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The relationship between growth and mortality for seven co-occurring tree species in the southern Appalachian Mountains
Peter H. Wyckoff,
Department of Biology, Duke University, Durham, NC 27708, USA
*Present address and correspondence: Peter H. Wyckoff, Division of Science and Mathematics, University of Minnesota, Morris Campus, Morris, MN 56267, USA (tel. 320-589-6347; fax 320-589-6371; e-mail firstname.lastname@example.org).
*Present address and correspondence: Peter H. Wyckoff, Division of Science and Mathematics, University of Minnesota, Morris Campus, Morris, MN 56267, USA (tel. 320-589-6347; fax 320-589-6371; e-mail email@example.com).
1Slow growth is associated with high mortality risk for trees, but few data exist to assess interspecific differences in the relationship between growth and mortality. Here we compare low growth tolerance for seven co-occurring species in the southern Appalachian Mountains: Acer rubrum, Betula lenta, Cornus florida, Liriodendron tulipifera, Quercus prinus, Quercus rubra and Robinia pseudo-acacia.
2For all species, mortality was greater for understorey individuals than for canopy trees. Species varied widely in the length of growth decline prior to death, ranging from 6 years for L. tulipifera to more than 12 years for Q. rubra.
3Growth-mortality functions differ among species, but we found little evidence of a trade-off between tolerance of slow growth and an ability to show rapid growth in high light conditions.
4A. rubrum stands out in its ability both to grow rapidly and to tolerate slow growth, suggesting that its density may increase at our study site as in other parts of the eastern United States. In contrast, C. florida shows high mortality (15% per annum) as a result of infection with dogwood anthracnose.
5We modified a forest simulation model, LINKAGES (which assumes that all species have the same ability to tolerate slow growth), to include our functions relating growth and mortality. The modified model gives radically altered predictions, reinforcing the need to rethink and re-parameterize existing computer models with field data.
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Ecologists and foresters have long noted that as tree growth rate declines, the probability of mortality increases (Monserud 1976). In contrast to fire, hurricanes and other agents of ‘catastrophic mortality’, this growth-related mortality results from long-term decline in vigour. Growth rates are thought to integrate the multiple stresses faced by a tree and, although tolerance of low growth is a surrogate measure of a species’ ability to tolerate stress (Givnish 1988), little is known about its interspecific variation. Forest simulation models incorporate a growth–mortality relationship when determining the probability of mortality, but most assume either that all species are equally tolerant of low growth or that a simulated individual is at risk when it drops below 10% of the ‘optimal growth rate’ for its species (Botkin 1993; Miller & Urban 1999; Hawkes 2000).
Only recently have field biologists begun to gather the data necessary to describe interspecific differences in the growth–mortality relationship for forest tree species (Buchman et al. 1983; Kobe et al. 1995; Pedersen 1998a, 1998b). We have developed and compared several statistical methods for estimating probability of mortality from growth rate (Wyckoff & Clark 2000) whose application is now tested for seven important tree species in the southern Appalachian Mountains.
A single, general estimate of the growth–mortality relationship for a species requires data sets that have a large number of dead trees covering a range of sizes. It also requires data sufficient to calculate the mortality rate for that species. Obtaining sufficient mortality data for large, non-senescing trees is problematic, because death of large individuals can be rare (often < < 1% year−1). Also, it is not clear if a single growth–mortality function is adequate to describe mortality risk for a species across all size classes, or if we must explicitly consider size either by developing size-specific growth–mortality functions or by adding size as a model variable.
We estimate growth–mortality functions for our seven species using the methods of Wyckoff & Clark (2000) before addressing the question of size-independence in the growth–mortality relationship. Of the few studies that address this question with data, Kobe et al. (1995) found that while growth rate increased with stem size, the relationship between growth and mortality did not change, and adding tree size did not improve the predictive power of their growth–mortality functions. However, no data for trees larger than 10 cm in diameter were presented. Sheil & May (1996) suggest that mortality rates in tropical forests differ between saplings and larger trees, but do not differ significantly with size for trees greater than 10 cm diameter at breast height (d.b.h.). They did not, however, present data specifically relating growth and mortality.
