Species and study sites
Our four focal species differ in light demand during their juvenile phase, ranging from the extremely light-demanding Silver birch and Scots pine, to the comparatively shade-tolerant Douglas fir (Mayer 1992; Burschel and Huss 1997). Japanese larch is intermediate between these extremes (CABI 2005; Dekker et al. 2007).
We collected our data in the densely forested Veluwe area, centrally located in the Netherlands. Our research area was the southern part of the Hoge Veluwe National Park (52°2′14″N, 5°50′41″E). In this area we located five sites with a dense and fully-stocked regeneration in canopy gaps (i.e. gap diameter in excess of the average height of the surrounding trees). Gaps were either natural or man-made, were always composed of natural regeneration of all four species, and had not been thinned or otherwise influenced by management. We harvested the saplings from the central part of these gaps. We attempted to harvest both live and dead saplings in equal numbers from the five locations, but larger gaps finally contributed slightly more live and dead individuals.
The study area has a humic podzol soil of coarse sand with low water-holding capacity and nutrient content (Anonymous 1975). Even though root competition will occur on these soils, in this paper we focus solely on the competition for light during the self-thinning phase. Long-term annual temperature at the nearest weather station is 9.4°C, the warmest month is July with 17.2°C on average, the coldest is February with −0.6°C. Average annual precipitation amounts to 860 mm, more or less equally distributed over the year (KNMI 2005).
Data collection
We used tree-ring analysis to study responses of saplings and trees to environmental conditions (Pollmann 2003; Rozas 2003), and to assess mortality as a function of previous growth (Bigler and Bugmann 2004; Bigler et al. 2004). As radial growth is strongly related to biomass increment in the four studied species (Dekker et al. 2007, 2008) it can be taken as an indicator of whole tree growth.
The live and dead saplings were harvested in the spring and summer of 2005. The live saplings were collected randomly from different canopy positions that were used as a proxy for light availability. For this we used a five-point Canopy Position Index (CPI) with: (1) the tree does not receive direct light, (2) the tree receives direct lateral light, (3) the tree receives direct overhead light on part of the crown, (4) the tree receives full overhead light on the whole crown and (5) the tree has an emergent crown that receives light from all directions (Clark and Clark 1992). This ordinal-scale visual estimation is used in both tropical and temperate forests (Jennings et al. 1999) and provides sufficient accuracy to differentiate between broad ecological strategies of species (Poorter et al. 2005; Sheil et al. 2006). We harvested six live individuals per species per CPI class, yielding a total of 120 live saplings.
The dead saplings were collected together with the live ones. We selected individuals that were fully overtopped, did not have an obvious alternative cause of death (e.g. damage) and therefore most likely died from light starvation, and showed signs of having recently died. ‘Recently’ was evaluated by checking whether a tree still had the remains of a crown (i.e. fine branches, not leaves), had to some extent flexible twigs, did not have an advanced level of stem rot at ground level, and did not have its stem and branches covered with algae, mosses or fungi. Together, such characteristics are reasonably accurate in discerning between trees that recently died or that died much earlier (Kobe et al. 1995; Kobe and Coates 1997). In the case of deciduous trees (Silver birch and Japanese larch) an individual was considered potentially alive, and was thus rejected, when it still had non-blackened buds and/or if the fine twigs were very flexible and moist inside. Based on the ages of the live and dead individuals (see Table 1 and “Results”) we estimated that dead saplings in most cases died <5 years ago. As we deliberately investigated saplings under field conditions, both the exact time and cause of death will to some level remain unclear.
Table 1 Sample sizes and averages per species for dbh, height and age
After recording CPI, height (m), and dbh (cm) we cut down the live and dead trees and took a stem disc at ground level. These discs were air dried and sanded (up to 800 grit) to obtain a smooth surface so that tree-ring boundaries were clearly detectable. Tree-ring widths were measured with a precision of 1/100 mm along two perpendicular radii using a LinTab measuring stage from RinnTec. The two tree-ring series per tree were subsequently averaged. A number of stem discs from the dead individuals showed an advanced level of decay, despite our selection criteria, making it impossible to accurately measure the tree rings. These samples were discarded, leaving a total of 158 dead saplings.
Finally, we made an empirical estimation of mortality by counting all dead and live individuals of the four species along three 30 m × 1 m transects (oriented NW–SE, NE–SW and E–W) in the largest of the five gaps. In total we counted 534 individuals which we used to calculate species-specific fractions of dead individuals. This can be taken as an estimate of the 5-year mortality rate since we applied the same criteria as described above to identify trees that recently died.
Data analysis
Radial growth
We used the single tree-ring series to construct a mean curve (chronology) per species for both live and dead individuals by averaging the tree-ring widths for each year (cf. Orwig and Abrams 1995; Pollmann 2003; Rozas 2003; cf. Bigler and Bugmann 2004). To document the variation in radial growth through time these chronologies were plotted together with the single tree-ring series. For the live saplings of each species we created a mean curve per crown position at harvest (CPI). Interpretation of the annual variation in relation to environmental factors, i.e. weather conditions, was beyond the scope of this study. Such analyses were constrained by the limited length of the time series as well as the fact that radial growth in self-thinning saplings is mostly determined by light competition (Wyckoff and Clark 2002). Instead, we focussed on the general growth level and the growth trend, separated in initial growth (first formed rings around the pith) and final growth (last formed five rings before death or harvest). We finally calculated average diameter and height-growth rate by dividing the dbh and tree height at harvest by the age of the tree. Differences between species were subsequently tested with a non-parametric Kruskal–Wallis test.
