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Structure and function of buttress roots in tropical oaks of Quercus spp. in windward and leeward cloud forest

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Title:
Structure and function of buttress roots in tropical oaks of Quercus spp. in windward and leeward cloud forest
Translated Title:
Estructura y función de las raíces de apoyo en los robles tropicales de Quercus spp. en el bosque nuboso de barlovento y sotavento ( )
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Book
Language:
English
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Johnson, Bridget
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Subjects / Keywords:
Oak   ( lcsh )
Winds   ( lcsh )
Costa Rica--Puntarenas--Monteverde Zone   ( lcsh )
Roble
Vientos
Costa Rica--Puntarenas--Zona de Monteverde
Tropical Ecology Summer 2010
Ecología Tropical Verano 2010
Genre:
Reports   ( lcsh )
Reports

Notes

Abstract:
Buttress roots of tropical trees are widely accepted to function in structural support, yet there is no current consensus about the processes that govern their formation. This study aims to determine if wind is a driving force in influencing the structure and function of the buttresses of Quercus spp. (Fagaceae) in Monteverde, Costa Rica. Two sampling sites of dissimilar wind exposure were designated. The first was a highly windy habitat at the ridge of a mountain. The second was at a lower elevation in the mountain’s shadow, which experienced less intense winds. Thirty-one adult individuals from the two locations were sampled for buttress frequency, height, length, thickness, and curvature on the windward and leeward sides of each tree. No significant trends were found between the buttress measurements and either location or species. Two nearly significant results were revealed regarding the ratio of leeward-to-windward buttress thickness and leeward buttress curvature. However, these results were contradictory and did not support the hypothesis of wind being the primary factor in determining buttress structure. Instead, it is likely that the formation of buttresses is a complex and multi-faceted process, and that wind is one of numerous ecological components that influences buttress structure.
Abstract:
Las raíces de los árboles tropicales son ampliamente aceptadas para funcionar en el soporte estructural, sin embargo, no existe un consenso actual sobre los procesos que rigen su formación. Este estudio tiene como objetivo determinar si el viento es una fuerza impulsora para influir en la estructura y función de los contrafuertes de Quercus spp. (Fagaceae) en Monteverde, Costa Rica. Dos sitios de muestreo de la exposición al viento disímiles fueron designados. El primero fue un hábitat de gran viento en la cresta de una montaña. El segundo fue a una elevación menor a la sombra de la montaña, que experimentó vientos menos intensos. Se tomaron muestras de treinta y un adultos individuales de los dos lugares para reforzar la frecuencia, altura, longitud, grosor y la curvatura de los lados de barlovento y sotavento de cada árbol. Sin tendencias significativas entre las mediciones de contrafuertes y ya sea de localización o de la especie. Dos resultados casi significativos se dieron a conocer con respecto a la relación de sotavento a barlovento-reforzar espesor y curvatura de sotavento contrafuerte. Sin embargo, estos resultados fueron contradictorios y no apoyan la hipótesis de que el viento es el factor principal en la determinación de reforzar la estructura. En su lugar, es probable que la formación de los contrafuertes es un proceso complejo y multifacético, y que el viento es uno de los numerosos componentes ecológicos que influyen en reforzar la estructura.
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Text in English.
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Born Digital

