QUANTITATIVE GENETIC MODELS FOR DEVELOPMENT, EPIGENETIC SELECTION, AND PHENOTYPIC EVOLUTION

INDIVIDUAL VARIATION OF ONTOGENIES: A LONGITUDINAL STUDY OF GROWTH AND TIMING

This study of growth and developmental time in the water strider Limnoporus canaliculatus (Heteroptera: Gerridae) is based on longitudinal data from specimens reared individually in the laboratory. I analyzed multivariate allometry using a common principal components approach. This technique identified patterns of variation that were uncorrelated both within and among instars and which remained fairly constant throughout the growth period; in contrast, the overall amount of variation increased from young to older instars. Negative correlations between size and subsequent growth increments indicated convergent growth in the first three instars, but there was a transition to positive correlations (divergent growth) in later instars. Analysis of covariation among measurements made in different instars showed strong ontogenetic autocorrelation and revealed patterns remarkably similar to those found in mammals and birds; yet corresponding analyses of growth increments showed mainly independent variation in different instars. Therefore, I conclude that the strong correlations among stage-specific measurements result from the part-whole relationships inherent to these cumulative size data, but do not reflect specific properties of the organisms studied. In contrast to size increments, instar durations of water striders were highly correlated throughout the larval period, indicating that individuals tended to develop at either relatively fast or relatively slow rates in all instars. The correlations between growth increments and instar durations were nil or negative, contrary to expectations from life-history theory. The results of these analyses of individual variation match the findings from other water striders and from interspecific comparisons in the genus Limnoporus, but information about physiological mechanisms of molting and growth in insects cannot completely explain the patterns observed.

MATERNAL INHERITANCE OF CONDITION AND CLUTCH SIZE IN THE COLLARED FLYCATCHER

Maternal effects may strongly influence evolutionary response to natural selection but they have been little studied in the wild. We use a novel combination of experimental and statistical methods to estimate maternal effects on condition and clutch size in the collared flycatcher, where we define "condition" to be the nongenetic component of clutch size. We found evidence of two maternal effects. The first (m) was the negative effect of mother's clutch size on daughter's condition, when mother's condition was held constant. The second (M) was the positive effect of mother's condition on daughter's condition, when mother clutch size was held constant. These two effects oppose one another because mothers in good condition also lay many eggs. The maternal effects were large: Experimentally adding an egg to a mother's nest reduced clutch sizes of her daughters by 1/4 egg (i.e., m = -0.25). Measured degree of resemblance between mother and daughter clutch sizes yielded M = 0.43. The results weakly support the presence of heritable genetic variation in clutch size: additive genetic variance/total phenotypic variance = 0.33. This estimate was highly variable probably because, as we show, mother-daughter resemblance may depend hardly at all on the amount of genetic variance when maternal effects are present. Daughter-mother regression (a standard method for estimating heritability) is consequently a poor guide to the amount of genetic variance in clutch size. Our results emphasize the value of combining field experiments with observations for studying inheritance.

Discovering phenotypic causal structure from nonexperimental data

The evolutionary potential of organisms depends on how their parts are structured into a cohesive whole. A major obstacle for empirical studies of phenotypic organization is that observed associations among characters usually confound different causal pathways such as pleiotropic modules, interphenotypic causal relationships and environmental effects. The present article proposes causal search algorithms as a new tool to distinguish these different modes of phenotypic integration. Without assuming an a priori structure, the algorithms seek a class of causal hypotheses consistent with independence relationships holding in observational data. The technique can be applied to discover causal relationships among a set of measured traits and to distinguish genuine selection from spurious correlations. The former application is illustrated with a biological data set of rat morphological measurements previously analysed by Cheverud et al. (Evolution 1983, 37, 895).

