Seedling crown orientation and interception of diffuse radiation in tropical forest gaps
Forest gaps are noted for high spatial and temporal heterogeneity in environmental conditions (Bazzaz and Wayne 1993). The diurnal radiation environment in a gap is typically characterized by a period of direct solar radiation bracketed by periods of diffuse radiation and occasional sunflecks. The duration and timing of direct sun received by a seedling depend upon gap size, canopy height, and critically, location within the gap (Smith et al. 1989, Canham et al. 1990, Sipe 1990, Wayne and Bazzaz 1993a, b). The geometry of the canopy opening above an individual plant will also generate marked spatial heterogeneity in the angular distribution of incident radiation. Here, “canopy opening” is defined as the spatial distribution of unobstructed sky from the phytocentric perspective of an individual leaf or seedling (corresponding to the image obtained from hemispherical photographs); in contrast, “gap” refers to a spatial patch in a plant community where the upper strata of vegetation are absent (cf. Brokaw 1982, Runkle 1982, Popma et al. 1988). The location and size of the canopy opening will depend on gap size, height and distribution of surrounding vegetation, and on the location of the seedling within the gap. A seedling colonizing a peripheral location at the gap edge may receive much more light from one direction than another, due to the asymmetry of the canopy opening overhead (Orians 1982). The location of the canopy opening for plants in and around gaps will effect direct and diffuse radiation very differently. Diffuse light, integrated over the day, is distributed fairly evenly across the entire sky (Gates 1980), so the position of the canopy opening above a plant will be the primary determinant of the spatial distribution of diffuse radiation. In contrast, the spatial distribution of direct radiation is determined by the position of the solar track and will only be modified by vegetation cover that falls along the sun’s path. A gap may have little or no effect on direct radiation, if the solar track does not intersect the canopy opening (cf. Rich et al. 1993).
The interception of radiation by an individual plant depends upon the amount and spatial distribution of radiation coupled with the size and orientation of the plant’s crown. At the leaf level, light capture is critically dependent on leaf orientation, i.e., the azimuth and angle of the lamina (Herbert 1983). Orientation of leaves towards the sun, either during development or on a diurnal basis (i.e., “solar-tracking”), is observed in a number of plant species of open habitats (Ehleringer and Forseth 1980, Werk and Ehleringer 1984, Koller 1986), but the orientation of leaves of forest plants has received little attention. Light interception at the whole plant level depends upon the interaction of leaf orientation with canopy architecture and the geometry of leaf display. The efficiency of light interception may be influenced by many factors, including branch angles (Honda and Fisher 1978, Fisher 1986) and branching patterns (Waller and Steingraeber 1985), leaf size and shape (Givnish 1984, Niklas 1989), phyllotaxy and internode lengths (Niklas 1988), leaf display and overlap (Chazdon 1985, Niklas 1988), tree inclination (Berner 1992), and overall crown shape (Horn 1971, Kuuluvainen 1992).
In this study, we examined the orientation and efficiency of leaf area display in tropical tree seedlings growing in natural forest gaps, in relation to the spatial distribution and directionality of direct and diffuse radiation. The study was conducted on four species of tropical pioneer trees, Cecropia obtusifolia Bertol. (Moraceae), Heliocarpus appendiculatus Turc. (Tiliaceae), Piper auritum Kunth (Piperaceae) and Trema micrantha (L.) Blume (Ulmaceae), that occupy similar environments but exhibit marked variation in leaf size and canopy architecture. The goals of the study were (1) to assess the directionality of diffuse and direct radiation in forest gaps, using directional statistics in the analysis of hemispherical canopy photographs; (2) to determine the orientation of seedling crowns through reconstruction of leaf area display using a canopy model, and to test for correlations between crown orientation and the directionality of direct vs. diffuse radiation; and (3) to estimate whole-plant light capture capacity and efficiency (sensu Warren Wilson 1981, Chazdon 1985) by integrating projected leaf area and incident radiation received from different sectors of the sky. Based on these analyses, the functional consequences of flexibility in canopy architecture and orientation were assessed at the whole plant level by comparing efficiency of light capture of each individual under canopy openings with differing geometries and orientations. We hypothesize that if observed variation in leaf display is adaptive, with respect to light interception, then an individual should be more efficient in the site in which it is growing than in sites with contrasting radiation regimes.
