The timing of abscission affects dispersal distance in a wind-dispersed tropical tree

Authors


Correspondence author. E-mail: maurer.189@osu.edu

Summary

  1. Seed dispersal is a short-term phenomenon with long-term consequences for population survival and spread. Physiological mechanisms that target the release of seeds to particular sets of environmental conditions that maximize the probability of long-distance dispersal should evolve if long dispersal distance enhances fitness.
  2. In this study, we use high-frequency censuses of seeds actually dispersed, high-frequency within-canopy meteorological observations and long-term measurements of above-canopy wind to investigate the environmental conditions that control the timing of seed abscission at different time-scales for a wind-dispersed tropical tree, Luehea seemannii.
  3. We show that seed abscission follows a typical seasonal pattern, is rare at night and is most prevalent during periods of prolonged updrafts, higher temperature, with negative feedback when the heat canopy flux is relatively high.
  4. We use phenomenological (super-WALD) and mechanistic (coupled Eulerian–Lagrangian closure) models to estimate the relative effects of the timing of seed release at different subannual temporal scales (seconds–hours) on the resulting long-term (season–decade) dispersal kernels. We find that periods of high wind speed increase the probability of long-distance dispersal between 100–1000 m, but decrease the probability at distances further than 1000 m relative to unbiased environmental conditions. We also find abscission during updrafts to increase the probability of long-distance dispersal at distances greater than 100 m.
  5. Synthesis: We observe preferential abscission during updrafts in a tropical wind-dispersed tree. We use mechanistic models and long-term wind statistics to estimate the dispersal consequences of preferential seed release in specific environmental conditions. We find that the timing of the dispersal season may be influenced by wind conditions that maximize long-distance dispersal; however, there are likely other environmental factors essential for their determination. Our approach provides a method to bridge between small turbulence scales and large ecosystem scales to predict dispersal kernels. These findings shed light on the evolutionary processes that drive optimization of the timing of seed abscission and may be incorporated into plant population movement models to increase their accuracy and predictive power.

Introduction

Seed dispersal determines the ability of plant populations to sustain viable metapopulations (Bohrer, Nathan & Volis 2005; Poethke, Dytham & Hovestadt 2011), maintain genetic diversity (Volis et al. 2005; Fayard, Klein & Lefevre 2009) and respond to climate change through migration (Kuparinen et al. 2009; Nathan et al. 2011; Kremer et al. 2012). Seed dispersal of an individual plant occurs once in its lifetime and is, intrinsically, a short-term (milliseconds–minutes) phenomenon. However, over ecological and evolutionary time-scales, patterns of many movement events of individuals accumulate to long-term (seasons – years) and large-scale (metres–kilometres) processes (Theoharides & Dukes 2007). Selection for traits that optimize the dispersive potential of seeds may act on processes at long time-scales, such as the timing of the annual seed dispersal season, as well as short time-scales, such as the exact moment a seed will be ejected from the pod or released from the branch.

Thompson & Katul (2008) showed that it is possible to integrate the probability density function of the expected end point of individual dispersal events to predict long-term dispersal kernels, if the long-term statistics of the wind (i.e. the distributions of speed, direction and turbulence) are known. However, phenomena at short time-scales bias the distribution of wind conditions that are encountered by the dispersing seeds relative to long-term wind distributions. For example, at very short time-scales, wind conditions experienced during the first few moments of seed flight may differ significantly from block-averaged conditions (i.e. 30-min mean wind speeds that are typically available from meteorological stations) due to canopy-induced turbulence (Bohrer et al. 2008), the aerodynamic shape of seeds (Greene & Johnson 1990; Lentink et al. 2009) or the environmental conditions that lead to seed abscission (Greene 2005; Wright et al. 2008; Greene & Quesada 2011). At longer time-scales, the distribution of wind conditions when seeds are available (i.e. the dispersal season) may differ from the distribution of wind conditions during the entire year (Wright et al. 2008). These biases in wind conditions may change the dispersal kernel and lead to higher mean dispersal distances and/or more frequent/stronger events of long-distance dispersal (LDD) (Nathan 2006; Nathan et al. 2008).

For plants that are dependent on LDD, a possible set of traits that could be optimized involves the timing of seed abscission such that seeds are released when external conditions favour LDD (Skarpaas & Shea 2007; Soons & Bullock 2008). Traditionally, experiments have attributed increased LDD probability to seed abscission during strong horizontal winds (Soons et al. 2004; Greene 2005; Jongejans et al. 2007; Greene, Quesada & Calogeropoulos 2008), by suggesting that strong horizontal winds are correlated with high turbulence, including upward vertical perturbations of the wind. Over the long term and large scale, vertical wind is a mean-zero process, which means that strong turbulence will produce both updrafts and downdrafts. Therefore, strong turbulence may both enhance and hinder dispersal over the course of each dispersal event. Dispersal models have shown that updrafts enhance LDD (Nathan et al. 2002; Tackenberg, Poschlod & Kahmen 2003; Bohrer et al. 2008), and therefore, we hypothesize that updrafts should provide the preferred release condition for wind-dispersed seeds that are dependent on LDD.

