Modeling long-term tree growth curves inresponse to warming climate: test cases from asubtropical mountain forest and a tropicalrainforest in Mexico

Martin Ricker, Genaro Gutierrez-Garcıa, and Douglas C. Daly

Abstract: The Earth’s temperature has increased 0.6 8C over the last 100 years, and further climate change is predictedto potentially raise it by 3.5 8C over the next century. More than half of the global annual net primary production of bio-mass is estimated to occur in the tropics, especially tropical evergreen forest. In temperate forests, increasing temperaturemay extend the non-frost growing season, and thus increase the CO2 sequestration rate, but some authors have also sug-gested a negative impact of warming in tropical forests from decreased photosynthetic activity. Using the PL model(Ricker and del Rıo 2004), we forecast growth of two Mexican tree species after climate warming. The model predictsthe high-mountain species Pinus hartwegii Lindl. to decrease its expected relative growth throughout its lifetime by10.6% as a consequence of a 0.6 8C temperature increase; in contrast, the tropical rainforest species Diospyros digynaJacq. is predicted to increase its expected relative growth throughout its lifetime by 25.4%. The key factor appears to bethe expected relationship between temperature and precipitation, rather than temperature alone. While one cannot expect auniversal response across sites, some standing tropical rainforests such as those at Los Tuxtlas in Mexico may constitutea carbon sink in a changing climate.

Resume : La temperature du globe a augmente de 0,6 8C au cours des 100 dernieres annees et on predit qu’elle pourraitaugmenter de 3,5 8C au cours des 100 prochaines annees avec la poursuite des changements climatiques. On estime queplus de la moitie de la production primaire nette annuelle globale de biomasse a lieu sous les tropiques, particulierementdans la foret tropicale sempervirente. Dans les forets temperees, l’augmentation de la temperature pourrait allonger la sai-son de croissance exempte de gel et par consequent augmenter le taux de sequestration du CO2, mais certains auteurs ontegalement suggere que le rechauffement climatique pourrait avoir un impact negatif dans les forets tropicales en reduisantl’activite photosynthetique. A l’aide du modele PL (Ricker et del Rio 2004), nous avons simule la croissance de deux es-peces d’arbre du Mexique apres un rechauffement climatique. Le modele predit que l’espece de haute montagne, Pinushartwegii Lindl., reduira de 10,6 % sa croissance relative prevue au cours de la duree de sa vie consequemment a une aug-mentation de temperature de 0,6 8C. Par contre, l’espece de foret ombrophile tropicale, Diospyros digyna Jacq., devrait se-lon la prediction du modele augmenter de 25,4 % sa croissance relative prevue au cours de la duree de sa vie. Le facteurcle semble etre la relation prevue entre la temperature et les precipitations plutot que la temperature seule. Bien qu’on nepuisse s’attendre a ce que tous les sites reagissent de la meme facon, certaines forets ombrophiles tropicales existantestelles que celles de Los Tuxtlas au Mexique pourraient constituer un puits de carbone dans un climat que change.

[Traduit par la Redaction]

Introduction

It is estimated that the Earth’s mean temperature has al-ready increased 0.6 8C over the last 100 years, and that fur-ther climate change may raise the Earth’s temperaturewithin the next century by another 3.5 8C (Meehl et al.2005). Tropical evergreen forests play a crucial role in the

balance and sequestration of carbon dioxide (CO2), becauseover half of the global annual net primary production of bio-mass is estimated to occur in the tropics (Melillo et al.1993).

Most trees in the temperate zone have discernible annualgrowth rings, and empirical studies of the relationship be-tween tree growth and climate in the temperate zone are typ-ically carried out with dendrochronological methods (Cookand Kairiukstis 1990). For many tree species and sites inthe lowland tropics without cold winters or strong climaticseasonality, however, trees do not form distinct annualgrowth rings, so it is not possible to determine ages bycounting growth rings (Jacoby 1989; Chambers et al. 1998;Pilar-Ibarra 2000). This has made long-term growth fore-casting in the tropics difficult. A renewed effort to measureless obvious annual tree rings in tropical trees has beenmade recently. Worbes (2002) reported that annual treerings exist in numerous tree species in more than 20 tropical

Received 20 October 2006. Accepted 17 November 2006.Published on the NRC Research Press Web site at cjfr.nrc.ca on7 July 2007.

M. Ricker1 and G. Gutierrez-Garcıa. Estacion de BiologıaTropical ‘‘Los Tuxtlas’’, Universidad Nacional Autonoma deMexico (UNAM), Apartado Postal 94, San Andres Tuxtla,Veracruz 95701, Mexico.D.C. Daly. The New York Botanical Garden, Bronx, New York,NY 10458–5126, USA.

1Corresponding author (e-mail: martin_tuxtlas@yahoo.com.mx).

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countries, where rhythmic growth is induced by marked sea-sonality caused by short drought periods or long-lasting in-undations. In an old-growth tropical wet forest at La Selva,Costa Rica, Fichtler et al. (2003) combined radiocarbon(14C) dating and tree-ring analysis to estimate the ages oflarge trees of canopy and emergent species, and found thatfive of the six species presented growth rings of annual for-mation. Similarly, Worbes et al. (2003) reported the exis-tence of annual rings in the wood of trees in a semi-deciduous natural forest stand in Cameroon. Still, many spe-cies on most sites in the moist lowland tropics lack discern-ible annual tree growth rings.

Ricker and del Rıo (2004) presented a new modeling ap-proach to derive the long-term age-diameter growth curvefor trees without detectable annual growth rings, using spe-cies- and site-specific data obtained in the short term (min-imum 1 year). Using this new indirect growth model, in thepresent paper we predict growth under climate change of arainforest tree species for which we had the data appropriateto the model. Furthermore, we show that the same model isapplicable and useful not only for tree species without an-nual growth rings, but also for those with annual growthrings, using as an example a high-mountain pine speciesfrom Mexico.