MATERIALS AND METHODS
Study site, species, and seedling establishment
The study was conducted at the Los Tuxtlas Tropical Biology Station, Veracruz, Mexico (18 [degrees] 36[minutes]N, 95 [degrees] 07[minutes]W), the northernmost remaining reserve of Neotropical rainforest. Mean annual temperature is 27 [degrees] C and annual precipitation exceeds 4700 mm, with a 2-3 mo dry season from March to May ([less than] 100 mm/mo) (Estrada et al. 1985). Canopy height of mature forest ranges from 20 to 35 m, and the predominant disturbance is the occurrence of tree and branch falls and the subsequent creation of canopy gaps (Martinez-Ramos et al. 1988). The four tropical pioneer tree species used in this study, Cecropia obtusifolia, Heliocarpus appendiculatus, Piper auritum, and Trema micrantha (hereafter referred to by generic names), are among the most commonly encountered colonizers of natural gaps (Popma et al. 1988). These species share many ecological attributes typical of tropical pioneer tree species (Bazzaz 1984), but exhibit markedly contrasting canopy architecture. Piper and Cecropia have few large leaves while Trema has many, small leaves. Cecropia does not branch until it has reached several metres in height, while in Trema branching begins in fairly small seedlings, and in Heliocarpus and Piper at heights of 50-100 cm (D. D. Ackerly, personal observations).
Seeds of each of the four species were collected from five to eight maternal parents in or near the Los Tuxtlas Station. Forest soil was collected from a road cut and mixed with washed beach sand in a 4:1 soil:sand ratio. Four hundred black, polyethylene bags were filled with [approximately equal to]2 L each of the soil mix plus 4 g of Agway 15:8:12 NPK slow-release fertilizer; holes were cut in the bottoms of the bag for drainage. In July 1990 each bag was planted with [approximately equal to]20+ seeds of one of the four species, for a total of 100 bags per species. The bags were placed in an enclosed screen house located in a large clearing at the Los Tuxtlas station (diffuse radiation [greater than]50% of maximum) and received natural rainfall; as seeds germinated, they were thinned to one seedling per bag.
In November 1990, 16 wk after sowing, the largest seedlings of each species were selected for the experiment; 36 Cecropia, 38 Heliocarpus, and 37 Piper were selected, but only nine Trema were available due to poor germination. Several naturally established seedlings of both Trema and Heliocarpus that were encountered in the study sites were added to the sample, as explained below. Sixteen natural gaps were located in the research zone of the Los Tuxtlas Station, varying in age and size. Within each gap, 4-12 positions were selected, separated by at least 0.5 m, to allow adequate space for growth of the seedlings. Dead wood, bark, and some vegetation were cleared from the immediate vicinity of the planting sites, and a shallow hole dug for transplanting. Individuals of each species were assigned randomly to the positions in the field; in Cecropia, Heliocarpus, and Piper, 2-6 plants were exchanged between their originally assigned positions in order to ensure that there was no correlation between initial size and a visual estimate of canopy openness at each site. The plants were transplanted into the holes in each site, still contained in the bags, and packed with soil around the outside so the soil levels inside and outside the bag were the same.
Incident radiation: quantity and directionality
Assessment of light environments and crown architecture was conducted between 28 January and 5 February 1991, 74-81 d after the seedlings were transplanted into the gaps. Light environments were assessed with 180 [degrees] hemispherical photographs taken with a Minolta 8 mm lens just above the crown of each seedling, and analyzed using SOLARCALC (Chazdon and Field 1987). Measures of diffuse and direct light in each site are presented in terms of daily photon flux density (PFD, in moles per square metre per day); these estimates are based on assumptions of a clear sky, and so overestimate actual PFD, particularly during cloudy periods of the year. The predicted radiation values, particularly for direct light, must therefore be interpreted with caution (see Discussion), though the relative values obtained for different sites will be less affected than the absolute levels. For this study we have modified SOLARCALC, following Rich (1989), to provide the canopy openness and the duration of direct solar radiation in numerous spatial sectors of the sky, and applied circular ([approximately equal to]directional) statistics (Batschelet 1981) to determine the mean directionality of diffuse and direct radiation, respectively. (These modifications are incorporated into SOLARCALC v6.03, available from D. D. Ackerly or R. Chazdon.)
To determine the spatial distribution of diffuse radiation we divided the sky into 49 regions, based on six annuli of 14 [degrees] elevation angle divided into eight 45 [degrees] sectors, plus a single circle at the zenith of 6 [degrees] radius (Fig. 1A). The proportional weighting of these sectors follows equations given by Rich (1989), based on the assumption of a uniform sky distribution of diffuse radiation. The digitized images of the hemispherical photographs occupied [approximately equal to]80 000 screen pixels, and these were sampled completely in order to determine the proportion of pixels in each of the 49 sectors that was unobstructed by the forest canopy (see Chazdon and Field 1987 for additional details of the program). The 14 [degrees] annuli are relatively wide, which introduces some error in the calculations, but were necessary because the parallel calculations of leaf display were very time consuming. For direct radiation, the solar track across each photograph was analyzed for Julian day 36 (5 February), as representative of the environment at the time of the architectural measurements. The solar track was divided into 24 half-hour intervals and the proportion of pixels unobstructed by vegetation within each interval was calculated, and then weighted by the estimated direct beam radiation for that interval (see Chazdon and Field 1987). The solar track for Julian day 36 represents the highest solar elevation since Julian day 313 (10 November), encompassing the entire period since the seedlings were transplanted to the gaps (Fig. 1A).
