Scaling

Schmidt‐Nielsen, Knut

doi:10.1017/cbo9781139167826

Cited by 2,490 publications

(43 citation statements)

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“…This scaling treats petiole length as varying little, or at least independently of leaf size. Alternatively, if petiole length and width are cooptimized, a slightly different scaling following "elastic similarity" as for animal legs might be expected (McMahon and Bonner 1983;Peters 1983;Schmidt-Nielsen 1984), with PW"*^^ a M (and M^ ^ PW^^A; Model B). Leaf mass is only rarely incident on a vertical petiole; instead, leaves are usually better modeled as end-loaded cantilevered beams (Niklas 1991b(Niklas , 1999.…”

Section: Modelmentioning

confidence: 99%

Fossil leaf economics quantified: calibration, Eocene case study, and implications

Royer¹,

Sack²,

Wilf³

et al. 2007

Paleobiology

116

219

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Abstract,•Leaf mass per area (M^) is a central ecological trait that is intercorrelated with leaf life span, photosjnthetic rate, nutrient concentration, and palatability to herbivores. These coordinated variables form a globally convergent leaf economics spectrum, which represents a general continuum running from rapid resource acquisition to maximized resource retention. Leaf economics are little studied in ancient ecosystems because they cannot be directly measured from leaf fossils. Here we use a large extant data set (65 sites; 667 species-site pairs) to develop a new, easily measured scaling relationship between petiole width and leaf mass, normalized for leaf area; this enables M^ estimation for fossil leaves from petiole width and leaf area, two variables that are commonly measurable in leaf compression floras. The calibration data are restricted to woody angiosperms exclusive of monocots, but a preliminary data set (25 species) suggests that broad-leaved gymnosperms exhibit a similar scaling. Application to two well-studied, classic Eocene floras demonstrates that M^ can be quantified in fossil assemblages. First, our results are consistent with predictions from paleobotanical and paleoclimatic studies of these floras. We found exclusively low-M^ species from Republic (Washington, U.S.A., 49 Ma), a humid, warm-temperate flora with a strong deciduous component among the angiosperms, and a wide M^ range in a seasonally dry, warm-temperate flora from the Green River Formation at Bonanza (Utah, U.S.A, 47 Ma), presumed to comprise a mix of short and long leaf life spans. Second, reconstructed M^ in the fossil species is negatively correlated with levels of insect herbivory, whether measured as the proportion of leaves with insect damage, the proportion of leaf area removed by herbivores, or the diversity of insect-damage morphotypes. These correlations are consistent with herbivory observations in extant floras and they reflect fundamental trade-offs in plant-herbivore associations. Our results indicate that several key aspects of plant and plant-animal ecology can now be quantified in the fossil record and demonstrate that herbivory has helped shape the evolution of leaf structure for millions of years.

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Section: Modelmentioning

confidence: 99%

Fossil leaf economics quantified: calibration, Eocene case study, and implications

Royer¹,

Sack²,

Wilf³

et al. 2007

Paleobiology

116

219

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“…ody size influences almost every aspect of the biology of a species, from physiology to life history (1)(2)(3)(4), and plays an important role in the organization of ecological communities (5)(6)(7)(8). Size-frequency distributions (SFDs) of species within clades and regional biotas represent a macroecological and macroevolutionary expression of the forces operating on body sizes over large temporal and spatial scales, and several models have attempted to explain the shapes of these distributions (9)(10)(11)(12)(13).…”

mentioning

confidence: 99%

Invariant size–frequency distributions along a latitudinal gradient in marine bivalves

Roy

Jablonski

Martien

2000

Proc. Natl. Acad. Sci. U.S.A.

123

140

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In the most extensive analysis of body size in marine invertebrates to date, we show that the size-frequency distributions of northeastern Pacific bivalves at the provincial level are surprisingly invariant in modal and median size as well as size range, despite a 4-fold change in species richness from the tropics to the Arctic. The modal sizes and shapes of these size-frequency distributions are consistent with the predictions of an energetic model previously applied to terrestrial mammals and birds. However, analyses of the Miocene-Recent history of body sizes within 82 molluscan genera show little support for the expectation that the modal size is an evolutionary attractor over geological time. Body size influences almost every aspect of the biology of a species, from physiology to life history (1-4), and plays an important role in the organization of ecological communities (5-8). Size-frequency distributions (SFDs) of species within clades and regional biotas represent a macroecological and macroevolutionary expression of the forces operating on body sizes over large temporal and spatial scales, and several models have attempted to explain the shapes of these distributions (9-13). However, little is known about how SFDs of marine invertebrates vary along major environmental gradients such as latitude, and contradictory predictions exist. For example, some authors have argued that size should increase with latitude within and among species even for ectotherms (14-16), whereas species-energy theory predicts decreasing size with latitude (16,17), and clade-specific or region-specific effects might overwhelm any general trends (18). In the most extensive biogeographic analysis of body size in marine invertebrates to date, we compare the SFDs of northeastern Pacific bivalve faunas among four biogeographic provinces, spanning 75 o of latitude. We then compare the shapes of these SFDs to the predictions of a theoretical model of body size based on energetics (10) and test the evolutionary predictions of this and other optimization models. Latitudinal Trends in Body SizeMethods. The latitudinal ranges and body sizes of 915 of the Ϸ950 species of marine bivalves recorded from the tropics to the Arctic along the northeastern Pacific continental shelf (depth Ͻ 200 m) were compiled through an extensive search of the primary literature and from major museum collections (19-21). All bivalve trophic groups are represented, including depositfeeding protobranchs, epifaunal pterioid and infaunal veneroid suspension-feeders, chemosymbiotic lucinoids, and carnivorous septibranchs. As a measure of body size for each species, we used the geometric mean of length and height of the largest known specimen. This standard metric for living and fossil mollusks (22-24) correlates closely with body mass [for the limited mass data available on the bivalves used in this study, log 2 [(length) 1͞2ϫ height] ϭ 5.507 ϩ 0.316 ϫ log 2 (mass), r 2 ϭ 0.81, P Ͻ 0.0001; highly significant relationships between linear shell measurements and body mass...

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“…general an increase in length of a bony element is accompanied by a larger increase in diameter (see, e.g., Schmidt-Nielsen, 1984). This is also seen in chicken leg bones.…”

Section: Scaling Of Fhe Neck By Elastic Similaritymentioning

confidence: 76%

Post natal development of the neck system in the chicken (Gallus domesticus)

Heidweiller

1989

Am. J. Anat.

131

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The lengths of several neck muscles and tendons and the length, width, and height of the cervical vertebrae and some additional distances were measured in the chicken in six post-hatching ontogenetic stages and adults. Each vertebra is characterized by a unique combination of growth rates. All increase most in length. Cranial and caudal width as well as height decreases relative to length during ontogeny. When the long dorsal neck muscles are assumed to provide the support for the weight of the head and half of the weight of the neck, the neck system evidently develops according to McMahon's elastic similarity theory. The assumption is justified also because the weights of head and neck together appeared to scale as predicted by elastic similarity. Short neck muscles show negative and tendons positive allometric growth, and long neck muscles grow isometrically relative to neck length. This growth pattern of the muscles and tendons is a direct consequence of the geometric relations of the different growth rates of the vertebrae.

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Scaling

Cited by 2,490 publications

References 0 publications

Fossil leaf economics quantified: calibration, Eocene case study, and implications

Fossil leaf economics quantified: calibration, Eocene case study, and implications

Invariant size–frequency distributions along a latitudinal gradient in marine bivalves

Post natal development of the neck system in the chicken (Gallus domesticus)

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