Physiologically, targeting updrafts is not a simple task. Forces in all directions, such as drag forces generated by wind flowing past the seed and the turbulent shaking of branches, will potentially detach the seeds when the wind is strong but not necessarily upward. Therefore, seeds need to combine directional aerodynamic shapes and release mechanisms that favour abscission when the applied force pulls the seed in the desired upward direction. This intuitive notion that wind-dispersed plants have morphological mechanisms to preferentially release seeds during updrafts was demonstrated in artificial settings in maple trees (Greene & Johnson 1992) and with the forb Tragopogon dubius (Greene & Quesada 2011).

We used field measurements (seed arrival and meteorological measurements) and long-term data sets (seed trap and meteorology) to disentangle the effects of different seasonal and meteorological forcing on seed abscission and dispersal at different time-scales in a natural tropical forest environment for the neotropical tree Luehea seemannii (Triana & Planch.). We used phenomenological and mechanistic dispersal models to integrate the short-term outcomes of these environmentally driven abscission conditions and resolve the consequences of these effects for long-term dispersal kernels.

Materials and methods

Site description

The study took place at the canopy crane research facility located in the 350-ha Parque Natural Metropolitano (PNM), Panama (8°59′N, 79°33′W). The approximately 100-year-old natural secondary forest is classified as a dry, lowland forest (Holdridge et al. 1971) and contains more than 300 tree species. Canopy heights range from 20 to 40 m. Annual precipitation averages 1740 mm. A single dry season extends from mid-December through April, and a single wet season that includes 90% of annual precipitation comprises the remainder of the year (http://biogeodb.stri.si.edu/physical_monitoring/).

Species description

Luehea seemannii (Triana & Planch.), Malvaceae, ranges throughout Mesoamerica and northern South America and is a canopy tree that reaches heights of 35 and 40 m at the PNM and Barro Colorado Island (BCI), respectively. The light-demanding seedlings only establish in forest gaps where light reaches the forest floor (Molofsky & Augspurger 1992). These establishment requirements favour LDD because forest gaps are rare, comprising less than 2% of forest area. The fruit is a hard dry capsule that splits open to expose the diaspores (Fig. 1). The diaspores are 4-mm-long samaras, weigh just 2·5 mg (fresh mass; SJW, unpublished data) and have a low fall velocity (0·7 ± 0·07 ms−1, mean ± 1 S.D. (Augspurger 1986)). Most fruit are oriented vertically (above the horizontal) so that the open fruit points skyward. The diaspores disperse towards the end of the dry season, when the trade winds are strongest, the forest canopy is relatively open due to deciduousness and the imminent wet season will provide the moisture necessary for successful germination (Nathan & Katul 2005; Wright et al. 2008; Bohlman 2010). In this study, we investigate the sensitivity of the seasonal dispersal kernel to varying wind distributions selected from environmental conditions and temporal ranges associated with the dispersal season.

Figure 1.

Luehea seemannii fruit in a tropical forest. Fruit pods hold many seeds in a start orientation, typically facing upward (above the horizontal). Cracks in the distal end of the pod widen during the season allowing the seeds to be released.

Seed count

Ten 1-m2 seed traps were placed underneath the crowns of each of the three L. seemannii used to determine seasonal seed release. Our dispersal models show up to 65% and 90% of seeds released will fall within 10 m and 30 m, respectively, from the release point. Therefore, we are confident our seed counts will encompass a wide range of both short- and long-distance dispersal events. We censused the traps at 30-min intervals from 6:00 am to 6:00 pm from 13 to 23 April 2010, inclusive. At each census, all traps were emptied, and the number of L. seemannii seeds in each trap was recorded. Total night-time seed release was documented at 6:00 am. Night-time seed release was excluded because the exact time of abscission during the night is not known. Just 12% of seeds were released during the night so their exclusion did not strongly affect our results. Counts during or immediately following rain events (17 of 335 observations) and counts influenced by the canopy crane knowingly shaking branches during fruit censuses (2 of 335 observations) were also removed from the data set.

Meteorological data

An 11-year data set (2000–2010) of hourly mean horizontal wind speed and temperature at the PNM crane research facility was acquired through the Smithsonian physical monitoring program (http://biogeodb.stri.si.edu/physical_monitoring/). A nine-month (February through October, 2007) data set of wind speed in three dimensions and turbulence (wind fluctuations, frictional velocity) above the canopy, summarized as 30-min block averaged statistics of 10 Hz measurements, was available from BCI (Bohrer 2007) roughly 50 km north-west of the PNM. A similar two-week data set was collected between 12 and 26 April 2010 in the PNM. Appendix S2 (Supporting Information) describes the methods used to process the two 10 Hz data sets and to collect ancillary data including air temperature, relative humidity, water vapour pressure and incoming, outgoing and net radiation at the PNM.