To calculate the mean directionality of either direct or diffuse radiation, the center of each sector of the sky was represented as a vector, with an azimuth ([Alpha]) and zenith angle (0). For the diffuse analysis, [Alpha] = 0 [degrees], 45 [degrees], 90 [degrees], 135 [degrees], 180 [degrees], 225 [degrees], 270 [degrees], and 315 [degrees] and 0 = 13 [degrees] , 27 [degrees], 41 [degrees], 55 [degrees], 69 [degrees], and 83 [degrees], plus a single vector overhead (0 = 0 [degrees] ) (Fig. 1A). For direct radiation, the angles, azimuths, and mean PFD intensity for each half-hour interval of the solar track on Julian day 36 were obtained from SOLARCALC (Fig. 1A). In directional statistics, the mean of a sample of directions is found by taking the Cartesian components of each vector, calculating the mean of each component, and then recalculating the corresponding vector from the arc-sine and arc-cosine of these mean values (Batschelet 1981). This technique was extended to the case of vectors distributed on a hemisphere by taking the three Cartesian components of each sky vector,
[x.sub.i] = sin [[Alpha].sub.i] sin [[Theta].sub.i]
[y.sub.i] = cos [[Alpha].sub.i] sin [[Theta].sub.i]
[z.sub.i] = cos [[Theta].sub.i]
and then calculating the weighted mean of these components. Two weighting factors were assigned to each vector: [p.sub.i], the proportion of direct or diffuse radiation represented by each sector, and [R.sub.i], the proportion of the sector unobstructed by the forest canopy. The resulting mean vector has an azimuth and zenith angle, representing the mean directionality of radiation, and a vector length between zero and one, which reflects the spatial dispersion of canopy openings (Batschelet 1981). Fig. 1B-D illustrates the resulting mean vectors, of diffuse and direct radiation, for three canopy openings of different size and orientation.
Assessment of canopy architecture and leaf area display
Plants that were leafless, dead, or subject to very high levels of herbivory on the existing leaves (more than [approximately equal to]75%) were excluded from the study, leaving 14 of 37 original transplants of Heliocarpus, 26 of 33 Cecropia, 33 of 37 Piper, and 8 of 9 Trema. Due to the low sample sizes, six additional Heliocarpus and seven Trema seedlings that were naturally established in the gaps included in this study (mostly occurring in the largest gap) were also included, providing a final sample size of 94 plants of the four species.
Canopy architecture of each plant was measured in detail for subsequent reconstruction of leaf display using a computer program, as described below. The geometric description of a plant canopy requires a topological record of the branching pattern together with measurements of up to 12 parameters per node (Table 1). During periods of intense direct solar radiation, particularly in the dry season, the leaves of tropical pioneer plants may alter leaf angles or wilt, reducing heat load and minimizing water loss. In this study little diurnal variation in leaf angles was observed (data not shown), probably due to the relatively low solar radiation and high relative humidity during the rainy season, in contrast to observations during the dry season (Chiariello et al. 1987; D. D. Ackerly, personal observation). The shape and size of the leaves were recorded by photographing each leaf individually, and the leaf length was measured along the midrib in order to scale the photograph. Photographs of leaves (on black and white negative film) were digitized using a Panasonic video camera and ColorSnap software, based on a Macintosh computer, and analyzed using Image 1.40 (National Institute of Health software) to determine leaf area. Architectural measurements (from a total of over 900 nodes on the 94 plants) were also used to calculate height, diameter, leaf numbers, total leaf area, branch numbers, individual leaf size, mean petiole length and diameter, and mean internode length for each species. Leaf longevity for the interval between transplanting and the census was calculated from successive measurements of leaf number and production rates (Williams et al. 1989).
The mean directionality of leaf area display was calculated in an analogous manner to the directionality of incident radiation. The three-dimensional geometry of the crown was reconstructed on the computer using the program YPLANT (R. W. Pearcy, unpublished manuscript). Starting from the base of the plant each internode and petiole is treated as a vector, and the position of the apex relative to the base is calculated from the azimuth, elevation angle, and length. The base of each leaf is then placed at the apex of its petiole, and its orientation is determined based on midrib azimuth and lamina azimuth and angle (see Herbert 1983). The shape of each leaf was recorded from digitized leaf images as an array of (x, y) coordinates in a plane. Small Trema leaves were described as simple polygons with 4-6 points, while some Heliocarpus leaves, which had very irregular margins due to herbivore damage, required over 30 points to accurately record leaf shape. Internal holes due to herbivores were not recorded. A photograph of each plant was taken from directly overhead at the time of the census, and these were used as a visual check of the accuracy of the computer reconstruction. The correspondence between the actual and reconstructed views of the crown was highly satisfactory (Fig. 2).
