Development and phenotypic correlations: the evolution of tooth shape in Sorex araneus

A universal power law for modelling the growth and form of teeth, claws, horns, thorns, beaks, and shells

Background

A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes.

Results

Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants.

Conclusions

The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12915-021-00990-w.

Modern morphometrics and the study of population differences: Good data behind clever analyses and cool pictures?

The study of phenotypic variation in time and space is central to evolutionary biology. Modern geometric morphometrics is the leading family of methods for the quantitative analysis of biological forms. This set of techniques relies heavily on technological innovation for data acquisition, often in the form of 2D or 3D digital images, and on powerful multivariate statistical tools for their analysis. However, neither the most sophisticated device for computerized imaging nor the best statistical test can produce accurate, robust and reproducible results, if it is not based on really good samples and an appropriate use of the 'measurements' extracted from the data. Using examples mostly from my own work on mammal craniofacial variation and museum specimens, I will show how easy it is to forget these most basic assumptions, while focusing heavily on analytical and visualization methods, and much less on the data that generate potentially powerful analyses and visually appealing diagrams.

Were ancient foxes far more carnivorous than recent ones?-Carnassial morphological evidence

Crown shape variation of the first lower molar in the arctic (Vulpes lagopus) and red foxes (Vulpes vulpes) was analyzed using five groups of morphotypes. Carnassial morphologies were compared between the species and between spatially and temporally distant populations: one Late Pleistocene (n = 45) and seven modern populations of the arctic fox (n = 259), and one Late Pleistocene (n = 35) and eight modern populations of the red fox (n = 606). The dentition of Holocene red foxes had larger morphotype variability than that of arctic foxes. The lower carnassials of the red fox kept have some primitive characters (additional cusps and stylids, complex shape of transverse cristid), whereas the first lower molars of the arctic fox have undergone crown shape simplification, with the occlusal part of the tooth undergoing a more pronounced adaptation to a more carnivorous diet. From the Late Pleistocene of Belgium to the present days, the arctic fox’s crown shape has been simplified and some primitive characters have disappeared. In the red fox chronological changes in the morphology of the lower carnassials were not clearly identified. The phyletic tree based on morphotype carnassial characteristics indicated the distinctiveness of both foxes: in the arctic fox line, the ancient population from Belgium and recent Greenland made separate branches, whereas in the red foxes the ancient population from Belgium was most similar to modern red foxes from Belgium and Italy.

High-Density Morphometric Analysis of Shape and Integration: The Good, the Bad, and the Not-Really-a-Problem

The field of comparative morphology has entered a new phase with the rapid generation of high-resolution three-dimensional (3D) data. With freely available 3D data of thousands of species, methods for quantifying morphology that harness this rich phenotypic information are quickly emerging. Among these techniques, high-density geometric morphometric approaches provide a powerful and versatile framework to robustly characterize shape and phenotypic integration, the covariances among morphological traits. These methods are particularly useful for analyses of complex structures and across disparate taxa, which may share few landmarks of unambiguous homology. However, high-density geometric morphometrics also brings challenges, for example, with statistical, but not biological, covariances imposed by placement and sliding of semilandmarks and registration methods such as Procrustes superimposition. Here, we present simulations and case studies of high-density datasets for squamates, birds, and caecilians that exemplify the promise and challenges of high-dimensional analyses of phenotypic integration and modularity. We assess: (1) the relative merits of "big" high-density geometric morphometrics data over traditional shape data; (2) the impact of Procrustes superimposition on analyses of integration and modularity; and (3) differences in patterns of integration between analyses using high-density geometric morphometrics and those using discrete landmarks. We demonstrate that for many skull regions, 20-30 landmarks and/or semilandmarks are needed to accurately characterize their shape variation, and landmark-only analyses do a particularly poor job of capturing shape variation in vault and rostrum bones. Procrustes superimposition can mask modularity, especially when landmarks covary in parallel directions, but this effect decreases with more biologically complex covariance patterns. The directional effect of landmark variation on the position of the centroid affects recovery of covariance patterns more than landmark number does. Landmark-only and landmark-plus-sliding-semilandmark analyses of integration are generally congruent in overall pattern of integration, but landmark-only analyses tend to show higher integration between adjacent bones, especially when landmarks placed on the sutures between bones introduces a boundary bias. Allometry may be a stronger influence on patterns of integration in landmark-only analyses, which show stronger integration prior to removal of allometric effects compared to analyses including semilandmarks. High-density geometric morphometrics has its challenges and drawbacks, but our analyses of simulated and empirical datasets demonstrate that these potential issues are unlikely to obscure genuine biological signal. Rather, high-density geometric morphometric data exceed traditional landmark-based methods in characterization of morphology and allow more nuanced comparisons across disparate taxa. Combined with the rapid increases in 3D data availability, high-density morphometric approaches have immense potential to propel a new class of studies of comparative morphology and phenotypic integration.

