of those stems (D).


Temperature data

Long-term climate data has been collected at BCI on an hourly basis since 1983 at the field station (clearing weather station) and since 1984 at the Lutz canopy tower. Temperature data (and all other abiotic data sets for BCI described in this study) are available at: Temperature data for this study was obtained from the clearing weather station due to large gaps in data collection at the Lutz tower. Recent activities around the clearing weather station may have influenced recent temperature readings ( bci.htm). However, comparisons of the daily average temperature readings for both stations reveals that these data are well correlated with each other (r = 0.7942) and this correlation has not decayed since 1999 (r = 0.8416).

For studying temperature trends at the site, we calculated an average temperature for each year of the study. Data were averaged by calculating monthly averages of hourly temperatures (day and night) and then averaging the monthly averages within each year. This reduces the impact of the timing of missing data on the averages.

Estimating metabolic rates

To estimate metabolic rate for each tree, we used a previously published relationship (West et al. 1999; Gillooly et al. 2002; Allen et al. 2005) that incorporates both the size of the individual and the temperature:


where λ is a constant (≈2) relating basal stem diameter (D) to metabolic rate (West et al. 1999), E is the average activation energy of C3 photosynthesis (≈0.32 eV; Allen et al. 2005), k is Boltzmann's constant (8.6 × 10−5 eVK) and T is air temperature in kelvin (K). Our results are not sensitive to a reasonable range of variation in values of either E or λ (see Diameter exponent and activation energy). This equation assumes that all species can be characterized by this same relationship. Equation 3 was used to estimate the metabolic rate for an individual tree, which was then used to calculate both estimated mean individual metabolic rate (i.e. averaged across individuals) and estimated total stand metabolic flux (i.e. summed over all individuals). When λ = 2, our model is an extension of resource-based self-thinning rules (e.g. Enquist et al. 1998).

Because temperature varies at multiple timescales, the effect of temperature on metabolic rate is more complicated than simply inserting an average temperature into the temperature term for the metabolic equation (eqn 3; Savage 2004). Therefore, temperature terms were calculated for each hourly data point, which were then used to calculate monthly averages of the temperature term. An average temperature term was determined for each census period by averaging 5-year blocks of monthly terms consisting of the 4 years prior to each census and the year in which the census began. As a result, the exact form of the relationship we are testing is: N1D2×eEkT, where <eE/kT> denotes that the average of the temperature term is taken across time, not across individuals as is the case with diameter (D2).

Finally, it should be noted that we have no measure of the scaling constant required to calibrate the metabolic rate for these trees. While the constant would allow us to comment on absolute metabolic flux of the forest, the proportional values are sufficient to evaluate the above hypotheses. Finally, we quantified the compensatory dynamics among size classes by calculating total metabolic flux for eight equal-width logarithmic bins to assess whether decreases in flux for small size classes due to decreasing numbers of small trees were matched by increases in flux for large size classes due to increasing numbers of large trees.

Diameter exponent and activation energy

The resource use exponent (λ = 2) and activation energy (0.32 eV) we used have been suggested as the theoretical expectations for these values (West et al. 1999; Allen et al. 2005), and have some empirical support (Enquist et al. 1998; Allen et al. 2005; Meinzer et al. 2005). However, the specific values for both of these exponents are controversial (Muller-Landau et al. 2006; Enquist et al. 2007). However, the general functional form of this relationship is, at least, a reasonable statistical description of the relationships between diameter, temperature and resource use or related responses (Clarke & Fraser 2004; Muller-Landau et al. 2006). Therefore, in order to test the sensitivity of our analysis to our specific choice of exponent and activation energy we varied these exponents and refit the exponent of the abundance-metabolic rate trade-off (eqn 2) to determine if this caused it to deviate from the predicted value of −1.

Long-term dynamics of potential limiting resources

Recent studies have suggested that changes in light availability (Graham et al. 2003), nitrogen availability (Magnani et al. 2007) or CO2 (Phillips et al. 1998) might be driving changes in tropical forests. Each of these possibilities was explored using either local data collected at BCI or the results of recent regional scale analyses.

Light availability

Photosynthetically available radiation (PAR) has been measured at BCI since 1990 at the Lutz tower using a LI-COR 190SB (for more details see: Daily total PAR values (Einsteins m−2) were summed for each year to obtain yearly total PAR.

Nitrogen availability

Recent papers have suggested that increased nitrogen deposition could increase nitrogen availability in forests (Magnani et al. 2007). However, a recent study suggests that nitrogen deposition rates in Central America have not changed substantially since the late 1800s (Galloway et al. 2004). To the best of our knowledge, there is no long-term monitoring of nitrogen availability in soils on the 50-ha plot. Nitrogen availability could either be increasing or non-changing at BCI. There is no reason to suspect that nitrogen levels have declined.


