The analysis of ontogenetic trajectories: when a change in size or shape is not heterochrony

Evolution, inactivation and loss of short wavelength-sensitive opsin genes during the diversification of Neotropical cichlids

Natural variation in the number, expression and function of sensory genes in an organism's genome is often tightly linked to different ecological and evolutionary forces. Opsin genes, which code for the first step in visual transduction, are ideal models for testing how ecological factors such as light environment may influence visual system adaptation. Neotropical cichlid fishes are a highly ecologically diverse group that evolved in a variety of aquatic habitats, including black (stained), white (opaque) and clear waters. We used cross-species exon capture to sequence Neotropical cichlid short wavelength-sensitive (SWS) opsins, which mediate ultraviolet (UV) to blue visual sensitivity. Neotropical cichlid SWS1 opsin (UV-sensitive) underwent a relaxation of selective constraint during the early phases of cichlid diversification in South America, leading to pseudogenization and loss. Conversely, SWS2a (blue-sensitive) experienced a burst of episodic positive selection at the base of the South American cichlid radiation. This burst coincides with SWS1 relaxation and loss, and is consistent with findings in ecomorphological studies characterizing a period of extensive ecological divergence in Neotropical cichlids. We use ancestral sequence reconstruction and protein modelling to investigate mutations along this ancestral branch that probably modified SWS2a function. Together, our results suggest that variable light environments played a prominent early role in shaping SWS opsin diversity during the Neotropical cichlid radiation. Our results also illustrate that long-term evolution under light-limited conditions in South America may have reduced visual system plasticity; specifically, early losses of UV sensitivity may have constrained the evolutionary trajectory of Neotropical cichlid vision.

Allometric Relationships for Cardiac Size and Longitudinal Function in Healthy Chinese Adults - Normal Ranges and Clinical Correlates

BACKGROUND

Cardiac size measurements require indexing to body size. Allometric indexing has been investigated in Caucasian populations but a range of different values for the so-called allometric power exponent (b) have been proposed, with uncertainty as to whether allometry offers clinical utility above body surface area (BSA)-based indexing. We derived optimal values for b in normal echocardiograms and validated them externally in cardiac patients.

METHODS AND RESULTS

Values for b were derived in healthy adult Chinese males (n=1,541), with optimal b for left ventricular mass (LVM) of 1.66 (95% confidence interval 1.41-1.92). LV hypertrophy (LVH) defined as indexed LVM >75 g/m^1.66 was associated with adverse outcomes in an external validation cohort (n=738) of patients with acute coronary syndrome (odds ratio for reinfarction: 2.4 (1.1-5.4)). In contrast, LVH defined by BSA-based indexing or allometry using exponent 2.7 exhibited no significant association with outcomes (P=NS for both). Cardiac longitudinal function also varied with body size: septal and RV free wall s', TAPSE and lateral e' all scaled allometrically (b=0.3-0.9).

CONCLUSIONS

An optimal b of 1.66 for LVM in healthy Chinese was found to validate well, with superior clinical utility both to that of BSA-based indexing and to b=2.7. The effect of allometric indexing of cardiac function requires further study.

INTEGRATING DEVELOPMENTAL EVOLUTIONARY PATTERNS AND MECHANISMS: A CASE STUDY USING THE GASTROPOD RADULA

Determining the connection between ontogeny and phylogeny continues to be a major theme in biology. However, few studies have combined dissection of pattern and process that lead to transformation of complex morphological structures. Here we examine the patterns and processes of shape change in a model system-the gastropod radula. This system is a simple one having only two processes: initial secretion and postsecretional movement of teeth. However, it produces a tremendous amount of shape variability and fusion patterns. To determine both pattern and mechanism of shape change in an evolutionary context, we use three complementary approaches and datasets. First, we use a phylogenetic hypothesis to determine the polarity of developmental events. Second, we perform a morphometric analysis of shape change using relative warp analysis that allows us to locate and compare the direction and magnitude of ontogenetic and phylogenetic shape divergence. These comparisons are the basis for testing hyptheses of heterochrony and heterotopy, and we show how our results do not conform to expectations of pure heterochrony. The rejection of heterochrony as a hypothesis is based on empirically demonstrating (1) initial shape differs in each taxon; (2) a single dimension of shape variability does not simultaneously describe ontogenetic and evolutionary shape changes; and (3) a significantly different shape and size covariance between taxa. This rejection is probably based on spatial changes in initial conditions and not spatial changes caused by the process itself. Finally, we construct a mechanistic model that explains how shape change happens based on the sequence of events during ontogeny. By using the parameters in the model as characters in the phylogenetic dataset, we show that different parts of the system have arisen at different times and become co-opted into the process. By integrating our analyses together we show that spatial process parameters can be responsible for our nonspatial patterns and that different ontogenetic processes can create similar end morphologies.

