Growth models and the expected distribution of fluctuating asymmetry

Multiplicative error accounts for much of the size-scaling and leptokurtosis in fluctuating asymmetry. It arises when growth involves the addition of tissue to that which is already present. Such errors are lognormally distributed. The distribution of the difference between two lognormal variates is leptokurtic. If those two variates are correlated, then the asymmetry variance will scale with size. Inert tissues typically exhibit additive error and have a gamma distribution. Although their asymmetry variance does not exhibit size-scaling, the distribution of the difference between two gamma variates is nevertheless leptokurtic. Measurement error is also additive, but has a normal distribution. Thus, the measurement of fluctuating asymmetry may involve the mixing of additive and multiplicative error. When errors are multiplicative, we recommend computing log  E ( l ) − log  E ( r ), the difference between the logarithms of the expected values of left and right sides, even when size-scaling is not obvious. If l and r are lognormally distributed, and measurement error is nil, the resulting distribution will be normal, and multiplicative error will not confound size-related changes in asymmetry. When errors are additive, such a transformation to remove size-scaling is unnecessary. Nevertheless, the distribution of l  −  r may still be leptokurtic.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 80, 57–65.     

Latitudinal clines in the grasshopper Dichroplus elongatus: Coevolution of the A genome and B chromosomes?

Argentine populations of Dichroplus elongatus (Orthoptera: Acrididae) are polymorphic for B chromosomes. Previous studies showed that B chromosomes affect body size and some fitness components in Northwestern populations. We studied phenotype and B′s variation patterns along a latitudinal cline as well as the relationship between karyotype and body size related traits in 17 populations from East. Body size related traits showed a ‘saw tooth’ pattern of variation being small at low and high latitudes and large at intermediate latitudes in most of the analysed populations. Analyses of variance and principal components demonstrated that in most analysed populations B carrier males are associated with a decrease in body size related traits with respect to individuals with standard karyotype. Accordingly with the relationship between karyotype and body size, an opposite pattern of latitudinal variation in the frequencies of B′s with respect to body size variation was observed in this area. i.e. smaller individuals tend to have a higher frequency of B chromosomes. The comparison of the differentiation of both karyotype and body size traits with molecular neutral markers demonstrated the relative importance of selection moulding chromosome and phenotype variation. The observed pattern of phenotypic variation is likely to be the result of local adaptation to season length along the latitudinal gradient. The observed contrary pattern of B′s clinal variation may reflect the population ability to maintain this chromosome in relation to the local adaptation. The available evidence indicates that the distribution of B chromosome frequency was shaped by selective factors.     

Complications inherent in scaling the basal rate of metabolism in mammals

The scaling of the basal rate of metabolism in mammals is reexamined. Both the power and level of the scaling function are sensitive to various factors that interact with body mass and rate of metabolism, including the precision of temperature regulation, food habits, and activity level. This sensitivity implies that the rate of metabolism is a highly plastic character in the course of evolution. Consequently, the singular effect of mass on the rate of metabolism is most effectively analyzed in ecologically and physiologically uniform sets of species, rather than in taxonomically defined groups, which often are ecologically and physiologically diverse. Otherwise, all fitted curves for mammals integrate a variety of competing factors, thereby reflecting the species used and denying unique analytic significance to the power in scaling relations. Kleiber's eutherian curve may represent a relatively uniform set of data because all the species included were domesticated and because selection for high rates of production (and high rates of metabolism) occurred in the process of domestication. In the analysis of scaling relationships, the standard error of estimate (Sy.x) is a more valuable measure of the residual variation than is (1.0-r2) because r2 is a non-linear measure of the conformation of data to the relation and because Sy.x, unlike r2, is independent of the units used in the scaling relationship. At present the best estimate indicates that total rate of metabolism scales proportionally to approximately m0.60 at small masses (less than 300 g), as long as small species do not enter torpor, and scales proportionally to approximately m0.75 at large masses (greater than or equal to 300 g). Physiological properties other than metabolism are potentially sensitive to secondary factors, so their scaling functions also would be most clearly defined for physiologically uniform groups of species. This view suggests that insight into the significance of scaling relations can be obtained by examining the residual variation around a scaling function as well as by examining conformation to the function.     

