Allometric growth in the Praying mantis Stagmatoptera biocellata

The growth of ten exoskeletal structures has been studied throughout the post-embryonic development in Stagmatoptera biocellata. The selection of an appropriate statistical procedure to analyse the data was discussed. In spite of theoretical prediction the least-squares regression technique turned out to be as efficient as the Bartlett (1949) procedure for studying growth. Longitudinal treatment of longitudinal data proved to be the best method for this kind of analysis. All the dimensions investigated showed some statistically significant degree of allometric growth and could be ascribed to certain class of allometry. The adaptative value of some allometric growth patterns was discussed in terms of physiological efficiency. A hypothesis put forth by Balderrama & Maldonado (1973) about the anatomic relationships between the parts involved in the mantis strike, received clear support from this analysis. A quantitative assessment of Dyar's (1890) and Przibram's (1912) rules and their modifications led us to conclude that they are untenable at least for the mantid Stagmatoptera biocellata. However, some periods of constant growth ratio could be identified during the post-embryonic development and the concept of maximum growth period was put forward as a complementary element for typifying structures.     

Dyar's rule and multivariate allometric growth in nine species of waterstriders (Heteroptera: Gerridae)

The constancy of postmoult/premoult ratios of measures of linear size during ontogeny in insect and other arthropods is widely known as Dyar's rule. We tested this rule in nine species of the waterstrider genera Gerris and Aquarius (Heteroptera: Gerridae), using two size variables: head width and a multivariate measure derived from the pattern of multivariate allometry common to the species considered. Allometric patterns were similar in two independent datasets of laboratory-reared and field-caught specimens. Although our data strictly followed Dyar's rule injust a few instances, all growth ratios varied within a limited range only. Growth ratios for head width differed more between moults than those for multivariate size. The relationship between growth ratios for the two size measures conformed to the predictions based on allometry. We discuss hypotheses of the possible adaptive significance of growth ratios, such as their relation to mobility and systematic differences between hemimetabolous and holometabolous insects, and emphasize the importance of allometry. Since Dyar's rule is consistent with available evidence of physiological mechanisms underlying growth and moulting control of insects and crustaceans, it can be used as a general frame of reference to test alternative growth models.     

The development of dragonfly larvae (Odonata: Anisoptera) from two streams in north-eastern Victoria, Australia

Developmental stages of larvae of eight species of Anisoptera from the Kiewa River and Middle Creek, Victoria, were determined and their phenology investigated. The last six to nine instars of each species were distinguished by size frequency and scatter plots, using labium width, metafemur and wing-pad measurements, and the early instars were estimated from Dyar's Law. This suggested between 11 to 14 instars. Four species appeared to be univoltine and four species semivoltine.     

The overwintering stages of Ectobius lapponicus (L.) (Dictyoptera: Blattidae)

An account is given of the overwintering stages of Ectobius lapponicus, involving the determination of a diapause in the egg and one of the nymphal instars. The significance of these periods in the life cycle is discussed.     

Developmental trait evolution in trilobites

We performed a tree-based analysis of trilobite postembryonic development in a sample of 60 species for which quantitative data on segmentation and growth increments between putative successive instars are available, and that spans much of the temporal, phylogenetic, and habitat range of the group. Three developmental traits were investigated: the developmental mode of trunk segmentation, the average per-molt growth rate, and the conformity to a constant per-molt growth rate (Dyar's rule), for which an original metric was devised. Growth rates are within the normal range with respect to other arthropods and show overall conformity to Dyar's rule. Randomization tests indicate statistically significant phylogenetic signal for growth in early juveniles but not in later stages. Among five evolutionary models fit via maximum likelihood, one in which growth rates vary independently among species, analogous to Brownian motion on a star phylogeny, is the best supported in all ontogenetic stages, although a model with a single, stationary peak to which growth rates are attracted also garners nontrivial support. These results are not consistent with unbounded, Brownian-motion-like evolutionary dynamics, but instead suggest the influence of an adaptive zone. Our results suggest that developmental traits in trilobites were relatively labile during evolutionary history.     

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).     