Empirical abscission model

Seed counts were used to estimate the seasonal bias of seed abscission. We call this metric seasonally adjusted seed abscission or ΔSa (see Appendix S1: Dispersal Season Determination). The seasonal log-normal abscission estimate had a low correlation to actual seed count data (r2 = 0·04), but was significant (P < 0·05). We constructed a multivariate regression model between ΔSa and the observed environmental variables to determine the subseasonal scale conditions that affect seed abscission (Table S1). All data were averaged into 90-min bins to reduce autocorrelation and account for potential overlap between seed counts directly before and after their corresponding 30-min wind statistics. We followed a stepwise procedure. At the first step, first- and second-order polynomial regression models between ΔSa and each environmental variable were evaluated. We then considered the subset of regression models that were statistically significant at the 95% CI. Of these significant models, we selected the model with the lowest Bayesian information criterion (BIC) value (Schwarz 1978).

To determine whether the addition of other environmental variables would lead to significant model improvement, we regressed first- and second-order polynomials of each of the environmental variables to the residuals of the previously selected model. Statistically significant regressions (if any) were deemed to yield significant model improvement. Of the statistically significant regressions (if any), we selected the one with the lowest BIC as the new best model. This procedure was repeated until no statistically significant regressions provided a better BIC. Although this procedure assumes second-order polynomials, we found that the selection of environmental variables was insensitive to this assumption. The goodness-of-fit of the final model was evaluated by testing the residuals for independence (Box–Ljung test), normality (Shapiro–Wilk test) and homoscedasticity (Breusch–Pagan test). Statistical analyses were performed using R version 2·15·1.

Model selection criteria

A Monte Carlo study was carried out to assess the skill and significance of the model selected. The basic protocol followed here is similar to what was presented in Beaulieu et al. (2012) and is designed to test for Type I and Type II errors. We started with the null hypothesis that our best-fit model is correct. To test for Type I errors, we generated a synthetic time series by randomly drawing (with replacement) from the residuals of the best-fit model and then added these random draws to the fitted values of the best-fit model. We then applied our fitting procedure to the synthetic time series. If our original determination of the best-fit model is correct, then this model should be selected to describe a strong majority of the synthetic series. Our procedure for testing for Type II errors was similar, except that this time we generated a synthetic time series by randomly drawing (with replacement) from the residuals of the second-best-fit model and then added these random draws to the fitted values of the second-best-fit model. We then applied our fitting procedure to this second synthetic series and determined the proportion of times that our best-fit model was selected. A small proportion would indicate that we would rarely accept the null hypothesis when it is false. These simulation schemes are appropriate because, in both the best-fit model and the second-best-fit model, the residuals can be considered independent (Ljung-Box test, 95% confidence level). A total number of 10,000 synthetic series were generated in the testing of both Type I and Type II errors. In a preliminary analysis, this number of synthetic series was found to be sufficient for the results to converge.

Sensitivity analysis to determine the effects of the timing of seed release

Different environmental conditions lead to seed abscission at different times. Over the long term, these differences accumulate to form a biased sample of the actual wind conditions. To estimate the potential effects of seed abscission timing on the dispersal kernel, we used two models forced with wind distributions derived from long-term wind observations at BCI. These distributions are broken into subsets based on combinations of weather and wind conditions associated with seed abscission in the best-fit abscission model (see Methods: 'Empirical abscission model'). Specific wind distributions and inclusion of abscission biases in either model are later described in the individual model methods. We use these simulations to estimate the sensitivity of the dispersal kernel (particularly the mean distance and LDD probability) to the environmental conditions affecting the timing of seed release. The resulting kernels are not evaluated for the specific dispersal distances and probability. Instead, each kernel is compared relative to the others and relative to a bench-mark case of unbiased, uniform-in-time release rate to quantify the relative long-term effects of the bias in wind conditions due to the selective timing of seed release under different environmental conditions.

Modelling long-term effects of environmentally triggered abscission – the super-WALD kernel

A good approximation of the dispersal kernel for slow-falling seeds in turbulent environments can be calculated with the WALD phenomenological kernel (Katul et al. 2005):

display math(eqn 1)

where math formula is the probability of landing at a distance x (m) from the source, zr is the height (m) above ground at which seeds were released from the mother plant, h is the mean height (m) of the top of the surrounding canopy, Θ is a scaling coefficient for turbulence defined as the ratio between the standard deviation of the 10 Hz measurements over a 30-min period of vertical wind fluctuation, math formula, and the mean wind speed above the canopy, math formula. Long-term Θ is determined from the slope of the correlation between math formula over the data set of high-frequency wind observations. The similarity constant, κ, is assumed to be 0·6 for within-canopy flow conditions (Thompson & Katul 2008), and Vt is the terminal fall velocity of the seed (m s−1). Here, we used Vt = 0·7 ± 0·07 m s−1, determined from the mean of measurements of 15 seeds (Augspurger 1986). The WALD kernel describes the distribution of dispersal distances in a given set of wind conditions, typical of a specific 30-min period.

