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Keywords:

  • base cations;
  • geological gradient;
  • intraspecific competition;
  • neighbourhood models;
  • nitrogen;
  • plant–plant interactions;
  • resource heterogeneity;
  • tree growth

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

1. The relationship between soil resource availability and competitive interactions remains unclear in forest ecosystems. If competition shifts from below-ground to above-ground across soil resource gradients, then competitive interactions should constrain growth across soil fertility levels. Alternatively, competition may be less important under stressful conditions associated with low soil resources.

2. We developed individual-based growth models as functions of local tree neighbourhood and measurements of soil resources for 10 common tree species from sites established across a soil resource gradient in north-west Lower Michigan, USA. We hypothesized that tree growth should increase with soil resource availability (rarely measured at local scales), but decrease with the density, size and proximity of neighbouring trees.

3. Correlations of growth to neighbourhood effects were strongest for species occupying primarily high-resource sites. Correlations of growth to soil resources were positive for species associated with high and intermediate fertility. In contrast, correlations of growth to soil water were negative for species associated with low fertility, suggesting that competitiveness of these species decreased with higher soil resources and concomitant decreases in irradiance.

4. Relationships between mean site-level tree growth and soil resources were much stronger than individual growth–local resource relationships. Weaker species-specific, individual-level trends likely arose from limited species distributions across each soil resource domain.

5.Synthesis. Neighbourhood interactions were more prevalent in species associated with high soil fertility sites, where canopy transmission of irradiance was low. For species dominant at low fertility, where canopy transmission of irradiance was relatively high, neighbourhood interactions were absent or negligible. The growth of intermediate-fertility species was negatively correlated with soil water, but decreasing site-level canopy openness with soil water suggests that these species were out-competed for irradiance as soil resources increased. Thus, irradiance likely mediated the stronger competitive interactions at higher-fertility sites.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Competition for resources between individual plants can structure communities (Davis et al. 1999; MacDougall & Turkington 2004), but how competitive interactions change across soil resource gradients is unresolved (Craine 2005; Brooker & Kikvidze 2008). Resource competition could substantially influence plant growth at all fertility levels (Tilman 1988), with allocation to resource acquisition structures decreasing in proportion to resource availability (Chen & Reynolds 1997; Casper, Cahill & Hyatt 1998; Aikio, Ramo & Manninen 2009). Alternately, resource competition could be most significant when resources are abundant (Grime 1979, 2001; Coomes et al. 2009), while competition could decrease as plants are required to tolerate the stressful conditions associated with low-resource availability (Coomes & Grubb 2000). Mitigation of competitive interactions with decreasing soil resource availability may lead to the dominance of facilitative interactions in low-resource environments (Lortie & Callaway 2006; Maestre et al. 2009).

Neighbourhood models of individual tree growth typically have not explicitly included soil resources and have either used purely phenomenological neighbourhood indices (Wright et al. 1998; He & Duncan 2000; Uriarte et al. 2004) or incorporated only crown-model estimates of light attenuation by neighbours (Canham et al. 1999; Canham, LePage & Coates 2004; Coates, Canham & LePage 2009). The rare studies that did consider soil resources did so indirectly by inferring fertility from vegetation (Canham et al. 2006) or assuming that residual variance of above-ground interactions could be ascribed to soil resources (McPhee & Aarssen 2001; Coates, Canham & LePage 2009). Soil resource availability for individual trees is difficult to characterize because of metre- to tree-scale (and coarser) spatial heterogeneity in resources (Finzi, Canham & Van Breemen 1998; Bigelow & Canham 2002; Reynolds et al. 2007; Townsend, Asner & Cleveland 2008; Lundholm 2009). Measuring effects of soil resource availability on individual tree growth requires local-scale resource measurements and distinguishing soil resource effects from other factors that influence growth, including ontogeny and neighbourhood interactions.

In addition to soil resource effects, individual growth may be influenced by interactions with neighbouring trees (including competition for light) and by ontogenetic effects whereby growth rate is a function of tree size (Stoll et al. 2002; Potvin & Dutilleul 2009). Ontogenetic and neighbourhood effects may be confounded in mature, relatively undisturbed forests. Small trees grow slowly in closed-canopy forests because they are suppressed and shaded by canopy trees (Coomes & Allen 2007; Vanhellemont et al. 2010). When growth is modelled as a function of tree size and neighbourhood effects, the slow growth of suppressed small trees may be attributed to their size rather than to the neighbourhood, especially if neighbourhood indices have low effective variability (Woods 2000; Thorpe et al. 2010). Separating ontogenetic from neighbourhood effects may be achieved by extrapolating a theoretical potential maximum growth for an individual of a given size and introducing neighbour and resource effects to reduce this maximum growth to the observed change in diameter (Canham, LePage & Coates 2004; Uriarte et al. 2004); this method requires broad effective neighbourhood variability (Coates, Canham & LePage 2009).

With increasing soil resource availability, competitive interactions between neighbouring trees could intensify because of the depletion of irradiance (Canham et al. 1999; Kunstler et al. 2011). Higher soil resource availability increases leaf thickness, size (Chen et al. 2010) and leaf area index (Granier, Loustau & Breda 2000), thereby decreasing canopy openness and increasing competition for photosynthetically active radiation (Dolle & Schmidt 2009). Light depletion because of reduced canopy openness may also be a consequence of changing species assemblages (Simioni et al. 2004; Dent & Burslem 2009) or intraspecific, resource-dependent variation in canopy characteristics (Henry & Aarssen 2001; Lefrancois, Beaudet & Messier 2008). In the absence of direct measurements of species-specific irradiance depletion across soil resource gradients, accurately separating light effects from other effects of crowding may be impossible.

