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.     

Patterns of growth in the presacral vertebral column of the leopard gecko (Eublepharis macularius)

Postnatal growth patterns within the vertebral column may be informative about body proportions and regionalization. We measured femur length, lengths of all pre‐sacral vertebrae, and lengths of intervertebral spaces, from radiographs of a series of 21 Eublepharis macularius, raised under standard conditions and covering most of the ontogenetic body size range. Vertebrae were grouped into cervical, sternal, and dorsal compartments, and lengths of adjacent pairs of vertebrae were summed before analysis. Femur length was included as an index of body size. Principal component analysis of the variance‐covariance matrix of these data was used to investigate scaling among them. PC1 explained 94.19% of total variance, interpreted as the variance due to body size. PC1 differed significantly from the hypothetical isometric vector, indicating overall allometry. The atlas and axis vertebrae displayed strong negative allometry; the remainder of the vertebral pairs exhibited weak negative allometry, isometry or positive allometry. PC1 explained a markedly smaller amount of variance for the vertebral pairs of the cervical compartment than for the remainder of the vertebral pairs, with the exception of the final pair. The relative standard deviations of the eigenvalues from the PCAs of the three vertebral compartments indicated that the vertebrae of the cervical compartment were less strongly integrated by scaling than were the sternal or dorsal vertebrae, which did not differ greatly between themselves in their strong integration, suggesting that the growth of the cervical vertebrae is constrained by the mechanical requirements of the head. Regionalization of the remainder of the vertebral column is less clearly defined but may be associated with wave form propagation incident upon locomotion, and by locomotory changes occasioned by tail autotomy and regeneration. Femur length exhibits negative allometry relative to individual vertebral pairs and to vertebral column length, suggesting a change in locomotor requirements over the ontogenetic size range.     

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus) as detected by principal-components analysis

The ontogeny of cranial sexual dimorphism in the Bornean orang-utan (Pongo pygmaeus pygmaeus) is examined by means of principal-components analysis (PCA). Normalized first components are called allometry vectors or vectors of relative growth and show that sexual dimorphism is present at all stages of growth. Two patterns of sexual dimorphism are present: (1) sexual differences at age groups 2 and 3 are the result primarily of differences in principal component II scores, reflecting mainly shape-related differences, and (2) age groups 5, 6, and 7 show a trend of stronger size-related shape differences with increasing age in the allometry vector along with decreasing differences in principal component II scores, reflecting an increase in size-related shape differences between the sexes. Age group 4 shows a combination of both patterns. Our results support Shea's hypothesis (1985a) that when using multigroup PCAs in closely related taxa, the allometry vector will generally estimate the shape variation resulting from the extension of common growth allometry patterns (ontogenetic scaling). The second and subsequent components summarize shape variation from slope and intercept differences between the groups, provided that ontogenetic scaling is not solely responsible for all the shape differences present. Subanalyses of those dimensions previously found to show ontogenetic scaling and acceleration follow this pattern well. The total sample provides a pattern whereby ontogenetically scaled dimensions possess a stronger influence over accelerated dimensions but still generally follow Shea's hypothesis. Finally, variously derived coefficients provided several interesting findings: (1) strong evidence was found against multivariate isometry for both the pooled and the separate samples, (2) multivariate allometric coefficients for both sexes follow the general growth pattern of negative scaling in neurocranial dimensions and positive scaling in the viscerocranium, and (3) multivariate slopes have a very high correlation with bivariate slopes relative to the same independent X variable, thereby lending further support to Jolicoeur's (1963a, b) allometry generalization.     

Postnatal long bone growth in terrestrial placental mammals: Allometry,life history,and organismal traits

The ontogenetic allometry of long bone proportions is poorly understood in Mammalia. It has previously been suggested that during mammalian ontogeny long bone proportions grow more slender (positive allometry; length ∝ circumference^>1.0), although this conclusion was based upon data from a few small‐bodied taxa. It remains unknown how ontogenetic long bone allometry varies across Mammalia in terms of both taxonomy and body size. We collected long bone length and circumference data for ontogenetic samples of 22 species of mammals spanning six major clades and three orders of magnitude in body mass. Using reduced major axis bivariate regressions to compare bone length to circumference, we found that isometry and positive allometry are the most widespread patterns of growth across mammals. Negative allometry (i.e., bones growing more robust during ontogeny) occurs in mammals but is largely restricted to cetartiodactyls. Using regression slope as a proxy for long bone allometry, we compared long bone allometry to life history and organismal traits. Neonatal body mass, adult body mass, and growth rate have a negative relationship with long bone allometry. At an adult mass of roughly 15–20 kg, long bone growth shifts from positive allometry to mainly isometry and negative allometry. There were no significant relationships between ontogenetic long bone allometry and either cursoriality or basal metabolic rate. J. Morphol. © 2012 Wiley Periodicals, Inc.     

