Effects of allometry,productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade''s evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.     

Invariant scaling of phytoplankton abundance and cell size in contrasting marine environments

Scaling relationships such as the variation of population abundance with body size provide links between individual organisms and ecosystem functioning. Previous work, in marine pelagic ecosystems, has focused on the relationship between total phytoplankton abundance and the assemblage mean cell size. However, the relationship between specific population abundance and cell size in marine phytoplankton has received little attention. Here, we show that cell size accounts for a significant amount of variability in the population abundance of phytoplankton species across a cell volume range spanning seven orders of magnitude. The interspecific scaling of population abundance and cell size takes a power exponent near −3/4. Unexpectedly, despite the constraints imposed on large phytoplankton by limited resource acquisition, the size scaling exponent does not differ between contrasting marine environments such as coastal and subtropical regions. These findings highlight the adaptive abilities of individual species to cope with different environmental conditions and suggest that a general rule such as the 'energetic equivalence' constrains the abundance of phytoplankton populations in marine pelagic ecosystems.     

Projecting human pharmacokinetics of therapeutic antibodies from nonclinical data

The pharmacokinetics (PK) of therapeutic antibodies is determined by target and non-target mediated mechanisms. These antibody-specific factors need to be considered during prediction of human PK based upon preclinical information. Principles of allometric scaling established for small molecules using data from multiple animal species cannot be directly applied to antibodies. Here, different methods for projecting human clearance (CL) from animal PK data for 13 therapeutic monoclonal antibodies (mAbs) exhibiting linear PK over the tested dose ranges were examined: simple allometric scaling (CL versus body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent and scaling from only cynomolgus monkey PK data. A better correlation was obtained between the observed human CL and the estimated human CL based on cynomolgus monkey PK data and an allometric scaling exponent of 0.85 for CL than other scaling approaches. Human concentration-time profiles were also reasonably predicted from the cynomolgus monkey data using species-invariant time method with a fixed exponent of 0.85 for CL and 1.0 for volume of distribution. In conclusion, we expanded our previous work and others and further confirmed that PK from cynomolgus monkey alone can be successfully scaled to project human PK profiles within linear range using simplify allometry and Dedrick plots with fixed exponent.     

Projecting human pharmacokinetics of therapeutic antibodies from nonclinical data: What have we learned?

The pharmacokinetics (PK) of therapeutic antibodies is determined by target and non-target mediated mechanisms. These antibody-specific factors need to be considered during prediction of human PK based upon preclinical information. Principles of allometric scaling established for small molecules using data from multiple animal species cannot be directly applied to antibodies. Here, different methods for projecting human clearance (CL) from animal PK data for 13 therapeutic monoclonal antibodies (mAbs) exhibiting linear PK over the tested dose ranges were examined: simple allometric scaling (CL versus body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent and scaling from only cynomolgus monkey PK data. A better correlation was obtained between the observed human CL and the estimated human CL based on cynomolgus monkey PK data and an allometric scaling exponent of 0.85 for CL than other scaling approaches. Human concentration-time profiles were also reasonably predicted from the cynomolgus monkey data using species-invariant time method with a fixed exponent of 0.85 for CL and 1.0 for volume of distribution. In conclusion, we expanded our previous work and others and further confirmed that PK from cynomolgus monkey alone can be successfully scaled to project human PK profiles within linear range using simplify allometry and Dedrick plots with fixed exponent.Key words: monoclonal antibody, pharmacokinetics, clearance, allometric scaling, species-invariant time method     

Cellular forms: The tri-axial cell. I

Without assuming a spheroidal shape for the cell, more general approximate deformation equations are derived which allow for non-uniformities in the external diffusion field and within the cell itself. It is found that in the absence of such non-uniformities, however, the only stable shapes are those in which the cell is spheroidal. Moreover, in conformity with previous results derived by somewhat different approximations, it is found that the spherical equilibrium is always stable and the approach monotonic unless, for a sufficiently large volume or a sufficiently high metabolic rate, there exist two non-spherical equilibria, one of prolate type and one of oblate type.     