Methods

The effects of climate variation on tree growth variationhas always been measured by analyzing radius or diametergrowth of the tree trunk. The reasons are not only that coresamples may permit analysis and direct measurement of an-nual growth rings directly, and that the perimeter of thetrunk can be measured readily when annual growth ringsare not available, but there is also considerable evidencethat diameter growth depends primarily on current photosyn-thesis (some reserve carbohydrates may be used for diametergrowth very early in the season). In contrast, height growthof many trees is made primarily at the expense of stored car-bohydrates, rather than products of current photosynthesis(Kozlowski 1962).

Data for Pinus hartwegiiA total of 30 high-mountain pine trees of Pinus hartwegii

Lindl. (Pinaceae) were located in June 2001 in the Ejido LaEncantada, Municipality General Zaragoza in the Sierra dePena Nevada, State of Nuevo Leon (23853’03@–23857’70@N,99848’57@–99848’85@W; 2935–3060 m above sea level),where the species is frequent but not dominant up to thetree line of about 3300 m. Core samples were taken approx-imately at breast height with a Pressler increment borer(5 mm � 36 cm, using Bardhal 3 as a lubricant oil). Gener-ally, one sample was taken from the northern side and an-other was taken from the eastern side of each tree. In thesemi-open forest, this avoids tree-ring variation due to asym-metrical crowns towards the south. Samples were then driedfor a week at room temperature, glued to a small piece ofcarrier wood, and the surface was sanded using a progres-sively finer grain (100, 280, 500). The core samples werecross-dated according to Swetnam et al. (1985) and Yama-guchi (1991). Tree rings along the core sample were meas-ured to the nearest 0.01 mm, using a slide stage micrometer

connected to a computer, following Robinson and Evans(1980). From the northern core samples of 30 trees withmeasurements for the years 1898–2000, a total of 2583 datapoints (radius increments) resulted. Corresponding cross-dated eastern core samples were available for 28 trees, andclimate data were obtained for the years 1961–1997(37 years). The subsequent analysis of growth under warmerclimate was modeled with increments averaged from thenorthern and eastern core samples of 28 trees with a total of1012 radius increments, corresponding to an average of 36.1increments per tree.

Monthly climate data (average daily maximum tempera-ture and total precipitation) for the years 1961–1997 wereavailable from three meteorological stations surrounding thesite: Uvalles in the State of Tamaulipas at 20 km distance,Matehuala (State of San Luis Potosı) at 82 km, and Iturbide(State of Nuevo Leon) at 101 km. The averages of the datavalues from the three stations were employed here. Averag-ing climate records from several surrounding stations de-creases small-scale noise, thereby potentially improving thestatistical relationship between tree growth and meteorologi-cal data (Blasing et al. 1981). The temperature range duringthe 37 measured years was 25.2–28.5 8C, and the range ofprecipitation was 308–812 mm.

Data for Diospyros digynaThe data on the tropical rainforest site originated from 92

Black Persimmon trees (Diospyros digyna Jacq.) (Ebena-ceae) that were located in an area of about 5 km � 4 km inthe vicinity of the Estacion de Biologıa Tropical ‘‘Los Tuxt-las’’, Municipality San Andres Tuxtla, in the State of Vera-cruz (18834’20@–18836’20@N, 95803’30@–95806’30@W, 100–500 m above sea level). The species is generally rare in theforest, but relatively abundant in certain forest patches nearthe coast. Tree trunk circumferences were measured atmarked heights with a tape (depending on buttresses approx-imately at breast height). Dividing by � = 3.14159 resultedin the diameter at breast height (DBH). The circumferencemeasurements were repeated twice. The growth periods var-ied between 282 and 454 d. The diameter increments werelinearly interpolated or extrapolated to 365 d (1 year). A to-tal of 265 diameter increments resulted for the 92 trees, cor-responding to an average of 2.9 increments per tree.

Climatic data for this site were available from the mete-orological station at Coyame, approximately 15 km air dis-tance from the study site. Daily maximum temperature wasaveraged, and total precipitation was summed up over thesame dates during which the increments were measured. Inthe same manner as with the diameter increment data, pre-cipitation was interpolated or extrapolated to 1 year, to beon the same scale. The range of average daily maximumtemperature during the 3 years of growth measurements was26.4–27.9 8C, and the range of precipitation was 3524–3907 mm (after interpolation or extrapolation to 1 year). Inaddition, for the correlation analysis of temperature and pre-cipitation (see Fig. 6, right), we used annual data of averagemaximum daily temperature and annual precipitation avail-able from Coyame for the years from 1953 to 1998(44 years, with 1962 and 1992 missing).

How can the effects of climate variation be modeled,when there are only three measurement years in the case of

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Diospyros digyna? The underlying assumption is that varia-tion in daily diameter or radial increment is generally due tovariation in temperature and (or) precipitation, without beinggenetically programmed, i.e., if there were August tempera-tures during the colder December days, the trees would re-spond with August growth (not taking into account differentday lengths). There is empirical evidence that this assump-tion approximately holds. Kozlowski et al. (1962) alreadywrote that an unseasonal drop in temperature in the middleof a growing season causes greatly decreased growth rates,which emphasizes the critical role of temperature in growthcontrol. For example, shoot growth of potted peach trees(Prunus persica (L.) Batsch) in growth chambers is stronglydependent on air temperature, including in the dark (Bermanand DeJong 1997). Northern trees respond with increasedgrowth to a prolongation of the non-frost growing season(e.g., Bergh et al. 2003). On the 4300 m high Nevado deColima volcano, growth of Pinus hartwegii trees on the tim-berline responded to increasing spring temperature, as wellas the summer monsoon precipitation (Biondi et al. 2005).Evergreen species (such as Diospyros digyna here) in asemi-deciduous tropical forest in Venezuela react in theirtrunk wood increment to the total annual amount of precipi-tation (Worbes 1999).

