Glob Change Biol. 2019;00:1–15. wileyonlinelibrary.com/journal/gcb  |  1© 2019 John Wiley & Sons Ltd 1  | INTRODUC TION Understanding tropical forest responses to atmospheric and cli‐ mate change is critical to modeling the future global carbon cycle. Repeated censuses of forest inventory plots have found increasing stocks of tree carbon in apparently undisturbed tropical forests in Amazonia (Baker et al., 2004; Phillips et al., 1998), Africa (Lewis et al., 2013), and Borneo (Qie et al., 2017). Globally, analysis of long‐term forest inventories suggests that old‐growth trop‐ ical forests are currently carbon sinks, sequestering an average Received: 20 April 2019  |  Accepted: 27 August 2019 DOI: 10.1111/gcb.14833 P R I M A R Y R E S E A R C H A R T I C L E Testing for changes in biomass dynamics in large‐scale forest datasets Ervan Rutishauser1  | Stuart J. Wright1 | Richard Condit2 | Stephen P. Hubbell3 | Stuart J. Davies4,5 | Helene C. Muller‐Landau1 1Smithsonian Tropical Research Institute, Ancon, Panama 2Morton Arboretum, Lisle, IL, USA 3Department of Ecology and Evolutionary Biology, University of California, Los Angeles, CA, USA 4Center for Tropical Forest Science‐Forest Global Earth Observatory, Smithsonian Tropical Research Institute, Panama City, Panama 5Department of Botany, National Museum of Natural History, Washington, DC, USA Correspondence Ervan Rutishauser, Smithsonian Tropical Research Institute, Box 0843‐03092 Balboa, Ancon, Panama. Email: er.rutishauser@gmail.com Funding information US Department of Energy; National Science Foundation; Smithsonian Tropical Research Institute; MacArthur Foundation Abstract Tropical forest responses to climate and atmospheric change are critical to the future of the global carbon budget. Recent studies have reported increases in estimated above‐ground biomass (EAGB) stocks, productivity, and mortality in old‐growth tropical forests. These increases could reflect a shift in forest functioning due to global change and/or long‐lasting recovery from past disturbance. We introduce a novel approach to disentangle the relative contributions of these mechanisms by de‐ composing changes in whole‐plot biomass fluxes into contributions from changes in the distribution of gap‐successional stages and changes in fluxes for a given stage. Using 30 years of forest dynamic data at Barro Colorado Island, Panama, we inves‐ tigated temporal variation in EAGB fluxes as a function of initial EAGB (EAGBi) in 10 × 10 m quadrats. Productivity and mortality fluxes both increased strongly with initial quadrat EAGB. The distribution of EAGB (and thus EAGBi) across quadrats hardly varied over 30 years (and seven censuses). EAGB fluxes as a function of EAGBi varied largely and significantly among census intervals, with notably higher produc‐ tivity in 1985–1990 associated with recovery from the 1982–1983 El Niño event. Variation in whole‐plot fluxes among census intervals was explained overwhelmingly by variation in fluxes as a function of EAGBi, with essentially no contribution from changes in EAGBi distributions. The high observed temporal variation in productivity and mortality suggests that this forest is very sensitive to climate variability. There was no consistent long‐term trend in productivity, mortality, or biomass in this forest over 30 years, although the temporal variability in productivity and mortality was so strong that it could well mask a substantial trend. Accurate prediction of future tropi‐ cal forest carbon budgets will require accounting for disturbance‐recovery dynamics and understanding temporal variability in productivity and mortality. K E Y W O R D S biomass dynamic, carbon fluxes, long‐term change, tropical forests 2  |     RUTISHAUSER ET Al. of 0.34 Mg C ha−1 year−1 (confidence intervals [CIs] = 0.17–0.47; Muller‐Landau, Detto, Chisholm, Hubbell, & Condit, 2014), albeit with a reduction in sink strength over time (Brienen et al., 2015; Qie et al., 2017). The causes of this increase and its consistency in space and time remain uncertain (Lewis, Lloyd, Sitch, Mitchard, & Laurance, 2009; Wright, 2010, 2013). Current knowledge of changes in old‐growth tropical forest carbon stocks is hampered by limited spatial and temporal coverage of monitoring plots, sen‐ sitivity to measurement errors and data correction procedures, and the confounding influences of disturbance‐recovery dynamics (Clark, Clark, et al., 2017; Muller‐Landau et al., 2014). There are multiple pathways through which anthropogenic global change could increase or decrease carbon stocks and fluxes in old‐growth tropical forests. Increasing atmospheric carbon dioxide could enhance tropical tree growth and forest productivity through increased photosynthesis and water use efficiency (Lloyd & Farquhar, 2008), and thereby increase forest carbon stocks (Figure 1a–c). Alternatively, rising temperatures and increasing drought frequency and/or intensity could increase tree mortality and thereby decrease forest carbon stocks (McDowell et al., 2018). The “Bigger and Faster” hypothesis proposes that growth, recruitment, and mortality are all increasing (Clark, Clark, et al., 2017); in this case, the net effect on biomass depends on the relative magnitude of the increases in productivity and mortality (Figure 1d–f). Some but not all studies have found evidence of increasing productivity (Brienen et al., 2015; Feeley, Wright, Supardi, Kassim, & Davies, 2007; Körner, 2015) and increasing mortality (Brando et al., 2014; Brienen et al., 2015; Liu et al., 2017; McDowell et al., 2018; Phillips et al., 2010). It is also possible that the observed increase in tropical forest bio‐ mass is due not to global change influences but to long‐lasting recovery from past disturbances in some (but not all) tropical forests (Figure 1g–i; Wright, 2010). There is growing evidence that past human‐induced or climatic disturbances continue to profoundly shape current forest composition (Brncic, Willis, Harris, & Washington, 2006; Levis et al., 2017; Magnabosco Marra et al., 2018), functioning (Doughty et al., 2015; McMichael, Matthews‐Bird, Farfan‐Rios, & Feeley, 2017; Oslisly et al., 2013), and extent (Mayle, Burbridge, & Killeen, 2000) in tropical regions. Forest succession