Size structure of populations within populations: leaf number and size in crowded and uncrowded Impatiens pallida individuals

Summary We compared the size distributions of leaves on naturally-occurring crowded and experimentally thinned uncrowded individuals of Impatiens pallida in southeastern Pennsylvania. Crowding decreased the number of leaves on individual plants and altered the distribution of leaf size. Crowded individuals had smaller leaves, but the size (length) inequality of the leaf population did not change. The relationships between the height of a plant and the mean and maximum length of its leaves were significantly different for crowded and uncrowded plants. There were weak positive relationships between height and total leaf area, and height and total number of leaves for uncrowded plants, whereas crowded plants showed tighter but curvilinear relationships between these variables. Our results point out the strengths and the limitations of viewing canopies as populations of modules.     

Plant Growth Analysis: Allometry, Growth and Interference in Orchardgrass and Timothy

A multiple regression procedure was used to evaluate allometricresponses to stand age and species population densities in monoculturesand mixtures of orchardgrass (Dactylis glomerata L., also knownas cocksfoot) and timothy (Phleum pratense L.). In each speciesthe allometry between shoot dry weight and either leaf areaor tiller number per plant was studied. Population density treatmentsaffected allometry by changing allometric exponents expressingthe ratio of relative growth rates of different plant characteristics.Allometric relationships changed as growth proceeded, and thetwo species differed in their allometric responses to treatments. Plant growth analysis, allometry, competition, Dactylis glomerata L., Phleum pratense L.     

Density Effects on Plant Height Growth and Inequality in Sunflower Populations

Comparisons between competing and non-competing sunflower （Helianthus annuus L.） populations demonstrate pronounced effects of density on plant height growth, height-to-crown width ratio, and s popuiaUon＇s height inequality. In the present study, non-destructive measurements of height and the prolected crown area of sunflower plants were taken at seven times from emergence to fruit maturation in even-aged monospeclflc stands with initial densities of 1, 4, 16, and 64 plants/m^2. The mean height of populations Increased and then decreased with increasing population density; the height Inequalities of uncrowded populations decreased during stand growth, whereas the height inequaiiUes of crowded popuisUons decreased first and then increased during stand development. The interindlvidual relationships between the relative height growth rate and height within uncrowded populations became significantly negative during population growth, whereas these relationships were negative first and then became positive during the development of crowded populations. In the uncrowded populations, the static Interindlvldual relationship between height-to-crown width ratio and volume was positive, whereas for the crowded population these relationships became negative with increasing competition for light. The data suggest that the plastic responses of plant height and height-to-crown width ratio to light competition will become more Intense with increasing competition Intensity. The results of the present study argue strongly for the Importance of size-dependent Individual-level plastic responses due to size-asymmetric light competition In generating the variations in population height inequality.     

Size-dependent Allometry of Tree Height, Diameter and Trunk-taper

The allometry of tree height with respect to trunk diameterand the allometry of trunk diameter with respect to distancefrom the top of the tree (i.e. trunk taper) were determinedfor 27 Robinia pseudoacacia trees differing in age and sizegrowing in an open field. The allometric (scaling) exponentfor height was > 1 for small and young trees and decreasedto 2/3 and then 1/2 as tree size and age increased. Similarly,the exponent for taper was > 1 near the tips of young andold trunks and converged onto values of 2/3 and 1/2 toward thebase of mature tree trunks. These observations indicate thata single 'optimal mechanical design principle' (i.e. elastic,stress or geometric self-similarity) neither holds true throughoutthe lifetime of R. pseudoacacia trees, nor does a single designprinciple govern the taper of a trunk throughout its entirelength. Rather, over the course of growth and development, theallometry of R. pseudoacacia tree height and trunk taper progressivelychanges, complying with geometric self-similarity for youngplants (and young portions of old plants) and subsequently givingthe appearance of elastic or stress self-similarity as plants(or portions of plants) get older and therefore larger. Analysesof published (and new) data suggest that the conclusions drawnfor R. pseudoacacia trees are likely to hold true for othertree species because stem growth in diameter is 'indeterminate'whereas growth in overall tree height is asymptotic and thereforeessentially 'determinate'.Copyright 1995, 1999 Academic Press Scaling, woody plants, Robinia pseudoacacia     