Consequently, one can measure growth during differentperiods of the year with varying average daily temperatureand accumulated precipitation. The corresponding treegrowth over that period of the year will be a reflection ofthe tree growth of the corresponding climate. Without prede-signed measurement intervals, in the case of Diospyros di-gyna the periods happened to be intervals of 282–454 d,reflecting the above-mentioned temperature and precipita-tion ranges.

Projections of the long-term growth curvesThe PL (= piecewise linear) model from Ricker and del

Rıo (2004) can project tree growth over any time frame, upto centuries. To understand the basic idea of the PL model,consider the following hypothetical scenario: A number ofdifferent-aged but genetically identical trees grow under ho-mogeneous environmental conditions. Short-term incrementmeasurements of the old (large) trees can tell us exactlyhow the young (small) trees will grow once they reach theage of the old trees, without having to wait until the youngtrees reveal that information by themselves. This approach isused to develop a regression model that relates relativegrowth to diameter. From this relationship, the long-termage–diameter curve is derived, that is to say, the expectedaverage growth curve of a statistical population of individualtrees. In this way it is possible to model 300 years of growthfor Diospyros digyna from increment data taken over 3 years.

The PL model does not necessarily take into account theappropriate climate, because it depends on growth data ofonly 1 or (as here) a few years. If the climate of these fewyears is not representative for the long term (i.e., decades oreven centuries), then the growth projections are biased inabsolute terms. Even when this is the case, however, the ef-fect of climate variation on these long-term growth curvescan be modeled in relative terms as a shift of the possiblybiased projection.

The multiple piecewise linear regression, statistical analy-

sis, and growth curve calculations were carried out withthe PL software developed by the first author, and avail-able at sciweb.nybg.org/science2/FieldResearch.asp. Themathematics and application of the PL model is describedin detail in Ricker and del Rıo (2004). Three extensions ofthe model, however, are published for the first time in thepresent paper. These are as follows:

(i) The model is applied to dendrochronological data oftrees with annual tree rings (here Pinus hartwegii). This isdone by calculating for each measurement year the annualincrement and the corresponding intermediate radius (seeRicker and del Rıo 2004, p. 214). In this case, the differentdata points are not from distinct individual trees with incre-ment variation from site and genetic factors. Instead, manydata points are from the same tree with increment variationamong years caused by climate differences among years. If(as here) the data points from several (here 28) trees arecombined, the problem of serial dependence (i.e., autocorre-lation) of the statistical residuals may result, because a fast-growing tree presents high increments year after year, and aslow-growing tree presents low increments repeatedly (e.g.,West 1995). Such serial dependence, however, is avoidedby including the variable ‘‘average increment’’, as explainedin point iii, and was not detected statistically in our two datasets. When it happens, the regression coefficients of ordi-nary least squares estimators remain unbiased, but the esti-mates of the variances and consequently the confidencecurves may be biased (Sullivan and Reynolds 1976; Mad-dala 1992, p. 243).

(ii) The growth curves are developed as a linear functionof environmental variables, such as temperature and precipi-tation. This is possible because the piecewise linear regres-sion is carried out technically as multiple linear regression(see Appendix 1 in Ricker and del Rıo 2004). The inclusionof the additional explaining variables does not affect muchthe mathematics of the PL model, as the additional variables(vari) can be included in the formulas of appendices 1 and 2in Ricker and del Rıo (2004) by means of the following sub-stitution: a0 = c0 + c1 � var1 + c2 � var2 + ... + ci � vari,where c1 to ci are the regression coefficients for i explainingvariables. In this substitution, it is furthermore possible toinclude a quadratic term for a given explaining variables asc1 � var1 + c2 � (var1)2 (curvilinear regression in Sokal andRohlf 1995, p. 665). This results in a parabola, or a curvedregression line that goes first up, reaches a maximum, andthen goes down (or vice versa). Such quadratic terms wereincluded in the case of Pinus hartwegii for the temperatureand in the case of Diospyros digyna for the precipitation, toachieve an improved fit with desirable characteristics of theresiduals.

(iii) The average of the annual increment over all meas-ured years of an examined tree (the variable ‘‘average incre-ment’’) is used as an index for the particular site conditionsof a tree, including nutrient availability, water access of theroots, and light exposure. Furthermore, this variable takesinto account possible genetic differences between individualtrees. For both species, it turned out to be a statisticallyhighly significant variable for explaining growth variation.

As in other applications of multiple linear regression, onehas to evaluate a number of models that lead to the finallyadopted one. Key aspects of the model that can be varied

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are the initial relative growth (corresponding to the Y-interceptfor logarithmic relative growth), the number of kinks, andthe possible inclusion of explaining environmental variables.Important criteria for the evaluation of the model are thenon-zero slopes of the explaining variables, and the charac-teristics of the residuals. Also, high correlations betweenthe explaining variables are to be avoided.

The number of necessary kinks was statistically deter-mined so as to get significantly different slopes betweenneighboring segments. The standardized residuals were ana-lyzed for normality with the Kolmogorov–Smirnov test, forserial independence with the von Neumann test, and for ho-moscedasticity with Bartlett’s test (see Sokal and Rohlf1995). Normality of the residuals is especially important, be-cause non-normality biases the projected average growthprojection.

ResultsThe results will be presented in three modeling steps as

follows.(1) The average growth path of 30 Pinus hartwegii trees

is modeled with radial increment data over 102 years. Only‘‘average increment’’ is included as an explaining variable,while climate variables are not yet taken into account. Thissimplification gives a good idea of what the PL model is ac-tually doing when taking an environmental variable into ac-count. Using only one explaining variable allows one tothink of the results still within a three-dimensional space.

