Theoretical Approaches to the Evolution of Development and Genetic · PDF file · 2012-06-01Theoretical Approaches to the Evolution ... evolution of genetic architecture. ... type

Theoretical Approaches to the Evolutionof Development and Genetic Architecture

Sean H. Rice

Department of Biological Sciences, Texas Tech University, Lubbock, Texas, USA

Developmental evolutionary biology has, in the past decade, started to move beyondsimply adapting traditional population and quantitative genetics models and has begunto develop mathematical approaches that are designed specifically to study the evolutionof complex, nonadditive systems. This article first reviews some of these methods,discussing their strengths and shortcomings. The article then considers some of theprincipal questions to which these theoretical methods have been applied, including theevolution 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, aswell as some consequences for other approaches to phenotypic evolution of discoveriesfrom theoretical studies of developmental evolution.

Key words: evolutionary theory; evolution of development; genetic architecture; canal-ization; modularity

Introduction

Heritable variation is the raw material ofevolution, and because most heritable pheno-typic variation is translated through develop-ment from genetic variation, a complete the-ory of phenotypic evolution must be ready toincorporate all the complexities of developmentand genetic architecture. This was one of themotivations for the emergence of evolution-ary developmental biology as a distinct field.However, much of the early interest in “evo–devo” came from developmental biologists whosaw the relevance of comparative studies basedon phylogenetic relationships. This is basically“devo” with a little bit of “evo” added for con-text. A truly synthetic theory needs to incorpo-rate development and genetic architecture intothe formal mathematical theory of evolutionand then connect this theory back to develop-mental data. Here I review some recent stepstoward such a synthesis.

Address for correspondence: Sean H. Rice, Department of BiologicalSciences, Texas Tech University, Lubbock, TX 79409. Voice: 806-742-3039. [email protected]

I first discuss some of the theoretical meth-ods that have recently been applied to studyingthe evolution of development and genetic ar-chitecture. My goal here is to outline how thesemethods work and what some of their strengthsand weaknesses are. I then discuss some of theprincipal things that we have learned from ap-plication of these methods.

Methods for Modeling theEvolution of Development and

Genetic Architecture

Quantitative Genetics

The most widely used approach to studyingthe evolution of continuous variables is quan-titative genetics (Roff 1997; Lynch & Walsh1998). Unfortunately, the very properties ofquantitative genetic models that make themparticularly useful for studying phenotypic evo-lution make them ill suited to the study of theevolution of genetic architecture.

Quantitative genetics theory makes severalsimplifying assumptions that make it math-ematically tractable. The most important ofthese for our purposes is the assumption that

Ann. N.Y. Acad. Sci. 1133: 67–86 (2008). C© 2008 New York Academy of Sciences.doi: 10.1196/annals.1438.002 67

68 Annals of the New York Academy of Sciences

only the additive contributions of genes to aphenotype play a significant role in evolution.The phenotypic consequences of nonadditivephenomena such as dominance and epistasisare averaged and grouped into components ofphenotypic variance (Lynch & Walsh 1998). AsI will discuss below, focusing only on additivecontributions of genes to phenotype precludesmost of the study of the evolution of geneticarchitecture.

Though many quantitative genetic modelstreat heritability and genetic covariance as fixedvalues, these change over a few generations(Bohren et al. 1966; Parker et al. 1970). Par-ticular attention has been paid to genetic co-variance since early studies suggested that thisevolves faster than additive genetic variance(Bohren et al. 1966). Understanding exactly whygenetic covariance changes has been difficultusing only the machinery of quantitative ge-netics. Although results can be obtained underthe assumption of weak selection and additivityof gene effects (Lande 1980), understanding thevariation in genetic covariance seen in exper-imental studies will require explicit models ofthe specific gene interactions underlying quan-titative traits (Riska 1989).

One approach is to study models of possi-ble gene interactions. One such model that hasreceived considerable attention is the resourcepartitioning model for two traits that are influ-enced by developmental processes that draw onthe same resources (Sheridan & Barker 1974).Several authors have used variants of the re-source partitioning model to study the evolu-tion of genetic covariance (Riska 1986; Houle1991; de Jong & van Noordwijk 1992). Thiswork showed that when gene products inter-act nonadditively, genetic covariance changesin response to selection on phenotype and thatthis change is often not what we would expectfrom an additive model. The logical extensionof these kinds of studies is to devise a set ofmethods that would allow us to investigate theevolutionary consequences of any kind of in-teraction between gene products. This is whatphenotype landscape theory does.

Phenotype Landscape Models

Phenotype landscape models treat the valueof some phenotypic trait (or set of traits) as afunction of a set of underlying factors, whichmay be any measurable quantities, genetic orenvironmental, that contribute to phenotype(Rice 1998, 2002b; Wolf et al. 2001). Phenotypictraits that are subject to direct selection are gen-erally represented by φ; underlying factors thatcontribute to development of such traits aregenerally represented by u (although we willsee cases where one trait plays both roles). Se-lection is captured by a separate function thatmaps phenotype to fitness. This structure is dif-ferent from that taken in population genetics(such as the modifier models discussed later),where genotypes are generally mapped directlyto fitness, skipping over phenotype. By explicitlyinserting phenotype between the levels of geno-type and fitness, phenotype landscape modelsallow us to distinguish between the ways thatgenes interact to influence phenotype (devel-opment and genetic architecture) and the waysthat phenotypic traits interact to influence fit-ness (selection).

An individual organism is a point on thelandscape, and a population is a distributionof such points. Figure 1A shows a phenotypelandscape in which the underlying factors con-tribute additively to phenotype; thus, the land-scape is uncurved. The contours are lines ofequal phenotypic value. Fitness is not repre-sented here, only phenotype as a function ofthe underlying factors. The landscape itself thusrepresents genetic architecture but says noth-ing about selection. Figure 1B shows a curvedphenotype landscape, meaning that here theunderlying factors interact nonadditively to in-fluence phenotype (this is actually one of thephenotype functions used in the resource par-titioning models mentioned earlier).

