Crossovers in seedling relative growth rates between low and high irradiance: analyses and ecological potential

Abstract

Species differences in relative performance in response to irradiance contribute to the maintenance of forest species diversity (Schnitzer & Carson 2001; Wright 2002). In Sack & Grubb (2001; henceforth ‘SG’), we introduced a crossover analysis, (i) to quantify approximately the crossover-point irradiances (CPIs) – the irradiances at which species-pairs change rank (crossover) in dry mass relative growth rates (RGRs); and (ii) to establish the percentage of species-pairs that crossover between 2 and 10% daylight (understorey vs gap irradiance). The reply of Kitajima & Bolker (2003; henceforth ‘KB’) is stimulating but, contrary to what they assert, the available evidence indicates that RGR crossovers are in fact frequent and potentially important. Crossover analysis, carefully applied, allows a resolution of species hierarchies impossible using the decade-old correlation analysis, thus providing higher power for interpretation. KB state that ‘recent comparative studies … have failed to detect substantial rank-reversals’ in species RGRs between low and high irradiance. However, the data from the available comparative studies show a wide range in the reported frequency of rank changes (‘crossovers’). For 12 studies (the seven reviewed by SG and five others in Table 1), between 8 and 68% of species-pairs crossed over in RGR between 2 and 10% daylight. Averaging the 12 studies, 27% of species-pairs crossed over from low to high irradiance – a minority, but a substantial one. Further, as emphasized by SG, longer-running studies are more reliable in showing crossovers that are likely to occur during establishment in the wild. Young seedlings tend to cross over in RGR at very low irradiances, but as the seedlings grow the CPIs tend to increase, often into the ecologically relevant range of irradiances (SG). To test this prediction, we plotted the seven studies’ median CPIs vs seedling growth time. The positive correlation was significant. Adding four additional studies for which total seedling growth time is available (Table 1) increases the significance (Pearson's r = 0·87, P = 0·001; all statistics performed with minitab release 13·32). KB argued that increases in median CPI are not relevant to crossovers – in fact, increasing CPIs directly represent the shifting upward of crossovers, and inevitably many crossovers move into the zone of interest, here the arbitrarily chosen range of 2–10% daylight irradiance. Some crossovers are bound to move upward out of this zone. KB questioned whether there was a relationship between percentage crossovers in the range 2–10% irradiance and median CPI. For the set of 12 studies, the percentage crossovers between 2 and 10% daylight irradiance were rank correlated with median CPIs (Spearman's r = 0·77, P = 0·003). Further, for the 11 studies for which total growth times are available, percentage crossovers between 2 and 10% daylight irradiance were rank-correlated with total growth times (Spearman's r = 0·62, P = 0·04). As another test, we compared the percentage crossovers between 2 and 10% daylight irradiance for the six studies that ran < 20 weeks with that for the six studies that ran ≥20 weeks. The shorter-running studies had a median of 12% crossovers, the longer-running studies 32% (P = 0·04, Mann–Whitney test). As described by SG, these studies concern diverse species; there is thus a robust tendency for longer-running studies to reveal more RGR crossovers in the ecologically relevant range of irradiances. We expect studies to show the same trend for given species in given conditions, harvested at different times (cf. Bloor 2001). As in controlled studies, in the wild species of seedlings frequently cross over in RGRs between understorey and gaps (Kaelke et al. 2001; Lusk 2002; Montgomery & Chazdon 2002). Species of saplings in deeply shading forests also frequently cross over between 2 and 10% daylight irradiance, in relative or absolute radial growth rates (31% of species-pairs cross over in Pacala et al. 1994; 57% in Lin et al. 2002). We hypothesized that a major reason for more crossovers in longer-running studies is the negative correlation between RGR and seed size, coupled with a tendency for smaller-seeded species to be more light-demanding. This pattern leads to small-seeded light-demanders growing rapidly in both low and high irradiance initially, due to their initially high specific leaf areas (SLAs), but less so in later growth. Other mechanisms are also likely to be partially responsible. KB recognize that our hypotheses are reasonable; they suggest, however, that the linkage between small seed size and high SLA is a ‘physiological strategy’ to ensure a high RGR early on. The evidence instead suggests that the linkage between small seed size and high SLA is primarily due to allometric scaling and biomechanics. Notably, the linkage occurs even in the absence of selection for high