- Top of page
- Materials and methods
- Supporting Information
Alternative explanations of tree diversity have emphasized the role of annual variability in seedling recruitment. Large annual variability in regeneration success that is weakly correlated across tree species (HilleRisLambers & Clark 2003; Clark et al. 2004), together with the stochastic timing of gap formation, could determine which species successfully capture canopy openings, rather than static competitive relationship between species (e.g. Runkle 1989). The long life spans of tree species relative to the scale of temporal variability may provide a buffer or storage effect that promotes species diversity by allowing tree species to persist through periods of low recruitment, when years of high fecundity or survivorship do not coincide with periods of gap formation, and thus maintain a positive long-term population growth rate (Chesson & Warner 1981; Warner & Chesson 1985).
Determining the relative importance of spatial and temporal variability in recruitment requires data on the regeneration success of tree seedlings across environmental conditions and years. Traditional techniques for measuring seedling survival require the monitoring of individual seedlings through time: seedlings are marked with unique identifiers that must be subsequently relocated in order to assess the status of each individual as alive or dead (Klein & Moeschberger 1999; Beckage & Clark 2003). This method is laborious and time-consuming, is prone to problems with lost seedling markers and is inefficient, as seedling mortality tends to be high, with most marked seedlings lost in the first year. These factors tend to limit the spatial and temporal extent of sampling. This is problematic because large sample sizes are required to characterize fully the range of variability in regeneration processes across space and time (Clark et al. 1999).
The characterization of seedling survival would be simplified if survivorship could be estimated directly from repeated counts of seedlings in permanently marked quadrats, without the need to mark and track individual seedlings. Lavine et al. (2002) developed a Bayesian method for estimating survival parameters from repeated count data that only requires data on numbers of individuals in age or size classes. We investigated the use of this methodology to estimate survival of Acer rubrum L. (red maple) seedlings in small overstorey gaps with or without dense understorey shrubs and to characterize the residual spatial and temporal variance in seedling survival. We specifically address the following questions. Do small canopy gaps increase seedling survival? Are the effects of canopy gaps on seedling survival mediated by understorey shrubs? Is the magnitude of temporal variability in seedling survival greater than that of spatial variability?
- Top of page
- Materials and methods
- Supporting Information
The observed seedling densities for 1993–98 with respect to gaps and Rhododendron are shown in Fig. 1. Seedling survival was affected by the understorey shrub Rhododendron, canopy gaps and seedling age class. Rhododendron had a large but negative effect on survival (βr, Table 1, Fig. 2a) with seedlings beneath Rhododendron being 0.41 times as likely to survive as seedlings in areas without the shrub. By contrast, the effect of canopy gaps on seedling survival was positive but relatively small (βg, Table 1, Fig. 2a); seedlings in canopy gaps were slightly more likely (1.13 times) to survive than those beneath closed canopy, but the 95% credible interval included 0. The small effect size and overlap with 0 suggest that the gap effect was weak. The canopy gap–Rhododendron interaction was similarly weak: there was a tendency for seedlings in gaps with Rhododendron to be less likely (0.78 times) to survive than those in gaps lacking the shrub, but the 95% credible interval again contained 0 (βgr, Table 1, Fig. 2a). The effect of seedling age class, however, was large, with Old seedlings nearly 4.3 times more likely to survive from one year to the next than were New seedlings (βd, Table 1, Fig. 2a). In addition, we estimated that only about half of the New A. rubrum seedlings were found by the end of the growing season (f, Table 1).
Figure 1. Observed densities of New and Old seedlings in gap and closed canopy conditions with Rhododendron present or absent (plot means and standard errors).
