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Keywords:

  • Barro Colorado Island;
  • hierarchical Bayesian model;
  • life-history traits;
  • light requirements;
  • niche partitioning;
  • Panama;
  • regeneration niche;
  • shade tolerance;
  • tropical rain forest

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

1.  Many hypotheses about species coexistence involve differential resource use and trade-offs in species’ life-history traits. Quantifying resource use across most species in diverse communities, although, has seldom been attempted.

2.  We use a hierarchical Bayesian approach to quantify the light dependence of recruitment in 263 woody species in a 50-ha long-term forest census plot in Panama. Data on sapling recruitment were obtained using the 1985–1990 and 1990–1995 census intervals. Available light was estimated for each recruit from yearly censuses of canopy density.

3.  We use a power function (linear log–log relationship) to model the light effect on recruitment. Different responses of recruitment to light are expressed by the light effect parameter b. The distribution of b had a central mode at 0.8, suggesting that recruitment of many species responds nearly linearly to increasing light.

4.  Nearly every species showed increases in recruitment with increasing light. Just nine species (3%) had recruitment declining with light, while 198 species (75%) showed increasing recruitment in both census intervals. Most of the increases in recruitment were decelerating, i.e. the increase was less at higher light (< 1). In the remaining species, the response to light varied between census intervals (24 species) or species did not have recruits in both intervals (41 species).

5.Synthesis. Nearly all species regenerate better in higher light, and recruitment responses to light are spread along a continuum ranging from modest increase with light to a rather strict requirement for high light. These results support the hypothesis that spatio-temporal variation in light availability may contribute to the diversity of tropical tree species by providing opportunities for niche differentiation with respect to light requirements for regeneration.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Many hypotheses about species coexistence involve differential resource use and trade-offs in species’ life-history traits (e.g. Tilman 1982, 2004; Rees et al. 2001; Silvertown 2004). Understorey light availability is one of the most limiting resources in tropical rain forests (Whitmore 1996), and its spatio-temporal variation is an important component of the regeneration niche and gap dynamics hypotheses for species coexistence (Grubb 1977; Denslow 1987). Treefall gaps increase heterogeneity in light conditions and may contribute to the diversity of tropical tree species by providing opportunities for niche differentiation with respect to light requirements (Ricklefs 1977; Brokaw 1985).

Empirical studies quantifying niche differentiation in regeneration have yielded inconsistent conclusions. Several studies suggest that species differentially respond to light levels, even if variations are subtle, and that tight species packing along the small range of light environments may contribute to coexistence (Denslow 1980; Kobe 1999; Svenning 2000; Poorter & Arets 2003). However, other studies conclude that many species in tropical rain forests share similar light requirements. While Hartshorn (1980) estimated that half of the tree species of the tropical lowland rain forest at La Selva, Costa Rica, required gaps for regeneration; other studies found that >80% of the tree species at Barro Colorado Island (BCI), Panama, regenerate at low light levels (Hubbell & Foster 1986; Welden et al. 1991; Condit, Hubbell & Foster 1996); and Wright et al. (2003) concluded that most of the same BCI species have intermediate light requirements.

Quantifying resource use in highly diverse communities is challenging because it theoretically involves measuring the continuous environmental variation of the resource and continuous variation in species responses (Lieberman, Lieberman & Peralta 1989; Wright et al. 2003). This is often not feasible, and previous studies have usually simplified the problem by either focusing on a small number of species (e.g. Brown & Whitmore 1992; Clark & Clark 1992; Van der Meer, Sterck & Bongers 1998; Svenning 2000; Poorter & Arets 2003; Uriarte et al. 2005; Queenborough et al. 2007), grouping species into broad growth form classes (Dupuy & Chazdon 2006), or using few categories of environmental conditions (e.g. gap/non-gap; Welden et al. 1991; Condit, Hubbell & Foster 1996; Barker, Press & Brown 1997).

Moreover, if forest inventories form the basis of the analyses, the samples usually contain only few individuals of the many rare species (Pitman et al. 1999). As a consequence, there are few studies quantifying the light response of recruitment across entire diverse tropical rain forest communities (but see Welden et al. 1991 for an analysis of 155 species).

