Gerald Moser

Christoph Leuschner

Dietrich Hertel

Sophie Graefe

Susanne Iost

Elevation effects on the carbon budget of tropical mountain forests (S Ecuador): The role of the belowground compartment

Keywords: tropical montane forest, belowground biomass, root production, wood increment, root/shoot ratio aboveground biomass, belowground biomass, fine root production, net 22 primary production, root/shoot ratio, SOC, tropical montane forest, wood increment

Elevation effects on the carbon budget of tropical mountain forests (S Ecuador): The role of the belowground compartment

C Leuschner, Gerald

Carbon storage and sequestration in tropical mountain forests and their dependence on 2 elevation and temperature are not well understood. In an altitudinal transect study in the 3 South Ecuadorian Andes, we tested the hypotheses that (i) aboveground net primary 4 production (ANPP) decreases continuously with elevation due to decreasing 5 temperatures, whereas (ii) belowground productivity (BNPP) remains constant or even 6 increases with elevation due to a shift from light to nutrient limitation of tree growth. [START_REF] Lieberman | Tropical forest structure 8 and composition on a large-scale altitudinal gradient in Costa Rica[END_REF] five tropical mountain forests between 1050 and 3060 m a.s.l., we investigated all major 8 above-and belowground biomass and productivity components, and the stocks of soil 9 organic carbon (SOC). Leaf biomass, stemwood mass and total aboveground biomass 10 (AGB) decreased by 50 to 70%, ANPP by about 70% between 1050 and 3060 m, while 11 stem wood production decreased 20fold. Coarse and large root biomass increased 12 slightly, fine root biomass 4fold, while fine root production (minirhizotron study) [START_REF] Clark | Detecting tropical forests´ responses to global climatic and 14 atmospheric change: current challenges and a way forward[END_REF] roughly doubled between 1050 and 3060 m. The total tree biomass (above-and 14 belowground) decreased from about 320 to 175 Mg dry mass ha -1 , total NPP from ca. 15 13.0 to 8.2 Mg ha -1 yr -1 . The belowground/aboveground ratio of biomass and 16 productivity increased with elevation indicating a shift from light to nutrient limitation 17 of tree growth. We propose that, with increasing elevation, an increasing nitrogen 18 limitation combined with decreasing temperatures causes a large reduction in stand leaf [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF] area resulting in a substantial reduction of canopy carbon gain toward the alpine tree 20 line. We conclude that the marked decrease in tree height, AGB and ANPP with 21 elevation in these mountain forests is caused by both a belowground shift of C 22 allocation and a reduction in C source strength, while a temperature-induced reduction 23 in C sink strength (lowered meristematic activity) seems to be of secondary importance. 24 Tropical rainforests occupy only some 12% of the terrestrial surface but contain about 2 55% of the biomass (Grace & Meir 2009). An accurate characterization of carbon stores 3 and net primary production in tropical forests will be fundamental for realistic global 4 and regional C budgets and for predicting how these will be affected by the changing 5 climate. Not only forest conversion, but also changes in temperature, [CO 2 ] and rainfall 6 may significantly affect the C sequestration potential of tropical forests (Grace et al . 7 1995). 8

There is no simple approach for obtaining information on the possible future response 9 of tropical old-growth rainforests to the expected changes in temperature, rainfall and 10 atmospheric [ CO 2 ]. Field manipulation studies may help to investigate forest responses 11 to altered rainfall and [CO 2 ] (e.g. da [START_REF] Costa | Effect 13 of 7 yr of experimental drought on vegetation dynamics and biomass storage of an 14 eastern Amazonian rainforest[END_REF]), but they are hardly practicable [START_REF] Hölscher | Ecology and use of old-13 growth and recovering montane oak forest in the Cordillera de Talamanca, Costa 14 Rica[END_REF] for studying long-term effects of elevated temperature on tropical forests. One source of 13 indirect information can be transect studies along latitudinal or altitudinal temperature 14 gradients, or meta-analyses of comprehensive data bases on forest ecosystem 15 functioning in different climates. Even though most gradient studies are suffering from 16 the fact that one or more environmental factors covary with the target variable, valuable 17 insights into the temperature dependence of productivity and carbon cycling in forests 18 have been achieved by comparing C pools and fluxes in forests differing in mean 19 temperature (e.g. Clark et al. 2001;[START_REF] Luyssaert | CO 2 16 balance of boreal, temperate, and tropical forests derived from a global database[END_REF]). [START_REF] Aiba | Structure, composition and species diversity in an altitude-21 substrate matrix of rain forest tree communities on Mount Kinabalu[END_REF] The majority of studies assessing C pools and C sequestration in tropical moist forests 21 have been conducted in lowland forests (e.g. [START_REF] Clark | Tropical rain forest tree growth and 22 atmospheric carbon dynamics linked to interannual temperature variation during 23 1984-2000[END_REF]Feeley et al. 2007), while 22 the C stores of tropical mountain forests are less well known. The decrease in tree size 23 with elevation indicates a reduction of the biomass C pool towards higher altitudes, 24 whereas reduced decomposition rates may cause higher amounts of soil organic carbon 25 (SOC) in tropical montane and upper montane forests as compared to lowland stands 26 (e.g. [START_REF] Grubb | A comparison of montane 1 and lowland rain forest in Ecuador. I. The forest structure, physiognomy and 2 floristics[END_REF]Tanner 1981;Schawe et al. 2007). 27 Clark et al. (2001) synthesized the available data on the biomass and productivity of 28 tropical forests based on published data for 39 forest sites. While numerous studies have 29 measured aboveground biomass, stem wood increment and fine litterfall, only very 30 limited or no data exist on other aboveground NPP components such as leaf herbivory, 31 organic leachates or the release of VOCs. More critical, however, is the scarcity of 32 information on belowground biomass and belowground NPP (BNPP). The biomass of 33 only and typically by excavating a few trees or digging a few monoliths (Clark et al. 2 2001). The data base is more comprehensive for fine root biomass (< 2 mm in diameter) 3 with 32 and 19 investigated tropical forest sites listed in the reviews of Vogt et al. 4 (1996) and [START_REF] Jackson | A 27 global analysis of root distribution for terrestrial biomes[END_REF]. A recent data compilation by Finér et al. (in press) 5 contains fine root biomass data from 83 tropical forest stands, mostly from lowland 6 sites. For Amazonian forests, [START_REF] Houghton | The spatial distribution of forest 18 biomass in the Brazilian Amazon[END_REF] report a mean root biomass value 7 of 21% (range 13-26%) of aboveground live tree biomass. 8 Only a small number of studies attempted to quantify fine root production (e.g. 9

Espeleta & Clark 2007; [START_REF] Metcalfe | The effects of water availability on root growth 25 and morphology in an Amazon rainforest[END_REF]), but often with inadequate methods. 10 Empirical data on the coarse root increment of tropical forests are virtually lacking. 11 Clark et al. (2001) proposed a range for the belowground net primary production of 12 tropical forests of 20 to 120% of aboveground NPP, which demonstrates the importance 13 of BNPP in productivity estimates. Such wide ranges in estimated root production 14 reflect the fact that our knowledge on BNPP in tropical forests is very limited causing 15 large uncertainties about carbon balance and C turnover in these forests. 16

In this study along a 2000-m elevation transect in South Ecuador, we collected a 17 unique dataset on above-and belowground biomass fractions and related carbon pools, 18 SOC, and above-and belowground productivity of five mountain forest stands situated 19 at elevations between 1000 and 3000 m a.s.l. The main focus is on root biomass and 20 The stands are situated on moderately steep slopes facing northeast to northwest, 11 except for stand #2 (10° inclination, Table 1). Study plots of 400 m 2 size were selected 12 in forest areas with no or only minimal signs of human influence (as indicated by 13 charcoal, stumps, or the presence of light-demanding pioneer trees). We used the 14 floristic and physiognomic classification system of [START_REF] Balslev | Mapa de vegetación del sur de Ecuador[END_REF] to select 15 forest patches that were representative for the forest vegetation of the respective 16 elevation. Parts of the stand without larger canopy gaps and unaffected by topsoil 17 disturbance due to animal activity were selected for study. Since pedological 18 investigations in Ecuadorian mountain forests had revealed that the soil properties can 19 vary significantly even over short distances, we chose a relatively small plot size of 20 20 m x 20 m. Large plots may thus include stands of considerable structural heterogeneity. 21 The extremely high need of labour for quantifying the root biomass and production 22 did not allow to study more than five stands in the transect. To cope with the problems 23 that arise from the lack of repetition at the stand level and in order to place our results in 24 a broader pan-tropical context, we completed our study with a meta-analysis of 25 altitudinal transect studies in tropical mountain forests . 26 In the study region on the eastern slopes of the Andes, precipitation shows a principal 27 increase with elevation from 1050 m to 3060 m (P. Emck and M. Richter, unpublished 28 data). The soil types change along the gradient due to changes in climate, bedrock type 29 and hydrology (Table 1). The mineral topsoil is moderately to highly acidic with 30 pH(CaCl 2 ) values between 2.9 and 3.9, while the organic top layers have higher pH 31 values and base saturations [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF]). The transect is characterized by a general, but 32 not continuous, increase in organic layer thickness with elevation. The availability of N 33 and 3060 m as is evidenced by decreasing gross N mineralization rates and extractable 2 concentrations of inorganic N [N inorg ], but increasing C/N ratios of the organic material 3 [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF]; Table 1). Such a trend is absent, or even reversed, in the mineral topsoil. 4

However, gross N mineralization rate and [N inorg ] were by a magnitude higher in the 5 organic top layers than in the mineral soil. 6

Along the 2000-m elevation transect, a characteristic change in tree species 7 composition takes place. Only canopy trees belonging to the family of Melastomataceae 8 occurred at all elevations; another five plant families were present at least in four of the 9 five stands. Most other families showed clear preferences for the pre-montane, montane 10 or upper montane belt (J. Homeier, pers. comm.). 11

