Survival of tree seedlings across space and time: estimates from long-term count data



  • 1Tree diversity in forests may be maintained by variability in seedling recruitment. Although forest ecologists have emphasized the importance of canopy gaps in generating spatial variability that might promote tree regeneration, the effects of canopy gaps on seedling recruitment may be offset by dense forest understories.
  • 2Large annual fluctuations in recruitment processes, coupled with the long life of forest trees, can provide an alternative mechanism for maintaining tree diversity. Evaluating the relative importance of spatial vs. temporal variability in recruitment, however, requires estimates of seedling survival that are extensive on both scales.
  • 3Estimates of survival derived from conventional statistical methods require that individual seedlings are monitored through time, and are therefore often limited in extent. We demonstrate a relatively fast and easy alternative approach to measuring survival that uses repeated counts of individuals in quadrats.
  • 4Annual seedling counts were used to quantify both the effects of small canopy gaps and understorey shrubs on the survival of Acer rubrum (red maple) seedlings and the magnitude of residual spatial and temporal variability in seedling survival.
  • 5We found that a dense understorey had a greater effect on seedling survival than did canopy gaps. Our canopy gaps had only a slight positive effect on seedling survival, and their benefit was offset by a large negative effect of the understorey shrub Rhododendron maximum.
  • 6Annual fluctuations in recruitment processes were seven times greater than spatial variability across transects and the effect of individual years on seedling survival was larger than even that of understorey shrubs.
  • 7The long life span of trees coupled with large annual variability in recruitment success across species may maintain the diversity of forest trees through a storage effect.


Competing explanations for patterns of tree diversity have alternately emphasized the role of spatial or temporal variability in tree regeneration (e.g. Grubb 1977; Pacala & Roughgarden 1982; Huston 1994; Kelly & Bowler 2002). Canopy gaps and resulting spatial variability in understorey light conditions have played a prominent role in explanations of forest diversity (Shugart 1984; Platt & Strong 1989; Botkin 1993). Light is a resource that limits tree seedling recruitment in many forest understories, and canopy gaps can raise light levels, leading to increased seedling recruitment and higher levels of species diversity (Pickett & White 1985; Canham 1988; Platt & Strong 1989; Pacala et al. 1994). Many forests support dense understories, however, that may compete with tree seedlings for resources such as light, limiting seedling recruitment even in canopy gaps (e.g. Veblen 1982; Yamamoto et al. 1995; HilleRisLambers & Clark 2003), and diminishing the efficacy of canopy gaps in promoting seedling recruitment. Variation in the density of forest understories across sites could lead to ambiguous evidence for the importance of canopy gaps in maintaining tree diversity (e.g. Beckage et al. 2000; Webb & Scanga 2001,Gutierrez et al. 2004).

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?

Materials and methods

field methods

We characterized seedling survival in second-growth forests at the Coweeta Hydrologic Laboratory (35°03′ N, 83°27′ W), North Carolina, in the southern Appalachian mountains, USA. Elevation in the 1626-ha Coweeta Basin ranges from 675 m to 1592 m. Field sites were located in mixed oak forests, which are found at mid elevations and intermediate moisture levels. Rhododendron maximum L. is a common evergreen shrub in the Coweeta Basin that forms a dense subcanopy layer 3–7 m in height with stem densities of 5000–17 000 ha−1 (Baker & Van Lear 1998) and leaf area indices of approximately 4.8–6.6 (J. HilleRisLambers, unpublished data).

Twelve experimental gaps were created in two mixed-oak stands at 850 m and 1100 m elevation. Sites had a north-eastern aspect, and slopes ranged from 30% to 70%. Up to five canopy trees were girdled to produce gaps, with standing dead trees, of approximately 300 m2 (expanded gap definition, Runkle 1981) and a gap diameter to canopy height ratio of approximately 0.95. Three of the six gaps at each elevation contained a dense, natural Rhododendron understorey. Twelve transects, consisting of 40 contiguous 1-m2 quadrats, were established at the planned site of each gap prior to gap formation. Pretreatment data were collected and experimental canopy gaps were created by girdling trees in late summer 1993. Girdled trees remained standing for the duration of our study, although large branches began to fall in the fourth year. Following gap creation, the central quadrats of each transect were exposed to gap conditions and the outer quadrats were subtended by the surrounding canopy. The border between gap and canopy conditions was ambiguous, reflecting the irregular canopy shapes of bordering trees. Therefore, we estimated survivorship parameters using the seedling counts from the central 16 quadrats and eight quadrats from each end of the transect (i.e. omitting a 4-m transitional area on each side of the gap edges). The inner 16 quadrats were in the canopy gap treatment (post-gap formation only) whereas the outer 16 quadrats and all pre-gap quadrats were considered the closed canopy treatment.

Seedlings and saplings (< 1.5 m in height) of A. rubrum were censused along transects annually in July or August from 1993 to 1998. Seedlings that had germinated in the current growing season were recognized by the presence of cotyledons and lack of terminal bud scale scars and were classified as ‘New’. All seedlings that had germinated prior to the census year were classified as > 1 year old (‘Old’ seedlings), although this group may include some vegetative reproduction. These age classes are natural groupings for estimating seedling survival because survival is initially low for newly germinated seedlings but relatively constant across the subsequent several years of life (Streng et al. 1989; Jones et al. 1994).

statistical methods

Seedling survival was modelled as a binomial process. The number of Old seedlings in year y + 1 in a given quadrat comprised the New and Old seedlings that survived from the previous year. We modelled this process as the sum of two binomials:

D y+1 ∼ Binomial(Ny,Sn) + Binomial(Dy,Sd)

where Dy+1 is the number of Old seedlings in year y + 1, Dy is the number of Old seedlings in year y and Ny is the number of New seedlings in year y. Our censuses were conducted annually, so Sn and Sd represent probabilities of seedlings surviving from year y to year y + 1 for New and Old seedlings, respectively. If we consider one quadrat across two censuses that span one year, the probability of observing Dy+1 is:


where x represents the number of surviving New seedlings from year y and the summation occurs across the set X of potential number of surviving new seedlings that could lead to Dy+1 (see supplementary Appendix S1).