In this study, we aim to quantify the response of recruitment to light availability across more than 80% of the 300 tree and shrub species occurring at BCI, Panama, and our approach explicitly addresses all three problems. Forest census data from the 50-ha Forest Dynamics Plot (FDP) at BCI provided information on the spatial location of more than 50 000 recruits of 263 species. Yearly canopy census data allowed an estimate of light availability across the 50-ha FDP with a spatial resolution of 5 m. We used a hierarchical Bayesian approach to quantify the response of recruitment to light availability for all species. The hierarchical Bayesian approach combines the probability models for the spatial distribution of recruits within species and the variation of the light response across species, including rare ones (e.g. Clark 2005; Condit et al. 2006). Moreover, the posterior distribution of parameter estimates provides direct information about the uncertainty associated with the parameter estimates (Ellison 2004).

We explore how the response of recruitment to light is distributed across the tree community and how it is related to the abundance of the species. Furthermore, we calculate a comparable measure of light requirements for recruitment, the light level at which recruitment falls to 50% of the maximum under high light. Our estimates of the sensitivity of recruitment to light availability can serve in a classification of tree species into functional groups (Swaine & Whitmore 1988).

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Study site

We analysed data from a 50-ha forest census plot on BCI, Panama (9°9′N, 79°51′W). Barro Colorado Island is a 1567-ha island in the Panama Canal, covered with tropical lowland moist forest. The plot consists of 48 ha of undisturbed old-growth forest and 2 ha of secondary forest about 100 years old (Foster & Brokaw 1982). The climate on BCI is warm throughout the year, but rainfall is seasonal with most of the 2500 mm falling from April to November (Windsor 1990; Windsor, Rand & Rand 1990). Elevation of the plot is 120–155 m a.s.l. (Hubbell & Foster 1983). Detailed descriptions of flora, fauna, geology and climate can be found in Croat (1978), Leigh, Rand & Windsor (1982) and Leigh (1999).

Recruitment data

All freestanding woody individuals ≥1 cm diameter at breast height (d.b.h.) were mapped, identified to species and measured in 1981–1983, 1985 and every 5 years thereafter (http://www.ctfs.si.edu; Hubbell & Foster 1983; Condit 1998). In this study, we use the census intervals from 1985 to 1990 and 1990 to 1995 and define every individual absent in the first census of each interval but present in the second as a recruit. To avoid edge effects of the light availability calculation, we excluded all recruits within 20 m of any edge of the plot. In the 1990 census, 33 069 recruits of 252 species were recorded, and in the 1995 census, 17 809 recruits of 233 species. We divided the plot (excluding the 20 m perimeter) into 17 664 5 × 5 m grid cells and computed the number of recruits of each species in each grid cell.

Estimation of light availability

Yearly canopy censuses were conducted from 1983 to 1996, except for 1994. We use the canopy census data to produce an index of the amount of light reaching any point in the forest. The canopy census includes a record of the height at which vegetation intersected vertical lines above points on a square, 5-m grid across the 50 ha. Presence versus absence of vegetation was recorded in six height intervals, 0–2, 2–5, 5–10, 10–20, 20–30 and ≥30 m, with the assistance of an ocular range finder. A single census of all 20 301 points on the grid was done annually.

If vegetation was present in a height interval, we assume it casts shade below exactly as would a flat circle of diameter 5 m placed at the vertical midpoint of the cell (for the topmost height category, we assumed the circle was at 35 m). For any point below, the vegetation obscures a section of the sky. Using trigonometry, we calculate the angle of sky so obscured by vegetation at position C, denoted αc (see Appendix S1 in Supporting Information). The total amount of sky obscured at any point P is the sum of αc over all cells C that are near enough to cast shade; we assume that points with a horizontal distance of ≤20 m from C are near enough. These assumptions mean that each cell of vegetation reduces light, even if there is another cell above it: the top layer removes a certain quantity of light, and the next layer below removes more. This approach seems reasonable, in that several layers of leaves directly above a point reduce light to a level lower than a single layer would. The assumption that the presence of vegetation can be modelled as a horizontal circle of diameter 5 m is arbitrary, and we acknowledge that this is only a crude way of converting canopy density above a point to light reaching the point. By using many surrounding points and many vertical layers (cf. Connell, Lowman & Noble 1997), we suggest that this method may be somewhat better at estimating light than methods based on only the tallest nearby trees (Lieberman et al. 1995) or the top layer of vegetation (Welden et al. 1991).