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usfldc doi - M39-00223
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Buttress roots of tropical trees are widely accepted to function in structural support, yet there is no current consensus about the processes that govern their formation. This study aims to determine if wind is a driving
force in influencing the structure and function of the buttresses of Quercus spp. (Fagaceae) in Monteverde, Costa Rica. Two sampling sites of dissimilar wind exposure were designated. The first was a highly windy
habitat at the ridge of a mountain. The second was at a lower elevation in the mountains shadow, which experienced less intense winds. Thirty-one adult individuals from the two locations were sampled for
buttress frequency, height, length, thickness, and curvature on the windward and leeward sides of each tree. No significant trends were found between the buttress measurements and either location or species. Two nearly significant results were revealed regarding the ratio of leeward-to-windward buttress thickness and leeward buttress curvature. However, these results were contradictory and did not support the hypothesis of wind being the primary factor in determining buttress structure. Instead, it is likely that the formation of
buttresses is a complex and multi-faceted process, and that wind is one of numerous ecological components that influences buttress structure.
Las races de los rboles tropicales son ampliamente aceptadas para funcionar en el soporte estructural, sin embargo, no existe un consenso actual sobre los procesos que rigen su formacin. Este estudio tiene como objetivo determinar si el viento es una fuerza impulsora para influir en la estructura y funcin de los contrafuertes de Quercus spp. (Fagaceae) en Monteverde, Costa Rica. Dos sitios de muestreo de la exposicin al viento dismiles fueron designados. El primero fue un hbitat de gran viento en la cresta de una montaa. El segundo fue a una elevacin menor a la sombra de la montaa, que experiment vientos menos intensos. Se tomaron muestras de treinta y un adultos individuales de los dos lugares para reforzar la frecuencia, altura, longitud, grosor y la curvatura de los lados de barlovento y sotavento de cada rbol. Sin tendencias significativas entre las mediciones de contrafuertes y ya sea de localizacin o de la especie. Dos resultados casi significativos se dieron a conocer con respecto a la relacin de sotavento a barlovento-reforzar espesor y curvatura de sotavento contrafuerte. Sin embargo, estos resultados fueron contradictorios y no apoyan la hiptesis de que el viento es el factor principal en la determinacin de reforzar la estructura. En su lugar, es probable que la formacin de los contrafuertes es un proceso complejo y multifactico, y que el viento es uno de los numerosos componentes ecolgicos que influyen en reforzar la estructura.
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Winds
Costa Rica--Puntarenas--Monteverde Zone
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Roble
Vientos
Costa Rica--Puntarenas--Zona de Monteverde
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Tropical Ecology Summer 2010
Ecologa Tropical Verano 2010
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Reports
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CIEE
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t Monteverde Institute : Tropical Ecology
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Structure and function of buttress roots in tropical oak s of Quercus spp. in windward and leeward cloud forest Bridget Johnson Department of Ecology, Evolution and Natural Resources, Rutgers University New Brunswick, New Jersey 08901 U S A ABSTRACT Buttress roots of tropical trees are widely accepted to function in structural support yet there is no current consensus about the process es that govern their formation This study aims to determine if wind is a driving force in influencing the structure and function of the buttresses of Quercus spp. (Fagaceae) in Monteverde, Costa Rica. Two sampling sites of dissimilar wind exposure were designated. The first was a highl y windy experienced less intense winds. Thirty one adult individuals from the two locations were sampled for buttress frequency, height, length, thickne ss, and curvature on the windward and leewar d sides of each tree. No significant trend s were found between the buttress measurements and either location or species. Two nearly significant results were revealed regarding the ratio of leeward to windward but tress thickness and leeward buttress curvature. However, these results were contradictory and did not support the hypothesis of wind being the primary factor in determining buttress structure. Instead, it is likely that the formation of buttresses is a com plex and multi faceted process and that wind is one of numerous ecological components that influences buttress structure. INTRODUCTION The root systems of trees not only support their canopies but also the aboveground ecological stratification of a fore st. surrounding biotic and abiotic environment (Ennos 1995 ) Various tropical canopy trees employ the intriguing root system of buttresse s. These large, exposed roots must cope with the conditions of the tropics: poor soil, a shallow substrate for root growth and water saturation (Jordan 1985) Although some resea rch indicates that buttresse s serve to specifically address such environmental factors, the m ost common conclusion about their chief function is that they provide structural support. T rees with buttresses have been proven to offer twice the stress resistance of non buttressed trees (Crook et al. 1997). However, the precise mechanisms directing buttress formation and structure hav e yet to be solidified There can be large variatio n of buttress formation at family, genus, and even species levels (Chapman et al. 1998). This indicates that buttress formation may be dependent to a degree on the specific conditions in which the tree dev elops. Wind can be a significant factor in determining ecological an d structural characteristics (Ennos 1997) Along mountain ridges that are highly exposed to wind, for example, trees have been found to have thicker trunk girth and more slender branches than their counterparts further down the mountain, which were more sheltered from direct wind action (Lawton 1982). It has been indicated that root systems, specifically buttress roots of tropical trees, can also be correlated with wind presence a nd intensity ( Richter

