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Relationships between stand growth andstructural diversity in spruce-dominated forests inNew Brunswick, Canada Xiangdong Lei, Weifeng Wang, and Changhui Peng Abstract: Relationships between stand growth and structural diversity were examined in spruce-dominated forests in NewBrunswick, Canada. Net growth, survivor growth, mortality, and recruitment represented stand growth, and tree species,size, and height diversity indices were used to describe structural diversity. Mixed-effects second-order polynomial regres-sions were employed for statistical analysis. Results showed stand structural diversity had a significant positive effect onnet growth and survivor growth by volume but not on mortality and recruitment. Among the tested diversity indices, theintegrated diversity of tree species and height contributed most to stand net growth and survivor growth. Structural diver-sity showed increasing trends throughout the developmental stages from young, immature, mature, and overmature foreststands. This relationship between stand growth and structural diversity may be due to stands featuring high structural di-versity that enhances niche complementarities of resource use because trees exist within different horizontal and verticallayers, and strong competition resulted from size differences among trees. It is recommended to include effects of speciesand structural diversity in forest growth modeling initiatives. Moreover, uneven-aged stand management in conjunctionwith selective or partial cutting to maintain high structural diversity is also recommended to maintain biodiversity andrapid growth in spruce-dominated forests. Re´sume´: La relation entre la croissance des peuplements et leur diversite´structurale a e´te´e´tudie´e dans des foreˆts domi-ne´es par l’e´pinette au Nouveau-Brunswick, Canada. La croissance nette, la croissance des survivants, la mortalite´et le re-crutement ont e´te´utilise´s comme variables repre´sentant la croissance des peuplements alors que l’espe`ce, la taille et desindices de diversite´de hauteur des arbres ont e´te´utilise´s pour de´crire la diversite´structurale. Les analyses statistiques onte´te´effectue´es a`l’aide de re´gressions polynomiales du deuxie`me degre´avec des effets mixtes. Les re´sultats montrent quela diversite´structurale des peuplements a un effet positivement significatif sur la croissance nette et la croissance des sur-vivants en volume, mais pas sur la mortalite´ni le recrutement. Parmi les indices de diversite´teste´s, celui qui inte`grel’espe`ce d’arbre et la hauteur contribue le plus a`expliquer la variation de la croissance nette du peuplement et la crois-sance des survivants. La diversite´structurale a tendance a`augmenter en fonction du stade de de´veloppement du peuple-ment, de jeune, immature, mature a`suranne´. Cette relation entre la croissance des peuplements et la diversite´structuralepourrait eˆtre due a`une meilleure comple´mentarite´des niches d’utilisation des ressources dans les peuplements montrantune grande diversite´structurale puisque les arbres sont pre´sents dans diffe´rentes strates horizontales et verticales, ainsiqu’a`la forte compe´tition entre les arbres de diffe´rentes tailles. Il est recommande´d’inclure les effets de la diversite´en es-pe`ces et de la diversite´structurale dans les efforts de mode´lisation de la croissance forestie`re. De plus, l’ame´nagement despeuplements ine´quiennes conjointement avec des coupes partielles ou de jardinage dans le but de maintenir une forte di-versite´structurale est aussi recommande´pour maintenir la biodiversite´et la croissance rapide des foreˆts domine´es parl’e´pinette.