Allometry of resource capture in colonial cnidarians and constraints on modular growth

1. Indeterminacy in growth of colonial organisms, such as corals, is commonly attributed to their modular construction which frees the colony from the allometric constraints that limit the size of single modules. However, as a colony grows, there may be a decrease in resource availability to interior modules because of active depletion and/or passive deflection by modules on the exterior. The effects of 'self-shading' on resource capture in modular animals are modelled using a simple allometric growth function.
2. The model assumes that resource capture by a module scales as an exponent ( γ ) of colony size (i.e. number of modules). Data taken from the literature indicate that model values of γ for light and prey capture range from – 0·80 to – 1·16 for branching and encrusting corals. Module-specific rates of resource use (i.e. metabolism) are less affected by colony size. Therefore, as a colony grows, net resource state eventually reaches zero, making further growth unsustainable or determinate.
3. The model also predicts an inverse relationship between module size and colony size such as that observed in Caribbean corals. This negative correlation results from the additive effects of module size and colony size on the degree of self-shading.
4. Resource capture is affected by growth form and flow regime, and the interaction between them can account for some of the morphological variation in corals and other colonial suspension feeders.     

Molar scaling in strepsirrhine primates

We examined how maxillary molar dimensions change with body and skull size estimates among 54 species of living and subfossil strepsirrhine primates. Strepsirrhine maxillary molar areas tend to scale with negative allometry, or possibly isometry, relative to body mass. This observation supports several previous scaling analyses showing that primate molar areas scale at or slightly below geometric similarity relative to body mass. Strepsirrhine molar areas do not change relative to body mass(0.75), as predicted by the metabolic scaling hypothesis. Relative to basicranial length, maxillary molar areas tend to scale with positive allometry. Previous claims that primate molar areas scale with positive allometry relative to body mass appear to rest on the incorrect assumption that skull dimensions scale isometrically with body mass. We identified specific factors that help us to better understand these observed scaling patterns. Lorisiform and lemuriform maxillary molar scaling patterns did not differ significantly, suggesting that the two infraorders had little independent influence on strepsirrhine scaling patterns. Contrary to many previous studies of primate dental allometry, we found little evidence for significant differences in molar area scaling patterns among frugivorous, folivorous, and insectivorous groups. We were able to distinguish folivorous species from frugivorous and insectivorous taxa by comparing M1 lengths and widths. Folivores tend to have a mesiodistally elongated M1 for a given buccolingual M1 width when compared to the other two dietary groups. It has recently been shown that brain mass has a strong influence on primate dental eruption rates. We extended this comparison to relative maxillary molar sizes, but found that brain mass appears to have little influence on the size of strepsirrhine molars. Alternatively, we observed a strong correlation between the relative size of the facial skull and relative molar areas among strepsirrhines. We hypothesize that this association may be underlain by a partial sharing of the patterning of development between molar and facial skull elements.     

Chondrocranial development in larval Rana sylvatica (Anura: Ranidae): morphometric analysis of cranial allometry and ontogenetic shape change

This study provides baseline quantitative data on the morphological development of the chondrocranium in a larval anuran. Both linear and geometric morphometric methods are used to quantitatively analyze size-related shape change in a complete developmental series of larvae of the wood frog, Rana sylvatica. The null hypothesis of isometry was rejected in all geometric morphometric and most linear morphometric analyses. Reduced major axis regressions of 11 linear chondrocranial measurements on size indicate a mixture of allometric and isometric scaling. Measurements in the otic and oral regions tend to scale with negative allometry and those associated with the palatoquadrate and muscular process scale with isometry or positive allometry. Geometric morphometric analyses, based on a set of 11 chondrocranial landmarks, include linear regression of relative warp scores and multivariate regression of partial warp scores and uniform components on log centroid size. Body size explains about one-quarter to one-third of the total shape variation found in the sample. Areas of regional shape transformation (e.g., palatoquadrate, otic region, trabecular horns) are identified by thin-plate spline deformation grids and are concordant with linear morphometric results. Thus, the anuran chondrocranium is not a static structure during premetamorphic stages and allometric patterns generally follow scaling predictions for tetrapod cranial development. Potential implications regarding larval functional morphology, cranial development, and chondrocranial evolution in anurans are discussed.     

