declines in mortality rates over time
We have shown that stand-level mortality rates decline with increasing census interval length, as predicted from theory, whether rates are simulated using the mortality rates of many species in a stand as subpopulations, or derived from monitoring cohorts of trees in long-term multicensus plots (Figs 1, 2 and 3, Tables 3 and 4). Although declines are modest on an annual basis, correcting for census interval differences using our empirically derived equation 3 may result in the re-appraisal of differences in dynamics between different forests. For example, two sites from Phillips’ (1996) analysis, Caño Rosalba (CR1), Venezuela, and Kade (K1), Ghana, both have reported annual turnover rates of 1.49%, but these are obtained from census intervals of 2 and 25 years, respectively. Census-corrected turnover rates suggest that Kade has higher annual turnover than Caño Rosalba (1.93% vs. 1.57%). More recently published studies further highlight how differing census interval lengths can impact on intersite comparisons: the annual mortality rate for Budongo, Uganda, between 1939 and 1993 is 1.05% (Sheil et al. 2000), while the reported rate at Pasoh, Malaysia, between 1987 and 1990 is 1.16% (Condit et al. 1999), 10% higher than Budongo. When the results are census-corrected Budongo has a higher mortality rate (1.42%) than Pasoh (1.26%).
The long-term plot data, while showing average declines in mortality rate with increasing census interval, are extremely variable. Of the 14 plots studied, 11 showed decreases, five of which were significant, while three, counter to our theoretical predictions, showed increases, of which two were significant (Sungei Menyala, Bukit Lagong). We suggest that these increases may be caused by long-term non-linear temporal changes in mortality and recruitment rates. Our methods of accounting for potential increases in mortality rates over the late 20th century assume that any change, if present, is linear. This may not be the case, and some non-linear changes in forest dynamics may cause increases in mortality rates with increasing census intervals, as calculated using the methods described in this paper. For example, if the recruits to a plot have differing mortality rates, and mortality distribution, compared with the stems that died, and these temporal changes are systematic and non-linear, then this would affect the changes in mortality rates we detect with lengthening census intervals, including scenarios where an increase in mortality rate with lengthening census intervals is discoverable. However, the precise cause(s) of these increases in mortality rates with increasing census interval requires further research.
A power function provides the best fit for 10 of the 14 long-term plots, and on average this was a best fit across the 14 plots. However, as discussed, the data are highly variable. This may be caused by inherent stochastic variation, or measurement errors, or may reflect different functional forms of decline in different forests. We do not know whether the distribution of mortality rates of stems in different forests are similar or quite different, thus at present it is unknown whether our empirical approach either identifies the correct functional form, or, indeed, that a single functional form is applicable to all forests. We firstly used a generic correction factor derived from the mean decline from all 14 long-term plots to correct other data. This is better than ignoring the census interval problem, but if different forests have different functional forms of decline, then a site-specific correction may be more appropriate. However, site-specific corrections will often be based on very few data points from a single site, or from a single small plot, and thus will include large stochastic variation leading to a poor estimate of the rate of decline for a single site. Some of the site-specific estimates from plots with only two intervals actually show very large increases in mortality with increasing census interval, for which there is no obvious cause, and this is likely to be merely variability in the system. For these reasons, we suggest that corrections may be done on both a generic, and where possible, site-specific basis. Nevertheless, we recommend a generic correction at this stage, as (i) the variation in mortality rates over short time periods and small sample sizes is known to be very large, and (ii) the simulation data suggest that different forests may have similar functional forms of decline.
The most striking result is that the long-term forest plot data show a much steeper rate of decline in mortality over shorter census intervals than the simulations using species as subpopulations (Fig. 3). The steepness of the decline in mortality rate with increasing census interval is governed by the distribution of mortality rates of all stems, with notably steep declines associated with a fraction of the population having much higher mortality rates than the rest (Sheil & May 1996). This suggests that trees in the cohorts measured in the long-term plots contained subpopulations with very high mortality rates, which once dead left trees with a relatively narrow distribution of mortality rates (hence the flattening of the curve in Fig. 3 beyond c. 15 years). These very high mortality subpopulations were not captured by the species mortality rates we included in equation 2. Three possible explanations for this are examined below. (i) The simulations sampled only commoner species and thereby may have under-represented rarer species, some of which may have very dynamic populations. (ii) The assumptions that mortality rates were equal for all individuals within a species and that the mortality rate of a given stem was constant and independent of other stems may be incorrect. (iii) There may have been temporal fluctuations in mortality.