maximum RGR, e.g. in tiny-seeded, shade-tolerant rainforest species (seed mass << 1 mg), and in tiny-seeded, short-lived plants of nutrient-poor soils in the Mediterranean and further north in Europe (Marañón & Grubb 1993; Metcalfe & Grubb 1997; Grubb 1998). KB propose that for crossovers to be ‘significant’, more than 50% crossovers are needed. However, such a 50% null model has no foundation in physiology, and it offers little of value for community ecology. Suppose we have a set of species in which 25% of species pairs cross over in RGR between low and high irradiance. We set up two large grids, one in understorey and one in a clearing. We plant the two grids identically, with a randomly selected pair of species in each grid square. Assuming that RGR determines eventual competitive outcomes (or, at least, that it is an index of effectiveness for establishment), and excluding interactions with other factors, the species distributions in the grids in understorey and clearing will eventually differ by ≈ 25%. A proportion this high suggests that shifts in RGR hierarchies across irradiances play a potentially large role in determining sun–shade population differences. Even if only 10% of species-pairs cross over in RGR from low to high irradiance, that feature must contribute to the maintenance of species richness in forest, unless the performance in low or high irradiance is negated in the field by the effects of other resources, herbivores or pathogens. SG proposed that RGR crossovers arise from species differences in resource retentiveness and resource acquisitiveness. We showed how the intercepts and slopes of the species’ regressions for RGR vs ln-transformed irradiance represent resource retentiveness and resource acquisitiveness in respect of irradiance – we refer to them, respectively, as dark loss rate (L) and light-responsiveness (R). We found a typical negative relationship between species’L and R, a relationship which for given species sets determines the range of irradiances in which species-pair crossovers tend to occur. KB seem to question whether the L vs R relationship arises mechanistically, because intercepts and slopes for a set of regressions (such as L and R for species’ regressions of RGR vs ln-transformed irradiance) are in general ‘unlikely to be independent of each other’– they are often negatively correlated. However, we note that the exact relationship between intercepts and slopes of a set of regressions is not predetermined; it depends where the regressions cross over each other in relation to the y axis, which in our case is fixed, non-arbitrarily, at irradiance = 0% daylight. For instance, if many regressions cross over at above 0% irradiance, there will arise a negative relationship between L and R; on the other hand, if many regressions cross over below 0% irradiance, there may be no relationship between L and R – or even a positive relationship. Thus the direction and the slope of the L vs R relationship for a species set depends on how many regression crossovers occur, and at how high an irradiance, as discussed in SG. In the hypothetical scenario proposed by KB, in which species share a light compensation point, the species’ regressions all cross over at that point, above 0% irradiance. As noted above, a negative L vs R relationship should be expected. The commonly found negative L vs R relationship holds as a corollary of the fact that log-linear regressions hold approximately for RGR vs irradiance data sets below saturation irradiance, and that the species’ regressions cross over where they do. SG hypothesized a mechanistic basis for the species differences in RGR responses to irradiances, and thus for the L vs R trade-off and the crossover patterns that follow. KB agree that species differences in RGR responses to irradiance (according to the log-linear model, species differences in L and R) arise from species differences in crucial morphological and physiological traits, and from the plasticity of these traits across irradiances (Walters & Reich 1999; SG). Some traits would especially increase L in magnitude (make L more negative, e.g. high dark respiration rate, short leaf lifespan); others would especially increase R (e.g. high photosynthetic light responsiveness, high specific leaf area). Links between traits of these two kinds, singly or in combination, will contribute to an L vs R trade-off, and thus play a part in driving substantial RGR crossovers in the ecologically relevant range of irradiance. KB recapitulate some of the advice we gave for controlled studies of seedlings in different irradiances, especially that pretreatment should be considered carefully. In this context, KB assert that pretreatment in high irradiance especially penalises fast-growing plants placed in shade, due to abnormal leaf abscission, and favours detection of crossovers. However, there are no reports in the relevant literature of such abnormal abscission of post-cotyledonary leaves. Pretreatment in high irradiance might indeed