Principal components for allometric analysis

Logarithmic bivariate regression slopes and logarithmic principal component coefficient ratios are two methods for estimating allometry coefficients corresponding to a in the classic power formula Y = BXa. Both techniques depend on high correlation between variables. Interpretation is logically limited to the variables included in analysis. Principal components analysis depends also on relatively uniform intercorrelations; given this, it serves satisfactorily as a method for summarizing many bivariate combinations. Unmodified major principal component coefficients cannot represent scaling to body weight; rather, they represent scaling to a composite size vector which usually is highly correlated with body size or weight but has an unspecified allometry. Thus, the concepts of proportionality and of isometry must be kept distinct.     

The scaling of the size and stiffness of primary flight feathers

Birds encompass a large range of body sizes, yet the importance of body size on feather morphology and mechanical properties has not been characterized. In this study, I examined the scaling relationships of primary flight feathers within a phylogenetically diverse sample of avian species varying in body size by nearly three orders of magnitude. I measured the scaling relationships between body mass and feather linear dimensions as well as feather flexural stiffness. The resnlts of an independent contrasts analysis to test the effects of phylogenetic history on the characters measured had no effect on the scaling relationships observed. There was slight, but not significant, positive allometry in the scaling of shaft diameter with respect to feather length across a range of body masses. The scaling of feather length and diameter against body mass was not significantly different from isometry. Flexural stiffness, however, exhibited strong negative allometry. Therefore, larger birds have relatively more flexible feathers than smaller birds. The more flexible primary feathers of large birds may reduce stresses on the wing skeleton during take-off and landing and also make these feathers less susceptible to mechanical failure. Conversely, the greater flexibility of these feathers may also reduce their capacity to generate aerodynamic lift.     

Evolution and dynamics of branching colonial form in marine modular cnidarians: gorgonian octocorals

Multi-branched arborescent networks are common patterns for many sessile marine modular organisms but no clear understanding of their development is yet available. This paper reviews new findings in the theoretical and comparative biology of branching modular organisms (e.g. Octocorallia Cnidaria) and new hypotheses on the evolution of form are discussed. A particular characteristic of branching Caribbean gorgonian octocorals is a morphologic integration at two levels of colonial organization based on whether the traits are at the module or colony level. This revealed an emergent level of integration and modularity produced by the branching process itself and not entirely by the module replication. In essence, not just a few changes at the module level could generate changes in colony architecture, suggesting uncoupled developmental patterning for the polyp and branch level traits. Therefore, the evolution of colony form in octocorals seems to be related to the changes affecting the process of branching. Branching in these organisms is sub-apical, coming from mother branches, and the highly self-organized form is the product of a dynamic process maintaining a constant ratio between mother and daughter branches. Colony growth preserves shape but is a logistic growth-like event due to branch interference and/or allometry. The qualitative branching patterns in octocorals (e.g. sea feathers, fans, sausages, and candelabra) occurred multiple times when compared with recent molecular phylogenies, suggesting independence of common ancestry to achieve these forms. A number of species with different colony forms, particularly alternate species (e.g. sea candelabrum), shared the same value for an important branching parameter (the ratio of mother to total branches). According to the way gorgonians branch and achieve form, it is hypothesized that the diversity of alternate species sharing the same narrow variance in that critical parameter for growth might be the product of canalization (or a developmental constraint), where uniform change in growth rates and maximum colony size might explain colony differences among species. If the parameter preserving shape in the colonies is fixed but colonies differ in their growth rates and maximum sizes, heterochrony could be responsible for the evolution among some gorgonian corals with alternate branching.     

The Dilemma of Choosing a Reference Character for Measuring Sexual Size Dimorphism,Sexual Body Component Dimorphism,and Character Scaling: Cryptic Dimorphism and Allometry in the Scorpion Hadrurus arizonensis