Static allometry of unicellular green algae: scaling of cellular surface area and volume in the genus Micrasterias (Desmidiales)

The surface area‐to‐volume ratio of cells is one of the key factors affecting fundamental biological processes and, thus, fitness of unicellular organisms. One of the general models for allometric increase in surface‐to‐volume scaling involves fractal‐like elaboration of cellular surfaces. However, specific data illustrating this pattern in natural populations of the unicellular organisms have not previously been available. This study shows that unicellular green algae of the genus Micrasterias (Desmidiales) have positive allometric surface‐to‐volume scaling caused by changes in morphology of individual species, especially in the degree of cell lobulation. This allometric pattern was also detected within most of the cultured and natural populations analysed. Values of the allometric S:V scaling within individual populations were closely correlated to the phylogenetic structure of the clade. In addition, they were related to species‐specific cellular morphology. Individual populations differed in their allometric patterns, and their position in the allometric space was strongly correlated with the degree of allometric S:V scaling. This result illustrates that allometric shape patterns are an important correlate of the capacity of individual populations to compensate for increases in their cell volumes by increasing the surface area. However, variation in allometric patterns was not associated with phylogenetic structure. This indicates that the position of the populations in the allometric space was not evolutionarily conserved and might be influenced by environmental factors.     

Inter-specific scaling of phytoplankton production and cell size in the field

This study tests the hypothesis that the interspecific scalingof phytoplankton production and cell size in the field followsthe -power scaling law. Published data of cell size and in situ,cell-specific carbon production rates by single phytoplanktonspecies, collected in surface waters of lakes, rivers, estuariesand oceans, are reviewed. Across more than nine orders of magnitudein cell volume, 98% of the variability in carbon productionrates was explained by cell size. The slope (b) in the log–logrelationship between carbon production rate and cell volumedid not differ significantly from 1, either for diatoms (b =1.01) or for dinoflagellates (b = 0.89). For all phytoplanktonspecies considered together, which included also cyanobacteriaand haptophytes, b took a value of 0.91, which is significantlyhigher than . The observed nearly isometric scaling relationshipsbetween production rate and cell volume suggest that there isno relationship between phytoplankton growth rate and cell size.The present analysis confirms recent evidence showing that phytoplanktonmetabolism in natural conditions does not follow the -powerscaling rule. It is argued that allometric models of planktongrowth and metabolism should incorporate scaling parametersmeasured in situ on natural phytoplankton assemblages, ratherthan those obtained in the laboratory with monospecific cultures.     

Ontogenic growth of the haemopoietic stem cell pool in humans

Recently, the size of the active stem cell pool has been predicted to scale allometrically with the adult mass of mammalian species with a 3/4 power exponent, similar to what has been found to occur for the resting metabolic rate across species. Here we investigate the allometric scaling of human haemopoietic stem cells (HSCs) during ontogenic growth and predict a linear scaling with body mass. We also investigate the allometric scaling of resting metabolic rate during growth in humans and find a linear scaling with mass similar to that of the haemopoietic stem cell pool. Our findings suggest a common underlying organizational principle determining the linear scaling of both the stem cell pool and resting metabolic rate with mass during ontogenic growth within the human species, combined with a 3/4 scaling with adult mass across mammalian species. It is possible that such common principles remain valid for haemopoiesis in other mammalian species.     

Geometric shape as a trait to study phytoplankton distributions in aquatic ecosystems

The geometric shape is traditionally used to calculate phytoplankton cell measurements (e.g. biovolume), but it can also play an important role in determining community distributions. Little is known about how geometric shapes relate to other morphological traits or to the environment. We explored whether shapes and related morphological traits are selected by environmental forcing. For this, samples were collected seasonally at 21 stations in coastal-marine waters of the Salento Peninsula (Italy). Phytoplankton taxa were classified in terms of geometric shape, biovolume (organism size) and surface-to-volume ratio (S:V). The relationship between greatest axial linear dimension (GALD) and S:V was assessed for each shape. A Canonical Correspondence Analysis (CCA) was performed to evaluate phytoplankton shape distribution on temporal and spatial scales. Phytoplankton community was characterized by high morphological diversity. GALD and S:V were inversely related in most of the shapes. CCA showed that phytoplankton shape distribution was influenced more by seasonal than by spatial variation: elongated shapes characterized the cold period; rounded and combined shapes the warmer period. Most of the shapes showed conservatism of the S:V and trade-off with the size. Geometric shapes represent an interesting feature to be considered in trait-based approaches to study phytoplankton distributions in aquatic ecosystems.     