(2) The average growth path of 28 Pinus hartwegii treesis modeled with radial increment data over 37 years, takinginto account average increment and temperature as explain-ing variables. Precipitation turned out to be highly correlatedwith temperature in the case of Pinus hartwegii, and there-fore is not included as an addional independent variable.

(3) The average growth path of 92 Diospyros digyna treesis modeled with increment data over 3 years, being based oncircumference measurements, and taking into account aver-age increment, temperature, and precipitation as explainingvariables.

Pinus hartwegii without climate dataFigure 1 top shows in gray the true (directly measured)

growth curves as a function of the calendar year, as revealedfrom the dendrochronological analysis. Different treesstarted growing in different years. The trunk core sampleswere taken in the year 2000 from trees with different ages(29–102 years) and radiuses (11.5–28.5 cm).

To apply the PL growth model, in Fig. 1 bottom, thegrowth curves of all trees were moved to a common startingpoint: at a radius of (approximately) 1 cm, the age wasstandardized to be zero. In this way, the growth path ofeach tree can be compared directly with the others, withoutthe problem that different trees started growing in differentcalendar years, or that at the start (age zero) they wouldhave distinct radiuses. As an explaining variable, the tree’saverage increment was included to model expected growthpaths for trees with different growth rates.

The three thick black lines in Fig. 1 bottom show thegrowth paths resulting from the PL model, corresponding tothe fastest-growing tree (0.450 cm/year), the average incre-

ment of all 30 trees (0.220 cm/year), and the slowest-growingtree (0.108 cm/year). The shape of the three modeledgrowth paths represents the growth curves’ average shapeof all trees, but not the growth curves’ shape of any partic-ular tree. The graph also shows clearly the resulting ‘‘coneform’’ of the growth paths: the further in the future theprojection, the greater the uncertainty of the resulting ra-dius under varying growth rates.

The two graphs in Fig. 2 show how the PL model worksfor trees with annual growth rings and how it takes an ex-plaining variable into account. Each increment datum wasdivided by the intermediate radius (radius + 0.5 � increment),and the logarithm of the result was taken. In Fig. 2 top, thelogarithmic relative growth was plotted over the radius. Thepiecewise linear regression resulted in two statistically sig-nificant kinks (at 4.2 cm and hardly recognizable at12.7 cm). The corresponding coefficient of determinationR2, adjusted for the number of variables, is 0.63. The regres-sion equations (with RG being relative growth) are as fol-lows (30 trees, core samples from 1898–2000):

0.2 cm £ radius £ 4.2 cm: ln(RG) = –1.8067 – 0.62895 �radius + 4.33743 � average increment; 4.2 cm £ radius £12.7 cm: ln(RG) = –4.0789 – 0.084032 � radius +4.33743 � average increment; 12.7 cm £ radius £28.6 cm: ln(RG) = –4.3325 – 0.064053 � radius +4.33743 � average increment; 0.11 cm/year £ average in-crement £ 0.5 cm/year

The slopes and kink radiuses of the piecewise linear re-gression determine the shape of the growth paths, while thevertical position determines the growth rate along thegrowth path. The average radius of all data points is9.8 cm, which in Fig. 2 top is indicated with a vertical blackline. If we cut through the graph along that black line, androtate the top graph around by 908, then we get to see thegraph of Fig. 2 bottom. Minimum, average, and maximumgrowth paths are now indicated as crosses instead of lines,and one can recognize that the multiple linear regressionhas produced actually a regression plane in a three-dimen-sional space. All points are plotted as standardized residualsabove and below the regression plane. This is done to beable to evaluate graphically the goodness-of-fit of the over-all regression model even when there are more than threedimensions as in the following models.

Note that the residuals in this PL regression do deviatesignificantly from a normal distribution, which causes suspi-cion about the accuracy of the vertical position of the re-gression plane, which may not result in the best (i.e., mostlikely) projections of the tree growth paths. Figures 1 and 2,however, show only a preliminary regression for demonstra-tion of the model process, so the characteristics of the resid-uals are of no consequence for our later conclusions.

Including temperature as an explaining variable forPinus hartwegii

The Pinus hartwegii data set for 1961–1997 containedfew data points with small trunk radiuses (<5 cm). Thus thedata do not determine adequately the regression line for rad-iuses that are smaller than the first kink radius, and it is ad-visable to fix the initial relative growth at a reasonable,although somewhat arbitrary value, such as 100% or 50%.A fixed initial relative growth value of 50% at average

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parameters of the two explaining variables provided a rea-sonable model (Fig. 3, middle left). This value correspondsto a Y-intercept for logarithmic relative growth of ln(50% /100%) = ln(0.5) = –0.693 in Fig. 3. The resulting modeland regression equations are as follows (28 trees, coresample data from 1961–1997):

3.0 cm £ radius £ 5.1 cm: ln(RG) = –37.2238 – 0.55694 �radius + 2.84926 � temperature – 0.056660 � (tempera-ture)2 + 3.95717 � average increment; 5.1 cm £ radius £15.1 cm: ln(RG) = –39.6871 – 0.075343 � radius +2.84926 � temperature – 0.056660 � (temperature)2 +3.95717 � average increment; 15.1 cm £ radius £28.4 cm: ln(RG) = –40.4675 – 0.023762 � radius +2.84926 � temperature – 0.056660 � (temperature)2 +3.95717 � average increment; 25.2 8C £ temperature £28.5 8C; 0.12 cm/year £ average increment £ 0.46 cm/year

The three piecewise linear segments have slopes that are

significantly different from each other, thus justifying the in-clusion of two kinks. The corresponding coefficient of deter-mination R2, adjusted for the number of explainingvariables, is 0.463. The standardized residuals do not deviatestatistically from a normal distribution, serial independence,or homoscedasticity. They are, however, slightly but signifi-cantly skewed to the left (g1 = –0.28) and leptokurtotic (g2 =0.55); both g values would be 0 in a perfectly normal distri-bution.