Sexual differences in morphology, ranging from subtle to extravagant, occur commonly in many animal species. These differences can encompass overall body size (sexual size dimorphism, SSD) or the size and/or shape of specific body parts (sexual body component dimorphism, SBCD). Interacting forces of natural and sexual selection shape much of the expression of dimorphism we see, though non-adaptive processes may be involved. Differential scaling of individual features can result when selection favors either exaggerated (positive allometry) or reduced (negative allometry) size during growth. Studies of sexual dimorphism and character scaling rely on multivariate models that ideally use an unbiased reference character as an overall measure of body size. We explored several candidate reference characters in a cryptically dimorphic taxon, Hadrurus arizonensis. In this scorpion, essentially every body component among the 16 we examined could be interpreted as dimorphic, but identification of SSD and SBCD depended on which character was used as the reference (prosoma length, prosoma area, total length, principal component 1, or metasoma segment 1 width). Of these characters, discriminant function analysis suggested that metasoma segment 1 width was the most appropriate. The pattern of dimorphism in H. arizonensis mirrored that seen in other more obviously dimorphic scorpions, with static allometry trending towards isometry in most characters. Our findings are consistent with the conclusions of others that fecundity selection likely favors a larger prosoma in female scorpions, whereas sexual selection may favor other body parts being larger in males, especially the metasoma, pectines, and possibly the chela. For this scorpion and probably most other organisms, the choice of reference character profoundly affects interpretations of SSD, SBCD, and allometry. Thus, researchers need to broaden their consideration of an appropriate reference and exercise caution in interpreting findings. We highly recommend use of discriminant function analysis to identify the least-biased reference character.     

Body size, locomotion, and long bone cross-sectional geometry in indriid primates.

The geometry of the midshaft cross-sections of the femur and humerus of five indriid species was analysed. Internal (marrow cavity) and external diameters were measured on X-rays in the anteroposterior (a-p) and mediolateral (m-l) planes; cross-sectional areas, second moments of area, and section moduli were calculated using formulae for a hollow ellipse. Cortical thickness, robusticity indices (relating external diameters to the length of the bones), and a-p/m-l shape variables were also calculated. Model II regression was supplemented by analyses of correlation between size and shape. Indriids are saltatory, i.e., their locomotion is dominated by the hind limbs. Accordingly, the femur is more rigid than the humerus, and it shows a consistent difference between the a-p and m-l planes in measures related to bending strength. Cortical thickness varies considerably both within and across species. The type specimen of the new species Propithecus tattersalli is virtually indistinguishable from P. verreauxi on the basis of its long bone cross-sectional geometry. Femoral robusticity is uncorrelated with size, but humeral robusticity decreases significantly with increasing size. Femoral shape variables (a-p/m-l) are all negatively correlated with body size, indicating that m-l dimensions of the femur increase at a faster rate than do a-p dimensions. The highly loaded plane of movement seems to be more reinforced in the smaller species. Contrary to static biomechanical scaling predictions of positive allometry, all cross-sectional parameters scale relatively close to isometry. It is concluded that either changes in locomotor performance must compensate for the weight-related increase in forces and moments or that the larger-bodied animals operate appreciably closer to the limits of their safety margins.     

Musculoskeletal determinants of pelvic sucker function in hawaiian stream gobiid fishes: Interspecific comparisons and allometric scaling

Gobiid fishes possess a distinctive ventral sucker, formed from fusion of the pelvic fins. This sucker is used to adhere to a wide range of substrates including, in some species, the vertical cliffs of waterfalls that are climbed during upstream migrations. Previous studies of waterfall‐climbing goby species have found that pressure differentials and adhesive forces generated by the sucker increase with positive allometry as fish grow in size, despite isometry or negative allometry of sucker area. To produce such scaling patterns for pressure differential and adhesive force, waterfall‐climbing gobies might exhibit allometry for other muscular or skeletal components of the pelvic sucker that contribute to its adhesive function. In this study, we used anatomical dissections and modeling to evaluate the potential for allometric growth in the cross‐sectional area, effective mechanical advantage (EMA), and force generating capacity of major protractor and retractor muscles of the pelvic sucker (m. protractor ischii and m. retractor ischii) that help to expand the sealed volume of the sucker to produce pressure differentials and adhesive force. We compared patterns for three Hawaiian gobiid species: a nonclimber (Stenogobius hawaiiensis), an ontogenetically limited climber (Awaous guamensis), and a proficient climber (Sicyopterus stimpsoni). Scaling patterns were relatively similar for all three species, typically exhibiting isometric or negatively allometric scaling for the muscles and lever systems examined. Although these scaling patterns do not help to explain the positive allometry of pressure differentials and adhesive force as climbing gobies grow, the best climber among the species we compared, S. stimpsoni, does exhibit the highest calculated estimates of EMA, muscular input force, and output force for pelvic sucker retraction at any body size, potentially facilitating its adhesive ability. J. Morphol. 2013. © 2013 Wiley Periodicals, Inc.     