From a theoretical perspective, individuals of all tree species could exert similar effects on the growth of neighbours (i.e. ecological neutrality per Hubbell 2001), certain species could compete more effectively (Poorter & Arets 2003; Caplat, Anand & Bauch 2008) and disproportionately suppress neighbour growth, or a combination of neutral and asymmetric interactions could occur (Adams, Purves & Pacala 2007; Vergnon, Dulvy & Freckleton 2009). Neighbourhood interactions have traditionally been assessed as size- and distance-dependent functions (Berger & Hildenbrandt 2000; Stadt et al. 2007), assuming that closer and/or larger trees should influence focal tree growth more substantially than smaller and/or farther-displaced trees. Simple size- and distance-dependent neighbourhood indices overlook the possibility of competitive asymmetry, effectively treating all species as equivalent competitors. Abundant evidence for differences between species pair-wise interactions and competitive capability (Stoll & Newbery 2005; Engel & Weltzin 2008; Coates, Canham & LePage 2009; McCarthy-Neumann & Kobe 2010) suggests that neighbourhood analyses should account for neighbour species identity (Uriarte et al. 2004; Coates, Canham & LePage 2009).

The major purpose of this study was to address how competitive interactions change with soil resource availability by examining individual tree growth in relation to local soil resource availability and interactions with neighbouring trees. Debate persists over the ecological relevance of the importance versus intensity of competition (Brooker & Kikvidze 2008). For this study, importance of competition was assessed relative to the amount of total variance in growth that could be explained by tree diameter or by local soil resource availability; it was not our intention to assess the absolute importance of competition (e.g. Freckleton, Watkinson & Rees 2009). Any soil resource required for plant physiological function could potentially limit individual growth if sufficiently rare, but we focus on Ca, water and N, which have been identified as correlates of stand-level productivity at these (Zak, Host & Pregitzer 1989; Baribault, Kobe & Rothstein 2010) and other sites (Joshi et al. 2003; Hogberg et al. 2006; Finzi 2009) or established as limitations to growth through experimental manipulations (Gradowski & Thomas 2008; Park et al. 2008; Finzi 2009; McDowell, Allen & Marshall 2009).

We build upon established methods for characterizing neighbourhood interactions (Wimberly & Bare 1996; Vettenranta 1999; Berger & Hildenbrandt 2000; Canham & Uriarte 2006; Zhao et al. 2006) and extend these methods by including soil resource availability [calcium (Ca), soil water, sum of nitrate (inline image) and ammonium (inline image) (ΣN), and potential nitrogen (N) mineralization] interpolated for each focal tree. As in similar studies, our phenomenological index of neighbourhood interactions implicitly measures net tree–tree interactions, including competition for light (Canham, LePage & Coates 2004), below-ground competition (Coomes & Grubb 2000), tree species effects on soil resource availability (Fujinuma, Bockheim & Balster 2005), indirect effects of tree species on soil biota and chemistry (McCarthy-Neumann & Kobe 2010), and contributions from unmeasured factors. Joint consideration of neighbourhood interactions, individual-tree soil resource availability and site-level measures of light interceptance could help resolve how competitive interactions change across broad variation in soil resources. We tested four hypotheses using the 10 most common deciduous species from 13 sites across broad soil resource gradients in north-west Lower Michigan:

Hypothesis 1: Individual tree growth is negatively related to interactions with neighbouring trees and positively related to local soil resource availability.

Hypothesis 2: Competitive interactions are more important at sites with higher soil resources.

Hypothesis 3: Intraspecific neighbour interactions are stronger than interspecific interactions.

Hypothesis 4: Site mean growth and individual-level growth are related to the same soil resources.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Study sites

Data for this study were collected in 13 mixed hardwood stands of the Manistee National Forest in the lower peninsula of Michigan, USA (c. 44º12′ N, c. 85º45′ W). In 1998 and 1999, these 13 sites were selected from a broader study of 76 sites; the latter were chosen by random sampling within classified landform strata of sites that ranged in age from what presently would be 80–100 years old (Host et al. 1988). The 13 sites used here were randomly selected within landform strata among sites that had no tree-cutting or other disturbance (e.g. adjacency to campgrounds) since establishment of the original study and that were large enough to accommodate a 240 × 41 m stand. All 13 sites were within an area of 960 km2 (maximum distance between sites of 38.1 km, average distance 15.76 km, maximum elevation difference 236 m) and are expected to have very similar climate. Mapped stands were established, wherever possible, in plots of 240 × 41 m, with all stems >10 cm d.b.h. included in the original census. Most plots conformed to these dimensions, but a sharp change in topography near site 4 necessitated a different plot shape (two 120 × 41 m rectangles connected by their ends at a 63° angle), while a road at site 6 required the longer dimension to be extended to 260 m. Sites 12 and 13 were adjacent halves of the one full-size plot that differed in species composition [e.g. absence of Populus grandidentata at site 13vs. 23% total Pgrandidentata stems at site 12 (see Table S2 in Supporting Information)] and soil resources.

Forest community composition in this region has been associated with particular glacial landforms and soil fertility levels (Zak, Host & Pregitzer 1989; Host & Pregitzer 1992; Baribault, Kobe & Rothstein 2010), with lowest resource conditions at outwash sites and maximum resource availability on moraines (Table S3). Nitrate and ammonium pools, along with potential N mineralization rate, increased from outwash through ice-contact and moraine landforms (Table S3). Extractable Ca concentration and soil volumetric water content also increased across the landforms (Table S3). Species composition shifts from dominance of Quercus alba and Quercus velutina on outwash plains through Quercus rubra on intermediate sites to Acer saccharum on moraines (Table 1, Table S2). Species distributions ranged from three (Fagus grandifolia) or four (Tilia americana) to 11 sites (Acer rubrum, Qrubra) (Table S2).