after disturbance would generate a pattern of increasing total biomass mortality and biomass productivity over time, similar to that expected under the “Bigger and Faster” hypothesis (Clark, Clark, et al., 2017), and constitutes a null hypothesis or non‐ global change hypothesis. Forest recovery post‐disturbance poses a particular challenge, as it may act at various spatial and temporal scales, and in only a subset of tropical forests. We propose to separate out the contributions of disturbance‐re‐ covery dynamics to temporal variation in forest carbon stocks by decomposing changes in whole‐plot biomass fluxes into contribu‐ tions from changes in the distribution of gap‐successional stages and changes in fluxes for a given stage (Figure 2). An old‐growth tropical forest is a shifting mosaic of patches at different stages of recovery (Watt, 1947; Whitmore, 1989), of which most are increasing in biomass at any given time (Körner, 2003a). Dividing a plot into small quad‐ rats provides a simple operational way to characterize this mosaic of stages, and quadrat initial EAGB (EAGBi) provides a useful proxy for age/time since disturbance (Bormann & Likens, 1979; Denslow, Ellison, & Sanford, 1998). Plot‐level EAGB fluxes (Figure 2c) then reflect the integration of functions for fluxes as a function of EAGBi (Figure 2a) with the distribution of EAGBi (Figure 2b). Both quadrat productiv‐ ity and mortality fluxes (Mg/ha) are expected to increase with EAGBi (Figure 2a), and consistent global change influences should be evident in directional changes in these functions over time—that is, in increases or decreases in fluxes when controlling for EAGBi. Climate variation could also contribute to temporal variation in productivity and mor‐ tality drivers, and thus in fluxes for a given EAGBi (Dong et al., 2012). In contrast, the distribution of quadrat EAGBi depends largely on the disturbance history at a site (Espírito‐Santo et al., 2014; Fisher, Hurtt, F I G U R E 1   Expected patterns of quadrat biomass fluxes in relation to initial estimated above‐ground biomass (EAGBi) for three possible scenarios (columns) consistent with increasing biomass stocks in tropical forests. In every panel, the solid line shows the pattern expected for an earlier census interval, and the dashed line for a later census interval. Increasing productivity due to “fertilization” (first column), means higher productivity for a given EAGBi in the second census interval (a, dashed line) than in the first one (a, solid line), no systematic difference in mortality after controlling for EAGBi (b), and thus higher net change in EAGB per EAGBi in the second census interval (c). Increasing productivity and mortality, as expected under “speeding up” (second column), means higher productivity and higher mortality in the second census interval (d, e) and diverse possible patterns for net change (f). Finally, recovery from disturbance (final column) is expected to show no systematic change in fluxes when controlling for EAGBi (g–i). Note that local quadrat productivity increases with initial quadrat EAGB in all scenarios and census intervals (first row, blue), as does the local mortality flux (second row, yellow). Quadrat‐level biomass net change (third row, black) is the difference between productivity and mortality fluxes, and is positive for low EAGBi, and becomes negative for high EAGBi      |  3RUTISHAUSER ET Al. Thomas, & Chambers, 2008), and can fluctuate from a dominance of early successional (i.e., low EAGBi) stages soon after disturbance (Figure 2b, time 1) to higher frequency of late successional quadrats longer after disturbance (Figure 2b, time 2). Using a large‐scale, long‐term forest plot dataset for Barro Colorado Island (BCI), Panama, we seek to disentangle the influences of disturbance recovery from potential global change by quantifying how local biomass dynamics vary with initial biomass, and evaluating whether these relationships change over time. Specifically, we tested for temporal variation in quadrat productivity, loss, and net change in biomass when controlling for initial biomass. To assess the degree to which similar biomass patches were consistently associated with sim‐ ilar forest structure across census intervals, we also examined how quadrat initial biomass was related to tree density (per area) and mean tree size at each census and compared these relationships over time. 2  | METHODS 2.1 | Study site Barro Colorado Island is located in central Panama (9°08' N, 79°510' W). Temperature averages 27°C and annual rainfall av‐ erages 2,657 mm (for 1926–2017; Paton, 2018), with a dry sea‐ son between January and April. The vegetation is moist tropical forest. The 50 ha forest dynamics plot was established in 1982 (Condit, 1998; Hubbell et al., 1999), and recensused in 1985 and every 5 years subsequently (Figure S1). All free‐standing woody stems with a diameter at breast height (DBH) ≥1 cm were mapped, tagged, and identified to species, and were measured in diameter at every census in which they remained alive. Diameter measure‐ ments were taken at 1.3 m height or above any buttress or major stem deformity. We omitted the initial census of 1982–1983 from analyses of biomass and biomass dynamics due to major differ‐ ences in the field measurement methods for large trees (Condit, 1998), leaving seven censuses and six 5 year intervals between 1985 and 2015. We omitted 1.2 ha of swamp and 1.9 ha of young forest from the analysis due to differences in species composition, structure, and dynamics (Condit, Hubbell, & Foster, 1996; Harms, Condit, Hubbell, & Foster, 2001), leaving 46.9 ha for analysis. (We note, however, that our results are robust to the inclusion of the young forest, as we would expect; see Supporting information C1). Supplemental materials provide additional details on the census methods (Supporting information A). 