Curvature of the landscape allows geneticarchitecture to evolve. To see this, consider thepoints a and b on the contour plot in Figure 1D.At point a the landscape slopes steeply in theu1 direction, meaning that a change in u1 has

Rice: Evolution of Development and Genetic Architecture 69

Figure 1. Examples of phenotype landscapescorresponding to (A) purely additive genetic effectsand (B) nonadditive (epistatic) effects. In panels Aand B, the vertical axis is phenotype, not fitness. (C)and (D) show contour plots of the landscapes in pan-els A and B, respectively. Shaded circles represent thedistribution of individuals within a population, andthe Q vectors are those described in the text.

a large effect on phenotype. A change in u2,though, produces little change in phenotype;moving along the u2 axis at point a primar-ily just changes the slope in the u1 direction.Thus, at point a, u1 has a strong direct effecton phenotype and u2 acts basically like a mod-ifier of u1. This situation is exactly reversedat point b, where u2 has a strong direct effectand u1 acts like a modifier. This example illus-trates why phenotype landscapes are useful forstudying the evolution of genetic architecture;the relative roles of different underlying factorschange as the population moves over a curvedlandscape.

This example also illustrates why quanti-tative genetics is poorly suited to study theevolution of genetic architecture; by assum-ing that genes contribute additively to pheno-type, quantitative genetics assumes a pheno-type landscape like that in Figure 1A and C, onwhich genetic architecture cannot evolve be-cause it is the same everywhere on the land-scape.

The general mathematical theory for evolu-tion on a phenotype landscape has been de-scribed by Rice (1998, 2002b). This theorydescribes evolution as the sum of a set of vectors(termed Q vectors) in the space of underlyingfactors, each vector corresponding to a differentaspect of the local geometry of the landscape.The simplest Q vector, Q 1, contains only firstderivatives of phenotype with respect to the un-derlying factors and captures just the effects ofdirectional selection to change the mean phe-notype. If the distribution of underlying varia-tion is normal and the landscape uncurved (asin Fig. 1C), then Q 1 is the only vector present.The vector Q 1,2 (containing both first and sec-ond derivatives of the landscape) appears oncurved landscapes (Fig. 1D) and captures theeffect of stabilizing selection to reduce pheno-typic variance. The equations for these vectorsare

Q 1 = 1w̄

∂w

∂φ

⟨P 2, D 1⟩ and

Q 1,2 = 12w̄

∂2w

∂φ2

⟨P 4, D 1 ⊗ D 2⟩ .

(1)

Here, Pn is a tensor containing all the nthmoments of the distribution of underlyingvariation, Dn is a tensor containing all the nthderivatives of phenotype with respect to the un-derlying factors, and w represents fitness. Thegeneral equation for all of the Q vectors presenton an arbitrarily complex landscape is given byRice (2002b).

The general theory of Q vectors appliesto an arbitrarily complex developmental sys-tem with an arbitrary distribution of underly-ing variation. For many of the questions thatwe are interested in, though, a more restrictedmodel is actually easier to work with. One wayto simplify the general phenotype landscapemodel is to focus on a subset of possible land-scape geometries. This approach is essentiallywhat quantitative genetics does by consideringonly additive effects. A more complex, thoughstill relatively tractable, set of models are themultilinear models (Hansen & Wagner 2001;Hermisson et al. 2003). In these models, many


underlying factors can interact, but each hasa linear effect on the interactions between theothers. Restricting our attention to a subset ofsurfaces increases our ability to study certainprocesses, such as the evolution of mutationalvariance (Hermisson et al. 2003). However, italso limits our ability to study other processes.For example, the third moment (measuringasymmetry) of the phenotype distribution can-not evolve on these multilinear landscapes.

Moments

The set of moments of a distribution char-acterize the shape of that distribution. Theeven moments measure symmetrical spreadabout the mean, and the odd moments measureasymmetry. The higher the order of a particu-lar moment, the more sensitive it is to outliers.Throughout this discussion, we will sometimescome across “higher” (greater than second) mo-ments of the distribution of underlying varia-tion. Because nearly all evolutionary theory iscouched in terms of the mean (first moment)and variance or covariance, it is worth brieflydiscussing why we need to consider higher mo-ments in any discussion of the evolution of ge-netic architecture.

One rule of evolution is that if we want to cal-culate the change over time in the nth momentof the distribution of phenotypes, we need toknow the current (n + 1)st and higher moments(Rice 2004b chap. 6; this fact follows from Price1970). When we model directional phenotypicevolution, we are studying the change in themean (first moment) of the phenotype distri-bution; we thus can model directional evo-lution, at least approximately, by consideringonly the variance of the current populationdistribution.

Most processes implicated in the evolutionof development and genetic architecture in-volve selection to change more than just themean phenotype in a population. Modelingthe evolution of canalization requires that weconsider the fourth moments of the distribu-tion of underlying variation; the same goes for

the evolution of genetic covariance. Selectionto change the overall degree of epistasis or tochange the curvature of a reaction norm actson the sixth moment (Rice 2004b). If we ac-cept that selection for canalization, modular-ity, and phenotypic plasticity are among theimportant factors influencing the evolution ofgenetic architecture, then we clearly cannot ig-nore these higher moments. Some models haveaddressed the evolution of phenotypic variancewithout appearing to involve higher moments(e.g., Lande & Arnold 1983; Rice 1998). Thisapproach is possible because these models as-sume a normal distribution of variation, andone property of the normal distribution is thatall higher moments can be written in terms ofthe variances and covariances. Most distribu-tions do not have this property, though, so thesemodels can lead to substantial errors if the ac-tual distributions that we are dealing with innature are not exactly normal.

Consider the two distributions in Figure 2.These two distributions have the same vari-ance and so would respond the same to di-rectional selection on an uncurved landscape.However, because neither is a normal distribu-tion, the higher moments are not constrainedto be functions of the variance. In fact, the sixthmoment of the distribution in Figure 2B is 10times larger than the sixth moment of the distri-bution in Figure 2A. Thus, if we are interestedin the evolution of phenotypic plasticity, selec-tion to change the curvature of a reaction normwould be 10 times stronger for the populationin Figure 2B than for the one in Figure 2A. Thisfact would be missed if we considered only thevariance.