[Traduit par la Re´daction] Introduction Relationships between species diversity and ecosystemproductivity have a long-standing relevance in ecology(Waide et al. 1999; Mittelbach et al. 2001). However, con-siderable controversy still exists concerning the generalforms of these relationships (Rosenzweig and Abramsky1993; Waide et al. 1999; Fridley 2002). The general conclu-sion among ecologists is that there is no single universalpattern and that patterns themselves are scale and taxon de-pendent (Mittelbach et al. 2001; Chase and Leibold 2002;Whittaker and Heegaard 2003). Mittelbach et al. (2001)classified these relationships into one of five patterns in ametaanalysis: positive, negative, hump-shaped, U-shaped,and no significant relationship. Recently, Laanisto et al. Received 3 December 2008. Accepted 2 June 2009. Published on the NRC Research Press Web site at cjfr.nrc.ca on 30 September 2009. X. Lei. Institut des sciences de l’environnement, De´partment des sciences biologiques, Universite´du Que´bec a`Montre´al (UQAM),Montre´al, QC H3C 3P8, Canada; Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing, 100091,P.R.China. W. Wang and C. Peng. 1 Institut des sciences de l’environnement, De´partment des sciences biologiques, Universite´du Que´bec a`Montre´al (UQAM), Montre´al, QC H3C 3P8, Canada. 1 Corresponding author (e-mail:
[email protected]). 1835 Can. J. For. Res. 39 : 1835–1847 (2009) doi:10.1139/X09-089 Published by NRC Research Press (2008) found that a unimodal species richness–productivityrelationship was significantly more common for herbaceousspecies than for woody species. This relationship appearedin grasslands more often than in forests. On the other hand,the influence of species diversity on productivity is also de-bated especially in forest communities where complex spa-tial structures and high longevity of dominant organismsexist (Huston et al. 2000; Vila`et al. 2003; Firn et al. 2007).Relationships are either negative (Huston 1980; Wardle etal. 1997; Firn et al. 2007), positive (Troumbis and Memtsas2000; Erskine et al. 2006; Vila`et al. 2007), or insignificant(Vila`et al. 2003). Two hypotheses explaining positive rela-tionships have been proposed: niche complementarity andsampling effects (Tilman et al. 1997; Tilman 1999; Hustonet al. 2000). The niche complementarity hypothesis proposesthat species-rich communities are able to more efficientlyaccess and utilize limiting resources because they containspecies with a diverse array of ecological attributes. Com-plementarity effects occur when interspecific niche differen-ces lead to more efficient acquisition of limiting resourcesand, therefore, higher productivity. The sampling effect hy-pothesis suggests that more biologically diverse commun-ities have increased productivity. Sampling effects arebelieved to occur when the most productive species aremore likely to be included in and come to dominate the bio-mass of species-rich polycultures. However, the transitionfrom sampling effect to complementarity effect throughtime was also identified (Pacala and Tilman 2002; Cardinaleet al. 2007). Thus, each hypothesis proposes an ecologicallydistinct mechanism.Maintaining both biodiversity and productivity is neces-sary for sustainable forest management. Stand structural di-versity, especially variations in tree height and diameter, isan important consideration in forest biodiversity conserva-tion. Noss (1990) discussed composition, structure, andfunction as components of biodiversity. Stand structural di-versity is an important part of biological diversity and af-fects other components of biodiversity, i.e., compositionaland functional diversity, and, consequently, economical,ecological, and social values of forest management practices(Noss 1990; Lexerød and Eid 2006). Structural diversity isoften defined as one or a combination of spatial distribution,species diversity, and variation in tree dimensions, such asthe size and height (Staudhammer and LeMay 2001;Pommerening 2002; McElhinny et al. 2005). Standing treesof different sizes provide a variety of habitats for differentflora and fauna. However, differences in structural diversitymay also be due to a variety of factors including environ-ment conditions, species composition, development stages,disturbance history, and management activities. A commonargument is that biodiversity can