12

Estimation of aboveground biomass and production 13

The forest structure and tree biometric data were investigated in samples of 80 trees 14 per stand that reached at least the lower canopy, without defining a minimum diameter 15 at breast height (DBH, at 1.3 m). These 80 trees covered an area of 827 m 2 in stand #1, 16 and of 360, 343, 290 and 96 m 2 (in horizontal projection) in the stands #2, 3, 4 and 5, 17 respectively, reflecting the increase in stem density (from 968 to 8317 ha -1 ) with 18 elevation. The smallest DBH of canopy trees was 5 cm at 1050 m and 3 cm at 3060 m. [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF] Along the transect from 1000 to 3000 m, mean DBH decreased to about 40%, canopy 20 height to about 30%, and leaf area index (LAI) to about 35% of its value at 1000 m 21 (Table 1). For more details on stand structure see [START_REF] Moser | Altitudinal changes 30 in stand structure and biomass allocation of tropical mountain forests in relation to 31 microclimate and soil chemistry[END_REF]. 22 Total aboveground tree biomass was estimated with allometric equations for the 80 23 canopy trees per stand based on measured DBH, tree height and wood specific gravity. [START_REF] Metcalfe | The effects of water availability on root growth 25 and morphology in an Amazon rainforest[END_REF] We ignored understorey trees and shrubs, and standing or lying dead trunks (see Wilcke 25 et al. 2005) since understorey biomass in mature tropical moist forests may typically 26 comprise less than 3% of aboveground biomass (Brown 1997). [START_REF] Baker | Increasing biomass in Amazonian forest 28 plots[END_REF] We used the pan-tropical allometric equation of [START_REF] Chave | Tree allometry and improved estimation of 12 carbon stocks and balance in tropical forests[END_REF] for wet tropical 28 forests. This equation estimates the total aboveground tree biomass including leaves, 29 twigs, branches, bark and boles, and bases on data of 2410 harvested trees from all over 30 the tropics. 31 We tested the applicability of this allometric equation to our stands in small samples 32 of three recently wind-thrown tree individuals per each stand, which were analyzed for 33 AGB tree = exp (-2.557 + 0.940 ln(σD 2 H)) 5 6 where AGB tree is the single-tree aboveground biomass (kg per tree), D is DBH (cm), H 7 is tree height (m) and σ is wood specific gravity (g cm -3 ), the latter being measured in a 8 subsample of 20 trees per plot by stem wood coring. We used stand-level means of 9 wood density for the remaining 60 trees because we found for σ a coefficient of 10 variation among the species of a stand of only 15-20%. Total aboveground biomass of 11 the stand (AGB) was calculated as the sum of the 80 trees of a plot. To obtain wood 12 biomass (trunks, branches, twigs), stand leaf biomass (B l ) was determined 13 independently (see below) and subtracted from AGB. 14 Stand leaf biomass was calculated from the measurement of annual leaf litter 15 production. Twelve litter buckets per stand equipped with 50 cm × 50 cm gauze sheets 16 of 1 mm-mesh width were positioned randomly in the 400 m 2 plots. During the 1-yr 17 measuring period, the litter was collected every three weeks in the stands #1 and 2, 18 where decomposition rates were high, and every six weeks in the three other stands, 19 starting on May 26, 2003. For estimating B l , only the tree leaf fraction was considered. 20

The small fractions of epiphyte leaves, leaves of understorey plants (including bamboo), 21 reproductive organs (flowers and fruits), twigs and the residual litter were determined 22 separately; they were included in the fine litter total. 23 We assumed that leaf growth and leaf abscission occurred at similar rates in the study 24 year, i.e. that leaf biomass in May 2003 and in May 2004 were equal. This would imply 25 that annual leaf litter production equalled annual leaf biomass production. 26 Leaf lifespan was recorded by establishing leaf survivorship curves for leaf 27 populations on 10-15 trees per stand that were selected randomly in the plots. In all 28 cases, small individuals (1.5 to 5 m high) of canopy tree species were selected since 29 continuous access to the upper canopy of large trees could not be provided. In the stands 30 #1 to 4, these trees were part of the understorey or lower canopy strata, whereas they 31 formed the uppermost canopy layer in stand #5. In May 2003, 24 twigs were marked in 32 the 10-15 trees of each plot resulting in 254-666 leaves observed per stand. Every three 33 to six weeks, the number of young, mature and dead leaves per marked twig was 1 counted. We registered the survivorship of all leaves of the first census until the last leaf 2 was shed. In the stands #3-5, the average lifespan of many leaves exceeded the 3 observation period of 19 months. In these cases, the average leaf lifespan in the leaf 4 population was obtained from linear extrapolation of the survivorship curves. Stand leaf 5 biomass (in Mg ha -1 ) was then calculated from equation ( 2 Annual stem wood production was calculated as the difference in wood biomass in May 17 2003 and in May 2004. 18 19

Measurement of root biomass and estimation of root production 20

The biomass of coarse and large roots (all roots > 2 mm in diameter) was determined 21 in 12-16 soil pits (40 cm × 40 cm) per stand that were dug to 60 cm soil depth. The 22 position of the pits was chosen randomly in the stands for obtaining stand-level 23 estimates of root biomass in the larger root diameter classes. Minimum stem distance 24 was 1 m to stay outside the reach of root buttresses and adventitious roots. [START_REF] Culmsee | Forest aboveground biomass 26 along an altitudinal transect in Sulawesi, Indonesia, and the role of extra-tropical 27 Fagaceae[END_REF] Consequently, our stand-level averages are most likely underestimates of coarse and 26 large root biomass (termed 'coarse roots' hereafter) because the root stocks of the trees 27 were not excavated. The root mass (biomass and necromass) in the soil pits was 28 extracted in steps of 10 cm-thick soil layers in the organic layer and the mineral soil. In 29 the laboratory, all coarse roots were washed and dried at 70 °C to constant dry mass. [START_REF] Duivenvoorden | A land-ecological study of soils, vegetation, and 31 plant diversity in Colombian Amazonia[END_REF] For analysing the bio-and necromass of roots < 2 mm in diameter (fine roots) in the 31 five stands, soil coring was conducted from March to May 2003 in soil profiles of 30 32 cm depth (organic layers and mineral soil, n = 20 per stand). A preliminary 33

F o r R e v i e w O n l y 9
investigation of a smaller number of soil cores to 60-80 cm depth had shown that at 1 least 75% of the profile total of tree fine root biomass was contained in the organic 2 layers and the mineral soil to 30 cm depth. Consequently, the fine root densities in the 3 subsoil were very low. In this study, only the profile totals of fine root biomass from the 4 organic layers and the mineral soil to 30 cm depth are considered. 5

Root sampling was conducted with a 33 mm wide and 50 mm long steel corer. The 6 soil material was stored at 4 °C in the laboratory of the Estación Científica San 7 Francisco, where processing took place within 30 days. Fine root biomass and 8 necromass were separated under a microscope according to the procedure described by 9

Leuschner et al. (2001). In this paper, only fine root biomass will be considered. For 10 details on fine root necromass and root decomposition see Moser et mm at random positions in each of the five stands. They were placed vertically to the 16 soil surface and installed to a depth of ca. 40 cm wherever possible. 17

In this study, only the uppermost 10 cm of the tube in the organic layers or mineral 18 topsoil were analyzed for fine root dynamics, because the very high stone content of the 19 mineral soil in the lowermost stand did not allow a deeper penetration of the tubes into 20 the soil at several measuring locations. For monitoring root growth, a root scanner 21 system (CI-600 Root Growth Monitoring System, CID Inc., USA) was inserted into the 22 tubes at monthly intervals from June 2005 to January 2007. However, only data from 23 November 2005 onwards were considered in the analysis in order to minimize errors in 24 root production estimation caused by disturbance effects during tube installation. The 25 images were analyzed for changes in fine root length using the software WinRHIZO 26 Tron (Régent, Quebec, Canada). Relative increases and relative losses in root length 27 (unit: cm cm -1 mo -1 ) were calculated by relating root length increase or root length loss 28 between two observation dates to the root length visible at the previous measuring date 29 (Graefe et al. 2008a). By relating this data to 12 months, we estimated the annual root 30 length production of the visible fine root population in the rhizotron tubes (Nadelhoffer 31 2000). By means of the root productivity in the uppermost 10 cm of the soil and the 32 For two reasons we assume that the P FR figure for the uppermost stand (3060 m) 3 derived from the minirhizotron data is an overestimate (Moser et al., in press). [START_REF] Ch | Large altitudinal 5 increase in tree root/shoot ratio in tropical mountain forests of Ecuador[END_REF] Consequently, we replaced these values by a lower production figure that was 5 calculated by extrapolating the P FR data of the stands #1-4 to 3060 m. The first reason is 6 that root growth and death events observed in the minirhizotron tubes in the uppermost 7 10 cm of the soil profile may not be representative for the root mass in the entire soil 8 profile, in particular in the very thick, acidic and moist organic soils at 3060 m. Second, 9 P FR could be overestimated at 3060 m because fine root growth is slower in lower 10 temperatures at higher elevations with the consequence that fine root initiation and 11 death in high-elevation forests require longer periods for reaching a steady state at the 12 tube surfaces than in low-elevation forests (Graefe et al. 2008b). Thus, slow-growing 13 roots at 3060 m could still have been in the recovery phase after the disturbance by the 14 tube installation. As a consequence, all subsequent calculations were conducted with the 15 extrapolated (conservative) fine root production (4.7 Mg ha -1 yr -1 ) and total BNPP 16 values (5.1 Mg ha -1 yr -1 ) for the 3060 m stand. 17

Measurement of soil organic carbon pools 30

Eighteen soil cores were extracted at random positions in each stand in April 2004; the 31 organic layer horizons were sampled using a 20 cm × 20 cm wooden frame. The two 32 organic layer horizons separated during soil sampling were designated as Oi (recently 33