Table 1.   Basic diameter statistics, spatial distribution and relative basal area for the ten most common species across our sites. At least 90% of stems for each species occurred across five or fewer sites. All species had similar minimum diameter because our census intentionally excluded trees smaller than c. 10 cm d.b.h. Sample size (n) refers to the number of focal trees for each species
SpeciesCodenSites > 10% total B.A.d.b.h.Rel. B.A.
MeanMinMax
Acer rubrumacru5543, 4, 9, 1317.59.549.70.099
Acer saccharumacsa6761, 2, 5, 8, 1018.29.258.50.135
Fagus grandifoliafagr1101, 5, 818.69.145.90.023
Fraxinus americanafram301, 7, 830.01055.70.015
Populus grandidentatapogr841, 4, 7, 9, 1331.91057.60.047
Prunus serotinaprse272, 5, 6, 829.31653.30.013
Quercus albaqual4863, 9, 11, 1219.99.355.60.114
Quercus rubraquru5892, 3, 4, 5, 1334.313.387.40.389
Quercus velutinaquve1843, 11, 1228.211.661.10.084
Tilia americanatiam1831, 6, 728.814510.081

Individual growth measurements

Stems of all mapped trees were measured at 1.37 m height using diameter tapes in 1999, 2005, 2007 and 2009. Growth increment was calculated as the change in diameter over the decade-long measurement interval for trees ≥10 cm diameter. Multi-stemmed individuals of T. americana (12% of stems) were treated as a single tree for assessing growth responses and as neighbours. For other species, similar results were obtained when treating multi-stemmed individuals as one or multiple trees and we report results based on the latter. For trees that grew into the ≥10-cm class during the census interval, growth was calculated as the difference between measured diameter and the 10-cm threshold; these in-growth trees also were included as neighbours. Intermediate census dates in 2005 and 2007 enabled calculation of growth increment over the 1999–2005 or 1999–2007 intervals for trees that died during 2005–2007 or 2007–2009; interval length was adjusted as appropriate. Individuals that grew after 1999 but died before 2005, 2007 or 2009 were included. We excluded from the growth analysis any trees that died during the interval but had not grown. Such trees could have contributed to local interactions via shading and resource uptake, so they were included as neighbours. Trees with final diameter <10 cm were not measured and thus are not included in the analysis. In our data, the 10- to 20-cm class showed near-zero growth, suggesting that strong competitive effects were experienced by most stems <20 cm diameter.

Resource measurements

Soil volumetric water was measured to 30 cm depth by time domain reflectometry (Environmental Sensors Inc., Sidney, BC, Canada). Measurements were made in August 2009 over a rainless period of 2 days at 5-m intervals along a central 200-m transect at each site. Soil nutrient analyses were conducted on composite samples each comprising three soil cores (2 cm diameter, 15 cm depth) collected in June 2009. Cores included the A horizon, the AE horizon, if present, and the portion of the organic horizon in which tree roots were observed, but excluded leaf litter. Samples were gathered at 10-m intervals along a central transect at each site and at 20-m intervals along longitudinal transects displaced 5 and 10 m from the central transect. Samples were air-dried prior to analysis.

Potential net N mineralization was determined by aerobic incubation. Initial concentrations of inline image and inline image were measured in a 6-g subsample of each composite. Soils were shaken for 2 h in 2 M KCl to extract inorganic N, and then, [inline image] and [inline image] were measured with a colorimetric assay using a fluorescent plate reader (ELx808 Absorbance Microplate Reader; BioTek Instruments, Inc, Winooski, VT, USA). A second set of 6-g subsamples was incubated aerobically in darkness at 25 °C for 28 days. Constant moisture content was maintained by periodic addition of deionised water, and post-incubation concentrations of inline image and inline image were measured by the same method. Potential net N mineralization was calculated as the difference between final and initial inorganic inline image

Base cations were extracted from 4-g subsamples shaken for 15 min in a Mehlich III solution (Carter 1993). Concentration of Ca2+ in extracts was measured with inductively coupled plasma atomic emission spectrometry (Optima 2100DV ICP Optical Emission Spectrometer; Perkin-Elmer, Shelton, CT, USA).

We imputed the values of Ca, soil water, ΣN and N mineralization at the coordinates of each tree using a distance-weighted average [R package yaImpute (Crookston & Finley 2007)] of the five nearest points. Including additional points did not change imputed values to at least the fifth decimal place. Uncertainty in resource estimates because of the imputation was not ascertained. Irradiance was measured as diffuse non-interceptance using a LAI 2000 (LI-COR Biosciences, Lincoln, NE, USA) at 30 cm above ground level in 2-m intervals along the centre of each site during August 2004. The mean and standard error of diffuse non-interceptance (Table S2) were used in site-level analysis.

Analysis

For each species, we modelled individual diameter growth (Gd) as a function of (i) tree diameter, (ii) interactions with neighbouring trees and (iii) each of the soil resource metrics. The model likelihood was based on a normal probability density for growth, which was confirmed by normally distributed residuals. We predicted mean tree growth for a given soil resource level and neighbourhood using models that were additive,

  • image(eqn 1)

and multiplicative,

  • image(eqn 2)

Most investigators have adopted only multiplicative functions similar to eqn 2 (Canham & Uriarte 2006); we saw no a priori reason to exclude an additive model (eqn 1) from testing. The default was to test the full model (eqns 1 or 2) for each species, but we also tested reduced models for which we provide a biological interpretation in Table S4. For the additive model (eqn 1), diameter effect was linear:

  • image(eqn 3)

where A is the slope of the relationship between growth and diameter. For the multiplicative model (eqn 2), diameter effect was a lognormal function:

  • image(eqn 4)

where δ represents the diameter at which maximum growth rate is expected to occur based on the data, and σ controls the rate the function achieves that maximum value.

All neighbourhood indices were size- and distance-dependent functions of the number of all neighbours within a set or estimated radius. For additive models:

  • image(eqn 5)

where B is a coefficient to control the relative contribution of the neighbourhood overall, α is an estimated exponent controlling the influence of neighbour diameter and β is an estimated exponent controlling the influence of distance to the focal tree. The sum is calculated for i = 1…n neighbours within either a fixed radius of 10 m or within a radius (≤10 m) estimated from the data. For multiplicative models, the neighbourhood effect was an exponential term, with distance in the denominator of the sum:

  • image(eqn 6)

The same definitions for B, α and β apply. To test for effects of neighbour species, we extended eqns 5 and 6:

  • image(eqn 7)

or

  • image(eqn 8)

where the index is calculated for j = 1…n neighbours of species i = 1…s. A species-specific coefficient λi, where 0 < λi < 1, was estimated for each neighbour species. As with eqns 5 and 6, B, α and β were assumed to be equal for all neighbour species in order to minimize the number of estimated parameters.