Next we use our growth–mortality functions to examine whether tolerances of low growth covary with growth rates among species, which would suggest a biological trade-off. Such trade-offs arise from differences among species in morphology and physiology, whereby adaptation to one set of conditions comes at the cost of suboptimal adaptation to others. Theory suggests that trade-offs may facilitate species coexistence (MacArthur & Levins 1967; Tilman 1982; Huston & Smith 1987). Pacala et al. (1996) used growth–mortality relationships to suggest that species coexist in a Connecticut forest via a trade-off in which some species grow fast in high light while others tolerate low growth.
We apply our growth–mortality functions using independently derived data from permanent plots at our field site to examine the distributions of mortality risk for trees growing in the field. Finally, we use our growth–mortality functions to test the implications of the assumption of uniform tolerance of low growth in the forest simulation model LINKAGES (Pastor & Post 1985, 1988; Post & Pastor 1996; He et al. 1999), which is typical of the broader class of JABOWA-FORET models in the way it calculates growth-related mortality (Botkin 1993). All simulated trees growing above a threshold growth rate are immune to growth-related mortality, regardless of species, but trees growing more slowly than the threshold experience high probability of mortality. For growing conditions typical of the southern Appalachian Mountains, we compare the patterns of forest development predicted by LINKAGES before and after modification with our growth–mortality functions.
Data were obtained from three study sites within the Coweeta Hydrologic Laboratory in the southern Appalachian Mountains (35°03′ N, 83°27′ W). Mean annual temperature is 13 °C and average annual rainfall is 220 cm (Swift et al. 1988). The three study sites represent cove forest (elevation: 800 m), mid-slope, mid-elevation mixed oak forest (1100 m), and northern hardwood forest (1400 m). Average temperature declines by 3.3 °C and precipitation increases by approximately 24% from the lowest to highest study site (Swank & Crossley 1988). Soils are primarily Ultisols and Inceptisols (Velbel 1988). Our data come from secondary forest, with a mean basal area of 28 m2 ha−1 in our three study areas. Overstorey vegetation consists of a mixture of early and mid-successional species (Table 1). Drought from 1985 to 1988 was followed by a decline in canopy oaks in mid-slope stands, with Quercus coccinea suffering the bulk of the increased mortality (Clinton et al. 1993). Important understorey species include Cornus florida, Acer pensylvanicum and Rhododendron maximum.
Our analysis of growth–mortality relationships requires three types of data: (1) growth rates of living individuals, ga, (2) growth rates of recently dead individuals, gd, and (3) estimated annual mortality rates for each of our seven species, θ. Field data collection and methods for calculating mortality rate are described in detail in Wyckoff & Clark (2000). Briefly, growth rates were determined using increment cores taken from living and recently dead Acer rubrum, Betula lenta, Cornus florida, Liriodendron tulipifera, Quercus prinus, Quercus rubra and Robinia pseudo-acacia (Radford et al. 1964). To locate live and recently dead individuals suitable for coring, we walked transects in each of our three study areas. We selected recently dead individuals with intact crowns to ensure that they did not die of catastrophic, growth-independent causes, and these were cored along with nearby living conspecific individuals of similar diameter. Based on the characteristics of dead trees in permanent plots, where year of death was known, we estimated that trees remain identifiable to species for an average of 5 years after death. High rates of decomposition at our field site mean that intact (and thus useful) increment cores could only be extracted for 2–3 years, and so ‘recently dead’ means 0–3 years in most cases.
Mortality rates were estimated from stem counts and from five 80 × 80 m permanent plots using data from four censuses conducted between 1991 and 1998. Stem counts were based on methods presented in Kobe et al. (1995): 5-m temporary plots were located at 20-m intervals on a subset of the transects used to locate trees for coring. Within these temporary plots, all living and identifiable dead stems were counted and annual mortality rates were calculated.