2.2 | Individual tree biomass calculation For all stems of dicot (non‐palm) species, we estimated above‐ ground biomass (EAGB) from individual DBH and species‐specific F I G U R E 2   Whole plot estimated above‐ground biomass (EAGB) fluxes (right column) in a given time period depends on the combination of how small‐scale fluxes vary with initial EAGB (EAGBi) (left column) and how EAGBi varies spatially across the plot and over time (middle column). Here, we illustrate this for productivity; the same integration holds for whole‐plot mortality. To distinguish the contribution of flux–EAGBi relationships from the contribution of EAGBi distributions to plot‐level biomass dynamics, we estimated what whole‐plot fluxes would be in each census interval if either the flux–EAGBi relationship or the EAGBi distribution were constant across census intervals. To calculate a single constant flux–EAGBi relationship (d) and a single constant EAGBi distribution (h), we averaged across all census intervals weighted equally. We then integrated the empirical flux–EAGBi relationship over the EAGBi distribution for each census interval under three scenarios: (i) interval‐specific flux–EAGBi relationships and interval‐specific EAGBi distributions (a–c); (ii) the average flux–EAGBi relationship and interval‐specific EAGBi distributions (d–f); (iii) interval‐specific flux–EAGBi relationships and the average EAGBi distribution (g–i) 4  |     RUTISHAUSER ET Al. wood density (WD) using a generic tropical forest biomass equation (Chave et al., 2014). For stems measured at heights other than 1.3 m, we first calculated taper‐corrected equivalent diameters at 1.3 m height using a generic taper correction equation for BCI: where D is diameter measured at height of measurement (HOM; in m; equation 2, Cushman, Muller‐Landau, Condit, & Hubbell, 2014). We applied this taper correction to avoid time‐dependent biases in plot‐level biomass stocks and fluxes associated with changes over time in the proportion of trees measured above 1.3 m and average measurement heights (Cushman et al., 2014). We also es‐ timated missing diameter measurements (1,192 of the 2,607,014 records) by simple linear interpolation between consecutive mea‐ surements. We then EAGB (in Mg dry biomass) of each stem in each census from its DBH, using the updated version of equation 7 of Chave et al. (2014), incorporating species‐level WD (in g/cm3) collected near the study site (Wright et al., 2010 and unpublished) and a climatic index that represents environmental influences on tree height allometries (E = 0.05645985 for BCI): EAGB=exp ( −2.024−0.896×E+0.920× log (WD) +2.795× log (DBH)−0.0461× log (DBH)2 ) (see Supporting information S2 for details of wood density assignment). For palms, we estimated biomass using a palm‐specific allome‐ tric equation based on DBH. For palm species that do not grow in DBH (all local palm species except Socratea exorrhiza), we first as‐ signed species‐specific median DBH to each palm stem in each cen‐ sus (Table S1). We EAGB (in Mg dry biomass) of each palm stem as based on the family‐wise specific allometric equation of Goodman et al. (2013), modified to include the log‐transformation correction factor (Baskerville, 1972). We recognize that this procedure results in systematic errors in biomass fluxes for palms that do not grow in diameter, because it fails to consider their height growth, and that better estimates would be possible if height data were available. Overall, palms other than Socratea account for 0.9% of the woody biomass and 1.8% of the estimated woody productivity on BCI. For multi‐stemmed trees, individual tree biomass was calculated as the sum of biomass of all live stems. Large (DBH > 50 cm) individ‐ uals of strangler fig species (Ficus costaricana, Ficus obtusifolia, Ficus popenoei, and Ficus trigonata), for which diameter measurements are unreliable measures of size, were excluded from the analysis by ex‐ cluding associated quadrats (Table S2). 2.3 | Quadrat‐level biomass stocks and fluxes Biomass stocks and fluxes were analyzed at the scale of 10 m quad‐ rats and for the plot as a whole. Analysis at the quadrat level aimed to quantify how local biomass fluxes vary with local initial biomass for each census interval, and to compare these relationships across census intervals. Initial biomass was calculated as the sum of bio‐ mass of all trees alive at the initial census. We calculated biomass fluxes per time in productivity, mortality, and net change using simple arithmetic estimators. That is, we calculated fluxes for each quadrat by summing over relevant trees (i) and dividing by the time interval measured separately for each tree: Productivity was calculated as the sum of the EAGB changes of sur‐ viving trees and the EAGB of recruits (including resprouts). Because the census dataset includes all stems >1 cm in diameter, biomass in‐ crement accounts for the vast majority of the woody productivity (97.5%; Figure S2). Biomass loss was calculated as the sum of EAGBi of all trees that died by the next census, as well as of large individual stems that died on multi‐stemmed individuals (see Supporting infor‐ mation A for details on the treatment of multi‐stemmed trees). For recruits and dead stems, the time interval used was the mean time between measurements for that quadrat and census interval. These arithmetic estimators systematically underestimate fluxes because they miss contributions from trees that recruited and died during the census interval, with larger biases for longer census intervals (Kohyama, Kohyama, & Sheil, 2019). However, all our census inter‐ vals were very similar in length (Figure S1), and thus, these biases do not confound our analysis. Estimated biomass stocks and fluxes are expressed on a quadrat basis (100 m−2), and can be converted to units of Mg/ha by multiplying by 100. We quantified the relationship of quadrat‐level biomass fluxes to initial biomass for each census interval using local regression and power function fits. We first illustrate the relationships for produc‐ tivity, mortality, and net change using local polynomial regression, specifically the locfit() function in R (Loader, 1999) with smoothing parameter (alpha) set to 0.7. To formally test for variation in EAGB productivity and loss among census intervals, each of these fluxes was modeled as power functions of EAGBi, with a power variance function structure (using package lme4; Bates, Mächler, Bolker, & Walker, 2015). We tested for differences among census intervals in power function “slopes” (exponents) and