F o r R e v i e w O n l y 11
shed litter) and OeOa (strongly decomposed material with no visible structure). The 1 latter horizon consisted of small aggregates of humic substances and a high density of 2 fine root mass. Mineral soil was sampled to a depth of 30 cm below the transition zone 3 from the organic OeOa to the mineral topsoil. At the majority of coring locations, the 4 bedrock was reached at this depth. The samples were taken with a soil auger of 10 cm in 5 diameter. For each horizon and stand, six composite samples were assembled from three 6 individual samples each. These composite samples were subject for further analysis. 7

During soil sampling organic layer thickness was determined at each sampling point. 8

The samples were transported in polyethylene (PE) bags to the laboratory of the ECSF 9 and weighed for the determination of soil dry mass. The soil was then homogenized by 10 hand, which involved cutting of the litter layer in approximately 1 cm × 1 cm pieces. 11

Stones, coarse woody debris and roots were removed carefully. Subsequently, the 12 samples were transported to Germany via airplane within one week and immediately 13 processed in the laboratories of the Institute for Soil Science and Site Ecology of 14 Dresden University of Technology. During transport the samples were cooled to 15 approximately 10 °C and care was taken that the temperature of the samples did not rise 16 above the average temperature at the location of origin. We did not freeze the soil 17 material because we expected that such a treatment would affect the soil microbial 18 community of tropical soils more severely than cooling for several days would do. [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF] Due to the nature of the bedrocks and the low pH of the mineral soil, the soils were free 20 of carbonate. Thus, all carbon in the soil is organic C (SOC). For the determination of 21 SOC an aliquot of each sample was dried (40 °C mineral soil; 60 °C organic layers) and 22 milled (vibratory disc mill RS 100, Retsch, Germany). Organic layer samples were 23 milled at 700 rpm for 45 s and mineral soil samples at 1400 rpm for 60 s. After milling, 24 the samples were dried again overnight at 40 °C. The amount of carbon was determined 25 by a thermal conductivity sensor after complete dry combustion at 1150 °C (CNS-26 Analyzer vario EL III, elementar, Hanau, Germany). The stocks of SOC were expressed 27 in kg ha -1 per horizon and as profile totals (organic layers plus mineral soil to 30 cm 28 depth). 29

The salt-extractable inorganic nitrogen concentration [N inorg ] was analysed in KCl-30 extracts of the organic layers and the mineral soil horizons twice in 2004. 10 g of 31 mineral soil or 5 g of organic layer material were suspended in 100 ml 0.1 M KCl-32 solution and shaken for two hours (180 rpm). The concentrations of nitrate and 33

Statistical analyses 5

Most of the aggregate data presented in this study refer to stand level data of C pools 6 and fluxes in a single forest stand per elevation. To cope with the problem of lacking 7 repetition on the stand level, we additionally conducted a meta-analysis of altitudinal 8 transect studies in tropical forests and analysed this data set in a similar way as the 9 Ecuadorian transect data. Linear and simple non-linear regression analyses were applied 10 to identify significant effects of elevation, mean air temperature, annual precipitation, 11 soil moisture, proton concentration of the mineral soil, and C/N ratio of the organic 12 layers on various biomass and production fractions. Additional regression analyses were 13 performed to search for significant correlations of these environmental factors with 14 elevation. All calculations were done using Xact software (SciLab, Hamburg, Germany, 15 version 8.0). For certain biomass and production fractions, differences between the five 16 stands were analysed with a non-parametric analysis of variance (Kruskal-Wallis test) 17 and a subsequent Mann-Whitney two-sample test (U-test) using the package SAS, 18 version 8.2 (SAS Institute, Cary, NC, USA). 19 [START_REF] Aiba | Structure, composition and species diversity in an altitude-21 substrate matrix of rain forest tree communities on Mount Kinabalu[END_REF]

21

RESULTS

22

Altitudinal trends in tree biomass and productivity 23

Total above-and belowground tree biomass decreased from 317 to 174 Mg dry mass 24 ha -1 (or 154 to 87 Mg C ha -1 ) between 1050 and 3060 m elevation, showing the 25 minimum at 2380 m a.s.l., where stem density was markedly smaller than in the 26 uppermost stand while mean tree height was relatively low. Aboveground live biomass 27 (AGB) decreased to about 60% of its value at 1050 m between 1050 and 1890 m 28 elevation and showed a further reduction to 40% in the uppermost stand at 3060 m 29 (Table 2). The stand total of tree leaf biomass increased with elevation in the lower part 30 of the transect from 6.8 (1050 m) to 9.7 Mg ha -1 (1890 m), but showed a sharp decrease 31 higher upslope to 3.6 Mg ha -1 at 3060 m. In contrast to AGB, belowground tree biomass 32 (BGB) nearly doubled between 1050 and 3060 m (32 to 63 Mg ha -1 ), being more or less 33 remained constant between 1050 and 2380 m and increased only higher upslope, fine 3 root biomass (d < 2 mm) showed a more or less continuous increase from 2.7 Mg ha -1 4 (1050 m) to 10.8 Mg ha -1 (3060 m). The proportion of leaf biomass in total biomass 5 remained unchanged between 1050 and 3060 m (2%), while fine root biomass 6 contributed by less than 1% at 1050 m and increased to about 6% at 3060 m. Total root 7 biomass (fine and coarse) accounted for roughly 10% of total biomass at 1050 m 8 (equivalent to a root/shoot biomass ratio of only 0.11), while roots contributed by about 9 35% to total biomass at 3060 m, yielding a R/S ratio > 0.5. 10

The production of leaf biomass was by far the most important single component of 11 aboveground productivity (ANPP) in all five forest stands, contributing by 50 to 65% to 12 ANPP. Only 5 to 25% of ANPP referred to wood growth which reached annual rates of 13 2.8 to 0.1 Mg dry mass ha -1 yr -1 or 1.4 to < 0.1 Mg C ha -1 yr -1 in the stands (Table 2). 14 Wood increment showed a steeper elevational decrease from 1050 to 3060 m (to about 15 5% of the value at 1050 m) than leaf production (reduction to about 35%). Moreover, 16 broken and abscised twigs and non-tree litter components (such as fallen epiphytes) 17 represented a larger carbon sink in the two uppermost stands (2380 and 3060 m) than 18 stem wood production. While wood production showed a more or less continuous 19 decrease from 1050 to 3060 m, leaf production remained stable up to 1890 m, but 20 dropped markedly higher upslope between 1890 and 3060 m. 21 Similar to root biomass, root productivity deviated in its vertical pattern from that of 22 ANPP. Coarse and large root increment as estimated from dendrometer readings and 23 root biomass excavations showed a substantial variation among the five stands but 24 revealed no significant trend with elevation. However, the highest coarse root 25 productivity was recorded in the stands at 3060 m and 1540 m elevation where the wind 26 exposure is higher than in the other three stands. Fine root production (P FR ) as estimated 27 from minirhizotron observations and root coring data was roughly 10 times larger than 28 coarse root production and showed a significant increase from 1050 m (2.3 Mg ha -1 yr -1 ) 29 to 3060 m (9.4 Mg ha -1 yr -1 ). Adding coarse and fine root production data gave total 30 belowground productivity (BNPP) figures in the range of 2.5 to 4.0 Mg ha -1 yr -1 for the 31 stands #1-4, but a much higher productivity (>10 Mg ha -1 yr -1 ) for the uppermost stand. [START_REF] Körner | A world-wide study of high altitude treeline temperatures[END_REF] When considering the more plausible conservative P FR estimate for the 3060 m stand 33 1 yr -1 in the uppermost stand which is still higher than at the four lower elevations. 2

Total NPP as the sum of ANPP and BNPP showed no trend over the 2000-m elevation 3 distance: for the stands at 1050, 1540, 1890 and 3060 m, very similar figures (12.4 -4 13.1 Mg dry mass ha -1 yr -1 or 6.1 -6.6 Mg C ha -1 yr -1 ) were calculated. A significantly 5 smaller NPP total was found only for stand #4 at 2380 m (7.9 Mg dry mass ha -1 yr -1 ) 6 and stand #5 at 3060 m, if the conservative P FR value is used (8.2 Mg ha -1 yr -1 ). The 7 marked decrease in ANPP along the slope, which is mainly caused by a reduction in 8 wood and leaf production, was at least partly compensated by a higher fine and coarse 9 root production at higher elevations. 10 11

Possible factors underlying the elevation effect on biomass and productivity 12

With a few exceptions (leaf biomass, non-tree litter), all aboveground biomass and 13 production components showed a significant negative correlation with elevation, while 14 this relationship was positive for fine root biomass and fine root productivity, either in a 15 linear or a non-linear way (Table 3). However, most of the investigated climatological 16 and edaphic factors were tightly correlated among each other, except for precipitation 17 with a close relation only to soil moisture, VPD and soil C/N ratio (Table 4). The 18 covariation among elevation, mean temperature, mean VPD and soil C/N ratio was 19 particularly strong. Consequently, the biomass and productivity components 20 investigated showed a similarly close relation to soil C/N ratio, temperature and VPD as 21 to elevation. Moreover, most of the biomass and production parameters revealed an 22 even tighter association with the C/N ratio of the organic Oi horizon than to elevation or 23 temperature. In contrast, the weakest correlation was detected between biomass or 24 productivity and precipitation (Table 3). [START_REF] Culmsee | Forest aboveground biomass 26 along an altitudinal transect in Sulawesi, Indonesia, and the role of extra-tropical 27 Fagaceae[END_REF] 26