Responses in allometric growth of two dominant species of subalpine meadow—Arundinella anomala and Miscanthus sinensis—to climate warming in Wugongshan Mountains,China

AimsArundinella anomala and Miscanthus sinensis are dominant species in the subalpine meadow of Wugongshan Mountains. Here we studied the effects of climate warming on allometric relationships among different growth components in the two species through simulated warming in natural habitat.
Methods The warming experiments were conducted with open-top chambers (OTCs) in natural habitat in a subalpine meadow community of Wugongshan Mountains. The two main Gramineae species, Arundinella anomala and Miscanthus sinensis, were selected as the study materials. Two sizes of OTCs were set up to create contrasting levels of warming (i.e. TD for low warming and TG for high warming). The morphological variables, such as the plant height and the basal diameter of shoots, were measured. Allometric analysis was conducted with the Smart Package in R software.
Important findings Significant or highly significant correlations and significant allometric relationships were found between and among growth components in both species. The allometry of the growth in most morphological features was strengthened and modified by simulated warming. Stem diameter and plant height, and spike length in A. anomala and M. sinensis changed from isometric to allometric following warming. The relationship The synchronized growth between stem diameter and spikelet in A. anomala was weakened, but their allometry was enhanced with increased warming. The allometric relationship between plant height and leaf length in A. anomala transformed into isometric growth, but it was in reversed pattern in M. sinensis. Warming promoted the plant height and leaf sheath length in A. anomala, whilst higher warming changed the growth relationship between plant height and leaf sheath length in M. sinensis. Similar allometric relationships among the leaf traits were observed, but warming did not significantly impact their allometric exponents. The results suggested that climate warming could have varied effects on different plants, and the differences are often related to the adaptability of plants.     

Shoot Growth and Mortality Patterns of Urtica dioica, a Clonal Forb

The growth and mortality patterns of the clonal forb Urticadioica were investigated at the level of the individual shootin two growing seasons, 1991 and 1992, in a natural stand. Shootheight and diameter at ground level of each shoot tagged inspring were measured repeatedly five times during the growingseason. Dry weights of these repeatedly measured shoots wereestimated using an allometric relationship between dry weight,height and diameter of harvested shoots. A large decrease inshoot density occurred with stand development from the beginningof the growing season in both the years: (1) shoot survivalrate was about 30% at the end of the growing season; (2) shootmortality rate per 10 x 10 cm subplot between censuses was positivelydependent on shoot density per subplot; (3) the mortality rateof individual shoots was negatively dependent on shoot size(height, diameter and weight) at each growing stage, suggestingone-sided competition between living and dying shoots; (4) shootsize (height, diameter and weight) variability in terms of thecoefficient of variation and skewness decreased in accordancewith shoot mortality. Symmetric competition between living shootswas detected by regression analysis based on a model for individualshoot growth considering the degree of competitive asymmetry.However, the competitive effect on individual shoot growth wasvery small (nearly absent). The mortality pattern of Urticadioica indicates that shoot self-thinning occurred from theearly growing stage as in non-clonal crowded monospecific stands,and contrasts with many clonal plants where shoot self-thinningrarely occurs or, if any, is confined only to a short periodof the later growing stage. The pattern of growth and competitionbetween living shoots of Urtica dioica contrasts with non-clonalcrowded plants undergoing intense competition (usually asymmetric)between individuals, but is a common feature of many clonalplants where shoot competition is supposed to be reduced by'physiological integration' between shoots. These form a newpattern not reported yet for clonal plants. It is pointed outthat clonal plants show a wider spectrum of the growth, competitionand mortality patterns of shoots than non-clonals. Some possiblemechanisms for the pattern of Urtica dioica are discussed.Copyright1995, 1999 Academic Press Shoot competition, diffusion model, individual shoot growth, shoot self-thinning, shoot size variability, Urtica dioica L     