Initial growth, final growth and crown position
As a crown position only applies to the moment of harvest and does not necessarily apply to the whole life span of a sapling, we checked whether a dominant or suppressed tree at the time of harvest always displayed a high or a low radial growth level. To do this, we ranked our data and for each species selected the 12 trees that displayed the highest growth in the first 3 years after establishment, as well as the 12 trees that displayed the lowest growth after establishment, so 24 out of the 30 live trees per species (80%) were part of this analysis. This avoids generating results based only on ‘extreme’ trees. A period of 3 years averages out random single-year fluctuations but is short enough to indicate a fast or slow growth start for a seedling. For each of the four species we tested whether initial and final growth, as well as CPI, differed between the two groups using a Kruskal–Wallis test. We additionally correlated initial growth with final growth by calculating Pearson’s r. We also did this for crown position at harvest by calculating Spearman’s rho. A positive relationship would indicate a trend in which trees that have a fast start continue to profit from this head start and end up high in the canopy, thereby linking CPI at harvest to a tree’s growth history.
Average 5-year final growth
For each individual we calculated the average radial growth of the last 5 years prior to death or harvest. We used this for the analysis of growth under different light availability, as well as for the analysis of mortality. The choice for this 5-year period was made after doing a Wilcoxon rank sum test for a difference in average growth between live and dead individuals, using the growth over the last 5, 4 and 3 years, respectively. The analysis with a 5-year period had the highest significance, and therefore yields the clearest differences in growth between live and dead individuals. Results using the 3, 4 and 5-year periods were very similar however, so the choice of period is not critical. This was also noted by Wyckoff and Clark (2002) and Kobe et al. (1995) who similarly used a 5-year average growth period. We performed a Kruskal–Wallis test to analyse differences in radial growth within species, depending on CPI.
Modelling and estimation of mortality
To analyse the relationship between radial growth and mortality we applied the model of Kobe et al. (1995) and Kobe and Coates (1997). It is based on a Maximum Likelihood method that estimates species-specific parameters of functions that model a sapling’s probability of mortality based on recent growth. Mortality probability in our case covers a period of 5 years, our limit to trees that recently died.
Let m(g) represent the probability of mortality at a given growth rate g, and h(g) the probability density of all growth rates. The expectation of mortality \( \bar{U} \) is then given by \( \bar{U} = \int\nolimits_{0}^{\infty } {{{m}}(g){{h}}(g){{d}}g} \) Let D denote the number of dead saplings which were found in a transect of N individuals, Q the number of dead stems, indexed by i, for which the growth rate is available, and R the number of live stems, indexed by j. Kobe et al. (1995) show that the likelihood L for such a dataset is given by
$$ L = (\bar{U}^{D} )(1 - \bar{U})^{N - D} \cdot \prod\limits_{i = 1}^{Q} {{\frac{{{{m}}(g_{i} ){{h}}(g_{i} )}}{{\bar{U}}}}} \cdot \prod\limits_{j = 1}^{R} {{\frac{{\{ 1 - {{m}}(g_{j} )\} {{h}}(g_{j} )}}{{1 - \bar{U}}}}} $$
(1)
Maximum likelihood can be employed to estimate parameters of the functions m(g) and h(g). We used a gamma density with parameters α and β to specify h(g):
$$ {{h}}(g) = {\frac{{g^{\alpha - 1} \beta^{\alpha } e^{ - g/\beta } }}{\Upgamma (\alpha )}} $$
(2)
For the probability of mortality m(g) we used an exponential decay with parameter A and B:
$$ {{m}}(g) = Ae^{-Bg} ,\quad {\text { where }}\, 0 < A \le 1 {\text{ and }} B > 0 $$
(3)
These are the same functional forms as used by Kobe et al. (1995), only the gamma density is parameterised differently. The expectation of mortality can then be written in closed form \( \bar{U} = A(B\beta + 1)^{ - \alpha } \).
In fitting Eq. 1 per species the likelihood L is maximised of obtaining the current dataset as a function of (1) the probability of encountering Q dead saplings and R live saplings, (2) the product of the probability densities that a dead sapling had growth history g
i
prior to death, and (3) the product of the probability densities that a live sapling had growth history g
j
.
Our main interest was in the parameters A and B of the exponential mortality function which contain information on differences in growth-related mortality between species. We tested whether A = 1, i.e. whether zero growth implies certain death. Note that A = 1 is on the boundary of parameter space and an ordinary likelihood ratio test is not available. We therefore used a non-parametric bootstrap test which employs the observed data to approximate the unknown sampling distribution of a test statistic by sampling observations with replacement (Efron and Tibshirani 1994). The test statistic used was the difference in log-likelihood for the model with A = 1 and the model with 0 < A≤1, and we used 1,000 bootstrap samples. A single bootstrap sample consisted of three parts, all drawn with replacement: a sample of size Q from the dead trees, a sample of size R from the live trees, and a sample of size N from the transect data. The non-parametric bootstrap, with 1,000 bootstrap samples, was also employed to create 95% confidence intervals for the parameter estimates, and thus for the mortality curves.