General Models and DynamicSufficiency

Our having to always look at higher mo-ments to study the evolution of a particularmoment brings up another issue relating to theuse of phenotype landscape models. I refer tothese models as being “general” because theycan be applied to any evolving developmental


Figure 2. Two distributions with the same meanbut different sixth moments.

system, regardless of the kinds of interactionsinvolved between genes and the environment,the distribution of variation within a popula-tion, or the kind of selection acting on the sys-tem. This does not mean, though, that theyanswer all our questions. One reason for thisis that we can use the most general phenotypelandscape models only to calculate what willhappen over one generation; they cannot beiterated indefinitely. Given the population dis-tribution in generation t, we can calculate themean in generation t + 1 only by using at leastthe variance in generation t. If we then wantto calculate the mean in generation t + 2, weneed the variance in generation t + 1, but thiscan be found only if we know at least the thirdmoment in generation t. Therefore, we can it-erate our model forward through time only ifwe specify all the moments in the current gen-eration, which is not practical. These modelsare thus not dynamically sufficient.

If we assume that all distributions relevant toour system are multivariate normal, then ourproblem is solved because all the higher mo-ments are functions of the second moments,so we can calculate them all. Applying this as-sumption makes phenotype landscape models

dynamically sufficient (Rice 1998). As I arguedearlier, though, this approach rapidly yields in-correct answers (and misleading conclusions)when we are dealing with real populations,which are never exactly normally distributed.Although models that can be iterated indefi-nitely are clearly useful as descriptions of spe-cial cases, and allow us to investigate the typesof dynamical behavior that evolution can ex-hibit, they are never truly general in the senseof applying to any evolving system.

Modifier Models

Modifier models focus on a few loci (usuallytwo or three) in which one locus acts as a mod-ifier of the expression of the others. Modifiermodels have been used to study the evolution ofdominance and of recombination (Feldman &Karlin 1971; Feldman & Krakauer 1976; Feld-man et al. 1997). In modifier models, genotypesmap directly to fitness, skipping over the inter-vening phenotype. The term epistasis, as used inthese models, thus refers to nonadditive contri-butions of loci to fitness. Therefore, even genesthat contribute additively to two different traitsmay be said to interact epistatically if the twotraits contribute nonadditively to fitness. Themodifier approach has been combined with themultilinear model approach by Kopp and Her-misson (2006). This method allows includingmore than three loci by assuming a specifickind of interaction among loci.

Because they borrow the well-establishedmethods of two-locus population genetics,modifier models are good for studying the rolethat linkage and recombination may play inthe evolution of genetic architecture. Recentapplications of modifier models include Masel’s(2005) study of the evolution of capacitance andLiberman and Feldman’s (2005, 2006) studiesof the evolution of epistatic interactions. Be-cause modifier models deal with a relativelysmall number of discrete genotypes, they aregood for dealing with discontinuities in themapping from genotype to fitness.


Functional Mapping Models

The approaches discussed above tend to fo-cus on one phenotypic trait, influenced bymany loci. When multiple traits are considered,they are represented by a vector of values (Rice2002b). Development, however, is a continu-ous process, and sometimes the “trait” that weare interested in is actually the growth processitself. The functional mapping approach (Maet al. 2002; Wu et al. 2002; Wu & Hou 2006)deals with this problem by focusing on an onto-genetic trajectory. The ontogenetic trajectory,an idea borrowed from models of heterochrony(Alberch et al. 1979; Rice 1997, 2002a), is a plotof some phenotypic trait as a function of timeor of another trait.

Earlier methods for analyzing ontogenetictrajectories simply compared the shapes of dif-ferent trajectories, making no attempt to mapthe shape of these curves to underlying geneticprocesses. This approach can provide somelimited insight into developmental evolution.Specifically, we can test whether or not a par-ticular evolutionary transformation could havecome about as a result of uniformly changingthe rate, duration, or timing of developmentalprocesses (Rice 2002a). Although changes ofthis sort (heterochrony) do sometimes appearto be important, they represent only a smallsubset of all of the ways in which developmentcan change.

Functional mapping models greatly increasethe utility of ontogenetic trajectories by param-eterizing them in such a way that we can applyquantitative trait locus (QTL) methods to them.By using some general assumptions about un-derlying physiology, this approach allows us todraw much richer conclusions from ontoge-netic trajectories that do not fit the restrictiveconditions of heterochrony.

Artificial Gene Networks

The artificial gene network approach is pri-marily computational, rather than analytical.Such studies generally emphasize computer

simulations, the results of which are inter-preted after the fact, rather than predictionsbased on the analysis of equations. Some ana-lytical results can be obtained, though, espe-cially for the earliest kinds of gene networkstudies.

A widely used approach to studying artifi-cial gene networks was devised by A. Wag-ner (1996). Models of this type posit a popu-lation of genetic networks, each designed to re-semble a set of transcription regulation genes.In each generation, recombination and muta-tion were simulated within each network, andthen a selection process was imposed favoringthose networks closest to a defined optimum.Wagner’s simulations showed that if there isepistasis in the networks, then the structure ofthe networks did evolve to become increasinglycanalized. This type of simulated gene networkhas been used more recently by Siegal andBergman (2002), to study the evolution of ge-netic architecture under different kinds of stabi-lizing selection, and by Azevedo et al. (2006), tostudy the consequences of sexual versus asexualreproduction.

General Results from TheoreticalStudies

The methods outlined above have been usedto investigate a wide range of questions. I nowconsider some of the major results.

Single-trait Distributions—Canalizationand Capacitance

Canalization refers to buffering of phenotypeagainst underlying genetic or environmentalvariation. This phenomenon (also referred toas “robustness”) has received extensive atten-tion from researchers, and it was the desire tomodel the evolution of canalization that moti-vated much of the early development of mod-ern theories for the evolution of developmentand genetic architecture (Wagner 1996; Wag-ner et al. 1997; Rice 1998, 2000; see reviews inde Visser et al. 2003 and Flatt 2005).