Stocks of soil organic carbon 27

The carbon stocks in the organic layers ranged between 11 Mg C ha -1 at 1050 m and 28 75 Mg ha -1 at 3060 m and reflected the general increase in organic layer depth with 29 increasing altitude (Table 1). In the 0-30 cm horizon of the mineral soil, the SOC pools 30 varied between 61 and 128 Mg C ha -1 with no significant elevational trend visible. The 31 total C stocks of organic layers and mineral soil varied between 106 Mg C ha -1 (stand 32 Elevational change in primary production [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF] Our study provides data not only on fine, coarse and large root biomass, but also on 20 root productivity using up-to-date approaches of fine root growth measurement. Thus, 21 we were able to analyze changes in total NPP (above-and belowground) with elevation, 22 instead of focusing on aboveground productivity only, which must lead to wrong 23 conclusions. [START_REF] Metcalfe | The effects of water availability on root growth 25 and morphology in an Amazon rainforest[END_REF] Stem wood increment showed a continuous and steep decline with elevation in this 25 transect which exceeded the reduction in annual leaf biomass production and canopy 26 fine litter fall. The data of seven other transect studies in the meta-analysis support these 27 altitudinal trends in stem wood and leaf production (Fig. 2B and2C). While the absolute 28 ANPP figures for a certain elevation differed more than fivefold among the sites due to 29 floristic, climatic and edaphic differences between the study regions, leaf production 30 was much less variable across this pan-tropical data set. Carbon allocation to leaves 31 must be a C sink of higher priority than stem wood growth in tropical mountain trees, 32 because it is needed to maintain a sufficiently large leaf area. 33

F o r R e v i e w O n l y 17
The elevational decrease in ANPP components contrasts with belowground 1 productivity which may consume similar or larger amounts of carbohydrates than wood 2 production in the Ecuadorian transect. At least in the two uppermost stands, a neglect of 3 root production would have led to unrealistic conclusions on the productivity of the 4 forests. When considering only the four stands between 1050 and 2380 m, we found 5 based on the minirhizotron approach a significant increase in P FR with elevation (from 6 2.3 to 3.7 Mg ha -1 yr -1 ). By including the much higher production value for the 7 uppermost stand at 3060 m (9.4 Mg ha -1 yr -1 ), even an exponential increase in P FR with 8 altitude appears. For several reasons, however, we assumed that the figure of 9.4 Mg ha - 9 1 yr -1 for the uppermost stand represents an overestimation of root productivity and we 10 consequently used a more conservative P FR value for this stand by extrapolating the 11 linear trend of the four lowermost stands to 3060 m (see Material and Methods section). 12 This reduced fine root production estimate for the uppermost stand (4.4 Mg ha -1 yr -1 ) 13 appears much more plausible than the original high value, given that canopy carbon 14 Despite great efforts to measure above-and belowground biomass and production as 3 precisely as possible, we were not able to quantify all relevant plant-related carbon 4 sinks. In particular, we ignored processes such as above-and belowground herbivory, 5 rhizodeposition, C transfer to mycorrhizal hyphae, and emission of volatile organic 6 compounds that, in most cases, have not yet been quantified in tropical forests ( ). This indicates that wood production is increasingly limited by environmental 16 constraints or assimilate shortage when approaching the uppermost limit of tree growth. 17

Bruijnzeel & Veneklaas (1998) proposed various environmental factors that could be 18 responsible for a growth reduction of tropical trees at higher elevations, among them (1) 19 reduced leaf temperatures and their effects on carbon gain, (2) periodic water shortage, 20

(3) temporal soil hypoxia resulting in reduced root activity, (4) nutrient shortage and/or 21 nutrient uptake limitation, (5) high concentrations of phenolic substances in the soil, [START_REF] Hertel | Fine root mass and fine root production in tropical moist 7 forests as dependent on soil, climate and elevation[END_REF] 22 high doses of UV-b radiation, and (7) exposure to strong winds. In the following, we 23 focus on factors directly or indirectly related to the acquisition and investment of carbon 24 for tree growth. [START_REF] Culmsee | Forest aboveground biomass 26 along an altitudinal transect in Sulawesi, Indonesia, and the role of extra-tropical 27 Fagaceae[END_REF] The NPP decrease along mountain slopes, as observed in this study, could have 26 different reasons: (i) a reduction in C source strength, i.e. decreased canopy carbon gain 27 at higher elevations, (ii) increased C consumption by plant respiration, and (iii) reduced 28 C sink strength, i.e. environmentally-induced reductions in tree growth at higher 29 elevations despite sufficient carbohydrate supply. Canopy carbon gain undoubtedly 30 decreases markedly with elevation in this transect, simply because the LAI at 3060 m 31 reaches only 40% of the stand leaf area at 1050 m. We estimate that the annual canopy 32 assimilation must decline by at least 50% between 1050 and 3060 m because light-33 Forest NPP could also decrease with elevation if plant respiration losses (relative to C 3 gain) were increasing with elevation. This possibility can definitely be excluded. A 4 rough extrapolation of stem wood and soil (and root) respiration measurements to the 5 stand level indicates that wood respiration must have decreased at least to a quarter of 6 its rate at 1050 m (Zach et al. 2008). Soil (and included root) respiration declined even 7 more rapidly than wood respiration [START_REF] Iost | Gradients in a 24 tropical mountain ecosystem of Ecuador[END_REF], leaving relatively more of the 8 assimilated carbohydrates for NPP at 3060 m than at 1050 m. 9

Whether sink limitation of growth, i.e. reduced meristematic activity of high-elevation 10 trees, is responsible for the reduction in NPP, may ultimately be decided only on the 11 basis of physiological studies in the laboratory. Indirect evidence from the Ecuador 12 transect seems to indicate that stem wood cambial activity is reduced with elevation 13 independently of carbohydrate supply because stem wood increment decreased much 14 more rapidly between 1050 and 3060 m (to 5% of its value at 1050 m) than did the leaf 15 area index as an estimator of canopy carbon gain (to about 35%). However, we also 16 observed a marked increase, perhaps a doubling, of fine root production from 1050 to 17 3060 m elevation which contradicts the assumption that the C sink caused by tree 18 meristematic activity is reduced from low to high elevation due to the temperature 19 reduction from 19 to 9 °C. The minirhizotron observations showed that the fine roots 20 grew indeed more slowly at higher elevation, but turned over as rapidly as at 1050 m 21 due to a reduced longevity (see Table 5). More important, the fine root system of the 22 stand at 3060 m was four times larger than that at 1050 m, resulting in a larger C sink 23 strength at higher than at lower elevations (Graefe et al. 2008b). It is not very likely that 24 stem wood growth is reduced due to environmental limitation of meristematic activity 25 but fine root growth of the same tree is not. 26 We conclude that the reduction in NPP by roughly 40% between 1050 and 3060 m 27 cannot primarily be attributed to a C sink limitation of tree growth. A much more 28 plausible explanation is that C source limitation is the predominant cause, i.e. an 29 elevational decrease in canopy carbon gain, which increasingly limits tree growth 30 Increasing C source limitation at higher elevation in the Ecuadorian mountain forests 3 is mostly a consequence of a reduction in leaf area, and not of reduced photosynthetic 4 activity. From foliar nutrient concentrations and soil chemical data, we conclude that a 5 combined effect of increasing N limitation and decreasing temperatures with increasing 6 elevation must primarily be responsible for this marked leaf area reduction. A large 7 reduction in the mass-specific gross N mineralization rate in the organic topsoil 8 measured by the 15 N pool dilution approach was found to be associated with a marked 9 increase in the C/N ratio (from 22 to 63 g g -1 ) of the organic top layer, and a 20-fold 10 decrease in the concentration of KCl-extractable inorganic N between 1050 and 3060 m 11 [START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF]). While N availability decreased markedly with elevation on a soil mass 12 basis, a much slighter decrease, or perhaps no change, was detected when N 13 mineralization was related to ground area because the depth of the organic layers 14 increased. Thus, the root systems of the high-elevation forests face a greatly reduced N 15 supply density (N release per soil volume) which may require the build-up of a more 16 extended and costly root system to maintain nutrient uptake. This could explain the 17 extraordinarily high amount of fine root biomass in these soils. 18 Nitrogen limitation of tree growth in general, and of leaf growth in particular, is 19 further indicated by a considerable decrease of foliar N concentrations and SLA in 20 upslope direction, and a concomitant increase in leaf longevity toward the uppermost 21 stand (see Table 5). Smaller and thicker leaves with lower N concentration are a typical 22 attribute of tropical trees at high elevations (Grubb & Tanner 1976, Grubb 1977). 23 Besides N shortage, harsh environments with cold nights and high radiation intensities, 24 as they occur in high-altitude environments, may also be the cause of leaves with high 25 C/N ratios and low SLA. However, extreme climatic factors as a cause of the formation 26 of durable, carbon-rich tree leaves could not explain why the trees at high elevations in 27

Ecuador reduce their stand leaf area, instead of forming a larger number of smaller 28 leaves adapted to the harsh environment, thereby compensating for the reduction in 29 individual leaf size. Moreover, the N pool in stand leaf biomass decreased to about 33% 30 between 1050 and 3060 m in this transect (see Table 5) indicating that the formation of 31 new leaves and/or the process of leaf expansion are increasingly limited by N shortage 32 F o r R e v i e w O n l y 21 toward higher elevations. This is support for the assumption that N limitation is the 1 primary cause of the marked leaf area and NPP reduction with elevation in this transect. 2

Increasing N limitation with elevation should also be the cause of the tremendous C 3 allocation shift from above-to belowground organs observed in our transect. Following 4 the resource balance hypothesis formulated by [START_REF] Bloom | Resource limitation in plants -an 32 economic analogy[END_REF], this shift is best 5 explained by a growing importance of limiting soil resources with increasing elevation. 6

Increasing C and nutrient allocation to roots may represent a compensatory measure of 7 the trees to cope with increasing growth limitation by nutrient shortage with elevation, 8 and in the case of the coarse and large root system, by the growing need for stable 9 anchorage due to high wind loads. Interestingly, Duivenvoorden and Lips (1995) 10 observed a similarly large shift of C allocation to roots in Amazonian lowland forests as 11 nutrient availability decreased. Girardin et al. (2010, in press) reported a more than 12 threefold increase in fine root biomass between 200 and 3000 m elevation in a Peruvian 13 altitudinal transect. In contrast, they observed a decrease, and not an increase, in fine 14 root production with elevation. Additional transect studies investigating the C balance 15 of tropical mountain forests are needed to draw more general conclusions on altitudinal 16 trends in belowground productivity. 17 We conclude that carbon budgets of tropical mountain forests, that ignore root 25 biomass and root productivity, will lead to wrong conclusions on the size and altitudinal 26 change of C storage and C sequestration in these ecosystems. High-elevation forests in 27 south Ecuador contain relatively large C stocks in biomass and soil despite their low 28 stunted stature, which is a consequence of large SOC pools and a high root biomass. 29 Aboveground and belowground biomass and productivity show opposite altitudinal 30 trends indicating a shift from predominant light to nutrient (N) limitation of tree growth 31 with increasing elevation. The large reduction in stand leaf area with elevation is most 32 likely a consequence of a more pronounced N limitation at higher elevations. We 33 Comments by four anonymous reviewers greatly improved the manuscript. 17 NPP per tree biomass (%)

  by both a belowground shift of C allocation and a reduction in C source strength, while a temperature-induced reduction in C sink strength (lowered meristematic activity) seems to be of secondary importance.