Thompson & Katul (2008) showed that WALD can be expanded to represent the expected long-term dispersal kernel, obtained as the convolution of many 30-min dispersal kernels, if the long-term distribution of the wind is known and assumed to fit a Weibull. A more accurate representation of the long-term wind distribution may be obtained through explicit integration of individual 30-min measurements over the entire period (following the approach in Wright et al.2008). The seasonally integrated super-WALD (SW) kernel will then follow the formulation of

display math(eqn 2)

where math formula is the WALD kernel (as a function of distance, x) for the observed 30-min mean wind conditions at a particular time math formula (described in eqn (eqn 1)). As super-WALD does not account for the variation of wind speed with height above the canopy, we assume the wind speed at a height of 5 m above the canopy as the effective wind speed. Super-WALD kernels were calculated using the statistics of the 30-min mean horizontal wind at PNM for the following scenarios: (1) full year of uniform seed release rate; (2) dispersal only during the observed dispersal season (sub-sampling of meteorological data was done following Garrity et al. 2011); (3) dispersal during the dispersal season only during daytime hours (6:00 am to 6:00 pm); (4) a subset of (3) but only during strong horizontal winds, that is, math formula > 0·5 m s−1 and (5) a subset of (3) but only in relatively high (above median) temperatures, that is, T50. The super-WALD kernel does not incorporate updrafts; therefore, we include higher horizontal winds, which typically lead to higher turbulence (i.e. more updrafts/downdrafts). We recalculated Θ based on the subset of wind observations that comply with the conditions of each case and then recalculated the dispersal kernel that corresponds with the appropriate release timing using eqns (eqn 1) and (eqn 2). The 11-year distributions of wind speed for all cases are presented in Figure S4. Figure S5 presents the day and night distributions of turbulence statistics (frictional velocity and vertical wind fluctuation inside the canopy) for 12–26 April 2010.

Effects of abscission in updrafts

Updrafts are a short-term process and are part of the turbulent fluctuations of vertical wind, which averages to near zero at the 30-min and longer time-scales. The coupled Eulerian–Lagrangian closure (CELC) model (Nathan & Katul 2005) is able to simulate turbulence by calculating random instantaneous (milliseconds–seconds) turbulent-driven excursions from a prescribed wind speed field and calculate the resulting three-dimensional trajectories of wind-dispersed seeds. In CELC, the prescribed horizontal wind speed field is homogeneous but includes a vertical profile – weaker wind inside the canopy and near the ground following Massman & Weil (1999) and logarithmically increasing wind speed above the canopy, following the Monin–Obukhov similarity theory. Similar variation is prescribed for the turbulence statistics. The trajectory calculations are repeated for many virtual seeds to produce the large sample necessary to calculate a representative dispersal kernel for the prescribed, half-hourly wind conditions. Repeated CELC simulations with different sets of prescribed, observation-based, above-canopy, half-hourly wind conditions are combined to form an overall seasonal kernel. In this way, the resulting kernel accounts for both short-term turbulence, through the effects on the trajectories of individual seeds, and longer-term wind conditions, through the combined sets of prescribed 30-min conditions. We used the same CELC set-up as reported in Wright et al. (2008). The fact that CELC utilizes both a turbulent time-scale (during the dispersal events) and a longer time-scale (by repeated simulations with different 30-min forcing) limit the negative effects of time-scale choice on the estimate of the kernel (Skarpaas, Shea & Jongejans 2011).

Inputs for CELC included the leaf drag coefficient (estimated here as 0·25) and the half-hourly wind and turbulence statistics above the canopy on BCI during a full dispersal season in 2007 (Bohrer 2007). Release height was assumed to be 40 m, corresponding to the canopy height at BCI, where we have season-long high-frequency measurements of wind and turbulence. Canopy structure representation in CELC is reduced to the description of the horizontally averaged vertical profile of leaf area density provided by Bohlman & O'Brien (2006) for BCI. Terminal velocity for each dispersal event was randomly selected from a Gaussian distribution, with the reported mean and standard deviation for L. seemannii. To reduce the 2-D dispersal distribution to a 1-D distance kernel, we converted the 2-D space to annuli centred on the release point. The number of seeds that arrived in each distance bin were summed and then normalized by bin width and the total number of seeds released (during the entire seasonal series of simulations), resulting in the probability a seed fell in each distance bin. We ignore dispersal distances ≥ 100 km, as these were typically caused by seeds ‘caught’ at the numeric top boundary of the model, causing unrealistically long dispersal distances due to numerical limitations.

To directly test the effects of release in updrafts, we ran two series of simulations with CELC: (i) bench-mark case – used to simulate the dispersal kernel when seed abscission rate is not affected by updraft; (ii) updraft-biased case in which the seed is initially caught in an upward eddy for a period of one eddy correlation time (calculated using formulation from Nathan & Katul (2005)). This biased case is used to simulate abscission that is induced by an updraft event at some point during the prescribed 30-min period. The initial vertical wind speed for each 30-min period is prescribed as the median updraft velocity (i.e. the 75th percentile of the vertical wind distribution, which includes roughly 50% updrafts and 50% downdrafts) assuming vertical velocity has a Gaussian distribution with mean 0 and the observed standard deviation, σW. This vertical eddy velocity is representative of a typical updraft for the wind conditions during each specific half hour and may or may not be larger than the terminal velocity of the seed. After the initial eddy correlation time period, the seed is allowed to experience the same wind statistics as in the bench-mark case, driven by the observed 30-min mean and turbulence statistics.