Methods for Studying Morphological Integration and Modularity

Morphological integration and modularity are closely related concepts about how different traits of an organism are correlated. Integration is the overall pattern of intercorrelation; modularity is the partitioning of integration into evolutionarily or developmentally independent blocks of traits. Modularity and integration are usually studied using quantitative phenotypic data, which can be obtained either from extant or fossil organisms. Many methods are now available to study integration and modularity, all of which involve the analysis of patterns found in trait correlation or covariance matrices. We review matrix correlation, random skewers, fluctuating asymmetry, cluster analysis, Euclidean distance matrix analysis (EDMA), graphical modelling, two-block partial least squares, RV coefficients, and theoretical matrix modelling and discuss their similarities and differences. We also review different coefficients that are used to measure correlations. We apply all the methods to cranial landmark data from and ontogenetic series of Japanese macaques,Macaca fuscatato illustrate the methods and their individual strengths and weaknesses. We conclude that the exploratory approaches (cluster analyses of various sorts) were less informative and less consistent with one another than were the results of model testing or comparative approaches. Nevertheless, we found that competing models of modularity and integration are often similar enough that they are not statistically distinguishable; we expect, therefore, that several models will often be significantly correlated with observed data.

Out on a limb: bandicoot limb co-variation suggests complex impacts of development and adaptation on marsupial forelimb evolution

Marsupials display far less forelimb diversity than placentals, possibly because of the laborious forelimb-powered climb to the pouch performed by most marsupial neonates. This is thought to result in stronger morphological integration (i.e., higher co-variance) within the marsupial forelimb skeleton, and lower integration between marsupial fore- and hind limbs, compared to other mammals. Possible mechanisms for this constraint are a fundamental developmental change in marsupial limb patterning, or alternatively more immediate perinatal biomechanical and metabolic requirements. In the latter case, peramelid marsupials (bandicoots), which have neonates that climb very little, should show lower within-limb and higher between-limb integration, compared to other marsupials. We tested this in four peramelid species and the related bilby, using partial correlation analyses of between-landmark linear measurements of limb bones, and Procrustes-based two-block partial least-squares analysis (2B-PLS) of limb bone shapes using the same landmarks. We find extensive between-limb integration in partial correlation analyses of only bone lengths, consistent with a reduction of a short-term biomechanical/allocation constraint in peramelid forelimbs. However, partial correlations of bone proportions and 2B-PLS reveal extensive shape divergence between correlated bone pairs. This result contradicts expectations of developmental constraints or serial homology, instead suggesting a function-driven integration pattern. Comparing visualizations from cross-species principal components analysis and 2B-PLS, we tentatively identify selection for digging and half-bounding as the main driver of bandicoot limb integration patterning. This calls for further assessments of functional versus developmental limb integration in marsupials with a more strenuous neonatal climb to the pouch.