  roots (i.e. roots > 2 mm in diameter) was measured at very few sites 1

  root productivity, the fractions with largest uncertainties. 21 Based on earlier work in the area (Leuschner et al. 2007; Moser et al. 2007; Graefe et 22 al. 2008a, b), we hypothesized that (i) aboveground NPP decreases continuously with 23 elevation driven by the more or less constant temperature decrease, whereas (ii) 24 belowground NPP remains constant or increases with altitude, reflecting a change in 25 resource limitation from predominant light limitation at low elevations to an increasing 26 nutrient limitation at high elevations. Several other environmental parameters were also 27 measured along this transect for identifying putative underlying causes of elevational 28 change in biomass and productivity. permanent forest plots between 1050 m and 3060 m a.s.l. at a 1 maximum distance to each other of 30 km in the South Ecuadorian provinces of 2 Zamora-Chinchipe and Loja. The lowermost stands #1 and 2 are within the Podocarpus 3 National Park at pre-montane elevation close to the park entrance at Bombuscaro, south 4 of the provincial capital Zamora (#1: S 04°06'54'', W 78°58'20''; #2: S04° 06'42'', W 5 78°58'20''). Stands #3 and 4 (montane elevation) are located in the adjacent Reserva 6 Biológica San Francisco (#3: S 03°58'35'', W 79°04'55''; #4: S 03°59'19'', W 7 79°04'55''). Stand #5 is a stunted upper montane forest located in the Cajanuma area of 8 the national park (S 04°06'771'', W 79°10'58''). Patches of treeless alpine paramo 9 vegetation are found about 200 m upslope of this stand (Fig.1). 10

  rooted uppermost organic horizons markedly decreased between 1050 1

  DBH, wood volume and wood specific gravity. The biomass figures were 1 sufficiently close to the predictions of the Chave equation which calculates the total 2 aboveground live biomass of a tree from:

  being the annual leaf litter production (in Mg ha -1 yr -1 ) and D l the average leaf 10 lifespan (in yr). The specific leaf area (SLA) and leaf N content per leaf area or leaf dry 11 mass were measured in six representative sun canopy leaf samples of each of the five 12 stands. Stand leaf area index (LAI) was calculated by multiplying B l with the stand 13 mean of SLA (Tab.1; Moser et al. 2007). 14 Stem growth was measured with 80 dendrometer tapes (UMS, Ibbenbühren, Germany; 15 resolution 0.1 mm) per stand that were read every six weeks starting in May 2003. 16

  the organic layers and the mineral topsoil (0-30 cm) we estimated 1 the fine root production in the soil profile (P FR ). 2

  Coarse root production was measured with 20 dendrometer tapes per stand, mounted 18 on superficially growing coarse and large roots at diameters in the range 20-300 mm.[START_REF] Iost | Soil respiration, microbial respiration and mineralisation in soils of 20 montane rainforests of Southern Ecuador: influence of altitude[END_REF] The tapes were read every six weeks, starting in May 2003. From diameter increment, 20 we calculated the relative volume increment of each measured coarse root segment.21 Based on the coarse root biomass data obtained in the soil pits, stand totals of coarse 22 root production were calculated (for details see Soethe et al.2006a, b).23 For expressing the biomass stocks and productivity components in terms of carbon, 24 we analyzed the C concentration in sub-samples of all biomass fractions using a CN 25 auto-analyzer (Vario EL III, elementar, Hanau, Germany) at the University of Göttingen 26 (live fine and coarse roots, stem wood, fine root and leaf litter: n = 20, leaves: n = 10-20 27 per stand). 2829

  determined photometrically with a continuous flow autoanalyzer 1 (Skalar Analytik GmbH, Germany). Nitrite was not considered separately but was 2 included in the nitrate fraction. 3 4

  and 2380 m and showing a large increase toward the uppermost 1 stand at 3060 m. While coarse and large root biomass (all roots > 2mm in diameter) 2

4

 4 Mg ha -1 yr -1 , see Material and Methods section), BNPP was estimated at 5.3 Mg ha - 1

4 DISCUSSION 5

 45 and 204 Mg ha -1 (stand #5) with no trend between 1050 and 2380 m and a very high 1 value close to the alpine timberline at 3060 m. 2 3 Elevational changes in biomass and soil carbon stocks 6 Our study is the first to investigate synchronously all major aboveground and 7 belowground biomass and production components in a long altitudinal transect in 8 tropical mountain forests. Other transect studies in tropical mountains (Hawaii: Raich et 9 al. 1997; Sabah, Malaysia: Kitayama & Aiba 2002; Puerto Rico: Weaver & Murphy 10 1990, Wang et al. 2003; Sulawesi, Indonesia: Culmsee et al. 2010) were less complete, 11 in most cases focusing only on aboveground compartments and often covering shorter 12 altitudinal distances. Root biomass was only investigated in the transects on Mt. 13 Kinabalu in Sabah and recently in the Peruvian Andes (Girardin et al., in press). 14 According to figure 2A, aboveground live biomass (AGB) tended to decrease with 15 elevation in all cited longer tropical mountain transects. The decrease was, however, not 16 always continuous with elevation, which may result from a marked tree species turnover 17 along the slope (as in Ecuador) or due to inadequate sampling of the local topographic 18 variability. Due to the large scatter in the biomass data of the seven transects, the pooled 19 data of the meta-analysis showed no significant AGB decrease between 500 and 3000 m 20 a.s.l. 21 One striking result of the Ecuador transect study is the more than fourfold increase in 22 standing fine root biomass from 1050 to 3060 m elevation. The few existing data on 23 root biomass in tropical mountain forests also indicate that fine root biomass does 24 increase, and not decrease, with elevation, which contrasts with the altitudinal patterns 25 found for AGB (Leuschner et al. 2007). A positive altitudinal trend in root biomass was 26 also reported from the transect studies by Kitayama & Aiba (2002) on the slopes of Mt. 27 Kinabalu and by Girardin et al. (2010, in press) in the Peruvian Andes. A compilation of 28 literature data of root biomass in tropical forest stands at different altitudes also supports 29 this finding (Hertel & Leuschner 2010). 30The Ecuadorian transect is also the first to provide detailed information on altitudinal 31 trends in coarse and large root biomass, and total root biomass. Clearly, our coarse root 32 data are doubtlessly underestimated in particular in the case of the lowermost stands 33 are lower, because the data base on excavations in soil pits at a 1 minimum stem distance of 1 m. We expect that the coarse and large root biomass 2 directly under the stems is greater than at larger stem distance. Consequently, the stand 3 averages of coarse and large root biomass should be higher than measured, particularly 4 in the stands # 1-3. Our data and those ofSoethe et al. (2006a, b) indicate that trees 5 develop greater amounts of coarse and large root biomass at sites with elevated wind 6 exposure, where a good anchorage is important. 7The carbon stocks in live tree biomass (above-and belowground) decreased from 154 8 (1050 m) to 87 Mg C ha -1 (3060 m) in the Ecuadorian transect, while the total C pool (C 9 stocks in biomass and soil) showed no significant elevational trend (range: 188 -291 10 Mg C ha -1 ). Remarkably, the largest ecosystem C pool was detected in the uppermost 11 stand (3060 m) close to the alpine tree line. Given that Amazonian lowland forests store 12 on average about 210 Mg C ha -1 in biomass (above-and belowground,Malhi et al. 13 2006) and 98 Mg C ha -1 in the soil (0-1 m, Batjes & Dijkshoorn 1999), our data indicate 14 that neotropical high-elevation forests can also contain substantial amounts of C in 15 biomass and soil despite a relatively small tree size. Inventories in other tropical 16 mountain forests are needed to confirm this assumption. 17

18

 18

  gain decreases by at least 50% from 1050 to 3060 m[START_REF] Moser | Altitudinal change in LAI and stand leaf 27 biomass in tropical montane forests -a transect study in Ecuador and a pan-tropical 28 meta-analysis[END_REF].15 Along the transect, fine root production correlated positively with elevation and with 16 variables indicating poor nutrient availability (i.e. high soil acidity, high C/N ratio and 17 high soil moisture). These factors are known to reduce fine root longevity (Eissenstat & 18 Yanai 1997; Eissenstat et al. 2000) and thus could have increased fine root mortality in 19 the soils at high elevations, thereby promoting fine root growth for compensating the 20 root mass loss. Further, there is the possibility that fine root growth is stimulated in the 21 high-elevation soils by the lowered mass-specific mineralization rates which reduce the 22 N (and P) supply rates per soil volume, but which could promote the exploration of 23 additional soil patches by root extension growth. Nutrient addition experiments are 24 needed to clarify what factors are responsible for the high values of fine root biomass 25 and productivity in the Ecuadorian upper montane forests. 26Adding the aboveground and belowground production figures allows to estimate stand 27 net primary production (NPP) and the related sequestration of carbon. NPP as the 28 difference between canopy carbon gain and total plant respiration was approximated 29 here by adding all biomass increment terms that were measured in the study. Based on 30 the most likely estimate of fine root production, our data indicate only minor or no 31 change in NPP from 1050 to 1890 m (13.1 -12.4 Mg dry mass ha -1 yr -1 ), but a marked 32 1890 to 3060 m (to about 8.2 Mg ha -1 yr -1 ), yielding a 1 reduction in NPP by about 40% between 1050 and 3060 m. 2