The simplest explanation of why the large-scale data sets did not include all the variation in mortality rates is that by including only species with ≥ 20 stems, we only included commoner species. These stems represent 35 ± 13% of all species at a site (range 13–58%), and 77 ± 13% of all stems at a site (range 44–97%). Conceivably, rarer species will show wider variation in mortality rates than commoner species; for example, very ‘early successional’ species, which often have high mortality rates, tend to occur at low densities in old-growth forests (Swaine 1994; Condit et al. 1995). Although comparing simulated declines with only very common species (≥ 80 stems), rather than species with ≥ 20 stems, did not show large differences at Pasoh and North Queensland, there was a large difference at BCI. This may be because BCI is known to have a large and relatively common pioneer community that is largely absent at Pasoh and in North Queensland (Condit et al. 1999). Thus the simulations may have under-represented the distribution of mortality rates within a stand.
All individuals within a species were assumed to have the same probability of dying, but any within-species differences could further increase heterogeneity. Examples include possible differences in mortality rate by size class, and differing mortality rates when stems of the same species occupy different microhabitats. Differences in the mortality rate of a given species by size class have been documented at several sites, thus these mechanisms could plausibly widen the distribution of mortality rates within a forest stand (Mervart 1972; Hubbell & Foster 1990; Vanclay 1991; Clark & Clark 1992).
The results from the simulations are constrained by the assumptions in equation 2, primarily that the probability of mortality of a given stem is constant and independent of its neighbours (Sheil & May 1996). Obvious violations of these assumptions include local competition for limiting resources, and the impact of other stems dying nearby. With local competition two identical individuals would have different probabilities of dying depending on the competitive interactions with their respective neighbours. This may explain why slow growing individuals have higher mortality rates than faster growing equivalent-sized individuals (Swaine et al. 1987a,b). Mortality events do impact on nearby trees, for example, increasing mortality through damage to the remaining trees or decreasing mortality through increasing levels of essential resources, such as light following canopy opening (Lewis 1998). The much steeper declines in mortality in the long-term plot data suggest these types of effects may be important processes in real populations.
Finally, the simulations do not include possible changes in the distribution of mortality rates over time. This is likely, because the environmental noise that affects processes that in turn affect tree mortality rates (e.g. droughts, Condit et al. 1995, wind events, Nelson et al. 1994, or diseases) may become more variable as the study period is extended. This is because environmental noise is not random (‘white noise’), but is characterized by strong correlations on many scales (‘pink noise’; Halley 1996; Gisiger 2001). The longer plots are monitored, the more likely it is that environmental conditions will be such that the mortality rates of some subpopulations will be temporarily increased, so leading to a longer ‘tail’ in the mortality rate distribution and increasing the steepness of decline in mortality with increasing census interval. The potential impact of temporal changes in mortality-rate distributions is considerable; for example, the Pasoh 50-ha plot showed highly significant differences in mortality rate between 1987 and 1990 (1.16%), and between 1990 and 1995 (1.60%) (Condit et al. 1999). Due to the large size of the Pasoh plot, these differences are very unlikely to be explained by very local mosaic/successional effects, which suggests that differing environmental conditions caused the differing stand mortality rates, and hence the distributions of mortality rates of the component subpopulations changed over time.
reanalysis of previous results
The conclusion that turnover rates have increased in tropical forests over the late 20th century is robust to the charge that this is an artefact due to the combination of data that vary in census interval (cf. Sheil 1995). Two tests using Phillips's (1996) expanded turnover data set show that the census interval effect does not affect Phillips’ conclusions about turnover increasing over time, whether using the generic census correction in equation 3 or site-specific corrections, where applicable (Fig. 4). To account for the increase in turnover, the declines in turnover with increasing census interval would have to be beyond the upper 99% CI of the decline parameter reported here, which is very unlikely.