be maintained by way of managing the structural diversity of stands (MacArthur andMacArthur 1961; Buongiorno et al. 1994; Franklin et al.2002). Therefore, stand structural diversity has been set as aconstraint or objective in forest harvesting decision makingpractices for multiobjective forest planning (Buongiorno etal. 1994; Gove et al. 1995; Kant 2002). In addition to beingindicative of overall biodiversity, measures of stand struc-tural diversity are also important for predicting future standgrowth and development (Pretzsch 1997; Liang et al. 2005).Understanding and quantifying these effects can aid ingrowth and yield modeling.Unfortunately, for the most part, previous studies have fo-cused on relationships between species diversity and produc-tivity. Only a few studies have taken into consideration theeffects of stand structural diversity on growth (Edgar andBurk 2001; Liang et al. 2005, 2007). It is understood thatsome uncertainties still exist in quantifying these relation-ships. For example, Liang et al. (2005) concluded that therelationship between growth and tree size diversity remainsunclear. The effects of structural diversity on growth are stilllargely unexplored, especially in the Canadian boreal forestregion. Owing to this, much remains to be done in under-standing how stand structural diversity affects growth withrespect to forest management goals of higher productivityand biodiversity.Therefore, the objective of this study is to examine rela-tionships between stand growth and structural diversity inspruce–balsam fir ( Abies balsamea (L.) Mill) (SPBF) for-ests in New Brunswick, Canada, to test the complementarityeffects hypothesis that states that stand structural diversityhas a positive effect on growth. Data and methods Sample plot data All data comes from the New Brunswick Permanent Sam-ple Plot Database (Porter et al. 2001). The SPBF plots wereselected where the proportion in volume of spruce trees was ‡ 0.6, which designated them as spruce-dominated foreststands. Sampling was carried out on 400 m 2 circular plots.All living trees >5.1 cm in diameter at breast height (DBH)were included in the study. Trees were measured two to fourtimes throughout a 2–6 year period. Tree age was attainedby using increment core samples taken from a minimum of two trees for each species class outside the plot area. Be-cause height and volume data were only available for treeswith a DBH >9.0 cm within the plots (Porter et al. 2001),trees whose DBHs were <9.0 cm were ignored. In total, 908measurements were collected, of which 142 plots weremeasured two times, 182 plots were measured three times,and 134 plots were measured four times. Between one andseven tree species inhabit each plot. The most frequent treespecies observed were black spruce ( Picea mariana (Mill.)BSP), white spruce ( Picea glauca (Moench) Voss), redspruce ( Picea rubens Sarg.), and balsam fir (Table 1). A to-tal of 21 tree species were identified throughout all theplots. Stand age varied from 32 to 203 years. The develop-ment stage of black spruce is defined as young ( £ 45 years),immature (46–70 years), mature (71–110 years), and over-mature ( ‡ 111 years) (Porter et al. 2001).For each measurement, the following stand variables werecalculated: periodic annual increment (PAI), periodic annualsurvivor growth (Ps), periodic annual mortality (Pm), peri-odic annual recruitment (Pr), number of trees per hectare( N , stems Á ha –1 ), the quadratic mean DBH (Dq, cm), and siteproductivity (Sp, m 3 Á ha –1 Á year –1 ), which was measured as themean annual increment by stand volume where a relation-ship PAI = Ps – Pm + Pr was determined. All incrementsand productivity components (PAI, Ps, Pm, and Pr) are ex-pressed in cubic metres per hectare per year and are calcu-lated as follows: 1836 Can. J. For. Res. Vol. 39, 2009 Published by NRC Research Press ½ 1 PAI ¼ð V s À V m þ V r Þ T  A ½ 2 Ps ¼ V s T  A ½ 3 Pm ¼ V m T  A ½ 4 Pr ¼ V r T  A where A is plot area, V s is the change in volume of livingtrees within a