Global CO2 levels have increased over the past few decades (Forster et al. 2007), which would imply that CO2 available to trees should also have increased.

Water availability

Annual precipitation for BCI was taken from the data collected at the Clearing near the field station from 1990 to 2005 (for more details see: We used the daily data file and summed these values for each year to determine annual precipitation (mm). Potential evapotranspiration at BCI was also measured at the field station clearing (for more details see: Daily values of PET (mm) were summed for each year to determine annual PET.


The dynamics of the forest on BCI clearly support hypothesis (1), and are consistent with a metabolic zero-sum dynamic without directional changes in resource availability (Figs 1 and and2).2). The total metabolic flux of all trees exhibited no directional trend over time, while other forest-level properties (i.e. abundance, biomass, total basal area) changed directionally (see Supplementary results). Total stand metabolic flux did not change directionally due to the trade-off between increased average metabolic rates of individual trees (resulting from increased average diameter and increased temperature) and decreased average abundance (Fig. 2). While the data support an inverse relationship between N and B, the data do not support either of the self-thinning models (Table 1). Furthermore, all biological measures of the forest either do not change directionally or decrease through time, while potential limiting resources appear to either increase or remain stable (Fig. 3). As such, the weight of evidence is consistent with a metabolic zero-sum dynamic and rejects both packing constraints and shifts in resource availability as drivers of the observed declines in abundance at BCI.

Figure 1
Long-term trends on the 50-ha forest dynamics plot at BCI, Panama. (a) Total abundance of trees (individuals per 50 ha) decreases through time (r2 = 0.96; P = 0.018), (b) total stand metabolic flux (proportional to the true total stand metabolic flux) ...
Figure 2
Relationship between average estimated resource use of an individual (1Ni=1ND2eEkT) and the total number of individuals (N) occurring on the BCI 50 ha plot. The exponent, fitted using reduced major axis regression ...
Figure 3
Time-series of PAR (a), precipitation (b) and PET (c), at BCI from 1990 to 2005. PAR did not change directionally from 1990 to 2005 (r2 = 0.0062; P = 0.77). Precipitation did not exhibit any directional changes (r2 = 0.0006; P = 0.93). PET data was only ...
Table 1
Tests of predictions of metabolic zero-sum and self-thinning models against observed trends at Barro Colorado Island

The sensitivity analyses indicate that our results are robust to reasonable variation in the form of the temperature and body size dependence of metabolic rate (Fig. 4a). The range of reasonable activation energy values includes those estimated in recent work purporting that the activation energy will be shallower than expected due to acclimation (Enquist et al. 2007). The range of diameter exponents includes those equivalent to the growth rate allometries recently estimated for BCI (Muller-Landau et al. 2006) and therefore our results are robust to potential differences in scaling exponents due to size-biased light competition. We also examined whether our results were sensitive to the spatial scale of our analysis. By dividing the 50 ha plot into smaller and smaller subplots (see Supplementary methods), we determined whether the observed relationship between abundance and average individual metabolic rate changed as the spatial scale of analysis decreased. We found that behavior predicted by metabolic zero-sum dynamics was observed until the size of a subplot equaled c. 6 ha (Fig. 4b). Below this size, slopes were significantly shallower than expected. This same type of pattern has been observed in estimates of biomass (Keller et al. 2001; Chave et al. 2003) and biomass accumulation (Feeley et al. 2007a) and was interpreted as indicating that below 6 ha the idiosyncrasies of gap-phase dynamics dominate and the signal of forest-level dynamics is weaker.

Figure 4
Parameter and spatial scale sensitivity analyses. (a) Results from the sensitivity analysis examining effects of varying the values of the diameter exponent (λ) and activation energy (E). The shaded area indicates combinations of λ and ...

Our results are also consistent with previous studies documenting that the numbers of trees with small diameters decreased dramatically, while the numbers of large trees increased only modestly (Condit et al. 1996, 1999). Because size-related differences in metabolic rate means not all trees will contribute equally to resource use, small changes in the abundance of larger size classes have a much greater influence on total metabolic flux than much larger changes in abundance in smaller size classes (Fig. 5). Our results also indicate that increases in per capita metabolic rate due to temperature played an important role in maintaining the metabolic zero-sum dynamic. Without this temperature effect, the small increase in the number of larger trees was not sufficient to balance the losses in the small size classes (Fig. 5). This supports the necessity of our extension of previous self-thinning models (e.g. Enquist et al. 1998) for understanding the observed dynamics of this system.