Soil resource effects were modelled both independently from the neighbourhood index and as an interactive term. For the additive model (eqn 1), an independent soil resource effect was included as another linear term:

  • image(eqn 9)

where C is an estimated scalar coefficient, and the soil resource is expressed in units of p.p.m. For the multiplicative model (eqn 2), an independent soil resource effect was included as a product,

  • image(eqn 10)

where C is an estimated exponent. Soil resources were also modelled as an interactive term with all of the different neighbourhood indices (5–8), where the soil resource value was included as a quotient of the coefficient B on the neighbourhood index. An alternate modelling framework intended to better separate neighbourhood from size effects (following Coates, Canham & LePage 2009) was not supported, so we report further details about this procedure in Appendix S1.To test for possible unmeasured effects of site, residuals from the best model for each species were compared across sites (Fig. S1). Residuals did not diverge by site; thus, growth models did not include a separate term for site effects.

Parameter estimation and model comparison

We estimated growth models for each of the 10 deciduous species in the data set for which we measured more than 20 focal individuals. The simplest models required estimation of two parameters and a variance term, while the most complex models required estimation of eight parameters and variance. Model parameters were estimated with maximum likelihood using a simulated annealing algorithm (Metropolis sampler) implemented in Delphi (Version 3.0; Borland Corporation, Austin, TX, USA), running each model for 50 000 iterations. We calculated the 95% confidence interval for each parameter through likelihood profiling. Whereas parameter estimation was performed in Delphi because of its efficiency, subsequent analysis was performed in R (The R Foundation for Statistical Computing, 2009, http://cran.r-project.org/). From the correlation of model-predicted growth versus observed growth, we calculated the square of the Pearson product–moment correlation coefficient (r2), which we used to determine goodness-of-fit. The slope values of these predicted versus observed relationships were used to check whether the model over- (slope > 1) or under-predicted (slope < 1) individual growth. All models for a given species were compared using Akaike’s Information Criterion corrected for small sample size (AICc) (Burnham & Anderson 2002). Models within two AICc units of the minimum AICc are considered to have equivalent empirical support, whereas models with ΔAICc > 2 are not well-supported by the data. To test our fourth hypothesis – that individual growth–resource patterns scale up to the site level – we used simple linear regression to assess relationships of mean soil resources to site-level properties, including mean tree growth, mean tree size, stand density and mortality rate.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Summary

Neighbourhood interactions were most influential, and soil resources most important, among species dominant at sites with higher-resource availability (Fig. 1, Table 2), supporting both our first and second hypotheses. Among the species at higher-fertility sites, there were positive relationships of growth to soil resources in four species and negative relationships of growth to neighbourhood index in five species (Table 2). Because there are strong repeatable relationships between species occurrence and site fertility as reflected in glacial landform (Host et al. 1988), we cannot definitively ascribe stronger neighbourhood and resource effects to either site resource availability or the characteristics of species that occur at high fertility. Thus, growth responses manifested by high (or low)-fertility species likely reflect both species and soil resource conditions.

image

Figure 1.  Normalized neighbourhood index as a function of neighbour (a) displacement and (b) diameter. For Fraxinus americana (fram), the neighbourhood index was defined only across a radius of 7.86 m and was restricted to zero at larger distances. Other species include Acer rubrum (acru), Acer saccharum (acsa) and Fagus grandifolia (fagr).

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Table 2.   Principal results summarized by species. Species are categorized by the soil fertility of sites at which each species is dominant, ordered (top to bottom) from high-resource moraines to low-resource outwash plains (Table S2), and by shade tolerance. The existence and direction of significant correlations of growth to diameter, neighbourhood and/or soil resource effects are indicated with ‘+’ or ‘−’ symbols; if neighbour species identity was important, this is denoted with ‘×’
Species*Predominant site typeShade toleranceEffect and direction of relationship
DiameterNeighbourhoodNeighbour speciesH2OΣNCa
  1. *Refer to Table 1 for species abbreviations.

  2. †Relationship supported by strongest r2 and a support threshold of ΔAICc < 2.5.

acsaMorainev. tolerant+×+  
tiamMorainetolerant+     
framMoraineintolerant+    
prseInt. morainemoderate+−†   +
fagrPoor morainev. tolerant+×+  
acruIce-contactmoderate+   
pogrIce-contactintolerant+   + 
quruIce-contactintolerant+    
quveOutwashintolerant+     
qualOutwashintolerant+    

Among species common at intermediate to lower-fertility sites, a negative correlation between individual growth and soil water for three species suggests increasing competition (likely for irradiance) with increased soil resources (Table 2). For only one of these species (A. rubrum), growth was weakly related to neighbourhood (Fig. 1, Table 2), supporting our second hypothesis that competitive interactions were weaker at low-resource sites.

We found competitive asymmetry in species-specific neighbour interactions in two of the ten species (Table 2), partially supporting our third hypothesis. Consistent with our expectation, intraspecific interactions were always of greatest magnitude, with extensive variation in the importance of interspecific interactions (Table S8).

Although soil resources are strongly correlated with stand productivity (Zak, Host & Pregitzer 1989; Baribault, Kobe & Rothstein 2010), they were relatively weakly correlated with individual tree growth. Soil resources explained up to 8.6% of variation in growth, whereas neighbourhood explained up to 19% and focal tree size explained 17% to 67%. In contrast, site means of basal area increment and diameter growth were more strongly correlated with soil resources (0.28 ≤ r2 ≤ 0.54). Because species composition changes across the resource gradient, the correlations of mean basal area increment to resources may arise from both direct resource effects on growth as well as indirect resource effects through changes in species composition.