Comparison of neuromuscular development in two dinophilid species (Annelida) suggests progenetic origin of Dinophilus gyrociliatus

BACKGROUND

Several independent meiofaunal lineages are suggested to have originated through progenesis, however, morphological support for this heterochronous process is still lacking. Progenesis is defined as an arrest of somatic development (synchronously in various organ systems) due to early maturation, resulting in adults resembling larvae or juveniles of the ancestors. Accordingly, we established a detailed neuromuscular developmental atlas of two closely related Dinophilidae using immunohistochemistry and CLSM. This allows us to test for progenesis, questioning whether i) the adult smaller, dimorphic Dinophilus gyrociliatus resembles a younger developmental stage of the larger, monomorphic D. taeniatus and whether ii) dwarf males of D. gyrociliatus resemble an early developmental stage of D. gyrociliatus females.

RESULTS

Both species form longitudinal muscle bundles first, followed by circular muscles, creating a grid of body wall musculature, which is the densest in adult D. taeniatus, while the architecture in adult female D. gyrociliatus resembles that of prehatching D. taeniatus. Both species display a subepidermal ganglionated nervous system with an anterior dorsal brain and five longitudinal ventral nerve bundles with six sets of segmental commissures (associated with paired ganglia). Neural differentiation of D. taeniatus and female D. gyrociliatus commissures occurs before hatching: both species start out forming one transverse neurite bundle per segment, which are thereafter joined by additional thin bundles. Whereas D. gyrociliatus arrests its development at this stage, adult D. taeniatus condenses the thin commissures again into one thick commissural bundle per segment. Generally, D. taeniatus adults demonstrate a seemingly more organized (= segmental) pattern of serotonin-like and FMRFamide-like immunoreactive elements. The dwarf male of D. gyrociliatus displays a highly aberrant neuromuscular system, showing no close resemblance to any early developmental stage of female Dinophilus, although the onset of muscular development mirrors the early myogenesis in females.

CONCLUSION

The apparent synchronous arrest of nervous and muscular development in adult female D. gyrociliatus, resembling the prehatching stage of D. taeniatus, suggests that D. gyrociliatus have originated through progenesis. The synchrony in arrest of three organ systems, which show opposing reduction and addition of elements, presents one of the morphologically best-argued cases of progenesis within Spiralia.

Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology

Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the null hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

A model framework for identifying genes that guide the evolution of heterochrony

Heterochrony, the phylogenic change in the time of developmental events or rate of development, has been thought to play an important role in producing phenotypic novelty during evolution. Increasing evidence suggests that specific genes are implicated in heterochrony, guiding the process of developmental divergence, but no quantitative models have been instrumented to map such heterochrony genes. Here, we present a computational framework for genetic mapping by which to characterize and locate quantitative trait loci (QTLs) that govern heterochrony described by four parameters, the timing of the inflection point, the timing of maximum acceleration of growth, the timing of maximum deceleration of growth, and the length of linear growth. The framework was developed from functional mapping, a dynamic model derived to map QTLs for the overall process and pattern of development. By integrating an optimality algorithm, the framework allows the so-called heterochrony QTLs (hQTLs) to be tested and quantified. Specific pipelines are given for testing how hQTLs control the onset and offset of developmental events, the rate of development, and duration of a particular developmental stage. Computer simulation was performed to examine the statistical properties of the model and demonstrate its utility to characterize the effect of hQTLs on population diversification due to heterochrony. By analyzing a genetic mapping data in rice, the framework identified an hQTL that controls the timing of maximum growth rate and duration of linear growth stage in plant height growth. The framework provides a tool to study how genetic variation translates into phenotypic innovation, leading a lineage to evolve, through heterochrony.

Revisiting de Beer's textbook example of heterochrony and jaw elongation in fish: calmodulin expression reflects heterochronic growth, and underlies morphological innovation in the jaws of belonoid fishes

Background

Heterochronic shifts during ontogeny can result in adaptively important innovations and might be initiated by simple developmental switches. Understanding the nature of these developmental events can provide insights into fundamental molecular mechanisms of evolutionary change. Fishes from the Suborder Belonoidei display a vast array of extreme craniofacial morphologies that appear to have arisen through a series of heterochronic shifts. We performed a molecular heterochrony study, comparing postembryonic jaw development in representatives of the Suborder Belonoidei, the halfbeak Dermogenys pusilla (where the lower jaw is considerably elongated compared to the upper jaw) and the needlefish Belone belone (where both jaws are elongated), to a representative of their sister group the Suborder Adrianichthyoidei, the medaka Oryzias latipes, which has retained the ancestral morphology.

Results

Early in development, the lower jaw displays accelerated growth both in needlefish and halfbeak compared to medaka, and secondary acceleration of the upper jaw is seen in needlefish later in their development, representing a case of mosaic heterochrony. We identified toothless extensions of the dentaries as innovations of Belonoid fishes and the source of heterochronic growth. The molecular basis of growth heterochronies in the Belonoidei was examined through comparing expression of skeletogenic genes during development of halfbeak and medaka. The calmodulin paralogue calm1 was identified as a potential regulator of jaw length in halfbeak as its expression gradually increases in the lower jaw, but not the upper jaw, in a pattern that matches its outgrowth. Moreover, medaka displays equal expression of calm1 in the upper and lower jaws, consistent with the lack of jaw outgrowth in this species.