The variables ‘‘temperature’’ and ‘‘average-increment’’explain significantly variation of logarithmic relativegrowth. Figure 3 top left shows the change of logarithmicrelative growth with increasing temperature. The regressionline is slightly curved, given the quadratic term for temper-ature in the regression model. The vertical black bar indi-cates growth at the average temperature of 26.9 8C (labeledwith ‘‘now’’), and the gray bar indicates growth at the 0.6 8C

Fig. 1. Above: True (directly measured) growth curves as a function of the year, as revealed from dendrochronological analysis, in gray.Bottom: All growth curves from the top graph were moved to a common starting point (0 years at approximately 1 cm radius). The modeledgrowth paths in thick black lines correspond to the average increment of all 30 trees, the fastest-growing tree, and the slowest-growing tree.The shape of the three modeled growth paths represents the growth curves’ average shape of all trees.

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increased temperature of 27.5 8C (labeled with ‘‘+0.6 8C’’).The graph below (Fig. 3 middle left) shows the correspond-ing piecewise linear regression line of logarithmic relativegrowth as a function of trunk radius. The regression linecorresponding to average temperature is shown again inblack, the line corresponding to increased temperature isshown in gray. Finally, the bottom graph (Fig. 3 bottomleft) projects the corresponding trunk radius as a functionof age, again in black at average temperature and in grayat increased temperature. The two thin growth curves inblack correspond to 95% confidence curves for the meas-ured variation of logarithmic relative growth at fixed turn-ing point radiuses and kink radiuses. At averagetemperature, the first turning point (26.9 8C) is at 2.5 yearsof age and 1.8 cm radius, the first kink point is at16.7 years and 5.1 cm radius, the second turning point is

at 60.0 years and 13.3 cm radius, the second kink point isat 69.0 years and 15.1 cm radius; the third turning pointwould be at 168.7 years and 42.1 cm radius, but falls out-side the range of measured radiuses.

The model predicts that the high-mountain species Pinushartwegii decreases its average expected relative growththroughout its lifetime by 10.6% as a consequence of a0.6 8C temperature increase. The logarithmic relative growthrate in Fig. 3 middle is 0.1120 less over the whole growthpath: the growth rate is 0.894 times (= e–0.1120) the growthrate without the temperature increase (100% – 89.4% =10.6%). The confidence curves (thin black lines) in Fig. 3bottom indicate that the differences in measured growth ratebetween average and increased temperature can be consid-ered statistically significant, because the gray line is outsidethe confidence curve belt.

Fig. 2. Piecewise linear regression of logarithmic relative growth as a function of radius, that derive the growth paths in Fig. 1 bottom. Theaverage radius of all data points is indicated as a vertical black line in Fig. 2 top. If we cut through the graph along that black line, androtate the top graph around by 908, then we get to see the graph of Fig. 2 bottom. The regression lines of Fig. 2 top are now crosses. Alldata points are presented as standardized residuals.

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Figure 4 top shows for Pinus hartwegii the highly signifi-cant relationship between logarithmic relative growth andaverage increment (as a dummy variable for site quality andgenetic differences among trees). When modeling growth atincreased temperature, the average increment was left un-varied at its average value for all trees, so the graph showsonly one bar (black on top and gray on bottom).

The graph in Fig. 5 left presents the annual increment as afunction of the radius. Again, the black increment curve cor-responds to growth under current climate, and the graycurve corresponds to the expected increment curve under a0.6 8C temperature increase. Each piecewise linear segmentin Fig. 3 middle corresponds to a distinct, curved line inFig. 5. Note that the three curved segments in this graphcorrespond to the three piecewise-linear segments in the re-lationship between logarithmic relative growth and radius.

Also, they are rather different from the negatively exponen-tial function or straight line assumed sometimes for the rela-tionship between increment and age (or diameter) indendrochronology (Cook and Kairiukstis 1990, pp. 99, 108).

Finally, the graph in Fig. 6 left shows the relationship be-tween temperature and precipitation for the region of Pinushartwegii, the Sierra de Pena Nevada. At this high-mountainsite, higher temperature is statistically correlated with lowerprecipitation (r = –0.60, n = 37). We assumed that also inthe future under a temperature increase, precipitation wouldremain highly correlated in this way with temperature.

Diospyros digynaIn the case of Diospyros digyna, initial relative growth

was not fixed but determined by the regression, giving as aresult 10.5% (corresponding to an intercept of –2.251 at

Fig. 3. Above: Logarithmic relative growth of the high-mountain tree species Pinus hartwegii (left) and the tropical rainforest species Dios-pyros digyna (right) as a function of average maximum daily temperature. Black bars refer to the mean temperature, the gray bars refer to a0.6 8C temperature increase. Middle: Piecewise linear regression curves of logarithmic relative growth as a function of trunk radius or dia-meter under average and increased mean temperature. Bottom: Mathematically corresponding average long-term growth curves (trunk radiusor diameter as a function of age). The thin black lines indicate the 95% confidence curves for the measured variation of annual increment.