Influence of adaptation to horizontal body position on pointing errors and visual estimation of a target position in humans

The central program of a targeted movement includes a component intended for to compensate for the weight of the arm; this is why the accuracy of pointing to a memorized position of the visual target in darkness depends on orientation of the moving limb in relation to the vertical axis. Transition from the vertical to the horizontal body position is accompanied by a shift of the final hand position along the body axis towards the head. We studied how pointing errors and visual localization of the target are modified due to adaptation to the horizontal body position; targeted movements to a real target were repeatedly performed during the adaptation period. Three types of experiments were performed: a basic experiment, and two different experiments with adaptation realized under somewhat dissimilar conditions. In the course of the first adaptation experiment, subjects received no visual information on the hand’s position in space, and targeted movements of the arm to a luminous target could be corrected using proprioceptive information only. With such a paradigm, the accuracy of pointing to memorized visual targets showed no adaptation-related changes. In the second adaptation experiment, subjects were allowed to continuously view a marker (a light-emitting diode taped to the fingertip). After such adaptation practice, the accuracy of pointing movements to memorized targets increased: both constant and variational errors, as well as both components of constant error (i.e.,X andY errors) significantly dropped. Testing the accuracy of visual localization of the targets by visual/verbal adjustment, performed after this adaptation experiment, showed that the pattern of errors did not change compared with that in the basic experiment. Therefore, we can conclude that sensorimotor adaptation to the horizontal position develops much more successfully when the subject obtains visual information about the working point position; such adaptation is not related to modifications in the system of visual localization of the target.     

Visuomotor Adaptation: How Forgetting Keeps Us Conservative

Even when provided with feedback after every movement, adaptation levels off before biases are completely removed. Incomplete adaptation has recently been attributed to forgetting: the adaptation is already partially forgotten by the time the next movement is made. Here we test whether this idea is correct. If so, the final level of adaptation is determined by a balance between learning and forgetting. Because we learn from perceived errors, scaling these errors by a magnification factor has the same effect as subjects increasing the amount by which they learn from each error. In contrast, there is no reason to expect scaling the errors to affect forgetting. The magnification factor should therefore influence the balance between learning and forgetting, and thereby the final level of adaptation. We found that adaptation was indeed more complete for larger magnification factors. This supports the idea that incomplete adaptation is caused by part of what has been learnt quickly being forgotten.     

Individual size variation reduces spatial variation in abundance of tree community assemblage,not of tree populations

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.     

Ecological scaling laws link individual body size variation to population abundance fluctuation

Scaling research has seen remarkable progress in the past several decades. Many scaling relationships were discovered within and across individual and population levels, such as species–abundance relationship, Taylor's law, and density mass allometry. However none of these established patterns incorporate individual variation in the formulation. Individual body size variation is a key evolutionary phenomenon and closely related to ecological diversity and species adaptation. Using a macroecological approach, I test 57 Long‐Term Ecological Research data sets and show that a power‐law and a generalized power‐law function describe well the mean‐variance scaling of individual body mass. This relationship connects Taylor's law and density mass allometry, and leads to a new scaling pattern between the individual body size variation and population abundance fluctuation, which is confirmed using freshwater fish and forest tree data. Underlying mechanisms and implications of the proposed scaling relationships are discussed. This synthesis shows that integration and extension of existing ecological laws can lead to the discovery of new scaling patterns and complete our understanding of the relation between individual trait and population abundance. Synthesis Scaling relationships are useful for community ecology as they reveal ubiquitous patterns across different levels of biological organizations. This work extends and integrates two existing scaling laws: Taylor's law and density‐mass allometry, and derives a new variance allometry between individual body mass and population abundance. The result shows that diverse individual body size is associated with stable population fluctuation, reflecting the effect of individual traits on population characteristics. Confirmed by several empirical data sets, these scaling relationships suggest new ways to study the underlying mechanisms of Taylor's law and have profound implications for fisheries and other applied sciences.     

A three-dimensional musculoskeletal model for gait analysis. Anatomical variability estimates

Three-dimensional coordinates defining the origin and insertion of 40 muscle units, and bony landmarks for osteometric scaling were identified on dry bone specimens. Interspecimen coordinate differences along the anterior-posterior axis of the pelvis and the long bone axes of the pelvis, femur and leg were reduced by scaling but landmark differences along the other axes were not. The coordinates were mapped to living subjects using close-range photogrammetry to locate superficial reference markers. The error of predicting the positions of internal coordinates was assessed by comparing joint centre locations calculated from local axes defining the orientation of segments superior and inferior to a joint. A difference was attributed to: anatomical variability not accounted for by scaling; errors in identifying and placing reference landmarks; the accuracy of locating markers using photogrammetry and error introduced by marker oscillation during movement. Anatomical differences between specimens are one source of error in defining a musculoskeletal model but larger errors are introduced when such models are mapped to living subjects.     

Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions.

It is often assumed that moment arms scale with size and can be normalized by body segment lengths or limb circumferences. However, quantitative scaling relationships between moment arms and anthropometric dimensions are generally not available. We hypothesized that peak moment arms of the elbow flexor and extensor muscles scale with the shorter distance (D(s)) between the elbow flexion axis and a muscle's origin and insertion. To test this hypothesis, we estimated moment arms of six muscles that cross the elbow, digitized muscle attachment sites and bone surface geometry, and estimated the location of the elbow flexion axis in 10 upper extremity cadaveric specimens which ranged in size from a 5'0" female to a 6'4" male. D(s) accurately reflected the differences in peak moment arms across different muscles, explaining 93-99% of the variation in peaks between muscles in the same specimen. D(s) also explained between 55% and 88% of the interspecimen variation in peak moment arms for brachioradialis, biceps, and ECRL. Triceps peak moment arm was significantly correlated to the anterior-posterior dimension of the ulna measured at the olecranon (r(2)=0.61, p=0.008). Radius length provides a good measure of the interspecimen variation in peaks for brachioradialis, biceps, and ECRL. However, bone lengths were not significantly correlated to triceps moment arm or anterior-posterior bone dimensions. This work advances our understanding of the variability and scaling dimensions for elbow muscle moment arms across subjects of different sizes.     

Which measures of diaphyseal robusticity are robust? A comparison of external methods of quantifying the strength of long bone diaphyses to cross‐sectional geometric properties

Measures of diaphyseal robusticity have commonly been used to investigate differences in bone strength related to body size, behavior, climate, and other factors. The most common methods of quantifying robusticity involve external diameters, or cross-sectional geometry. The data derived from these different methods are often used to address similar research questions, yet the compatibility of the resulting data has not been thoroughly tested. This study provides the first systematic comparison of externally derived measures of postcranial robusticity, with those based upon cross-sectional geometry. It includes sections taken throughout the skeleton, comparisons of prediction errors associated with different measurements, and analysis of the implications of different methods of body size standardization on the prediction of relative bone strength. While the results show reasonable correlations between diaphyseal diameters and strengths derived from cross-sectional geometry, considerable prediction errors are found in many cases. A new approach to externally based quantification of diaphyseal robusticity based upon moulding of sub-periosteal contours is proposed. This method maximizes correlation with cross-sectional geometry (r(2) = .998) and minimizes prediction errors in all cases. The results underscore the importance of accurate periosteal measurement in the quantification of bone strength, and suggest that, regardless of theoretical scaling predictions, external area based robusticity estimates involving the product of diaphyseal diameters are most directly comparable to cross-sectional geometric properties when they are standardized using the product of body mass and bone length.     

Evolution in Hawaiian cave-adapted isopods (Oniscidea: Philosciidae): vicariant speciation or adaptive shifts?

Diatom plastid genes are examined with respect to codon adaptation and rates of silent substitution (Ks). It is shown that diatom genes follow the same pattern of codon usage as other plastid genes studied previously. Highly expressed diatom genes display codon adaptation, or a bias toward specific major codons, and these major codons are the same as those in red algae, green algae, and land plants. It is also found that there is a strong correlation between Ks and variation in codon adaptation across diatom genes, providing the first evidence for such a relationship in the algae. It is argued that this finding supports the notion that the correlation arises from selective constraints, not from variation in mutation rate among genes. Finally, the diatom genes are examined with respect to variation in Ks among different synonymous groups. Diatom genes with strong codon adaptation do not show the same variation in synonymous substitution rate among codon groups as the flowering plant psbA gene which, previous studies have shown, has strong codon adaptation but unusually high rates of silent change in certain synonymous groups. The lack of a similar finding in diatoms supports the suggestion that the feature is unique to the flowering plant psbA due to recent relaxations in selective pressure in that lineage.     

Oblique scaling: an algorithm to correct for a non-perpendicular camera view in tendon strain measurements

Image distortion due to a non-perpendicular camera view introduces serious errors in tendon and ligament strain measurements when data are recorded using a single camera. These errors can be corrected with the oblique scaling algorithm using two pairs of scaling markers attached to the tendon surface. Computer simulations show that application of this algorithm reduces errors over 100 times to less than 0.06%. The method is relatively insensitive to measurement errors in the scaling marker distance but sensitive to the accuracy of alignment of the scaling markers. It can be concluded that the oblique scaling algorithm eliminates the influences of a non-perpendicular camera view in single-camera tendon and ligament strain measurements.     