The bulk of the data contributing to our estimates of mortality rate come from the permanent plots, of which three are located near our low-elevation transects and one each near our mid- and upper-elevation transects. A Bayesian approach was used to combine stem count and permanent plot data to estimate mortality rates for all seven species (equations 13–18 in Wyckoff & Clark 2000).
radial growth as a predictor of mortality
Growth increments were measured with the Windendro (Régent Instruments Inc., Quebec City, Canada) measuring system, which provides resolution to 0.01 mm. Automatic ring detection was not used. To predict mortality, we used radial growth rates averaged over the five most recent growth years. Data are consistent with other recent growth-mortality studies, and thus results are comparable (Kobe et al. 1995; Kobe 1996; Wyckoff & Clark 2000). To assess whether results change with the duration of growth rate intervals, we also used 1-, 2-, 3- and 10-year averages. This analysis showed that all intervals were strong predictors of mortality.
We did not cross-date annual growth rings as samples were taken in dense second growth forest stands where ring width is most influenced by light competition and other neighbourhood effects. There is therefore little year-to-year variation in tree growth and any climate signal is too weak to allow accurate cross-dating (Phipps 1985). Average ring width for living trees in our data set decreased slightly but steadily from 1977 to 1996 (range: 1.29–1.04 mm), but year to year variations were minimal and did not correlate with the substantial annual fluctuations in temperature and rainfall (http://coweeta.ecology.uga.edu/webdocs/coweeta/html/ronprecip.html). While living trees showed consistent annual growth of just over 1 mm, dead trees grew by an average of only 0.39 mm in the year before death, and this approximately 60% reduction is more than an order of magnitude larger than any yearly climate signal recorded in our data.
Stem size correlates with mortality rate to the extent that small, suppressed trees are more likely to die. We used correlations and regressions to examine relationships among stem diameter and both absolute and relative growth rate, as well as mortality rate. Size can enter our formulation of the growth–mortality relationship, either directly through the size of the trees used to calculate growth rate distributions and the resulting growth mortality functions (see equations below) or indirectly through the size of trees used to calculate the mortality rate for a species. For Acer rubrum, the most abundant species in our data set, we examined both direct and indirect effects of size by subdividing the data before fitting size-specific growth–mortality functions.
We examined the growth histories of living and recently dead individuals for each species using generalized linear least squares regression (SPLUS, Insightful Corp., Seattle, USA). Growth was regressed against time before coring (in years) and status (live vs. dead trees), with a significant interaction term (time × status) indicating differences in slopes among live and recently dead individuals. Regression analyses were modified to account for uneven sample sizes and autocorrelation.
Next, for each of seven species, we applied two methods (A and B described in Wyckoff & Clark 2000) for estimating growth–mortality functions. We start with a data set GN for each species, containing A living trees and D recently dead trees. Method A is based on separately fitting gamma distributions to growth rates, g, of living and recently dead individuals using the likelihood for recently dead trees:
where λd and ρd are fitted parameters, and gi is the growth rate of the ith recently dead tree. The likelihood for growth rates of live trees differs only in having parameter subscripts a rather than d and a sample size of A rather than D. The resulting gamma fits are then combined with estimated annual mortality rate, θ, to yield probability of mortality, p(d), for a given growth rate:
where Q is a ratio of growth rates of living and recently dead trees:
Equation 2 comes from the odds ratio of growth-rate-dependent survival. This approach circumvents the problem of obtaining a sample sufficiently large to estimate the distribution of dead tree growth rates. Bootstrapped confidence intervals were estimated for method A.
Method B involves scaling the numbers of live and dead trees in accordance with expected annual mortality rate prior to estimating the growth–mortality function. Again, scaling is necessary because dead trees are rare. In this paper, method B estimates of mortality probability are based on a Weibull distribution because this best fitted the data, although other functional forms may be used. With this method, we directly fit the growth–mortality relationship p(d|g), using the likelihood
Unlike the growth–mortality function used in method A (equation 2), equation 3 does not explicitly show the mortality rate θ. However, this likelihood depends implicitly on θ, because θ represents the fraction of dead trees in the sample. Unlike method A, method B allows for a probability statement regarding how growth rates influence mortality, using a likelihood ratio test and a null model of growth-independent mortality, but it does not allow for the calculation of confidence intervals. Both methods provide estimates similar to a non-parametric model (method C in Wyckoff & Clark 2000).