How many more? Sample size determination in studies of morphological integration and evolvability

1. The variational properties of living organisms are an important component of current evolutionary theory. As a consequence, researchers working on the field of multivariate evolution have increasingly used integration and evolvability statistics as a way of capturing the potentially complex patterns of trait association and their effects over evolutionary trajectories. Little attention has been paid, however, to the cascading effects that inaccurate estimates of trait covariance have on these widely used evolutionary statistics. 2. Here, we analyze the relationship between sampling effort and inaccuracy in evolvability and integration statistics calculated from 10-trait matrices with varying patterns of covariation and magnitudes of integration. We then extrapolate our initial approach to different numbers of traits and different magnitudes of integration and estimate general equations relating the inaccuracy of the statistics of interest to sampling effort. We validate our equations using a dataset of cranial traits, and use them to make sample size recommendations. 3. Our results suggest that highly inaccurate estimates of evolvability and integration statistics resulting from small sample sizes are likely common in the literature, given the sampling effort necessary to properly estimate them. We also show that patterns of covariation have no effect on the sampling properties of these statistics, but overall magnitudes of integration interact with sample size and lead to varying degrees of bias, imprecision, and inaccuracy. 4. Finally, we provide R functions that can be used to calculate recommended sample sizes or to simply estimate the level of inaccuracy that should be expected in these statistics, given a sampling design.

Wing Shape Variation in the Taxonomic Recognition of Species of Diachlorus Osten-Sacken (Diptera: Tabanidae) from Colombia

We evaluated the directional asymmetry between right and left wings and quantified the intraspecific and interspecific variation of the wing shape of 601 specimens of the genus Diachlorus to determine to what extent the geometrical variation discriminates six species distributed in six protected areas of Colombia. Geometric analyses were performed, integrating Procrustes methods, principal component analyses, cluster analyses, linear and quadratic discriminant analyses, and evaluations of shape changes. In Diachlorus, left and right wings did not present significant asymmetry but a geometrical analysis was allowed for species identification and, in some cases, the origin of the specimens using the variation of wing shape; the best-assigned species was Diachlorus leticia Wilkerson & Fairchild, while the worst was Diachlorus jobbinsi Fairchild, which also had the highest intraspecific variation, while Diachlorus fuscistigma Lutz had the lowest variation. Diachlorus fuscistigma and Diachlorus leucotibialis Wilkerson & Fairchild were the most similar species, while D. leucotibialis and Diachlorus nuneztovari Fairchild & Ortiz were the most disimilar. The specimens with the most different wing shape belonged to Chocó (especially those of D. jobbinsi), the geographically farthest area from the others in the study; however, no correlation was observed between geometric and geographical distances. Linear discriminants were better than nonlinear (quadratic) discriminant analyses in predicting species membership, but the opposite was true for predicting area membership. Based on our data, we hypothesized that other species of Diachlorus could also be discriminated using geometric morphometry of the wing shape.

Gene networks, occlusal clocks, and functional patches: new understanding of pattern and process in the evolution of the dentition

Our understanding of the evolution of the dentition has been transformed by advances in the developmental biology, genetics, and functional morphology of teeth, as well as the methods available for studying tooth form and function. The hierarchical complexity of dental developmental genetics combined with dynamic effects of cells and tissues during development allow for substantial, rapid, and potentially non-linear evolutionary changes. Studies of selection on tooth function in the wild and evolutionary functional comparisons both suggest that tooth function and adaptation to diets are the most important factors guiding the evolution of teeth, yet selection against random changes that produce malocclusions (selectional drift) may be an equally important factor in groups with tribosphenic dentitions. These advances are critically reviewed here.