IBSEM: An Individual-Based Atlantic Salmon Population Model

Ecology and genetics can influence the fate of individuals and populations in multiple ways. However, to date, few studies consider them when modelling the evolutionary trajectory of populations faced with admixture with non-local populations. For the Atlantic salmon, a model incorporating these elements is urgently needed because many populations are challenged with gene-flow from non-local and domesticated conspecifics. We developed an Individual-Based Salmon Eco-genetic Model (IBSEM) to simulate the demographic and population genetic change of an Atlantic salmon population through its entire life-cycle. Processes such as growth, mortality, and maturation are simulated through stochastic procedures, which take into account environmental variables as well as the genotype of the individuals. IBSEM is based upon detailed empirical data from salmon biology, and parameterized to reproduce the environmental conditions and the characteristics of a wild population inhabiting a Norwegian river. Simulations demonstrated that the model consistently and reliably reproduces the characteristics of the population. Moreover, in absence of farmed escapees, the modelled populations reach an evolutionary equilibrium that is similar to our definition of a ‘wild’ genotype. We assessed the sensitivity of the model in the face of assumptions made on the fitness differences between farm and wild salmon, and evaluated the role of straying as a buffering mechanism against the intrusion of farm genes into wild populations. These results demonstrate that IBSEM is able to capture the evolutionary forces shaping the life history of wild salmon and is therefore able to model the response of populations under environmental and genetic stressors.

Quantifying polymorphism and divergence from epigenetic data: a framework for inferring the action of selection

Epigenetic modifications are alterations that regulate gene expression without modifying the underlying DNA sequence. DNA methylation and histone modifications, for example, are capable of spatial and temporal regulation of expression—with several studies demonstrating that these epigenetic marks are heritable. Thus, like DNA sequence, epigenetic marks are capable of storing information and passing it from one generation to the next. Because the epigenome is dynamic and epigenetic modifications can respond to external environmental stimuli, such changes may play an important role in adaptive evolution. While recent studies provide strong evidence for species-specific signatures of epigenetic marks, little is known about the mechanisms by which such modifications evolve. In order to address this question, we analyze the genome wide distribution of an epigenetic histone mark (H3K4me3) in prefrontal cortex neurons of humans, chimps and rhesus macaques. We develop a novel statistical framework to quantify within- and between-species variation in histone methylation patterns, using an ANOVA-based method and defining an F_ST -like measure for epigenetics (termed epi- F_ST), in order to develop a deeper understanding of the evolutionary pressures acting on epigenetic variation. Results demonstrate that genes with high epigenetic F_ST values are indeed significantly overrepresented among genes that are differentially expressed between species, and we observe only a weak correlation with SNP density.

Epigenetic resolution of the 'curse of complexity' in adaptive evolution of complex traits

The age of most genes exceeds the longevity of their genomic and physiological associations by many orders of magnitude. Such transient contexts modulate the expression of ancient genes to produce currently appropriate and often highly distinct developmental and functional outcomes. The efficacy of such adaptive modulation is diminished by the high dimensionality of complex organisms and associated vast areas of neutrality in their genotypic and developmental networks (and, thus, weak natural selection). Here I explore whether epigenetic effects facilitate adaptive modulation of complex phenotypes by effectively reducing the dimensionality of their deterministic networks and thus delineating their developmental and evolutionary trajectories even under weak selection. Epigenetic effects that link unconnected or widely dispersed elements of genotype space in ecologically relevant time could account for the rapid appearance of functionally integrated adaptive modifications. On an organismal time scale, conceptually similar processes occur during recurrent epigenetic reprogramming of somatic stem cells to produce, recurrently and reversibly, a bewildering array of differentiated and persistent cell lineages, all sharing identical genomic sequences despite strongly distinct phenotypes. I discuss whether close dependency of onset, scope and duration of epigenetic effects on cellular and genomic context in stem cells could provide insights into contingent modulation of conserved genomic material on a much longer evolutionary time scale. I review potential empirical examples of epigenetic bridges that reduce phenotype dimensionality and accomplish rapid adaptive modulation in the evolution of novelties, expression of behavioural types, and stress-induced ossification schedules.