Numerical allometric growth of the ommatidia,antennal sensilla,and teeth of foretibial combs in the milkweed bug Oncopeltus fasciatus Dallas (Heteroptera : Lygaeidae)

Oncopeltus fasciatus (Heteroptera : Lygaeidae), the milkweed bug, was bred in captivity. Sampling showed that individuals grow exponentially through their 6 developmental stages with an average linear increase per molt of 42% for the females and 41% for the males. The number of ommatidia per eye grows with negative allometry from an average of 30 in the first instar to 860 in the male and 820 in the female adult. The total number of sensilla on the 2 flagellar segments of an antenna increases with negative allometry during the 5 nymphal stages from a mean of 239 in the first instar to 2462 in the last. At this point, this allometric growth pattern is sharply broken by distinct numerical increase to 7163 on the adult flagellum. The number of teeth composing the foretibial comb, the tool for grooming the distal flagellar segment, grows with negative allometry through all 6 developmental stages. Calculations using previously published data from the migratory locust, Locusta migratoria, revealed the same growth pattern of antennal sensilla: uniform allometric growth during the nymphal development, broken by a conspicuous upward jump to the adult number of sensilla. In the American cockroach, Periplaneta americana, this growth pattern of antennal sensilla holds only for the male; the female continues the nymphal allometric growth into the adult stage. These observations on allometric growth fit three theoretical explanations: 1. Smooth allometric growth is evidence for an aut-adaptation to increasing size. 2. Ex-adaptations to novel ecological niches cause breaks in allometric growth patterns. 3. Chapman's rule, which states that increased mobility correlates with greater olfactory sensitivity, correctly predicts the observed breaks in the allometric growth patterns in the abundance of antennal sensilla.     

Larvae of lycaenid butterflies that parasitize ant colonies provide exceptions to normal insect growth rules

Fourth instar larvae of Maculinea species of lycaenid butterfly live as social parasites inside Myrmica ant nests. They show highly unusual growth patterns, with small but regular growth in early phytophagous instars, followed by >10 times the growth predicted by extrapolating the early growth rate (following Dyar's rule) during the final carnivorous instar. This produces striking allometry between head and body size in full-grown larvae (ratios of 4–5% compared with 8–10%). Larvae of the Myrmica ant hosts have a similar growth. Data for c. 150 other lycaenid species showed that species with similar life-histories exhibit the same unusual growth pattern (Phengaris spp., Lepidochrysops spp., Niphanda fused); all others have regular growth throughout their larval life, including the carnivorous species that are parasitic on ants from the first instar. It is suggested that Maculinea-type growth pattern has arisen convergently in at least three unrelated lineages of lycaenids. Selection pressures might include the need for reduced early growth to produce late instars that are small enough to be integrated as brood mimics into ant social systems, combined with the need to achieve at least the same adult size as the ancestral species. Trophic pressures that operate on both sedentary ant and butterfly larvae, which must survive long periods of starvation and grow rapidly when food is abundant, may also be involved.     

Ontogenetic allometry and body composition of the common bottlenose dolphin (Tursiops truncatus) from the U.S. mid‐Atlantic

Growth in common bottlenose dolphins (Tursiops truncatus) was investigated through examination of sex‐specific, ontogenetic changes in the mass of 38 discrete body compartments, utilizing stranded dolphins in good body condition (n = 145). Ontogenetic allometry and the body composition technique were used to quantitatively describe growth patterns. Although adult males were significantly larger than adult females in total body mass (TBM) and total length, overall patterns of growth were remarkably similar between sexes. The integument, locomotor muscle, and vertebral column together represented 50%–58% of TBM across all life history categories, although their relative contributions varied ontogenetically. Young dolphins invested the greatest percentage of TBM in integument, while locomotor muscle was the single largest body component in adults. In both sexes (1) most muscle groups displayed positive allometry, (2) most skeletal elements displayed negative allometric or isometric growth, (3) most abdominal viscera associated with digestion displayed positive allometry, and (4) the brain displayed negative allometric growth. Reproductive tissues exhibited the highest rates of growth in both sexes, and increased as a percentage of TBM with maturity. This study provides an integrated view of bottlenose dolphin growth and a quantitative baseline of body composition for future monitoring of this sentinel species of ecosystem health.     