We calculated the shading index for each point of the plot’s 5-m grid at height = 2 m because this is the approximate height of recruits at 1 cm d.b.h. For each grid cell, we averaged the shading index s at its four corners and for all years of a census interval, i.e. 6 years for the first interval (1985–1990) and 5 years for the second (1990–1995; no canopy census was done in 1994).

To convert the estimates of mean shading to an estimate of light availability at each grid cell and in each census interval, we made use of 396 direct measurements of relative irradiance by Wirth, Weber & Ryel (2001), who provide a probability distribution of irradiance l at 1 m height in December 1993 at BCI. We matched their distribution of irradiance with our probability distribution of canopy shading, s. We assumed the 5th, 25th, 50th, 75th and 95th percentiles of the two distributions match, allowing a simple conversion of each value s to l by using the regression line through the percentiles (Appendix S1). Using this conversion, we found that average light availability in the understorey was 2% in both census intervals.

Hierarchical Bayesian model

We used a hierarchical Bayesian framework to assess the light response of recruitment across the tree and shrub species at BCI. Our model involves a data model, a process model and parameter models (Fig. 1).

image

Figure 1.  Graphical representation of the hierarchical model.

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Data enter our model as observed recruit numbers inline image of each species (i) in each 5 × 5 m grid cell (j). We assume that inline image varies around the predicted inline image following a negative binomial distribution (data model or likelihood)

  • image

Recruit distributions are not only affected by the light conditions but also by the distribution of seed trees, spatially heterogeneous seed dispersal by animals or spatially heterogeneous soil conditions (e.g. Uriarte et al. 2005; Comita, Condit & Hubbell 2007). The negative binomial incorporates the resulting spatial autocorrelation of recruit numbers at <5 m into the clumping parameter ci. Autocorrelation of recruitment at larger scales (>5 m) was negligible: autocorrelation for adjacent grid cells was <0.2 for 252 of the 263 species we studied, and there was no correlation in recruitment across cells separated by 20 m or more.

We compared seven functional relationships to describe the dependence of the number of recruits on light availability: constant, linear, semi-log, log–log, sigmoid and Michaelis–Menten. For each model, we judged the fit to data using the Akaike Information Criterion (AIC; Akaike 1974). When all 263 species were tested, the log–log relationship was selected as the best model for the highest proportion of species (excluding the constant model). For the species, for which the log–log relationship was not the best model, the best model was significantly better than the log–log relationship (i.e. AIC difference >2) only in 36 cases.

Thus, we use a power function (log–log relationship) to model the light effect on recruitment (process model). The log of the predicted number of recruits inline image of each species (i) in each 5 × 5 m grid cell (j) given light availability lj is

  • image

In this model, ai represents a measure of the mean log of the number of recruits to be expected, and bi measures the strength of the light response of species i. For values of b < 0, the number of recruits decreases with increasing light. For 0 < b < 1, the number of recruits increases in a decelerating way with increasing light; for = 1, it is a linear relationship; and for b > 1, the number of recruits increases in an accelerating way with light (Fig. 2).

image

Figure 2.  Illustration of the three types of light response of recruitment: negative (b < 0), decelerating (0 < b < 1) and accelerating (b > 1). The number of recruits at average light conditions is 0.001 in all three cases (a = −3).

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We then describe the variation of a and b across the community (parameter model). We used normal distributions for both parameters,

  • image

with hyperparameters μa and μb describing the community-wide means of a and b, and σa and σb measuring the between-species variation of both characteristics. Model runs without hyperdistributions confirmed that both variables were normally distributed across the community. These runs also revealed that for species with >100 recruits, parameter estimates were largely determined by the data, whereas for species with <100 recruits, parameter estimates for b were ‘pulled’ towards the community-wide mean.

