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He K, Hui C, Yao W, Wang J, Wang L, Li Q, Shi P. Evidence That Field Muskmelon ( Cucumis melo L. var. agrestis Naud.) Fruits Are Solids of Revolution. PLANTS (BASEL, SWITZERLAND) 2023; 12:4186. [PMID: 38140513 PMCID: PMC10747953 DOI: 10.3390/plants12244186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Revised: 12/02/2023] [Accepted: 12/15/2023] [Indexed: 12/24/2023]
Abstract
In nature, the fruit shapes of many plants resemble avian eggs, a form extensively studied as solids of revolution. Despite this, the hypothesis that egg-shaped fruits are themselves solids of revolution remains unvalidated. To address this, 751 Cucumis melo L. var. agrestis Naud. fruits were photographed, and the two-dimensional (2D) boundary coordinates of each fruit profile were digitized. Then, the explicit Preston equation (EPE), a universal egg-shape model, was used to fit the 2D boundary coordinates to obtain the estimates of the EPE's parameters of each fruit. Under the hypothesis that egg-shaped fruits are solids of revolution, the fruit volumes were estimated using the solid of revolution formula based on the estimated EPE's parameters. To test whether the fruits are solids of revolution, the fruit volumes were measured by using a graduated cylinder and compared with the estimated volumes using the solid of revolution formula. The EPE was demonstrated to be valid in describing the 2D profiles of C. melo var. agrestis fruits. There was a significant correlation between the measured fruit volumes using the graduated cylinder and the estimated fruit volumes using the solid of revolution formula based on the estimated EPE's parameters. Acknowledging potential measurement errors, particularly fruit fuzz causing air bubbles during volume measurements, we recognize slight deviations between measured volumes and estimated values. Despite this, our findings strongly suggest that C. melo var. agrestis fruits are solids of revolution. This study contributes insights into the evolutionary aspects of fruit geometries in plants with egg-shaped fruits and introduces a practical tool for non-destructively calculating fruit volume and surface area based on photographed 2D fruit profiles.
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Affiliation(s)
- Ke He
- Architectural Design and Research Institute, Shenzhen University, #3688 Nanhai Avenue, Shenzhen 518000, China;
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
| | - Cang Hui
- Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7602, South Africa;
- Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Cape Town 7945, South Africa
| | - Weihao Yao
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
| | - Jinfeng Wang
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
| | - Lin Wang
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
| | - Qiying Li
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
| | - Peijian Shi
- Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Nanjing 210037, China; (W.Y.); (J.W.); (L.W.); (Q.L.)
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Guo X, Reddy GV, He J, Li J, Shi P. Mean-variance relationships of leaf bilateral asymmetry for 35 species of plants and their implications. Glob Ecol Conserv 2020. [DOI: 10.1016/j.gecco.2020.e01152] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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3
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Leaf Bilateral Symmetry and the Scaling of the Perimeter vs. the Surface Area in 15 Vine Species. FORESTS 2020. [DOI: 10.3390/f11020246] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
The leaves of vines exhibit a high degree of variability in shape, from simple oval to highly dissected palmatifid leaves. However, little is known about the extent of leaf bilateral symmetry in vines, how leaf perimeter scales with leaf surface area, and how this relationship depends on leaf shape. We studied 15 species of vines and calculated (i) the areal ratio (AR) of both sides of the lamina per leaf, (ii) the standardized symmetry index (SI) to estimate the deviation from leaf bilateral symmetry, and (iii) the dissection index (DI) to measure leaf-shape complexity. In addition, we examined whether there is a scaling relationship between leaf perimeter and area for each species. A total of 14 out of 15 species had no significant differences in average ln(AR), and mean ln(AR) approximated zero, indicating that the areas of the two lamina sides tended to be equal. Nevertheless, SI values among the 15 species had significant differences. A statistically strong scaling relationship between leaf perimeter and area was observed for each species, and the scaling exponents of 12 out of 15 species fell in the range of 0.49−0.55. These data show that vines tend to generate a similar number of left- and right-skewed leaves, which might contribute to optimizing light interception. Weaker scaling relationships between leaf perimeter and area were associated with a greater DI and a greater variation in DI. Thus, DI provides a useful measure of the degree of the complexity of leaf outline.