The macroevolutionary consequences of phenotypic integration: from development to deep time

Phenotypic integration is a pervasive characteristic of organisms. Numerous analyses have demonstrated that patterns of phenotypic integration are conserved across large clades, but that significant variation also exists. For example, heterochronic shifts related to different mammalian reproductive strategies are reflected in postcranial skeletal integration and in coordination of bone ossification. Phenotypic integration and modularity have been hypothesized to shape morphological evolution, and we extended simulations to confirm that trait integration can influence both the trajectory and magnitude of response to selection. We further demonstrate that phenotypic integration can produce both more and less disparate organisms than would be expected under random walk models by repartitioning variance in preferred directions. This effect can also be expected to favour homoplasy and convergent evolution. New empirical analyses of the carnivoran cranium show that rates of evolution, in contrast, are not strongly influenced by phenotypic integration and show little relationship to morphological disparity, suggesting that phenotypic integration may shape the direction of evolutionary change, but not necessarily the speed of it. Nonetheless, phenotypic integration is problematic for morphological clocks and should be incorporated more widely into models that seek to accurately reconstruct both trait and organismal evolution.

Bite of the cats: relationships between functional integration and mechanical performance as revealed by mandible geometry

Cat-like carnivorous mammals represent a relatively homogeneous group of species whose morphology appears constrained by exclusive adaptations for meat eating. We present the most comprehensive data set of extant and extinct cat-like species to test for evolutionary transformations in size, shape and mechanical performance, that is, von Mises stress and surface traction, of the mandible. Size and shape were both quantified by means of geometric morphometrics, whereas mechanical performance was assessed applying finite element models to 2D geometry of the mandible. Additionally, we present the first almost complete composite phylogeny of cat-like carnivorans for which well-preserved mandibles are known, including representatives of 35 extant and 59 extinct species of Felidae, Nimravidae, and Barbourofelidae. This phylogeny was used to test morphological differentiation, allometry, and covariation of mandible parts within and among clades. After taking phylogeny into account, we found that both allometry and mechanical variables exhibit a significant impact on mandible shape. We also tested whether mechanical performance was linked to morphological integration. Mechanical stress at the coronoid process is higher in sabertoothed cats than in any other clade. This is strongly related to the high degree of covariation within modules of sabertooths mandibles. We found significant correlation between integration at the clade level and per-clade averaged stress values, on both original data and by partialling out interclade allometry from shapes when calculating integration. This suggests a strong interaction between natural selection and the evolution of developmental and functional modules at the clade level.

Testing the inhibitory cascade model in Mesozoic and Cenozoic mammaliaforms

Background

Much of the current research in the growing field of evolutionary development concerns relating developmental pathways to large-scale patterns of morphological evolution, with developmental constraints on variation, and hence diversity, a field of particular interest. Tooth morphology offers an excellent model system for such ‘evo-devo’ studies, because teeth are well preserved in the fossil record, and are commonly used in phylogenetic analyses and as ecological proxies. Moreover, tooth development is relatively well studied, and has provided several testable hypotheses of developmental influences on macroevolutionary patterns. The recently-described Inhibitory Cascade (IC) Model provides just such a hypothesis for mammalian lower molar evolution. Derived from experimental data, the IC Model suggests that a balance between mesenchymal activators and molar-derived inhibitors determines the size of the immediately posterior molar, predicting firstly that molars either decrease in size along the tooth row, or increase in size, or are all of equal size, and secondly that the second lower molar should occupy one third of lower molar area. Here, we tested the IC Model in a large selection of taxa from diverse extant and fossil mammalian groups, ranging from the Middle Jurassic (~176 to 161 Ma) to the Recent.

Results

Results show that most taxa (~65%) fell within the predicted areas of the Inhibitory Cascade Model. However, members of several extinct groups fell into the regions where m2 was largest, or rarely, smallest, including the majority of the polyphyletic “condylarths”. Most Mesozoic mammals fell near the centre of the space with equality of size in all three molars. The distribution of taxa was significantly clustered by diet and by phylogenetic group.