The evolution of multivariate maternal effects

There is a growing interest in predicting the social and ecological contexts that favor the evolution of maternal effects. Most predictions focus, however, on maternal effects that affect only a single character, whereas the evolution of maternal effects is poorly understood in the presence of suites of interacting traits. To overcome this, we simulate the evolution of multivariate maternal effects (captured by the matrix M) in a fluctuating environment. We find that the rate of environmental fluctuations has a substantial effect on the properties of M: in slowly changing environments, offspring are selected to have a multivariate phenotype roughly similar to the maternal phenotype, so that M is characterized by positive dominant eigenvalues; by contrast, rapidly changing environments favor Ms with dominant eigenvalues that are negative, as offspring favor a phenotype which substantially differs from the maternal phenotype. Moreover, when fluctuating selection on one maternal character is temporally delayed relative to selection on other traits, we find a striking pattern of cross-trait maternal effects in which maternal characters influence not only the same character in offspring, but also other offspring characters. Additionally, when selection on one character contains more stochastic noise relative to selection on other traits, large cross-trait maternal effects evolve from those maternal traits that experience the smallest amounts of noise. The presence of these cross-trait maternal effects shows that individual maternal effects cannot be studied in isolation, and that their study in a multivariate context may provide important insights about the nature of past selection. Our results call for more studies that measure multivariate maternal effects in wild populations.

In numerous organisms, mothers influence the phenotype of their offspring by transmitting hormones, antibodies and nutrients to the embryo. Evolutionary studies that make predictions about the evolution of these maternal effects typically focus, however, on single maternal characters only, in isolation of other traits. This contrasts with insights from quantitative genetics where reliable predictions about evolutionary change can only be made when measuring multiple traits simultaneously. The current study is therefore the first to make formal predictions about the evolutionary properties of multiple maternal effects. We show that maternal phenotypic characters generally give rise to developmental interactions in which one maternal character affects multiple offspring characters. In turn, such interactions can give rise to correlations between different traits in parent and offspring, which constrain evolutionary responses to sudden change. In addition, we find that the rate of environmental change directly affects some of the measurable properties of maternal effects: in rapidly changing environments, multivariate maternal effects are negative, so that offspring attain phenotypes that are different from their mothers, whereas positive maternal effects where offspring are more similar to their mothers occur in slowly changing environments. Hence, multivariate maternal effects provide a clear signature of the past selective environment experienced by organisms.

Epigenetics and sex-specific fitness: an experimental test using male-limited evolution in Drosophila melanogaster

When males and females have different fitness optima for the same trait but share loci, intralocus sexual conflict is likely to occur. Epigenetic mechanisms such as genomic imprinting (in which expression is altered according to parent-of-origin) and sex-specific maternal effects have been suggested as ways by which this conflict can be resolved. However these ideas have not yet been empirically tested. We designed an experimental evolution protocol in Drosophila melanogaster that enabled us to look for epigenetic effects on the X-chromosome–a hotspot for sexually antagonistic loci. We used special compound-X females to enforce father-to-son transmission of the X-chromosome for many generations, and compared fitness and gene expression levels between Control males, males with a Control X-chromosome that had undergone one generation of father-son transmission, and males with an X-chromosome that had undergone many generations of father-son transmission. Fitness differences were dramatic, with experimentally-evolved males approximately 20% greater than controls, and with males inheriting a non-evolved X from their father about 20% lower than controls. These data are consistent with both strong intralocus sexual conflict and misimprinting of the X-chromosome under paternal inheritance. However, expression differences suggested that reduced fitness under paternal X inheritance was largely due to deleterious maternal effects. Our data confirm the sexually-antagonistic nature of Drosophila’s X-chromosome and suggest that the response to male-limited X-chromosome evolution entails compensatory evolution for maternal effects, and perhaps modification of other epigenetic effects via coevolution of the sex chromosomes.