normalized intercepts, with these intercepts calculated as the predictions for the median EAGB value of 125.0 Mg/ha. CIs were computed by bootstrapping over quadrats (1,000 times). We evaluated the sensitivity of the results to different local regression models, and the consistency between the power function and local regression results. For each census interval, our analyses of quadrat‐level fluxes excluded quadrats affected by any one or more of three prob‐ lems. First, analyses excluded quadrats if any stem had a change in HOM >10 cm during that census interval. Second, analyses ex‐ cluded quadrats that ever had a strangler fig larger than 50 cm DBH. Finally, analyses excluded quadrats where an individual stem had an unreasonably large change in DBH in that census interval, such that its absolute biomass change was >0.98 Mg/ha (this threshold was DBH=D×exp (0.0247× (HOM−1.3)), AGB=0.0417565×DBH 2.7483 , EAGB change= ∑ (EAGBfinal i−EAGBinitial i) timei .      |  5RUTISHAUSER ET Al. chosen because it is 20% of the mean productivity per hectare com‐ puted over all quadrats and census intervals that met the first two criteria). We excluded between 389 and 1,288 of the 4,669 possible quadrats (i.e., not in swamps or in young forest), depending on the census interval, mostly because of the first rule removing quadrats with a change in measurement height (Table S2). We did not remove or correct unlikely but less influential diameter changes, because in a dataset of this size, these random errors will tend to cancel out, whereas attempts to filter or correct such changes have strong po‐ tential to introduce systematic biases (because it is easier to detect some types of errors than others, Muller‐Landau et al., 2014). The results were robust to varying filtering methods (Figure S7). We evaluated consistency in or differences among censuses in the probability distribution of quadrat‐level EAGB using empirical cumulative density functions. We specifically tested for differences among censuses in selected percentiles (5th, 10th, 25th, 50th, 75th, 90th, and 95th), by evaluating whether CIs overlapped. We esti‐ mated CIs on the percentiles by bootstrapping over quadrats. We evaluated the sensitivity of our results to the spatial grain of quadrats, applying the same methods for smaller (8.33 m) and larger (12.5, 15.15 m) quadrats (Figures S8–S10). 2.4 | Disentangling sources of temporal variation in whole‐plot fluxes To distinguish the contribution of flux–EAGBi relationships from the contribution of EAGBi distributions to plot‐level biomass dynamics, we estimated what whole‐plot fluxes would be in each census inter‐ val if either the flux–EAGBi relationship or the EAGBi distribution was constant across census intervals. To calculate a single constant flux– EAGBi relationship and a single constant EAGBi distribution, we aver‐ aged across all census intervals weighted equally. We then integrated the empirical flux–EAGBi relationship over the EAGBi distribution (Figure 2) for each census interval under three scenarios: (a) inter‐ val‐specific flux–EAGBi relationships and the average EAGBi distri‐ bution; (b) the average flux–EAGBi relationship and interval‐specific EAGBi distributions; and (c) interval‐specific flux–EAGBi relation‐ ships and interval‐specific EAGBi distributions. For each flux–EAGBi relationship, fluxes for the central 90% of the EAGBI distribution (from the 5th to 95th percentile) were estimated from EAGBi using fits of the locfit function to the full distribution, as above (α = 0.7). In the tails of the distribution, fluxes were estimated as equal to the means for the corresponding interval (i.e., the 0–5th percentile inter‐ val or the 95th–100th percentile interval), to avoid undue influence of a few points. 2.5 | Forest structure For each census interval, forest structure was quantified by analyzing the distributions over 10 × 10 m quadrats of the numbers of trees ≥ 1, 10, and 60 cm, and of quadratic mean diameter (Dg= �∑ DBH 2 ∕n, in cm). We quantified how these structure measures varied with quadrat EAGB in each census interval by fitting local regressions (R function locfit with α = 0.7), and calculating values expected for se‐ lect quadrat EAGB (corresponding to the 10th, 25th, 50th, 75th, and 90th percentiles computed for all censuses combined). We tested whether there were changes over time in the values expected for selected quadrat EAGB or in the plot‐level means, by comparing CIs obtained by bootstrapping over quadrats. 3  | RESULTS 3.1 | Quadrat‐level biomass fluxes Mean quadrat EAGB productivity and EAGB mortality loss both in‐ creased with initial quadrat EAGB in each census interval, with uncer‐ tainty rising in parallel (Figures 3 and 4a,b; Figure S2). Both fluxes were well‐fit by power functions of EAGBi (Figure 4a,b; Figures S5 and S6). Mean EAGB net change was positive for low EAGBi and became negative in quadrats with EAGB> ~3 Mg/100 m2 (equivalently 300 Mg/ha; Figure 4c). There was substantial variation among census intervals in EAGB fluxes as a function of EAGBi. This is visually evident from examination of the differences in EAGB‐specific fluxes from the mean flux over cen‐ sus intervals (Figure 4d–f), and is quantified by differences in parameter values of the power function fits (Figure 5; power functions were good fits to the data, as is evident from their concordance with local regres‐ sions in Figures S5 and S6). Productivity fluxes in the 1985–1990 census interval averaged 10%–30% higher than the mean over census intervals for all but the highest values of EAGBi (Figure 4d, blue line). The next highest productivity fluxes were in the most recent census interval, and the lowest productivity fluxes were in 2000–2005 (Table S6). EAGB loss also varied among census intervals, with above‐average EAGB loss for lower EAGBi in some census intervals (2005–2010 and 2010–2015) and for higher EAGBi in other intervals (1995–2000). The power function fits reflected these patterns, with significant variation among census intervals in the normalized intercepts, the estimated fluxes at the mid‐ point of the EAGBi distribution (here 125 Mg/ha; Figure 5a,b; Table S6). For productivity, the first census interval had by far the largest inter‐ cept, with subsequent declines to 2000–2005, and then increases since 2005 (Figure 5a). For mortality, the intercept tended to increase after the 1990–1995 census interval. The slopes (exponents) of the power functions showed little variation among census intervals (mostly over‐ lapping CIs, Figure 5c,d). CIs for EAGB loss and net flux were wide (Figures S3 and S4), limiting the power to test for significant differences among census intervals (Figure 4d–f; Figure S3 and S4). Results were qualitatively consistent for other quadrat sizes (Figures S8–S10). 