FORM AND FUNCTION IN MARINE PHYTOPLANKTON

What is presented here is a tentative synthesis of morphological, cytological, physiological and ecological data on planktonic algae, which I hope will help in the understanding of mutual relationships. Emphasis is put on the marine phytoplankton although effort has been made to include the more significant limnological information. (1) All the algal classes, but two, are present in the marine plankton – which makes 13 classes. Many or most of them possess one or several features that are commonly viewed as animal characters, and so Bacillariophyceae (diatoms) are the more typical ‘algae’ in marine plankton. Coincidently or not, they have received much more attention than any other class. (2) Both structurally and morphodynamically, colonies of cells often appear as something else or something more than sums of cells. (3) There is a profuse variety of flagellar types and flagellar appendages, whose functional significance is open to investigation. In general, swimming velocity (ca. 1 m h^-l) exceeds sedimentation rate (ca. 0·7 m day^-1) by one order of magnitude or more. (4) Very few phytoplankters can truly be described as “naked”. Cell coverings fall into eight major categories which differ by chemical composition, structure and ontogeny. An additional, external organic coating may be widespread. Mucus and microfibrils may also be more common than previously thought. (5) The variability of chloroplast morphology and ultrastructure has not been explored for functional relationships. (6) Evidence for the presence of intracellular bacteria and viruses is rapidly increasing. (7) The suspension of algal cells in the medium depends on a number of morphological factors whose effects are often opposite. The sinking rate increases with increasing cell size and is maximum for spheroid (not spherical) shapes; colonies sink faster than the individual cells. The incidence of various shapes, appendages, mucilage and cell orientation is, essentially, intricate and/or insufficiently known. Lipidic inclusions are no longer viewed as floating devices but the ancient theory of ionic exchange has been revived. As now understood, the suspension of phytoplankton is no more a matter of floating, but rather exploring different layers and being tossed around by physical entrainment. However, questions remain the same: how do the “morphological adaptations” contribute to this, and how do different forms compare to each other? (8) As far as the absorption of nutrients is concerned, there is an advantage for phytoplankters to be small and either motile or rapidly sinking. The permeability of the various cell coverings has been ignored. The advantage of being small is confirmed by the consideration that growth rates and all the metabolic rates decrease with increasing size. However, the balance of photosynthesis against respiration for varying sizes is a complex problem. (9) After an extensive review of the literature, the existence of several “shade species” is confirmed (without ensuring that light is the responsible factor). These taxa exhibit the full range of shapes, sizes, structures and behaviour, so that the relevant morphological adaptations, if any, are at least polymorphic. (10) Although grazing certainly moulds the size spectrum and the algological spectrum of phytoplankton to a large extent, the effect of a given morphological feature can hardly be generalized, except that long appendages, mucilages, and probably colonies discourage grazers. The role of bioluminescence and trichocyst expulsion may also be considered. (11) The hope of correlating cell size with a single factor of the environment, whether temperature or something else, should be abandoned since many more factors are involved. On the other hand, multi-parametric models can justify or predict which cell size predominates under a given set of conditions (note the works of H. J. Semina and co-workers, T. R. Parsons and M. Takahashi, and E. A. Laws). (12) The ratio of surface area to volume of the cell is a meaningful physiological index. Its relative conservation among the vagaries of sizes and shapes, and its ecological regulation need further investigation. (13) Considering the profusion of data that has accumulated on the structure and functioning of planktonic algae, and realizing that sophisticated techiques are available for both kinds of studies, now is the time, it seems, for fruitful research into the relationships between form and function. Such research will certainly increase our understanding of specific variability, adaptation and diversity.     