Timing of gene expression from different genetic systems in shaping leucine and isoleucine contents of rapeseed (Brassica napus L.) meal

Experiments were conducted on rapeseed (Brassica napus L.) using a diallel design with nine parents: Youcai 601, Double 20-4, Huashuang 3, Gaoyou 605, Zhongyou 821, Eyouchangjia, Zhong R-888, Tower and Zheshuang 72. The seed developmental process was divided into five stages, namely initial (days 1-15 after flowering), early (days 16-22 after flowering), middle (days 23-29), late (days 30-36), and maturing (days 37-43) developmental stages. The variation of dynamic genetic effects for leucine and isoleucine contents of rapeseed meal was analysed at five developmental stages, across different environments using the genetic models with time-dependent measures. The results from unconditional and conditional analyses indicated that the expression of diploid embryo, cytoplasmic and diploid maternal plant genes were important for leucine and isoleucine contents at different developmental stages of rapeseed, particularly at the initial and early developmental stages. Among different genetic systems, nutrition quality traits were mainly controlled by the accumulative or net maternal main effects and their GE interaction effects, except at maturity when the net diploid embryo effects were larger. The expression of genes was affected by the environmental conditions on 15, 22, 29 or 36 days after flowering, but was more stable at mature stage. For the isoleucine content the narrow-sense heritabilities on 15, 22, 29, 36, and 43 days after flowering were 43.0, 65.7, 60.1, 65.5 and 78.2%, respectively, while for the leucine content the corresponding narrow-sense heritabilities were relatively smaller. The interaction heritabilities were more important than the general heritabilities at the first three developmental times. The improvement for isoleucine content could be achieved by selection based on the higher narrow-sense heritabilities. Various genetic systems exhibited genetic correlations among the developmental times or leucine and isoleucine contents. A simultaneous improvement of leucine and isoleucine contents seems possible because of the significant positive genetic correlation components from different genetic systems at different developmental times.

Genetic changes in plant growth and their associations with chromosomes from Gossypium barbadense L. in G. hirsutum L

Cotton (Gossypium spp.) plant growth is an important time-specific agronomic character that supports the development of squares, flowers, boll retention, and yield. With the use of a mixed linear model approach, we investigated 14 cotton chromosome substitution (CS-B) lines and their chromosome-specific F(2) hybrids for genetic changes in plant growth that was measured during the primary flowering time under two environments. The changes in additive and dominance variances for plant height and number of mainstem nodes are reported, showing that additive effects for these two traits were a key genetic component after initial flowering occurred in the field. Time-specific genetic variance components were also detected where phenotypic values observed at time t were conditioned on the events occurring at time t - 1, demonstrating new genetic variations arising at several time intervals during plant growth. Results also revealed that plant height and number of nodes shared some common influence due to additive effects during plant development. With the comparative analyzes, chromosomes associated with the genetic changes in plant growth were detected. Therefore, these results should add new understanding of the genetics underlying these time-specific traits.

Ontogeny of additive and maternal genetic effects: lessons from domestic mammals

Evolution of size and growth depends on heritable variation arising from additive and maternal genetic effects. Levels of heritable (and nonheritable) variation might change over ontogeny, increasing through "variance compounding" or decreasing through "compensatory growth." We test for these processes using a meta-analysis of age-specific weight traits in domestic ungulates. Generally, mean standardized variance components decrease with age, consistent with compensatory growth. Phenotypic convergence among adult sheep occurs through decreasing environmental and maternal genetic variation. Maternal variation similarly declines in cattle. Maternal genetic effects are thus reduced with age (both in absolute and relative terms). Significant trends in heritability (decreasing in cattle, increasing in sheep) result from declining maternal and environmental components rather than from changing additive variation. There was no evidence for increasing standardized variance components. Any compounding must therefore be masked by more important compensatory processes. While extrapolation of these patterns to processes in natural population is difficult, our results highlight the inadequacy of assuming constancy in genetic parameters over ontogeny. Negative covariance between direct and maternal genetic effects was common. Negative correlations with additive and maternal genetic variances indicate that antagonistic pleiotropy (between additive and maternal genetic effects) may maintain genetic variance and limit responses to selection.

