It's all relative: allometry and variation in the baculum (os penis) of the harp seal, Pagophilus groenlandicus (Carnivora: Phocidae)

We compared allometry and variation in the baculum (os penis), mandible, and humerus of the harp seal, Pagophilus groenlandicus. This species is presumed to have a promiscuous mating system in which choice of mate by females during intromission with different males is likely. The baculum is large and grows throughout life so may be an honest indicator of males' quality (size) or viability (age). We predicted that bacular size would exhibit stronger allometry relative to body size than mandibles or humeri. The baculum is less functionally (mechanically) constrained than mandibles or humeri so we also predicted it would be more variable, though less variable than sexually selected traits which do not function as honest indicators. Our sample (N=67 seals) represented broad ranges of size and age (0–35 yr) so we compared variation using residuals from allometric regressions of skeletal measurements on body length. Bacular size was isometric to body length until ∼ 137 cm (when some seals enter puberty) in body length then was highly positively allometric; mandibular and humeral size were negatively allometric to body length throughout growth. Bacula were more variable than mandibles or humeri. Bacular size in large specimens (>137 cm in body length) was related strongly to body length and weakly to age. We interpret bacular size to be an uncheatable honest indicator of male quality and viability. High bacular variation conforms with theoretical predictions of females' asymmetrical choice of mate and choice of extremes, and may reflect corresponding anatomical variation among females. Some bacular variation may also result incidentally from positive allometry coupled with lifelong bacular growth, which can amplify early differences between reproductive and somatic growth, enabled by weak selection on bacular form in relation to function.     

Size-dependent growth and the development of inequality in maize,sunflower and soybean

Links were investigated between allometry of plant growth and dynamics of size structure of well-fertilized, irrigated crops of soybean (Glycine max L.), sunflower (Helianthus annuus L.) and maize (Zea mays L.) grown at standard plant-population densities (D), as in commercial crops (D = 30, 6 and 8.5 plants m-2, respectively), and at high densities (2D). Patterns of size-dependent growth of shoot and seed mass accumulation were distinctly different among species. In soybean and sunflower, non-linear relationships between size and subsequent growth led to strong hierarchical populations in terms of both shoot and seed biomass. Curvilinear (soybean) and sigmoid (sunflower) size-dependent growth determined strongly asymmetrical (soybean) and bimodal (sunflower) frequency distributions of shoot biomass indicating predominantly size asymmetrical competition among individuals. In comparison, a lower plant-to-plant variation coupled with a typical linear allometry of growth to plant size indicated symmetrical two-sided plant interference in maize. Despite the weak development of hierarchies in shoot biomass, a strong inequality in reproductive output developed in crowded populations of maize indicating an apparent breakage of reproductive allometry.     

Relative growth of the limbs and trunk in the African apes

Examination of relative growth and allometry is important for our understanding of the African apes, as they represent a closely related group of species of increasing body size. This study presents a comparison of ontogenetic relative growth patterns of some postcranial dimensions in Pan paniscus, Pantroglodytes, and Gorilla gorilla. Interspecific proportion differences among the three species are also analyzed. It is stressed that reliable ontogenetic information can only be obtained if subadults are examined-growth data cannot be inferred from static adult scaling. Results indicate that some postcranial relative growth patterns are very similar in the three species, suggesting differential extrapolation of a common growth pattern, whereas for other proportion comparisons the growth trends differ markedly among the species, producing distinct shape differences in the adults Interspecific shape changes among the three species are characterized by positive allometry of chest girth and negative allometry of body height and leg length. It is suggested that relative decrease of leg length with increasing body size among the African pongids might be expected on biomechanical grounds, in order to maintain similar locomotor abilities of climbing arborealism and quadrupedal terrestrialism. Relative to body weight or trunk length, the limbs of the bonobo (Pan paniscus) are longer than in the common chimpanzee or the gorilla, with a lower intermembral index. This may most closely resemble the primitive condition for the African apes.     

Temperature-mediated transitions between isometry and allometry in a colonial, modular invertebrate

The evolutionary success of animal design is strongly affected by scaling and virtually all metazoans are constrained by allometry. One body plan that appears to relax these constraints is a colonial modular (CM) design, in which modular iteration is hypothesized to support isometry and indeterminate colony size. In this study, growth rates of juvenile scleractinians (less than 40mm diameter) with a CM design were used to test this assertion using colony diameters recorded annually for a decade and scaling exponents (b) for growth calculated from double logarithmic plots of final versus initial diameters. For all juvenile corals, b differed significantly among years, with isometry (b=1) in 4 years, but positive allometry (b>1) in 5 years. The study years were characterized by differences in seawater temperature that were associated significantly with b for growth, with isometry in warm years but positive allometry in cool years. These results illustrate variable growth scaling in a CM taxon and suggest that the switch between scaling modes is mediated by temperature. For the corals studied, growth was not constrained by size, but this outcome was achieved through both isometry and positive allometry. Under cooler conditions, positive allometry may be beneficial as it represents a growth advantage that increases with size.     