trade-offs and community composition
To identify possible trade-offs between growth in high light and low growth tolerance, we compared survival at low growth rates with mean growth rates for codominant and suppressed trees growing in five 80 × 80 m permanent plots. Individuals 20–40 cm in diameter were used to represent those with canopy exposure (i.e. not completely overtopped by the canopy of a neighbouring tree): 64 of 67 trees in this size class had substantial canopy exposure (and thus exposure to light) when observed via low-elevation aerial photography. Understorey individuals 5–15 cm d.b.h. were considered to be predominantly suppressed: 195 of 198 observed individuals had no measurable canopy exposure to light (Wyckoff and Clark, unpublished data).
To examine the implications of growth–mortality functions for population dynamics of our seven species, we used our growth–mortality functions to predict the mortality risk of trees growing in permanent plots. For each of the seven species, we fit a gamma function to the distribution of growth rates, g,
(λ and ρ are fitted parameters) and the Weibull relationship between growth and mortality (with fitted parameters b and c),
and we used a variable change to determine the density of mortality risk, δ, across each population
This density describes how mortality risk is spread across the population. The integral of this density, s(δ), is the fraction of the population at a mortality risk less than a given value of δ,
To determine the implications of our fitted relationships for the predictions of an individual-based computer simulation model, we modified the LINKAGES model (Pastor & Post 1985) to include our growth–mortality functions. The assumption of uniform tolerance of low growth was replaced with fitted functions relating growth and mortality for each of our seven species. Simulations including only our seven species were run for climate and soil conditions typical of our study site. Growing season length and monthly temperatures and precipitation were based on Swift et al. (1988), and variable soil characteristics on Velbel (1988) and Helvey & Hewlett (1962). Model runs simulated 300 years of growth in 20 1/12-ha plots, starting with an unforested environment.
We determined growth rate and diameter for over 500 cored trees of the seven species (Table 2). Mortality rates were estimated by combining stem counts of 542 trees with observed mortality for 835 individuals located in permanent plots, tracked over 7 years.
Table 2. Summary of tree ring growth rate data for seven co-occurring tree species
5-year average radial growth rate mm yr−1 (SD)
5-year average radial growth rate mm yr−1 (SD)
Slowest growth rate 5-year average in mm
Annual radial growth rates increase linearly with diameter for all species except for Cornus and Robinia (Fig. 1). All dead Acer, Betula, Liriodendron and Quercus prinus were of small diameter, but dead trees of other species spanned the diameter range. Mortality rate declined with increasing diameter for all species (as shown for two species in Fig. 2).
The confounding effects of tree size on growth rates are often minimized by reporting either basal area increment or a relative growth rate, rather than radial increment. Neither approach is helpful with our data: conversion to basal area increments merely compounds the effect of size (as larger trees also grow faster) and relative growth rates (radial increment/tree radius) of trees in our study area decline with tree size (data not shown). Small (< 10 cm d.b.h.), recently dead trees have higher relative growth rates (prior to dying) than do large (> 10 cm d.b.h.) live trees, and the relationship between relative growth rate and mortality is therefore weak.
For all species, radial growth rates decline prior to death (Fig. 3a–g, Table 2). These comparisons were limited to diameter ranges that included sufficient numbers of dead trees, and living individuals larger than the largest dead individual were therefore excluded (i.e. in analysis of Acer, Betula, Liriodendron and Quercus prinus). For Acer and Betula, the period of decline begins approximately 11 years before death (Fig. 3a–b), for the two oaks this period may exceed 12 years (Fig. 3e–f), but in Cornus, Liriodendron and Robinia, the effect is only seen 6–8 years before death. Paradoxically, for these last three species, dying trees appear to have grown faster than the live ones prior to the period of decline. Slopes from regressions expressing growth rate as a function of years before coring are significantly different (P < 0.05) for live and dead trees for all seven species, although, when autoregression is assumed (Fritts 1976) only Acer and Cornus are significant, with Quercus prinus nearly so (P = 0.068).