Results

Observations: seed abscission is determined by meteorological conditions

Seed abscission is intermittent, as can be seen by the large deviations from predicted seasonal distribution of seed release (ΔSa, Fig. S3). The majority of seeds were released during a few large events. Over 158 half-hour periods, we found all meteorological variables to be significantly directly correlated with the rate of seed abscission, with the exception of math formula. Because most environmental variables were intercorrelated (Table S2), it is not surprising that many variables show significant effects. The variable with the highest predictive power of seed abscission was the root mean square of the upward wind perturbations, σWup (r2adj = 0·490, P < 0·001), which indicates that updrafts have the strongest effect of any environmental variable on seed abscission in L. seemannii. In the subsequent steps of the regression analysis, the sensible heat flux (H), temperature (T) and mean horizontal wind speed (ū) also significantly affected abscission, but the addition of further environmental variables did not significantly improve the fit. Null hypotheses of independence and homoscedasticity were not rejected (P = 0·72 and P = 0·62, respectively). However, the residuals were not normally distributed (P < 0·001). While non-normality can in principle introduce biases, our parameter estimates from ordinary least-squares were consistent with the results of a robust regression. The seed abscission model resulting from the stepwise procedure (r2adj = 0·714, P < 0·001) follows:

display math(eqn 3)

We used Markov Chain Monte Carlo analysis to test the significance of adding each of the above model variables. σWup was selected as the first predictor variable in a strong majority (89%) of the cases (Fig. S6a). Wmax was selected as the first predictor variable in almost all of the remaining cases. Thus, if our best-fit model accurately describes the data, then σWup would be correctly identified as the most important predictor variable with 89% probability. The probability that H was chosen as the second predictor variable, conditional on σWup being previously chosen, was 73% of cases (Fig. S6b). Similarly, probability of choosing T as the third variable conditional on have previously chosen σWup and H was 76% (Fig. S6c), and the probability of choosing ū as the fourth variable conditional on having previously chosen σWup, H and T was 74% (Fig. S6d). If ū was not chosen in the fourth step, the next most likely outcome (23%) was that no model gave a statistically significant improvement to the fit. Overall, the independent variables of the best-fit model were chosen in 37% of the synthetic series. Because of the relatively low proportion of cases for which ū was chosen, including it as a predictor variable should be regarded as speculative. In our analysis of Type II error, we found that the second-best-fit model consisting of σWup, H and T was selected in 56% of the series. The best fit was (spuriously) selected 2% of the time, indicating relatively low probability of incorrectly accepting the null hypothesis. Following the results from the Monte Carlo study, the most significant model (evaluated in Fig. 2) (r2adj = 0·646, P < 0·001) follows:

display math(eqn 4)
Figure 2.

Modeled abscission vs. measured abscission (eqn (eqn 4), r2 = 0.646, P < 0.001). Solid line is the 1 : 1 line.

This model was selected as the final abscission model, which describes positive feedback towards abscission during periods of updrafts and high temperature and a negative feedback towards abscission during temperature-driven highly convective periods. Coefficients to the model correspond to a 30-min estimate of seed abscission.

Modelling: integrating abscission conditions to predict long-term dispersal kernels

We created dispersal kernels using the super-WALD model, with 11-year wind data from PNM and corresponding 11-year dispersal season–timing observations from BCI. The results show that kernels representing cases 1–3 have very similar shapes (Fig. 3). The strong wind conditions (case 4) show the highest probability of dispersing between 20–255 m. From 255–4988 m, the high temperature conditions (case 5) show the highest probability, with yearly conditions (case 1) having the highest probability of distances further than 4988 m. The dispersal probabilities near these transitions are on the order of 10−4–10−7; however, we show for each case that roughly 1% of the seed population will travel at least 1 km and 0·1% of the seed population will travel multiple km. For the yearly conditions, the 99·9% cumulative threshold was not reached in the maximum search area of this study (25 km). Although the strong wind kernel becomes less probable than the yearly and daytime dispersal season kernels, the mean dispersal distance under strong wind conditions (91 m) is further than the means of the yearly, seasonal and daytime, seasonal conditions (67, 63 and 84 m, respectively). The high-temperature kernel has the furthest mean dispersal distance at 105 m.

Figure 3.

Super-WALD dispersal kernels presented as the probability seeds disperse a given distance under five sets of environmental conditions. The inset provides a key to the environmental conditions. Both the probability of seed arrival and distance are on logarithmic scales. Vertical lines correspond to the distance to which the listed percentage of seeds have traveled.

Modelling: determining the effects of abscission in updrafts

Dispersal kernels were calculated by the CELC model using two cases: one with an updraft bias and the other, a control with no bias for updraft-driven seed abscission. Dispersal distance is consistent between each case up to roughly 100 m, as can be seen by the equivalent distance travelled by the first cumulative 99% of seeds. At distances further than 100 m, we find a shift to higher dispersal distance probability in the updraft-biased scenario relative to the control scenario (Fig. 4). At the cumulative 99·9% seed population threshold, the control case sees dispersal distances of 364 m, compared to distances of 840 m (2·3 times as far). This roughly 2 : 1 dispersal distance ratio of the updraft case vs. the control case continues for the duration of the seed population, and the difference in probability of LDD of the updraft case becomes as large as an order of magnitude more than the control case for dispersal distances larger than 10 km. Although this distance corresponds to a probability on the order of 10−5–10−6, integration of the kernel shows roughly 0·01% of the seed population will travel further than 10 km. The mean dispersal distance during the updraft case is 28% further than the mean dispersal distance during the control case.