The multiplicative model framework exhibited the best performance for eight species, while the additive framework was best supported for the remaining two species (Table 3). No obvious factor (e.g. species, site type and taxonomy) distinguishes these species groups. Prediction bias of the best model for each species was typically low; slopes of 0-intercept regressions between predicted versus observed growth were always >0.9. Growth in all species was positively related to focal tree diameter (Fig. 2).

Table 3.   Supported models for realized growth framework. The amount of growth variance predicted by complex models (those that included at least one term in addition to diameter) was typically higher than the variance explained by diameter alone. This improvement (Add. var. expl.) represents the difference between diameter-only r2 and the r2 of the top supported model. If the diameter-only model was supported, then it is not presented separately. Modifications (Table S4) to full models, which are denoted by the same equation numbering scheme found in the Materials and methods section, are identified in superscript. General model type (additive or multiplicative) is indicated in Model column with numbers corresponding to equation numbers in the Materials and methods section. Similarly, neighbourhood type in the Ngb column corresponds to equation numbers
Species*Best and supported modelsr2Diameter-only models
ModelNgb.Res.knΔAICcModelAdd. var. expl.ΔAICcr2
  1. *Refer to Table 1 for species abbreviations.

  2. †Log-normal diameter effect.

  3. ‡β = 0.

  4. ¶Estimated radius.

  5. §Equivalent to potential growth.

acru15H2O65570.0000.3480.02213.030.326
acsa28H2O66820.0000.6350.03670.960.599
fagr17H2O61130.0000.4220.16316.680.259
fram1†5‡¶6300.0000.5730.190  
fram23301.0310.383   
fram15‡4301.4360.3930.010  
fram26‡5301.9030.3910.008  
pogr2ΣN4840.0000.2390.0674.570.172
prse2Ca4270.0000.7580.0865.360.672
prse2H2O4280.1060.7200.048  
prse26Ca6272.4280.7990.127  
qual2H2O44890.0000.2610.02022.950.241
quru2H2O45910.0000.6230.03455.540.589
quve41840.0000.273   
tiam231800.0000.388   
tiam2Ca41800.7060.3920.004  
image

Figure 2.  Individual growth as linear (eqn 3) or log-normal (eqn 4) functions of diameter for Acer rubrum (acru), Acer saccharum (acsa), Fagus grandifolia (fagr), Fraxinus americana (fram), Populus grandidentata (pogr), Prunus serotina (prse), Quercus alba (qual), Quercus rubra (quru), Quercus velutina (quve) and Tilia americana (tiam).

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Low- to moderate-fertility species: minimal neighbourhood and resource effects

Growth of the two species associated with the lowest fertility sites, Qalba and Qvelutina, was unrelated to neighbourhood (Fig. 3, Table 3, Table S7). Among species occurring at intermediate soil fertility, A. rubrum, Qrubra and Pgrandidentata, only growth of Arubrum was negatively, but weakly, related to neighbourhood (r2 increase of 2.2% above diameter effect), with expected growth approximately 1 mm year−1 in the lowest-index neighbourhood, but <0.1 mm year−1 in a high-index neighbourhood (Fig. 4, Table 3 and Table S7).

image

Figure 3.  Predicted diameter growth of Populus grandidentata, Prunus serotina, Quercus alba and Quercus rubra as a function of soil resource, holding diameter constant at the mean value for each species (solid lines with symbols). Diameter held constant at minimum and maximum diameter values is presented as dashed lines.

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image

Figure 4.  Predicted diameter growth for Acer rubrum and Fagus grandifolia plotted as a function of soil water with neighbourhood and diameter held constant (a, b) and as a function of neighbourhood with soil water and diameter held constant (c, d). Mean values for constant terms are represented by solid lines with symbols; maximum and minimum values for constant terms are represented by dashed lines.

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Growth was negatively correlated, however, with soil water for Qalba, Q. rubra and A. rubrum (Figs 3 and 4, Table 3 and Table S7). Water explained 2.0–3.4% growth variance in these species (Table 3); growth from minimum to maximum water decreased from 1.3 to 0.9 mm year−1 for Arubrum, 3.4 to 2.2 mm year−1 for Qrubra, and 1.4 to 0.7 mm year−1 for Qalba (Fig. 3). The highest recorded volumetric water (21%) would not suppress growth in any of these species. Consequently, the apparently negative effect of water likely encapsulates shade-induced decreases in growth: site-level canopy openness was negatively correlated with soil water (r = −0.69 for Arubrum, r = −0.46 for Qalba, r = −0.72 for Qrubra). In contrast, neighbourhood was not correlated (r = −0.058) with soil water for A. rubrum, the sole low- to moderate-fertility species for which neighbourhood was significant, indicating that shading effects across sites were not captured by the neighbourhood index. A tree of a given species could have similar neighbourhood indices (sizes of and distances to neighbours) at two sites, but experience different levels of shading because of inter- and intraspecific variation in light interception by neighbours (Montgomery 2004). Across sites, mean canopy openness decreased from 12% to 1% with increased soil resource availability (Fig. 5). Within sites, there was extremely low variability in canopy openness and much greater variability in soil resource availability (Fig. 5).

image

Figure 5.  Canopy diffuse non-interceptance as a function of each measured soil resources. Uncertainty quantified as standard error bars for both vertical (diffuse non-interceptance) and horizontal (soil resource) axes, with diffuse non-interceptance presented on a log scale. Sampling intensity differed, with 80–100 samples for diffuse non-interceptance, 110 samples for soil water, but less than 80 samples for soil nutrients.

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Among the species at low- to moderate-fertility sites, the only one for which a soil resource was positively correlated with growth was Pgrandidentata. Inclusion of ΣN explained 6.7% more growth variance than diameter alone (Table 3, Table S7); growth was expected to increase from 1.8 to 3.2 mm year−1 across the domain of ΣN (Fig. 3).