The crown was then reconstructed to calculate projected leaf area, [P.sub.i], where i = 1 to 49 representing the same 49 orientations used to determine the distribution of diffuse radiation (Fig. 1A). The mean orientation of the crown ([[Theta].sub.c], [[Alpha].sub.c]) was calculated as the mean of the 49 directional vectors, each one weighted by the projected area in that direction. The contribution of individual leaf angle to overall crown orientation was assessed by calculating the mean orientation ([[Theta].sub.a], [[Alpha].sub.a]) of individual leaves on each plant, weighting the vector for each leaf in proportion to its area. The efficiency of leaf exposure within each plant was calculated in three dimensions as:
exposure efficiency = [summation of] [P.sub.i]([P.sub.i]/[L.sub.i]) where i = 1 to 49/[summation of] [P.sub.i] where i=1 to 49,
where [L.sub.i] is the projected area of individual leaves, in the absence of leaf overlap (cf. Honda and Fisher 1978 and Chazdon 1985 for similar calculations based on vertical projections). Angular efficiency (Chazdon 1985) was calculated for the vertical projection only as L/[A.sub.T], where [A.sub.T] is total plant leaf area.
Correlation of directional data
Circular statistics have been applied primarily to azimuthal and temporal data, involving distributions on a circle, whereas the analyses conducted here involve distributions of vectors on a hemisphere. We present a new test for correlation between vectors on a hemisphere, based on Monte Carlo randomization techniques. The angle subtended by each pair of vectors was calculated as the arc-cosine of the vector product:
[Beta] = [cos.sup.-1]([x.sub.1][x.sub.2] + [y.sub.1][y.sub.2] + [z.sub.1][z.sub.2]),
where [(x, y, z).sub.i] are the Cartesian components of the mean vectors for diffuse radiation (f), direct radiation (r), crown orientation (c), or mean leaf orientation (a), for each plant. The strength of correlation between two vector distributions was determined as the mean value of [Beta], where values approaching zero indicate perfect correspondence of each pair of vectors. To test for statistical significance, the mean [Beta] value was tested against the distribution of values obtained in repeated randomizations (N = 1000) of the two distributions, to determine the probability of obtaining by chance a value as low or lower than the observed value. Tests of the Monte Carlo method, using vector distributions with no true association, produced correct Type I error levels (results not shown), validating the application of the method for significance testing in this study.
Calculation of light capture efficiency
Following Warren Wilson (1981) and Chazdon (1985), the ratio of the total quantity of light intercepted by the crown (J, in moles per day) relative to incident radiation per unit area on the horizontal (I, in moles per square metre per day) provides a measure of light interception capacity (C, in square metres) of an individual plant. This can also be considered as the area of a flat surface that would intercept the same amount of light as the actual crown. Light interception efficiency (E) is the ratio of the light interception capacity (C) to total plant leaf area ([A.sub.T]). This provides a dimensionless parameter representing the quantity of light captured by the particular crown relative to the quantity intercepted by a flat surface of equal total leaf area; it can also be considered a measure of light capture per unit leaf area, normalized for overall ambient availability. Self-shading of lower leaves may result in C [less than] [A.sub.T], while a crown strongly oriented towards a low angle light source may potentially have C [greater than] [A.sub.T]. Diffuse radiation capture by each plant was calculated as the product of projected leaf area and incident diffuse radiation, summed over the 49 sky orientations, and direct radiation capture as the product of projected leaf area and direct radiation, summed over the half-hour intervals during the day (Fig. 1A).
Assessing the adaptive significance of crown orientation
The adaptive significance of crown orientation, with respect to light interception, was quantified in two ways. First, for each plant a canopy opening was simulated with equivalent size, based on calculation of weighted canopy openness, but centered on the zenith so that radiation was received from directly overhead. The efficiency of diffuse light capture in this simulated opening was calculated using the same formulas as above, and compared with the actual efficiency of the plants in the canopy openings occupied in the field. If the orientation of the crown enhances light capture in situ, then observed efficiency should be higher than the simulated efficiency. If a plant were perfectly oriented towards its canopy opening, light capture under an opening centered on the zenith will be reduced approximately in proportion to the cosine of the zenith angle of the plant’s actual canopy opening.
The second approach was based on comparisons of light capture by each plant in its own site vs. light capture in the sites of other conspecifics in the study. Light capture, based on spatial integration of crown display and light availability, was calculated for all [TABULAR DATA FOR TABLE 2 OMITTED] possible pairings of plants and canopy openings for each species, a total of over 2000 values. The mean efficiency of light capture in alternative sites, relative to efficiency in situ, was calculated for each plant and the proportion of sites in which efficiency was less than in the original site was tallied for each species. The causes of variation in efficiency were assessed by conducting a multiple regression of light capture efficiency in each alternative site in relation to the differences in the directionality of diffuse radiation and in canopy openness of the alternative canopy opening relative to the opening above the plant in its own site. As above, if responses of crown orientation are adaptive with respect to light capture, we predict the mean efficiency to be lower in alternative sites.
