The principles of cellular geometry scaling

Cellular dimensions profoundly influence cellular physiology. For unicellular organisms, this has direct bearing on their ecology and evolution. The morphology of a cell is governed by scaling rules. As it grows, the ratio of its surface area to volume is expected to decrease. Similarly, if environmental conditions force proliferating cells to settle on different size optima, cells of the same type may exhibit size-dependent variation in cellular processes. In fungi, algae and plants where cells are surrounded by a rigid wall, division at smaller size often produces immediate changes in geometry, decreasing cell fitness. Here, we discuss how cells interpret their size, buffer against changes in shape and, if necessary, scale their polarity to maintain optimal shape at different cell volumes.     

Ontogeny, phylogeny, and morphology in anuran larvae: morphometric analysis of cranial development and evolution in Rana tadpoles (Anura: Ranidae)

Comparative studies of chondrocranial morphology in larval anurans are typically qualitative in nature, focusing primarily on discrete variation or gross differences in the size or shape of individual structures. Detailed data on chondrocranial allometry are currently limited to only two species, Rana sylvatica and Bufo americanus. This study uses geometric morphometric and multivariate statistical analyses to examine interspecific variation in both larval chondrocranial shape and patterns of ontogenetic allometry among six species of Rana. Variation is interpreted within the context of hypothesized phylogenetic relationships among these species. Canonical variates analyses of geometric morphometric datasets indicate that species can be clearly discriminated based on chondrocranial shape, even when whole ontogenies are included in the analysis. Ordinations and cluster analyses based on chondrocranial shape data indicate the presence of three primary groupings (R. sylvatica; R. catesbeiana + R. clamitans; and R. palustris + R. pipiens + R. sphenocephala), and patterns of similarity closely reflect phylogenetic relationships. Analysis of chondrocranial allometry reveals that some patterns are conserved across all species (e.g., most measurements scale with negative allometry, those associated with the posterior palatoquadrate tend to scale with isometry or positive allometry). Ontogenetic scaling along similar allometric trajectories, lateral transpositions of individual trajectories, and variable allometric relationships all contribute to shape differences among species. Overall patterns of similarity among ontogenetic trajectories also strongly reflect phylogenetic relationships. Thus, this study demonstrates a tight link between ontogeny, phylogeny, and morphology, and highlights the importance of including both ontogenetic and phylogenetic data in studies of chondrocranial evolution in larval anurans.     

Ambulacral growth allometry in edrioasteroids: functional surface‐volume change in ontogeny and phylogeny

McKinney, M. L. & Sumrall, C. D. 2010: Ambulacral growth allometry in edrioasteroids: functional surface‐volume change in ontogeny and phylogeny. Lethaia, Vol. 44, pp. 102–108. Most organisms do not maintain geometric similarity as they grow, in large part because of surface‐volume interactions. Because respiratory and food‐acquiring organs are dependent on surface area, which increases more slowly than volume, organisms have evolved many strategies to increase the efficiency of, and/or the functional surface areas of these organs. Here, we report some preliminary results comparing area of the feeding apparatus (ambulacra) versus the volume of the theca for a suite of isorophid edrioasteroid species at various ontogenetic sizes. Regression of log (ambulacral area) on log (thecal volume) indicates a strongly constrained allometric pattern whereby the ontogenies of all measured species fall on or near the same line (r² = 0.962, n = 55), with a slope (k) = 0.654 (± 0.018). This slope and associated 0.05 standard error (0.618–0.690) is within the bounds of that expected from increasing surface area to keep pace with the metabolic demands of increasing thecal size. This allometric value is also comparable to the size scaling of metabolism and respiratory and feeding surfaces in many living and a few fossil invertebrates (k ～ 0.5–0.9). The edrioasteroid species analysed show a very wide variety of changes in ambulacral length, width and sinuosity, documenting many different patterns for achieving the same goal of increasing surface area to keep pace with volume increase. There is no evidence of increasing feeding efficiency. □Edrioasteroid, allometry, ambulacrum, surface‐volume, echinoderm.     