Conclusions

Heterochronic shifts in jaw growth have occurred repeatedly during the evolution of Belonoid fishes and we identify toothless extensions of the dentaries as an important innovation of this group. Our results suggest that calm1 contributes to jaw heterochrony in halfbeak, potentially driving further heterochronic shifts in jaw growth across the Suborder Belonoidei, such as the upper jaw acceleration observed in needlefish.

Evolution of hominin cranial ontogeny

Hominin evolution is characterized by two main trends, transition to bipedality and increase in brain size. Fossil evidence shows that both trends had a major impact on the structure and function of the hominin skull. This chapter asks how evolutionary modification of the cranial ontogenetic program led to morphological reorganization of the hominin skull and ultimately to hominin cranial diversity. Three major mechanisms of evolutionary developmental reorganization are proposed: modified prenatal development of the cranial base and face reflects adaptation to bipedality; high rates of neurocranial growth during early postnatal ontogeny are essential to attain large brain sizes; taxon-specific modification of facial development reflects dietary adaptation and-in the genus Homo-a general trend toward neoteny.

Allometries and the morphogenesis of the molluscan shell: a quantitative and theoretical model

This article explores the close relationships between growth rate and allometries of molluscan shells. After reviewing the previous theoretical approaches devoted to the understanding of shell form and its morphogenesis, we present a free-form vector model which can simulate apertural shape changes and nonlinear allometries. Shell morphology is generated by iteratively adding a growth increment onto the last computed aperture. The first growth increment defines so-called growth vectors which are assumed to be constant in direction (relative to the last computed aperture position) during a simulation of a shell (ontogeny). These growth vectors are uniformly scaled at each time step according to various growth rate curves that are used to simulate the mantle growth over time. From the model, we derive morphometric variables that illustrate the ontogenetic trajectories in time-size-shape space. We investigate the effects of changing the growth curves types, growth rate parameters and growth vector maps on the direction, speed and patterns of ontogenetic allometries. Because this model focuses the issue on time, it highlights a plausible effect of growth rate on shell shape and illustrates some fundamental geometrical properties of the logarithmic spiral, in particular the close relationship between the size and the geometry of growth increments. This model could be used to develop a mathematically data-driven approach where experimentally obtained growth curves could be used as inputs in the model. More generally, our study recalls the role of growth rates in the generation of allometries.

Endocranial shape changes during growth in chimpanzees and humans: a morphometric analysis of unique and shared aspects

Compared to our closest living and extinct relatives, humans have a large, specialized, and complex brain embedded in a uniquely shaped braincase. Here, we quantitatively compare endocranial shape changes during ontogeny in humans and chimpanzees. Identifying shared and unique aspects in developmental patterns of these two species can help us to understand brain evolution in the hominin lineage. Using CT scans of 58 humans and 60 chimpanzees varying in age from birth to adulthood, we generated virtual endocasts to measure and analyze 29 three-dimensional endocranial landmarks and several hundred semilandmarks on curves and the endocranial surface; these data were then analyzed using geometric morphometric methods. The ontogenetic shape trajectories are nonlinear for both species, which indicates several developmental phases. Endocranial shape is already distinct at birth and there is no overlap between the two species throughout ontogeny. While some aspects of the pattern of endocranial shape change are shared between humans and chimpanzees, the shape trajectories differ substantially directly after birth until the eruption of the deciduous dentition: in humans but not in chimpanzees, the parietal and cerebellar regions expand relatively (contributing to neurocranial globularity) and the cranial base flexes within the first postnatal year when brain growth rates are high. We show that the shape changes associated with this early "globularization phase" are unique to humans and do not occur in chimpanzees before or after birth.

Functional mapping of human growth trajectories

Human height is an important trait from biological and social perspectives. Genes have been widely recognized to be involved in human body growth, but their detailed controlling mechanisms are poorly understood. Here, we present a computational model for functional mapping of quantitative trait loci (QTLs) that control trajectories of human height growth through an interactive network. The model integrates mathematical equations of human growth curves into the mixture model-based functional mapping framework, allowing the identification and mapping of individual QTLs responsible for the developmental pattern of human growth. The model was derived on a random sample of subjects from a natural population, for each of which molecular markers within candidate genes or throughout the entire genome are typed and height data from childhood to adulthood are collected. A series of testable hypotheses are formulated about the genetic control of developmental timing and duration at different stages. The model was used to characterize epistatic QTLs for height growth hidden in 548 Japanese girls which is a semi-real data set with simulated the marker genotypes. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the genetic and developmental mechanisms of human body growth and its associated diseases.

Theoretical approaches to the evolution of development and genetic architecture

Developmental evolutionary biology has, in the past decade, started to move beyond simply adapting traditional population and quantitative genetics models and has begun to develop mathematical approaches that are designed specifically to study the evolution of complex, nonadditive systems. This article first reviews some of these methods, discussing their strengths and shortcomings. The article then considers some of the principal questions to which these theoretical methods have been applied, including the evolution of canalization, modularity, and developmental associations between traits. I briefly discuss the kinds of data that could be used to test and apply the theories, as well as some consequences for other approaches to phenotypic evolution of discoveries from theoretical studies of developmental evolution.