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Shi P, Zhao L, Ratkowsky DA, Niklas KJ, Huang W, Lin S, Ding Y, Hui C, Li BL. Influence of the physical dimension of leaf size measures on the goodness of fit for Taylor's power law using 101 bamboo taxa. Glob Ecol Conserv 2019. [DOI: 10.1016/j.gecco.2019.e00657] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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5
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Barnes RSK, Hamylton SM. Isometric scaling of faunal patchiness: Seagrass macrobenthic abundance across small spatial scales. MARINE ENVIRONMENTAL RESEARCH 2019; 146:89-100. [PMID: 30928018 DOI: 10.1016/j.marenvres.2019.03.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2018] [Revised: 03/23/2019] [Accepted: 03/24/2019] [Indexed: 06/09/2023]
Abstract
Following earlier studies across 2115 → 33 m2 scales (Barnes and Laurie, 2018), patchiness of macrobenthic abundance in intertidal Queensland seagrass was assessed by dispersion indices, spatial autocorrelation and hotspot analysis across a hierarchically-nested series of smaller scales (5.75 → 0.09 m2). Overall patterns of distribution and abundance over larger extents and with greater lag were mirrored across these smaller ones. Assemblage abundance per station varied by a factor of >10, but all three approaches showed effective constancy of total assemblage patchiness across all sub-2115 m2 scales (across-scales-mean Lloyd's IP of 1.06 and global Moran's I of 0.13). Equivalent constancy was also shown by most numerically-dominant species (scaling exponent β = 0.93-1.15). Decreasing patchiness of some species with decreasing scale, however, resulted in two no longer being patchily dispersed across small scales. Significant hotspots of abundance occurred at a constant proportion of stations across scales, against a background of randomly scattered peak-abundance points.
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Affiliation(s)
- R S K Barnes
- School of Biological Sciences and Centre for Marine Science, University of Queensland, Brisbane, 4072, Queensland, Australia; Biodiversity Program, Queensland Museum, Brisbane, 4101, Queensland, Australia.
| | - Sarah M Hamylton
- School of Earth & Environmental Sciences, University of Wollongong, Wollongong, 2522, New South Wales, Australia
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6
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Leaf Fresh Weight Versus Dry Weight: Which is Better for Describing the Scaling Relationship between Leaf Biomass and Leaf Area for Broad-Leaved Plants? FORESTS 2019. [DOI: 10.3390/f10030256] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Leaf dry mass per unit area (LMA) is considered to represent the photosynthetic capacity, which actually implies a hypothesis that foliar water mass (leaf fresh weight minus leaf dry weight) is proportional to leaf dry weight during leaf growth. However, relevant studies demonstrated that foliar water mass disproportionately increases with increasing leaf dry weight. Although scaling relationships of leaf dry weight vs. leaf area for many plants were investigated, few studies compared the scaling relationship based on leaf dry weight with that based on leaf fresh weight. In this study, we used the data of three families (Lauraceae, Oleaceae, and Poaceae, subfamily Bambusoideae) with five broad-leaved species for each family to examine whether using different measures for leaf biomass (i.e., dry weight and fresh weight) can result in different fitted results for the scaling relationship between leaf biomass and area. Reduced major axis regression was used to fit the log-transformed data of leaf biomass and area, and the bootstrap percentile method was used to test the significance of the difference between the estimate of the scaling exponent of leaf dry weight vs. area and that of leaf fresh weight vs. area. We found that there were five species across three families (Phoebe sheareri (Hemsl.) Gamble, Forsythia viridissima Lindl., Osmanthus fragrans Lour., Chimonobambusa sichuanensis (T.P. Yi) T.H. Wen, and Hibanobambusa tranquillans f. shiroshima H. Okamura) whose estimates of the scaling exponent of leaf dry weight to area and that of leaf fresh weight to area were not significantly different, whereas, for the remaining ten species, both estimates were significantly different. For the species in the same family whose leaf shape is narrow (i.e., a low ratio of leaf width to length) the estimates of two scaling exponents are prone to having a significant difference. There is also an allometric relationship between leaf dry weight and fresh weight, which means that foliar water mass disproportionately increases with increased leaf dry weight. In addition, the goodness of fit for the scaling relationship of leaf fresh weight vs. area is better than that for leaf dry weight vs. area, which suggests that leaf fresh mass might be more able to reflect the physiological functions of leaves associated with photosynthesis and respiration than leaf dry mass. The above conclusions are based on 15 broad-leaved species, although we believe that those conclusions may be potentially extended to other plants with broad and flat leaves.