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growth without temperature increase in Fig. 3 middle right).The three piecewise linear segments have slopes that are sig-nificantly different from each other. The resulting model andregression equations are as follows (92 trees, repeated perim-eter measurements with tape on marked height, 1996–1998):

4.8 cm £ diameter £ 22.7 cm: ln(RG) = –175.1097 –0.075467 � diameter + 0.086736 � precipitation –0.000011616 � (precipitation)2 + 0.37730 � temperature +1.45304 � average increment; 22.7 cm £ diameter £65.9 cm: ln(RG) = –176.2926 – 0.023310 � diameter +0.086736�precipitation –0.000011616� (precipitation)2 +

0.37730 � temperature + 1.45304 � average increment;65.9 cm £ diameter £ 138.9 cm: ln(RG) = –177.2337 –0.0090402 � diameter + 0.086736 � precipitation –0.000011616 � (precipitation)2 + 0.37730 � tempera-ture + 1.45304 � average increment; 3524 mm £ precipi-tation £ 3907 mm; 26.40 8C £ temperature £ 28.30 8C;0.19 cm/year £ average increment £ 2.19 cm/year

The corresponding adjusted coefficient of determinationR2 is 0.689. The analysis of standardized residuals did not de-tect significant deviation from normality, serial independence,or homoscedasticity. The distribution of the standardized re-siduals is again a little skewed to the left (g1 = –0.29), butshows no significant kurtosis.

Figure 3 right shows the corresponding graphs. The aver-age temperature for the Diospyros digyna trees at Los Tuxt-las was 27.3 8C (black bar in Fig. 3 top right), the increasedtemperature was 27.9 8C (gray bar). The first turning pointof the growth curve at average temperature in Fig. 3 bottomright is at 36.3 years age and 13.3 cm diameter, the firstkink point was at 55.9 years and 22.7 cm diameter, the sec-ond turning point was at 97.7 years and 42.9 cm diameter,the second kink point was at 144.8 years and 65.9 cm diam-eter, and the third turning point was at 235.2 years and110.6 cm diameter.

In contrast with Pinus hartwegii, under increased temper-ature the tropical rainforest species Diospyros digyna is pre-dicted to increase its expected relative growth throughout itslifetime by 25.4%. The logarithmic relative growth rate inFig. 3 middle increases by 0.2264 over the whole growthpath: the growth rate becomes 1.254 times (= e0.2264) thegrowth rate without the temperature increase (125.4% –100% = 25.4%). The confidence curves in Fig. 3 bottomright (thin black curves) indicate that the differences inmeasured growth rate between average and increased tem-perature can be considered statistically significant also inthis species. Figure 4 middle shows the highly significant re-lationship between logarithmic relative growth and a tree’saverage increment. The parabolic (quadratic) relationship oflogarithmic relative growth as a function of precipitation inthe final model for Diospyros digyna is presented in Fig. 4bottom.

On the right in Fig. 5, the increment as a function of thetrunk diameter is presented also for Diospyros digyna. Againthe black line shows the increment curve under average tem-perature, and the gray curve shows the expected growthunder a 0.6 8C temperature increase. Note again that eachpiecewise linear segment in Fig. 3 middle right generates itsown curved segment in this graph.

The graph in Fig. 6 on the right shows the relationship be-tween temperature and precipitation in the Los Tuxtlas re-gion, where the Diospyros digyna trees were located. Theblack cross indicates the average precipitation at averagetemperature, the gray cross shows the precipitation at in-creased temperature. In the case of Diospyros digyna, bothcrosses are off and under the line, because the 3 years ofgrowth measurement with its corresponding climate weredrier than the 44-year average. This fact may cause a certainunderestimation of the predicted absolute growth curves inthe case of Diospyros digyna for both temperature scenarios,but still permits conclusions about the relative change result-ing from a temperature increase.

Fig. 4. Above and middle: Highly significant relationship for bothspecies between logarithmic relative growth and average annual in-crement as an indicator for a tree’s site quality and possibly alsogenetic differences. Bars show the mean average increment valuesemployed for the average growth curves in Fig. 3 (here the samevalue for both temperatures). Bottom: The regression model forDiospyros digyna includes a quadratic term for precipitation. Forpredicting growth under increased temperature, precipitation wasassumed to remain unchanged at its average value (black and graybar).

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The correlation between temperature and precipitation atthis rainforest site is positive but statistically nonsignificant(r = 0.23, n = 44). Therefore, in contrast with the high-mountain site of Pinus hartwegii, precipitation was assumedto remain constant under a temperature increase.

Discussion

We analyzed tree growth in response to warming climate,employing the PL model from Ricker and del Rıo (2004).Annual tree rings were present in the trunk wood of Pinushartwegii but absent in Diospyros digyna. Although thepresence of annual growth rings makes the long-term predic-tions more accurate, the PL model can take as input short-termincrement measurements of different-sized trees to predictlong-term growth, and we used this approach with four meas-urements taken over 3 years for Diospyros digyna. An advant-age to include Pinus hartwegii is that the annual growth ringsmake it possible to test the PL model empirically.

The PL model is a statistical regression model that servesto disentangle different effects ‘‘hidden in data clouds.’’ Theapproach is inductive as it attempts to understand the overallobservations. This contrasts with ‘‘process models’’ that takea deductive approach by attempting to establish cause andeffect throughout growth processes (Courbaud 2000; Bald-win et al. 2001; Johnsen et al. 2001). While regression mod-

els depart from given observations and lead to hypotheseshow they came about, process models are the reverse, de-parting from hypotheses and leading eventually to a compar-ison with observed data. While the differences between thetwo types of approaches need not be discussed further here,we note that both approaches are valid to contribute to abetter scientific understanding about the causes of treegrowth variation.

In this study we predict that, as a consequence of a 0.6 8Ctemperature increase, the high-mountain species Pinus hart-wegii in the Sierra de Pena Nevada (Mexico) will decreaseits expected average relative growth by 10.6% throughoutits lifetime (122 years on average, starting with 1 cm diame-ter at 0 years), as reflected by the shift of the piecewise lin-ear regression lines in Fig. 3 middle. In contrast, the tropicalrainforest species Diospyros digyna in Los Tuxtlas is pre-dicted to increase its expected relative growth by 25.4%throughout its lifetime (291 years).