Canalization is generally thought to evolve inresponse to stabilizing selection, defined here asselection to reduce phenotypic variance (Rice2004b). We can visualize the process as evolu-tion of a population toward parts of the pheno-type landscape that minimize phenotypic vari-ance. If the underlying factors are uncorrelatedand have equal variances, then points of max-imum canalization for a particular phenotypicvalue are points of minimum slope along thecontour corresponding to that value. However,changing the shape of the distribution of un-derlying variation will change the position ofpoints of maximum canalization (compare pop-ulations A and B in Fig. 3). Points of maximumor minimum canalization along a contour oc-cur wherever the vector Q 1,2 (from Equation 1)is normal to the contour line.

Nearly all analytical models that incorporatenonadditive interactions between loci (Wagneret al. 1997; Rice 1998; Proulx & Phillips 2005)or between genes and environmental variables(Gavrilets & Hastings 1994) exhibit some sortof canalization under stabilizing selection. Thesimplest genetic models focus on variation re-sulting from mutation, but in fact variation re-sulting directly from mutation is probably lessrelevant to developmental evolution than areother sources of variation, such as recombina-tion, migration, and environmental fluctuation.Selection is efficient at reducing variation re-sulting directly from mutation, so the responseof a population to selection to reduce variationis likely to be a rapid change in the mutation–selection equilibrium rather than a restructur-ing of genetic architecture (Wagner et al. 1997;Rice 2000).

Selection acts on the entire distribution ofvariation in a population, and this distributionmay look different from the distribution of mu-tational effects alone. Hermisson et al. (2003)used a multilinear model to study the conse-quences of allowing the distribution of addi-tive genetic variation to evolve as a populationmoves over a phenotype landscape. They foundthat if different underlying factors have differ-ent mutation rates, then at mutation–selection

Figure 3. Two populations at points of maximumcanalization along their contour, as determined bythe shape of the landscape and the distribution ofunderlying variation.

equilibrium the population distribution tendsto elongate along the axis corresponding to theunderlying factor with the highest mutationrate. This effect shifts the point of maximumcanalization away from the point of minimumslope and yields an equilibrium state resem-bling the population at point B in Figure 3 (thelandscape in Fig. 3 is in fact a multilinear land-scape). Significantly, the equilibrium was not ata point that minimized mutational variance.

Several simulated gene network studies havedemonstrated that canalization can evolve in

silico. A. Wagner (1996) found canalizationaround an optimum regulatory network. Sie-gal and Bergman (2002) used a similar simu-lation approach to study cases in which therewas no optimum phenotype but rather just se-lection to minimize variance among one’s de-scendants. This study found that genetic archi-tecture evolves to minimize phenotypic varia-tion even when there is no single “best” phe-notype to be canalized. There has been someconfusion about this work resulting from dif-ferent uses of the term stabilizing selection. Siegal& Bergman define stabilizing selection as “selec-tion for a particular optimum gene expressionpattern.” Therefore, they interpret their resultsas showing that canalization can evolve withoutstabilizing selection. This definition of stabilizing

selection is consistent with that given in many in-troductory texts, but it is not the same as the def-inition used in most of the evolutionary geneticsliterature, where stabilizing selection is defined asselection to reduce phenotypic variance and is


captured mathematically by the second partialderivative of fitness with phenotype [or the par-tial regression of fitness on (φ − φ̄)2] (Lande &Arnold 1983; Rice 1998; Rice 2004b). A popu-lation may thus experience stabilizing selection,with a corresponding evolution of canalization,even when it is not near an optimal pheno-type (Rice 1998). Under this definition, Siegal& Bergman’s simulations imposed stabilizingselection within each lineage, so their result isexactly in line with prior predictions.

Azevedo et al. (2006) used simulated genenetworks to compare the evolution of geneticarchitecture in asexual and sexual popula-tions. They found that “mutational robustness”(canalization against mutational variation)evolved in both sexual and asexual populationswhen mutation rates were high but only in sex-ual populations when mutation rates were lowor mutation was excluded. The key to this ob-servation is that gene networks in sexual pop-ulations underwent recombination, whereasthose in asexual populations did not. Canal-ization thus evolved primarily in response tounderlying variation produced by recombina-tion. This effect still registered as “mutationalrobustness,” meaning that the genetic architec-ture that buffered against recombination varia-tion also buffered against mutational variation.

The phenomenon of a system that is bufferedagainst one source of underlying variation alsobeing buffered against other sources of underly-ing variation has been called congruence (Ancel& Fontana 2000). Congruence is usually dis-cussed in the context of comparing environ-mental canalization with mutational canaliza-tion and has been seen as important because ofthe limitations on mutational canalization dis-cussed earlier. However, as the above examplemakes clear, mutation is not the only sourceof genetic variation. In addition to recombina-tion, mutation, and environmental variation,the phenotypic (and genetic) variation withina local population is influenced by migration(Proulx & Phillips 2005). All these processescontribute variation that spurs selection forcanalization.

Canalization clearly can evolve, and it doesso in simulated genetic systems. Exactly howimportant selection for canalization is in struc-turing development in natural populations,though, is less clear. Other processes, such asselection for a particular covariance betweentraits (discussed later), also modify developmentand will tend to pull populations away frompoints of maximum canalization. Also, depend-ing on the structure of the landscape, achievingmaximum canalization for multiple traits at thesame time may not be possible.

One observation that was long thought toprovide evidence for canalization is that pop-ulations often express increased heritable vari-ation after being perturbed either genetically(such as through the introduction of new alle-les of large effect) or environmentally. In fact,though, several processes can cause variationto increase after perturbations even if the traitwas not initially canalized (Goodnight 1988;Cheverud & Routman 1996; Hermisson &Wagner 2004).

A more direct way to assess whether geneticarchitecture is likely to have been structured byselection for canalization (or some other pro-cess) would be to reconstruct the phenotypelandscape underlying a trait of interest. Themost direct way would be to use a mechanis-tic model for development of the trait. Nijhoutet al. (2006) recently used this approach for bodysize in Manduca. They drew on empirical studiesto identify three underlying factors that jointlyare sufficient to determine body size, and theycalculated the function that maps these traitsto size; this function is a phenotype landscape.This is an important approach that will surelybecome more common as we learn more aboutthe mechanics of different developmental pro-cesses. Even with such a landscape, though, wecannot tell if a population is at a point of maxi-mum canalization without further informationabout the distribution of variation of the under-lying factors.