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Spatial Segregation Facilitates the Coexistence of Tree Species in Temperate Forests. FORESTS 2018. [DOI: 10.3390/f9120768] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Competition between plants has an important role during the natural succession of forest communities. Niche separation between plants can reduce such interspecific competition and enable multispecies plant to achieve coexistence, although this proposition has rarely been supported in experiments. Plant competition can be captured by spatial segregation of the competing species to avoid fierce direct conflicts for nutrients and light. We investigated a site of 400 m × 1000 m in Beijing Pine Mountain National Nature Reserve that was established for protecting Chinese pine and some rare fungi. Six dominant tree species (Fraxinus chinensis Roxb., Syringa reticulata (Blume) H. Hara var. amurensis (Rupr.) J. S. Pringle, Quercus mongolica Fisch. ex Ledeb., Armeniaca sibirica (L.) Lam., Pinus tabuliformis Carrière, and Ulmus pumila L.) were individually marked. Metrics of spatial segregation, based on the theory of spatial point process, were calculated to detect spatial competition. The corresponding type (species)-specific probabilities and the p-values from a spatially implicit test revealed significant overall spatial segregation between the six tree species. We further used the cross-type L-function to check the spatial correlation between Chinese pine and the other tree species, and detected a significant spatial repulsion relationship with four other tree species. Our study shows that each of the six dominant tree species occupies a different subarea in the landscape to effectively reduce direct spatial competition. We thus argue that patchy distributions of different tree species could be common in late forest community succession, and the coexistence of plants could be maintained over a large spatial scale. Management intervention, such as thinning the densities of dominant tree species, could be used to foster species coexistence and ensure the productivity of commercial stands.
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Cobain MRD, Brede M, Trueman CN. Taylor's power law captures the effects of environmental variability on community structure: An example from fishes in the North Sea. J Anim Ecol 2018; 88:290-301. [PMID: 30426504 DOI: 10.1111/1365-2656.12923] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2018] [Revised: 10/20/2018] [Accepted: 11/08/2018] [Indexed: 11/30/2022]
Abstract
Taylor's power law (TPL) describes the relationship between the mean and variance in abundance of populations, with the power law exponent considered a measure of aggregation. However, the usefulness of TPL exponents as an ecological metric has been questioned, largely due to its apparent ubiquity in various complex systems. The aim of this study was to test whether TPL exponents vary systematically with potential drivers of animal aggregation in time and space and therefore capture useful ecological information of the system of interest. We derived community TPL exponents from a long-term, standardised and spatially dense data series of abundance and body size data for a strongly size-structured fish community in the North Sea. We then compared TPL exponents between regions of contrasting environmental characteristics. We find that, in general, TPL exponents vary more than expected under random conditions in the North Sea for size-based populations compared to communities considered by species. Further, size-based temporal TPL exponents are systematically higher (implying more temporally aggregated distributions) along hydrographic boundaries. Time series of size-based spatial TPL exponents also differ between hydrographically distinct basins. These findings support the notion that TPL exponents contain ecological information, capturing community spatio-temporal dynamics as influenced by external drivers.
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Affiliation(s)
- Matthew R D Cobain
- Ocean and Earth Science, University of Southampton, NOCS, Southampton, UK
| | - Markus Brede
- Agents, Interaction and Complexity Group, Electronics and Computer Science, University of Southampton, Southampton, UK
| | - Clive N Trueman
- Ocean and Earth Science, University of Southampton, NOCS, Southampton, UK
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9
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Abstract
Leaf shape and symmetry is of interest because of the importance of leaves in photosynthesis. Recently, a novel method was proposed to measure the extent of bilateral symmetry in leaves in which a leaf was divided into left and right sides by a straight line through the leaf apex and base, and a number of equidistant strips were drawn perpendicular to the straight line to generate an equivalent number of differences in area between the left and right parts. These areal differences are the basis for a measure of leaf bilateral symmetry, which was then examined to see how well it follows Taylor’s power law (TPL) using three classes of plants, namely, 10 geographical populations of Parrotia subaequalis (H.T. Chang) R.M. Hao et H.T. Wei, 10 species of Bambusoideae, and 10 species of Rosaceae. The measure of bilateral symmetry followed TPL for a single species or for a class of closely related species. The estimate of the exponent of TPL for bamboo plants was significantly larger than for the dicotyledonous trees, but its goodness of fit was the best among the three classes of plants. The heterogeneity of light falling on branches and leaves due to above-ground architectural patterns is an important contributor to leaf asymmetry.