Download figure to PowerPoint
Table 1. Means, medians and 95% credible intervals for parameter estimates. Model terms are defined in the Methods. Superscripts denote a particular component of a given vector
|Term|| ||Mean||Median||2.5%||97.5%||Odds ratio (mean)|
|Find probability||f|| 0.51|| 0.51|| 0.44|| 0.56||–|
|Canopy gap||βg|| 0.12|| 0.12||−0.10|| 0.34||1.13|
|Rhododendron–gap interaction||βgr||−0.25||−0.25||−0.64|| 0.14||0.78|
|Old age class||βd|| 1.46|| 1.46|| 1.14|| 1.77||4.29|
|Transect random effect|
| Variance|| 0.05|| 0.04|| 0.01|| 0.18||–|
| 0.00|| 0.00||−0.25|| 0.25||1.00|
| 0.09|| 0.09||−0.14|| 0.33||1.09|
| 0.02|| 0.02||−0.23|| 0.28||1.02|
| 0.07|| 0.06||−0.23|| 0.41||1.07|
| Transects|| 0.20|| 0.18||−0.11|| 0.63||1.22|
| 0.19|| 0.19||−0.02|| 0.41||1.21|
| 0.11|| 0.10||−0.20|| 0.48||1.12|
| 0.02|| 0.01||−0.28|| 0.34||1.02|
|Year random effect|
| Variance|| 2.66|| 1.72|| 0.48||10.43||–|
| 0.59|| 0.54||−0.38|| 1.87||1.80|
| Years|| 0.81|| 0.76||−0.15|| 2.07||2.25|
| 1.00|| 0.94|| 0.05|| 2.30||2.71|
| 0.86|| 0.82||−0.10|| 2.14||2.37|
Figure 2. Posterior distributions of selected model parameters and derived quantities: (a) the effect of canopy gaps (βg), Rhododendron understories (βr), the gap–Rhododendron interaction (βgr) and seedling age class (effect of being an Old seedling, βd) on A. rubrum seedling survival; (b) variability (standard deviation) in survival associated with years (σy) and transects (σt); and (c) the ratio of σy to σt. All posteriors have been smoothed using a gaussian kernel estimator.
Download figure to PowerPoint
Seedling survival was approximately seven times more variable across years than across transects (σy = 1.6 vs. σt = 0.22, Fig. 2b) with the 95% credible interval on this ratio ranging from 2.5 to 22.8 (Fig. 2c). The estimated transect random effects on seedling survival were relatively small, varying from −0.26 to 0.19 (Table 1). By contrast, the year random effect on survival ranged from −1.8 to 1.0, which was larger than any fixed effect except seedling age class (Table 1). The 95% credible interval included 0 for 11 of the 12 transect effects and for three of the five year effects, suggesting considerable uncertainty in these estimates.
We computed the posterior survival probabilities in all canopy gap–Rhododendron combinations for New and Old seedlings after removing year and transect effects, and these are shown on the untransformed probability scale in Fig. 3. Canopy gaps had only a weak effect on seedling survival, resulting in either slight decreases in median survival probability if Rhododendron was present or slight increases if Rhododendron was absent, i.e. a difference of approximately 0.02 in each case. Rhododendron, by contrast, had a strong and consistent negative effect on survival of both New and Old seedlings, regardless of canopy condition: median survival probabilities were decreased by the presence of the understorey shrub by up to 0.21 (Fig. 3). Survival probability was strongly dependent on age class: survival probability of Old seedlings was 0.13–0.25 higher than New seedlings across Rhododendron and canopy gap treatments.
Figure 3. Posterior distributions of seedling survival in all canopy gap–Rhododendron combinations for New (newly germinated) and Old seedlings on the untransformed probability scale. Parameters were estimated from 6 years of census data for A. rubrum. The posteriors have been smoothed using a gaussian kernel estimator. We refer to gap conditions as G+ (vs. canopy, G–) and to the presence of Rhododendron as R+ (vs. non Rhododendron, R–).
Download figure to PowerPoint
Strong correlations were found between some model parameters. The total number of imputed new seedlings, N, was strongly and negatively correlated with the estimates of findability f (ρ = −0.96), indicating a trade-off between the probability of finding a new seedling, f, and the imputed number of actual New seedlings present, N. Lower find probabilities resulted in larger numbers of imputed seedlings (Lavine et al. 2002). Transect and year effects were also often strongly correlated, as were and (ρ = 0.90).