Goodness of Fit of Discriminant Functions from the Vector Space of Fixed Variates

Alternative proofs of some of KSHIRSAGAR's (1971) results on testing discriminant functions or canonical variables in the vector space of fixed variates are given. These results are derived in terms of the original variates unlike KSHIRSAGAR (1971) who derives the results by using random orthogonal transformations and triangular decompositions of the original matrix variates.     

Craniometric Variation In The Northern And Central Plains

Abstract

Cranial measurements of 13 male and 12 female samples from the Central and Northern Plains region were subjected to canonical analysis. The samples include historic or protohistoric crania that can be ascribed to the Arikara, Mandan, Pawnee, Ponca and Omaha tribes. In addition, two samples belong to the archaeologically defined St. Helena Focus. Both sexes yielded five significant canonical variates, although only four were readily interpretable. The first canonical variate is clearly a Siouan-Caddoan discriminator and reflects variation in cranial vault height. St. Helena sites associate with the Arikara on this axis, supporting previous craniometric analyses which suggest a relationship between these two groups. Subsequent canonical variates deal with more particular aspects of craniometric variation among groups, but are still interpretable in historic or evolutionary terms. The classificatory analysis shows that the Arikara sites are closely related. A major exception to this is the Sully site, which frequently misclassifies with non-Arikara groups. This suggests that the Sully crania have little collective reality; and that there may be non-Arikara components represented at the Sully Site.     

Pollinator size and its consequences: Robust estimates of body size in pollinating insects

Body size is an integral functional trait that underlies pollination‐related ecological processes, yet it is often impractical to measure directly. Allometric scaling laws have been used to overcome this problem. However, most existing models rely upon small sample sizes, geographically restricted sampling and have limited applicability for non‐bee taxa. Allometric models that consider biogeography, phylogenetic relatedness, and intraspecific variation are urgently required to ensure greater accuracy. We measured body size as dry weight and intertegular distance (ITD) of 391 bee species (4,035 specimens) and 103 hoverfly species (399 specimens) across four biogeographic regions: Australia, Europe, North America, and South America. We updated existing models within a Bayesian mixed‐model framework to test the power of ITD to predict interspecific variation in pollinator dry weight in interaction with different co‐variates: phylogeny or taxonomy, sexual dimorphism, and biogeographic region. In addition, we used ordinary least squares regression to assess intraspecific dry weight ~ ITD relationships for ten bees and five hoverfly species. Including co‐variates led to more robust interspecific body size predictions for both bees and hoverflies relative to models with the ITD alone. In contrast, at the intraspecific level, our results demonstrate that the ITD is an inconsistent predictor of body size for bees and hoverflies. The use of allometric scaling laws to estimate body size is more suitable for interspecific comparative analyses than assessing intraspecific variation. Collectively, these models form the basis of the dynamic R package, “pollimetry,” which provides a comprehensive resource for allometric pollination research worldwide.     

Recent Selective Sweeps in North American Drosophila melanogaster Show Signatures of Soft Sweeps

Adaptation from standing genetic variation or recurrent de novo mutation in large populations should commonly generate soft rather than hard selective sweeps. In contrast to a hard selective sweep, in which a single adaptive haplotype rises to high population frequency, in a soft selective sweep multiple adaptive haplotypes sweep through the population simultaneously, producing distinct patterns of genetic variation in the vicinity of the adaptive site. Current statistical methods were expressly designed to detect hard sweeps and most lack power to detect soft sweeps. This is particularly unfortunate for the study of adaptation in species such as Drosophila melanogaster, where all three confirmed cases of recent adaptation resulted in soft selective sweeps and where there is evidence that the effective population size relevant for recent and strong adaptation is large enough to generate soft sweeps even when adaptation requires mutation at a specific single site at a locus. Here, we develop a statistical test based on a measure of haplotype homozygosity (H12) that is capable of detecting both hard and soft sweeps with similar power. We use H12 to identify multiple genomic regions that have undergone recent and strong adaptation in a large population sample of fully sequenced Drosophila melanogaster strains from the Drosophila Genetic Reference Panel (DGRP). Visual inspection of the top 50 candidates reveals that in all cases multiple haplotypes are present at high frequencies, consistent with signatures of soft sweeps. We further develop a second haplotype homozygosity statistic (H2/H1) that, in combination with H12, is capable of differentiating hard from soft sweeps. Surprisingly, we find that the H12 and H2/H1 values for all top 50 peaks are much more easily generated by soft rather than hard sweeps. We discuss the implications of these results for the study of adaptation in Drosophila and in species with large census population sizes.     