Areal growth in the human fetal parietal bone

The areal growth of the human fetal parietal bone is described using 51 dissected right parietal bones of Japanese fetuses ranging from the fifth month to term. Their shadows were taken on printing paper and analyzed by a sonic digitizer. The absolute growth of the projected area of the fetal parietal bones progresses at a fairly constant rate during the latter half of the fetal period, despite some deceleration in the 9–10th month. By allometric analysis, the allometric coefficients against crown-rump length are 2.201 for males, 2.202 for females, and 2.204 for both sexes, respectively. The allometry is essentially monophasic, showing no inflection point, indicating a change in the slope of the regression line; that is, the growth of the human fetal parietal bone is continuous with a constant specific growth rate. These results are discussed in connection with growth in thickness of the bone.     

Phyletic size change and brain/body allometry: A consideration based on the African pongids and other primates

A problematic aspect of brain/body allometry is the frequency of interspecific series which exhibit allometry coefficients of approximately 0.33. This coefficient is significantly lower than the 0.66 value which is usually taken to be the interspecific norm. A number of explanations have been forwarded to account for this finding. These include (1) intraspecificallometry explanations, (2) nonallometric explanations, and (3) Jerison’s “extraneurons” hypothesis, among others. The African apes, which exhibit a lowered interspecific allometry coefficient, are used here to consider previous explanations. These are found to be inadequate in a number of ways, and an alternative explanation is proposed. This explanation is based on patterns of brain and body size change during ontogeny and phytogeny. It is argued that the interspecific allometry coefficient in African apes parallels the intraspecific one because similar ontogenetic modifications of body growth separate large and small forms along each curve. In both cases, body size differences are produced primarily by growth in later postnatal periods, during which little brain growth occurs. Data on body growth, neonatal scaling, and various lifehistory traits support this explanation. This work extends previous warnings that sizecorrected estimates of relative brain size may not correspond very closely to our understanding of the behavioral capacities of certain species in lineages characterized by rapid change in body size.     

Equilibrium and balanced growth of a vegetative crop

MODEL: A previously developed dynamic model, NICOLET, designed to predict growth and nitrate content of a lettuce crop, is subjected to (virtual) constant environmental conditions. For every combination of shoot and root environment, the cell sap, here assumed to reside in the "vacuole" compartment, equilibrates at a certain nitrate concentration level. This, in turn, defines the composition of the crop in terms of carbon and nitrogen content in each of the three compartments of the model. Growth under constant environmental conditions is defined as "equilibrium" growth (EG). If, in addition, the source strengths of carbon and nitrogen balance each other, as well as the sink strength of the growing crop, the growth is said to be "balanced" (BG). RESULTS: It is shown that the range of BG approximately coincides with the range of "mild" nitrogen stress, where reduction in nitrogen availability results in a mild reduction of relative growth rate (RGR). Beyond a certain low nitrate concentration in the cell sap, the N-stress becomes "severe" and the loss of growth increases considerably. CONCLUSIONS: The model is able to mimic the five central observations of many constant-environment growth-chamber experiments, namely (1) the initial exponential growth and later decline of the RGR, (2) the constant chemical composition, (3) the equality of the RGR and the relative nutrient supply rate (RNR), (4) the proportionality between the N : C ratio and the RNR, and (5) the proportionality between the water content and the reduced N content. Guidelines for the optimal combination of the shoot and root environments are suggested.     

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.     

Stochastic ontogenetic allometry: the statistical dynamics of relative growth

Background

In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, , where and are the logarithmic sizes of two traits at any given time t. Realistically, however, stochasticity is an inherent property of ontogenetic allometry. Due to the inherent stochasticity in both and , the ontogenetic allometry coefficients, and k, can vary with t and have intricate temporal distributions that are governed by the central and mixed moments of the random ontogenetic growth functions, and . Unfortunately, there is no probabilistic model for analyzing these informative ontogenetic statistical moments.