Allometric scaling in small colonies of the scleractinian coral Siderastrea siderea (Ellis and Solander)

Although most physiological traits scale allometrically in unitary organisms, it has been hypothesized that modularity allows for isometric scaling in colonial modular taxa. Isometry would allow increases in size without functional constraints, and is thought to be of central importance to the success of a modular design. Yet, despite its potential importance, scaling in these organisms has received little attention. To determine whether scleractinian corals are free of allometric constraints, we quantified metabolic scaling, measured as aerobic respiration, in small colonies (< or =40 mm in diam.) of the scleractinian Siderastrea siderea. We also quantified the scaling of colony surface area with biomass, since the proposed isometry is contingent upon maintaining a constant ratio of surface area to biomass (or volume) with size. Contrary to the predicted isometry, aerobic respiration scaled allometrically on biomass with a slope (b) of 0.176, and colony surface area scaled allometrically on biomass with a slope of 0.730. These findings indicate that small colonies of S. siderea have disproportionately high metabolic rates and SA:B ratios compared to their larger counterparts. The most probable explanations for the allometric scaling of aerobic respiration are (1) a decline in the SA:B ratio with size such that more surface area is available per unit of biomass for mass transfer in the smallest colonies, and (2) the small size, young age, and disproportionately high growth rates of the corals examined. This allometric scaling also demonstrates that modularity, alone, does not allow small colonies of S. siderea to overcome allometric constraints. Further studies are required to determine whether allometric scaling is characteristic of the full size range of colonies of S. siderea.     

An ontogenetic perspective on the study of sexual dimorphism, phylogenetic variability, and allometry of the skull of European ground squirrel, Spermophilus citellus (Linnaeus, 1766)

Most studies of morphological variability in or among species are performed on adult specimens. However, it has been proven that knowledge of the patterns of size and shape changes and their covariation during ontogeny is of great value for the understanding of the processes that produce morphological variation. In this study, we investigated the patterns of sexual dimorphism, phylogenetic variability, and ontogenetic allometry in the Spermophilus citellus with geometric morphometrics applied to cross-sectional ontogenetic data of 189 skulls from three populations (originating from Burgenland, Banat, and Dojran) belonging to two phylogenetic lineages (the Northern and Southern). Our results indicate that sexual dimorphism in the ventral cranium of S. citellus is expressed only in skull size and becomes apparent just before or after the first hibernation because of accelerated growth in juvenile males. Sexes had the same pattern of ontogenetic allometry. Populations from Banat and Dojran, belonging to different phylogroups, were the most different in size but had the most similar adult skull shape. Phylogenetic relations among populations, therefore, did not reflect skull morphology, which is probably under a significant influence of ecological factors. Populations had parallel allometric trajectories, indicating that alterations in development probably occur prenatally. The species’ allometric relations during cranial growth showed characteristic nonlinear trajectories in the two northern populations, with accelerated shape changes in juveniles and continued but almost isometric growth in adults. The adult cranial shape was reached before sexual maturity of both sexes and adult size after sexual maturity. The majority of shape changes during growth are probably correlated with the shift from a liquid to a solid diet and to a lesser degree due to allometric scaling, which explained only 20 % of total shape variation. As expected, viscerocranial components grew with positive and neurocranial with negative allometry.     

Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents

It has been hypothesized that most morphological evolution occurs by allometric differentiation. Because rodents encapsulate a phenomenal amount of taxonomic diversity and, among several clades, contrasting levels of morphological diversity, they represent an excellent subject to address the question: how variable are allometric patterns during evolution? We investigated the influence of phylogenetic relations and ecological factors on the results of the first quantification of allometric disparity among rodents by exploring allometric space, a multivariate morphospace here derived from, and encapsulating all, the ontogenetic trajectories of 34 rodent species from two parallel phylogenetic radiations. Disparity was quantified using angles between ontogenetic trajectories for different species and clades. We found an overlapping occupation of allometric space by muroid and hystricognath species, revealing both clades possess similar abilities to evolve in different directions of phenotypic space, and anatomical diversity does not act to constrain the labile nature of allometric patterning. Morphological features to enable efficient processing of food serve to group rodents in allometric space, reflecting the importance of convergent morphology, rather than shared evolutionary history, in the generation of allometric patterns. Our results indicate that the conserved level of morphological integration found among primates cannot simply be extended to all mammals.     

Head shape evolution in monitor lizards (Varanus): interactions between extreme size disparity,phylogeny and ecology

Characterizing patterns of observed current variation, and testing hypotheses concerning the potential drivers of this variation, is fundamental to understanding how morphology evolves. Phylogenetic history, size and ecology are all central components driving the evolution of morphological variation, but only recently have methods become available to tease these aspects apart for particular body structures. Extant monitor lizards (Varanus) have radiated into an incredible range of habitats and display the largest body size range of any terrestrial vertebrate genus. Although their body morphology remains remarkably conservative, they have obvious head shape variation. We use two‐dimensional geometric morphometric techniques to characterize the patterns of dorsal head shape variation in 36 species (375 specimens) of varanid, and test how this variation relates to size, phylogenetic history and ecology as represented by habitat. Interspecific head shape disparity is strongly allometric. Once size effects are removed, principal component analysis shows that most shape variation relates to changes in the snout and head width. Size‐corrected head shape variation has strong phylogenetic signal at a broad level, but habitat use is predictive of shape disparity within phylogenetic lineages. Size often explains shape disparity among organisms; however, the ability to separate size and shape variation using geometric morphometrics has enabled the identification of phylogenetic history and habitat as additional key factors contributing to the evolution of head shape disparity among varanid lizards.     