Projected on a 100-year time horizon, this translates into adecrease in the expected trunk diameter of Pinus hartwegiiafter 100 years of growth from 22.2 to 19.6 cm (an 11.7%decrease at this age) as a consequence of 0.6 8C temperatureincrease, while the expected diameter for Diospyros digynais predicted to increase in the same time frame from 44.0 to56.8 cm (a 29.1% increase at this age).

The combination of higher CO2 concentrations, elevated

Fig. 5. Annual trunk increment as a function of trunk radius or diameter. Again, the black increment curves represent growth under meantemperature, and the gray curves represent growth under a 0.6 8C temperature increase. Note that each piecewise linear segment in Fig. 3middle corresponds to a curved segment here.

Fig. 6. The relationship between annual precipitation and average temperature at the two sites. The data points represent 37 measurementyears for the Sierra de Pena Nevada (where Pinus hartwegii is located) and 44 years for Los Tuxtlas (where Diospyros digyna is located).The black crosses indicate values for average growth predictions, and the gray crosses indicate values for growth predictions under a 0.6 8Ctemperature increase. For Los Tuxtlas, both crosses are under the line, because the 3 years of growth measurement with its correspondingclimate were drier than the 44-year average.

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temperature, and modified precipitation changes photosyn-thesis and respiration rates, thereby modifying net primaryproduction. In the southern United States, loblolly pine(Pinus taeda L.) is expected to grow better under increasedtemperature and elevated CO2 (Alemayehu et al. 1998; Te-skey 1998; Valentine et al. 1998). On the other hand, slashpine (Pinus elliottii Engelm.) could present reduced growth(Cropper 1998). The exact response depends on the changein precipitation plus the trees’ site conditions such as soilnutritients, light environment, and competition (see Rotzeret al. 2005 for references), as well as genetic differencesamong tree species (Graumilch 1991; Rehfeldt et al. 1999;Sonesson and Eriksson 2000; Nigh et al. 2004). The distinctresponse among different species could lead to a change inthe species composition of forests over time (Wullschlegeret al. 2003; Laurance et al. 2004).

In general, the literature reports two direct effects of cli-mate change on tree growth. First, increasing temperatureaccelerates tree growth physiologically, when water avail-ability is not limiting. Kozlowski et al. (1962) summarizedthe role of temperature in tree growth. Temperature exertseffects on growth by altering rates of processes such as pho-tosynthesis, respiration, cell division and elongation, enzy-matic activity, chlorophyll synthesis, water uptake, andtranspiration. A number of case studies highlight the pivotalrole of temperature in tree growth. The productivity of sev-eral Canadian timber species in British Columbia in the gen-era Pinus, Picea, and Pseudotsuga increased as temperatureincreased (Nigh et al. 2004). Also in British Columbia,mean annual temperature and mean temperature in the cold-est month were the most effective variables for predicting20-year height and survival in 118 populations representingtwo subspecies of Pinus contorta Douglas ex Loudon (Re-hfeldt et al. 1999).

In northern forests, increasing temperature extends the non-frost growing season. The consequence is a longer growingseason, a consequent increase of the CO2 sequestration rate,and thus a buffer effect of climate change. Misson (2004) re-ported that bole increment in Quercus petraea (Mattuschka)Liebl. in Belgium was controlled by temperature, as it af-fected the phenological process of bud burst and thus thegrowing season length. Bergh et al. (2003) modeled the effectof climate change on four tree species in Scandinavia and Ice-land. Elevated temperatures were predicted to increase netprimary production by between 5% and 27% for coniferousstands, largely due to an earlier start of the growing season.

Under certain conditions, however, precipitation can over-ride temperature, meaning that precipitation rather than tem-perature limits and controls growth. Correlations of spot ormultispot rainfall with growth-layer thicknesses in generalhave yielded significant correlation coefficients of 0.4–0.8(Glock and Agerter 1962). In central Panama, Cordia allio-dora (Ruiz & Pav.) Oken, Pseudobombax septenatum (Jacq.)Dugand, and Annona spraguei Saff. presented annual growthrings at three distinct sites across the country, located nearweather stations, and at two of the sites precipitation wasthe limiting factor, while on the Caribbean site, with moretotal rainfall and more rain during the dry season, minimumtemperature was the limiting factor (Devall et al. 1995). Thelatter result is similar to ours, where temperature is a limit-ing factor for Diospyros digyna in Los Tuxtlas.

The projected relationship between temperature and pre-cipitation is of key importance for examining the effect ofclimate change on tropical forests. This may explain whydifferent authors have reached contradictory conclusionsabout the effects of elevated temperature on tree growth intropical forests. Clark et al. (2003) reported for six speciesat La Selva in Costa Rica that mean annual growth averagedover the two coolest measurement years (1984–1985 and1985–1986) was 81% greater than in the record-hot 1997–1998 measurement year. This, however, is not the wholestory, as Clark et al. (2003, p. 5856) also mention in theirstudy that the strong El Nino events in 1997–1998 broughtnot only record-high temperatures but also rainfall minima.Thus, any possible increase in growth was probably limitedby lack of water availability.

In another paper, Clark (2004, p. 480) cited several stud-ies showing that leaf temperatures above 26–34 8C lead tosharp declines in photosynthetic rates in tropical forests.But what they refer to is the phenomenon called ‘‘middaydepression of photosynthesis’’, in which a plant closes itsstomates, when vapor pressure differences between leaf andair increases above 40 mPa/Pa under higher temperature.This phenomenon is therefore a function more of waterstress than temperature, and is best known from semiaridand arid regions (Roy and Salager 1992; Zotz and Winter1996, p. 92; Pons and Welschen 2003).