Neighbourhood effects in high-fertility species

Among the five species that predominated at sites of higher soil fertility, growth was negatively related to neighbourhood index for four species (F. americana, F. grandifolia, Asaccharum and Prunus serotina). While neighbourhood index formulations varied among species (Table 3), neighbourhood effects explained from c. 3.6% (interacting with soil water) in Asaccharum to 19% total variance in Famericana (Fig. 6, Table 3 and Table S7). Additionally, growth of Fgrandifolia was positively related to soil water (Fig. 4), that of Pserotina with soil water and Ca (Fig. 3) and that of Asaccharum with soil water through an interaction with neighbourhood index (Fig. 6, Table 3).

image

Figure 6.  Predicted diameter growth as a function of neighbourhood. For Acer saccharum (a), predicted growth holding diameter constant at its mean value was calculated using minimum (1%, dotted line), mean (7%, solid line with symbols) and maximum (16% dashed line) measured soil water values. For Fraxinus americana (b), diameter held constant at its minimum and maximum values is presented as dashed lines and the mean value as the solid line with symbols.

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For Famericana, expected growth decreased substantially across the neighbourhood domain, from 5.5 to 2.7 mm year−1 (Fig. 6). For Fgrandifolia, holding neighbourhood constant at its mean value, growth was expected to change across the soil water gradient from 0.5 to 1.2 mm year−1 (Fig. 4). Evaluated at mean water availability, a growth rate of 1.1 mm year−1 could be expected in the least suppressive neighbourhood, compared with nearly zero growth in the most suppressive neighbourhood (Fig. 4). For Pserotina, mean growth increased from 1.4 to 3.4 mm year−1 across the range of Ca; neighbourhood index explained 4.6% variance in addition to Ca (Table 3) and reduced expected growth from 1.5 mm year−1 in neighbourhood configurations corresponding to the lowest neighbourhood index to 0.6 mm year−1 in the highest (figure not shown).

In Asaccharum, the effects of neighbouring trees on growth increased with soil water availability. At minimum soil water, growth was expected to decrease from 0.04 to 0 mm year−1 across the range in neighbourhood index, while at maximum soil water, expected growth decreased from 0.65 to 0.06 mm year−1 with increases in neighbourhood index (Fig. 6). Growth in a minimum neighbourhood configuration was expected to increase from 0.04 to 0.65 mm year−1 across the range in soil water, but only from 0 to 0.06 mm year−1 in a maximum neighbourhood configuration (Fig. 6). Thus, competition for water or light may increase with soil water availability as trees can support denser canopies.

Conspecific neighbour effects

For Asaccharum and Fgrandifolia, accounting for species of neighbouring individuals explained more growth variance than a species-neutral neighbourhood model (Table 3 and Table S7); for both species, conspecific neighbours had the strongest magnitude of effect. For Asaccharum, interactions with Tamericana suppressed growth most strongly after intraspecific interactions (Fig. 6, Table S8). For Fgrandifolia, interactions with Asaccharum suppressed growth most strongly after conspecific interactions; influence of other species was negligible (Fig. 4, Table S8).

Growth–resource relationships at the site level

Site-level growth–resource relationships were stronger than individual growth–resource relationships (Table 4). The strongest correlation of individual growth with any single soil resource was for Pserotina and Ca (partial r2 = 0.086), but all relationships of site mean basal area to site mean soil resources were stronger. By simple linear regression, mean BAI was significantly (P < 0.05) related to ΣN (R2 = 0.539), volumetric soil water (R2 = 0.500), Ca (R2 = 0.378) and potential N mineralization rate (R2 = 0.278). Mean basal area increment was significantly related to all four soil resources, but mean diameter growth was related only to ΣN. Neither stem density nor mortality rate was related to any resource (Table 4). The influence of soil resources on site-level mean growth may in part be mediated by changes in species composition associated with landform/site fertility. Outwash sites (11 and 12), characterized by lower-resource availability (Table S3), were dominated by Qalba and Qvelutina (Table S2), both species with relatively low mean growth rates (Table S10) and diameters (Table S9). In contrast, at poor and intermediate moraines with higher resources (Table S3) where Qrubra dominates (Table S2), mean growth rates (Table S10) and mean diameters (Table S9) were greater than for the outwash sites.

Table 4.   Site-level correlations of mean individual basal area index (BAI) growth, mean diameter, stem density and mortality rate with the soil resource metrics. Sample size was 13 for all relationships. Correlation strength presented as R2, with parameter estimates for slope and intercept, both with 95% confidence intervals
Res.Mean BAIMean sizeDensityMortality
 R2
Ca0.4350.3220.0140.001
H2O0.5460.2970.0260.047
ΣN0.5810.4410.0030.008
N min.0.3440.2680.0390.005
 Slope
Ca2.18 (0.43, 3.93)3.10 (−0.072, 6.28)−24.3 (−166, 117.1)−0.06 (−1.52, 1.40)
H2O0.37 (0.13, 0.61)0.46 (−0.038, 0.95)−4.97 (−26.6, 16.6)−0.07 (−0.29, 0.15)
ΣN0.10 (0.04, 0.16)0.15 (0.03, 0.26)0.46 (−5.29, 6.20)0.01 (−0.05, 0.07)
N min.0.31 (0.01, 0.6)0.46 (−0.08, 1.00)−6.46 (−29.1, 16.2)−0.02 (−0.26, 0.21)
 Intercept
Ca7.00 (6.10, 7.90)22.51 (20.88, 24.15)598 (525, 670)2.41 (1.66, 3.17)
H2O5.68 (4.20, 7.15)21.06 (18.02, 24.09)617 (485, 749)2.78 (1.44, 4.13)
ΣN6.28 (5.23, 7.34)21.46 (19.44, 23.48)582 (482, 682)2.28 (1.26, 3.30)
N min.7.08 (6.10, 8.05)22.60 (20.89, 24.31)603 (531, 676)2.44 (1.69, 3.20)

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Competition and soil resource effects