- Top of page
- Materials and methods
- Supporting Information
We estimated annual survival probabilities for both newly germinated and established A. rubrum seedlings using 6 years of seedling count data. We found that canopy gaps had only a slight positive influence on seedling survival whereas the understorey shrub Rhododendron had a large negative effect on survivorship. The presence of Rhododendron offset the beneficial effects of canopy gaps, supporting observations that forest understories are an important determinant of tree regeneration patterns (Clinton et al. 1994; Lorimer et al. 1994; George & Bazzaz 1999; Beckage et al. 2000; HilleRisLambers & Clark 2003). Light levels in our gaps increased modestly beginning in the year following gap creation, with the proportion of light reaching the understorey ranging from 11% in canopy gaps to 5% beneath closed canopy, both outside of Rhododendron, to 2% beneath Rhododendron where there was no measurable increase following gap creation (Beckage et al. 2000). Small canopy gaps have been postulated to promote tree regeneration and maintain forest diversity in temperate forests (e.g. Barden 1979; Runkle 1981), but we found little evidence of this in the seedling survival of A. rubrum in our 20-m-diameter canopy gaps. Although A. rubrum is considered shade-tolerant (Burns & Honkala 1990), tree species that are more tolerant of shade, such as beech or hemlock, might respond more strongly to gaps of this size and nature. The lack of a strong recruitment response to small canopy gaps, however, is consistent with other studies of forest regeneration (Busing & White 1997; Beckage et al. 2000; Webb & Scanga 2001; Beckage & Clark 2003). Temperate forests in this region of the United States are subjected to frequent and intense hurricane disturbances that cause extensive areas of large blowdowns (Greenberg & McNab 1998). We suggest that large canopy gaps, such as result from severe tropical disturbances, with corresponding disturbance to the forest understorey may be necessary to increase seedling survival and maintain the high levels of tree diversity observed in forests of this region.
Annual variability in seedling survival of A. rubrum was much larger than spatial variability in survival across transects. The effects of individual years on seedling survival were larger than even our strongest treatment effect, i.e. the presence of the shrub Rhododendron (Table 1). Large interannual variability in seedling survival may have been driven by variation in environmental variables such as precipitation. The strong negative effect on seedling survival in Year 2 (Table 1), for instance, may have resulted from an unusually dry spring that year. Red maple seedlings emerge from winter dormancy in April in this region and, in 1995, precipitation was only 24–50% of that received in April of the other years of our study. Acer rubrum seedlings are not tolerant of drought (Barton & Gleeson 1996; Beckage & Clark 2003), so this dry period would be expected to result in low seedling survival (as shown in Table 1, Fig. 1). Annual fluctuations in the establishment and survival of seedlings can also be caused by biological factors such as seed or seedling predator abundance or variable seed rain (Clark et al. 1998; Beckage & Clark 2005), as well as by other environmental variables besides precipitation.
Large annual fluctuations in recruitment processes can allow diverse tree species to capture vacant sites in different years rather than available sites being consistently dominated by the best competitor (Kelly & Bowler 2002). Our estimates of large annual variability in seedling survival are similar to other long-term studies that have consistently found large annual fluctuations in recruitment processes such as seed production (Clark et al. 2004), survival (Streng et al. 1989) and seedling establishment (Boerner & Brinkman 1996; Connell & Green 2000). Large annual fluctuations in seedling recruitment, together with periodic hurricane disturbances that create large canopy openings, could lead to the high diversity of overstorey trees observed in temperate forests of the southern Appalachian mountains (Whittaker 1956). Frequent large disturbances, recruitment limitation of most tree species in most years and large annual variability in recruitment that is only weakly correlated across species may together promote tree diversity through a storage effect (Clark et al. 1998, 2004; Hubbell et al. 1999; Kelly & Bowler 2002). Our results also emphasize the need for including multiple years of sampling as increased spatial coverage will not capture the large annual variability observed in long-term studies.