Furcation, field-splitting, and the evolutionary origins of novelty in arthropod photoreceptors

Arthropod photoreceptor evolution is a prime example of how evolution has used existing components in the origin of new structures. Here, we outline a comparative approach to understanding the mutational origins of novel structures, describing multiple examples from arthropod photoreceptor evolution. We suggest that developmental mechanisms have often split photoreceptors during evolution (field-splitting) and we introduce "co-duplication" as a null model for the mutational origins of photoreceptor components. Under co-duplication, gene duplication events coincide with the origin of a higher level structure like an eye. If co-duplication is rejected for a component, that component probably came to be used in a new photoreceptor through regulatory mutations. If not rejected, a gene duplication mutation may have allowed the component to be used in a new structure. In multiple case studies in arthropod photoreceptor evolution, we consistently reject the null hypothesis of co-duplication of genetic components and photoreceptors. Nevertheless, gene duplication events have in some cases occurred later, allowing divergence of photoreceptors. These studies provide a new perspective on the evolution of arthropod photoreceptors and provide a comparative approach that generalizes to the study of any evolutionary novelty.

When size makes a difference: allometry, life-history and morphological evolution of capuchins (Cebus) and squirrels (Saimiri) monkeys (Cebinae, Platyrrhini)

Background

How are morphological evolution and developmental changes related? This rather old and intriguing question had a substantial boost after the 70s within the framework of heterochrony (changes in rates or timing of development) and nowadays has the potential to make another major leap forward through the combination of approaches: molecular biology, developmental experimentation, comparative systematic studies, geometric morphometrics and quantitative genetics. Here I take an integrated approach combining life-history comparative analyses, classical and geometric morphometrics applied to ontogenetic series to understand changes in size and shape which happen during the evolution of two New World Monkeys (NWM) sister genera.

Results

Cebus and Saimiri share the same basic allometric patterns in skull traits, a result robust to sexual and ontogenetic variation. If adults of both genera are compared in the same scale (discounting size differences) most differences are small and not statistically significant. These results are consistent using both approaches, classical and geometric Morphometrics. Cebus is a genus characterized by a number of peramorphic traits (adult-like) while Saimiri is a genus with paedomorphic (child like) traits. Yet, the whole clade Cebinae is characterized by a unique combination of very high pre-natal growth rates and relatively slow post-natal growth rates when compared to the rest of the NWM. Morphologically Cebinae can be considered paedomorphic in relation to the other NWM. Geometric morphometrics allows the precise separation of absolute size, shape variation associated with size (allometry), and shape variation non-associated with size. Interestingly, and despite the fact that they were extracted as independent factors (principal components), evolutionary allometry (those differences in allometric shape associated with intergeneric differences) and ontogenetic allometry (differences in allometric shape associated with ontogenetic variation within genus) are correlated within these two genera. Furthermore, morphological differences produced along these two axes are quite similar. Cebus and Saimiri are aligned along the same evolutionary allometry and have parallel ontogenetic allometry trajectories.

Conclusion

The evolution of these two Platyrrhini monkeys is basically due to a size differentiation (and consequently to shape changes associated with size). Many life-history changes are correlated or may be the causal agents in such evolution, such as delayed on-set of reproduction in Cebus and larger neonates in Saimiri.

Evolutionary basis of parallelism in North American scincid lizards

This study uses a phylogenetic framework to explore the causes of parallelism in two North American scincid lizard assemblages: the skiltonianus and fasciatus species groups of the genus Plestiodon. Each group consists of several closely related species with conserved neonate morphology; features that distinguish species become accentuated during ontogeny, and these differences often resemble different endpoints along a developmental continuum. This continuum is believed to be an expression of the ancestral ontogeny, and has led to the hypothesis that evolutionary change in development has generated much of the observed morphological diversity. However, progress on understanding these mechanisms is limited by a lack of well-supported phylogenetic data for the fasciatus group, and for Plestiodon in general. Recent phylogenetic studies on the skiltonianus group have revealed previously undetected cases of parallelism, and raise the possibility that similar cases have yet to be discovered in the fasciatus group. Here, I estimate a phylogeny to test the monophyly of the fasciatus group and infer its relationship with other North American Plestiodon using 2537 bp from six mtDNA genes. I use the phylogeny to reconstruct the mode (graduated vs. punctuated) and direction of body size evolution, to map the evolution of two predominant color morphs, and to test whether size and color pattern evolve concertedly. The results show that the morphotypes of the traditional fasciatus group constitute good species, but that the species group is rendered paraphyletic by several geographically overlapping species that deviate from the fasciatus-like ontogeny. Body size evolution has occurred gradually and bi-directionally, and shifts to large body size have been consistently associated with the loss of the striped color pattern during ontogeny. I show that parallelism, a lack of rigorous phylogenetic analysis, and a reliance on shared ontogenetic features for predicting phylogenetic relatedness, has misled the traditional systematics of these lizards, but that general ideas concerning the role of development in their morphological evolution remain supported. I close by proposing that the processes influencing repeated phyletic patterns in the skiltonianus and fasciatus groups represent adherence to an ancestral ground state, and discuss the importance of using phylogenies for the initial characterization of evolutionary changes in development.