The relationship between genotype, developmental stability and mating performance: disentangling the epigenetic causes

Developmental stability (DS) may confer an advantage in competition for mates. The present study tests this hypothesis using Drosophila immigrans, and proposes a novel approach to help broadly define the epigenetic factors causing such an effect. We first estimated the magnitude of isofemale heritability in sternopleural bristle fluctuating asymmetry (FA), using replicate genetic lines extracted from nature. Positional FA (PFA) exhibited significant among-line variation, and the heritability estimate of 0.10 (0.046 s.e.m.) was statistically significant. Among individual males, there was a significant positive relationship between PFA and copulation latency (time elapsed between introduction of females and copulation) and duration, but not copulation frequency. Moreover, high-DS lines exhibited significantly shorter copulation latency and duration compared with low-DS lines. When these components of sexual performance were again contrasted between lines with among-individual differences in bristle asymmetry controlled statistically, significant line effects on copulation latency and duration disappeared. The results suggest that deficits in the developmental apparatus underlying one particular trait can compromise individual sexual performance, and weaken the hypothesis that FA is a cue of overall 'genetic quality'.

A general population genetic theory for the evolution of developmental interactions

The development of most phenotypic traits involves complex interactions between many underlying factors, both genetic and environmental. To study the evolution of such processes, a set of mathematical relationships is derived that describe how selection acts to change the distribution of genetic variation given arbitrarily complex developmental interactions and any distribution of genetic and environmental variation. The result is illustrated by using it to derive models for the evolution of dominance and for the evolutionary consequences of asymmetry in the distribution of genetic variation.

Geometric estimates of heritability in biological shape

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.

Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance-covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t - 1 implies the generation of episodes of new genetic variation arising during the interval t - 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.

Phenotypic plasticity is the major determinant of changes in phenotypic integration in Arabidopsis

•  The way in which novel genetic variation affects the patterns of phenotypic integration in natural populations is addressed here. •  An experimental study is presented of the variability in integration caused by interpopulation hybridization and consequent genetic reshuffling, as well as by changes in the physical environment in the model system Arabidopsis thaliana (Brassicaceae). •  Our results show a basic invariance of sets of covarying traits in A. thaliana, with changes in nutrient availability as the principal factor accounting for major departures from the general pattern and where differences in the genetic background of the recombinant lines are less important. In A. thaliana, the relationships among vegetative and reproductive traits form distinct clusters in multivariate space. A high degree of congruence was found between differences in the multivariate mean phenotype and the pattern of phenotypic integration, as expected on the basis of recent theoretical models. •  This relationship might indicate strong selective constraints acting on the specialized life history of these populations, which are spring ephemerals inhabiting ruderal habitats and prone to competition avoidance.

Body weight and tail length divergence in mice selected for rate of development

A series of mouse lines has been produced by 19 generations of restricted index selection for rate of development during early and late ontogeny. The selection program was based on an index with the following four replicated selection treatments: E(+) and E(-) were selected to alter birth to 10-day body weight gain while holding late gain for both selection lines constant; correspondingly, L(+) and L(-) were selected to alter 28- to 56-day body weight gain holding early gain for both lines constant. Herein, we characterize response to selection for growth rate by analyzing age-specific mouse body weight and tail lengths and for growth curves using a logistics model. Selection on developmental rate has resulted in divergence in both age-specific and growth curve traits. E(+) and L(+) lines reached identical weights during the late selection interval, then diverged to unique mature weights. E(-) and L(-) lines similarly achieved identical weights during late selection and diverged to unique mature weights. However, the shapes of early and late growth curves were significantly divergent, and at least two distinct growth patterns are shown to result from selection. Response in body weight gain was accompanied by similar, though less pronounced, change in tail length traits. Significant response during intervals of restricted growth was also found, especially in lines selected for late gain. The evolution of the growth trajectory under restricted index selection is discussed in terms of drift and available additive genetic variation and covariation.