Ontogenetic scaling of bite force in lizards and turtles

Because selection on juvenile life-history stages is likely strong, disproportionately high levels of performance (e.g., sprint speed, endurance, etc.) might be expected. Whereas this phenomenon has been demonstrated with respect to locomotor performance, data for feeding are scarce. Here, we investigate the relationships among body dimensions, head dimensions, and bite force during growth in lizards and turtles. We also investigate whether ontogenetic changes in bite performance are related to changes in diet. Our analyses show that, for turtles, head dimensions generally increase with negative allometry. For lizards, heads scale as expected for geometrically growing systems. Bite force generally increased isometrically with carapace length in turtles but showed significant positive allometry relative to body dimensions in lizards. However, both lizards and turtles display positive allometric scaling of bite force relative to some measures of head size throughout ontogeny, suggesting (1) strong selection for increased relative bite performance with increasing head size and (2) intrinsic changes in the geometry and/or mass of the jaw adductors during growth. Whereas our data generally do not provide strong evidence of compensation for lower absolute levels of performance, they do show strong links among morphology, bite force, and diet during growth.     

On birds: scale effects in the neognath hindlimb and differences in the gross morphology of wings and hindlimbs

Scale effects on whole limb morphology (i.e. bones together with in situ overlying muscles) are well understood for the neognath forelimb. However, scale effects on neognath gross hindlimb morphology remain largely unexplored. To broaden our understanding of avian whole limb morphology, I investigated the scaling of hindlimb inertial properties in neognath birds, testing empirical scaling relationships against the model of geometric similarity. Inertial property data – mass, moment of inertia, centre of mass distance, and radius of gyration – were collected from 22 neognath species representing a wide range of locomotor specializations. When scaled against body mass, hindlimb inertial properties scale with positive allometry. Thus, in terms of morphology, larger bodied neognaths possess hindlimbs requiring disproportionately more energy to accelerate and decelerate relative to body mass than smaller bodied birds. When scaled against limb length, hindlimb inertial properties scale according to isometry. In the subclade Land Birds (sensu Hackett et al.), hindlimb inertial properties largely scale according to positive allometry. The contrasting results of positive allometry vs. isometry in neognaths are due to how hindlimb length scales against body mass. Negative allometry of hindlimb inertial properties, which would reduce terrestrial locomotion costs, would probably make the hindlimb susceptible to mechanical failure or too diminutive for its many ecological functions. Comparing the scaling relationships of wings and hindlimbs highlights how locomotor costs influence the scaling of limb inertial properties. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 110 , 14–31.     

Do Changes in Morphology and Prey-Capture Movements Facilitate a Dietary Transition in Juvenile Colorado pikeminnow, Ptychocheilus lucius?

Ontogenetic diet shifts in juvenile fishes are sometimes associated with proportional changes to the feeding mechanism. In addition, many piscivorous teleosts transition from invertebrate-prey to fish-prey when the mouth attains a specific diameter. Allometric (disproportionate) growth of the jaws could accelerate a young fish’s ability to reach a critical gape diameter; alternately by opening the lower jaw to a greater degree, a fish might increase gape behaviorally. We investigated the ontogeny of feeding morphology and kinematics in an imperiled piscivore, the Colorado pikeminnow (Ptychocheilus lucius) in a size range of individuals across which a diet shift from invertebrate-prey to prey-fishes is known to occur. We predicted that: (1) the feeding apparatus of the fish would grow proportionally with the rest of the body (isometric growth), that (2) anatomical gape diameter at the known diet transition would be a similar gape diameter to that observed for other piscivorous juvenile fishes (15–20 mm) and (3) feeding kinematic variables would scale isometrically (that is, change in direct proportion to body length) as juvenile pikeminnow became larger. Furthermore, we also asked the question: if changes in feeding morphology and kinematics are present, do the changes in morphology appear to generate the observed changes in kinematics? For juvenile Colorado pikeminnow, the majority of the morphological variables associated with the skull and jaws scale isometrically (that is, proportionally), but seven of eight kinematic variables, including functional gape, scale with negative allometry (that is, they became disproportionately smaller in magnitude). In contrast with the overall trend of isometry, two key aspects of feeding morphology do change with size; the lower jaw of a young Colorado pikeminnow becomes longer (positive allometry), while the head becomes shallower (negative allometry). These findings do not support the hypothesis that morphological ontogenetic changes directly generate changes in feeding kinematics; in fact, allometric jaw growth would, a priori, be expected to generate a larger gape in older fish—which is the opposite of what was observed. We conclude that ontogenetic morphological changes produce a more streamlined cranium that may reduce drag during a rapid, anteriorly directed strike, while concomitant behavioral changes reduce the magnitude of jaw movements—behavioral changes that will facilitate a very rapid opening and closing of the jaws during the gape cycle. Thus, for juvenile pikeminnow, speed and stealth appear to be more important than mouth gape during prey capture.     