A geometric morphometric analysis of heterochrony in the cranium of chimpanzees and bonobos

Despite several decades of research, there remains a lack of consensus on the extent to which bonobos are paedomorphic (juvenilized) chimpanzees in terms of cranial morphology. This study reexamines the issue by comparing the ontogeny of cranial shape in cross-sectional samples of bonobos (Pan paniscus) and chimpanzees (Pan troglodytes) using both internal and external 3D landmarks digitized from CT scans. Geometric morphometric methods were used to quantify shape and size; dental-maturation criteria were used to estimate relative dental age. Heterochrony was evaluated using combined size-shape (allometry) and shape-age relationships for the entire cranium, the face, and the braincase. These analyses indicate that the bonobo skull is paedomorphic relative to the chimpanzee for the first principal component of size-related shape variation, most likely via a mechanism of postformation (paedomorphosis due to initial shape underdevelopment). However, the results also indicate that not all aspects of shape differences between the two species, particularly in the face, can be attributed to heterochronic transformation and that additional developmental differences must also have occurred during their evolution.

Functional mapping - how to map and study the genetic architecture of dynamic complex traits

The development of any organism is a complex dynamic process that is controlled by a network of genes as well as by environmental factors. Traditional mapping approaches for analysing phenotypic data measured at a single time point are too simple to reveal the genetic control of developmental processes. A general statistical mapping framework, called functional mapping, has been proposed to characterize, in a single step, the quantitative trait loci (QTLs) or nucleotides (QTNs) that underlie a complex dynamic trait. Functional mapping estimates mathematical parameters that describe the developmental mechanisms of trait formation and expression for each QTL or QTN. The approach provides a useful quantitative and testable framework for assessing the interplay between gene actions or interactions and developmental changes.

The effects of hybridization on growth allometry and craniofacial form in Sulawesi macaques

The present research investigates the effects of hybridization between Macaca maurus and M. tonkeana on adult male form and patterns of growth allometry. Comparisons of adult hybrid mean phenotypic values with the adult averages of the parental species indicate a condition of heterosis for cranial vault length and crown-rump length. Negative heterosis is indicated for body mass. Regression parameters describing growth allometry are generated for four craniofacial measurement variables and one body measurement using both least squares and reduced major axis regression. Comparisons of hybrid and parental regression slopes and intercepts using analysis of covariance and t-tests suggest that there is a hybrid pattern of growth allometry characterized by an increase in regression slope values coupled with lower intercept values compared to those of the parental species and the parental averages for most regression parameters. Multivariate analyses of the adult and ontogenetic morphometric data indicate significant differences across species taxa in form and shape during development and adulthood. Our finding of significant differences between hybrids and their parental taxa in growth allometry and craniofacial form and shape during development challenges the assumption often made regarding the reproductive and taxonomic significance of observed ontogenetic divergence between Neandertals and modern humans. We propose that anthropological primatology, with its goal of developing nonhuman primate models for investigating human evolution, can provide a biologically relevant means by which to empirically estimate the taxonomic significance of morphological and ontogenetic divergence observed in the hominid fossil record.

A hyperspace model to decipher the genetic architecture of developmental processes: allometry meets ontogeny

To better utilize limited resources for their survival and reproduction, all organisms undergo developmental changes in both body size and shape during ontogeny. The genetic analysis of size change with increasing age, i.e., growth, has received considerable attention in quantitative developmental genetic studies, but the genetic architecture of ontogenetic changes in body shape and its associated allometry have been poorly understood partly due to the lack of analytical tools. In this article, we attempt to construct a multivariate statistical framework for studying the genetic regulation of ontogenetic growth and shape. We have integrated biologically meaningful mathematical functions of growth curves and developmental allometry into the estimation process of genetic mapping aimed at identifying individual quantitative trait loci (QTL) for phenotypic variation. This model defined with high dimensions can characterize the ontogenetic patterns of genetic effects of QTL over the lifetime of an organism and assess the interplay between genetic actions/interactions and phenotypic integration. The closed forms for the residual covariance matrix and its determinant and inverse were derived to overcome the computational complexity typical of our high-dimensional model. We used a worked example to validate the utility of this model. The implications of this model for genetic research of evo-devo are discussed.

Functional mapping of quantitative trait loci that interact with the hg mutation to regulate growth trajectories in mice

The high growth (hg) mutation increases body size in mice by 30-50%. Given the complexity of the genetic regulation of animal growth, it is likely that the effect of this major locus is mediated by other quantitative trait loci (QTL) with smaller effects within a web of gene interactions. In this article, we extend our functional mapping model to characterize modifier QTL that interact with the hg locus during ontogenetic growth. Our model is derived within the maximum-likelihood context, incorporated by mathematical aspects of growth laws and implemented with the EM algorithm. In an F2 population founded by a congenic high growth (HG) line and non-HG line, a highly additive effect due to the hg gene was detected on growth trajectories. Three QTL located on chromosomes 2 and X were identified to trigger significant additive and/or dominant effects on the process of growth. The most significant finding made from our model is that these QTL interact with the hg locus to affect the shapes of the growth process. Our model provides a powerful means for understanding the genetic architecture and regulation of growth rate and body size in mammals.