Notes on the postembryonic development and ecology of Grosphus hirtus Kraepelin, 1901 (Scorpiones, Buthidae) from the Parc National d’Ankarafantsika, northwest Madagascar

Among several specimens of Grosphus hirtus Kraepelin (Scorpiones, Buthidae), obtained in Madagascar, Mahajanga Province, Parc National d’Ankarafantsika, Station Forestière d’Ampijoroa, and then held in captivity, the courtship and mating behaviour of two females was observed. These two animals gave birth in captivity to 26 and 37 offspring of which two and three reached maturity, respectively. The duration of the five instars needed to reach the adult stage in both males and females averaged 14, 112, 117, 274, and 334 days. These developmental periods are much longer than those of Grosphus flavopiceus Kraepelin, the only other species in this genus studied, and longer than those of most examined species of Buthidae. Morphometric values for the different instars are presented from the individual offspring and from specimens collected in the wild. On the basis of these values, the average growth factor (Dyar's constant) per moult for three different measured structures was calculated from the pooled data. Dyar's constant is expressed for the first time in scorpions of the genus Grosphus. Instars growth factors are also comparable to other species of Buthidae.     

Developmental strategies in Ectobius pallidus (Dictyoptera: Blattidae)

Ectobius pallidus has a semivoltine life cycle, overwintering as an egg and intermediate nymphal instar. A range of instars may overwinter, although the exact composition of an overwintering population varies annually. A number of developmental pathways are defined, involving both quiescence and diapause. The proportion of an instar following each pathway also varies annually. In ‘advanced’ years more 3rd and 4th instars enter diapause. The ecological significance of the different developmental strategies is discussed.     

Geographical variation in allometry in the guppy (Poecilia reticulata)

Variation in static allometry, the power relationship between character size and body size among individuals at similar developmental stages, remains poorly understood. We tested whether predation or other ecological factors could affect static allometry by comparing the allometry between the caudal fin length and the body length in adult male guppies (Poecilia reticulata) among populations from different geographical areas, exposed to different predation pressures. Neither the allometric slopes nor the allometric elevations (intercept at constant slope) changed with predation pressure. However, populations from the Northern Range in Trinidad showed allometry with similar slopes but lower intercepts than populations from the Caroni and the Oropouche drainages. Because most of these populations are exposed to predation by the prawn Macrobrachium crenulatum, we speculated that the specific selection pressures exerted by this predator generated this change in relative caudal fin size, although effects of other environmental factors could not be ruled out. This study further suggests that the allometric elevation is more variable than the allometric slope.     

Ontogenetic allometry, heterochrony, and interspecific differences in the skull of African apes, using tridimensional Procrustes analysis

Ontogenetic studies of African ape skulls lead to an analysis of morphological differences in terms of allometry, heterochrony, and sexual dimorphism. The use of geometric morphometrics allows us 1) to define size and shape variations as independent factors (an essential but seldom respected condition for heterochrony), and 2) to calculate in percentage of shape changes and to graphically represent the parts of shape variation which are related to various biological phenomena: common allometry, intraspecific allometry, and allometric and nonallometric shape discrimination. Three tridimensional Procrustes analyses and the calculation of multivariate allometries, discriminant functions, and statistical tests are used to compare the skulls of 50 Pan troglodytes, and 50 Gorilla gorilla of different dental stages. The results both complement and modify classical results obtained from similar material but with different methods. Size and Scaling in Primate Morphology, New York: Plenum, p. 175-205). As previously described by Shea, the common growth allometric pattern is very important (64% of total shape variation). It corresponds to a larger increase of facial volume than of neurocranial volume, a more obliquely oriented foramen magnum, and a noticeable reshaping of the nuchal region (higher inion). However, the heterochronic interpretation based on common allometry is rather different from Shea. Gorillas differ from chimpanzees not only with a larger magnitude of allometric change (rate peramorphosis), as is classically said, but also grow more in size than in shape (size acceleration). In other words, for a similar stage of growth, gorillas have the size and shape corresponding to older chimpanzees, and for a similar shape, gorillas have a larger size than chimpanzees. In contrast, sexual dimorphism actually corresponds to allometric changes only, as classically demonstrated (time hypermorphosis). Sexual dimorphism is here significant in adult gorillas alone, and solely in terms of allometry (size-related shape and size, given that sagittal and nuchal crests are not taken into account). The study also permits us to differentiate two different shape variations that are classically confused in ontogenetic studies: a very small part of allometric shape change which is specific to each species (1% of the total shape variation), and nonallometric species-specific traits independent of growth (8% of total shape change). When calculated in terms of intraspecific allometries (including common allometry and noncommon allometry), shape changes are more extensive in gorillas (36% of total shape change) than in chimpanzees (29% of total shape change). The allometric differences mainly concern the inion, which becomes higher; the position of the foramen magnum, more dorsally oriented; and the palate, more tilted in adult gorillas than in adult chimpanzees. In contrast, nonallometric species-specific traits in gorillas are the long and flat vault characterized by a prominent occipital region, the higher and displaced backward glabella, and the protrusive nose. Biomechanical schemes built from shape partition suggest that the increased out-of-plumb position of the head during growth is partially compensated in gorillas by a powerful nuchal musculature due to the peculiar shape of the occipital region.     