Allometry of human fertility and energy use

The flux of energy and materials constrains all organisms, and allometric relationships between rates of energy consumption and other biological rates are manifest at many levels of biological organization. Although human ecology is unusual in many respects, human populations also face energetic constraints. Here we present a model relating fertility rates to per capita energy consumption rates in contemporary human nations. Fertility declines as energy consumption increases with a scaling exponent of ?1/3 as predicted by allometric theory. The decline may be explained by parental trade‐offs between the number of children and the energetic investment in each child. We hypothesize that the ?1/3 exponent results from the scaling properties of the networked infrastructure that delivers energy to consumers. This allometric analysis of human fertility offers a framework for understanding the demographic transition to smaller family sizes, with implications for human population growth, resource use and sustainability.     

枕骨三维形态在现生人群间的变异

与面颅、脑颅和颅底不同,枕骨与人群间遗传信息的关系不明确且研究较少。传统形态测量方法对枕骨的研究难以全面反映枕骨的形态信息。为更加精细地探究枕骨形态与人群的关系,本文以亚洲、非洲和欧洲地区的103例现生男性头骨为研究对象,通过三维几何形态测量和多元统计分析的方法对枕骨三维形态和异速生长模式在人群间的差异进行了研究。研究结果表明,枕骨的大小和形状在现生人群中具有显著差异,然而这种差异并不足以区分不同人群。现代人枕骨的三维形态具有较大的变异,主要表现在枕外隆凸点的突出程度、上下相对位置以及枕平面与项平面的比例,其次表现在星点位置在前后、内外以及上下方向上的变化,斜坡的倾角变化等方面。异速生长的分析表明,不同人群中存在不同的异速生长模式,但是非洲和欧洲人群也存在相似的趋势。本研究认为枕骨三维形态在反映人群间遗传关系上作用较小,支持枕骨形态可能更多受到功能和环境等因素的影响。     

28 Lipid composition of members of the algal class chlorarachniophyceae

The algal class Chlorarachniophyceae is comprised of a small group of unicellular eukaryotic algae that are often characterized by an unusual amoeboid morphology. This morphology is hypothesized to be the result of a secondary endosymbiosis in which a green alga was engulfed as prey by a nonphotosynthetic amoeba or amoebaflagellate. Whereas much is known about the phylogenetic relationships of individual chlorarachniophytes to one another, and to possible ancestral host organisms in the genera Cercomonas and Heteromita, little is known about their physiology, particularly that of their lipids. In an initial effort to characterize the lipids of this algal class, seven organisms were examined for their fatty acid and sterol composition. These included Bigelowiella natans, Chlorarachnion globusum, Chlorarachnion reptans, Gymnochlora stellata, Lotharella amoeboformis, Lotharella globosa, and Lotharella sp. Fatty acids associated with chloroplast‐associated glycolipids, cytoplasmic membrane‐associated phospholipids, and storage triglycerides were characterized. Glycolipid fatty acids were found to be of limited composition, containing principally eicosapentaenoic acid [20:5(n‐3)] and hexadecanoic acid (16:0), which ranged in relative percentage from 67–90% and 10–29%, respectively, in these seven organisms. Triglyceride‐associated fatty acids were found to be similar. Phospholipid fatty acid composition was more variable. The principal phospholipid fatty acids, 16:0 (25–32%) and a compound tentatively identified as docosapentaenoic acid [22:5(n‐3)] (26–35%), were found along with a number of C18 and C20 fatty acids. All organisms contained two sterols as free sterols. These were tentatively identified as 24‐ethylcholesta‐5,22E‐dien‐3b‐ol (stigmasterol; 70–95%) and 24‐methylcholesta‐5,22E‐dien‐3b‐ol (brassicasterol; 5–30%).     