Methodology/Principal Findings

This study treats and as correlated stochastic processes to formulate the exact probabilistic version of each of the ontogenetic allometry coefficients. In particular, the statistical dynamics of relative growth is addressed by analyzing the allometric growth factors that affect the temporal distribution of the probabilistic version of the relative growth rate, , where is the expected value of the ratio of stochastic to stochastic , and and are the numerator and the denominator of , respectively. These allometric growth factors, which provide important insight into ontogenetic allometry but appear only when stochasticity is introduced, describe the central and mixed moments of and as differentiable real-valued functions of t.

Conclusions/Significance

Failure to account for the inherent stochasticity in both and leads not only to the miscalculation of k, but also to the omission of all of the informative ontogenetic statistical moments that affect the size of traits and the timing and rate of development of traits. Furthermore, even though the stochastic process and the stochastic process are linearly related, k can vary with t.     

Effects of temperature, salinity, and fish size on growth and consumption of juvenile bluefish

Consumption and growth rates of juvenile bluefish Pomatomus saltatrix increased with increasing temperature and decreased with increasing fish size in short-term (7 days) experiments. Salinity had no effect on growth or consumption rate in a short-term experiment. In a long-term (90 days) mesocosm experiment, consumption and growth rates declined with increasing body size. Predictive equations developed from short-term experiments did not adequately predict observed consumption rates in the mesocosm experiment. However, growth in the mesocosm experiment was similar to field growth. Also, mesocosm consumption rates and consumption rates calculated using field growth and mesocosm growth efficiencies were similar to published independent field estimates of consumption rate. Our results indicate that experiments to determine the effects of temperature and the allometry of body size on growth and consumption rates should be conducted over long time periods simulating field conditions. Juvenile bluefish have rapid growth and their individual cumulative consumption is large. This result suggests that bluefish may have a large effect on their prey populations. This effect has yet to be quantified.     

Allometry of head and body size in Holocene foragers of the South African Cape

Opportunities to assess morphological allometry in small-bodied human populations are rare. The foragers of the Later Stone Age of the South African Cape are characteristically small-bodied. Previous studies have shown that during the period of ca. 3500 to 2000 years BP (uncalibrated (14) C dates), the regional population shows transient reduced stature, body mass, and cranial size, a pattern that has been tentatively tied to demographic pressure on resources. This study examines the relationships among cranial size (centroid size) and body size (femoral length, femoral head diameter, and bi-iliac breadth) during the second half of the Holocene (N = 62). Reduced major axis regression indicates negative allometry of cranial centroid size with body size. Residuals (from ordinary least squares regression of cranial centroid size on body size) are regressed on radiocarbon date to examine temporal changes in the relationship between cranial and body size. Cranial and pelvic sizes are most conserved through time, while more ancient skeletons possess shorter femora and smaller femoral heads. The relationship between cranial centroid size and femoral length shows larger and more variable residuals at more recent dates, indicating a greater or more variable disassociation between cranial size and stature relative to more ancient skeletons. A similar, but nonsignificant relationship exists between cranial size and bi-iliac breadth. These results provide insights into the use of aspects of body size and proportionality in the assessment of health in past populations.     

Trade-off between height growth and stem diameter growth for an evergreen Oak, Quercus glauca, in a mixed hardwood forest

1. Patterns of stem growth of a mid-successional evergreen Oak species ( Quercus glauca ) in a mixed hardwood forest were examined to explore the trade-off relationship between stem-diameter growth and height growth.
2. The mean cross-sectional area (and the corresponding mean diameter) of a stem at a point in time was defined as the stem volume divided by tree height. Based on this definition, a simple equation representing the trade-off relationship between the height growth and mean diameter growth was formulated.
3. In the long term, allocation to height growth was encouraged at the seedling stage and it gradually declined with time, with the decline in the suppressed seedlings being more pronounced than in the dominant trees.
4. However, both the suppressed and the dominant trees showed acceleration of height growth at various ages. Such a fluctuation in the allocation of biomass to height growth is likely to have been caused by chronological changes in light conditions, and meandered the trajectory of allometry between the height and mean diameter.
5. The observed stem growth patterns of the individual trees could explain the chronological changes in the diameter–height relationship of the population.     

Morphometrical study of physical growth of laboratory-bred cynomolgus monkeys aged from zero to 9 years

The relative growth was examined in laboratory-bred cynomolgus monkeys (Macaca fascicularis) aged from zero to 9 years. The principal component analysis and multivariate allometry were applied to the biometrical data. As the result of the principal component analysis, the cumulative contribution ratio of the 1 st (PC 1) and 2 nd (PC 2) principal components accounted for 99.0 percent. According to the eigen vector values of each morphological site (14 sites), PC 1 was acceptable not only as a size factor but also as a shape factor of the morphological growth changes from birth to the 3rd year of life in both sexes. PC 2 was acceptable as a shape factor of the morphological differences between sexes after the 3rd year of life. As the result of the multivariate allometric analysis applied to the same data, proximate sites of the trunk showed relatively high growth rates compared to distal ones of the trunk. The head, limbs and arms grew slowly in contrast to the trunk. Thus, we could demonstrate the relative growth of cynomolgus monkeys morphometrically.     