Figure 4.

The coupled Eulerian–Lagrangian closure (CELC) dispersal kernels presented as the probability seeds disperse a given distance under two sets of environmental conditions. The inset provides a key to the environmental conditions. Both the probability of seed arrival and distance are on logarithmic scales. Vertical lines correspond to the distance to which the listed percentage of seeds have traveled.

Discussion

Dispersal is a very short-term event (seconds–minutes) which, aggregated over many events over days and seasons, controls the slow, long-term dynamics (years – millennia) of population spread and survival. Therefore, we hypothesize that the physiological traits that control the timing of seed release should be selected to respond to environmental conditions in a way that will optimize the resulting dispersal. The species we studied, L. seemannii, is shade-intolerant and depends on germination in canopy gaps, which are rare in its closed canopy forest habitat. These establishment limitations suggest Lseemannii would benefit from LDD, which provides a large ‘search area’. Selection should favour morphological traits that promote LDD in this tree. The dispersal unit morphology (light weight, thin ‘wings’, upward-facing capsule) suggests that selection for LDD has affected the seed traits to increase their flight time and dispersal distance. The mean dispersal distance may also be affected by long-term (multi-annual) interactions between population viability, seedling survival, habitat and climate (Kuparinen et al. 2009; Nathan et al. 2011). However, in this study, we focus on subannual time-scales. We use super-WALD kernels to test the effects of environmental variables such as wind speed and the seasonal and diurnal distributions of the wind and CELC to test the effects of seed release in updraft conditions.

Effects of the timing of the dispersal season

The year-round super-WALD kernel (case 1) had the highest probability of dispersing further than 4 km and the highest mean long dispersal distance for the farthest 0·1% of seeds (Fig 3). However, the mean dispersal distance is higher during seasonal daytime conditions (84 m) (case 3) compared to the year-round (67 m) and dispersal season (63 m) conditions. While the mean wind speed (ū) for the seasonal daytime case is higher than both the seasonal and year-round cases (Fig. S4), the year-round wind speed distribution shows a thicker tail, indicating more frequent events of relatively strong wind. This is due to the fact that there are more extreme turbulent wind gusts during the wet season than during the dry season, as indicated by the wind speed skewness and kurtosis (Table S3). Nonetheless, our study species, and most other wind-dispersed species in central Panama, disperse their seeds during the dry season. These findings suggest that the timing of the dispersal season is not driven only by consideration of dispersal distance and that other factors, such as the impending rains that favour germination and seedling establishment, may also lead to selective forces that determine the timing of the dispersal season.

In our simulations, we neglect the effects of spatial heterogeneity and the seasonality of canopy structure. It is probable that the effects of reduced canopy density during the dry season play an important role. During the dispersal season, canopy density is at its minimum, which improves dispersal distance (Nathan & Katul 2005), and the canopy is rich with temporary gaps caused by leafless deciduous trees surrounded by evergreen trees (Bohlman 2010), which leads to ejection hotspots and increased LDD probability (Bohrer et al. 2008, 2009). These effects cannot be resolved by either the super-WALD or the CELC models as they are driven by the spatial interaction between canopy heterogeneity and turbulence. Due to these model limitations, we cannot rule out wind as a selective driver of the timing of the dispersal season.

Effects of daytime release

As seen in our seed trap data, daytime abscission was roughly an order of magnitude greater than night-time abscission. Wind conditions at night tend to be weaker than those during the day. During the strongly convective tropical periods, daytime means of math formula = 0·540 m s−1, u* = 0·280 m s−1 and σWup = 0·223 m s−1 were much larger than night-time means of math formula = 0·334 m s−1, u* =  0·168 m s−1 and σWup = 0·158 m s−1 (Fig. S5). The daytime vertical wind is more negatively skewed (−0·518 m s−1) than night-time vertical wind (−0·437 m s−1), demonstrating a thicker above-mean tail and higher tendency for updrafts. These statistics, and correspondingly, our simulation results, suggest that seeds will have higher chances to uplift and experience LDD with the strongly convective conditions during the day rather than during the night.

Table 1. Summary of the statistics from the stepwise empirical model selection for seed abscission, expressed as the residual from the expected seasonal seed availability rate, ΔSa
Model: ΔSa =Environmental variable (x) and Monte Carlo parameter index BIC
T RH W95 Wmax Wmin σ W σ Wup math formula u * gust σ U H SWnet VPD ZE
123456789101112131415
  1. The table shows the r2 of linear, quadratic and second-order polynomial regression between different combinations of environmental variables, x, and ΔSa. At each iteration, the variable with the highest r2 (highlighted bold) among those with a significant relationship was added to the model. The type of relationship for this variable (linear, quadratic) was also determined according to the highest r2. Bayesian information criterion (BIC) analysis was used to determine whether adding this variable to the model is justified. In each iteration, the lowest model BIC value is shown on the last column. BIC values of the last iteration are left blank, as no BIC was lower than that of the previous iteration. The significance of the improvement to the model in comparison with the simpler model from the previous iteration was tested using a Markov Chain Monte Carlo analysis (Figure S6).