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Madden LV, Hughes G, Moraes WB, Xu XM, Turechek WW. Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence. PHYTOPATHOLOGY 2018; 108:656-680. [PMID: 29148964 DOI: 10.1094/phyto-07-17-0234-rvw] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor's power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.
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Affiliation(s)
- L V Madden
- First and third authors: Department of Plant Pathology, Ohio State University, Wooster 44691; second author: Crop and Soil Systems Research Group, SRUC, King's Buildings, Edinburgh EH9 3JG, UK; fourth author: NIAB, East Malling Research, New Road, East Malling, ME19 6BJ, UK; and fifth author: United States Department of Agriculture-Agricultural Research Service, U.S. Horticultural Research Laboratory, 2001 South Rock Road, Ft. Pierce, FL 34945
| | - G Hughes
- First and third authors: Department of Plant Pathology, Ohio State University, Wooster 44691; second author: Crop and Soil Systems Research Group, SRUC, King's Buildings, Edinburgh EH9 3JG, UK; fourth author: NIAB, East Malling Research, New Road, East Malling, ME19 6BJ, UK; and fifth author: United States Department of Agriculture-Agricultural Research Service, U.S. Horticultural Research Laboratory, 2001 South Rock Road, Ft. Pierce, FL 34945
| | - W Bucker Moraes
- First and third authors: Department of Plant Pathology, Ohio State University, Wooster 44691; second author: Crop and Soil Systems Research Group, SRUC, King's Buildings, Edinburgh EH9 3JG, UK; fourth author: NIAB, East Malling Research, New Road, East Malling, ME19 6BJ, UK; and fifth author: United States Department of Agriculture-Agricultural Research Service, U.S. Horticultural Research Laboratory, 2001 South Rock Road, Ft. Pierce, FL 34945
| | - X-M Xu
- First and third authors: Department of Plant Pathology, Ohio State University, Wooster 44691; second author: Crop and Soil Systems Research Group, SRUC, King's Buildings, Edinburgh EH9 3JG, UK; fourth author: NIAB, East Malling Research, New Road, East Malling, ME19 6BJ, UK; and fifth author: United States Department of Agriculture-Agricultural Research Service, U.S. Horticultural Research Laboratory, 2001 South Rock Road, Ft. Pierce, FL 34945
| | - W W Turechek
- First and third authors: Department of Plant Pathology, Ohio State University, Wooster 44691; second author: Crop and Soil Systems Research Group, SRUC, King's Buildings, Edinburgh EH9 3JG, UK; fourth author: NIAB, East Malling Research, New Road, East Malling, ME19 6BJ, UK; and fifth author: United States Department of Agriculture-Agricultural Research Service, U.S. Horticultural Research Laboratory, 2001 South Rock Road, Ft. Pierce, FL 34945
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Shi P, Ratkowsky DA, Wang N, Li Y, Zhao L, Reddy GV, Li BL. Comparison of five methods for parameter estimation under Taylor’s power law. ECOLOGICAL COMPLEXITY 2017. [DOI: 10.1016/j.ecocom.2017.10.006] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Wang H, Xu M. Individual size variation reduces spatial variation in abundance of tree community assemblage, not of tree populations. Ecol Evol 2017; 7:10815-10828. [PMID: 29299260 PMCID: PMC5743614 DOI: 10.1002/ece3.3594] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Revised: 10/03/2017] [Accepted: 10/08/2017] [Indexed: 11/09/2022] Open
Abstract
Research on individual trait variation has gained much attention because of its implication for ecosystem functions and community ecology. The effect of individual variation on population and community abundance (number of individuals) variation remains scarcely tested. Using two established ecological scaling laws (Taylor's law and abundance-size relationship), we derived a new scaling relationship between the individual size variation and spatial variation of abundance. Tested against multi-plot tree data from Diaoluo Mountain tropical forest in Hainan, China, the new scaling relationship showed that individual size variation reduced the spatial variation of community assemblage abundance, but not of taxon-specific population abundance. The different responses of community and population to individual variation were reflected by the validity of the abundance-size relationship. We tested and confirmed this scaling framework using two measures of individual tree size: aboveground biomass and diameter at breast height. Using delta method and height-diameter allometry, we derived the analytic relation of scaling exponents estimated under different individual size measures. In addition, we used multiple regression models to analyze the effect of taxon richness on the relationship between individual size variation and spatial variation of population or community abundance, for taxon-specific and taxon-mixed data, respectively. This work offers empirical evidence and a scaling framework for the negative effect of individual trait variation on spatial variation of plant community. It has implications for forest ecosystem and management where the role of individual variation in regulating population or community spatial variation is important but understudied.