Fifth dimension of life and the 4/5 allometric scaling law for human brain

Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.     

Active and resting metabolism in birds: allometry, phylogeny and ecology

Variation in resting metabolic rate is strongly correlated with differences in body weight among birds. The lowest taxonomic level at which most of the variance in resting metabolic rate and body weight is evident for the sample is among families within orders. The allometric exponent across family points is 0.67. This exponent accords with the surface area interpretation of metabolic scaling based on considerations of heat loss. Deviations of family points from this allometric line are used to examine how resting metabolic rates differ among taxa, and whether variation in resting metabolic rate is correlated with broad differences in ecology and behaviour. Despite the strong correlation between resting metabolic rate and body weight, there is evidence for adaptive departures from the allometric line, and possible selective forces are discussed.
The allometric scaling of active metabolic rate is compared with that of resting metabolic rate. The allometric exponents for the two levels of energy expenditure differ, demonstrating that active small-bodied birds require proportionately more energy per unit time above resting levels than do active large-bodied birds. No consistent evidence was found to indicate that the different methods used to estimate active metabolic rate result in systematic bias. Birds require more energy relative to body size when undertaking breeding activities than at other stages of the annual cycle.     

骆驼刺根瘤菌的超微结构研究

用透射电子显微镜研究骆驼刺根瘤中的根瘤菌。结果表明。在成熟的骆驼刺根瘤中,根瘤菌的大小、数量、形态、分布位置及精细结构随寄主细胞的发育程度不同而异。早期侵染细胞中,根瘤菌小,数量少,一般呈球形或椭球形,位于细胞壁附近及靠近核区的地方,没有聚磷酸盐颗粒和聚羟基丁酸。成熟侵染细胞中,根瘤菌个体较大,数量较多．多呈棒状,少数为球形或椭球形。有很多根瘤菌还呈现明显的“T”形、“Y”形或“V”形,菌体占满了整个细胞,这时的根瘤菌大多数含有聚羟基丁酸和聚磷酸盐颗粒。而在衰老的侵染细胞中,根瘤菌细胞质收缩,电子密度增高．形状变得很不规则,有的根瘤菌解体,呈现膜泡状结构,菌体中含有数量不等的聚羟基丁酸和聚磷酸盐颗粒。球状根瘤菌从侵染初期到侵染细胞裂解的整个阶段中都仔在。并且观察到的处于分裂状态的根瘤菌都是球状菌,因此可以推测骆驼刺根瘤中是以球状根瘤菌来进行增殖的。     

Sample size and mass range effects on the allometric exponent of basal metabolic rate

The controversial relationship between body mass and basal metabolic rate in animals revolves around two questions: what is the allometric scaling exponent and what is the functional basis for it? For mammals, the first question could be resolved if measurements from all 4600 extant species were available, but this study shows that data for only 150 species, spanning three to four orders of magnitude variation in body mass, are sufficient to accurately determine the exponent. Because the currently available data set includes about 600 species that vary over five orders of magnitude in body size, further increases in sample size are unlikely to change the estimate of the scaling exponent.     

FURTHER EVIDENCE FOR ANOMALOUS SIZE SCALING OF RESPIRATION IN PHYTOPLANKTON1

Respiration per unit mass decreases as organism size increases among metazoans and heterotrophic unicells. The rate of decrease is described by a power function of organism mass; the exponent of the power function is 0.75 (Three-fourths Rule). Previously unanalyzed respiration rates for 11 species of phytoplankton ranging in size over four orders of magnitude show a size-scaling exponent of 1.13 (SE, ±0.15), which is statistically different from 0.75. This result confirms the result of an earlier study of eight phytoplankton species indicating that size scaling of respiration is absent or minimal in phytoplankton, in contrast to the pattern of heterotrophic unicells. The size-related range of respiration rates per unit mass across the full size spectrum of phytoplankton would be approximately 18–fold if respiration were scaled according to the Three-fourths Rule. If respiration does not scale with size or scales minimally with size, as suggested by present evidence, the size-related range of rates will be much smaller or negligible. The apparent anomaly of size scaling for phytoplankton respiration is potentially of great ecological and adaptive significance in unicellular algae.     