growth–mortality functions for seven co-occurring species
The seven species exhibit differences in tolerance of low growth, as illustrated by method B growth–mortality functions (Fig. 4). To determine whether estimates might be sensitive to the specific length of the series (5 years), we also fit functions based on 1-, 2-, 3-, 4- and 10-year growth averages. Slow growth was correlated with mortality risk for series of all lengths (1 to 10 years), but more years at a given slow growth rate leads to increased risk. With 5 years of growth history, likelihood ratio tests using a null model of growth-independent mortality were significant for all species except Betula (Table 3). Little Betula mortality occurs even at the lowest growth rates. Overall, however, growth rate is a strong predictor of mortality.
Table 3. Parameter values for method A (equation 1) and method B (equation 3) growth–mortality functions and significance tests for method B
Method A (Gamma)
Method B (Weibull)
Method B Negative log likelihood
Living trees λl (95% CI)
Living trees ρl (95% CI)
Dead trees λd (95% CI)
Dead trees ρd (95% CI)
The extent of interspecific differences in mortality risk depends on growth rate. Propagated error in mortality parameters λl, ρl, λd, ρd, and θ, Table 3) yields bootstrapped 95% confidence intervals for method A growth–mortality functions that show differences across the continuum of seven species (Table 4). The extreme species (i.e. those exhibiting the best and poorest tolerance of low growth) show little overlap and, across much of the range of growth rates, non-overlapping confidence intervals are seen for other species comparisons. For example, method A growth–mortality functions for Betula, Cornus and Quercus rubra show differences at 0.4–0.6 mm annual radial growth (Fig. 5a), the range corresponding to the highest concentration of data. Bootstrapped 95% confidence intervals for all seven species at 0.2 mm average annual radial growth (a low growth rate where all species experience mortality risk) are tight for all except Cornus and Robinia (Fig. 5b).
Table 4. Estimated mortality rates and confidence intervals for seven co-occurring trees species
Annual mortality rate
95% confidence interval
The effect of diameter on growth–mortality functions was examined using Acer. When the size-independent mortality rate, θ, is assumed for data sets consisting of either exclusively small diameter trees (< 10 cm d.b.h.) or exclusively large diameter trees (> 10 cm d.b.h.), small and large tree growth–mortality functions diverge (Fig. 6a). However, when the same data sets are combined with a ‘size appropriate’ mortality rate (θ<10cmd.b.h. or θ>10cmd.b.h.), growth mortality functions for small and large diameter trees converge and are similar to the size independent growth mortality function for Acer (Figs 4 and 6b).
trade-offs between low growth tolerance and growth rate
We found no correlation between low growth survival and growth rate of canopy-sized individuals of the seven species (not shown). Exclusion of Cornus and Robinia, the two species having the highest mortality rates and the broadest confidence intervals around their growth–mortality functions (Fig. 5), resulted in only a weak trade-off between these factors (Fig. 7a; r= 0.58, NS). There is no relationship between understorey growth and low-growth survival for these same five species (Fig. 7b).
growth–mortality functions applied to other growth data
Growth–mortality functions based on tree ring data were applied to trees growing in five 80 × 80 m permanent plots by comparing distributions of growth rates for our seven species with annual probability of mortality for a given 5-year growth rate (Fig. 8). For all species except Quercus rubra, the modal growth rate is sufficiently low to yield some degree of mortality risk.
On average, our growth rates estimated from re-measured trees tend to be lower than those estimated from tree rings, potentially inflating predicted mortality rates. In addition, growth rates for trees in census plots are based on 2–5 years of data, whereas our growth–mortality functions were based on 5 years of growth data. Direct comparison between the two graphs in each panel in Fig. 8 may therefore overstate mortality risk, because a tree growing slowly for 2 years is less likely to die than a tree growing slowly for 5. Because of these complications, we compare mortality risk among species in the plots only to search for general patterns, not to make specific predictions.