A unified statistical model for functional mapping of environment-dependent genetic expression and genotype x environment interactions for ontogenetic development

The effects of quantitative trait loci (QTL) on phenotypic development may depend on the environment (QTL x environment interaction), other QTL (genetic epistasis), or both. In this article, we present a new statistical model for characterizing specific QTL that display environment-dependent genetic expressions and genotype x environment interactions for developmental trajectories. Our model was derived within the maximum-likelihood-based mixture model framework, incorporated by biologically meaningful growth equations and environment-dependent genetic effects of QTL, and implemented with the EM algorithm. With this model, we can characterize the dynamic patterns of genetic effects of QTL governing growth curves and estimate the global effect of the underlying QTL during the course of growth and development. In a real example with rice, our model has successfully detected several QTL that produce differences in their genetic expression between two contrasting environments. These detected QTL cause significant genotype x environment interactions for some fundamental aspects of growth trajectories. The model provides the basis for deciphering the genetic architecture of trait expression adjusted to different biotic and abiotic environments and genetic relationships for growth rates and the timing of life-history events for any organism.

A general framework for analyzing the genetic architecture of developmental characteristics

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive x additive epistatic effects on stem height growth trajectories in a forest tree.

A unifying statistical model for QTL mapping of genotype × sex interaction for developmental trajectories

Most organisms display remarkable differences in morphological, anatomical, and developmental features between the two sexes. It has been recognized that these sex-dependent differences are controlled by an array of specific genetic factors, mediated through various environmental stimuli. In this paper, we present a unifying statistical model for mapping quantitative trait loci (QTL) that are responsible for sexual differences in growth trajectories during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by sex-stimulated differentiation in growth form that is described by mathematical functions. A typical structural model is implemented to approximate time-dependent covariance matrices for longitudinal traits. This model allows for a number of biologically meaningful hypothesis tests regarding the effects of QTL on overall growth trajectories or particular stages of development. It is particularly powerful to test whether and how the genetic effects of QTL are expressed differently in different sexual backgrounds. Our model has been employed to map QTL affecting body mass growth trajectories in both male and female mice of an F2population derived from the large (LG/J) and small (SM/J) mouse strains. We detected four growth QTL on chromosomes 6, 7, 11, and 15, two of which trigger different effects on growth curves between the two sexes. All the four QTL display significant genotype-sex interaction effects on the timing of maximal growth rate in the ontogenetic growth of mice. The implications of our model for studying the genetic architecture of growth trajectories and its extensions to some more general situations are discussed.

A mechanistic model for genetic machinery of ontogenetic growth

Two different genetic mechanisms can be proposed to explain variation in growth trajectories. The allelic sensitivity hypothesis states that growth trajectory is controlled by the time-dependent expression of alleles at the deterministic quantitative trait loci (dQTL) formed during embryogenesis. The gene regulation hypothesis states that the differentiation in growth process is due to the opportunistic quantitative trait loci (oQTL) through their mediation with new developmental signals. These two hypotheses of genetic control have been elucidated in the literature. Here, we propose a new statistical model for discerning these two mechanisms in the context of growth trajectories by integrating growth laws within a QTL-mapping framework. This model is developed within the maximum-likelihood context, implemented with a grid approach for estimating the genomic positions of the deterministic and opportunistic QTL and the simplex algorithm for estimating the growth curve parameters of the genotypes at these QTL and the parameters modeling the residual (co)variance matrix. Our model allows for extensive hypothesis tests for the genetic control of growth processes and developmental events by these two types of QTL. The application of this new model to an F(2) progeny in mice leads to the detection of deterministic and opportunistic QTL on chromosome 1 for mouse body mass growth. The estimates of QTL positions and effects from our model are broadly in agreement with those by traditional interval-mapping approaches. The implications of this model for biological and biomedical research are discussed.

Functional Mapping of Quantitative Trait Loci Underlying Growth Trajectories Using a Transform-Both-Sides Logistic Model

The incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci (QTL) underlying growth trajectories. A theoretical framework for implementing a QTL mapping strategy with growth laws has been established. This framework can be generalized to an arbitrary number of time points, where growth is measured, and becomes computationally more tractable, when the assumption of variance stationarity is made. In practice, however, this assumption is likely to be violated for age-specific growth traits due to a scale effect. In this article, we present a new statistical model for mapping growth QTL, which also addresses the problem of variance stationarity, by using a transform-both-sides (TBS) model advocated by Carroll and Ruppert (1984, Journal of the American Statistical Association 79, 321-328). The TBS-based model for mapping growth QTL cannot only maintain the original biological properties of a growth model, but also can increase the accuracy and precision of parameter estimation and the power to detect a QTL responsible for growth differentiation. Using the TBS-based model, we successfully map a QTL governing growth trajectories to a linkage group in an example of forest trees. The statistical and biological properties of the estimates of this growth QTL position and effect are investigated using Monte Carlo simulation studies. The implications of our model for understanding the genetic architecture of growth are discussed.