Predicted daily PFD for the microsites of all individuals in the experiment ranged from 1.2 to 10 mol[center dot][m.sup.-2][Delta][d.sup.-1], and the proportion of PFD received as direct light ranged from 0 to 88% (Table 2). Diffuse PFD was skewed towards lower values with a secondary peak above 3 mol[center dot][m.sup.-2][center dot][d.sup.-1]. This cluster of high values reflects a group of plants growing in one very large gap utilized in this study (Fig. 1D). In contrast, the distribution of predicted direct PFD declines monotonically; the lack of a peak at high values of direct PFD is due to the north orientation of the large gap such that it received little direct radiation. There were no significant differences among species in direct, diffuse, or total PFD or the proportion of total received as direct PFD.
Directionality of incident radiation
The distributions of directional vectors for both radiation and crown display are plotted in polar coordinates, providing a two-dimensional representation of vectors pointing to locations on a hemisphere. In these plots, the position of a point relative to the center represents the compass azimuth of the corresponding vector and the distance of the point from the center is proportional to zenith angle; this representation of the hemisphere is equivalent to the Hill projection of fish-eye lenses, except that east and west are not reversed as they are in the photographs (cf. Fig. 1). The mean vectors of diffuse radiation are clustered around the zenith (Fig. 3). The zenith angles of these vectors provide a measure of the spatial asymmetry of diffuse radiation around the zenith; mean of the zenith angles was 17.5 [degrees] , with a range from 1.6 [degrees] to 31.4 [degrees]. The azimuth angles represent the mean directionality of radiation, independently of the degree of asymmetry (except that a perfectly symmetric canopy opening would have a vertical mean radiation vector with no azimuth component). Azimuthal distributions may be tested for non-uniformity around the circle using Rayleigh’s test (Batschelet 1981), where a positive result indicates that the azimuths are significantly clustered around the mean value. The mean azimuth angle was 70 [degrees], and the distribution was significantly nonuniform (r = 0.41, P [less than] 0.001), indicating a tendency for the center of the canopy openings to be located to the east of the plants in this study. The predominance of eastward-facing canopy openings reflects the east-facing slope of the local topography. The distribution of mean direct radiation vectors is completely different, as they are located along the solar track for the day of the analysis, Julian day 36. The mean zenith angle was 39.5 [degrees] (range 35 [degrees] 59.2 [degrees]) and the mean azimuth was 166 [degrees], reflecting the low path of the sun across the southern sky. The locations of the mean direct vectors reflect the distribution of canopy openings that coincide with the solar track. The average angle between the mean vectors of diffuse and direct radiation was 40.6 [degrees], due to the angular distance between the low solar angles at this time of year relative to the location of canopy openings over the plants. This mean was significantly lower than expected by chance (mean with random pairings = 42.15 [degrees], P [less than] 0.001), reflecting a slight association between the portions of the canopy opening that coincide with the solar track and the entire distribution of unobstructed sky.
Canopy architecture and directionality of crown display
At the initial census, the four species differed significantly in height, diameter, main stem leaf numbers, and mean leaf size (Table 3). Cecropia and Piper had the fewest and largest leaves per plant, while Heliocarpus had 3 times as many leaves, but smaller average leaf size. Trema seedlings had an intermediate number of main stem leaves, relative to the others, and the [TABULAR DATA FOR TABLE 3 OMITTED] smallest individual leaf size. Trema was the only species branching at the time of measurement, resulting in higher mean leaf numbers per plant (branching was observed both on individuals germinated from seed for the experiment and those naturally established in the gaps). The negative associations between leaf number and size resulted in similar total leaf area in all four species. Trema also had the shortest petioles, which average [less than]2 cm in length, while Piper petioles averaged [greater than]9 cm. Mean leaf longevity ranged from 93 to 175 d for the four species, and in 90% of the individual plants at least half of the leaves present at the time of transplanting had been lost and replaced by the time of the census.
The distribution of crown orientation vectors was centered on the zenith, similar to the distribution of diffuse radiation vectors. The mean zenith angle was 11.1 [degrees] (range 0 [degree]-21.7 [degrees]) and the mean azimuth was easterly, at 103.1 [degrees] . The crown orientation azimuths were less clustered than diffuse radiation azimuths, but the distribution was significantly nonuniform (r = 0.239, P [less than] 0.01, Rayleigh’s test). An alternative measure of crown orientation was calculated based on the mean of the individual orientation vectors for the leaves on each plant. Mean leaf orientation vectors were less tightly clustered around the zenith, with an average zenith angle of 16.3 [degrees] (range 2.0 [degrees]-35.6 [degrees]). Similar to both crown orientation and diffuse radiation, the mean azimuth of the vectors was easterly (94.6 [degrees]) and the distribution was significantly nonrandom (r = 0.263, P [less than] 0.001).