Figure 5
Changes within size classes of metabolic flux (a) and abundance (b) between 1990 and 2005. X-axis: centre of the size class in logarithmic space. Y-axis: size classes with increased abundance or metabolic flux since 1990 are positive, decreases are negative. ...

Because we only have four data points suitable for our analyses, some caution should be used in interpreting our results. Obviously, further tests of a metabolic zero-sum dynamic involving longer time-series and/or experimental tests are needed. However, because we are still able to clearly distinguish among models we feel that our conclusions are reasonably robust and warrant further investigation of this concept in forests. Furthermore, the importance of tropical forests to conservation and global carbon budgets makes it necessary to make use of existing, though sometimes limited, time-series (Condit et al. 1996; Condit 1998a; Laurance et al. 2004; Losos & Leigh 2004; Feeley et al. 2007b; Chave et al. 2008). Despite the short nature of the time-series our framework successfully describes the observed behavior of the system in response to changes in average tree size. The processes driving this shift in size structure are not yet well understood. One reasonable possibility is simply that natural growth of individual trees has been compensated for by increased mortality in the smaller size classes. Alternatively, some studies have implicated climate change as the driver of declines in small trees (Condit et al. 1996), while others have suggested that succession, in response the anthropogenic activities, may be occurring in this forest (Sheil & Burslem 2003). While self-thinning-based successional mechanisms are insufficient for describing the overall dynamics of the forest (Table 1), succession may still be responsible for the increase in average individual size. The success of the metabolic zero-sum framework suggests that in order to predict future dynamics of abundance (and biomass; see Supporting Information) of tropical trees it will be necessary to understand the processes that affect the individual size distribution. Finally, our results highlight the importance of incorporating the effects of temperature on the rates of biological processes (Enquist et al. 2003; Allen et al. 2005), because both size and temperature played important roles in the dynamics of this forest.

Further testing will be necessary to assess the general utility of a zero-sum approach for understanding the long-term dynamics of ecosystems. Previous work has shown that the long-term dynamics of a desert rodent community also exhibit metabolic zero-sum dynamics, with maintenance of relatively constant rates of resource use due to a similar trade-off between metabolic rate and abundance of small and large individuals (White et al. 2004; Ernest et al. 2008). That the long-term dynamics of tropical forests and desert rodents can be explained using this relatively simple framework suggests that it may apply more generally across habitat types and taxonomic groups. The extent of generality likely depends on how often the two key assumptions – that overall resource supply does not change directionally over time and that organisms tend to use a constant fraction of available resources – are met in different ecosystems. Obviously, the zero-sum does not apply when resources are not limiting, such as immediately following major disturbance events. The fact that it appears to apply to both tropical trees and desert rodents suggests that the long-term rates of limiting resource supply that impose the zero-sum may be more constant than the environmental variables that cause temporal variation in body size and species composition.

The utility of the zero-sum framework arises in large part from the fact that it synthesizes important components from two influential and general theories in ecology: the zero-sum constraint from the unified neutral theory of biodiversity (Hubbell 2001) and differences between individuals and species in resource use from the metabolic theory of ecology (Brown et al. 2004). The resulting simple mathematical framework not only combines the role of community and ecosystem-level constraints and the importance of differences among individuals and species in their rates of resource use, but is easily applied to both plants and animals and is equally relevant to tropical and desert systems.

Supplementary Material



We especially thank R. Condit for considerable discussion, which substantially improved this project. We also thank J. Chave, D. Storch, N. Swenson, J. Stegen and several anonymous referees for helpful comments on the manuscript, and also J. Chave for providing biomass data. The Forest Dynamics Plot of BCI is made possible through the support of the U.S. National Science Foundation, the John D. and Catherine T. MacArthur Foundation, the Smithsonian Tropical Research Institute and through the hard work of over 100 people from 10 countries over the past two decades. The BCI Forest Dynamics Plot is part of the Center for Tropical Forest Science, a global network of large-scale demographic tree plots. Environmental data sets were provided by the Terrestrial-Environmental Sciences Program of the Smithsonian Tropical Research Institute. Our thanks to Steve Patton for making these data publically available and for helpful conversations regarding their use. EPW was supported by an NSF Postdoctoral Fellowship in Bioinformatics (DBI-0532847) and JHB by a sabbatical fellowship from the National Center for Ecological Analysis and Synthesis.


SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article:

Appendix S1 Supplemental methods, results, and discussion.

Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.


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