Clark et 7 8 9

 78 al. 2001a, b).Is tree growth limited by C sink or C source strength at high elevations? 10A more or less continuous decrease of tree height with elevation is perhaps the most 11 obvious structural change occurring in our 2000-m altitudinal transect. In many other 12 mountain forests, tropical and temperate, tree size tends to decrease with altitude more 13 or less continuously, and not abruptly, toward the alpine tree line (Liebermann et al. 14 1996; Raich et al. 1997; Aiba & Kitayama 1999; Pollmann & Hildebrand 2005; Shi et 15 al. 2008

  rate (leaf-area basis) does not change significantly along 1 the 2000-m elevation distance (B. Wittig, pers. comm.). 2

  towards higher elevation, though at different intensities in the aboveground and 31 belowground tree compartments. It is striking that estimated canopy C gain andNPP 32 seem to decrease at roughly similar rates between 1050 and 3060 m (by about 40 and > 33 ). Nevertheless, co-limitation of tree growth by reduced C source 1 strength cannot be excluded. 2

  Yet, we cannot rule out that other factors such as increasing soil moisture and more 18 frequent soil hypoxia are also contributing to the observed reduction in LAI and the 19 increase in R/S ratio with elevation, since LAI and R/S showed a close relation to those 20 factors as well. Multi-factorial growth experiments with tropical trees are needed to 21 disentangle the physiological effects of those environmental factors that change in 22 concert along tropical mountain slopes. 23 24

7 ACKNOWLEDGEMENTS 8

 78 photosynthetically active radiation and P. Emck & M. Richter, University of Erlangen, 12 for precipitation data. We are grateful to the Fundación Científica San Francisco 13 (Nature and Culture International) for the permission to work in the RBSF and ECSF, to 14 the Ministerio del Ambiente in Quito for research permits and to the Deutsche 15 Forschungsgemeinschaft (DFG) for financial funding within the Research Unit 402. 16

8 FAO ( 2007 ) 27 of

 8200727 1997) Estimating biomass and biomass change of tropical forests: a primer. 1 FAO Forestry Paper, 134. 2 Bruijnzeel IA, Procter J (1995) Hydrology and biogeochemistry of tropical montane 3 cloud forest: what do we really know? In: Tropical montane cloud forests (eds 4 Lawrence HS, Juvrik JO, Scatena FN), pp. 38-78. Springer, New York, Ecological 5 Studies, 110. 6 Bruijnzeel LA, Veneklaas EJ (1998) Climatic conditions and tropical montane forest 1992) Costs and benefits of constructing roots of small diameter. 1 Journal of Plant Nutrition, 15, 763-782. 2 Eissenstat DM, Yanai RD (1997) The ecology of root lifespan. Advances in Ecological 3 Research, 27, 1-60. 4 Eissenstat DM, Wells CE, Yanai RD, Whitbeck JL (2000) Building roots in a changing 5 environment: implications for root longevity. New Phytologist, 147, 33-42. 6 Espeleta K-F, Clark DA (2007) Multi-scale variation in fine-root biomass in a tropical 7 rain forest: a seven year study. Ecological Monographs, 77, 377-404. State of the Word's Forests. Rom. 9 Feeley KJ, Wright SJ, Nur Supardi MN, Kassim AR, Davies SJ (2007) Decelerating 10 growth in tropical forest trees. Ecology Letters, 10, 461-469. 11 Finér L, Ohashi M, Noguchi K, Hirano Y (in press) Factors causing variation in fine 12 root biomass in forest ecosystems. Forest Ecology and Management (in press). 13 Girardin CAJ, Malhi Y, Aragao LEOC, Mamani M, Huaraca W et al. (2010) Net 14 primary production and its allocation along a tropical forest elevational transect in 15 the Peruvian Andes. Global Change Biology. 16 Grace J, Meir P (2009) Tropical rain forests as old-growth forests. In: Old-Growth 17 Forests. (eds Wirth C, Gleixner G, Heimann M), pp. 391-408. Springer, Berlin, 18 Heidelberg. Ecological Studies, 207. 19 Grace J, Lloyd J, McIntyre J, Miranda A, Meir P, Miranda H, Nobre C, Moncrieff J, 20 Massheder J, Malhi Y, Wright I, Gash J (1995) Carbon dioxide uptake by an 21 undisturbed tropical rain forest in south-west Amazonia 1992-1993. Science, 270, 22 778-780. 23 Graefe S, Hertel D, Leuschner Ch (2008a) Fine root dynamics along a 2,000-m 24 elevation transect in South Ecuadorian mountain forests. Plant and Soil, 231, 155-25 166. 26 Graefe S, Hertel D, Leuschner Ch (2008b) Estimating fine root turnover in tropical 27 forests along an elevational transect using minirhizotrons. Biotropica, 40, 536-542. 28 Grubb PJ (1977) Control of forest growth and distribution on wet tropical mountains 29 with special reference to mineral nutrition. Annual Reviews of Ecology and 30 Systematics, 8, 567-601. 31 Grubb PJ, Tanner EVJ (1976) The montane forests and soils of Jamaica: a reassessment. 32 Journal of the Arnold Arboretum, 57, 33-68. 33 Ecuador (eds Beck E, Bendix J, Kottke I, Makeschin F, Mosandl R), pp. 229-1 242. Springer, Berlin, Ecological Studies, 198. 2 Moser G, Leuschner Ch, Röderstein M, Graefe S, Soethe N, Hertel D (in press) 3 Biomass and productivity of fine and coarse roots in five tropical mountain forests 4 along an altitudinal transect in South Ecuador. Plant Ecology and Diversity. 5 Nadelhoffer KJ (2000) The potential effects of nitrogen deposition on fine-root 6 production in forest ecosystems. New Phytologist, 147, 131-139. 7 Pollmann W, Hildebrand R (2005) Structure and the composition of species in 8 timberline ecotones of the Southern Andes. In: Mountain ecosystems -studies in 9 treeline ecology (eds Broll G, Keplin B) pp. 117-151. Springer, Berlin. 10 Raich JW, Russel AE, Vitousek PM (1997) Primary productivity and ecosystem 11 development along an elevational gradient on Mauna Loa, Hawai'i. Ecology, 78, 12 707-721. 13 Richter M, Diertl K-H, Bussmann RW, Peters T (2008) Vegetation structures and 14 ecological features of he upper tree line ecotone. In: Gradients in a Tropical 15 Mountain Ecosystem of Ecuador (eds Beck E, Bendix J, Kottke I, Makeschin F, 16 Mosandl R), pp. 229-242. Springer, Berlin, Ecological Studies, 198. 17 Schawe M, Glatzel S, Gerold G (2007) Soil development along an altitudinal transect in 18 a Bolivian tropical montane rainforest: Podzolization vs. hydromorphy. Catena, 69, 19 83-90. 20 Shi P, Körner C, Hoch G (2008) A test of the growth-limitation theory for alpine tree 21 line formation in evergreen and deciduous taxa of the eastern Himalayas. 22 Functional Ecology, 22, 213-220. 23 Soepadmo E (1993) Tropical rain forests as carbon sinks. Chemosphere, 27, 1025-1039. 24 Soethe N, Lehmann J, Engels C (2006a). Root morphology and anchorage of six native 25 tree species from a tropical montane forest and an elfin forest in Ecuador. Plant 26 and Soil, 279, 173-185. 27 Soethe N, Lehmann J, Engels C (2006b). The vertical pattern of rooting and nutrient 28 uptake at different altitudes of a south Ecuadorian montane forest. Plant and Soil, 29 286, 287-299. 30 Takyu M, Aiba S-I, Kitayama K (2003). Changes in biomass, productivity and 31 decomposition along topographical gradients under different geological conditions 32

1 7 period

 7 Mean annual air temperature and relative air humidity were measured at 1.5 m height inside the stands, 2 soil moisture in 10 cm depth of the mineral soil; given are annual means, minimum and maximum (in 3 brackets) for the period April 2003 -March 2004; bedrock types after Litherland et al. 1994; soil 4 classification (FAO system), pH(CaCl 2 ) of the mineral topsoil (0 -30 cm), C/N ratio of the organic layer 5 (L/Of1) and soil organic carbon (SOC; organic layers and 0-30 cm of mineral soil) after Iost (2007); 6 rainfall data are extrapolated from own measurements in a gap at approximately 1050 m (measuring Mai 2003 -Mai 2004), and from measurements in gaps at 1950, 2680 and 3170 m done by P. 8 Emck & M. Richter (3-year means, unpublished); data on forest structure, as mean diameter in breast 9 height (DBH), stem density, basal area and canopy height were measured for 80 trees per plot (Moser et 10 al. 2008); KCl-extractable inorganic N measured in April 2004 by Iost (2007, median and range), gross N 11 mineralization according to 15 N isotopic pool dilution approach (3 sites only), the pool of KCl-extract. N 12 in the org. layers is a rough estimate derived from N inorg concentrations and humus mass; LAI derived 13 from annual leaf litter fall, specific leaf area (SLA) and leaf lifespan (Moser et al. 2007).