Correlations between directionality of light and crown orientation
Fig. 4 presents the correlated distributions of the mean directionality of diffuse radiation in each canopy opening together with the mean orientation of the seedling crowns. The closed circles represent the location of the mean diffuse radiation vector for each plant’s canopy opening, and these are connected by a line to the open circle, representing the vector of crown orientation for the plant. The lines provide a visual representation of the angle [Beta], subtended by each pair of vectors (see Materials and methods: Correlation of directional data). The mean values of [Beta] ranged from 9.3 [degrees] to 12.4 [degrees] for the four species, and were significantly lower than expected by chance in all cases (Table 4). This result indicates that the orientation of leaf area on each plant was strongly correlated with the directionality of incident diffuse radiation. The mean orientation of individual leaves on each plant was also significantly [TABULAR DATA FOR TABLE 4 OMITTED] correlated with the directionality of diffuse radiation ([Beta] = 9.8 [degrees]-11.6 [degrees]) and with the overall orientation of the crown ([Beta] = 4.56 [degrees]-5.57 [degrees], Table 4). There was no correlation between the spatial dispersion of diffuse radiation and the dispersion in leaf or crown orientation (see Ackerly 1993).
In contrast, the mean angles between the directionality of leaf area display and direct radiation ranged from 34.2 [degrees] to 40.9 [degrees], while the angles expected from a random association between the two vector distributions ranged from 34.6 [degrees] to 41.8 [degrees] (Table 4). The small difference between the observed and expected angles was statistically significant for three of the four species, but the much greater absolute values of the observed angles indicates that crown orientation, from a biological perspective, was not associated with direct radiation. These results confirm the visually apparent lack of correlation between the overall distributions of direct radiation and crown orientation (cf. Figs. 3 and 4).
Light interception efficiency
In small plants, [C.sub.f] (diffuse light interception capacity) was almost identical to total leaf area, as there was little overlap among the small number of leaves; in larger plants, [C.sub.f] increased less than total leaf area, due to leaf overlap and/or changing leaf angle distributions (Fig. 5A). Light interception efficiency for diffuse radiation, [E.sub.f](= [C.sub.f]/[A.sub.T]) ranged from [approximately equal to]0.5 to 1.05; values greater than one, observed on smaller plants, indicate that the crown intercepts more diffuse radiation than an equivalent leaf area displayed horizontally. [E.sub.f] declined with increasing leaf area ([r.sup.2] = 0.189, P [less than] 0.001, Fig. 5B). Analysis of covariance indicated a significant difference in the slope of this relationship among species. The decline was greatest in Cecropia, intermediate in Trema and Piper, and not statistically significant in Heliocarpus. The reduction in light interception efficiency in larger plants was due to reductions in both angular efficiency of leaves and the mean exposure efficiency (i.e., increased self-shading as leaf area increases) (multiple regression, [F.sub.2.88] = 111, P [less than] 0.001 for both factors).
Light capture efficiency for direct beam radiation, [E.sub.r] (calculated for a subset of 43 plants due to an irretrievable loss of computer files), ranged from about 0.5 to 1.37 and was significantly correlated with values of [E.sub.f] ([r.sup.2] = 0.349, P [less than] 0.001). The high values of [E.sub.r] suggest that some of the plant canopies were efficiently oriented for capture of direct beam radiation, in contrast to the results above. Further analysis indicates that [E.sub.r] was negatively correlated with the angle between the mean directions of diffuse and direct radiation (correlation between [E.sub.r] and sine of angle between mean diffuse and direct radiation vectors, [r.sup.2] = 0.237, P [less than] 0.001); in other words the high efficiencies occurred when direct and diffuse radiation were received from similar portions of the sky, and resulted from the overall orientation of the crown towards diffuse radiation.
Consequences of crown orientation for light interception
Simulated interception of diffuse light in a canopy opening of equivalent size centered on the zenith was less than interception in the actual canopy opening for 85 of 91 plants. As predicted, the ratio of simulated to observed light capture was less for plants growing under canopy openings that were centered farther from the zenith (Fig. 6A), and was significantly correlated with the cosine of zenith angle of the canopy opening ([r.sup.2] = 0.521, P [less than] 0.0001). For plants in the most asymmetric radiation environment, the responses of crown orientation enhanced diffuse light interception by as much as 30% relative to an opening centered on the zenith.
The efficiency of diffuse light capture for each plant assessed under the canopy openings of other conspecifics ranged from 0.55 to 1.16 relative to efficiency in situ. The in situ value was greater than that in the alternative site in 75% of all cases. The mean and range of values was similar for the four species (results not shown). In all four species multiple regressions indicated that the reduction in light interception was most strongly correlated with the difference between the vectors of the alternative canopy opening and the plant’s original canopy opening (P [less than] 0.0001 in all cases, results not shown). In Cecropia and Trema there was also a significant effect of the difference in the size of the openings, based on indirect site factors (P = 0.022 and P [less than] 0.0001, respectively). We were not able to determine which aspects of canopy morphology may have differed among plants of small and large gaps, so the explanation for this gap size effect is not known. The ratio of mean efficiency for each plant in the sites of all conspecifics relative to efficiency in situ ranged from 0.83 to 1.06 (Fig. 6B). The mean of this distribution is 0.952, which was significantly lower than 1 (one-sample t test, P [less than] 0.001). The converse interpretation of this result is that the observed responses of seedling crown orientation to the angular distribution of diffuse radiation increased light interception by an average of 5%, relative to that expected if the variation in crown orientation was randomly distributed across different gap locations.