Measurement of ¹⁵N relaxation rates in perdeuterated proteins by TROSY-based methods

While extracting dynamics parameters from backbone (15)N relaxation measurements in proteins has become routine over the past two decades, it is increasingly recognized that accurate quantitative analysis can remain limited by the potential presence of systematic errors associated with the measurement of (15)N R(1) and R(2) or R(1ρ) relaxation rates as well as heteronuclear (15)N-{(1)H} NOE values. We show that systematic errors in such measurements can be far larger than the statistical error derived from either the observed signal-to-noise ratio, or from the reproducibility of the measurement. Unless special precautions are taken, the problem of systematic errors is shown to be particularly acute in perdeuterated systems, and even more so when TROSY instead of HSQC elements are used to read out the (15)N magnetization through the NMR-sensitive (1)H nucleus. A discussion of the most common sources of systematic errors is presented, as well as TROSY-based pulse schemes that appear free of systematic errors to the level of <1 %. Application to the small perdeuterated protein GB3, which yields exceptionally high S/N and therefore is an ideal test molecule for detection of systematic errors, yields relaxation rates that show considerably less residue by residue variation than previous measurements. Measured R(2)'/R(1)' ratios fit an axially symmetric diffusion tensor with a Pearson's correlation coefficient of 0.97, comparable to fits obtained for backbone amide RDCs to the Saupe matrix.     

Local adaptation with high gene flow: temperature parameters drive adaptation to altitude in the common frog (Rana temporaria)

Both environmental and genetic influences can result in phenotypic variation. Quantifying the relative contributions of local adaptation and phenotypic plasticity to phenotypes is key to understanding the effect of environmental variation on populations. Identifying the selective pressures that drive divergence is an important, but often lacking, next step. High gene flow between high‐ and low‐altitude common frog (Rana temporaria) breeding sites has previously been demonstrated in Scotland. The aim of this study was to assess whether local adaptation occurs in the face of high gene flow and to identify potential environmental selection pressures that drive adaptation. Phenotypic variation in larval traits was quantified in R. temporaria from paired high‐ and low‐altitude sites using three common temperature treatments. Local adaptation was assessed using Q_ST–F_ST analyses, and quantitative phenotypic divergence was related to environmental parameters using Mantel tests. Although evidence of local adaptation was found for all traits measured, only variation in larval period and growth rate was consistent with adaptation to altitude. Moreover, this was only evident in the three mountains with the highest high‐altitude sites. This variation was correlated with mean summer and winter temperatures, suggesting that temperature parameters are potentially strong selective pressures maintaining local adaptation, despite high gene flow.     

Coevolution of body size and metabolic rate in vertebrates: a life‐history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non‐linearity of the relationship between MR and body mass. This ‘statistical’ view must be replaced with the life‐history perspective that ‘allows’ organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation ‘decisions’ that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those ‘decisions’ form a wealth of life‐history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single‐cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life‐history evolution is the best way forward.     

Habitat primary production and the evolution of body size within the hartebeest clade

Local adaptation is a key process in the evolution of biological diversity but relatively few studies have identified the selective forces that drive trait divergence at low taxonomic levels, particularly amongst mammals. Variation in body size across taxa is fundamental as shown by allometric relationships with numerous physiological, morphological and life-history traits. Differences in adult size across cohorts within populations of temperate ungulates are determined by variation in trophic resource availability during growth, suggesting that natural selection might promote the evolution of size divergence across sister taxa through local adaptation to variation in habitat productivity. We tested this hypothesis in the hartebeest ( Alcelaphu s sp.), an antelope lineage including eight extant (or recently extinct) allopatric subspecies that evolved within the last million years and colonized all the African savannahs. We predicted that body size across the subspecies should correlate positively with habitat productivity across taxon ranges. Mean body size of all the hartebeest taxa was quantified using skull length from museum specimens, and climatic variables were used as surrogates of habitat productivity. Body size across subspecies was positively correlated with rainfall, suggesting that variation in habitat primary production may drive morphological evolution between taxa. Focusing at a low taxonomic level has allowed us to identify a critical selective force that may shape divergence in body size, without the confounding effect of variation in trophic niche. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 92 , 431–440.