EVOLUTION OF STATIC ALLOMETRIES: ADAPTIVE CHANGE IN ALLOMETRIC SLOPES OF EYE SPAN IN STALK‐EYED FLIES

Julian Huxley showed that within‐species (static) allometric (power‐law) relations can arise from proportional growth regulation with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow‐sense allometry. Here, we present the first phylogenetic comparative study of narrow‐sense allometric exponents based on a reanalysis of data on eye span and body size in stalk‐eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong evidence that male slopes were tracking “optima” based on sexual dimorphism and relative male trait size. This tracking was slow, however, with estimated times of 2–3 million years for adaptation to exceed ancestral influence on the trait. Our results are therefore consistent with adaptive evolution on million‐year time scales, but cannot rule out that static allometry may act as a constraint on eye‐span adaptation at shorter time scales.     

Relative growth and morphological sexual maturity of the freshwater crab Trichodactylus fluviatilis Latreille 1828 (Decapoda,Trichodactylidae) from west central São Paulo State,Brazil

An analysis of relative growth was performed to determine the size at morphological sexual maturity of Trichodactylus fluviatilis Latreille 1828. Samples were collected by trapping at night from January 2010 through June 2011 from the Barreiro River (22°34′42″S; 49°11′92″W), west central São Paulo State, Brazil. The following measurements were obtained (mm): carapace width (CW) (independent variable), cheliped propodus length (PL), cheliped propodus height (PH), cheliped propodus width (PW), first pleopod length, and abdomen width (AW). The males showed positive allometry in the juvenile and adult stages for the following relationships: PL vs. CW, PH vs. CW, and PW vs. CW. In the females, a positive allometry was observed for AW vs. CW in the juvenile stage, and a negative allometry was observed for this relationship in the adult stage. The differential growth of the chelipeds in males could be related to territorial conflict and courtship, whereas the changes in the growth of the female abdomen most likely favor higher reproductive success.     

Larval growth and allometry in the cabbage butterfly Pieris brassicae (Lepidoptera: Pieridae)

By adopting a longitudinal study design and through geometric morphometrics methods, we investigated individual and ontogenetic variation in size, shape and timing during larval development of the cabbage butterfly Pieris brassicae under laboratory conditions. We found that ontogenetic size progression departs modestly, but significantly, from growth at a constant rate and that size at hatching contributes considerably to determine the size of the individual at all subsequent stages. As for the shape, ontogenetic allometry is much more conspicuous than static allometry, the latter in many cases being close to isometry. Analysis of developmental timing revealed a stage of apparently more effective developmental control at stage 3, supported by both the relatively small variance in cumulative developmental time up to stage 3 and by the pattern of correlation between duration of single stages. While presenting detailed quantitative aspects of growth in P. brassicae, in particular with respect to individual variation, this study and the associated dataset can provide a basis for further explorations of the post‐embryonic development in this insect and contribute to the ongoing investigations on growth regulation and control in insects.     

A model for analyzing growth kinetics of a slowly growing Mycobacterium sp

This report describes a simple method for quantifying viable mycobacteria and for determining generation time. We used statistical models and computer analysis of growth curves generated for the slowly growing mycobacterium Mycobacterium paratuberculosis under controlled conditions to derive a mathematical formula relating the dependent variable, growth, to the independent variables, log10 number of organisms in the inoculum (inoculum size) and incubation time. Growth was measured by a radiometric method which detects 14CO2 release during metabolism of a 14C-labeled substrate. The radiometric method allowed for early detection of growth and detected as few as three viable bacteria. The coefficient of variation between culture vials inoculated with the same number of M. paratuberculosis was 0.083. Radiometric measurements were highly correlated to spectrophotometric and plate count methods for measuring growth (r = 0.962 and 0.992, respectively). The proportion of the total variability explained by the model in a goodness of fit test was 0.9994. Application of the model to broth cultures provided accurate estimates of the number of M. paratuberculosis (standard error = 0.21, log10 scale) and the growth rate (coefficient of variation, 0.03). Generation time was observed to be dependent upon the number of organisms in the inoculum. The model accurately described all phases of growth of M. paratuberculosis and can likely be applied to other slowly growing microorganisms.     