Sizing up allometric scaling theory

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks-the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets.     

Decoding Size Distribution Patterns in Marine and Transitional Water Phytoplankton: From Community to Species Level

Understanding the mechanisms of phytoplankton community assembly is a fundamental issue of aquatic ecology. Here, we use field data from transitional (e.g. coastal lagoons) and coastal water environments to decode patterns of phytoplankton size distribution into organization and adaptive mechanisms. Transitional waters are characterized by higher resource availability and shallower well-mixed water column than coastal marine environments. Differences in physico-chemical regime between the two environments have been hypothesized to exert contrasting selective pressures on phytoplankton cell morphology (size and shape). We tested the hypothesis focusing on resource availability (nutrients and light) and mixed layer depth as ecological axes that define ecological niches of phytoplankton. We report fundamental differences in size distributions of marine and freshwater diatoms, with transitional water phytoplankton significantly smaller and with higher surface to volume ratio than marine species. Here, we hypothesize that mixing condition affecting size-dependent sinking may drive phytoplankton size and shape distributions. The interplay between shallow mixed layer depth and frequent and complete mixing of transitional waters may likely increase the competitive advantage of small phytoplankton limiting large cell fitness. The nutrient regime appears to explain the size distribution within both marine and transitional water environments, while it seem does not explain the pattern observed across the two environments. In addition, difference in light availability across the two environments appear do not explain the occurrence of asymmetric size distribution at each hierarchical level. We hypothesize that such competitive equilibria and adaptive strategies in resource exploitation may drive by organism’s behavior which exploring patch resources in transitional and marine phytoplankton communities.     

Patterns of cranial shape variation in the Papionini (Primates: Cercopithecinae)

Traditional classifications of the Old World monkey tribe Papionini (Primates: Cercopithecinae) recognized the mangabey genera Cercocebus and Lophocebus as sister taxa. However, molecular studies have consistently found the mangabeys to be diphyletic, with Cercocebus and Mandrillus forming a clade to the exclusion of all other papionins. Recent studies have identified cranial and postcranial features which distinguish the Cercocebus-Mandrillus clade, however the detailed similarities in cranial shape between the mangabey genera are more difficult to reconcile with the molecular evidence. Given the large size differential between members of the papionin molecular clades, it has frequently been suggested that allometric effects account for homoplasy in papionin cranial form. A combination of geometric morphometric, bivariate, and multivariate methods was used to evaluate the hypothesis that allometric scaling contributes to craniofacial similarities between like-sized papionin taxa. Patterns of allometric and size-independent cranial shape variation were subsequently described and related to known papionin phylogenetic relationships and patterns of development.Results confirm that allometric scaling of craniofacial shape characterized by positive facial allometry and negative neurocranial allometry is present across adult papionins. Pairwise comparisons of regression lines among genera revealed considerable homogeneity of scaling within the Papionini, however statistically significant differences in regression lines also were noted. In particular, Cercocebus and Lophocebus exhibit a shared slope and significant vertical displacement of their allometric lines relative to other papionins. These findings give no support to narrowly construed hypotheses of uniquely shared patterns of allometric scaling, either between sister taxa or across all papionins. However, more general allometric trends do appear to account for a substantial proportion of papionin cranial shape variation, most notably in those features which have influenced traditional morphological phylogenies. Examination of size-uncorrelated shape variation gives no clear support to molecular phylogenies, but underscores the absence of morphometric similarities between the mangabey genera when size effects are controlled. Patterns of allometric and size-uncorrelated shape variation indicate conservatism of cranial form in non- Theropithecus papionins, and suggest that Papio represents the primitive morphometric pattern for the African papionins. Lophocebus exhibits a divergent morphometric pattern, clearly distinguishable from other papionins, most notably Cercocebus. These results clarify patterns of cranial shape variation among the extant Papionini and lay the groundwork for studies of related fossil taxa.