There is another approach to reconstruct-ing phenotype landscapes that does not requiremechanistic knowledge of development and, at


least approximately, scales the landscape ac-cording to the distribution of variation in eachunderlying factor. Regression-based QTL anal-ysis (Visscher & Hopper 2001; Feingold 2002)basically involves constructing a multivariateregression of a phenotypic trait on a set ofmarkers distributed throughout the genome.In most regression-based QTL studies, the co-efficients of this regression are tested against asampling distribution, and those markers corre-sponding to statistically significant coefficientsare reported as putative QTLs. The entire anal-ysis, though, effectively estimates the pheno-type landscape, for which the individual QTLsplay the roles of underlying factors. There arethree points along each axis, presumably cor-responding to different dosages of an allele atsome locus closely linked to the marker.

Because such analyses generally start by im-posing strong divergent selection on differentstrains and then produce inbred lines with ex-treme phenotypes, the original population dis-tribution probably sat near the middle of the re-constructed landscape. The presence of a pointof minimal slope in this region, although not aconclusive demonstration, is at least consistentwith the hypothesis that the genetic architec-ture of that trait has been shaped by stabilizingselection. By contrast, if no point of minimumslope is found within the range of variation inthe population, then selection for robustnessalone is unlikely to explain the observed geneticarchitecture.

Figure 4 illustrates this approach by usingdata from Shimomura et al. (2001) on QTLs in-fluencing circadian rhythms in mice. The land-scape in Figure 4 has a saddle point near thecenter of the graph. Saddle points are pointsof zero slope at which the surface curves awaypositively in some directions and negatively inothers. A population sitting near such a point isthus well canalized. These data are thus consis-tent with the hypothesis that the genetic archi-tecture of this trait was substantially structuredby stabilizing selection. The specific trait in thisexample, dissociation, measures the degree towhich different parts of the circadian cycle are

Figure 4. (A) Phenotype landscape for a traitrelating to circadian rhythms in mice, reconstructedfrom data in Shimomura et al. (2001). (B) Aquadratic surface fit to the data in panel A.

decoupled from one another. This value is nearzero in the original population and is somethingthat is probably always under strong stabilizingselection (it is generally maladaptive to have noconnection between when an organism goes tosleep and when it wakes up). It is thus not sur-prising that this trait behaves as though it is wellcanalized.

Adaptation of Higher Moments

Selection could in principle act to changethe third moment of a phenotype distribution(measuring the degree of asymmetry of thedistribution) by moving the population to re-gions of the phenotype landscape with different


average curvature. Though we have no specialname for this sort of selection, it will happenanytime that fitness drops off more steeply onone side of an optimum phenotype than onthe other side. Such “skewing” selection shouldmodify genetic architecture by pushing a pop-ulation toward regions of the phenotype land-scape at which the mean curvature is high.

Figure 5 shows a landscape that exhibits ex-actly the geometry that we would expect if therehas been selection to skew the phenotype dis-tribution (data from Shimomura et al. 2001).Unlike the saddle point in Figure 4, the surfacein Figure 5 curves in the same way in all direc-tions. As a consequence, the mean curvature isnonzero, meaning that a symmetrical distribu-tion of underlying factors will produce an asym-metrical phenotype distribution. One hint thatwe have a reasonable picture of this phenotypelandscape is that the distribution of this traitin the F2 generation of mice is in fact stronglynegatively skewed (Fig. 5C). Though not an in-dependent test of the data (these are the micefrom which the data in the figure came), thisfinding at least confirms that our reconstruc-tion of the landscape from nine points is not faroff the shape of the actual surface.

That this trait has evolved to a place onits phenotype landscape that should producea skewed phenotype distribution might befortuitous—there is also a region of very lowslope near the center of the figure. In fact,though, this is a trait for which we should ex-pect selection to favor a skewed phenotype dis-tribution. The phenotypic trait represented inFigure 5, “phase,” measures the time at whichmice wake up relative to when it gets dark(which is when wild mice begin foraging). Aphase value of zero means that the mouseawakes precisely when the lights go off, a nega-tive value means that the mouse wakes up early,and a positive value means that it awakes afterdark. Foraging studies suggest that, at least fornocturnal desert rodents, there is a substantialcost to foraging later at night because resourceshave been depleted by early foragers (Kotleret al. 1993; Brown et al. 1994). Waking up late

Figure 5. (A) Phenotype landscape for the trait“phase” (discussed in the text) reconstructed from thesame source as Figure 4. (B) Best-fit cubic surfacecorresponding to data in panel A. (C) Distribution ofthe trait among the F2 progeny.

thus probably carries a substantial fitness cost.By contrast, waking up early does not imposesuch a cost; individuals simply wait until dark tobegin foraging (Shimomura et al. 2001). There-fore, it is plausible that the genetic architecture


of this trait has been shaped by selection to bothminimize phenotypic variation and to skew, inthe direction that is least damaging, what vari-ation remains.

This method of constructing phenotypelandscapes has some serious limitations. We areconstructing the landscape by using only threepoints along each axis, which is not particularlygood resolution. Therefore, we must comparethe observed F2 phenotype distribution withwhat we would predict from our reconstructedlandscape (Fig. 5). Also, most methods of QTLanalysis involve selecting different strains fordifferent extreme phenotypes and then cross-ing these. We can thus view a slightly largerregion of the phenotype landscape than wasinhabited by the original population. Unfortu-nately, it also means that all information aboutthe distribution of variation in the original pop-ulation is lost.

That the extreme phenotypes crossed to gen-erate the data were derived from variation in aninitial population means that there is some cor-respondence, though not perfect, between thescaling of the axes on our reconstructed land-scape and the amount of variation that was ini-tially present in the population. Unfortunately,strong selection followed by inbreeding makesit impossible for us to know whether the under-lying factors were initially correlated with oneanother (i.e., if the alleles at the loci in questionwere in gametic equilibrium or not). Some ofthese problems could perhaps be alleviated bynoting the patterns of variation among extremephenotypes in the population before selectionand inbreeding.