Sheil's (1995) original critique of the evidence for increasing turnover over the late 20th century also suggests that the apparent increase could be explained by a single event, the 1982–83 El Niño Southern Oscillation (ENSO), as many of the recent data spanned this event. However, the rigorous assessment of the hypothesis that the apparent increase in turnover rates is due to a short-term response to an extreme synchronized global event, such as the 1982–83 ENSO, or more generally to a possible late 20th century increase in the frequency and intensity of ENSO events, is beyond the scope of this paper. Quantifying to what extent a forest is ‘ENSO-affected’ and quantifying whether ENSO events are more intense and frequent later in the 20th century, and then understanding whether individual ENSO events are driving local and global changes in turnover values, remains a challenge for ecologists (Lewis et al. 2004b; Malhi & Wright 2004). However, recent analyses from Amazonia have shown that growth, recruitment and mortality rates have simultaneously increased within the same plots over the 1980s and 1990s, as has net above-ground biomass, both in areas largely unaffected, and in those strongly affected, by ENSO events (Baker et al. 2004; Lewis et al. 2004a; Phillips et al. 2004). Factors that potentially explain such widespread and simultaneous changes should be the subject of detailed investigations.
If turnover rates have been increasing over time, as current evidence suggests, then it becomes important to know when the plots to be compared were measured. Comparing data from, say, the 1960s with data from the 1990s may lead to erroneous conclusions. Indeed, if forest dynamics have been accelerating over recent decades then standardizing for the year of monitoring will need to become standard practice. More generally, as evidence accumulates that ecosystems are responding to global change, particularly to increases in atmospheric carbon dioxide concentrations, nitrogen inputs, temperature increases and changes in rainfall patterns, much ecological data may become difficult to interpret without considering when studies took place.
The Old World forest plots compiled by Phillips (1996) were censused much earlier in the last century than the New World plots, with mean mid-years of 1971 and 1982, respectively. Adjusting turnover rates from the New and Old World plots to a common census interval length, using equation 3, and a common mid-year of monitoring gives almost identical turnover rates for the New and Old World tropics (1.81 vs. 1.80% a−1). This result seems sensible, as there is no a priori reason why many plots from many soil types and climates from one continent should have higher turnover rates than many plots from many soil types and climates from three other continents combined. The current best estimate of the pan-tropical average annual turnover rate for tropical forests is therefore 1.81% (mode = 2.06, median = 1.78, SD = 0.64, min = 0.60, max = 3.71), for an average census mid-year of 1978 and a census interval length of one (using equation 3). Forests can therefore be defined as less or more dynamic based on the number of standard deviations standardized plot turnover data are from the mean, or in relation to the median or mode, due to the strong right skew (0.69) and lesser leptokurtosis (0.39) of the distribution.
Mortality, recruitment and turnover rates decline with increasing census interval, as previously shown theoretically, and now demonstrated empirically. This effect should be taken into account. In addition, stand dynamic rates are highly variable over short time-scales and small spatial scales. The frequency of measurement and plot size needed for any field study will clearly depend upon the questions being asked and resources available. For example, the most accurate stand level rates for comparisons with other plots will always come from monitoring many trees for many years, while trends over time are probably most accurately elucidated by annual measurements. However, common protocols are required for comparative studies. Currently, probably the most common census interval length is the 5-year interval, which is becoming a de facto standard (seemingly due to resource constraints). In order to maximize intercensus and intersite comparability we therefore recommend collecting and reporting results in intervals as near to 5 years as possible, as well as reporting results for each interval and for the longest period possible. This combination of results reduces census interval problems, and provides the most accurate results. If adequate data are available, then the calculation of a site-specific correction factor using the methods described in this paper may be appropriate. For comparisons where census intervals do unavoidably vary, and robust local corrections are unavailable, then standardization to account for the census interval artefact, using equation 3, will be necessary.