For five of the seven species, most individuals are at low risk of mortality (Fig. 9). For example, most individuals of Acer experience a low mortality risk, resulting in a cumulative probability where > 90% of all individuals have mortality risk < 0.2 (Fig. 9a), whereas mortality risk is high for the entire population of Cornus (Fig. 9c). Cornus is not found in the canopy, but for the other six species predicted mortality risk declines markedly as trees move from the understorey (5–15 cm d.b.h.) into the canopy (20–40 cm d.b.h.). Acer, Betula and Liriodendron survive understorey conditions better than the two oak species (not shown).
effects of growth–mortality function on the linkages model
The unmodified LINKAGES model predicts early dominance by Acer, followed by a rise in dominance of the two Quercus species (Fig. 10a). When modified to include our fitted growth–mortality functions, Acer remains the most dominant species for the entire 300-year period (Fig. 10b) because recruitment of Quercus rubra fails. Although Quercus rubra becomes established, individuals die before reaching diameters sufficient to contribute significantly to stand basal area.
Our results suggest a strong relationship between growth and mortality for the seven species studied. The species exhibit a continuum of low-growth tolerance, although we see little evidence of a trade-off between growth and stress tolerance. Our results also suggest that growth–mortality relationships should be interpreted with caution.
Although we find a general relationship between growth and mortality, we cannot yet determine that the relationship is independent of stand structure. Our data set is large and includes growth rates from more than 500 living and recently dead trees. The fact that large trees grew fastest and experienced low mortality is consistent with size-independent growth–mortality relationships but does not preclude size dependence.
An especially large sample size allowed us to explore the effects of diameter on the growth–mortality relationship for Acer. Growth rates increased and mortality decreased with diameter for Acer, as for the other species. When growth–mortality functions were fit to small, slow growing trees with a mortality rate calculated from trees of all diameters (θ), the resulting function predicted a lower probability of mortality for a given growth rate than when we used a higher, size-appropriate mortality rate (θ<10cmd.b.h.) (Fig. 6). Conversely, when we fit fast growing, large diameter trees with θ, rather than the more appropriate lower mortality rate (θ>10cmd.b.h.), predicted mortality rates at a given growth rate were inflated. The growth–mortality function fit for all Acer trees with a size-independent mortality rate (used throughout this paper) is similar to the separate growth–mortality functions calculated for large and small trees when the latter are fit using a size-appropriate mortality rate (Fig. 6). This suggests, at least for Acer, that diameter-independent growth–mortality functions are adequate.
Another concern comes from Cornus, raising questions about how much variance in the growth–mortality relationship exists within a species. The poor tolerance of low growth in Cornus at our study site is caused by dogwood anthracnose disease. A population not suffering from the disease would presumably exhibit a different growth–mortality relationship. Epidemic disease can be avoided when parameterizing growth–mortality functions, but variation in more subtle stresses – due, for instance, to limited availability of light, nutrients or water – are more difficult to measure and/or avoid. Reassuringly, the one published study that includes cross-site comparisons of growth–mortality functions found little geographical variation in the relationship for a given species (Kobe 1996). This suggests that growth–mortality relationships parameterized with field data may be robust.
With the exceptions of Cornus and Robinia, annual mortality rates for our study species were low, averaging 1–3% (Table 4), consistent with reports from similar forests (Parker et al. 1985; Runkle 1990). Most mortality occurs in the small, suppressed size classes (Figs 1 and 2), and death of large trees is rare. Coweeta's forests were affected by logging and the chestnut blight in the early 1900s (Swank & Crossley 1988). A drought from 1985 to 1988 led to elevated mortality for canopy-size trees, with red oaks (Quercus coccinea and, to a lesser extent, Quercus rubra) suffering disproportionately (Clinton et al. 1993). High mortality of Quercus rubra continued into the 1990s: here Quercus rubra exhibits a high annual mortality rate of 2.7% (Table 4) (though its growth–mortality function is nearly identical to Quescus prinus, whose annual mortality rate is less than 1% (Fig. 4)). Few individuals of any species (with the exception of Robinia) have reached senescence (Boring & Swank 1984), and this relative youth explains the pattern in Fig. 1, in which the number of dead trees decreases and growth rates increase with diameter.