3.2 | Whole plot biomass stocks and fluxes The probability distribution of EAGB density over 10 × 10 m quad‐ rats varied only slightly among censuses, and showed no clear direc‐ tional change (Figure 6a). The 5th–50th percentiles of quadrat EAGB increased slightly from 1985 to 2000, and then decreased again to values similar to initial ones (Figure 6c). In contrast, the 90th percen‐ tile increased slightly over the study period (Figure 6c). 6  |     RUTISHAUSER ET Al. F I G U R E 3   Quadrat‐level mean annual estimated above‐ground biomass (EAGB) productivity (Mg 100 m−2 year−1) as a function of initial quadrat biomass (EAGB in Mg/100 m2) for each 5 year census interval, for individual 10 × 10 m quadrats (points), together with local polynomial regression lines for individual census intervals (colored solid lines) and for all census intervals combined (black dashed lines). Confidence envelopes were computed from bootstrapping over quadrats. For each census interval, analyses excluded quadrats with problematic EAGB change measurements (see Section 2 for details); N is the number of quadrats included for each census interval. The range of data shown here is truncated, but all points were included in the analyses. Note that EAGB stocks and fluxes can be converted to units of Mg/ha by multiplying by 100 F I G U R E 4   Variation among census intervals in quadrat estimated above‐ground biomass (EAGB) productivity (a), loss (b), and net change (c) as a function of above‐ground biomass (EAGB) at the initial census for 10 × 10 m quadrats, together with the corresponding differences from the mean (per initial EAGB) across all census intervals (d–f). Patterns were quantified using local polynomial regression; regression lines are displayed as solid lines for initial EAGB values spanning the 2nd–98th percentiles of the respective census interval, and as dotted lines outside this range. Confidence envelopes were computed by bootstrapping over quadrats, and are shown for the 2nd–98th percentiles of initial EAGB using shading. Analyses excluded quadrats with problematic EAGB change measurements (see methods for details). Note that productivity (a) and loss (b) are shown on log scales, and their differences from the mean are expressed in percentages (d,e) whereas the net change (c) and its difference from the mean (f) are shown on linear scales. Note that EAGB stocks and fluxes can be converted to units of Mg/ha by multiplying by 100      |  7RUTISHAUSER ET Al. Temporal variation in whole‐plot EAGB fluxes as estimated by integrating temporal variation in flux–EAGBi relationships and EAGBi distributions was due almost entirely to temporal vari‐ ation in flux–EAGBi relationships for a given EAGBi, with almost no contribution of temporal variation in the EAGBi distribution (Figure 7; Table S4 scenario b). Temporal patterns in whole‐plot fluxes thus roughly mirrored those in fluxes as a function of EAGBi. Productivity flux was highest in 1985–1990, then dropped steeply, and has increased over the last three census intervals. Mortality loss flux dropped between the first and second census interval, and tended to increase since then, albeit CIs are wide. These pat‐ terns in estimated whole‐plot fluxes mirrored calculated fluxes from summing over quadrats, although the exact pattern in pro‐ ductivity is highly sensitive to data cleaning and correction proce‐ dures (Figures S7–S17). 3.3 | Changes in forest structure The mean density of stems >1 cm dbh increased modestly after the 1982–1983 drought, then thinned rapidly from 1990 to 2005, and was stable from 2005 to 2015 (Figure 8a, black points and lines). The same pattern was evident when controlling for focal quadrat biomass density (Figure 8a, colored lines). The density of stems ≥10 cm dbh in the plot as a whole increased slowly to 1995 and then decreased to 2010, with parallel patterns in all but the lowest biomass quadrats (Figure 8b). The density of large stems (≥60 cm dbh) remained es‐ sentially constant over time (Figure 8c; Table S5). Quadratic mean F I G U R E 5   Variation among census intervals in the intercepts (a, b) and slopes (c, d) of power function relationships of quadrat‐level productivity (a, c) and losses to mortality (b, d) to initial above‐ ground biomass. Intercepts are normalized, and represent the values at the overall midpoint estimated above‐ground biomass (EAGB) value (1.25 Mg/100 m2, i.e., an EAGB density of 125 Mg/ha). Confidence intervals were computed from bootstrapping over quadrats (see Table S2 for parameter values). Analyses excluded quadrats with problematic EAGB change measurements (see Section 2 for details) F I G U R E 6   Probability density distribution (a) and cumulative probability distribution (b) of estimated above‐ground biomass (EAGB) density across all 10 × 10 m quadrats, with insets in (b) magnified to show inter‐census variation for cumulative probabilities of 0.05–0.1 and 0.9–0.95. (c) Variation over time in seven specific percentiles of the EAGB distribution over quadrats (colored points and lines) and in the overall mean EAGB density at the 50 ha scale (black solid points and lines). In panel (c), vertical lines show the 95% confidence intervals (CIs) from bootstrapping over quadrats, and horizontal gray shading shows the CIs for values in 2015 to enable easy visual assessment of how other years compare. The illustrated curves in panels (a) and (b) are truncated at the 0.2th and 99.8th percentiles of the distribution, but all values were included in analyses. Note that the EAGB densities can be converted to units of Mg/ha by multiplying by 100 8  |     RUTISHAUSER ET Al. stem DBH increased from 1985 to 2000, and then leveled off, with parallel patterns for all quadrat biomass densities (Figure 8d). 