Notes on Allometry and Prediction of Body Mass and Age of Giraffes

Quantification of how biological structures change during growth is essential for understanding how giraffes work. Allometry is the best arithmetical tool for analyzing changes that occur during growth. It measures how well the rate of change in one structure is associated with the rate of change in another in the species of interest. If the association is close, then allometry can be used, as in this chapter, to predict the age of a giraffe (from, say, its height) or its body mass (from its length and girth), with great accuracy. The best predictions are made if the data used to make predictions are derived from the particular species, and this type is referred to as ontogenetic allometry. A second type—interspecific allometry—uses data collected from other species to make predictions about the species of interest (like giraffes). Predictions using this second method are less accurate but are useful for establishing anatomical, physiological, and biochemical differences between the species of interest and all other comparable species.

A highly conserved ontogenetic limb allometry and its evolutionary significance in the adaptive radiation of Anolis lizards

Diversifications often proceed along highly conserved, evolutionary trajectories. These patterns of covariation arise in ontogeny, which raises the possibility that adaptive morphologies are biased towards trait covariations that resemble growth trajectories. Here, we test this prediction in the diverse clade of Anolis lizards by investigating the covariation of embryonic growth of 13 fore- and hindlimb bones in 15 species, and compare these to the evolutionary covariation of these limb bones across 267 Anolis species. Our results demonstrate that species differences in relative limb length are established already at hatching, and are resulting from both differential growth and differential sizes of cartilaginous anlagen. Multivariate analysis revealed that Antillean Anolis share a common ontogenetic allometry that is characterized by positive allometric growth of the long bones relative to metapodial and phalangeal bones. This major axis of ontogenetic allometry in limb bones deviated from the major axis of evolutionary allometry of the Antillean Anolis and the two clades of mainland Anolis lizards. These results demonstrate that the remarkable diversification of locomotor specialists in Anolis lizards are accessible through changes that are largely independent from ontogenetic growth trajectories, and therefore likely to be the result of modifications that manifest at the earliest stages of limb development.

Ontogenetic and static allometry of hind femur length in the cricket Gryllus bimaculatus (Orthoptera: Gryllidae) with implications for evo-devo of morphological scaling

The evolution of morphological allometry or scaling is a long-standing enigma in biology. Three types of allometric relationships have been defined: static, ontogenetic and evolutionary allometry. However, the theory of the interrelationship between these three types of allometry have not been tested in Orthopterans and to a lesser extent in hemimetabolous insects. Here, the ontogenetic allometry of hind femur length in the cricket Gryllus bimaculatus was observed to be slightly positive as compared with a negative allometric relationship for Orthopterans in general, while the instar-specific static allometries were highly variable. The findings give support for the size-grain hypothesis in Orthoptera and indicate that ontogenetic allometries may not predict evolutionary allometries. The current model for the developmental basis of allometry derived from holometabolous insects is extended into a phylogenetic context and the potential of G. bimaculatus and other Orthopterans for further experiments of evo-devo of morphological scaling is discussed.

A quadratic approach to allometry yields promising results for the study of growth

Julian Huxley (1924) came to the conclusion that intra-specific growth usually follows a sequence of power curves. So Huxley claimed that during growth sudden changes in the growth rate can occur. The restudy of his material, however, reveals that his observations closely follow single quadratic curves. As a result the intra-specific allometry studied by Huxley is comparable to ontogenetic allometry. The quadratic factor of the quadratic equations obtained, represents the growth rate; it shows the constant increase (positive factor) or decrease (minus factor) of one of the measurements for a constant increase in the other measurement with which it is compared. The quadratic factor explains the entire growth process and is the same for the smaller (younger) and larger (older) specimens. It could probably permit the prediction of the shape of larger and/or smaller animals not yet found, or give a clue to some evolutionary changes. By using the quadratic parabola there is no need to postulate “sudden changes in the growth curve” and so it appears that Huxley’s power curve can be abandoned.

Biological interpretations of the biphasic model of ontogenetic brain–body allometry: a reply to Packard

Allometry is a description of organismal growth. Historically, a simple power law has been used most widely to describe the rate of growth in phenotypic traits relative to the rate of growth in overall size. However, the validity of this standard practice has repeatedly been criticized. In an accompanying opinion piece, Packard reanalysed data from a recent study on brain–body ontogenetic allometry and claimed that the biphasic growth model suggested in that study was an artefact of logarithmic transformation. Based on the model selection, Packard proposed alternative hypotheses for brain–body ontogenetic allometry. Here, I examine the validity of these models by comparing empirical data on body sizes at two critical neurodevelopmental events in mammals, i.e. at birth and at the time of the peak rate of brain growth, with statistically inferred body sizes that are supposed to characterize neurodevelopmental processes. These analyses support the existence of two distinct phases of brain growth and provide weak support for Packard's uniphasic model of brain growth. This study demonstrates the importance of considering alternative models in studies of allometry, but also highlights that such models need to respect the biological theoretical context of allometry.

Morphological evolution of the skull roof in temnospondyl amphibians mirrors conservative ontogenetic patterns

Addressing the patterns of ontogenetic allometry is relevant to understand morphological diversification because allometry might constrain evolution to specific directions of change in shape but also facilitate phenotypic differentiation along lines of least evolutionary resistance. Temnospondyl amphibians are a suitable group to address these issues from a deep-time perspective because different growth stages are known for numerous Palaeozoic and Mesozoic species. Herein we examine the patterns of ontogenetic allometry in the skull roof of 15 temponspondyl species and their relationship with adult morphological evolution. Using geometric morphometrics, we assessed ontogenetic and evolutionary allometries of this cranial part and the distribution of adult shapes in the morphospace to investigate whether these patterns relate to each other and/or to lifestyle and phylogeny. We found conspicuous stereotyped ontogenetic changes of the skull roof which are mirrored at the evolutionary level and consistency of the adult shape with phylogeny rather than lifestyle. These results suggest that the evolution of adult cranial shape was significantly biased by development towards pathways patterned by ontogenetic change in shape. The retrieved conserved patterns agree with a widespread evolutionary craniofacial trend found in amniotes, suggesting that they might have originated early in tetrapod evolutionary history or even earlier.