Removing allometric effects of body size in morphological analysis

In the present paper, a normalization technique to scale data that exhibit an allometric growth is presented and the way it has to be used is described. It is shown how the method has been derived from the theoretical equations of allometric growth. Consequently, the method completely removes all the information related to size, not only scaling all individuals to the same size, but also adjusting their shape to that they would have in the new size according to allometry. In the particular case of isometry when the measures are of identical dimension, this normalization coincides with ratios (one of the most popular methods but only valid in this particular case). This procedure is a theoretical generalization of the technique used by Thorpe (1975, Biol. J. Linn. Soc.7, 27-43; 1976, Biol. Rev.51, 407-452) which was recorded as one of the most efficient methods in the empirical evaluation done by Reist (1985, Can. J. Zool.63, 1429-1439).     

Development of secondary sexual characters in the seabob shrimp Xiphopenaeus kroyeri (Heller 1862) (Crustacea,Decapoda, Penaeidae): a scanning electron microscope study

The development of secondary sexual characters, the petasma, and thelycum growth were studied in Xiphopenaeus kroyeri. In adult females, the thelycum is a single plate and its anterolateral portion is characterized by a reduced hood. The aperture resembles a transverse ridge. In immature stages, the ridge has a space between the plates, which becomes narrower as it reaches the end of development. The female gonopore is ‘comma’ shaped. In adult males, the endopods of the petasma are linked at the dorsomedial margin by a large quantity of cincinnuli. In juveniles, cincinnuli gradually increase in number until they join both endopods. At the end of development the petasma is T-shaped. The male gonopore is C-shaped. The relative growth of the petasma total length versus juvenile body length showed a highly positive allometry, whereas in adults the growth was isometric. For the relationship carapace length versus thelycum width, the juvenile phase of females is characterized by an isometry and the adult phase by a negative allometry.     

Branching and self-organization in marine modular colonial organisms: a model

Despite the universality of branching patterns in marine modular colonial organisms, there is neither a clear explanation about the growth of their branching forms nor an understanding of how these organisms conserve their shape during development. This study develops a model of branching and colony growth using parameters and variables related to actual modular structures (e.g., branches) in Caribbean gorgonian corals (Cnidaria). Gorgonians exhibiting treelike networks branch subapically, creating hierarchical mother-daughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecological-physiological limit to growth or maximum number of mother branches (k). Shape is preserved by maintaining a constant ratio (c) between the total number of branches and the mother branches. The size frequency distribution of mother branches follows a scaling power law suggesting self-organized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with rr/2 or c>r>0). Ecological/physiological constraints limit growth without altering colony form or the interaction between r and c. The model described the branching dynamics giving the form to colonies and how colony growth declines over time without altering the branching pattern. This model provides a theoretical basis to study branching as a simple function of the number of branches independently of ordering- and bifurcation-based schemes.     

The allometric pattern of sexually size dimorphic feather ornaments and factors affecting allometry

The static allometry of secondary sexual characters is currently subject to debate. While some studies suggest an almost universal positive allometry for such traits, but isometry or negative allometry for nonornamental traits, other studies maintain that any kind of allometric pattern is possible. Therefore, we investigated the allometry of sexually size dimorphic feather ornaments in 67 species of birds. We also studied the allometry of female feathers homologous to male ornaments (female ornaments in the following) and ordinary nonsexual traits. Allometries were estimated as reduced major axis slopes of trait length on tarsus length. Ornamental feathers showed positive allometric slopes in both sexes, although that was not a peculiarity for ornamental feathers, because nonsexual tail feathers also showed positive allometry. Migration distance (in males) and relative size of the tail ornament (in females) tended to be negatively related to the allometric slope of tail feather ornaments, although these results were not conclusive. Finally, we found an association between mating system and allometry of tail feather ornaments, with species with more intense sexual selection showing a smaller degree of allometry of tail ornaments. This study is consistent with theoretical models that predict no specific kind of allometric pattern for sexual and nonsexual characters.