The other side of canalization is capaci-tance, the expression—when a population ex-periences a new selection regime—of newheritable phenotypic variation. The term ca-

pacitance refers to the fact that the exposure ofsuch variation could facilitate adaptive evolu-tion and raises the possibility that developmentand genetic architecture could be structuredto buffer phenotype under stabilizing selectionand then abruptly express new heritable varia-tion under conditions of directional or disrup-

tive selection. Capacitance could arise in twodifferent ways. In one scenario, an environ-mental change (or other perturbation) causesgenetic variation that is already present, butnot expressed, to suddenly be expressed as phe-notypic variation. In the second scenario, theperturbation causes the production of new ge-netic variation.

The phenomenon of capacitance actuallyarises easily from a wide range of models ofdevelopmental evolution and genetic architec-ture (Bergman & Siegal 2003; Hermisson &Wagner 2004; Masel 2005). Furthermore, theexpression of novel variation when a popula-tion is stressed has been observed in severaltaxa (True & Lindquist 2000; Fares et al. 2002;Queitsch et al. 2002). Although this expressionof variation may facilitate adaptive evolution, itdoes not follow that these systems have evolved,wholly or in part, from selection for evolvabil-ity. As noted above, the expression of varia-tion is expected when a canalized system isdisrupted and is a common occurrence evenin noncanalized systems that involve substan-tial epistasis. Furthermore, error-prone DNArepair increases mutation rates when a popu-lation is stressed, but this is probably becauseerror-prone repair is better than no repair atall, rather than selection to produce variation.

Though most instances of capacitance areprobably by-products of genetic architectureand DNA repair systems, it is in principle pos-sible for at least a limited kind of capacitance toevolve as a direct result of selection for variabil-ity. Masel (2005) used a modifier model to showthat selection can lead to the fixation of modi-fier alleles that express variation at an optimalrate.

Multiple Trait Distributions—Modularity,Correlation, and Entanglement

Adaptation of an entire organism requiresthat different traits be able to evolve indepen-dently of one another. If any change in any un-derlying factor influenced every trait, then therewould be no such independence and adaptive


Figure 6. Two linear landscapes. Gradient vec-tors point uphill on their corresponding landscapes.The angle between these vectors determines the cor-relation between traits.

evolution would be effectively impossible. Thisproblem is avoided if the genetic architectureallows suites of traits that function together tovary independently of one another. Along withcanalization, modularity (especially as it relatesto evolvability) is among the principal motiva-tions for research into the evolution of geneticarchitecture (Hansen 2006).

Modularity is sometimes taken to imply thatdifferent sets of genes influence different mod-ules (Wagner & Altenberg 1996). This infer-ence is not necessarily true, though, becausethere can be evolutionarily independent mod-ules that are influenced by many of the samegenes. The genetic covariance between twotraits is a function of the distribution of un-derlying variation and the genetic architecturethat maps that variation to phenotypic vari-ation. In an additive system (i.e., no epista-sis) with underlying factors distributed inde-pendently, the genetic covariance between twotraits is determined by the orientation of thetwo phenotype landscapes (Fig. 6). If the un-derlying factors have equal variances and nocovariance, the correlation between two traitsis simply cor(φ1, φ2) = cos(θ), where θ is the

Figure 7. Two cases in which the correlationbetween the two traits is zero.

angle between the two gradient vectors (Rice2004a).

Figure 7 shows two cases in which two dif-ferent traits are genetically independent of oneanother. In Figure 7A each trait is influencedby a different underlying factor, whereas inFigure 7B both traits are influenced by the sametwo factors. Clearly, though, the traits in caseB are just as independent as are those in caseA; furthermore, there are an infinite numberof possible scenarios in which both underlyingfactors contribute to both traits, but the traits re-main independent. What matters is the relativeorientation of the two phenotype landscapes. Infact, there is no reason to expect cases such asthat in Figure 7A, where traits are independentbecause they are influenced by nonoverlapping


sets of genes, are the norm. Though thetwo cases in Figure 7 both exhibit zerocovariance between the traits, they may notbe identical with respect to evolvability. In theexample in Figure 7B, each trait can change asa result of mutations in either underlying fac-tor, meaning that each presents a larger targetfor mutations than do the traits in Figure 7A,each of which can be influenced by mutationsin only one underlying factor. Though moremutations influence each trait in the secondcase, those mutations have a smaller effect thanin the first case; the total mutational varianceshould thus be the same. Having a shorter wait-ing time until some mutation (albeit a small one)comes along, though, could influence evolvabil-ity. Supporting this claim, Hansen (2003) foundthat in simulations, evolvability was not maxi-mized in systems with minimal pleiotropy.

Some studies based on simulated gene net-works have suggested that selection for evolv-ability will in general favor increased modu-larity and decreased epistasis for fitness be-tween different loci (Pepper 2003, Altenberg2004). Using a modifier model, Liberman andFeldman (2006) showed that this result doesnot follow when loci are sufficiently closelylinked. This outcome is not surprising whenwe note that recombination, which is an ex-plicit part of Liberman and Feldman’s model,is another process that reduces evolvability,here by actually destroying potentially adaptivevariants.

The other side of modularity is developmen-tal covariance between traits. Such covariancereduces the ability of traits to evolve indepen-dently but may increase the probability thatthey covary in adaptive ways. In quantitativegenetics, patterns of covariation between traitsare traditionally summarized using an additivegenetic covariance matrix, otherwise known asa G matrix. The G matrix is an estimator ofthe expected parent–offspring covariance ma-trix, which is what determines how selectioninfluences multivariate evolution in a system inwhich all phenotype landscapes are linear (Rice2004b).

Classical quantitative genetics tended to treatG matrices as fixed, but it is now universally ac-cepted that patterns of genetic covariance canand do evolve in natural populations. Jones et al.