favour the detection of crossovers, but not beyond those expected to occur in nature. Because the plants grow faster, they might escape more quickly from the period in which seed-size differences drive RGR hierarchies at both low and high irradiances – and thus show crossovers sooner that would otherwise develop in later establishment. The advice of KB that differs most radically from ours concerns the suggested study length. KB encourage more short-term controlled experiments, considering longer-term controlled studies subject to such ‘potential pitfalls’ as the effects of ontogeny and pot-limitation. However, these effects in pot experiments are two of those that require further study for science to progress. Both effects are potentially relevant in the field – changes in form occur naturally in the field (Kohyama & Hotta 1990; Sack et al. 2002). Also, competition may increasingly limit soil resource availability as seedlings establish in the forest, and studies are needed to determine whether this effect may parallel pot-limitation. Thus, longer-running controlled and field-based studies are needed to increase our understanding of RGR rank hierarchies under different irradiances, in longer-term establishment. Crossover analysis relies on solving for the intersections of regressed lines, a standard statistical approach (Zar 1999) with current empirical applications in chemistry, economics and engineering (Kupka & Meloun 2001; Ladany & David 2001). Despite its usefulness this analysis, like any other, should not be applied as a black box. By taking due care and investigating and dealing with any problems that arise, such ‘drawbacks’ as those claimed by KB are resolvable. First, KB assert that crossover analysis does not apply the ‘50% null model’ described above. One could certainly apply that model by simply testing whether the determined percentage crossovers differ from 50%; however, this null model allows only low interpretive power, as discussed above. Second KB state that crossover analysis might be ‘biased by structural error’ when the ‘true’ shape of the RGR light response is unknown. As part of their test simulation, KB generate artificial Michaelis–Menten (MM)-type data sets and artificial log-linear (LL) type data sets. KB then correctly show that CPIs differ when LL lines are applied to the MM-type data sets, and when MM lines are applied to the LL-type data sets. We concede that fitting such different types of line to data sets can produce different crossover patterns; the LL and MM curves fit the data differently because they are of distinct shapes, especially toward the upper end of the range of irradiances. However, these KB simulations do not replicate the careful use of crossover analysis as we described it. We advised fitting lines that empirically suit the data well – we suggested using LL for data sets that include RGRs below saturation irradiance, and MM when more data are available, including RGRs above saturation irradiance. In the other part of their simulation, KB apply the LL and MM lines to the original data of Poorter (1999) for RGRs ranging up to 25% daylight. These data sets are saturation responses, and are thus typically well approximated by the MM but not the LL (for eight out of 15 species RGR plateaus or decreases between 12 and 25% daylight); using the LL leads to bad fits. In SG we used the LL for data up to only 12% daylight in Poorter (1999); in this range the LL plots fit the data well. Notably, when KB used the MM plot for the MM-like data (up to 25% daylight) of Poorter (1999), they found 23% crossovers, close to 26%, the value we found using the LL plot for data up to 12% daylight (SG). Thus any ambiguity about crossover patterns can be minimized by fitting lines to the RGR response data that suit the shape of the plotted data. If there is a question about whether a non-linear function approximates the obvious shape of the data, transformed residuals can be used to test its appropriateness (Seber & Wild 1989). The third ‘drawback’ claimed for crossover analysis is that it is sensitive to measurement error. Measurement error is a potential problem in all analyses. KB show that adding noise can aggravate the problems created by fitting lines that do not match the data. In the KB simulations, however, the added error is excessive – we calculate for the RGR data of Poorter (1999) that the measurement error which, at very worst, one strives to achieve, ± 5% error, in fact falls below 1 on the ‘noise amplitude’ axes for KB's Fig. 1(a,b). Despite the excessive noise added, the CPI findings were remarkably robust in the one case in KB's simulation in which lines were well fitted, i.e. when the MM lines were fitted to MM data (their Fig. 1a). Using confidence intervals for the CPIs (Kastenbaum 1959; Robison 1964; Carter et al. 1991) will ensure further robustness to measurement error. We note that not every data set may be amenable to determining narrow CPI confidence intervals; data for numerous irradiances may