Conclusions

Overall, the IC Model was supported as a plesiomorphic developmental system for Mammalia, suggesting that mammal tooth size has been subjected to this developmental constraint at least since the divergence of australosphenidans and boreosphenidans approximately 180 Ma. Although exceptions exist, including many ‘condylarths’, these are most likely to be secondarily derived states, rather than alternative ancestral developmental models for Mammalia.

Differential evolvability along lines of least resistance of upper and lower molars in island house mice

Variation within a population is a key feature in evolution, because it can increase or impede response to selection, depending on whether or not the intrapopulational variance is correlated to the change under selection. Hence, main directions of genetic variance have been proposed to constitute “lines of least resistance to evolution” along which evolution would be facilitated. Yet, the screening of selection occurs at the phenotypic level, and the phenotypic variance is not only the product of the underlying genetic variance, but also of developmental processes. It is thus a key issue for interpreting short and long term evolutionary patterns to identify whether main directions of phenotypic variance indeed constitute direction of facilitated evolution, and whether this is favored by developmental processes preferably generating certain phenotypes. We tackled these questions by a morphometric quantification of the directions of variance, compared to the direction of evolution of the first upper and lower molars of wild continental and insular house mice. The main phenotypic variance indeed appeared as channeling evolution between populations. The upper molar emerged as highly evolvable, because a strong allometric component contributed to its variance. This allometric relationship drove a repeated but independent evolution of a peculiar upper molar shape whenever size increased. This repeated evolution, together with knowledge about the molar development, suggest that the main direction of phenotypic variance correspond here to a “line of least developmental resistance” along which evolution between population is channeled.

Epigenetic effects on the mouse mandible: common features and discrepancies in remodeling due to muscular dystrophy and response to food consistency

Background

In wild populations phenotypic differentiation of skeletal structures is influenced by many factors including epigenetic interactions and plastic response to environmental influences, possibly blurring the expression of genetic differences. In contrast, laboratory animals provide the opportunity to separate environmental from genetic effects. The mouse mandible is particularly prone to such plastic variations because bone remodeling occurs late in postnatal ontogeny, in interaction with muscular loading. In order to understand the impact of this process on mandible morphology, we investigated how change in the masticatory function affects the mandible shape, and its pattern of variation. Breeding laboratory mice on food of different consistencies mimicked a natural variation in feeding ecology, whereas mice affected by the murine analogue of the Duchenne muscular dystrophy provided a case of pathological modification of the mastication process.

Results

Food consistency as well as dystrophy caused significant shape changes in the mouse mandible. Further differences were observed between laboratory strains and between sexes within strains, muscular dystrophy causing the largest morphological change. The directions of the morphological changes due to food consistency and muscular dystrophy were discrepant, despite the fact that both are related to bone remodeling. In contrast, directions of greatest variance were comparable among most groups, and the direction of the change due to sexual dimorphism was parallel to the direction of main variance.

Conclusions

Bone remodeling is confirmed as an important factor driving mandible shape differences, evidenced by differences due to both the consistency of the food ingested and muscular dystrophy. However, the resulting shape change will depend on how the masticatory function is affected. Muscular dystrophy caused shape changes distributed all over the mandible, all muscles being affected although possibly to a different degree. In contrast, the chewing function was mostly affected when the mice were fed on hard vs. soft food, whereas grinding likely occurred normally; accordingly, shape change was more localized. The direction of greatest variance, however, was remarkably comparable among groups, although we found a residual variance discarding age, sex, and food differences. This suggests that whatever the context in which bone remodeling occurs, some parts of the mandible such as the angular process are more prone to remodeling during late postnatal growth.