Ax + B0.2680.2220.3020.3430.2510.2410.388−0.0190.1470.2350.1820.0310.1070.2550.073
Ax2 + B0.2770.2100.3240.3880.2690.2390.443−0.0200.1100.2280.158−0.0120.0480.2910.066
Ax2 + Bx + C0.3180.2430.3180.4010.2580.226 0.490 0.0210.1780.2190.1970.0940.1650.2790.054 391.7
AσWup2 + BσWup + Cx + D0.5090.4910.5330.4800.4800.517 0.5190.5140.4880.5010.5440.4800.4980.483
AσWup2 + BσWup + Cx2 + D0.5100.4890.5510.4800.4830.534 0.5390.5350.4930.5190.5790.4840.5120.481 372.2
AσWup2 + BσWup + Cx2 + Dx + E0.5120.4960.5810.4870.4900.559 0.5580.5510.4920.574 0.573 0.5200.5120.477
AσWup2 + BσWup + CH2 + Dx + E0.6460.6370.5710.5710.5780.570 0.5800.5700.5700.570 0.5750.6530.588 364.8
AσWup2 + BσWup + CH2 + Dx2+E0.6500.6290.5740.5700.5770.570 0.5950.5720.5700.571 0.5700.6780.585
AσWup2 + BσWup + CH2 + Dx2 + Ex  + F 0.660 0.6590.5900.5690.5680.575 0.6380.5780.5670.605 0.5940.6720.581
AσWup2 + BσWup + CH2 + DT+Ex  + F 0.6420.6390.6390.6520.638 0.6740.6460.6380.643 0.6440.6500.639–.
AσWup2 + BσWup + CH2 + DT + Ex2 + F 0.6400.6400.6390.6500.639 0.6940.6500.6390.648 0.6460.6720.641
AσWup2 + BσWup + CH2 + DT  + Ex2 + Fx + G 0.6680.6400.6310.6460.639  0.714 0.6450.6340.655 0.6400.6750.635 347.6
AσWup2 + BσWup + CH2 + DT + Emath formula 2 + Fmath formula + Gx + H 0.7130.7090.7110.7110.707  0.7070.7100.713 0.7080.7200.708
AσWup2 + BσWup + CH2 + DT + Emath formula 2 + Fmath formula + Gx2 + H 0.7100.7100.7110.7100.707  0.7070.7090.711 0.7090.7380.710
AσWup2 + BσWup + CH2 + DT + Emath formula 2 + Fmath formula + Gx2 + Hx + I 0.7320.7020.7040.7080.701  0.7010.7050.708 0.7030.7360.709

Effect of seed abscission at high wind speed and high temperature

It is interesting to note that heat flux and temperature, which have been shown to influence seed abscission in previous studies in the same tropical environment but for a different species, Jacaranda copaia, which disperses during the wet season (Wright et al. 2008), were also found to significantly influence the high-frequency seed release timing of L. seemannii, which disperses during the dry season. Previous studies demonstrated that drying of the dispersal unit increases seed abscission (Greene & Johnson 1992; Jongejans et al. 2007). It is possible that temperature provides the mechanism for the daytime release through the drying and opening of the pod. Both temperature and humidity have a significant positive effect on abscission; however, the strong correlation between temperature and humidity led to humidity not having a significant independent effect on abscission.

Strong wind (red line, Fig. 3) and high temperature (cyan line, Fig. 3) show enhanced dispersal probabilities at moderate distances (100–5000 m) compared to yearly, seasonal and seasonal daytime cases. LDD at strong wind becomes less probable around the 99th percentile (~1 km) of seeds released, whereas high-temperature LDD becomes less probable around the 99·9th percentile (few km). We found the ratio between vertical wind fluctuations and mean horizontal wind speed, Θ, to be the reason for the observed differences between the shape of the dispersal kernel with strong wind and other seasonal kernels. At our site and typical of other tropical sites, low values of math formula are characteristic of weather conditions with high thermally driven turbulence and therefore high Θ. This occurs because strong wind produces more shear-driven eddies that tend to be smaller and less energetic than thermally driven eddies. Θ shows a twofold reduction when wind is subsampled from math formula > 0·5 m s−1compared to the year-round and daytime dispersal season and high temperature winds (0·59, 1·31, 1·25 and 1·18, respectively). Combined, higher math formula and lower Θ create large effects on the shape of the dispersal kernel, particularly, increasing the mean dispersal distance while reducing the probability of LDD.