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1984). Evidence exists for a trend in buttress structure in trees exposed to high wind action Windward buttresses functioned in ensuring that the tree was not uprooted from oncoming wind, and utilized tensile forces. Such b uttresses specialized in tension were found to be long, thin, and without extensive bending It was found that leeward buttresses functioned in preventing the tree from slumping backward under the force of the wind, thus acting through compression. These compressiv e buttresses were associated with shorter, thick er, and more gnarled buttresses (Nicoll and Ray 1996 ; Crook et al. 1997 ) This study investigates the role of wind in the structure of buttress roots of Quercus spp (Fagaceae) in Monteverde, Costa Rica. This genus of tropical oak generally displays well developed buttresses ( Haber et al. 2000). Individuals from Quercus spp in two sit es of differing wind intensity we re sampled for buttress structure. I intend to address the following inquiry: In response to d estabilizing wind pressure, do individuals of Quercus spp. in regions of high wind activity more strongly display compressive and tensile buttress roots on the leeward and windward sides, respectively, than do their counterparts in regions of low wind expo sure? That is, have cer t a in trees reacted to environmental conditions by engineering root systems designed to specifically resist wind damage? It was predicted that trees in the windier habitat would have a more pronounced difference between leeward and wi ndward buttresses than would trees in the habitat with less intense winds. Higher wind impact is expected to result in oaks strongly displaying tensile buttresses on the windward side to prevent uprooting and compressive buttresses on the leeward side to i nhibit sinking. Trees in the less windy environment have not developed under such harsh conditions, and are predicted not to demonstrate such a strong patter n due to lower potential for wind damage. This project ultimately aims to determine if buttress ro ots are an adaptation against wind destabilization. Adaptation in this sense refers to a behavioral, physiological, or morphological trait that increases the fitness of an organism in its environment If buttress roots serve to structurally support the tree, they effectively increase the fitness of the tree by maintaining firm contact with the ground, which is crucial to development and survival. METHODS Study Site T wo study sites were surveyed near Monteverde, Costa Rica, in t he province of Puntarenas on the Pacific slope of the Cordillera de Tilarn This mountain range comprises the Continental Divide, which cuts northwest to southeast across the center the country The Divide in this region is composed of river canyons, ridges, and peaks and forms an irregular mesa. The mountain creates distinct weather systems on each of the Atlantic and Pacific slopes; the latter is drier and more seasonal. Located within the cloud forest of the Pacific slope, Monteverde experiences mild, montane temperatures with daily highs of 20 26 C and lows of 9 16 C and its total average annual rainfall is 2.5 m. Northeast trade winds are year round on the Divide and generally 20 40 km per hour. windy misty season of November February or March Dry season on the Pacific slope lasts anywhere from of December to mid May

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experiences diminished trade winds due to warm air masses on the Pacific slope bl ockin g their passage (Haber et al. 2000). The first site was on a ridge of the Continental Divide, which had an elevation of 1650 m This habitat i s a l ower montane wet forest Holdridge life zone (Karen Masters, pers. com. ) Due to its high altitude, it i s highly exposed to moisture and trade winds from the northeast The second site was located in the cloud forest surrounding the Estacin Biolgica Monteverde on the Pacific slope of the mountain at an elevation of 1500 m Its Holdridge life zone i s a pre montane wet forest (Karen Masters, pers. com. ) Located in the shad ow of the mountain, this site i s sheltered from direct wind damage; it thus experiences less exposure to wind than does the first site. Study Organism Quercus is a genus of tropical oak. I t is wind pollina ted and has unisexual flowers. Three of the f our species of Quercus that occur in the Monteverde region were sampled : Q. corrugata Q. insignis and Q. brenesii These species are generally found to exhibit buttressing. Quercus corrugata is a large canopy ridge oak with a height of 20 35 m and an elevation of 1550 1800 m. Quercus insignis is a common canopy tree on the Pacific slope and is generally found, along with Q. brenesii at 1500 m and below (Haber et al. 2000). Thirty one individ uals of Quercus spp. were sampled for buttress presence and characteristics. At the ridge, 11 trees, all of Q. corrugata were assessed. Twenty individuals were evaluated at the lower elevation and were members of three Quercus species: Q. insignis (13), Q brenesii (6), and Q. corrugata (1). Investigation Because the focus of the research is on the influence of wind on root growth, directional quadrants were visually established and only those buttresses in the windward and leeward quadrants were conside red. As wind advances from the northeast, windward roots were considered to rest between east and north, while leeward buttresses were between west and south. Roots that were partially in a desired quadrant were included in measurements Once these quadran ts were established, different aspects of the root anatomy of the tree were measured: buttress frequency, length, height, width, and curvature. F requency refers to the number of buttresses within each q uadrant of interest. Length wa s estimated as the dista nce along the top of the buttress from where it joins the trunk or bole, to where it ends, submerged in the ground. Buttress height ran from the point of intersection with the trunk to the ground closest to the trunk (as the ground often sank further from the trunk) Average width, or thickness, wa s measured at the point halfway down th e height of the root. T o quantify the curvature of the roots, a central line running down the length of the root was designated, and t he number of times the body of the root transected the line was noted as an indicator of curvature.