plot during the inventory period T , V m is themortality with respect to volume of a plot during the inven-tory period T , and V r is the recruitment with respect to vo-lume of a plot during the inventory period T . The standcharacteristics are summarized in Table 2. Stand structural diversity indices Stand structural diversity indices used in the study aresummarized in Table 3. Because species, diameter, andheight are commonly measured to indicate changes in hori-zontal and vertical stand structure (Staudhammer andLeMay 2001), stand structural diversity was measured bytree species, DBH, and height for this study. Structural di-versity indices were used based on the Shannon–Wienerindex (Magurran 2004) because it is widely used in forestresearch (Buongiorno et al. 1994; Kuuluvainen et al. 1996;Staudhammer and LeMay 2001). The Shannon–Wienerindex is based on both species richness and evenness. Withthe Shannon–Wiener index approach, DBH and height hadto be grouped into discrete classes. For DBH, 2, 4, and6 cm classes were tested, and for height, 2, 3, 4, and 5 mclasses were tested to calculate the index. It was discoveredthat a tree size diversity by 4 cm DBH for the width classesand a tree height diversity by 2 m height for the heightclasses showed high correlation coefficients with the sameindex based on the other class widths. Therefore, 4 cm and2 m were used for the DBH and height classes, respectively,for the study. In addition to the diversity index of tree spe-cies (Hs), DBH class (Hd), and height class (Hh), the inte-grated diversity among them was also tested including theintegrated diversity of species and size (Hsd), the integrateddiversity of species and height or the species profile index(Hsp, Pretzsch 1996), and the mean structural diversity in-dex (Hsdh) of the three diversity indices of species, DBHclass, and height class (Hsdh). Hsdh was adopted because itperformed better than the combined methods in rankingstructural diversity according to Staudhammer and LeMay(2001). The Shannon–Wiener index is based on the basalarea of tree species, DBH class, and height class where themaximum value occurs when the basal area is evenly dis-tributed in all species or size classes.Because of the sensitivity of the Shannon–Wiener indexand its uncertainty to changes in class width, the Gini coef-ficient was also applied because it does not require arbitra-rily classified diameter classes, and it performs better thanother stand structural diversity measurements applied to for-est management planning (Lexerød and Eid 2006). The Ginicoefficient is a measurement of heterogeneity and quantifiesthe deviation from perfect equality. It has a minimum valueof zero when all trees are of equal size and a theoreticalmaximum of one when all trees but one have a value of zero. Therefore, higher values indicate greater size diversity.It was calculated for both tree diameter and height. Thesummary statistics derived from all indices used in the studyare given in Table 4. Statistical analysis Correlation analysis was performed to evaluate relation-ships among the diversity index using first measurement of plots. The structural diversity index was also compared dur-ing different forest developmental stages. Most publishedstudies used linear and quadratic terms to test for signifi-cance and curvilinearity when evaluating relationships be-tween species diversity and productivity (Huston et al.2000; Mittelbach et al. 2001) Therefore, second-order poly-nomial regressions were adapted to fit the data and to ex-plore relationships between stand growth and structuraldiversity. Because stand density, age, and site quality areknown to influence stand growth and may affect relation-ships between diversity and productivity (Fridley 2002; Firn Table 1. Summary of species composition(proportion of volume).Tree species Mean ± SD RangeBlack spruce 0.39±0.43 0–1White spruce 0.09±0.22 0–1Red spruce 0.29±0.35 0–1Total spruce 0.85±0.12 0.6–1Balsam fir 0.05±0.08 0–0.38Other* 0.10±0.11 0–0.40 *Tree species were