代谢异速生长理论及其在微生物生态学领域的应用

新陈代谢是生物的基本生理过程,影响生物在不同环境中参与物质循环和能量转化的过程.代谢速率作为生物体重要的生命过程指标,几乎影响所有的生物活性速率,且在很多研究中均表现出异速生长现象.所谓代谢异速是指生物体代谢速率与其个体大小(或质量)之间存在的幂函数关系.代谢异速生长理论的提出,从机制模型角度解释了代谢异速关系这一普遍存在的生命现象.该理论利用分形几何学及流体动力学等原理,从生物能量学角度阐释了异速生长规律的机理,证实了3/4权度指数的存在;但同时有研究表明,权度指数因环境因素等影响处于2/3-1范围之间而非定值.随着研究工作的深入,代谢异速生长理论研究从起初的宏观动植物领域拓展到了微生物领域,在研究微生物的代谢异速生长理论时,可将微生物的可操作分类单元(Operational taxonomic unit,OTU)或具有特定功能的功能群视为一个微生物个体,基于其遗传多样性和功能多样性特征进行表征,以便于将微生物群落多样性与其生态功能性联系起来,使该理论在微生物生态学领域得到有效的补充和完善.尽管细菌具有独特的生物学特性,但与宏观生物系统中观测到的现象表现出明显的一致性.有研究表明,3个农田土壤细菌基于遗传多样性的OTU数的平均周转率分别为0.71、0.80和0.84,介于2/3与1之间,可能与生物代谢异速指数有一定关联,为微生物代谢异速指数的研究提出了一个参考解决方案.鉴于微生物个体特征和生物学特性,在分析代谢速率与个体大小关系中,从微生物单位个体的定义、个体大小表征到计量单位的统一,仍需更多的理论支持.分析了代谢异速生长理论在微生物与生态系统功能关系研究中的可能应用,延伸了该理论的应用范围,并对尚待加强的研究问题进行了评述和展望.     

Codon usage and tRNA content in unicellular and multicellular organisms

Choices of synonymous codons in unicellular organisms are here reviewed, and differences in synonymous codon usages between Escherichia coli and the yeast Saccharomyces cerevisiae are attributed to differences in the actual populations of isoaccepting tRNAs. There exists a strong positive correlation between codon usage and tRNA content in both organisms, and the extent of this correlation relates to the protein production levels of individual genes. Codon-choice patterns are believed to have been well conserved during the course of evolution. Examination of silent substitutions and tRNA populations in Enterobacteriaceae revealed that the evolutionary constraint imposed by tRNA content on codon usage decelerated rather than accelerated the silent-substitution rate, at least insofar as pairs of taxonomically related organisms were examined. Codon-choice patterns of multicellular organisms are briefly reviewed, and diversity in G+C percentage at the third position of codons in vertebrate genes--as well as a possible causative factor in the production of this diversity--is discussed.      

Stem and wood allometric relationships in Cacteae (Cactaceae)

Allometric relationships in organisms are considered a universal phenomenon. A positive scaling has been reported between stem size and cellular size of tracheary elements in wood of different vascular plants, but few studies have been carried out in slow-growing succulent plants. The aim of this study was to evaluate if a relationship exists between size, growth form and wood cell size among individual species of Cacteae. Forty-four species belonging to 16 genera of the tribe Cacteae with differing growth forms and sizes were studied. When analyzing plant size, we found a positive allometric scaling and the larger-sized species showing a higher percentage of succulent tissue and less accumulation of wood tissue. The positive scaling found between plant size (height and diameter) and vessel elements and fiber length support the universality of the allometric relationship proposed for other vascular plants with non-succulent stems. Notably, wide-band tracheids do not scale with plant size or growth form. Succulence associated with narrow vessel elements with distinctive helical secondary walls and wide-band tracheids suggest they are the key adaptations to tolerate drought and provide support to the stems of most taxa in Cacteae. Fibers do not have the primary role of giving mechanical support; therefore, we assume the scarce fibers in clusters represent reaction wood that, along with the fundamental tissue, maintains the vertical position and shape of those species growing in rocky cracks. Our results with species having short succulent stems support the universal theory of positive allometric scaling of vascular plants.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.     

Flow similarity,stochastic branching,and quarter-power scaling in plants

The origin of allometric scaling patterns that are multiples of one-fourth has long fascinated biologists. While not universal, quarter-power scaling relationships are common and have been described in all major clades. Several models have been advanced to explain the origin of such patterns, but questions regarding the discordance between model predictions and empirical data have limited their widespread acceptance. Notable among these is a fractal branching model that predicts power-law scaling of both metabolism and physical dimensions. While a power law is a useful first approximation to some data sets, nonlinear data compilations suggest the possibility of alternative mechanisms. Here, we show that quarter-power scaling can be derived using only the preservation of volume flow rate and velocity as model constraints. Applying our model to land plants, we show that incorporating biomechanical principles and allowing different parts of plant branching networks to be optimized to serve different functions predicts nonlinearity in allometric relationships and helps explain why interspecific scaling exponents covary along a fractal continuum. We also demonstrate that while branching may be a stochastic process, due to the conservation of volume, data may still be consistent with the expectations for a fractal network when one examines sub-trees within a tree. Data from numerous sources at the level of plant shoots, stems, and petioles show strong agreement with our model predictions. This theoretical framework provides an easily testable alternative to current general models of plant metabolic allometry.