4  | DISCUSSION Here, we proposed and applied a straightforward way to control for successional stage in analyses of forest biomass change, by compar‐ ing forest patches at similar stages of gap recovery, as inferred by similar EAGBi density. Our analyses revealed strong temporal varia‐ tion in forest woody productivity and loss fluxes both at the whole plot level and when controlling for local (10 × 10 m) gap phase. There was no consistent long‐term trend in productivity, mortality, or bio‐ mass in this forest over 30 years, although the interannual variability in productivity and mortality is so strong that it could well mask a substantial trend. Woody productivity varied ~25% among 5 year census intervals, and woody losses ~15%, between 1985 and 2015. Because this variability is consistent even after controlling for gap phase, we conclude it arises from interannual variation in driving fac‐ tors, most obviously climate. 4.1 | Temporal climate variation in the tropics and its impacts Tropical forests experience biologically important interannual climate variation in temperature, solar radiation, water availabil‐ ity, and the frequency and intensity of major storms. Interannual climate variation in tropical forests is related in part to irregu‐ larly periodic climate oscillations, including the El Niño Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO). In much of the tropics, the El Niño phase of ENSO is as‐ sociated with drier, sunnier, and hotter conditions, whereas the La Niña phase is associated with wetter, cloudier, and cooler con‐ ditions (Holmgren, Scheffer, Ezcurra, Gutiérrez, & Mohren, 2001; Marengo, Tomasella, Alves, Soares, & Rodriguez, 2011). The AMO also influences climate variation at our site and other areas in the region (Elder, Balling, Cerveny, & Krahenbuhl, 2014). Tropical tree recruitment, growth, and mortality all vary among years in relation to such local climate variation, and thus, stand‐level productivity and mortality fluxes vary as well. Extended periods of drier than normal conditions—that is, droughts—are associated with increased mortality and decreased F I G U R E 7   Time series of hypothetical whole‐plot productivity (a), loss (b), and net change (c) expected with and without variation among census intervals in functions specifying how estimated above‐ground biomass (EAGB) fluxes vary with initial biomass, and with and without variation among census intervals in initial EAGB distributions (EAGBi). See Section 2 for details. Vertical lines show 95% confidence intervals obtained by bootstrapping over quadrats. The points are placed at the mid‐points of the census intervals, and jiggered horizontally to increase readability. Values are given in Table S3. Note that EAGB stocks and fluxes can be converted to units of Mg/ha by multiplying by 100. PDF, probability density function F I G U R E 8   Variation among censuses in forest size structure at the whole plot level (black) and for different initial EAGB in 10 × 10 m quadrats (colors). 95% Confidence intervals (vertical lines) were obtained from bootstrapping over quadrats, but are generally smaller than the dot size. The density of large stems and mean diameter are not reported for 1982 due to inconsistencies in measurement methods (Condit, 1998). DBH, diameter at breast height      |  9RUTISHAUSER ET Al. productivity in many tropical forests (Feldpausch et al., 2016; Phillips et al., 2009). The severe 1982–1983 El Niño made the dry season on BCI longer and harsher than normal, and was associated with higher tree mortality rates. Similarly, many sites in the Amazon and south‐ east Asia experienced elevated mortality during and after El Niño droughts (e.g., Brando et al., 2014; McDowell et al., 2018; Phillips et al., 2010; Qie et al., 2017; Rowland et al., 2015). El Niño droughts in the Amazon were also associated with decreased leaf area index, decreased photosynthesis (attributed to both stomatal closure and lower leaf area), and decreased woody productivity during the drought periods (Aguilos, Hérault, Burban, Wagner, & Bonal, 2018; Asner, Townsend, & Braswell, 2000; Rowland et al., 2014; Santos et al., 2018). Tree‐ring studies generally find that woody productivity is positively correlated with annual precipitation (Alfaro‐Sánchez, Muller‐Landau, Wright, & Camarero, 2017; Schippers, Sterck, Vlam, & Zuidema, 2015), consistent with the idea that dry years are bad for productivity. Temporal variation in woody growth in relation to water availability could be explained in part by shifts in allocation (rather than simply differences in total GPP and NPP), with trees allocating to increased xylem growth in wet pe‐ riods after droughts in order to replace drought‐damaged xylem (Trugman et al., 2018). Although most studies have emphasized the negative effects of drier periods, drier years also bring higher solar radiation, and this can lead to more favorable conditions for forest productivity and tree survival if the dryness is not too extreme. On BCI, the drier periods of the 1987–1988 and 1997–1998 El Niños (Figure S18) were associated with elevated fruit production (Detto, Wright, Calderón, & Muller‐Landau, 2018), and the 5 year cen‐ sus periods encompassing these events featured above‐average woody productivity (this study, Meakem et al., 2017). El Niño events are associated with reduced rainfall during the wet season across northern South American and southern Central America (Ropelewski & Halpert, 1987). Moisture availability remains ample and reduced cloud cover and great solar radiation relieves light limitation (Graham, Mulkey, Kitajima, Phillips, & Wright, 2003), providing a straightforward explanation for observed increases in productivity (Detto et al., 2018; Wright & Calderón, 2006). Consistent with these findings, a previous analysis of multiple moist and wet tropical forests, including BCI, found higher tree growth in census intervals with higher solar radiation (Dong et al., 2012). There are also reasons why dry years might exhibit lower rather than higher mortality. Reduced light limitation in sunnier years might reduce mortality rates for shaded