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Affiliation(s)
- Hua‐Feng Wang
- Hainan Key Laboratory for Sustainable Utilization of Tropical BioresourcesInstitute of Tropical Agriculture and ForestryHainan UniversityHaikouChina
| | - Meng Xu
- Department of MathematicsPace UniversityNew YorkNYUSA
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14
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Cheng L, Hui C, Reddy GVP, Ding YL, Shi PJ. Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis. Ecol Evol 2017; 7:9651-9660. [PMID: 29187997 PMCID: PMC5696391 DOI: 10.1002/ece3.3483] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2017] [Accepted: 09/14/2017] [Indexed: 11/08/2022] Open
Abstract
Pseudosasa amabilis (McClure) (Poales: Gramineae) is a typical bamboo species naturally distributed in large area of south China and famous for its culm strength. Although bamboos were found to share the same development rule, the detailed internode morphology of bamboo culm was actually not fully expressed. We explored internode morphology of P. amabilis using 11 different physical parameters in different dimensions (1–4). As Taylor's power law (TPL) is generally applicable to describe relationship between mean and variance of population density, here we used TPL to evaluate the differences between internodes, and further, the relationship between dimension and TPL. Results showed that length (L), hollow radius (HR), hollow area (HA), hollow cylinder volume (HCV), total cylinder volume (TCV), density (De), and weight (W) all presented positive skewed distribution in varying degrees. For the basic one‐dimensional parameters, the 9th internode was the longest, the 7th the heaviest, while thickness (T) decreased with internodes. Diameter (D) decreased in general but with an inconspicuous local mode at the 5–6th internodes, potentially due to the rapid height growth. The longest (9th) internode was the “turning point” for T‐D and HR‐D relationships. Scatter plot changing trends of W to the one‐dimensional parameters after the heaviest (7th) internode were reversed, indicating a deceleration of growth speed. TPL was not holding well in one‐dimensional parameters (R2: 0.5413–0.8125), but keep increasing as the parameter's dimension increasing (R2 > 0.92 for two‐dimensional, R2 > 0.97 for three‐dimensional, and R2 > 0.99 for four‐dimensional parameters.), suggesting an emergence mechanism of TPL related to both the physical dimensions of morphological measures and the allometric growth of bamboo. From the physical fundamental level, all existences are the expression of energy distribution in different dimensions, implying a more general rule that energy distribution holds better TPL in higher dimension level.
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Affiliation(s)
- Liang Cheng
- Department of New Energy Science and Technology Bamboo Research Institute Nanjing Forestry University Nanjing Jiangsu China
| | - Cang Hui
- Centre for Invasion Biology Department of Mathematical Sciences African Institute for Mathematical Sciences Stellenbosch University Matieland South Africa
| | - Gadi V P Reddy
- Western Triangle Agricultural Research Centre Montana State University Conrad MT USA
| | - Yu-Long Ding
- Department of New Energy Science and Technology Bamboo Research Institute Nanjing Forestry University Nanjing Jiangsu China
| | - Pei-Jian Shi
- Department of New Energy Science and Technology Bamboo Research Institute Nanjing Forestry University Nanjing Jiangsu China
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