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Additional observations The direction of the slope of the substrate of each tree w as also noted but not quantified Obvious surrounding biotic curiositie s, like epiphytic growth, were also given attention. RESULTS Investigation Each tree generally had multiple buttresses on both the leeward and windward sides. An average of the five measurements of the buttresses frequency, height, length, thickness, and curvature on each side was determined in order to have a single value for each measurement for each side of the tree. These averages were then used in statistical analyses to investigate trends. However, raw average height, length, and thickness values w ere not utilized, as the different sizes of trees would naturally produce different sized buttr esses independent of location. Instead, the ratio of average leeward buttress height and average windward buttress height for each tree was determined This corrected for the tree size difference and allowed for a comparison of the relative heights of leeward and windward buttresses. The same was done for length and thickness since each wa s also suspected to be dependent on tree size The average f requ ency and curvature values were used without modification because they were deemed independent of tree size. The first set of statistical analyses compared buttress qualities according to location, that is, between the ridge and the shadow of the mountain. The Wilcoxo n test was used to test for a relationship between location and buttress parameters of each of the leeward and windward sides. No significant trend s were found be tween any of the five parameters The second set of statistical analyses was a sp ecies wise comparison of buttress characteristics The Kruska l Wallis test was utilized to test for a correlation between the three Quercus species and the five buttress traits No significant relationship between species and buttress frequency, height, le ngth, or curvature was found. There was a nearly significant correlation between species and the ratio of thickness in leeward to windward buttresses: Q. corrugata and Q. insignis had a low ratio of leeward to windward b uttress thickness (0.91 and 0.90 res pectively), while Q. brenesii had a notably higher ratio (2.21), and this difference was v ery nearly significant (Kruskal Wallis test, 2 = 5.67 df = 2, P = 0 .059 ) (Fig. 1).

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Figure 1. Ratio of average buttress thickness on the leeward to windward side of each tree in Quercus spp S ample sizes include 6 individuals of Q. brenesii 12 of Q. corrugata and 13 of Q. insignis A second nearly significant trend was found regarding average leeward buttress cu rvature across species (Kruskal Wallis test 2 = 4.66 df = 2, P = 0.097 ) (Fig. 2). Figure 2 Average curvature of leeward side buttress roots in Quercus spp. S ample sizes include 6 individuals of Q. brenesii 12 of Q. corrugata and 13 of Q. insignis 0 0.5 1 1.5 2 2.5 3 3.5 Mean ratio of leeward to windward buttress thickness Species Q. brenesii Q. corrugata Q. insignis 0 0.2 0.4 0.6 0.8 1 1.2 Mean curvature of buttresses on leeward side of tree Species Q. brenesii Q. corrugata Q. insignis