A general model for the origin of quarter-power scaling in land plants predicts allometry, allometric curvature, and allometric covariation within and across land plants.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

The utility of cranial ontogeny for phylogenetic inference: a case study in crocodylians using geometric morphometrics

The degree to which the ontogeny of organisms could facilitate our understanding of phylogenetic relationships has long been a subject of contention in evolutionary biology. The famed notion that ‘ontogeny recapitulates phylogeny’ has been largely discredited, but there remains an expectation that closely related organisms undergo similar morphological transformations throughout ontogeny. To test this assumption, we used three‐dimensional geometric morphometric methods to characterize the cranial morphology of 10 extant crocodylian species and construct allometric trajectories that model the post‐natal ontogenetic shape changes. Using time‐calibrated molecular and morphological trees, we employed a suite of comparative phylogenetic methods to assess the extent of phylogenetic signal in these trajectories. All analyses largely demonstrated a lack of significant phylogenetic signal, indicating that ontogenetic shape changes contain little phylogenetic information. Notably, some Mantel tests yielded marginally significant results when analysed with the morphological tree, which suggest that the underlying signal in these trajectories is correlated with similarities in the adult cranial morphology. However, despite these instances, all other analyses, including more powerful tests for phylogenetic signal, recovered statistical and visual evidence against the assumption that similarities in ontogenetic shape changes are commensurate with phylogenetic relatedness and thus bring into question the efficacy of using allometric trajectories for phylogenetic inference.     

Regional occupancy in unicellular eukaryotes: a reflection of niche breadth,habitat availability or size‐related dispersal capacity?

1. The distribution patterns of unicellular and multicellular organisms have recently been shown to differ profoundly, with the former probably being mostly cosmopolitan, whereas the latter are mostly restricted to certain regions. However, the within‐region distribution patterns of these two organism groups may be rather similar. 2. We predicted that the degree of regional occupancy in unicellular eukaryotes would be related to niche characteristics, dispersal ability and size, as has been found previously for multicellular organisms. The niche characteristics we considered were niche position, that measures marginality in species habitat distribution, and niche breadth, that measures amplitude in species habitat distribution. Niche characteristics were determined using Outlying Mean Index (OMI) analysis. 3. We found that the regional occupancy in our model group of unicellular eukaryotes, stream diatoms, was primarily a reflection of the niche position of a species or, more generally, habitat availability. Thus, non‐marginal species (i.e. species that occupied common habitat conditions across the region) tended to be more widely distributed than marginal species (i.e. species that were restricted to a limited range of rare habitat conditions). This finding was further supported by the general linear model, with niche position, niche breadth, maximum size and attachment mode as explanatory variables: niche position was by far the most important variable accounting for variability in regional occupancy, with significant amounts of additional variation related to niche breadth and maximum size of diatoms. 4. Thus, the degree of regional occupancy among unicellular eukaryotes may be primarily governed by habitat availability, supporting former findings for multicellular organisms.     

Similarities in butterfly emergence dates among populations suggest local adaptation to climate

Phenology shifts are the most widely cited examples of the biological impact of climate change, yet there are few assessments of potential effects on the fitness of individual organisms or the persistence of populations. Despite extensive evidence of climate‐driven advances in phenological events over recent decades, comparable patterns across species' geographic ranges have seldom been described. Even fewer studies have quantified concurrent spatial gradients and temporal trends between phenology and climate. Here we analyse a large data set (~129 000 phenology measures) over 37 years across the UK to provide the first phylogenetic comparative analysis of the relative roles of plasticity and local adaptation in generating spatial and temporal patterns in butterfly mean flight dates. Although populations of all species exhibit a plastic response to temperature, with adult emergence dates earlier in warmer years by an average of 6.4 days per °C, among‐population differences are significantly lower on average, at 4.3 days per °C. Emergence dates of most species are more synchronised over their geographic range than is predicted by their relationship between mean flight date and temperature over time, suggesting local adaptation. Biological traits of species only weakly explained the variation in differences between space‐temperature and time‐temperature phenological responses, suggesting that multiple mechanisms may operate to maintain local adaptation. As niche models assume constant relationships between occurrence and environmental conditions across a species' entire range, an important implication of the temperature‐mediated local adaptation detected here is that populations of insects are much more sensitive to future climate changes than current projections suggest.