Figure 1 :

 1 Figure 1: Topographic map of the study area with its location in the south of Ecuador, position of

Figure 2 :

 2 Figure 2: Aboveground (A -D) and belowground (E -H) biomass and production fractions in

16 17 Figure 3 :

 173 Figure 3: Stem wood production (A) and LAI (B), and their dependence on annual mean air

Figure 4 : 4 Page

 44 Figure 4: Above-and belowground trend lines of tree biomass and productivity extrapolated

  FR than other methods (Graefe et al. 2008a, Moser et al. in press). In June 14 2005, we installed 10 transparent minirhizotron tubes with an external diameter of 70 15

	11	al. (in press).
	12	Fine root production (P FR ) was estimated from minirhizotron observation of fine root
	13	birth, growth and death in the five stands; this technique was found to give more reliable
		data on P

Table 1 :

 1 Location and stand characteristics of the five study sites in South Ecuador:

	1	in tropical lower montane forests on Mount Kinabalu, Borneo. Oecologia, 134,
	2	397-404.
	3	Tanner EVJ (1981) The decomposition of leaf litter in Jamaican montane rain forests.
	4	Journal of Ecology, 69, 263-273.
	5	Vogt KA, Vogt DJ, Palmiotto PA, Boon B, O'Hara J, Asbjornsen H (1996) Review of
	6	root dynamics in forest ecosystems grouped by climate, climatic forest type and
	7	species. Plant Soil, 187, 159-219.
	8	Wang HQ, Hall CAS, Scatena FN, Fetcher N, Wu W (2003) Modelling the spatial and
	9	temporal variability in climate and primary productivity across the Luquillo
	10	Mountains, Puerto Rico. Forest Ecology and Management, 179, 69-94.
	11	Weaver PL, Murphy PG (1990) Forest structure and productivity in Puerto-Rico
	12	Luquillo Mountains. Biotropica, 22, 69-82.
	13	Wilcke W, Hess T, Bengel C, Homeier J, Valarezo E, Zech W (2005) Coarse woody
	14	debris in a montane forest in Ecuador: mass, C and nutrient stock, and turnover.
	15	Forest Ecology and Management, 205, 139-147.
	16	Zach A, Horna V, Leuschner C (2008) Elevational change in woody tissue CO 2 efflux
	17	in a tropical mountain rain forest in southern Ecuador. Tree Physiology, 28, 67-74.
	18
		28

Table 2 :

 2 Above-(AGB) and belowground biomass (BGB) and above-(ANPP) and

	14
	15
	Stand no.	1	2	3	4	5
	Coordinates	S 04°06'54''	S 04°06'42''	S 03˚58'35''	S 03˚59'19''	S 04˚06'71''
		W 78°58'02''	W 78°58'20''	W 79˚04'65''	W 79˚04'55''	W 79˚10'58''
	Elevation (m a.s.l.)	1050	1540	1890	2380	3060
	Inclination (°)	26	10	31	28	27
	Air temperature (°C)	19.4	17.5	15.7	13.2	9.4
	(min-max)	(11.5-30.2)	(11.2-26.7)	(7.9-29.4)	(7.0-25.1)	(3.1-18.8)
	Rainfall (mm yr -1 )	c. 2230	c. 2300	c. 1950	c. 5000	c. 4500
	Relative air humidity (%)	88.7	88.9	90.8	93.3	93.5
	(min-max)	(15.5-100)	(31.7-100)	(15.7-100)	(34.0-100)	(28.6-100)
	Bedrock types	Leuco-and	Leuco-and	Black phyllites,	Black phyllites,	Black phyllites,
		hornblende,	hornblende,	quartzite,	quartzite,	quartzite,
		granodiorites	granodiorites	metasiltstone,	metasiltstone,	metasiltstone,
				metasandstone	metasandstone	metasandstone
	Soil types	Alumic Acrisol Alumic Acrisol Gleyic	Gleyic	Podzol
				Cambisol	Cambisol
	Organic layer thickness	48	243	305	214	435
	(mm)
	Soil moisture (vol.%)	29.7	30.3	35.4	44.7	49.1
	(min-max)	(15.3-38.5)	(20.4-43.5)	(27.4-44.7)	(35.7-48.7)	(39.5-59.5)
	Soil pH (CaCl 2 )	3.94	3.90	3.52	3.26	2.86
	SOC: organic layers	11.1	50.5	36.5	47.8	75.1

10 36.34 26.08 39.21 62.77 15.47 17.55 12.46 18.73 33.14 Total Tree Biomass 317.17 203.83 199.03 145.03 174.97 153.57 98.95 96.53 66.50 86.68

	Page 33 of 42					Global Change Biology
	1
	Production (Mg ha Tree leaves Reprod. organs Twigs Epiphytes	-1 yr -1 ) F 5.05 5.06 0.91 0.43 1.13 0.93 0.28 0.58 o r 4.96 0.36 0.88 0.25 R 2.64 0.11 0.39 0.25 e v 1.79 0.07 0.39 0.21 F o r R e v i e w 2.54 2.57 2.51 1.34 0.92 0.45 0.21 0.18 0.05 0.03 0.55 0.45 0.43 0.19 0.19 0.14 0.29 0.13 0.13 0.11	O n l y
	Bamboo Other components	0.00 0.41	0.00 0.34	1.55 0.34	0.12 0.14 i 0.20 0.04 e	0.00 0.21	0.00 0.17	0.78 0.17	0.06 0.07	0.10 0.02
	Total fine litter Stem wood incre-		7.78 2.82	7.34 1.58	8.34 0.87	3.65 0.22	2.70 0.14 w 3.89 1.37	3.69 0.77	4.20 0.42	1.84 0.11	1.37 0.07
	ment
	Total ANPP Coarse roots Fine roots 2 Total BNPP 2		10.60 0.17 2.28 2.45	8.92 0.79 3.16 3.95	9.21 0.23 2.97 3.20	3.87 0.23 3.72 3.95 10.29 2.84 0.89 9.40 (4.42)	5.26 0.08 1.06 O 4.46 0.38 1.50 n 4.62 0.11 1.35 l 1.14 1.88 1.46 y	1.95 0.11 1.79 1.90	1.44 0.42 4.70 (2.21) 5.12
								(5.31)			(2.66)
	Total NPP	2		13.05 12.84 12.41 7.85 12.96	6.40	6.34 6.08	3.85	6.56
								(8.15)			(4.10)
	6
						32

Table 3 :

 3 Results of regression analyses relating various biomass and production fractions to elevation and six climatic and edaphic variables.

	1
	2	Elevation in m a.s.l., mean air temperature in °C, vapour pressure deficit VPD in hPa, annual precipitation in mm yr -1 , soil moisture in vol.%, proton concentration of
	3	mineral soil derived from pH value, C/N ratio of the organic Oi layer. Significant relations are printed in bold (p=0.05), negative relationships are indicated by -, non-
	4	linear relationships are marked with *. 1 Regression analyses were calculated considering the extrapolated fine root production value for the 3060 m stand
	5
			Elevation		Temperature	VPD		Precipitation	Soil moisture	Proton concentration	C/N ratio
		Dependent	r 2	adj	p	r 2	adj	p	r 2	adj	p	r 2	adj	p	r 2	adj	p	r 2	adj	p	r 2	adj	p
		Biomass
		Leaves	-0.25 0.112	0.31 0.096	0.31 0.097	-0.65 0.031	-0.44 0.068	-0.49 0.058	-0.59 0.040
		AG wood	-0.81 0.045 *	0.86 0.032 *	0.61 0.037	-0.38 0.081	-0.50 0.055	-0.18 0.133	-0.98 0.003 *
		AGB	-0.85 0.036 *	0.82 0.034 *	0.63 0.033	-0.41 0.073	-0.53 0.050	-0.21 0.124	-0.99 0.002 *
		Coarse roots	0.13 0.149	-0.18 0.131	-0.01 0.191	0.14 0.145	0.12 0.153	0.48 0.059	0.46 0.064
		Fine roots	0.87 0.006	-0.86 0.007	-0.63 0.033	0.16 0.140	0.61 0.036	0.80 0.012	0.77 0.015
		BGB	0.58 0.040	-0.64 0.032	-0.83 0.041 *	0.57 0.043	0.82 0.043 *	0.78 0.014	0.87 0.006
		Total biomass -0.88 0.025 *	0.88 0.027 *	0.69 0.080 * -0.24 0.114	-0.36 0.085	-0.83 0.040 *	-0.93 0.014 *
		Production
		Leaves	-0.79 0.013	0.83 0.009	0.87 0.006	0.85 0.007	0.93 0.002	0.77 0.015	0.93 0.002
		Reproductive organs	-0.97 0.006

* 0.

95 0.009

* 0.

82 0.043

	0.39 0.078	0.60 0.108
	*

* 0.

55 0.119 * 0.97 0.006

* Twigs -0.

84 0.008 0.82 0.010 0.93 0.002 0.84 0.009 0.91 0.003 0.54 0.048 0.93 0.015 * Wood -0.98 0.003 * 0.99 0.002 * 0.95 0.009

		Coarse roots	0.07 0.168	0.07 0.168	-0.16 0.274	-0.24 0.331	-0.14 0.236	0.19 0.129	0.18 0.132
		Fine roots	1		0.92 0.003	-0.90 0.004	-0.79 0.013	0.54 0.049	0.78 0.014	0.73 0.019	0.91 0.003
		Total BNPP	1	0.74 0.018	-0.73 0.020	-0.51 0.052	0.30 0.099	0.52 0.052	0.65 0.030	0.79 0.013
		Total NPP	1		-0.71 0.023	0.72 0.021	0.87 0.006	-0.95 0.001	-0.90 0.004	-0.52 0.514	-0.77 0.15
		LAI				-0.80 0.013	0.81 0.011	0.86 0.007	-0.90 0.004	-0.90 0.004	-0.68 0.026	-0.91 0.003
	1	BNPP/ANPP N pool in leaf 1 biomass	0.86 0.007 -0.54 0.048	* F o r R e v i e w 0.37 0.081 0.80 0.049 * O n l y 0.08 0.060 * -0.90 0.004 -0.98 0.004 * 0.55 0.047 0.98 0.004 * 0.96 0.001 0.58 0.041 0.64 0.032 -0.92 0.002 -0.73 0.020 -0.56 0.045 -0.79 0.014 0.85 0.035 * 0.98 <0.001 F o r R e v i e w O n l y
		Tree ANPP		-0.93 0.002	0.92 0.003	0.97 0.001	0.74 0.019	0.95 0.001	0.87 0.030 *	0.95 0.009 *
		Non-tree litter --0.19 0.293	-0.15 0.272	-0.16 0.276	0.30 0.100	-0.08 0.230	-0.02 0.206	0.10 0.158
		Total ANPP		-0.85 0.007	0.86 0.007	0.90 0.004	0.86 0.007	0.92 0.003	0.69 0.026	0.92 0.003
									34 35

Table 4 :

 4 Results of correlation analyses between six environmental variables and elevation in the five Ecuadorian

	1
	2	study plots (Pearson correlation coefficient r and p).
	3	Elevation in m a.s.l., mean air temperature in °C, VPD in hPa, annual precipitation in mm yr -1 , soil moisture in vol.%, proton
	4	concentration (pH) of the upper mineral soil in mol L -1 , C/N ratio of the organic Oi layer in g g -1 . Significant relationships are printed
	5	in bold (p < 0.05), negative relationships are indicated by -.
	6
			Elevation		Temperature	VPD		Precipitation	Soil moisture	Proton concentration
			r	p	r	p	r	p	r	p	r	p	r	p
	Temperature + 1.00 <0.001
	VPD		-0.97 0.002	+ 0.97 0.002
	Precipitation	+ 0.80 0.053	-0.80 0.051	-0.88 0.025
	Soil moisture + 0.97 0.003	-0.97 0.002	-0.99 <0.001	+ 0.90 0.019
	Proton concentration	+ 0.93 0.011	-0.95 0.006	-0.88 0.023	+ 0.72 0.083	+ 0.91 0.015
	C/N ratio	+ 0.