武功山亚高山草甸群落优势植物野古草和芒异速生长对气候变暖的响应

气候变暖正持续影响着陆地生态系统的结构和功能, 一直是备受关注的热点问题。异速生长关系被认为是生物界中的一种普遍规律, 但我们对于气候变暖如何影响植物异速生长特征所知甚少。该文采用开顶式增温小室对野外自然生境进行模拟增温的方法, 研究了气候变暖对江西武功山亚高山草甸植物群落优势种野古草(Arundinella anomala)和芒(Miscanthus sinensis)异速生长特征的影响。结果表明: 野古草和芒的大多数形态指标之间均具有显著或极显著相关生长关系和异速生长关系, 气候变暖强化了两种禾本科植物大多数形态特征之间的异速生长, 或改变了其原有的生长关系。气候变暖还导致野古草和芒的基部茎粗与其高度、穗长间由原有的等速生长关系转变为异速生长关系; 野古草基部茎粗与小穗数间的异速生长随着温度升高而趋于增强。气候变暖导致野古草个体高度与其叶片长度的异速生长关系转变为等速生长关系, 而芒有相反表现。同时, 增温促进了野古草株高及叶鞘长的生长, 较强增温则改变了芒株高和叶鞘长之间的生长关系; 野古草和芒的叶片形态特征之间几乎都表现为类似的异速生长关系, 增温对其异速生长指数无显著影响。研究表明气候变暖对不同植物和植物构件具有差异性影响, 这种差异性往往与植物的适应性有关。     

Relationships between Height, Diameter and Weight Distributions of Chenopodium album Plants in Stands: Effects of Dimension and Allometry

Frequency distributions of height (H), stem diameter (D) anddry weight (W) of Chenopodium album plants in even-aged monoculturesat the initial plant densities of 400, 800 and 1200 plants m^-2(400-, 800- and 1200-plots) were compared. The height distributionsat the end of the growing season were bimodal for the 400-plotbut L-shaped for the 800- and 1200-plots. The distributionsof diameter and dry weight were L-shaped for all the plots.When the size measures were expressed on the log scale so asto eliminate effects of the differences in dimension, frequencydistributions of log W and log H for the 400-plot were bimodal.In contrast, the log D distributions were bell-shaped for allthe plots. To elucidate factors responsible for the differences in frequencydistributions among log size measures, we examined allometricrelationships between log size measures. They were all non-linearall non-linear mainly because the allometric relationships weremarkedly different between the plants forming the upper-mostleaf layer ('upper' plants) and the suppressed plants ('lower'plants). A striking feature was that the heights of the 'upper'plants were almost uniform in spite of their varied diameters.Continuous monitoring of growth of the individual plants inthe stand revealed that the height of the 'upper' plants becameuniform just after the canopy closure, at about 30 d after emergence,and that uniform growth in height of these plants continuedfor about 70 d until the end of the growing season. On the otherhand, growth of the suppressed 'lower' plants terminated atvarious stages before flowering. The 'height convergence' ofthe 'upper' plants was thus identified as a key factor for thesegregation of the plants into the two groups of distinctlydifferent allometries. Since the segregation of the plants into 'upper' and 'lower'plants was reflected in their dry weights, frequency distributionsof log W were similar to those of log H. The bell-shaped distributionsof log D were attributed to the overlapping of the diametersof slender 'upper' plants with those of larger 'lower' plants.Significance of 'height convergence' is discussed.Copyright1995, 1999 Academic Press Chenopodium album L., fat hen, height, size structure, bimodal distribution, L-shaped distribution, allometry, growth     

Patterns of Trunk Diameter, Tree Height and Crown Depth in Crowded Abies Stands

The size structure of trees in crowded, even-aged Abies (fir)stands of ‘Shimagare’ or ‘wave-regenerated’sub-alpine forests is analyzed. Tree-height distributions showconsistently smaller variation and less positive skewness thanthe distributions of trunk diameter and crown depth (tree heightminus height of the lowest branch). This difference is associatedwith changes in the relationships between trunk diameter, treeheight and crown depth as stands age. These, in turn, resultfrom self-pruning of the lower foliage crown due to competitionfor light in crowded stands. Abies, diameter-height curve, competition, size distribution, stand development, tree geometry, wave-regeneration     

Theoretical Relationships Between Mean Plant Size, Size Distribution and Self Thinning under One-sided Competition