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Additional observations Few of the samples trees were situated on perfectly level ground; most were on a substrate that was sloped, to widely varying extents. There did not appear to be a pattern in the slope of the ground at the lower elevation, but many of the Q. corrugata on the ridge were on gr ound that was sloped northward or northeastward, toward oncoming trade winds. While most roots and trunks of oaks at the lower elevation were bare, Q. c orrugata on the ridge had extensive epiphytic growth on their trunks down to the roots. It was thus chal lenging to get exactly accurate values of certain measurements, especially thickness, of the buttresses of the ridge oaks. DISCUSSION The lack of statistically significant trends indicates that t here were no notable differences in buttress frequency, hei ght, length, thickness, or curvature between ridge and shadow oaks. In the species comparison, there was also no pattern found in buttress frequency or curvature, nor any differences between leeward and windward ratios of height or length between species. The se findings do not support the original hypothesis. It was expected that Quercus spp. on the ridge which was solely Q. corrugata would most strongly display windward tensile and leeward compressive buttresses. This would involve a greater buttress hei ght and length in the tensile roots, and compressive roots would be characterized by greater buttress thickness and curvature. Quercus brenesii and Q. insignis were found exclusively at the shadow location so they were expect ed to show less of a tendency for distinct ten sile and compressive buttresses due to less intense wind conditions. Yet the statistical analyses showed no statistically significant patterns. With regard to the nearly significant finding of the relationship between species and leeward si de buttress thickness, the results were not expected. It was hypothesized that the ridge oaks, namely Q. corrugata would have compressive roots, which are shorter and thicker, on their leeward sides. Yet results indicate that the leeward to windward ratio of ave rage buttress thickness is less than one, signifying that leeward side buttresses were actually thinner than the windward side buttresses. Further, Q. brenesii which was expected to have a low ratio due to its position on the low wind mountain shad ow, had a rather high ratio (>1.0) This indicates that this species had thicker leeward buttresses than windward buttresses. Yet, Q. insignis at the same location as Q. brenesii had a ratio almost equal to that of Q. corrugata From these data, i t does no t appear that the type of habitat or wind presence affect the thickness of buttresses of Quercus spp Rather it may be that Q. brenesii is especially receptive to wind action and creates thicker, compressive leeward buttresses and thinner, tensile windwar d buttresses in order to combat wind damage, as was originally predicted for Q. corrugata at the wind intense ridge. It is also possible that this is just a characteristic of the species and develops independently of wind intensity. The relationship betw een average curvature of leeward buttresses and species was also clos e to significant The result of highest curvature among the compressive, leeward buttresses belonging to Q. corrugata confirms the hypothesis of ridge individuals displaying most clearly the tensile compressive distinction between windward and leeward quadrants, respectively. Q. insignis was found to have less curvature on the

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leeward buttresses, also as was expected due to its position in the shadow of the mountain; this habitat had less wind exposure, and thus it would be less vital to have the wind resistant tensile compressive structure. It was unexpected that Q. brenesii would have a leeward buttress curvature value that was closer to Q. corrugata than to Q. insignis ; since, Q. insigni s and Q. brenesii were located at the shadow, it was predicted that they would have similar buttress structure if buttress growth indeed responds to the environmental condition of wind. The two nearly significant results are contradictory when viewed in l ight of my hypothesis. Quercus corrugata ought to have had compressive leeward buttresses that were short, thick, and curved. Yet results show that it displayed thin and curved leeward buttresses. Although they appear to have the one expected quality of mo re curved leeward roots, thi s alone is not sufficient to call such roots completely compressive. Quercus brenesii and Q. insignis should have shared similar buttress structure due to their shared habitat of the mountain shadow. Yet they differed greatly in both leeward buttress curvature and in average buttress thickness. These data and the lack of significant trends seem to indicat e that wind was not the driving force in determining buttress formation. The small sampling size of trees assessed in the study may limit the reliability of the results. The amount of epiphytic growth on the roots may have also skewed the accuracy of certa in measurements, particularly that of root thickness. This then casts doubt on the nearly significant result involving the species wise leeward windward buttress thickness ratio. It is also possible that the chosen sites we re not typical of windblown or wi nd shadow forests Wind intensity may not be sufficiently different between the ridge and the shadow site to produce adequately distinct environmental pressures to lead to unique buttress formation. Perhaps more differences in buttress structure would be f ound by sampling oaks at an even lower elevation. However, the altitudinal difference may also impact the structure of roots and the overall ecology of the habitat. The ideal experiment would have involved two habitats of relatively equal altitude with ver y dissimilar wind conditions, such that wind impact is the only variable. Another variable that would be helpful in controlling is that of different species; results may have been more in line with the hypothesis if just one species was studied. However, f or the scale of this project, it was not possible to set controls for all environmental factors, and thus the results must be considered with caution. However, sampling error is most likely not entirely responsible for the findings. As the results provide d no distinctly significant trends in buttress structure according to location or to species, other factors may be responsible for or wield a stronger influence than wind in buttress formation. One such element may be slope. It was observed that many of th e sampled trees in both locations wer e situated on sloped surfaces. In multiple studies the up slope side of trees had more buttressing to compensate for the crown of the downward side of the tree (Warren et al. 1988 ; Young and Perkocha 1994 ) This may ex plain why Q. corrugata on the ridge, most of which were observed to slope northward, did not reflect the characteristic wind induced structure; the slope may have influenced buttress structure in that more roots were situated on the northward side, followi ng the pattern established by previous research. Ground inclination may thus act as a stronger force in determining buttress placement and structure in Quercus spp. than wind impact. Another possible factor influencing buttress formation in Quercus spp at both sampled sites is crown asymmetry, or uneven distribution of aerial shoots. Young and