We sometimes observed that the number of Old seedlings in a quadrat in a given year (i.e. Dy+1) exceeded the total of New and Old seedlings observed in the previous year (Ny + Dy), indicating an error in the previous year's census. This discrepancy could result from the germination of some seedlings after the annual censuses were completed or from a failure to count all seedlings present in a quadrat (i.e. ‘missed’ seedlings). Seedling germination following completion of the annual census would result in an undercount of New seedlings (Ny) while ‘missing’ seedlings could potentially affect either age class. We believe, however, that counting errors (i.e. ‘missed’ seedlings) would primarily apply to the New seedling class (Ny) because they were generally shorter in stature (≤ 5 cm) than Old seedlings and more likely to be overlooked in the ground-layer vegetation. We accounted for this error by modelling the observed number of New seedlings, ny, as a binomial process: ny ∼ Bin(Ny,f), where Ny is the ‘true’ number of New seedlings present in the quadrat at the end of the growing season, and f is the probability of the census-taker finding each of the Ny seedlings. We assumed that the numbers of New seedlings were distributed as a Poisson random variable with rate parameter λ, which was allowed to vary across years and transects, as well as with gap/Rhododendron conditions, but which was constant across the 16 quadrats within the gap or canopy portion of a transect. The Poisson distribution is often used to model seedling densities (Clark et al. 1999; Keyes et al. 2001) and is particularly appropriate when sources of extra-Poisson variability are explicitly conditioned, as is the case in our analysis. The probability of observing Dy+1 for one quadrat across two censuses is then


We modelled fixed and random effects on the survival probability, S, of New and Old seedlings using a logit link, where logit(S) =  + t + y + Idβd. F is the design matrix for the fixed effects and β is the vector of estimated fixed effects. The vector β consists of the intercept (β0), the effect of the understorey shrub Rhododendronr), the effect of gaps (βg) and the interaction of Rhododendron and canopy gaps (βgr). T and U are the design matrices for the transect and year random effects, and βt and βy are the vectors of estimated transect and year random effects. Id is a vector of indicator variables that take a value of 1 if a seedling is classified in the Old age class or 0 otherwise. βd is the estimated effect of being in the Old age class on seedling survival. We treated βt and βy as random effects that were distributed as Normal(0, inline image) and Normal(0, inline image), respectively.

We adopted a Bayesian approach to model fitting that allowed the quantification of uncertainty in model parameters in the form of probability distributions (Gelman et al. 2003). A Bayesian analysis combines the observed data in the form of a likelihood function with prior evidence or beliefs represented by prior probability distributions to yield the posterior probability distribution of model parameters. The posterior probability distribution provides the basis for all inference through probability statements on model parameters. The explicit calculation of the posterior distribution is often intractable in complex models and an alternative approach is to simulate a large number of random samples from the posterior distribution using Markov Chain Monte Carlo simulation (MCMC; Gilks et al. 1996). In MCMC simulation, random samples are generated from the posterior distribution and these samples are summarized to make inferences about model parameters. We present the results of our analysis using both graphical plots and 95% credible intervals for each parameter of interest based on the samples generated from the posterior distribution. We describe our likelihood function, prior distributions and implementation of MCMC in Appendix S1. The computer code used to fit the model is available from the first author's website (


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).

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 MeanMedian2.5%97.5%Odds ratio (mean)
Find probability f  0.51 0.51 0.44 0.56
Canopy gapβg 0.12 0.12−0.10 0.341.13
Rhododendron βr−0.88−0.87−1.29−0.550.41
Rhododendron–gap interactionβgr−0.25−0.25−0.64 0.140.78
Old age classβd 1.46 1.46 1.14 1.774.29
Transect random effect
 Variance inline image  0.05 0.04 0.01 0.18
inline image  0.00 0.00−0.25 0.251.00
inline image  0.09 0.09−0.14 0.331.09
inline image  0.02 0.02−0.23 0.281.02
inline image −0.12−0.10−0.60 0.260.89
inline image  0.07 0.06−0.23 0.411.07
 Transects inline image  0.20 0.18−0.11 0.631.22
inline image −0.26−0.25−0.55−0.030.77
inline image  0.19 0.19−0.02 0.411.21
inline image −0.02−0.02−0.26 0.190.98
inline image −0.26−0.23−0.73 0.070.77
inline image  0.11 0.10−0.20 0.481.12
inline image  0.02 0.01−0.28 0.341.02
Year random effect
 Variance inline image  2.66 1.72 0.4810.43
inline image  0.59 0.54−0.38 1.871.80
inline image −1.84−1.87−2.94−0.570.16
 Years inline image  0.81 0.76−0.15 2.072.25
inline image  1.00 0.94 0.05 2.302.71
inline image  0.86 0.82−0.10 2.142.37
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.

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–).

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 inline image and inline image (ρ = 0.90).


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.


We are indebted to Ed Iverson for his statistical advice. This research was supported by NSF Grant DEB 9632854.