be required, especially before saturation or inhibition. Properties of the crossover analysis are summarized in Table 2. KB discuss two other analyses, but these are not alternatives to crossover analysis. These analyses, as applied for nearly a decade, involve simply testing for parametric correlation or rank correlation of RGRs at low and high irradiances. The parametric correlation coefficient is most problematic: it conflates the frequency of crossovers with the intensity of given crossovers. Also, the parametric correlation cannot account for intraspecific variability of RGR (i.e. in the plot of RGR at high vs at low irradiance, the error bars around each species’ point). The rank-correlation between RGRs at high and low irradiance can at least take account of ties, which often occur among species’ RGRs at low or high irradiance (Sokal & Rohlf 1995). A positive correlation between species’ RGRs at low and high irradiance simply means that > 50% of species-pairs do not cross over; 49% might. Properties of the correlation analyses are summarized in Table 2. We agree with KB that a trade-off between RGR at high irradiance and survival at low irradiance is a potentially prevalent mechanism for species coexistence (Kitajima 1994; Kitajima 1996; KB). However, it is too early to exclude other mechanisms, of which there are many that may function to maintain diversity (Grubb 1977). Species differences in survival rates at different irradiances are clearly important, caused by plant physiology and especially by interactions with pathogens and herbivores. Crossovers in RGR across irradiances also have major potential, given the high frequency of crossovers reported. Further, more studies are needed of the effects of irradiance combined with variation in the supply of other resources, and with the impacts of pathogens and herbivores (e.g. Howe 1990; Sack & Grubb 2002). It is important to keep this discussion in perspective. In most studies so far, species were chosen to span the full range of light demand. However, in species-rich forests most species are strongly shade-tolerant. For such groups, coexistence may depend more on differences in other properties than on irradiance responses (whether in RGR or survival rate), including, for example, annual variation in fruiting and dispersal (Grubb 1977). It is worth asking whether variation in irradiance could promote species richness only through a trade-off between RGR at high irradiance and survival rate at low irradiance. KB hypothesize that some woody plants are ‘fast growers’ in any irradiance, and others ‘hardy survivors’. In an extreme view of this ‘grow vs live’ trade-off, crossovers in performance across irradiances would not be a mechanism for irradiance to contribute to the maintenance of species richness. If such a ‘grow vs live’ trade-off does indeed shift dominance across irradiances, there must then be major differences across irradiances in the relative importances of RGR vs survival rate in determining dominance. For instance, survival rate should preferentially drive dominance in deeper shade, and RGR preferentially in higher irradiance. There is no experimental support for this hypothesis. Some have proposed that in the understorey, species differences among RGRs might be negligible, but even small RGR advantages can have dramatic consequences over several years. Further, rankings in RGR and survival rate at given irradiances are sometimes independent, and sometimes run in parallel (Walters & Reich 1996; Walters & Reich 2000; Lin et al. 2002; Lusk & Del Pozo 2002; Montgomery & Chazdon 2002; Wyckoff & Clark 2002; Bloor 2003). At a given irradiance, the two combined probably determine success (Kobe 1999). As more data become available, crossover patterns can be investigated for RGR, for survival, and for their combined effects in plants of different sizes. It is clearly important to go beyond the simple correlation of performance at two irradiances. A thought experiment illustrates the resolution possible in principle through crossover analysis. Suppose we analyse RGR crossovers and determine the CPI for species A and B. It is, by its definition, the level at which to set a light ‘dimmer switch’ to equalize the species’ RGRs at given sizes. If one raises the dimmer switch above the CPI, both species increase their RGR, but of the two species, A grows fastest. If one lowers the switch below the CPI, both species slow their growth – but now species B grows fastest. CPIs for survival rates have similar implications. Changes to the dimmer switch for large sets of species could thus profoundly affect interspecies performance hierarchies. In a forest, irradiance varies hugely in space and time, as do soil resources and biotic factors. Given such variation, crossovers have a strong potential to drive patterns of species dynamics and coexistence. L.S. was supported during this work by a Putnam Fellowship at the Arnold Arboretum (Harvard University). We thank Paul Moorcroft for helpful discussion.