96 0.004 -0.97 0.002 -0.94 0.008 + 0.86 0.030 + 0.96 0.005 + 0.96 0.004

	F o r
	R
	e v
	i e
	w
	O n l
	y
	36

Table 5 :

 5 Leaf and root traits, and various biomass and production ratios of the five forest stands. 1 AGB -aboveground biomass, ANPP -aboveground net primary production, BGB -belowground biomass, 2 BNPP -belowground net primary production, n.d. -no data; 1 from Moser et al. (2007). 2 from Graefe et al.3 (2008b).3 for the stand at 3060 m: extrapolated fine root production estimate from the trend line of stands 1 -

	4
	5	4 in brackets.
	6
		Stand no.			1	2	3	4	5
		Elevation (m a.s.l.)			1050	1540	1890	2380	3060
		Leaves Mean leaf longevity (months) 1			16.2	19.1	23.6	23.7	24.5
		N pool in leaf biomass (Mg ha Leaf N content / area (mmol m -1 ) -2 ) Leaf N content / dry mass (mmol g C/N in leaf biomass (g g -1 ) C/N in leaf litter (g g -1 )	-1 )	0.21 0.024 0.026 0.025 0.025 0.025 0.21 0.25 0.09 0.07 2.18 1.86 1.82 1.26 1.39 31.4 35.8 41.3 59.8 58.1 28.6 47.8 48.0 59.9 61.9
		Roots Mean fine root longevity (months) 2		11.2	n.d.	15.3	n.d.	8.4
		N pool in root biomass (Mg ha	-1 )		0.053 0.091 0.053 0.055 0.059
		C/N in fine root biomass (organic layers)	23.2	29.1	43.4	55.2	91.1
		C/N in fine root litter (organic layers)	23.6	26.9	33.1	44.2	60.1
		Ratios
		Fine root/leaf biomass ratio			0.39	0.70	0.63	1.20	2.98
		Stem wood increment per wood mass (%)	1.0	1.0	0.5	0.2	0.1
		Coarse root growth per coarse root biomass (%)	0.6	2.6	1.2	0.7	1.7
		BGB/AGB ratio			0.11	0.22	0.15	0.39	0.56
		ANPP per AGB (%) BNPP per BGB (%) 3			3.7 7.6	5.3 10.9	5.3 12.3	3.9 10.1	2.5 16.4
							(8.5)

Global Change Biology


Ridha Hambli
email: ridha.hambli@univ-orleans.fr

Abdelwahed Barkaoui

Multiscale Approach for Bone Remodeling Simulation Based on Finite Element and Neural Network Computation

Keywords: Multiscale, Hierarchical, Bone remodeling, Finite element, Neural network

In this paper, a novel multiscale hierarchical model based on finite element analysis and neural network computation was developed to link mesoscopic and macroscopic scales to simulate bone remodeling process. The finite element calculation is performed at macroscopic level and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume elements of bone taken from different bone sites, a neural network is trained to approximate the responses at meso level and transferred at macro level.

Introduction

The bone adaptation process called remodeling process must address changes in its morphological and mechanical properties over time, at multiple levels, allowing for a more accurate description of the bone architecture [START_REF] Rho | Mechanical properties and the hierarchical structure of bone[END_REF][START_REF] Carter | Skeletal function and form: Mechanobiology of Skeletal Development, Aging and Regeneration[END_REF]. This process occurs at different time and spatial scales in hierarchical way with interacting phenomenon between the different scales [START_REF] Rho | Mechanical properties and the hierarchical structure of bone[END_REF][START_REF] Carter | Skeletal function and form: Mechanobiology of Skeletal Development, Aging and Regeneration[END_REF]. Therefore, an accurate simulation of bone remodeling should include different length scales. In the last few years, a general strategy has emerged for the design of multiscale methods in order to capture the macroscale behavior of the solutions. A large number of methods are based on numerical homogenization procedure [START_REF] Viceconti | Multiscale modelling of the skeleton for the prediction of the risk of fracture[END_REF], others introduce a new methods, and among them the artificial neural networks (NN) has attracted a growing interest in recent years [START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF]. In this paper, a hybrid method for bone remodeling multiscale simulation using finite element analysis and NN computation is proposed. The motivation to develop such hierarchical approach in the frame work of bone modeling is that a part of the mechanisms affecting bone strength are observed at trabecular level and cannot be described in precise way at macro level like microcracks accumulation, stress concentration du to tabecular network, bone cells activities and mass or chemical transport. Meshing the entire femur with its trabecular architecture generates some millions of finite elements with a huge computational time. The NN approach is beneficial if the numerical analysis of the complex model is time consuming or unfeasible [START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF].

Method

The hybrid FENN method is a simulation procedure in which a continuum model is discretized into smaller submodels composed of RVE (fig. 1). Changes in the material distribution at macro level will have an effect on the stress/strain field, thus affecting the mechanical state of each RVE in the subsequent iteration. At the completion of every iteration, a new FE analysis is performed to update the mechanical parameters distribution in the macro level. A trained NN is applied locally to determine structural and mechanical change at meso level. The local results are passed back to the macro level.

The proposed methodology follows this iterative procedure until convergence is achieved.

A schematic illustration of the hierarchical approach is presented in Fig. 1.

The meso approach can be summarized by the five following steps: (i) FE remodeling simulation of the RVE for different combinations of bone inputs (ii) Averaging the RVE outputs.

Neural network

Neural Networks models are composed of a large number of inter-connected processing elements called neurons, organized in layers. [8]. The single neuron performs a weighted sum of the inputs i

x that are generally the outputs of the neurons of the previous layer m v , adding threshold value i b and producing an output given by:

L i i i im m b x w v 1 (1)
m m v exp 1 1 v f (2)
Where is a parameter defining the slope of the function.

To apply the NN, a training phase is needed which consists of an optimization procedure in order to determine the weights of the NN. the combinations of local applied stress (4 levels) and cycle frequency (5 levels) covering the range of mechanically observed/computed stresses and fequencies [START_REF] Hambli | Strain-damage coupled algorithm for cancellous bone mechano-regulation with spatial function influence[END_REF][START_REF] Hambli | Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation[END_REF].

Finite element model for bone remodeling

The set of equation describing the fully coupled change in the bone density is given by [START_REF] Hambli | Strain-damage coupled algorithm for cancellous bone mechano-regulation with spatial function influence[END_REF][START_REF] Hambli | Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation[END_REF]:

R R S S dt d If R S S (3) 0 dt d If F R S S S ( 4
)
F F S S dt d If F S S ( 5
)
D D S S dt d If D S S ( 6
)
Where is the bone density, t is time and S is the coupled strain-damage stimulus function.

R , F and D denote respectively bone resorption rate, bone forming rate and damage resorption rate.

R S ,

F S and D S denote respectively target levels of strain-damage energy density for bone resorption, formation and damage resorption.

The averaging relation of each RVE outputs, RVE i y , is expressed by :

dV y V y O V i o RVE i 1 (7)
Where o V and i y denote respectively the RVE reference domain and the output at every finite element location i.

Simulation of 3D femur head remodeling

To illustrate the capabilities of the FENN method, the remodeling of a 3D model of femur head has been studied. There are two materials in the macro model, trabecular bone and cortical bone. Marrow is considered only in the porous regions at the RVEs level. A 3D mesh is generated using tetrahedral elements. The model is run in alternating load and unload increments during 1000 iterations (days) with a fixed number of cycles per day (7000 cycles/day).

Since the investigation scale of the present work corresponds to one or some trabeculae level, we assume that the bone behaviour is purely elastic with isotropic averaged properties from nanoscale level.

Results

In Figure 2 the distribution of the bone density is presented for both macro (a) and meso levels (b). The local RVE result is averaged and transferred to the entire femur for more accurate prediction of bone density.

Conclusion

In this study, the focus was on the development and the implementation of a novel multiscale approach for bone remodeling simulation using finite element simulation and neural network computation. The NN algorithm has been incorporated into a finite element code to link meso and macro scales and provide local and rapid computation at the meso scale. Actually, the proposed multiscale approach doesn't take into account biological mechanisms. The aim was to provide a framework using FE and NN methodology for a rapid and accurate multiscale modeling of bone.

  (iii) Steps (i) and (ii) supply training data in the form of a 'design of experiments' (DoE) table for NN training. (iv) Training the NN based on the numerical DoE. (v) Incorporation of the NN into the macro FE model to link meso-to-macro scales.

Figure 1 .

 1 Figure 1.Multiscale hierarchical approach for bone analysis. NN is incorporated into the FE code Abaqus via the routine UMAT.

imw

  are the network weights.Input signals cumulated in the neuron block are activated by a nonlinear function given by:

Figure 2 .

 2 Figure 2.Contour of trabecular bone density predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.

Acknowledgements

This work has been supported by French National Research Agency (ANR) through TecSan program (Project MoDos, n°ANR-09-TECS-018).