Mandible shape in hybrid mice

Hybridisation between closely related species is frequently seen as retarding evolutionary divergence and can also promote it by creating novel phenotypes due to new genetic combinations and developmental interactions. We therefore investigated how hybridisation affects the shape of the mouse mandible, a well-known feature in evo-devo studies. Parental groups corresponded to two strains of the European mouse sub-species Mus musculus domesticus and Mus musculus musculus. Parents and hybrids were bred in controlled conditions. The mandibles of F(1) hybrids are mostly intermediate between parental phenotypes as expected for a complex multigenic character. Nevertheless, a transgressive effect as well as an increased phenotypic variance characterise the hybrids. This suggests that hybridisation between the two subspecies could lead to a higher phenotypic variance due to complex interactions among the parental genomes including non-additive genetic effects. The major direction of variance is conserved, however, among hybrids and parent groups. Hybridisation may thus play a role in the production of original transgressive phenotypes occurring following pre-existing patterns of variance.

Developmental and genetic mechanisms for evolutionary diversification of serial repeats: eyespot size in Bicyclus anynana butterflies

Serially repeated pattern elements on butterfly wings offer the opportunity for integrating genetic, developmental, and functional aspects towards understanding morphological diversification and the evolution of individuality. We use captive populations of Bicyclus anynana butterflies, an emerging model in evolutionary developmental biology, to explore the genetic and developmental basis of compartmentalized changes in eyespot patterns. There is much variation for different aspects of eyespot morphology, and knowledge about the genetic pathways and developmental processes involved in eyespot formation. Also, despite the strong correlations across all eyespots in one butterfly, B. anynana shows great potential for independent changes in the size of individual eyespots. It is, however, unclear to what extent the genetic and developmental processes underlying eyespot formation change in a localized manner to enable such individualization. We use micromanipulations of developing wings to dissect the contribution of different components of eyespot development to quantitative differences in eyespot size on one wing surface. Reciprocal transplants of presumptive eyespot foci between artificial selection lines and controls suggest that while localized antagonistic changes in eyespot size rely mostly on localized changes in focal signal strength, concerted changes depend greatly on epidermal response sensitivities. This potentially reflects differences between the signal-response components of eyespot formation in the degrees of compartmentalization and/or the temporal pattern of selection. We also report on the phenotypic analysis of a number of mutant stocks demonstrating how single alleles can affect different eyespots in concert or independently, and thus contribute to the individualization of serially repeated traits.

Predicting evolutionary patterns of mammalian teeth from development

One motivation in the study of development is the discovery of mechanisms that may guide evolutionary change. Here we report how development governs relative size and number of cheek teeth, or molars, in the mouse. We constructed an inhibitory cascade model by experimentally uncovering the activator-inhibitor logic of sequential tooth development. The inhibitory cascade acts as a ratchet that determines molar size differences along the jaw, one effect being that the second molar always makes up one-third of total molar area. By using a macroevolutionary test, we demonstrate the success of the model in predicting dentition patterns found among murine rodent species with various diets, thereby providing an example of ecologically driven evolution along a developmentally favoured trajectory. In general, our work demonstrates how to construct and test developmental rules with evolutionary predictability in natural systems.

Morphological differentiation of aboriginal human populations from Tierra del Fuego (Patagonia): Implications for South American peopling

This study aims to integrate the craniofacial morphological variation of southern South American populations with the results of mtDNA haplogroup variation, to discuss the South America peopling. Because the causes of morphological differentiation of Fueguian populations are still a controversial subject, the comparison with neutral variation could contribute to elucidate them. Samples of human remains from South America regions were used to analyze the evolutionary relationships. Several craniofacial traits observed in frontal and lateral view were analyzed by means of geometric morphometrics techniques, and the evolutionary relationships based on morphological and molecular data were established in base to ordination analyses. The results from the facial skeleton agree with those obtained from mtDNA haplogroup frequencies, with La Pampa/Chaco samples detached from the Patagonian samples. Hence, the same mechanism that accounts for the pattern of frequency of haplogroups could explain the variation found in facial skeleton among the samples. It is suggested that such geographic pattern of craniofacial and molecular diversity may reflect the effect of genetic drift that occurred in the small founding populations isolated by distance or geographic barriers. Conversely, the results obtained using the traits from the lateral view slightly differ from the molecular results, showing differences between southernmost Patagonian and the other samples. Therefore, mechanisms other than genetic drift (e.g., natural selection) could have acted to shape the pattern observed in some craniofacial structures present in the lateral view, characterized by the fact that the southernmost Patagonian samples display the most robust and dolichocephalic crania.