Kinematics of cranial ontogeny: Heterotopy, heterochrony, and geometric morphometric analysis of growth models

In this paper, we examine the relationship between the classical concepts of heterotopy, heterochrony and ontogenetic allometry as descriptive and as explanatory categories in the investigation of evolutionary developmental novelty in the hominid skull. We use concepts of kinematic analysis of locomotion to propose a methodological framework for the kinematic analysis of cranial form change during ontogeny. We argue that a combination of geometric-morphometric methods with graphics visualization tools currently represents the most adequate means to analyze the kinematics of ontogeny. Using cranial growth models, we simulate how evolutionary modifications of developmental processes impinge on morphological patterns of ontogeny, and explore how differences in ontogenetic patterns can tentatively be traced back to underlying process differences. Our analyses indicate that minor alterations in growth parameters elicit complex patterns of ontogenetic modification that are difficult to describe with the standard repertoire of heterochronic terminology. The proposed kinematic and model-based approach is used in a comparative analysis of cranial ontogeny in Neanderthals and anatomically modern humans, indicating that early ontogenetic modification of a small set of growth parameters is a major source of evolutionary novelty during hominid evolution.

Theoretical morphology of developmental asymmetries

Morphospaces are theoretical tools to explore the morphological organization of living and fossil organisms. They have been used mostly by the paleontological community in an effort to get the most out of one of the only pieces of evidence that fossil material usually provide: the morphology of hard parts. The expectation with the establishment of theoretical morphospaces is that, by abstracting and modeling the fundamental parts of form, the multiple processes that generate the phenotypes of embryonic and adult structures will be better understood. In this essay, we suggest that ontogenetic trajectories can be used as the generative functions that build morphospaces, and propose approaches to build theoretical models for the establishment of left-right asymmetries during vertebrate heart embryogenesis.

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

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

MORPHOMETRIC HETEROCHRONY AND THE EVOLUTION OF GROWTH

Heterochrony has been an influential perspective on the evolution of morphologies, a circumstance mostly due to a strategic shift of the theory to the analysis of growth and measurable traits. A difficulty in testing hypotheses of heterochrony in the morphometric realm, and therefore in establishing its evolutionary relevance, has been the absence of an explicit criterion of homology in comparisons supposed to reveal paedomorphosis and peramorphosis. Based on the formalism of ontogenetic and allometric trajectories, we defined a criterion of primary homology in the context of morphometric characters that requires only a comparison between metric traits from ontogenetic series of two or more taxa. On the one hand, such a criterion allows for the calculation of values of shape slopes and allometric coefficients in descendants supposedly affected by changes in ontogenetic timing, thereby supplying an analytical tool for testing hypotheses of heterochrony. On the other hand, the concept of morphometric homology establishes the descriptive limits of paedomorphosis and peramorphosis, showing, for example, that the model of sequential hypermorphosis applied to the evolution of human encephalization is not within the descriptive scope of the morphological markers of heterochrony. Sequential hypermorphosis is a successful model of morphometric evolution, as further illustrated by the match between our mathematical deductions and the empirical results obtained by analyses of brain growth data. By exploring the properties of multiphasic polynomial functions, we deduce equations that define the relationship between developmental delay or acceleration and their effect on adult brain size. Together with the primary criterion of homology, we demonstrate that sequential hypermorphosis could generate the large modern human brain, but such brain is neither paedomorphic nor peramorphic. Our approach based on homology and allometry indicates that the evolution of growth is richer in phenomena than heterochrony can account for, and accordingly we argue that morphometric theory can expand its descriptive and heuristic scope by looking beyond the limits imposed by paedomorphosis and peramorphosis.

Functional mapping for quantitative trait loci governing growth rates: a parametric model

Are there-specific quantitative trait loci (QTL) governing growth rates in biology? This is emerging as an exciting but challenging question for contemporary developmental biology, evolutionary biology, and plant and animal breeding. In this article, we present a new statistical model for mapping QTL underlying age-specific growth rates. This model is based on the mechanistic relationship between growth rates and ages established by a variety of mathematical functions. A maximum likelihood approach, implemented with the EM algorithm, is developed to provide the estimates of QTL position, growth parameters characterized by QTL effects, and residual variances and covariances. Based on our model, a number of biologically important hypotheses can be formulated concerning the genetic basis of growth. We use forest trees as an example to demonstrate the power of our model, in which a QTL for stem growth diameter growth rates is successfully mapped to a linkage group constructed from polymorphic markers. The implications of the new model are discussed.

Statistical estimators of frontal sinus cross section ontogeny from very noisy data

Cross-sectional areas of human frontal sinuses in the occipitofrontal projection are a good surrogate for frontal sinus volumes. This study looks at these areas in a dataset of some 200 children and 100 adults of both sexes. As measured by planimetry of roentgenograms, the areas are extremely variable ("noisy" in a statistical sense). In fact, they appear to be distributed log-normally with quite high variance. The mean of the distribution is evidently a function of age and the variances differ by sex. After logarithmic transformation, the data are adequately fitted by one sigmoid curve for each sex. Our discussion highlights implications of this finding for the biological aspects of frontal sinuses and methodological issues in ontogenetic analysis of data so noisy.