Competitive interactions generally strengthened as soil resource availability increased (our second hypothesis, and consistent with Grime 1979, 2001), as supported by two lines of evidence. First, neighbourhood interactions were important for four of the five species dominant at sites with high-resource availability but were only weakly correlated with growth for one (Arubrum) of the five species dominant at intermediate/lower-resource sites. For the high-fertility species, diameter growth was positively related to soil resources but negatively related to neighbourhood, supporting our first hypothesis. Evidence for increasing neighbour interactions was derived from growth models for single species, but species composition changes across the sampled soil resource gradient (Baribault, Kobe & Rothstein 2010), so species and resource effects were confounded. We cannot definitively determine whether stronger neighbourhood interactions arose from shifts in traits unique to the species that typically occupy sites of high soil fertility (Kranabetter & Simard 2008) or direct effects of increasing resource availability (Janse-ten Klooster, Thomas & Sterck 2007; Liancourt, Viard-Cretat & Michalet 2009). Nevertheless, correlations between soil resource availability and interceptance of irradiance suggest that stronger competitive interactions at higher soil fertility are mediated through greater shading. Greater shading at high fertility likely arises as a result of changes in species composition (Canham et al. 1994) as well as mineral nutrient effects on leaf production within species (Chen et al. 2010).

Second, the negative correlation of growth to soil water in three species (Qalba, Qrubra and Arubrum) common at lower-fertility sites, and which are relatively shade intolerant (Kobe et al. 1995), was likely due to increased shading as soil water increased. Although not characterized by the neighbourhood indices, this result also supports increasing competition with resources. Suppression of growth by increasing water availability is unlikely across the range of water levels that we measured (McDowell, Allen & Marshall 2009); in fact, higher water availability is associated with increased growth of seedlings and saplings (Schreeg, Kobe & Walters 2005; Kobe 2006). Across all sites at which these species occurred, canopy openness was negatively correlated with soil water (and other soil resources, Fig. 5), but neighbourhood was unrelated to soil water for Arubrum (the only low-fertility species for which neighbourhood was supported). A given neighbourhood index, which is based on the diameter and local density of trees, could be associated with a range of irradiance levels at different sites because of interspecific (Canham et al. 1999) and intraspecific (Dolle & Schmidt 2009) variation in light transmittance through tree crowns. Neighbourhood indices with explicit light attenuation functions have not accounted for the potential influence of soil resources on species-specific light transmittance (Lefrancois, Beaudet & Messier 2008; Chen et al. 2010).

Species dominant at low soil fertility may have escaped light limitation because canopies transmitted higher irradiance (Fig. 5) and stem densities were substantially lower (Table 1). Slower growth of low-fertility species at sites with higher water and soil nutrient availability (Schreeg, Kobe & Walters 2005) could have resulted because such sites were dominated by species with denser canopies (Canham et al. 1994; Burton et al. 2009) that reduced light transmittance. Weak or absent neighbourhood effects in species dominant at low soil fertility may have been principally a consequence of species distributions (Coates, Canham & LePage 2009) – there were too few individuals of low-fertility species growing at high-fertility sites to detect a correlation between growth and neighbourhood effects because of shading. When shade-intolerant Arubrum and Qalba did occur under higher-fertility conditions, they likely established when irradiance levels were higher (Wang, Larsen & Kronenfeld 2010), as indicated by the larger diameters of individuals of these species. These results are consistent with the interpretation that these species fail to effectively compete at sites with more plentiful soil resources (Craine 2005; Brooker & Callaway 2009) and support that low-fertility species are eliminated from high-fertility sites because of growth sensitivity to shading. Overall, our results support that the distribution of these species across soil resource gradients arises from a species trade-off between survival in low soil resource conditions and growth in high-resource environments (Schreeg, Kobe & Walters 2005; Gaucherand, Liancourt & Lavorel 2006; Gravel et al. 2010), where low-fertility species are eliminated by shading.

The neighbourhood effects that we detected for species associated with high soil fertility also may have been mediated through light competition. Transmission of irradiance was uniformly lower at sites with higher soil availability of water, Ca and N (Fig. 5), suggesting increased competition for light (Lintunen & Kaitaniemi 2010). Two of the most shade-intolerant species associated with high soil fertility, Famericana and P. serotina (Kobe et al. 1995), exhibited some of the highest neighbourhood effects (Table 3). Although our analysis likely underestimates neighbourhood effects for all species (see below), the stronger importance of local-scale soil resource availability for species common at high soil fertility is consistent with increasing competitiveness in the presence of abundant resources (Reiter et al. 2005).

Intraspecific neighbour interactions were more influential than interspecific interactions in two of the five species for which growth was related to neighbourhood index, consistent with our third hypothesis. More closely related individuals should theoretically be in more intensive competition for the same resources (Uriarte, Canham & Root 2002; Canham et al. 2006; Zhao et al. 2006) and thus unable to partition available resources with highest efficiency (Boyden, Binkley & Stape 2008). In addition, high local conspecific density in intraspecific pairs could increase effects of natural enemies or differential species-based chemical feedbacks (McCarthy-Neumann & Kobe 2010). For Asaccharum, negative intraspecific interactions were nearly 30% more important than interspecific interactions and for Fgrandifolia, 14%. Even with evidence of suppressive intraspecific interactions for only two species, competitive asymmetry has important implications for silviculture. Both in multi-species plantations (Boyden, Binkley & Senock 2005; Forrester, BauhuS & Cowie 2006) and in selection management of natural systems (Schwartz, Nagel & Webster 2005; Gronewold, D’Amato & Palik 2010), it would be useful to promote residual stand structures (Bauhus, Puettmann & Messier 2009) consisting of the least antagonistic neighbour interactions.