As we did not have prior knowledge of the parameters, we used non-informative flat priors for all parameters:

  • image

We restricted c to values <100 because for c > 10, the negative binomial already approximates a spatially homogeneous Poisson distribution (Bolker 2008). Altogether, the joint posterior distribution for the full model is:

  • image

with spp being the number of species with recruits in the respective census interval. The last three lines denote the likelihood, the priors and the hyperpriors, respectively.

Model implementation and diagnostics

Posterior distributions of the parameters were obtained using a Markov chain Monte Carlo method that is a hybrid of the Metropolis–Hastings algorithm and the Gibbs sampler (Gelman et al. 1995; Condit et al. 2006). Parameter values are sequentially updated as in the Gibbs sampler, but acceptance depends on the likelihood ratios as in the Metropolis–Hastings algorithm (Muller-Landau et al. 2008). The proposal distribution is a normal distribution centred on the current value of the given parameter. The step width for each parameter, i.e. the standard deviation of the proposal distribution, is constantly adjusted during the burn-in period in such a way that the acceptance rate is kept around 0.25 (Gelman et al. 1995).

To speed up the convergence of the Gibbs sampler, we weakened the correlation of a and b by centring the light data at average log10 light (inline image)

  • image

Thus, ai measures the mean log of the predicted number of recruits at average light conditions. Mean log10 of l was −1.7 for the period 1985–1990 and −1.8 for 1990–1995. We used an average value of inline image, corresponding to a relative irradiance of 2%, for the analysis of both periods to keep parameter estimates comparable.

We monitored convergence by running two chains with different initial values and used Gelman and Rubin’s convergence diagnostics and a value of 1.1 to detect the convergence (Gelman & Rubin 1992; Gelman et al. 1995). Convergence required 500–5100 iterations. We used a burn-in period of 7000 iterations and additional 10 000 iterations were used for analysis. We computed the posterior parameter distributions for observed recruit numbers and light availability estimations for two intervals (1985–1990, 1990–1995). All analyses were carried out using the software package R version 2.5.0 (R Development Core Team 2007). The R-code is available in Appendix S2.

Analysis of results

From the posterior distributions, we computed the mean and 95% credible intervals (CI) of all parameters for the two periods (1985–1990, 1990–1995). We define maximum recruitment as recruitment at high light conditions, where high light is 20% relative irradiance, since 20% is close to the brightest the forest understorey ever gets. For each species, we calculated the light level at which the recruitment falls to 50% (Light50) of maximum recruitment. To compare model fits with data, we calculated the mean number of observed recruits in ten light intervals corresponding to 10th percentiles of light estimates across the 50-ha plot. Total abundance of each species across 50 ha in 1990 (i.e. number of individuals ≥1 cm d.b.h.) was used in comparing species. All BCI inventory data, including recruitment, can be downloaded from http://www.ctfs.si.edu.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Community-level pattern of light response

Mean posterior estimates of the light response of recruitment (b) ranged from −0.6 to 3.3, with most species falling between 0 and 1, i.e. these species take advantage of higher light levels with a decelerating response of recruitment to light (Fig. 3; Table S1). When mean posterior estimates of b were compared between census intervals, 101 species (38%) showed a decelerating response of recruitment with increasing light availability (0 < b < 1) in both census intervals, 54 species (21%) showed an accelerating response (b > 1), and recruitment of nine species (3%) decreased with light availability (b < 0). For the remaining 99 species (38%), b indicated different types of light response for the two census intervals or species did not have recruits in both intervals.

image

Figure 3.  Mean posterior estimates of the light dependence of recruitment (b) for the tree species at BCI, Panama, for the two census intervals (1985–1990 and 1990–1995).

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For 97 species, the 95% CI of b did not include zero in either census interval. There were only three species with a negative b and a CI that did not include zero: Xylopia macrantha in both census intervals, Trichilia tuberculata only in the first interval, and Drypetes standleyi and Licania platypus only in the second interval. There were 18 species with b > 1 and a 95% CI > 1 in both intervals, i.e. an accelerating response of recruitment to light availability. These included many species of the common pioneer genera, e.g. Cecropia, Croton, Miconia, Palicourea, Spondias, Zanthoxylum. Posterior estimates of the community-wide mean of b (μb) were 0.80 for 1985–1990 and 0.85 for 1990–1995, and the standard deviation (σb) was 0.76 and 0.72, for the two census intervals, respectively.