(2003) used simulations to study the evolutionof G matrices under different conditions; theyfound that the pattern of genetic covariationis stabilized when mutations have substantialpleiotropic effects.

An important special case of evolution ofcovariance between traits is the evolution ofphenotypic plasticity. Phenotypic plasticity hastraditionally been studied using quantitative ge-netic models, treating either the value of a traitin different environments (Via & Lande 1985)or the reaction norm itself (Scheiner 1993) astraditional quantitative traits (see Via et al. 1995for a review). More recently, though, severalauthors have begun to treat the evolution ofphenotypic plasticity as a problem within de-velopmental evolution, either as a variation oncanalization (Debat & David 2001) or as a caseof the evolution of developmental covariance(Rice 2004b, chap. 8).

The key to modeling the evolution of pheno-typic plasticity as a kind of developmental co-variance is recognizing that an environmentalvariable can be both an underlying factor forsome phenotypic trait and, simultaneously, atrait in its own right (albeit generally not a heri-table trait). That an environmental variable canbe thought of as a phenotypic trait may seemless odd when we recognize that we are sayingsimply that the environment that an individuallives in is one of the factors that, jointly withthe rest of its phenotype, determines its fitness.

Using this approach, Rice (2004b) showedthat selection on the slope of a reaction norminvolves two Q vectors, one of which is thesame as the vector corresponding to canaliza-tion (Q 1,2 in Equation 1 above) and the otheris a vector pointing in the direction of maxi-mum sensitivity of the trait φ to the environ-mental factor. The sum of these two vectorsmoves the population precisely to the point onthe landscape corresponding to the optimal re-action norm slope (assuming that such a point


exists and is reachable). The evolution of re-action norm slope thus does seem to containthe term for the evolution of canalization as acomponent. Rice also considered selection tochange the curvature (rather than the slope) ofa reaction norm and showed that this processis influenced by the sixth moment of the dis-tribution of underlying variation, meaning thatoutliers strongly affect the evolution of reactionnorm curvature.

Environment’s Role in Developmentand Inheritance

Classical evolutionary theory tended to treatthe “environment” as something that influencesselection but that is separate from the genet-ics or development of organisms. The exam-ple above shows that it can be fruitful to treatsome environmental variables as part of theprocess of development—and even as one ofthe organism’s phenotypic traits (Rice 2004b).Though in the simple model for the evolutionof phenotypic plasticity I treated the environ-mental variable as nonheritable, often the en-vironment really should be considered part ofthe genetic architecture. Environmental factorsthemselves may be heritable if parents influ-ence the environment of their offspring (Laland& Sterelny 2006). Furthermore, given that theenvironment includes other organisms withwhich an individual interacts, the environmentcontains genes, some in close relatives. Wolf(2003) demonstrated that taking into accountinteractions with relatives can lead to substan-tial changes in quantitative genetic parameters.

In fact, the environment can influence her-itability even if no environmental parametersare heritable. Consider a trait, φ, that is a lin-ear function of a genetic factor, ug, and an envi-ronmental factor, ue. Now consider the trait inboth parents and their offspring. For simplicity,assume that the genetic factor is passed on withperfect fidelity (such as in an asexual haploid or-ganism), but the environment experienced byoffspring is potentially different from the envi-ronment of their parents; call the parent’s envi-

ronment uep and their offspring’s environmentueo. We can now write the values of the trait inparents (φp) and offspring (φo) as

φp = u g + u ep and

φo = u g + u eo.(2)

Rice (2004a) shows that for this simple case,the regression of offspring phenotype on parentphenotype (i.e., the heritability of φ) is given by

βo,p = h 2

= var(u g) + cov(u g, u ep) + cov(u g, u eo) + cov(u ep, u eo)var(u g) + var(u ep) + 2cov(u g, u ep)

.

(3)

The environmental factor clearly influencesheritability. Two of the terms in Equation 3basically capture the heritability of the en-vironment. The covariance between parentalgenotype and offspring environment [cov(ug,ueo)] is expected to be important when par-ents partially construct their offspring’s envi-ronment, which is common among organismswith parental care (Laland & Sterelny 2006).The covariance between parent’s environmentand their offspring’s environment will be im-portant in cases in which, for example, femalesprefer to lay eggs in the type of environment inwhich they were born.

The most surprising thing about Equation 3is the presence of cov(u g, u ep), the covariancebetween parents’ genotype and their environ-ment, in both the numerator and denominator.This term thus influences heritability even ifthe offsprings environment is completely inde-pendent of their parents’ environment. Thatis, if an environmental factor influences pheno-type, and if there is any correlation between theparents’ genotypes and the environments thatthey experience, then heritability of phenotypeis altered even if the environmental factor itselfis not heritable (Schlichting 1989; Rice 2004a).This example assumes only additive effects ofthe genotype and the environment. If we allowfor any nonadditive interactions between anyof the underlying factors, then heritability canevolve even in a constant environment with nochange in mean phenotype (Rice 2004b).


Epistasis and Genetic Covariance

If there are epistatic interactions betweenthe underlying factors, then the covariance be-tween traits is no longer simply a function ofthe angle between the gradient vectors (Rice2004a). There are two important consequencesof this statement. First, correlation betweentraits that is due in part to epistatic interac-tions will change as the total amount of under-lying variation in the population changes, evenif the shape of the underlying distribution re-mains constant. Second, epistatic interactionsinfluence other joint moments of the phenotypedistribution, not just covariance. As a result, as-sociations between traits resulting from epistasisare likely to influence evolutionary dynamics inways that are undetectable to traditional quan-titative genetic analyses.

One situation in which epistasis should havesignificant consequences for phenotypic evo-lution is the case of strongly developmentallycorrelated traits. If the patterns of epistasis fortwo strongly correlated traits are slightly dif-ferent, the ability of the population to evolveagainst the correlation will tend to be asym-metrical. Figure 8 illustrates the consequencesof modifying by a small amount the pattern ofepistasis for one of two traits that are stronglydevelopmentally correlated. A slight differencein curvature has little if any effect on the abilityof the population to respond to selection thatgoes with the covariance (i.e., selecting to in-crease or decrease both traits, if the covarianceis positive) but creates substantial asymmetry inthe response to selection against the correlation(antagonistic selection). This effect is most pro-nounced when the two phenotype landscapesnearly coincide with one another.