Developmental basis of evolutionary digit loss in the Australian lizard Hemiergis

Loss of limb skeletal elements is a recurring theme in tetrapod evolution, but the developmental mechanisms underlying this phenomenon remain largely unknown. The Australian lizard genus Hemiergis offers an excellent model system to study limb reduction among closely related, naturally occurring populations with different numbers of digits. Evolutionary digit loss in Hemiergis does not result from simple truncation of a pentadactyl skeletal developmental program. Rather, the duration of embryonic expression of the patterning molecule Sonic hedgehog (SHH) is shortened in limbs with reduced numbers of digits, and is correlated with decreased cell proliferation in the posterior aspect of the limb. Moreover, this comparative analysis suggests an early role for SHH in specification of digit identity and later importance in maintaining cell proliferation and survival. Subtle changes in spatial or temporal regulation of SHH may alter proliferation and patterning of the developing limb, thereby effecting divergence in adult limb morphology among closely related species. In contrast, expression of MSX and Distal-less proteins were similar among embryos from different populations.

Developmental morphology of limb reduction in Hemiergis (Squamata: Scincidae): chondrogenesis, osteogenesis, and heterochrony

Digit loss is a common theme in tetrapod evolution that may involve changes in several developmental processes. The skink genus Hemiergis provides an ideal model to study these processes in closely related taxa: within three Western Australian Hemiergis species, digit quantity ranges between two and five. For three consecutive reproductive seasons, gravid females of Hemiergis were collected in the field and their embryos prepared for histological analysis of limb skeletal development (chondrogenesis and osteogenesis). Comparative studies of skeletal developmental morphology demonstrate that limbs with fewer than five digits do not result from a simple truncation of a putative ancestral (five-digit) developmental program. The developmental and adult morphologies in two-, three-, and four-digit Hemiergis are neither predicted nor explained by a simple model of heterochrony involving either chondrogenesis or osteogenesis. In postnatal Hemiergis, digit number and relative limb length do not correlate in a simple linear fashion. Instead, limb size and digit reduction may correlate with substrate conditions and burrowing behavior.

Functional mapping of quantitative trait loci underlying the character process: a theoretical framework

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.

Evidence for parallel ecological speciation in scincid lizards of the Eumeces skiltonianus species group (Squamata: Scincidae)

We identify instances of parallel morphological evolution in North American scincid lizards of the Eumeces skiltonianus species group and provide evidence that this system is consistent with a model of ecological speciation. The group consists of three putative species divided among two morphotypes, the small-bodied and striped E. skiltonianus and E. lagunensis versus the large-bodied and typically uniform-colored E. gilberti. Members of the group pass through markedly similar phenotypic stages during early development, but differ with respect to where terminal morphology occurs along the developmental sequence. The morphotypes also differ in habitat preference, with the large-bodied gilberti form generally inhabiting lower elevations and drier environments than the smaller, striped morphs. We inferred the phylogenetic relationships of 53 skiltonianus group populations using mtDNA sequence data from the ND4 protein-coding gene and three flanking tRNAs (900 bp total). Sampling encompassed nearly the entire geographic range of the group, and all currently recognized species and subspecies were included. Our results provide strong evidence for parallel origins of three clades characterized by the gilberti morphotype, two of which are nested within the more geographically widespread E. skiltonianus. Eumeces lagunensis was also nested among populations of E. skiltonianus. Comparative analyses using independent contrasts show that evolutionary changes in body size are correlated with differences in adult color pattern. The independently derived association of gilberti morphology with warm, arid environments suggests that phenotypic divergence is the result of adaptation to contrasting selection regimes. We provide evidence that body size was likely the target of natural selection, and that divergences in color pattern and mate recognition are probable secondary consequences of evolving large body size.

Heterochrony, maternal effects, and phenotypic variation among sympatric pupfishes

Variation in ontogeny can produce phenotypic variation both within and among species. I investigated whether changes in timing and rate of growth were a source of phenotypic variation in a putative incipient species group of pupfish (Cyprinodon spp.). On San Salvador Island, Bahamas, sympatric forms of pupfish differ in morphology but show only partial reproductive isolation in the laboratory. Offspring from two forms and two geographical areas and their hybrids were bred in the laboratory, and ontogenetic trajectories of their feeding morphology were followed until maturity. In the Bahamian pupfish the two forms grow along similar size but not shape trajectories. Two heterochronic parameters, onset and rate of growth, alter shape trajectories in the Bahamian pupfish. Similar forms from different geographical areas (Florida and the Bahamas) grow along parallel shape trajectories, differing only in one heterochronic parameter, the onset shape. Hybrids within and between the pupfish forms produced intermediate feeding morphologies that were influenced by their maternal phenotype, suggesting that maternal effects may be a source of phenotypic variation in shape that can persist to maturity. In Cyprinodon, small changes in multiple heterochronic parameters translate into large phenotypic differences in feeding morphology.