white pine ( Pinus strobus L.), jack pine( Pinus banksiana Lamb.), red pine ( Pinus resinosa Ait.), easternwhite-cedar ( Thuja occidentalis L.), eastern hemlock ( Tsugacanadensis (L.) Carrie`re), tamarack ( Larix laricina (Du Roi) K.Koch), red maple ( Acer rubrum L.), sugar maple ( Acer saccharum Marsh.), yellow birch ( Betula alleghaniensis Britt.),gray birch ( Betula populifolia Marsh.), beech ( Fagus grand-ifolia Ehrh.), white ash ( Fraxinus americana L.), white birch( Betula papyrifera Marsh.), trembling aspen ( Populus tremu-loides Michx.), largetooth aspen ( Populus grandidentata Michx.), black ash ( Fraxinus nigra Marsh.), and balsam poplar( Populus balsamifera L.). Table 2. Stand summary used for modeling.Stand parameter* Mean ± SD RangeAge (years) 90±27 32–203Dq (cm) 18.4±3.7 11.1–32.2 N (stems Á ha –1 ) 1132±457 250–2975Stand BA (m 2 Á ha –1 ) 28.41±9.25 5.92–54.50Standing volume (m 3 Á ha –1 ) 173.20±65.28 26.23–351.50Sp (m 3 Á ha –1 Á year –1 ) 2.068±0.922 0.177–6.107Mean height (m) 13.1±1.5 9.2–17.8PAI (m 3 Á ha –1 Á year –1 ) 3.487±1.721 0.053–12.951Ps (m 3 Á ha –1 Á year –1 ) 3.306±1.663 0.053–10.427Pm (m 3 Á ha –1 Á year –1 ) 2.525±2.934 0.0–15.893Pr (m 3 Á ha –1 Á year –1 ) 2.705±2.897 0.0–15.895 *Dq, quadratic mean diameter; N , the number of stems per hectare;BA, basal area; Sp, site productivity; PAI, periodic annual increment;Ps, periodic annual survivor growth; Pm, periodic annual mortality; Pr,periodic annual recruitment. Lei et al. 1837 Published by NRC Research Press et al. 2007; Liang et al. 2007), stand age, Sp, N , and Dqwere applied as additional independent variables to carryout second-order modeling to test the effects of site factorsand stand initial conditions on relationships. Multicollinear-ity is encountered when a number of correlated explanatoryvariables exist within a regression analysis that may causeinaccurate model parameterization, decreased statisticalpower, and the exclusion of significant predictor variables(Graham 2003). The variance inflation factor (VIF) is acommon way to detect multicollinearity phenomena. VIFsof the predictor variables were tested, and collinearity pat-terns between N and Dq (VIF > 4) were found. Therefore,only Dq was saved in the model. Plots were repeatedlymeasured; as a result, growth measurements from individualplots were expected to be correlated. Mixed-effects modelswere employed for repeated measurements following theSAS MIXED procedure (SAS Institute Inc. 2002). Becausemodels were developed for four response variables (PAI,Ps, Pm, and Pr) and eight explanatory variables (Hs, Hd,Hh, Hsd, Hsp, Hsdh, GCd, and GCh) separately, 32 modelswere tested in total: ½ 5 growth ij ¼ b 0 þ b 1 diversity ij þ b 2 diversity 2 ij þ b 3 Age ij þ b 4 Sp ij þ b 5 Dq ij þ m i þ 3 ij where growth ij and diversity ij are one of the measurementsof growth (PAI, Ps, Pm, and Pr) and the stand structural Table 3. Stand structural diversity indices used in this study.Index Equation DescriptionTree speciesdiversity index Hs ¼ À X mi ¼ 1 p i  log p i , where p i is the proportion of basal areafor the i th species and m is the number of speciesShannon–Wiener index for species(Magurran 2004)Tree size diversity index Hd ¼ À X d i ¼ 1 p i  log p i ; where p i is the proportion of basal areafor the i th diameter class and d is the number of diameterclassesShannon–Wiener index by diameter classes(Buongiorno et al. 1994)Tree heightdiversity index Hh ¼ À X hi ¼ 1 p i  log p i , where p i is the proportion of basal areafor the i th height class,and h is the number of height classesShannon–Wiener index by height classes(Staudhammer and LeMay 2001)Integrated diversityindex of tree speciesand size Hsd ¼ À X mi ¼ 1 X d j ¼ 1 p ij  log p ij ; where p ij is the proportion of basalarea in the j th diameter class of the i th species, m is the num-ber of species, and d is the number of diameter classesIntegrated Shannon–Wiener index forspecies and diameter (Buongiorno et al.1994)Species profileindex Hsp ¼ À X mi ¼ 1 X 3 j ¼ 1 p ij  log p ij ; where p ij is the proportion of basalarea of species i in height class j , m is the number of species,class 1, 100%–81% of maximal tree height (hmax); class 2,80%–51% of hmax; class 3, 50%–0% of hmaxShannon–Wiener index calculation for theproportion of tree species in differentstand layers; indicates integrated diversityof species and height (Pretzsch 1996)Mean structuraldiversity indexHsdh = (Hs + Hd + Hh)/3 Mean value of tree species, size, and heightindices (Staudhammer and LeMay 2001)Gini coefficient forDBH GCd ¼ X ni ¼ 1 ð 2 j À n À 1 Þ BA j X ni ¼ 1BA j ð n À 1 Þ , where BA j is the basal area of the tree withrank j , j is the rank of a tree in ascending order from 1 to n byDBH, and n is the number of treesMeasurements of the deviation fromperfect equality (Lexerød and Eid 2006)Gini coefficient forheight GCh ¼ X ni ¼ 1 ð 2 j À n À 1 Þ BA j X ni ¼ 1BA j ð n À 1 Þ , where BA j is the basal area of the tree withrank j ; j is the rank of a tree in ascending order from 1 to n byheight; n is the number of treesMeasurements of the deviation fromperfect equality (Lexerød and Eid 2006) Table 4. Summary of structural diversity indicesused in the study ( n = 908).Index Mean ± SD RangeHs 0.521±0.380 0.0–1.539Hd 1.585±0.299 0.653–2.354Hh 1.415±0.221 0.664–1.956Hsd 2.355±0.380 1.172–3.410Hsp 1.173±0.419 0.155–2.267Hsdh 1.174±0.251 0.452–1.749GCd 0.335±0.080 0.151–0.546GCh 0.101±0.023 0.048–0.191 Note: The structural diversity indices Hs, Hd, Hh, Hsd,Hsp, Hsdh, GCd, and GCh are defined in Table 3. 1838 Can. J. For. Res. Vol. 39, 2009 Published by NRC Research Press diversity index (Hs, Hd, Hh, Hsd, Hsp, Hsdh, GCd, andGCh), respectivley, for plot i at time j ; Age is stand age;Sp and Dq are as previously defined, and b 0 – b 5 are para-meters of the fixed effects, m i $ N ð 0 ; s 2 m Þ is the randomplot effect, and 3 i $ N ð 0 ; s 2 e Þ is the random error. The inte-grated diversity index included Hsd, Hsp, and Hsdh withinthe models, and therefore, interactions among tree species,tree size, and height were included.It is necessary to characterize the behavior of the cova-riance structure of the plot random effect (G matrix) andthe repeated random effect (R matrix) when using the mixedmodel (eq. 5). The covariance structure was chosen amongthe candidates of unstructured (UN), compound symmetry(CS), and first-order autoregressive (AR(1) based on themethod of restricted maximum likelihood). Therefore, ninecombinations of covariance structures for plot and repeatedrandom effects were tested for each model. Two commonlyused information criteria including the Akaike’s informationcriterion (AIC) and the Bayesian information criterion (BIC)were applied to select the covariance structure that best de-scribes the data (Littell et al. 1996). The error covariancestructure possessing the smallest values of AIC and BIC isidentified as the most desirable.When the linear regression term ( b 1 ) in a relationship wasdeemed significant but the quadratic term ( b 2 ) was not, therelationship was categorized as monotonic positive or nega-tive according to the symbol on the linear term. The rela-tionship was deemed curvilinear if the quadratic term wassignificantly different from zero, and the overall model wassignificant. If both linear and quadratic effects were signifi-cant, it was then established whether it was significantly un-imodal (hump-shaped or U-shaped) using a statistical testdeveloped by Mitchell-Olds and Shaw (1987). This test de-termines whether a curvilinear relationship reaches a maxi-mum or minimum within the observed range of diversity(Waide et al. 1999; Chase and Leibold 2002). When boththe linear and quadratic term effects were significant but nounimodal shape was detected, the relationship was classifiedas concave increasing, concave decreasing, convex increas-ing, or convex decreasing according to the sign of the quad-ratic terms and the predicted values corresponding to themaximum and minimum of the explainable variables. Forall analyses, a significance level of a = 0.05 