Other parameters

Mean posterior estimates of the log of the mean number of recruits at average light conditions (a) ranged from −4.3 to −0.88 (i.e. 0.02–53 recruits per hectare; Fig. 4 and Table S1). The minimum roughly corresponded to one individual in the sampling area, while the maximum corresponded to about 0.1 individuals per 5 × 5 m grid cell. Posterior estimates of the community-wide mean of a (μa) were −3.017 and −3.162, and posterior estimates of the standard deviation (σa) were 0.88 and 0.84, for the two census intervals, respectively. The distribution of a across the community was skewed to the right.

image

Figure 4.  Mean posterior estimates of the log10 of the mean number of recruits at average light conditions (a) and the clustering parameter of the negative binomial distribution (c) for the tree species at BCI, Panama, for the two census intervals (1985–1990 and 1990–1995).

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The distribution of the clustering parameter of the negative binomial was bimodal (Fig. 4; Table S1). Thirty species showed pronounced clustering (c < 1) in both census intervals, 32 only in the first and nine only in the second census interval, while for the majority of the species either spatial clustering did not occur or could not be detected due to the small number of recruits (c > 10). The correlation between b and c is −0.13 in the first census interval and −0.18 in the second, indicating that recruits of more light-demanding species tend to be slightly more clustered than recruits of shade-tolerant species.

Consistency between census intervals

Comparing mean posterior estimates for the two census intervals showed that the log of the mean number of recruits (a) tended to be slightly higher in the first census interval 1985–1990 than in the second census interval 1990–1995 (Fig. 5a). However, parameter estimates were consistent over the two intervals. Likewise, the estimates of the strength of the light response of recruitment (b) were consistent over the two analysed time intervals (Fig. 5b).

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Figure 5.  Posterior means of parameters of the light dependence of recruitment for the tree species at BCI, Panama, for the two census intervals (1985–1990, 1990–1995). Parameters are (a) log10 of the mean number of recruits at average light conditions a, and (b) the light effect b. The line represents the 1:1 relationship.

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Observed versus predicted recruitment rates

Mean posterior parameter estimates predicted the mean number of recruits under different light conditions. Model fits are shown for two species with positive (Trichilia pallida) and negative (Trichilia tuberculata) response to light (Fig. 6). Model fits for the remaining species are available in Fig. S1.

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Figure 6.  Model fit for the predicted number of recruits at different light conditions vs. the observed number of recruits for two selected species. Mean number of recruits in intervals of tenth percentiles of light in the 5 × 5 m grid cells (large dots), observed number of recruits in the 5 × 5 m grid cells (small dots), predicted number of recruits using posterior means for the second interval 1990–1995 (line). Grid cells without recruits were assigned a small number (1.5e−5).

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Uncertainty and sample size

The uncertainty of parameter estimates decreased rapidly with the number of recruits (Fig. 7). When recruit numbers were low, the 95% CI of a spanned up to an order of magnitude (Fig. 7a). Likewise, CIs for b ranged over more than one type of light response, i.e. b < 0, 0 < b < 1, b > 1, when few recruits were available for parameter estimation (Fig. 7b). However, for 46% of the species with >20 recruits, parameter estimates significantly determined the type of light response (95% CI of b neither including 0 nor 1), as opposed to 7% of the species with <20 recruits. When the number of recruits increased to >50 (100), this proportion increased to 59% (66%), as opposed to 10% (15%) for species with <50 (100) recruits. Below ten recruits, spatial aggregation could not be detected, but also for larger numbers of recruits, the clustering parameter c often did not contain information and varied over the entire range of allowed values (0–100) (Fig. 7c).

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Figure 7.  Uncertainty of estimates (width of the 95% credible interval) of (a) the log10 of the mean number of recruits at average light conditions a, (b) the light dependence of recruitment b, and (c) the clustering parameter of the negative binomial distribution c as a function of the number of sampled recruits. Uncertainty estimates are given for 233 tree species at BCI, Panama, for the second census interval (1990–1995).