The rapid decline of Cornus, with an annual mortality rate (from 1993 to 1998) of almost 15% (Table 4), is striking. Anecdotal evidence suggests that the effects of anthracnose are not as severe for individuals growing in high-light environments, but clearly the disease can devastate populations growing beneath closed canopies.
variation in low growth tolerance between species
We obtained two types of information regarding stress-induced mortality for our seven species. First, individuals of all seven species exhibit an extended period of decline prior to death, and species vary in the duration of this decline (for example, compare Betula with Liriodendron, Fig. 3). Our observations of longer growth chronologies, however, indicate that periods of stress-induced slow growth are not always lethal (data not shown), an observation consistent with other studies (Canham 1985, 1990).
Secondly, our growth–mortality functions indicate differences among species in tolerance of low growth (Figs 4 and 5). These interspecific differences can be detected because the amount of data necessary to identify a growth–mortality relationship as significant for a given species is often small (e.g. a sample of 29 Robinia trees had a significant method B growth–mortality function) (Tables 2 and 3). The amount of data necessary for narrow confidence intervals across a range of growth rates, however, is much larger and depends on a tight estimate of annual mortality rate (e.g. Betula, for which we sampled 71 trees and θ was confidently estimated) (Tables 2 and 3, Fig. 5).
Growth–mortality functions reported here are based on 5 years of growth history (Figs 4 and 5). Our analysis demonstrates that functions can be fitted to more or fewer years of growth and still show a strong relationship between growth and mortality. This allows functions to be adapted to their intended use (e.g. the time step used in a particular model). Interspecific differences in length of pre-mortality decline in growth (Fig. 3), however, suggest that different lengths of growth history should be used to determine the growth–mortality function for different species.
applications of growth–mortality functions
Our data show little evidence for a trade-off between rapid growth and low growth tolerance (Fig. 7). Pacala et al. (1996) argue that long-term coexistence of species in the Connecticut forest they studied may require such a trade-off. At Coweeta, Acer clearly escapes the constraints of a trade-off as it shows the most rapid growth of our seven species while also tolerating low growth and could therefore become increasingly important both here and elsewhere (Abrams 1998).
We used our growth–mortality functions to predict the distribution of mortality risk for our seven species in permanent plots (Figs 8 and 9). Results indicate that most individual Cornus and Robinia trees experience high mortality risk and these species could become locally rare (Fig. 9). Mortality risk is low for most individuals of the other five species, with a median risk of less than 2% for all five species.
implications for forest simulation models
The observed interspecific differences in tolerance of low growth have important implications for JABOWA-FORET-type forest simulation models (Fig. 10) as, when modified with our growth–mortality functions, predicted forest development changes dramatically. The collapse of Quercus rubra in the modified model may suggest that the model's growth functions, which indirectly determine mortality functions in JABOWA-FORET models, need revision (Graumlich 1989; Pacala & Hurtt 1993; Loehle & LeBlanc 1996; Hawkes 2000). Although a recent review supports our findings that mortality functions are in need of revision (Keane et al. 2001) and several authors have called for rethinking and re-parameterizing the entire structure of these models (Clark 1993; Pacala et al. 1993; Loehle 1996), old formulations remain in use (Post & Pastor 1996; He et al. 1999). Efforts are currently underway to utilize field studies in order to bring a new degree of biological realism to this class of models (Graumlich 1989; Leemans 1992; Pacala et al. 1996; Linder et al. 1997), and could benefit from considering the link between growth and mortality parameterized here.
This work was supported by the National Science Foundation (NSF) Grants BSR944146, DEB9453498, DEB9632854 (to J. S. Clark), DEB9701088 (to J. S. Clark and P. H. Wyckoff) and a NSF Predoctoral Fellowship (to P. H. Wyckoff). We thank M. Lavine and J. Anderson for statistical advice and W. Schlesinger, N. Christensen, B. Strain, D. Urban and T. Wyckoff for comments on this manuscript.