Influence of incubation temperature on morphology, locomotor performance, and early growth of hatchling wall lizards (Podarcis muralis)

Eggs of wall lizards (Podarcis muralis) were incubated at three temperatures approaching the upper limit of viability for embryonic development in this species (26, 29, and 32 degrees C) to assess the influence of temperature on various aspects of hatchling phenotype likely affecting fitness. The thermal environment affected size and several morphometric characteristics of hatchling lizards. Hatchlings from eggs incubated at 32 degrees C were smaller (snout-vent length, SVL) than those from 26 and 29 degrees C and had smaller mass residuals (from the regression on SVL) as well as shorter tail, head, and femur relative to SVL. Variation in the level of fluctuating asymmetry in meristic and morphometric traits associated with incubation temperatures was quite high but not clearly consistent with the prediction that environmental stress associated with the highest incubation temperatures might produce the highest level of asymmetry. When tested for locomotor capacity in trials developed at body temperatures of 32 and 35 degrees C, hatchlings from the 32 degrees C incubation treatment exhibited the worst performance in any aspect considered (burst speed, maximal length, and number of stops in the complete run). Repeated measures ANCOVAs (with initial egg mass as covariate) of snout-vent length and mass of lizards at days 0 and 20 revealed significant effects of incubation temperature only for mass, being again the hatchlings from eggs incubated at 32 degrees C those exhibiting the smallest final size. All together, our results evidenced a pervasive effect of thermal regime during incubation (and hence of nest site selection) on hatchling phenotypes. However, incubation temperature does not affect hatchling phenotypes in a continuous way; for most of the analysed traits a critical threshold seems to exist between 29 and 32 degrees C, so that hatchlings incubated at 32 degrees C exhibited major detrimental effects. J. Exp. Zool. 286:422-433, 2000.

Experimental analysis of character coupling across a complex life cycle: pigment pattern metamorphosis in the tiger salamander, Ambystoma tigrinum tigrinum

Developmental relationships among characters are expected to bias patterns of morphological variation at the population level. Studies of character development thus can provide insights into processes of adaptation and the evolutionary diversification of morphologies. Here I use experimental manipulations to test whether larval and adult pigment patterns are coupled across metamorphosis in the tiger salamander, Ambystoma tigrinum tigrinum (Ambystomatidae). Previous investigations showed that the early larval pigment pattern depends on interactions between pigment cells and the lateral line sensory system. In contrast, the results of this study demonstrate that the major features of the adult pigment pattern develop largely independently of both the early larval pattern and the lateral lines. These results suggest that ontogenetic changes that occur across metamorphosis decouple larval and adult pigment patterns and could thereby facilitate independent evolutionary modifications to the patterns during different stages of the life cycle.

The epigenetic impact of weaning on craniofacial morphology during growth

Miniature pigs (Sus scrofa) were used as a model to investigate whether the time of weaning (a nongenetic factor) affects skeletal growth rates for both pre- and postweaning time periods. Control litters were weaned at the normal time of 32 days. Two litters were weaned early (at 20 days) and two late (at 46 days). We digitized cranial landmarks from radiographs taken three times a week for a total of 70 days. We used analysis of covariance to test for differences in growth rates between pre- and post-weaning periods, as well as differences in growth rates among treatments. In both the late weaned pigs and the controls, facial length, facial width, basicranial length, and basicranial width growth rates slowed significantly at the time of weaning. However, in the early weaned pigs, there were no significant changes in growth rates for any of the facial or basicranial measurements at weaning. Furthermore, the postweaning rates of growth were different among treatments. One possible implication is that early growth rates could be under tight genetic control while later growth rates can be epigenetically regulated through nutritional changes.

Developmental quantitative genetic models of evolutionary change

Discussions about evolutionary change in developmental processes or morphological structures are predicated on specific quantitative genetic models whose parameters predict whether evolutionary change can occur, its relative rate and direction, and if correlated change will occur in other related and unrelated structures. The appropriate genetic model should reflect the relevant genetical and developmental biology of the organisms, yet be simple enough in its parameters so that deductions can be made and hypotheses tested. As a consequence, the choice of the most appropriate genetic model for polygenically controlled traits is a complex tissue and the eventual choice of model is often a compromise between completeness of the model and computational expediency. Herein, we discuss several developmental quantitative genetic models for the evolution of development and morphology. The models range from the classical direct effects model to complex epigenetic models. Further, we demonstrate the algebraic equivalency of the Cowley and Atchley epigenetic model and Wagner's developmental mapping model. Finally, we propose a new multivariate model for continuous growth trajectories. The relative efficacy of these various models for understanding evolutionary change in developmental and morphological traits is discussed.