Developmental constraints vs. variational properties: How pattern formation can help to understand evolution and development

This article suggests that apparent disagreements between the concept of developmental constraints and neo-Darwinian views on morphological evolution can disappear by using a different conceptualization of the interplay between development and selection. A theoretical framework based on current evolutionary and developmental biology and the concepts of variational properties, developmental patterns and developmental mechanisms is presented. In contrast with existing paradigms, the approach in this article is specifically developed to compare developmental mechanisms by the morphological variation they produce and the way in which their functioning can change due to genetic variation. A developmental mechanism is a gene network, which is able to produce patterns in space though the regulation of some cell behaviour (like signalling, mitosis, apoptosis, adhesion, etc.). The variational properties of a developmental mechanism are all the pattern transformations produced under different initial and environmental conditions or IS-mutations. IS-mutations are DNA changes that affect how two genes in a network interact, while T-mutations are mutations that affect the topology of the network itself. This article explains how this new framework allows predictions not only about how pattern formation affects variation, and thus phenotypic evolution, but also about how development evolves by replacement between pattern formation mechanisms. This article presents testable inferences about the evolution of the structure of development and the phenotype under different selective pressures. That is what kind of pattern formation mechanisms, in which relative temporal order, and which kind of phenotypic changes, are expected to be found in development.

Cranial Modularity Shifts during Mammalian Evolution

The mammalian skull has been studied as several separate functional components for decades, but the study of modularity is a more recent, integrative approach toward quantitative examination of independent subsets of highly correlated traits, or modules. Although most studies of modularity focus on developmental and genetic systems, phenotypic modules have been noted in many diverse morphological structures. However, few studies have provided empirical data for comparing modules across higher taxonomic levels, limiting the ability to assess the broader evolutionary significance of modularity. This study uses 18-32 three-dimensional cranial landmarks to analyze phenotypic modularity in 106 mammalian species and demonstrates that cranial modularity is generally conserved in the evolution of therian mammals (marsupials and placentals) but differs between therians and monotremes, the two extant subclasses of Mammalia. Within therians, cluster analyses identify six distinct modules, but only three modules display significant integration in all species. Monotremes display only two highly integrated modules. Specific hypotheses of functional and developmental influences on cranial bones were tested. Theoretical correlation matrices for bones were constructed on the basis of shared function, tissue origin, or mode of ossification, and all three of these models are significantly correlated with observed correlation matrices for the mammalian cranium.

Developmental regulation of skull morphology II: ontogenetic dynamics of covariance

Canalization may play a critical role in molding patterns of integration when variability is regulated by the balance between processes that generate and remove variation. Under these conditions, the interaction among those processes may produce a dynamic structure of integration even when the level of variability is constant. To determine whether the constancy of variance in skull shape throughout most of postnatal growth results from a balance between processes generating and removing variation, we compare covariance structures from age to age in two rodent species, cotton rats (Sigmodon fulviventer) and house mice (Mus musculus domesticus). We assess the overall similarity of covariance matrices by the matrix correlation, and compare the structures of covariance matrices using common subspace analysis, a method related to common principal components (PCs) analysis but suited to cases in which variation is so nearly spherical that PCs are ambiguous. We find significant differences from age to age in covariance structure and the more effectively canalized ones tend to be least stable in covariance structure. We find no evidence that canalization gradually and preferentially removes deviations arising early in development as we might expect if canalization results from compensatory differential growth. Our results suggest that (co)variation patterns are continually restructured by processes that equilibrate variance, and thus that canalization plays a critical role in molding patterns of integration.