Detecting neighbourhood effects

We suspect that neighbourhood effects were partially masked in our sites because of the limited range of variation in neighbourhood conditions; the growth of most trees, particularly of small diameter, was probably suppressed by interactions with neighbours (Uriarte et al. 2004). Despite limited variation in neighbourhood densities, neighbourhood still explained substantial growth variation for some species. For Famericana, neighbourhood explained 19% growth variance, likely because this shade-intolerant species responded more strongly to neighbourhood variability than the shade-tolerant species with which it co-occurs. Our sites were relatively static with low mortality (c. 2 stems ha−1 year−1), limited gap formation and restricted opportunity for trees to be released from competition. Release from competition dramatically increases growth (Noguchi & Yoshida 2009; Stan & Daniels 2010), and greater variation in neighbourhood conditions generally results in greater measured effects of neighbourhood on growth (Uriarte et al. 2004; Zhao et al. 2006; Olano et al. 2009; Simard 2009; Thorpe et al. 2010; Vanhellemont et al. 2010). For example, in forests of mixed northern temperate species encompassing unmanaged stands and 30–60% basal area removal, neighbourhood explains 25.8–77.3% total growth variance (Coates, Canham & LePage 2009).

However, some of the difference in growth variation associated with neighbourhood can be attributable to the statistics used to measure goodness-of-fit. We used the square of the Pearson correlation coefficient (r2) to measure goodness-of-fit, but many other studies (e.g. Uriarte et al. 2004; Coates, Canham & LePage 2009) use the coefficient of determination (R2) based on a simple linear regression through the origin of predicted versus observed values. The interpretation of R2 for models with the origin as the intercept is problematic (Myers 1986), however, and leads to unrealistically high estimates of amount of total variance explained. For example, predicted versus observed values for the supported model of Qvelutina generated r2 = 0.273 (Table 2), but the origin–intercept regression of those same values produced R2 = 0.920. Thus, it is difficult to directly compare our results with previous studies.

Because trees generally grew faster on higher-fertility sites, soil resource effects could have been subsumed by diameter effects (i.e. accumulation of past growth). Thus, we tested models that excluded diameter, but the amount of growth variation explained by resources did not increase.

Individual- and site-level effects

Past research at our sites identified N (Zak, Host & Pregitzer 1989), Ca and soil water (Baribault, Kobe & Rothstein 2010) as strong correlates of site-level productivity, but our current results do not support similarly high correlations of individual growth with any of these resources for any species, contrary to our fourth hypothesis. At the individual level, growth is determined by resource availability and acquisition, which is related both to tree size and to local neighbourhood (Canham et al. 1999). At the site level, productivity is the aggregate growth of all surviving trees.

Significant relationships of growth to resource availability likely were more difficult to detect for single species than for all species because most species had restricted distributions (Table S2). For example, 65% of all Qalba individuals occurred only at sites 11 and 12 (Table S2), where the range in Ca availability was <3% of the total range, soil water 56% of its range and ΣN 8% of its range (Table S3). Such a sharply restricted domain of resource availability may have precluded detecting stronger growth–resource correlations. Our results are consistent with other studies that have found that individual growth is most strongly correlated with tree size (Monserud & Sterba 1996; Andreassen & Tomter 2003; Laubhann et al. 2009), and that site mean growth is often substantially correlated with soil resources (Pastor et al. 1984; Zak, Host & Pregitzer 1989; Reich et al. 1997; Wallace et al. 2007; Bedison & McNeil 2009; Devine & Harrington 2009; McDowell, Allen & Marshall 2009).

Both stochastic variability in growth and measurement error introduced by diameter tapes could contribute to variance in individual growth (Wyckoff & Clark 2005; Clark et al. 2007), but this individual-scale noise exerts less influence at the site level, allowing a stronger correlation of mean site growth to soil resources. In addition, the discrepancy between the individual and stand also may be due to difference in spatial scales between measured soil resources and the area over which a tree acquires resources (Das & Chaturvedi 2008; Kalliokoski, Nygren & Sievanen 2008; Yanai et al. 2008). Mycorrhizal networks also could connect trees across a broad area (Simard 2009), decoupling local soil resources from plant available resources.

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Two lines of evidence from this study support that the importance of competition increased across resource gradients. First, competitive neighbourhood interactions (H1) were important primarily for species dominant at sites of high-resource availability (H2). Second, increasing soil water was associated with slower growth in three species dominant at low-resource sites, signifying decreased competitiveness (H2) for light at higher-resource sites. The magnitude of predicted neighbourhood effects varied widely, but included complete suppression of growth at some of the highest neighbourhood indices. Intraspecific neighbour interactions were strongest in two species (H3), though divergent species distributions likely precluded identifying other species effects. Overall, our results support that competitive interactions strengthened with site fertility and that these interactions likely were mediated through increased competition for irradiance.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

We thank S. Grandy, D. Rothstein and M. Walters for insight about sampling, resource analysis and model design. D. Coomes, E. Holste, D. Minor, B. Bachelot, A. Maguire, D. Rozendaal and two anonymous referees provided helpful feedback in preparing the manuscript. Indispensable field and laboratory assistance was provided by M. Erickson, D. Minor, J. Bramer, A. Maguire, A. Pierce and A. Stinson. In addition, we thank A. Finley and B. Walters for access to USFS FIA data. The research was supported by the Michigan Agriculture Experiment Station (NRSP-3, National Atmospheric Deposition Program) and NSF (DEB 0958943).

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  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Appendix S1. Theoretical potential growth modelled using a composite of collected and USFS FIA data.

Figure S1. Assessment of potential plot effects by model residual comparison.

Table S1. Site occupancy by species.

Table S2. Soil resource availability by site.

Table S3. Biological interpretation of neighbourhood model parameters and model variations.

Table S4. Theoretical potential growth model selection and parameters.

Table S5. Summary statistics for USFS FIA plot data from northern Lower Michigan.

Table S6. Model framework comparison: realised growth versus theoretical potential growth.

Table S7. Estimated model parameters: species-independent neighbourhood.

Table S8. Estimated model parameters: species-dependent neighbourhood.

Table S9. Mean basal area increment for each species at each site.

Table S10. Mean diameter for each species at each site.

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