The spatial distribution of ambient radiation represents a component of environmental heterogeneity that has received relatively little attention in forest ecophysiology. This study evaluated the plasticity of crown orientation in four species of pioneer trees in response to spatial heterogeneity in the light environment of natural forest gaps. The display of crown leaf area was strongly associated with the directionality of diffuse radiation, but not with the location of the solar track. It is often difficult to assess the consequences for carbon gain attributable to variation in traits that exhibit phenotypic plasticity in response to environmental variation. Due to the plasticity, variation in the trait is directly associated with the environment, so independent effects of the two factors on growth cannot be decoupled. Computer simulations and models address this problem by evaluating performance of a particular phenotype across a range of environments. In this study, simulations of leaf display allowed us to assess the performance of each plant in a variety of gap light environments. The observed responses of canopy architecture illustrate that phenotypic characteristics at the whole plant level are influenced by fine-grained heterogeneity, i.e., variability perceived by the individual. Plasticity in crown orientation is therefore a potentially adaptive trait that may contribute to lifetime performance of the individual in relation to patterns of heterogeneity experienced during the life cycle.
Our study adds an important dimension to previous considerations of environmental heterogeneity in forest gaps. The spatial locations of seedlings establishing in gaps differ in the predominant directionality of radiation, due to the position of the canopy opening overhead, from the plant’s perspective. In forest gaps the directionality of diffuse and direct radiation may be decoupled if the solar track does not intersect the canopy opening. The spatial location of the solar track is precisely defined by latitude and time of year and the mean directionality of direct radiation is constrained to fall near to this track, even if partly obstructed by clouds and vegetation. In contrast, the spatial distribution of diffuse radiation will be primarily determined by the geometry of the canopy opening. The results of the vector correlation analysis provide strong evidence that the plant canopies oriented towards the diffuse component of daily radiation (i.e., towards canopy openings). If there was actually little direct radiation at the time the canopies were measured, then this correlation simply represents a response to the angular distribution of total radiation. However there are always periods of clear weather between the “nortes,” winter storms characteristic of this time period at Los Tuxtlas, so it is certain that the plants received some direct radiation. Thus, the results imply that the phototropic mechanisms underlying crown orientation are differentially responsive to direct and diffuse components of the radiation environment. Similarly, Berner (1992) suggested that the inclination of large trees on steep slopes in the montane tropics was a response to differential light availability. Downslope inclination was observed on slopes oriented in all directions, which suggests a predominant influence of diffuse rather than direct radiation.
The correlation between overall crown orientation and the mean orientation of individual leaves demonstrates that the primary factor underlying the adjustment of crown display was responses in the angle and azimuth of individual leaves. The orientation of individual leaves and the overall crown towards diffuse radiation raises two sets of questions. First, from a physiological perspective, what mechanisms will result in differential perception of the directional sources of diffuse and direct radiation? Two important types of phototropic responses may be distinguished: (1) reversible heliotropic movements (i.e., “solar-tracking”), maintaining the lamina perpendicular or parallel to the sun’s rays (Ehleringer and Forseth 1980, Koller 1986); and (2) developmental responses in the petiole that orient the lamina in response to directional light sources perceived during leaf expansion, but are irreversible once the leaf matures (Werk and Ehleringer 1984, Zhang et al. 1991). Of the four species studied here, only Heliocarpus has a well-developed pulvinus, at the attachment point of the petiole and the leaf. Leaves exhibit nyctinastic movements, moving down into a vertical position after dark, but diurnal heliotropic movements have not been observed. On the other hand, Cecropia leaves, when shaded by neighbors, exhibit marked reorientation of the leaf lamina, controlled by irreversible torsion of the petiole. Trema petioles, though much shorter than those of Cecropia (Table 3), may also twist and bend, reorienting the leaf lamina (D. D. Ackerly, unpublished observations), and Piper probably possesses a similar mechanism.
It is not immediately apparent whether the known mechanisms of phototropic responses could lead to differential perception of diffuse and direct light sources. One possibility is that diffuse radiation is enriched in blue wavelengths, and would elicit greater phototropic responses than direct beam radiation. The proportion of blue light in the PFD spectrum is greatest in blue skylight, such as that received from the canopy opening on a clear day. Under cloudy skies and under vegetation cover, however, the enrichment of blue is slight or negligible (Lee and Downum 1991, Endler 1993), Additionally, the blue light response saturates at very low light levels so any difference between direct and diffuse radiation would probably not be detected. Alternatively, it is possible that the diffuse light received from the canopy opening has a greater effect because it is present throughout the day, while direct radiation is intermittent due to cloudiness and canopy cover. Phototropic growth responses in Helianthus have a lag time of [approximately equal to]1 h (Shell and Lang 1976), so intermittent direct radiation may not be sufficient to trigger a response.