As yet there is no comprehensive theory in plant populationecology to explain relationships between mean plant size, sizedistribution and self-thinning. In this paper, a new synthesisof plant monocultures is proposed. If the reciprocal relationshipbetween plant biomass and plant population density among variousstands of even-aged plant populations holds, the same reciprocalrelationship must exist between cumulative mass and cumulativenumber of plants from the largest individual within a population,assuming strict one-sided competition (which is an extreme conditionfor competition for light among plants). The two parametersof the relationship between cumulative mass and cumulative numberwithin a stand both correlate with maximum plant height in thestand. One parameter equals the reciprocal of the potentialmaximum plant mass per area, which is expressed by the productof maximum plant height and dry-matter density. The other parametercorrelates with the potential maximum individual plant mass,which is allometrically related to maximum plant height. Asa stand develops, the growth rate of the smallest individualswill become zero due to suppression from larger individuals,and they will die; i.e. self-thinning will occur. The slopeof the self-thinning line is expressed through the coefficientsof allometry between height and mass and between dry matterdensity and height. When the former coefficient is 3 and thelatter is 0, the gradient exactly corresponds to the value expectedfrom the 3/2 power rule, but it can take various values dependingon the values of the two coefficients. Competition among individualsdetermines size-density relationships among stands, which inturn determine the size structure of the stand. The size structureconstrains the growth of individuals and results in self-thinningwithin the stand.Copyright 1999 Annals of Botany Company. Monoculture, plant population, self-thinning, competition, hierarchy, size-structure.     

Foliage Profile, Size Structure and Stem Diameter-Plant Height Relationship in Crowded Plant Populations

The relationships between vertical foliage profile of an individualplant, competition between individuals, size structure and allocationpattern between stem diameter (D) and plant height (H) wereinvestigated using canopy photosynthesis and two-dimensionalcontinuity equation models including D and H as two independentvariables. Broad-leaved type plants (more foliage mass in theupper layer than in the lower layer of the canopy of an individualwhen grown in isolation) showed curvilinear D-H relationshipand bimodal H distribution, and underwent more asymmetric competitionthan coniferous type plants (more foliage mass in the lowerlayer than in the upper layer of the canopy of an individualwhen grown in isolation) under crowded conditions. Coniferoustype plants showed almost linear D-H relationship (i.e. simpleallometry) and unimodal H distribution, and underwent more symmetriccompetition than broad-leaved type plants under crowded conditions.However, in both the cases D distributions were unimodal. Allocationpatterns between D and H affected these features only a little.These simulation results can explain many actual data alreadypublished. The value of     

A Canopy Photosynthesis Model for the Dynamics of Size Structure and Self-thinning in Plant Populations

A dynamic model for growth and mortality of individual plantsin a stand was developed, based on the process of canopy photosynthesis,and assuming an allometric relationship between plant heightand weight, i.e. allocation growth pattern of plant height andstem diameter. Functions G(t, x), for the mean growth rate ofindividuals of size x at time t, and M(t,x), for the mortalityrate of individuals of size x at time t, were developed fromthis model and used in simulations. The dynamics of size structurewere simulated, combining the continuity equation model, a simpleversion of the diffusion model, with these functions. Simulationsreproduced several well-documented phenomena: (1) size variabilityin terms of coefficient of variation and skewness of plant weightincreases at first with stand development and then stabilisesor decreases with an onset of intensive self-thinning; (2) duringthe course of self-thinning, there is a power relationship betweendensity and biomass per unit ground area, irrespective of theinitial density and of the allocation-growth pattern in termsof the allometric parameter relating plant height and weight.The following were further shown by simulation: (a) competitionbetween individuals in a crowded stand is never completely one-sidedbut always asymmetrically two-sided, even though competitionis only for light; (b) plants of ‘height-growth’type exhibit a greater asymmetry in competition than plantsof ‘diameter-growth’ type, (c) the effect of competitionon the growth of individuals in a crowded stand converges toa stationary state, even when the stand structure still changesgreatly. All of these theoretical results can explain recentempirical results obtained from several natural plant communities.Finally, a new, general functional form for G(t, x) in a crowdedstand is proposed based on these theoretical results, insteadof a priori or empirical growth and competition functions. Canopy photosynthesis, competition mode, continuity equation, self-thinning, simulation, size distribution     