understory tree, and fewer and smaller storms may reduce mortality due to wind‐ throws, lightning, and landslides (Aubry‐Kientz, Rossi, Wagner, & Hérault, 2015; Espírito‐Santo et al., 2010; Guzzetti, Peruccacci, Rossi, & Stark, 2008; Yanoviak, Gora, Burchfield, Bitzer, & Detto, 2017). Interannual variation in temperature may also contribute to in‐ terannual variation in tropical forest carbon dynamics. Warmer years have been associated with lower tropical tree growth in sev‐ eral studies (Clark, Piper, Keeling, & Clark, 2003; Dong et al., 2012; Schippers et al., 2015). Temperature directly affects photosynthesis and respiration rates, with photosynthesis responding unimodally to temperature, and respiration increasing continuously with tempera‐ ture (Lloyd & Farquhar, 2008; Slot & Winter, 2017). Furthermore, high leaf temperatures increase vapor pressure deficits and water demand, leading to stomatal closure, and it is this effect on water relations that appears to be the main contributor to temperature limitation on productivity (Aguilos et al., 2018; Slot & Winter, 2017). Higher atmospheric carbon dioxide concentrations increase plant water use efficiency, and may thereby partly mitigate the negative effects of higher temperatures and drier conditions on productivity (Holtum & Winter, 2010). In addition to the direct effects of climate on plant physiological function and mortality risk, climate may also influence forest car‐ bon cycles indirectly by causing shifts in allocation, stand structure, functional composition, and influences of interacting species. Plants may increase or decrease allocation to woody growth, including add‐ ing to or drawing down carbon stores, depending on past and cur‐ rent climate conditions (Clark, Clark, & Oberbauer, 2013; Doughty et al., 2014; Trugman et al., 2018). Past mortality events from cli‐ mate alter tree age and size distributions, gap phase distributions, and thereby stand‐level carbon budgets (Anderegg, Schwalm, et al., 2015; Chazdon, 2003; Clark, 2007). Differential recruitment, survival, and growth of plant functional types under particular cli‐ mate conditions also alters functional composition, and thereby the response of forests to future climate. For example, mortality of drought‐intolerant species under drought can shift composition to‐ ward more drought‐tolerant species, with implications for forest car‐ bon budgets and resilience to future droughts (Esquivel‐Muelbert et al., 2019; McDowell et al., 2008; Ouédraogo, Mortier, Gourlet‐ Fleury, Freycon, & Picard, 2013). The proliferation of pathogens and insect herbivores, and thus their effects on trees, is also highly sen‐ sitive to climate conditions (Anderegg, Hicke, et al., 2015; Van Bael et al., 2004). 4.2 | Detecting and attributing long‐term change Tropical forests are experiencing global atmospheric and climate change. Mean atmospheric CO2 concentration is increasing continu‐ ously, with an increase of 15% over the duration of our study (from 346 ppm in 1985 to 400 ppm in 2015, Figure S18g). Temperatures are increasing in most tropical regions, and precipitation patterns are changing in region‐specific ways (Buckley & Huey, 2016; Malhi & Wright, 2004). At our site, the focal 30 year period exhibited trends of +0.15°C per decade in daily maximum temperature, +0.04°C per decade in daily minimum temperature, +5 mm/year in annual pre‐ cipitation, +0.05% soil moisture per year, and −1.3 W m−2 year−1 in annual solar radiation. Trends in annual means of these BCI climate metrics over the 30 year period alone were not statistically signifi‐ cant after Bonferroni correction (individual p‐values of .075, .44, .66, .033, and .48, respectively), reflecting the relative strength of interannual variation. This interannual variation limits the ability to detect long‐term trends—but failure to reject the null hypothesis of 10  |     RUTISHAUSER ET Al. no increase should not be misinterpreted as support for constant climate conditions. These atmospheric and climate changes are hypothesized to be changing tropical forest carbon dynamics (Lewis, Malhi, & Phillips, 2004). CO2 is needed for photosynthesis, and physiological models suggest that the observed increase in CO2 should increase growth (Phillips & Lewis, 2014), although there is uncertainty about the degree to which growth responses are limited by availability of other nutrients, and within‐plant carbon demands (Körner, 2009, 2003b; Wright et al., 2011). Spatial variation in climate among tropical forests is associated with variation in tropical forest car‐ bon stocks and fluxes (Álvarez‐Dávila et al., 2017; Becknell, Kissing Kucek, & Powers, 2012; Poorter et al., 2016; Taylor et al., 2017), suggesting that directional climate changes should also change forest carbon budgets in the long term. As discussed above, tropi‐ cal forests are also sensitive to temporal variation in climate condi‐ tions, further suggesting that climate change will matter. However, the relationship of short‐term to long‐term climate responses is not straightforward, because the importance of particular mecha‐ nisms shifts with the timescale. Allocational shifts to/from woody productivity, reproductive output, and carbohydrate stores play a large role in variation over seasonal to annual time scales (Dickman et al., 2018; Doughty et al., 2014), but are likely to play little role at decadal and longer time scales. In contrast, shifts in functional composition of the tree community are likely to play a large role in responses to long‐term climate variation (van der Sande et al., 2016), but very little role in short‐term responses. Such composi‐ tional shifts are in general expected to decrease the sensitivity of forest carbon fluxes to climate variation, as the forest becomes in‐ creasingly dominated by species that do relatively well in the new climate conditions (Esquivel‐Muelbert et al., 2019; Fauset et al.., 2015; Feldpausch et al., 2016). However, evidence of long‐term changes in tropical forest carbon cycling is mixed, with divergent patterns across stud‐ ies. Increasing woody productivity and mortality were found in analyses of the RAINFOR network of Amazonian plots (Brienen et al., 2015), but not in site‐specific studies of BCI (this study) or La Selva (Clark, Asao, et al., 2017; Clark et al., 2013; Clark, Clark, et al., 2017). On average, studies report increased biomass den‐ sities in old‐growth tropical forests (Brienen et al., 2015; Chave et al., 2008, Lewis et al., 2009; Muller‐Landau et al., 2014; Qie et al., 2017; Rutishauser, Wagner, Herault, Nicolini, & Blanc, 2010), but this pattern too is not universal (this study, Chave et al., 2008; Clark, Clark, et al., 2017; Feeley et al., 2007) and the causes of observed increases continue to be debated (Clark, 2004; Lewis et al., 2009; Muller‐Landau, 2009; Wright, 2013). It is notable that two of the most intensive long‐term studies of focal sites, this 30 year study of BCI and Clark, Clark, et al. (2017)'s 40 year study of La Selva, find multidecadal stability in forest structure and dy‐ namics, in striking contrast to the “Bigger and Faster” hypothesis. The large uncertainty surrounding estimated fluxes and their long‐term trends observed here, even with such a large‐scale long‐term study, highlights the difficulty of accurately capturing changes in forest dynamics from field data (Clark, Asao, et al., 2017). Wagner, Rutishauser, Blanc, and Herault (2010) calculated that estimating even the mean EAGB loss within 20% error with 95% confidence in a particular forest would require ~200 ha‐years of monitoring, far more than the usual size and duration of most forest monitoring experiments. The effort required to accurately estimate a long‐term trend is much higher still—even a trend as large as 1% a year amounts to only 10% a decade, within the error limits of the Wagner et al. (2010) calculation. Detection of long‐ term trends is further complicated by sensitivity of estimated trends to the precise methods of data quality assessment and qual‐ ity control (QAQC; Figure S18). Many common QAQC procedures result in systematic biases in whole‐plot statistics (Cushman et al., 2014; Muller‐Landau et al., 2014). Our analysis followed current best practices for calculating EAGB fluxes, including standardizing effective POM (Cushman et al., 2014) and avoiding data “clean‐ ing” procedures that can systematically bias whole‐plot statistics (Muller‐Landau et al., 2014). 4.3 | Conclusion and future directions The tropical forest on BCI exhibited large temporal variability in stand‐level productivity and mortality fluxes over 30 years, even after controlling for disturbance‐recovery dynamics, but no long‐ term trend. Observed temporal variability was aligned to some degree with ENSO‐related climate variation, but with a markedly different pattern than is usually reported, highlighting the complex‐ ity of tropical forest climate responses. While the drier conditions of El Niño events have been associated with increased tree mor‐ tality and reduced productivity in the Amazon (Feldpausch et al., 2016; Lewis, Brando, Phillips, Heijden, & Nepstad, 2011), the drier and sunnier conditions during El Niño events were associated with enhanced productivity and no change in mortality on BCI (Detto et al., 2018; Meakem et al., 2017). No long‐term directional trend in productivity, mortality, or biomass was evident in our data, but such a trend could well be obscured by the strong interannual variation. A better understanding of tropical forest responses to climate variation and long‐term trends requires both more data and in‐ tegration with mechanistic models. Although climate and atmo‐ spheric change is global, climate effects are locally variable, and forest responses are dependent on a myriad of other local factors, including species composition and disturbance history, resulting in highly variable EAGB dynamics (Clark et al., 2013). Future mul‐ tisite analyses of large plot datasets using the methods developed here could provide insights into temporal and spatial variation in tropical forest carbon fluxes (Chave et al., 2008; van der Sande et al., 2016; Wagner et al., 2016). However, any studies based on extant plot datasets are likely to fall short of what is needed to quantify overall trends given high temporal and spatial variability, and the nonsystematic placement of sampling plots (Marvin et al., 2014; McMichael et al., 2017; Saatchi et al., 2015; Wright, 2006). Improvements in remote sensing ultimately promise more compre‐ hensive and consistent measurements of tropical forest structure      |  11RUTISHAUSER ET Al. and function, and their change over time (Bastin et al., 2018; Rödig et al., 2018; Saatchi et al., 2011), although the contribution of re‐ covery from past disturbances remains to be resolved (McMichael et al., 2017; Palace et al., 2017). Studies integrating mechanis‐ tic models with data on climate drivers and forest dynamics are uniquely well suited to gleaning insights into the ultimate mech‐ anisms behind observed patterns and to disentangling the roles of temperature, rainfall, atmospheric carbon dioxide, soils, species composition, and site history (Levine et al., 2016; Schippers et al., 2015). ACKNOWLEDG EMENTS E.R. and S.J.D. were supported by the Next Generation Ecosystem Experiments‐Tropics, funded by the US Department of Energy, Office of Science, Office of Biological and Environ‐ mental Research. We gratefully acknowledge the contributions to the Barro Colorado Island 50 ha plot of Robin Foster, co‐ founder of the plot; Rolando Pérez and Salomón Aguilar for species identification; Suzanne Lao for data management; Steven Dolins for database design; and hundreds of field‐work‐ ers over the years. The BCI forest dynamics plot dataset was made possible by the financial support of the National Science Foundation, the Smithsonian Tropical Research Institute, and the MacArthur Foundation. We thank Deborah A. Clark and an anonymous reviewer for constructive comments on this manuscript. CONFLIC T OF INTERE S T All authors declare no conflict of interest. ORCID Ervan Rutishauser https://orcid.org/0000‐0003‐1182‐4032 R E FE R E N C E S Aguilos, M., Hérault, B., Burban, B., Wagner, F., & Bonal, D. (2018). What drives long‐term variations in carbon flux and balance in a tropical rainforest in French Guiana? 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Glob Change Biol. 2019;00:1–15. https ://doi.org/10.1111/ gcb.14833