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Light response and abundance

Across the community, the strength of the light response of recruitment (b) decreased slightly with abundance. In a linear regression, the effect of log10 of abundance on b was significant (P < 0.0001, n = 233, r2 = 0.07, intercept = 1.19, slope = −0.155). While b varied over a broad range for species with intermediate abundance, the most abundant species had a b close to zero, i.e. showed hardly any response of recruit numbers to light availability. For rare species (<50 recruits), however, b was largely determined by the community-wide mean and the relationship is not informative for them.

Light requirements for recruitment

The light intensity where recruitment fell to 50% of maximum recruitment (Light50) was heavily skewed to the right (Fig. 8). Fifty-six species (22% of the total) in the first interval had Light50 < 2%, the understorey light average, i.e. they recruited well at low light. At the opposite end, 81 species (32% of the total) in the first interval had Light50 > 10% and thus only recruited well at high light. The second census interval had similar results, with 35 species recruiting well at average light and 84 requiring high light. The median Light50 in the two census intervals was 7.7% and 8.5%.

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Figure 8.  Estimates of the light level at which recruitment falls to 50% of recruitment under high light conditions (i.e. at 20% light, Light50) for the tree species at BCI, Panama. Estimates are based on the means of posterior means of the species’ parameters from both census intervals (1985–1990, 1990–1995).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Our results broadly support the notion that light requirements for recruitment are distributed along a continuum (Denslow 1987; Wright et al. 2003) and that species belong to broad regeneration guilds rather than partitioning the light gradient at a fine scale (Hubbell & Foster 1986). The distribution of the light response of recruitment (b) had a strong central mode, with many species showing a nearly linear light response, suggesting that the majority of species share intermediate light requirements for recruitment (Wright et al. 2003). Using the hyperparameters of the posterior distribution of light dependence across the community, recruitment of 13% of the species is expected to decrease with increasing light availability, while recruitment of 87% of the species benefits from higher light, 46% in a decelerating manner and 41% in an accelerating manner.

Recruitment of only 20% of the species reached 50% or more of their maximum recruitment at light levels lower than the average in the forest understorey at BCI suggesting that relatively few species recruit well in the deepest forest shade. Thus, the ability to regenerate at low-light conditions may not be as widespread among tree species at BCI as we thought (Hubbell & Foster 1986; Welden et al. 1991; Condit, Hubbell & Foster 1996). Rather, nearly all species regenerate better in increasing light, and they are spread along a continuum from modest response to a rather strict requirement for high light. Species specialized to recruit in high-light conditions (b > 1) are more common (41%) than expected from the rarity of large gaps (Hubbell & Foster 1986; Hubbell et al. 1999).

Our results are consistent with the findings of a community-wide analysis of sapling distributions with respect to light in a temperate rain forest in Chile (Lusk, Chazdon & Hofmann 2006). In that study, half the species were randomly distributed with respect to canopy openness, whilst the remainder was non-randomly distributed. The majority of tree species were also found to have intermediate shade tolerance, and niche overlap was not smaller than expected.

There are several caveats we must consider. The basis of our analysis is the distribution of saplings with respect to the estimated light levels integrated over 6 years during which the recruit surpassed the 1 cm d.b.h. threshold. Based on mean growth at 1 cm d.b.h. (<1 mm year−1), we estimate the average age of individuals reaching the 1 cm d.b.h. threshold to be 10–20 years. Therefore, the establishment of seedlings and subsequent growth and mortality may have occurred under light conditions different from those at the time of the study (Denslow 1987; Kobe 1999). However, we believe that our approach gives reasonable estimates of light requirements for recruitment not only for fast-growing species, but also for slower-growing species, due to the temporal correlation of light availability caused by the slow dynamics of the canopy cover (the correlation between the light estimates for both census intervals was 0.76).

Recruitment success in terms of our study integrates both growth and survival of plants during the 5 years of the census interval. Growth and mortality of seedlings and saplings are likely to vary with light availability (e.g. Montgomery & Chazdon 2002; Iriarte & Chazdon 2005; Aiba & Nakashizuka 2007). Since recruits only enter our census at 1 cm d.b.h., we cannot separate the impact of light on growth from the impact on survival.