Effects of abscission in updrafts

Long-distance dispersal of wind-dispersed seeds in forests is dependent on ejection of the seeds above the canopy (Nathan et al. 2002; Bohrer et al. 2008). During its dispersal event, a seed spends a few seconds to minutes in the air, held up by turbulent eddies that produce updrafts that are faster than its terminal fall velocity. As the long-term mean vertical wind is near zero, short-term turbulent fluctuations are the major source of uplift. While at a longer time-scale turbulence is a chaotic process, at short time-scales turbulent motion is characterized by organized waves – eddies. If a seed can time its release to co-occur with the passage of an upward eddy (ejection), it can ‘ride’ this eddy for a short period before the eddy breaks and dissipates. The average time for eddy dissipation is the eddy dissipation time, which we used in the CELC model. This short period (few seconds) of upward motion may be long enough and the updraft strong enough for the seed to be ejected above the canopy and into the stronger horizontal winds aloft that can carry seeds long distances.

The CELC model simulation confirmed that updraft-targeted seed release generates a higher probability of LDD. Dispersal events will only be meaningful when leading to seedling establishment, which in most instances involved LDD to escape predation and/or find suitable habitat (Thompson et al. 2009). Yearly seedling establishment events may occur at dispersal probabilities as low as 10−10 (Nathan 2006), which demonstrates our large LDD advantage during updraft conditions at probabilities of 10−5–10−6 to be significant. Furthermore, from seed counts per individual fruit (385 ± 53, n = 18) and on the order of 103 fruit per tree, we estimate the total annual seed production per individual to be on the order of 105–106 seeds, and roughly 107–109 during each tree's lifetime. By factoring these magnitudes into our calculated dispersal kernels, we show that when released in an updraft hundreds of seeds per individual per dispersal season (and tens-hundreds of thousands in a lifetime) will travel more than 1 km farther than seeds whose release does not target updrafts.

The idea that ejections (updrafts) enhance dispersal distances may seem intuitive, yet it has seldom been directly modelled or measured. Nathan et al. (2002) used the CELC model to show that ejected seeds would have a large LDD advantage over those seeds not ejected from the canopy. Our CELC simulation is the first to compare dispersal distance of seeds that were released uniformly without respect to updrafts with seeds released preferentially in updraft conditions. Although updraft bias may play an important role in both abscission timing and dispersal distance, it remains difficult to incorporate into dispersal kernel models. The problem arises because targeted abscission and turbulent momentum ejections are coupled phenomena that operate at very short time-scales. Timing the release to favour LDD is only possible if short-term high-frequency information is used. The challenge for the plant is to detect these conditions and target the release of seeds to these turbulence ejection events. In the case of wind-dispersed seeds, a closer inspection of the dispersal unit may resolve the link between morphology and LDD.

Greene & Johnson (1992) showed that drag from horizontal wind (induced with a household fan) affected the rate of seed abscission in a maple tree and that the shape of the maple seed wings and detachment mechanisms interacted with the wind direction such that under updrafts the seeds deflected at a larger angle which increased their probability of detachment of the peduncle. In a wind-tunnel experiment, Greene & Quesada (2011) showed that the shape of the capitulum of T. dubius suppresses seed release in downdrafts and therefore provides a morphological mechanism for updraft-selective release. Our study is the first to observe this updraft bias phenomenon in a natural environment and a tropical tree. The fruits of L. seemannii have an upward-facing cone that opens narrow cracks that begin at its top end (Fig. 1). Bernoulli's equation along a vertical streamline starting from the seed location and extending outward through the pod crack describe the physical mechanism through which the seed pod orientation interacts with updrafts to generate lee-side wake vortices that create a pressure gradient strong enough to dislodge the seeds.

Conclusions

To correctly estimate the movement capability of dispersing seeds, the full range of time-scales of the signal that drives seed release in plants must be represented by the modelling methods used to predict dispersal kernels. Super-WALD kernels that were generated with long-term wind observations, subselected for particular seed release dynamics, showed that the timing of the dispersal season does not necessarily optimize dispersal distance. At shorter time-scales, preferential dispersal timing during the daytime with frequent updrafts increased dispersal distances and LDD. Mechanistic dispersal simulations showed that including an updraft bias to the abscission conditions would further increase the probability of LDD.

Our finding of preferential abscission during updrafts is consistent with recent hypotheses, model simulations and laboratory experiments (Tackenberg, Poschlod & Kahmen 2003; Bohrer et al. 2008; Soons & Bullock 2008; Greene & Quesada 2011). To date, this study and those of Greene & Johnson (1992) and Greene & Quesada (2011) are the only ones that report cases of morphological mechanisms for upward-directional abscission bias. This research highlights the need to further investigate the mechanisms of seed abscission in wind-dispersed plants. Specifically, we suspect that further inspection of the morphology of their specialized dispersal units will show how this has evolved in many species to select release events during environmental conditions that will lead to optimal LDD.

Acknowledgements

We thank Ran Nathan for early discussion that helped inspire this study. We thank Mirna Samaniego for data collection assistance. KM was supported by the Smithsonian Tropical Research Institute (STRI), a French Graduate Fellowship through the Department of Civil, Environmental & Geodetic Engineering, an Ohio State University Fellowship and an NSF IGERT Fellowship #DGE-0504552 awarded through the University of Michigan Biosphere-Atmosphere Research Training (BART) program. GB was supported by NSF grant #DEB-0918869. Any opinions, findings and conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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