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.     

Post-weaning cranial ontogeny in two bandicoots (Mammalia,Peramelomorphia, Peramelidae) and comparison with carnivorous marsupials

The ontogeny of the skull has been studied in several marsupial groups such as didelphids, microbiotheriids, and dasyurids. Here, we describe and compare the post-weaning ontogeny of the skull in two species of bandicoots, Echymipera kalubu (Echymiperinae) and Isoodon macrourus (Peramelinae), analyzing specific allometric trends in both groups, describing common (and specific) patterns, and discussing them on functional and phylogenetic grounds. Growth patterns were analyzed both qualitatively and quantitatively, including bivariate and multivariate analyses of allometry. We also evaluated character transformation and phylogenetic signals of the allometric patterns in several groups of marsupials and some placentals. We identified morphological changes between juvenile and adult stages in both species of peramelids, many related to the development of the trophic apparatus. Notable differences were detected in the patterns of growth, suggesting divergences in ontogenetic trajectories between both species. Both bivariate and multivariate methods indicate that positive allometries in E. kalubu apply to longitudinal dimensions, whereas in I. macrourus, positive allometries are restricted to vertical dimensions of the skull. The comparison of the allometric trends of two bandicoots with previously studied taxa reveals that although peramelids exhibit a particularly short gestation period and divergent morphology compared to other marsupials, their pattern does not show any particular trend. Some allometric trends seem to be highly conserved among the species studied, showing weak phylogenetic signal. Marsupials in general do not show particular patterns of post-weaning skull growth compared with placentals.     

The Evolution of Positive Allometry of Weaponry in Horned Lizards (Phrynosoma)

The allometry of weapons and other conspicuous structures has long fascinated biologists. Recently, a debate has arisen about the roles of sexual and natural selection in driving the allometry of structures, with some authors suggesting that positive allometry is exclusively the result of sexual selection. Although some studies, often focusing on weapons, support this hypothesis, others have shown that many naturally selected structures also exhibit positive allometry. We study the allometry of the cranial horns in 14 species of horned lizards (Phrynosoma). These horns are purely defensive weapons and so are under natural, as opposed to sexual, selection. In almost all cases, the length of these horns is positively allometric through ontogeny (intraspecifically) and through evolution (interspecifically). Our findings demonstrate that positive allometry can be the product of natural selection, suggesting that the function of structures may dictate allometry and not the type of selection. For example, it is possible that weapons tend to be positively allometric. Our findings also suggest that longer horns may arise through the prolongation of horn growth, and that the horns that are most effective at defense from predators attacking a lizard from above are integrated with one another. Finally, we find that species with unusual horn morphologies have diverged from other species in their horn allometries, indicating that the evolution of morphological diversity can be mediated through the evolution of allometry.     

Separation of cat flea (Siphonaptera: Pulicidae) instars by individual rearing and head width measurements

Two methods to verify whether head width measurements fit Dyar's rule were evaluated for the separation of instars of the cat flea, Ctenocephalides felis (Bouché). Individual rearing was a reliable method of determining larval instar but was labor-intensive. The mean observed head widths were significantly different for each instar (first instar, 0.164 mm; second instar, 0.201 mm; third instar, 0.260 mm) and showed no sexual dimorphism. Head capsule width increased roughly 25% from instar to instar with geometrically progressing growth in accordance with Dyar's rule. However, head capsule width cannot be used to determine the instar of randomly selected larvae because the measurements overlap broadly between instars.     

ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.