was used.To test how much stand structural diversity contributed tothe model fitting, we calculated the AIC difference betweenmodels with (eq. 5) and without diversity effects. Becauseeach diversity index was included in the model separately,we compared these models to find the index that contributedmost to stand growth. For the same response variable, thebest model was determined using Akaike’s weight ( w k ),which can be directly interpreted as the probability that amodel is suitable (Buckland et al. 1997; Ouzennou et al.2008), and is calculated as ½ 6 w k ¼ exp ðÀ 0 : 5 ð AIC k À AIC min ÞÞ X ni ¼ 1 exp ðÀ 0 : 5 ð AIC i À AIC min ÞÞ where w k is the Akaike’s weight of the model k , AIC k is theAIC value of the model k , and AIC min is the minimal AICvalue among the candidate models. A model with maximum w k is the best. Results Correlations between different structural diversityindices Table 5 shows that Hs has a weak correlation with thetree size and tree height diversity indices (Hd, Hh, GCd,and GCh) representing, consequently, different dimensionsof diversity. However, indices that integrate species, size,and height (Hsd, Hsp, and Hsdh) are always highly corre-lated with other indices with the exception of Hh and Hsp.The Gini coefficients (GCd and GCh) showed moderate cor-relation coefficients with other indices. High correlationshave been observed between the Gini coefficients for DBHand height. All structural diversity indices are included toexamine their sensitivity to stand growth within the models. Structural diversity at different developmental stages All structural diversity indices show a general increasingtrend with developmental stages from young, immature, ma-ture, and overmature forest stands (Fig. 1). Higher values in-dicate greater structural diversity. Therefore, older forestspossess more complex stand structure in terms of tree spe-cies composition, tree size structure, and vertical structurethan do young forest stands. Relationships between stand growth and structuraldiversity indices Among all combinations of three covariance structures forG and R matrices, UN for the G matrix and the CS for the Rmatrix were found to be the most desirable structure becausethey produced the smallest AIC and BIC values for all mod-els. Plot random effects were significant in all models (Waldtest, p < 0.001). So UN and CS covariance structures wereselected to model the variance components of plot and re-peated random effects in the final models, respectively. Ta-bles 6–9 present parameter values, their significance, AIC,BIC, plot random effect variance, random error variance of linear mixed models, changes of AIC ( D AIC) and weightedAIC ( w k ). D AIC and w k are only applied to models with sig-nificant diversity effects. The Sp was significant in all mod-els of PAI and Ps, whereas Dq was significant in all modelsof Pm and Pr. The effects of GCd and GCh were not signifi-cant in all models.Significant positive linear relationships were found be-tween Hs and PAI, Hsp and PAI ( p < 0 .01; Fig. 2, Table 6),Hs and Ps, and Hsp and Ps ( p < 0.01; Table 6). There weresignificant linear and quadratic effects between PAI and Hd,PAI and Hh ( p < 0.01; Table 6), and Ps and Hh ( p < 0.01;Table 7), and therefore, the Mitchell-Olds and Shaw (1987)test was performed for these models to examine whether thepresence of an internal maximum (hump-shaped) or mini-mum (U-shaped) existed. No unimodal relationships weredetected ( p = 0.4253 for PAI and Hd, p = 0.6808 for PAIand Hh, and p = 0.7996 for Ps and Hh). Owing to this, theserelationships were classified as concave increasing accordingto the sign of the quadratic terms and predicted values. Sig-nificant quadratic effects were also observed between PAIand Hsdh and Ps and Hd. However, the integrated diversityof tree species and size was not significant in all models.Neither significant linear nor quadratic effects of any diver-sity index were observed for Pm and Pr (Tables 8 and 9, Lei et al. 1839 Published by NRC Research Press