Allometric relationships to assess ontogenetic adaptative changes in three NE Atlantic commercial sea cucumbers (Echinodermata,Holothuroidea)

Holothuria arguinensis, Holothuria mammata and Holothuria forskali are three common sea cucumber species found in the NE Atlantic, traded in international markets and susceptible to capture. Allometric relationships reveal if the scaling relationships between biometric characters are proportional with growth, being a useful tool to understand species growth strategies. Allometric relationships of the three species were estimated and compared between them and with populations from different regions. These allometric relationships revealed that the three species have negative allometric growth. However, they have different growth strategies between them and reveal different regional intra-specific growth strategies when compared to other populations, suggesting ontogenetic adaptation as a consequence of external factors.

     

Allometric Relationships in Field-grown Soybean

Allometric relationships in plants uncover size-correlated variationsin form and development and characterize the relative growthof a part of a plant in comparison with a whole. Stable allometricrelationships in ontogeny can be used as components of cropmodels and to estimate plant parameters that are difficult tomeasure. Our objective was to discover whether stable allometricrelations exist in ontogeny of field-grown soybeans (GlycinemaxL.). We used field data on vegetative stages, plant height,stem weight, and leaf weight of 16 soybean cultivars measuredon farms and on the experiment station of Mississippi StateUniversity during 1993–1995 growing seasons. The numberof observed crops for each cultivar ranged from one to 14. Stemheights displayed linear log-log dependencies on the vegetativestage, before and after the breakpoint stage, which typicallywas between the ‘fourth node’ and ‘sixth node’vegetative stages. Slopes of the log-log dependencies afterthe breakpoint stage were similar in all cultivars. Stem masshad log-log linear dependencies on stem height. Slopes of thesedependencies differed among cultivars grown under the same conditions,and among crops of the same cultivar grown under different conditions.Water stress could be a modifier of these relationships. Theproportion of leaf weights in the total weight of leaves andstems decreased linearly as the vegetative development progressed.Since allometric relations are stable for a specific crop, theycan be used to forecast vegetative development as soon as theyare established.Copyright 1998 Annals of Botany Soybean,Glycine maxL., allometry, vegetative development.     

Modes of ontogenetic allometric shifts in crocodylian vertebrae

During postnatal ontogeny of vertebrates, allometric trends in certain morphological units or dimensions can shift drastically among isometry, positive allometry, and negative allometry. However, detailed patterns of allometric transitions in certain timings have not been explored well. Identifying the presence and nature of allometric shifts is essential for understanding the patterns of changes in relative size and shape and the proximal factors that are controlling these changes mechanistically. Allometric trends in 10 selected vertebrae (cervical 2–caudal 2) from hatchlings to very mature individuals of Alligator mississippiensis (Archosauria, Crocodylia) are reported in the present study. Allometric coefficients in 12 vertebral dimensions are calculated and compared relative to total body length, including centrum, neural spine, transverse process, zygapophysis, and neural pedicle. During the postnatal growth, positive allometry is the most common type of relative change (10 of the 12 dimensions), although the diameter of the neural canal shows a negative allometric trend. However, when using spurious breaks (i.e. allometric trends subdivided into growth stages using certain growth events, and key body sizes and/or ages), vertebral parts exhibit various pathways of allometric shifts. Based on allometric trends in three spurious breaks, separated by the end of endochondral ossification (body length: approximnately 0.9 m), sexual maturity (1.8 m), and the stoppage of body size increase (2.8 m), six types of ontogenetic allometric shifts are established. Allometric shifts exhibit a wide range from positive allometry restricted only in the early postnatal stage (Type I) to life‐long positive allometry (Type VI). This model of ontogenetic allometric shifts is then applied to interpret potential mechanisms (causes) of allometric changes, such as (1) growth itself (when allometric trend gradually decreases to isometric or negative allometric change: Type II–IV allometric shift); (2) developmental constraint (when positive allometry is limited only in the early growth stage: Type I allometric shift); and (3) functional or biomechanical drive (when positive allometry continues throughout ontogeny: Type VI allometric shift).     