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Pekocha (1994) found that crown asymmetry was a more critical factor than was wind during buttress formation in tropical broad leaved forests in Panama and Costa Rica. Buttress formation wa s greatest and heaviest on the opposite side of crown symmetry (Young and Perkocha 1994) It has also been proposed that buttresses serve to address episodic asymmetric canopy loads, and persist after the need to correct it has gone, such that buttresses are as relics of directional stress in the past (Chapman et al. 1998). Such directional stress often takes the form of gap openings, toward which canopy trees have been known to grow (Young and Perkocha 1994). Buttresses may repr esent the history of gap dynamics in a forest ( Young and Perkocha 1994; Chapman et al. 1998 ). Canopy asymmetry may thus considerably influence buttress formation and structure of Quercus spp It follows that the ecology of oaks may be critical in its growt h, as presence and structure of the surrounding trees in a forest can create canopy gaps and result in directional growth and buttresses. This study initially aimed to determine if wind is a sufficiently critical environment factor to lead to structural a daptation in the roots system of certain tropical trees. Although no evidence was found in this study to expressly confirm this, its absence does not necessarily allow for the conclusion that wind is not important in the growth of Quercus spp nor does it follow that buttresses do not provide structural support against wind action. Rather, the development of trees and their roots is a complex process with many possible abiotic and biotic factors influencing growth. Future research may build on this study b y including substrate slope and crown asymmetry in analyzing the buttresses of Quercus spp to ascertain their importance in root system formation. The next chapter in the chronicle of rese arch on tropical buttress roots is awaited, and there are innumerab le paths of investigation to pursue. ACKNOWLEDGEMENTS I extend my gratitude to Karen Masters for valuable guidance and advising throughout the research process. I appreciate t he useful advice of Raquel Mart nez as well as her help in statistical analysis. I am also grateful for suggestions in the developmental stages of the project Also, I would like to thank Victoria for her company in the searc h fo r elusive cloud forest oaks, as well as Rachel for helping me photograph buttresses in action. LITERATURE CITED Chapman C. A., L. Kaufman, and L. J. Chapman. 1998. Buttress formation and directional stress experienced during critical phases of t ree d evelopment. Journal of Tropical Ecology 14 : 341 349. Crook, M.J ., A.R. Ennos, and J.R. Banks. 1997. The function of buttress roots: a comparative study of the anchorage systems of buttressed ( Aglaia and Nephelium ramboutan species) and non buttressed ( Mallotus wrayi ) tropical trees. Journal of Experimental Botany 48 : 1703 1716. Ennos A.R. 1995. Development of buttresses in rainforest trees. In: Wind and trees Coutts, M.P. and John Grace, eds. Cambridge University Press, Vancouver, BC, pp. 293 301. Ennos A. R. 1997 Wind as an ecological factor. Trends in Ecology and Evolution 12 : 108 111. Haber W. A., W. Zuchowski, and E. Bello. 2000. An Introduction to Cloud Forest Trees: Monteverde, Costa Rica. Mountain Gems Publications, Monteverde. Jordan, C.F. 1985. Nutrient Cycling in Tropical Ecosystems. John Whiley and Sons, New York.

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Lawton R. O. 1982. Wind stress and elfin stature in a montane rainforest tree: an adaptive explanation. American Journal of Botany 69 : 1224 1230. Nicoll, B. C. and D. Ray. 1996. Adaptive growth of tree root systems in response to w ind action and site conditions. Tree Physiology 16 : 891 898. Richter, W 1984. A structural approach to the function of buttresses of Quararibea asterolepis Ecology 65 : 1429 1435. Warren S. D., H. L. Black, D. A. Eastmond, and W. H. Whaley. 1988. Structural function of buttresses in Tachigalia versicolor Ecology 69 : 532 536. Young T. P. and V. Perkocha 1994. Treefalls, crown asymmetry, and buttresses. Journal of Ecology 82 : 319 324