The use of seedling counts to estimate seedling survival can lead to better characterization of patterns of tree recruitment. The labour required to mark and track large numbers of seedlings over long time periods may contribute to the limited characterization of seedling survival using traditional statistical techniques (Clark et al. 1999). Our new statistical methodology relies on repeated seedling counts rather than long-term monitoring of individual seedlings, substantially reducing the field effort required to derive survival probabilities, and enabling ecologists to sample spatial and temporal variability more broadly. In addition, seedling survival can be estimated from already existing count data, provided that seedlings were censused within categories with similar survival (e.g. our New and Old seedlings). In the absence of extensive data on seedling recruitment, forest regeneration can be modelled using shorter-term studies (e.g. Ribbens et al. 1994) or projections of future forest composition based on relative densities of recruits (Runkle 1981; see also Acevedo et al. 1995). The former approach is likely to miss important variability in regeneration processes while the latter assumes that subsequent survival will not vary across species, an assumption that is unlikely to be true. Although our methodology may reduce effort in the field, there is a trade-off between ease of data collection and information content of the data – census data contain less information on seedling survival than do marked seedling data. Lavine et al. (2002) explored this trade-off using 100 simulated datasets and found that the ratio of information content of census seedling studies to marked seedling studies tends to 0 as new seedling survival approaches old seedling survival. Fortunately, this is unlikely to be the case for most species. In addition, the statistical analysis that we present differs from traditional survival analyses in that we model transition probabilities between years rather than time to death. The time to death approach allows for probability of mortality to change continuously as seedlings age, a characteristic that might be desirable in some situations.
Our analysis suggests that we found only half of the new seedlings that were present at the end of the growing season (i.e. f = 0.51). A low find probability could have resulted from several causes. First, A. rubrum seedlings may have germinated for an extended period over the growing season, so that many seedlings may not have emerged until after our annual censuses were completed in the beginning of July to mid August across years. This explanation receives only limited support from a study of A. rubrum germination showing that the timing of germination varied annually, with nearly 50% of seedlings emerging in July in some years (HilleRisLambers & Clark 2005). Second, New seedlings that were present at the time of the census may have been missed by census takers. Ground-layer vegetation can make it difficult to spot small seedlings, which predominately belong to the ‘New’ age class. Third, vegetative reproduction (root suckers) would be classified as Old seedlings based on their physical appearance, without ever having passed through a New seedling stage, resulting in a lowered find probability. Similarly, misidentification of seedling age, i.e. erroneously placing a New seedling in an Old seedling class, may also have occurred on occasion for seedlings that germinated early in the growing season. In reality, all of these errors probably contributed to some extent to our low find probability, but we do not have data to distinguish between their relative importance.
We assumed conditional independence between adjacent quadrats and did not model additional spatial structure in our seedling survival model. We initially explored the strength of spatial correlation between adjacent quadrats in our transects using a Gaussian random field model, which indicated that this additional model structure was not needed to account for spatial effects. This result was consistent with another investigation of spatial structure in seedling survival, which we conducted using a separate data set (from the same study area) and was presented in a more theoretical paper (Lavine et al. 2002), where we concluded that there was not a clear need to model spatial correlation in adjacent quadrats. Although the previous model and data did not include environmental information, such as gaps and Rhododendron, this additional information should only reduce residual spatial autocorrelation. While we assume in our current model that survival is equivalent across adjacent quadrats, after conditioning for the presence of Rhododendron, gap environment, year and plot, we could have included a quadrat-specific random effect to account for additional variability across quadrats. The random effects model could be structured so as to account for spatial correlation. This might be necessary in some situations where there is significant environmental variation that strongly affects seedling survival, varies over adjacent quadrats and is not specifically conditioned upon.