The second question is, what are the consequences of different leaf orientations for carbon assimilation when direct and diffuse radiation are received from different sectors of the sky? Can orientation towards diffuse light enhance carbon gain and plant performance? Due to the light saturation of carbon assimilation, leaves do not need to be oriented towards direct sun in order to fully utilize the available energy. If the direct beam has an intensity of 1800 [[micro]mol][center dot][m.sup.-2][center dot][s.sup.-1] and the light response of photosynthesis saturates at 500 [[micro]mol][center dot][m.sup.-2][center dot][s.sup.-1] (see light curves for Heliocarpus in Fetcher et al. 1987), then a leaf may be inclined almost 75 [degrees] away from the solar beam before incident radiation declines below the photosynthetic saturation point. In contrast the intensity of diffuse radiation is much lower, and any inclination of the leaf away from diffuse light sources, such as a canopy opening, would result in a reduction in both light energy and carbon gain. The total radiation on a leaf represents the sum of the components from various directions, multiplied by the corresponding sines of incidence. Optimal orientation with respect to two or more sources of light in different locations will depend upon their consistency and intensity, mediated by the light response curve of photosynthesis. Simulations indicate that if there is a sporadic, high intensity light source (e.g., the sun passing behind a forest canopy), and a more consistent lower intensity source (such as a large canopy opening away from the solar track), orientation should be biased towards the latter to maximize assimilation, because all of the energy received from the bright source will still be captured effectively by an inclined leaf (D. D. Ackerly, unpublished data).
This analysis addresses crown orientation and the spatial distribution of radiation at only one point in time. Strictly speaking, analysis of the adaptive value of the correspondence between crown orientation and diffuse radiation depends on the dynamics and consequences of these parameters throughout the life cycle of the plant. Our conclusions regarding the adaptive value of crown orientation depend on the assumptions that (1) increased interception of diffuse light enhances carbon gain and growth, and (2) faster growth rates are correlated with lifetime fitness. The first assumption is supported by a growth analysis of these plants conducted over a 2-mo period following these measurements, which demonstrated a positive correlation between relative growth rate and diffuse radiation (Ackerly 1993). Similar results are reported for seedlings of a variety of tropical pioneer tree species (Fetcher et al. 1987, Popma and Bongers 1988, Oberbauer et al. 1993, King 1994). The second assumption is supported by strong evidence of size- and light-dependent mortality in pioneer trees, as these species do not tolerate shading and quickly die if they do not maintain their crowns in high light environments (e.g., Augspurger 1984, Alvarez-Buylla and Martinez-Ramos 1992). Over time, as these plants grow in height, the spatial structure of the light environment will change as they reach different strata of the forest (Smith et al. 1992). Thus, the adaptive value of these traits also depends on the plant’s capacity to respond dynamically to changes in its environment. In pioneer plants, tracking of environmental changes is facilitated by their short leaf longevity (Ackerly 1995). Replacement of the canopy leaf population every few months will allow the readjustment of crown orientation, even if orientation is regulated by irreversible responses during the development of each leaf.
We thank R. Pearcy for generously allowing us to utilize the YPLANT model while still under development, and for hospitality to D. D. Ackerly during a visit to the University of California, Davis. S. Assman, S. Bassow, G. Berntson, R. Chazdon, D. Karpa, R. Monson, R. Pearcy, P. Wayne, and two reviewers offered comments and suggestions that greatly improved the manuscript. S. Sinaca and B. Traw were excellent field assistants, and B. Bhudhikanok, J. Grayman, E. Jewett, S. Perkins, and B. Traw provided extensive assistance digitizing leaves. This research was supported by the Committee for Latin American Studies, Harvard University, a National Science Foundation Dissertation Improvement Grant to D. D. Ackerly and a National Science Foundation grant to F. A. Bazzaz.
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RELATED ARTICLE: TABLE 1. Architectural parameters measured for reconstruction of leaf area display by YPLANT (R. W. Pearcy, unpublished manuscript), a computer model of canopy architecture. Angles were measured to the nearest 5 [degrees], lengths to 1 mm, and diameters to 0.1 mm.
Internodes and petioles:
Orientation: Azimuth of any inclination of internode or petiole, when viewed from directly overhead; measured from base to apex.
Angle: Angle of inclination from horizontal (90 [degrees] = vertical).
Length: Internode length from node to node, petiole length from node to point of attachment with lamina.
Diameter: Diameter midway along length.
Midrib azimuth: Azimuth of midrib from base to apex, viewed from directly above.
Leaf azimuth: Azimuth of leaf lamina, along the steepest inclination.
Leaf angle: Angle of inclination of lamina along steepest tilt; always a positive number indicating departure from horizontal, with leaf azimuth indicating direction of downward tilt.
Leaf length: Length from attachment point of petiole to farthest point along midrib.
Leaf shape: Recorded by photographing each leaf, and digitizing margin in (x, y) coordinates; leaf length measurement used to scale image.
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