A model for analyzing growth kinetics of a slowly growing Mycobacterium sp.

This report describes a simple method for quantifying viable mycobacteria and for determining generation time. We used statistical models and computer analysis of growth curves generated for the slowly growing mycobacterium Mycobacterium paratuberculosis under controlled conditions to derive a mathematical formula relating the dependent variable, growth, to the independent variables, log10 number of organisms in the inoculum (inoculum size) and incubation time. Growth was measured by a radiometric method which detects 14CO2 release during metabolism of a 14C-labeled substrate. The radiometric method allowed for early detection of growth and detected as few as three viable bacteria. The coefficient of variation between culture vials inoculated with the same number of M. paratuberculosis was 0.083. Radiometric measurements were highly correlated to spectrophotometric and plate count methods for measuring growth (r = 0.962 and 0.992, respectively). The proportion of the total variability explained by the model in a goodness of fit test was 0.9994. Application of the model to broth cultures provided accurate estimates of the number of M. paratuberculosis (standard error = 0.21, log10 scale) and the growth rate (coefficient of variation, 0.03). Generation time was observed to be dependent upon the number of organisms in the inoculum. The model accurately described all phases of growth of M. paratuberculosis and can likely be applied to other slowly growing microorganisms.     

Modes of ontogenetic allometric shifts in crocodylian vertebrae

During postnatal ontogeny of vertebrates, allometric trends in certain morphological units or dimensions can shift drastically among isometry, positive allometry, and negative allometry. However, detailed patterns of allometric transitions in certain timings have not been explored well. Identifying the presence and nature of allometric shifts is essential for understanding the patterns of changes in relative size and shape and the proximal factors that are controlling these changes mechanistically. Allometric trends in 10 selected vertebrae (cervical 2–caudal 2) from hatchlings to very mature individuals of Alligator mississippiensis (Archosauria, Crocodylia) are reported in the present study. Allometric coefficients in 12 vertebral dimensions are calculated and compared relative to total body length, including centrum, neural spine, transverse process, zygapophysis, and neural pedicle. During the postnatal growth, positive allometry is the most common type of relative change (10 of the 12 dimensions), although the diameter of the neural canal shows a negative allometric trend. However, when using spurious breaks (i.e. allometric trends subdivided into growth stages using certain growth events, and key body sizes and/or ages), vertebral parts exhibit various pathways of allometric shifts. Based on allometric trends in three spurious breaks, separated by the end of endochondral ossification (body length: approximnately 0.9 m), sexual maturity (1.8 m), and the stoppage of body size increase (2.8 m), six types of ontogenetic allometric shifts are established. Allometric shifts exhibit a wide range from positive allometry restricted only in the early postnatal stage (Type I) to life‐long positive allometry (Type VI). This model of ontogenetic allometric shifts is then applied to interpret potential mechanisms (causes) of allometric changes, such as (1) growth itself (when allometric trend gradually decreases to isometric or negative allometric change: Type II–IV allometric shift); (2) developmental constraint (when positive allometry is limited only in the early growth stage: Type I allometric shift); and (3) functional or biomechanical drive (when positive allometry continues throughout ontogeny: Type VI allometric shift).     

Tail growth tracks the ontogeny of prehensile tail use in capuchin monkeys (Cebus albifrons and C. apella)

Physical anthropologists have devoted considerable attention to the structure and function of the primate prehensile tail. Nevertheless, previous morphological studies have concentrated solely on adults, despite behavioral evidence that among many primate taxa, including capuchin monkeys, infants and juveniles use their prehensile tails during a greater number and greater variety of positional behaviors than do adults. In this study, we track caudal vertebral growth in a mixed longitudinal sample of white-fronted and brown capuchin monkeys (Cebus albifrons and Cebus apella). We hypothesized that young capuchins would have relatively robust caudal vertebrae, affording them greater tail strength for more frequent tail-suspension behaviors. Our results supported this hypothesis. Caudal vertebral bending strength (measured as polar section modulus at midshaft) scaled to body mass with negative allometry, while craniocaudal length scaled to body mass with positive allometry, indicating that infant and juvenile capuchin monkeys are characterized by particularly strong caudal vertebrae for their body size. These findings complement previous results showing that long bone strength similarly scales with negative ontogenetic allometry in capuchin monkeys and add to a growing body of literature documenting the synergy between postcranial growth and the changing locomotor demands of maturing animals. Although expanded morphometric data on tail growth and behavioral data on locomotor development are required, the results of this study suggest that the adult capuchin prehensile-tail phenotype may be attributable, at least in part, to selection on juvenile performance, a possibility that deserves further attention.