Moreover, tropical canopy tree species may be adapted tohigher temperatures to start with. In a seedling study ofeight canopy tree species, covering the latitudinal range ofrainforests in eastern Australia (cool-temperate to tropicalrainforest), Cunningham and Read (2003) found that the ma-jority of the temperate species showed maximum growth be-tween 26 and 30 8C, whereas the maximum growth for thetropical species in their study was above 30 8C. The abilityof plants to acclimatize to increased temperature was dis-cussed by Mohr and Schopfer (1995, pp. 544–546), whoalso mentioned the induction of heat-shock proteins whentemperature rises suddenly from around 30 8C to approxi-mately 40 8C.

It is unlikely that moisture changes will be uniformthroughout regions worldwide under climate change, eventhough most climate models predict increases in tempera-tures almost everywhere after a few decades of increases ingreenhouse gases. Malhi and Wright (2005, p. 14) reportedan average warming of about 0.26 8C per decade worldwidein tropical rainforest regions since the mid-1970s, but statedthat there is much uncertainty in how tropical precipitationregimes will respond to changes in the global atmosphere.Globally, evaporation rates are expected to increase, the at-mosphere is expected to become more humid, and rainfallrates are expected to increase. Especially at lower latitudes,such as the rainforest site in Los Tuxtlas, an absolute in-crease in moisture is expected (Trenberth et al. 2003, p.1212).

In stark contrast, deforestation of large forest areas islikely to lead to reduced regional precipitation and thus lesswater availability for remaining forest patches (Shukla et al.1990; Cramer et al. 2004). In coastal areas such as LosTuxtlas, however, deforestation is not likely to reduce rain-fall or be linked to reduced tree growth rates, because it islocated in the Gulf of Mexico, and most precipitation comes

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in directly from the sea. Therefore, no deceleration effect ontree growth from future deforestation is expected for the Di-ospyros digyna growth modeling in this paper.

The second direct effect of climate change on tree growth,reported in the literature, consists of increasing CO2 concen-trations in the air accelerating tree growth, although nutrientavailability in the soil can override this factor. Chambersand Silver (2004) argue that studies on elevated CO2 in nat-ural ecosystems worldwide have demonstrated increases ofnet primary productivity from 0% to 25%. Interestingly, re-view of the available literature suggests that there are stronglinks between temperature and precipitation on the onehand, and CO2 and soil nutrients on the other, but not somuch between these pairs of factors.

Under experimentally controlled atmospheric CO2 andsoil-nitrogen availability in a study of Populus tremuloidesMichx. over 2.5 growing seasons, elevated CO2 had a sus-tained positive effect on carbon-gain capacity and above-ground biomass accumulation only under conditions of highnitrogen availability. Under lower leaf-nitrogen concentra-tion, they found that gains in net CO2-assimilation rate werelargely offset by increased dark respiration and fine-rootturnover under elevated CO2 (Curtis et al. 2000).

While in temperate ecosystems, low nitrogen availabilityoften limits net primary productivity, in the highly weath-ered soils typical of tropical forests, phosphorus is the mostcommonly limiting element. According to Chambers andSilver (2004), it is not clear yet to what extent phosphoruslimitation inhibits the growth response of trees to elevatedCO2 in tropical forests, because plants have evolved severalmechanisms to alleviate low-phosphorus stress.

Nutrient availability and the tree species in question, aswell as the additive effects of CO2 and temperature increase,may explain the different results of different studies frommodeling the effect of changing CO2 concentrations. For ex-ample, no CO2-induced growth enhancement was foundamong subalpine conifers in a dendrochronological study inthe Sierra Nevada, California (Graumilch 1991). In agrowth-chamber experiment with seedlings of Pinus sylvest-ris L. and Picea abies (L.) H. Karst., the effects of elevatedCO2 were small, compared with the effect of elevated tem-perature (Sallas et al. 2003). On the other hand, a 350-year-old deciduous forest at Hubbard Brook in New Hampshire(USA) might store about twice as much carbon when theCO2 concentration is doubled and temperature is also in-creased by 5 8C (Rastetter et al. 1997). Finally, in a studyby Rotzer et al. (2005) with a process model for a site insouthern Germany, an increase or decrease in trunk diametergrowth depended on the combined effects of temperature,precipitation, and CO2 concentration.

In our study, an increasing CO2 concentration could havean additional effect of accelerating growth of Diospyros di-gyna in the Los Tuxtlas rainforest. On the other hand, itcould at least partially counteract the reduced growth of Pi-nus hartwegii at the high-mountain site. How much thiscould affect our long-term growth projection is unclear. AtLos Tuxtlas, it is known that phosphorus availability is lim-ited (Ricker et al. 2000), so the additional predicted growthacceleration due to a CO2 increase may be small.

Tree turnover, measured as rates of tree mortality and re-cruitment, has apparently increased since the 1950s, based

on 40 tropical forest sites worldwide (Phillips and Gentry1994; Phillips 1996). In a follow-up study, Phillips et al.(1998) found that tree biomass growth (measured via basalarea) exceeded losses from tree death in 38 of 50 Neotropi-cal sites, and suggested that standing Neotropical forestsmay constitute significant carbon sinks, even when analyz-ing a number of possible biases in the data collection (Phil-lips et al. 2002). This conclusion is supported by Grace etal. (1995) and Malhi et al. (1998), whose direct measure-ments over trees of undisturbed tropical rainforest in Brazilshowed that the forest is a net absorber of CO2. While onecannot expect a universal response across sites in thetropics, our study suggests that the Los Tuxtlas rainforest,as exemplified by Diospyros digyna, constitutes a carbonsink in a changing climate.

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