Plastic Response of Crown Architecture to Crowding in Understorey Trees of Two Co-dominating Conifers

Crown architecture and growth rate of trunk height, trunk diameterand lateral branches of understorey trees (5–10m tall)were compared between two co-dominating conifers,Abies sachalinensisandPiceaglehnii, in relation to the index of local crowding intensity,W,represented as a function of density, distance and basal areaof taller neighbours. For the two conifers, the growth of trunkheight and diameter was decreased and crowns became flat withincreasingW, keeping crown projection area. Self-pruning oflower branches was more intense inAbiesthan inPiceain crowdedconditions, while both conifers showed similar crown forms inless crowded conditions. These results suggest that the growthin lateral branches exceeded that in height in crowded conditions,especially inAbies. Tree age of both conifers increased withincreasingW, resulting from the low growth rate in crowded conditions.The age of the longest and lowest branch ofPicea, up to 150years, was positively correlated with the tree age ranging from70 to 250 years, whereas that ofAbieswas constant at around30 years irrespective of tree age varying from 40 to 140 years.This result agrees with the observation that agedAbieshad moreflat-shaped crowns than in agedPiceain crowded conditions. Theseresults suggest that each conifer adapted to crowding in differentways: high elongation of branches with high turnover rate forAbiesandviceversaforPicea. Abies; crown form; neighbourhood interference; Picea; plasticity     

Allometric growth and carbon storage in the mangrove Sonneratia apetala

Allometric growth reflects different allocation patterns and relationships of different components or traits of a plant and is closely related to ecosystem carbon storage. As an introduced species, the growth and carbon storage of Sonneratia apetala are still unclear. To derive allometric relationships of the mangrove S. apetala and to estimate carbon storage in mangrove ecosystems, we harvested 12 individual Sonneratia apetala trees from four different diameter classes in the Futian National Nature Reserve, Guangdong, China. Allometric growth models were fitted. The results showed that diameter at breast height (DBH) and wood density were better variables for predicting plant biomass (including above- and below-ground biomass) than plant height. There were significant power function relationships between biomass and DBH, with a mean allometric exponent of 2.22, and stem biomass accounted for 97% of the variation in S. apetala total biomass. Nearly isometric scaling relationships were developed between stem biomass and other biomass components. To better understand the carbon stocks of the S. apetala ecosystem, we categorized all trees into five age classes and quantified vegetation carbon storage. The S. apetala vegetation carbon storage ranged from 96.48 to 215.35 Mg C ha^?1, and the carbon storage significantly increased with stand age. The allometric equations developed in this study are useful to estimate biomass and carbon storage of S. apetala ecosystems.

     

Variation in the ontogenetic allometry of horn length in bovids along a body mass continuum

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass.     

A comparison of 12 tree species of Amazonian caatinga using growth rates in gaps and understorey, and allometric relationships

1. The relative growth rate of saplings of 12 species from an oligotrophic lowland rain forest were measured in treefall gaps and understorey. Mean relative height growth ( R _H) within treefall gaps was found to be slowest for tall-tree species with branched saplings, intermediate for subcanopy trees and fastest for tall-tree species with unbranched saplings. Most species had similar R _H within the understorey. R _H values were not related to leaf mass per unit area (LMA) or foliar N concentrations.
2. Allometric relationships between the total leaf area (TLA) and height were dependent upon light conditions; in general saplings of a given height had a greater TLA in treefall gaps than in understorey. The species with the largest estimated TLA values in gaps tended to have the greatest R _H values in gaps; no such trend emerged in the understorey. The values of the allometric coefficients were not related to foliar properties.
3. The relationship between stem diameter and height was only weakly dependent on light conditions and the relationship between the growth rates in these dimensions was also weak. The lack of plasticity may reflect the fact that the height–diameter relationship has little bearing on a sapling's tolerance of shade.
4. One way of accommodating the dependence of allometry upon irradiance is to add R _H as a covariate. We derive a relationship between growth rates from this resource-dependent allometric equation and show that it reasonably describes measurements taken in the caatinga forest.