Another concern is that our calculated light availability obviously is only a rough index of the light environment in the forest, unable to capture spatial variation at scales <5 m horizontally or vertically. Measuring light directly at every recruit, however, would involve prohibitive time and labour. Until laser-mapping data of the forest are available, the method we propose offers an objective and straightforward measure of how much vegetation is blocking the sky above any tree of any height. The consistency of the derived light response between the two census intervals indicates that our light index contains information relevant to the species’ performance. Interestingly, our light estimation procedure is similar to the index that best described gap light index obtained by hemispherical photographs in a temperate forest in Japan (Takashima, Kume & Yoshida 2006). The latter estimates also accounted for shading from topography, but we ignored this at BCI due to the relatively flat topography.

The power function does not capture the saturation of recruit numbers at very high light levels for some pioneer species with b > 1 (e.g. Cecropia insignis, Croton billbergianus, Miconia argentea, Palicourea guianensis, Spondias radlkoferi; Fig. S1). Thus for these species, we overestimate the number of recruits at very high light and predicted recruit numbers beyond light levels found in forests gaps (c. 20%) should be used with caution.

A final caveat is the low number of individuals per area for the many rare species in such a diverse forest (Pitman et al. 1999). Hierarchical Bayesian methods explicitly account for this problem by superimposing a form of variation across the community and by providing direct measures of uncertainty associated with parameter estimates (e.g. Clark 2005; Condit et al. 2006). We could significantly determine the type of light response (i.e. negative, decelerating or accelerating) for nearly half of the species (44%) with at least 20 recruits. For 167 (75%) of the 224 species with recruits in both census intervals, light response was consistent across the two intervals, i.e. mean posterior estimates of light dependence indicated the same type of light response (negative, decelerating or accelerating). However, applying the rather strong criterion, that the width of the 95% CI of b be <0.5, about 100 recruits were necessary. This is certainly a large number for rare species. The main point of the Bayesian approach, however, is that the response of rare species need not be known to estimate the community-wide variation.

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Light response of recruitment is only one aspect of species’ performance under heterogeneous environmental conditions. To arrive at a more complete understanding of species’ life-history traits, differential response of growth and survival to light conditions have to be analysed for different ontogenetic stages (Clark & Clark 1992; Poorter et al. 2005). Such analyses will allow extending existing species classifications into functional groups on the basis of light (or other resource) dependence of all vital rates in several life stages (Condit, Hubbell & Foster 1996). Ultimately, only mechanistic models accounting for species differences will allow investigations of the consequences of species’ similarities or differences for coexistence and to determine the relative importance of niche partitioning versus chance events (Grubb 1977; Brokaw & Busing 2000; Wright 2002).

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

We thank Liza Comita and Inés Ibáñez for advice on hierarchical Bayesian modelling, Helene Muller-Landau for providing the step width-adjusting routine of the Metropolis–Hastings algorithm, and Helene Muller-Landau and Robin Chazdon for valuable comments on the manuscript. N.R. was supported by a research grant from the Center for Tropical Forest Science, and R.C. by a fellowship from the National Center for Ecological Analysis and Synthesis (Santa Barbara, CA, USA). The BCI plot has been made possible through the support of the U.S. National Science Foundation, the John D. and Catherine D. McArthur Foundation and the Smithsonian Tropical Research Institute. We thank the dozens of field assistants and botanists who have collected data on trees and carried out the canopy censuses in the BCI plot over the past 25 years.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Appendix S1. Calculation of the shading index using canopy density and conversion of the shading index to relative irradiance.

Appendix S2. R code to generate posterior distributions of the parameters of the hierarchical Bayesian model.

Figure S1. Model fits for the predicted number of recruits at different light conditions versus the observed number of recruits for the woody species at Barro Colorado Island, Panama.

Table S1. Posterior means, lower and upper limits of the credible interval (CI−, CI+) of the parameters of the hierarchical Bayesian model and the light level at which recruitment falls to 50% (Light50) of recruitment at 20% light for the woody species at Barro Colorado Island, Panama.

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JEC_1552_sm_FigS1.pdf78KSupporting info item
JEC_1552_sm_TableS1.pdf279KSupporting info item

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