Because even highly correlated traits willprobably have at least slightly different geneticarchitectures, the phenomenon of asymmetri-cal responses to antagonistic selection shouldbe the rule, rather than the exception, in mul-tivariate evolution. In fact, asymmetrical re-sponses to antagonistic selection have beennoted for some time and recognized as de-

Figure 8. Consequence of introducing differen-tial curvature into a system of two traits that arestrongly correlated. The point marked (+ −) indicateswhere the population would have to move to increasetrait 1 by one unit while decreasing trait 2 by oneunit. The point marked (− +) is the converse, thepoint at which trait 1 is decreased, and trait 2 in-creased, each by one unit. (A) These two points areequidistant from the starting point, meaning that thepopulation could as easily evolve in one direction asthe other. (B) Differential curvature of the landscapefor trait 1 has substantially moved the point (− +),meaning that it will require significantly more time toevolve to decrease trait 1 and increase trait 2 than toevolve the same phenotypic distance in the oppositedirection.

viations from quantitative genetic predictions(Nordskog 1977; Scheiner & Istock 1991). Suchasymmetries appear in many studies, thoughthey are not always noted in the articles.


Figure 9. Examples of asymmetrical responses to antagonistic selection. (A–C) Traitsare positively correlated, and the two trajectories represent the results of selecting againstthe correlation. (D) Traits are negatively correlated, and two replicates are shown for eachdirection. Data are from Nordskog 1977 (panel A), Bell & Burris 1973 (panel B), Rutledgeet al. 1973 (panel C), and Zijlstra et al. 2003 (panel D). Panels A–C are after Roff (1997).

Figure 9 shows four examples from diverse or-ganisms.

Developmental Entanglement

The examples of an asymmetrical responseto selection suggest that traits can be associatedin ways that are not accurately captured bycovariance. Rice (2004a) used the term entan-

glement to describe the general case in which se-lection to change some moment of a phenotypedistribution also leads to change in some othermoment. Genetic covariance, which causes se-lection on the mean (first moment) of one traitto influence the evolution of the mean of an-other trait, is one kind of entanglement, butthere are many other ways in which the evolu-tion of different traits can be linked.

Figure 10 shows a simple case in which twotraits are uncorrelated, so selection to changethe mean of one has no effect on the mean of theother, but are nonetheless entangled such thatstabilizing selection on one changes the mean

of the other. Rice (2004a) provides an exampleof three phenotypic traits that are entangledsuch that directional selection on any one traitchanges the covariance between the other twotraits. Given the complexity of developmentalsystems, forms of entanglement other than co-variance between traits are probably common.

Drift

Nearly all theoretical research into the evo-lution of development has focused on selectionas the process driving evolution. Drift undoubt-edly plays a role, though, and may well be moreimportant in developmental evolution than itis in the evolution of mean phenotypes. Rice(1998) calculated the strength of canalizing se-lection moving a population along a phenotypecontour and found that this force becomes weakas a population approaches a point of maxi-mum canalization. Furthermore, the point ofmaximum canalization along a contour is afunction of the distribution of variation within


Figure 10. Example of entanglement in whichtraits 1 and 2 are uncorrelated, but selection to re-duce the variance of trait 1 would cause directionalchange in the mean of trait 2. The vectors ∇φ1 and∇φ2 point in the directions of maximum increase intraits φ1 and φ2, respectively. Stabilizing selectionon φ1 will push the population from point A towardpoint B, where the landscape is less steep and there-fore phenotype is more buffered against underlyingvariation.

the population, which is likely to change be-cause of random sampling if population size isreduced. We thus expect that moderate-sizedpopulations, even if they are large enough forselection to keep them near an optimal pheno-type contour, may well drift along the contouraway from points of maximum canalization.

Such developmental drift on a curved land-scape could facilitate speciation. Gavrilets(2003) and Gavrilets and Gravner (1997) haveemphasized the significance for speciation of“holey” adaptive landscapes. These are land-scapes on which the regions of highest fitnessare not isolated peaks but rather form a networkof interconnecting ridges. This is exactly whatwe expect for fitness landscapes over the spaceof underlying factors (Rice 1998, 2000). Here,the ridges of high fitness correspond to opti-mal phenotype contours. Temporarily isolatedpopulations that drift away from one anotheron an optimal contour can rapidly wind up onopposite sides of a fitness “hole.” If such popu-lations come back into contact (geographically,not on the phenotype landscape), hybrids will

not lie on the optimal contour and will be se-lected against.

Conclusion

We now have a fairly large catalogue of pro-cesses that in principle can lead to the evolutionof development and genetic architecture. Theseprocesses include all kinds of selection that actto change the shape of the phenotype distri-bution (e.g., selection for canalization, integra-tion, phenotypic plasticity, and evolvability) aswell as drift in development that may yield nochange in mean phenotype. Most, if not all,of these processes probably do influence de-velopmental evolution in natural populations.These phenomena—and others that are sure toarise—suggest that we will need to make somechanges both in the ways that we gather dataand the ways that we build theories.

Most of the data used in traditional evo–devo research comes directly from developmen-tal biology. It is thus largely concerned withspecific genes that have large effects when mu-tated in the lab and has little to say about thedistribution of genetic variation that actuallycontributes to phenotypic variation in naturalpopulations. The details of the distribution ofunderlying genetic and environmental varia-tion are even more important to understand-ing how the development of a trait evolves thanthey are to understanding the evolution of traititself. Empirical research in evo–devo may thushave to expand out of the lab and into the fieldmore than it has.

On the theory side: Phenotypic evolution-ary theory has been dominated by quantitativegenetics, which was made tractable and use-ful by minimizing the relevance of most of thephenomena that this review has discussed. Sev-eral innovative researchers have devised waysto apply the concepts of quantitative genet-ics to developmental evolution. However, thepresence of fourth moments in models for theevolution of even simple phenomena such ascanalization, and the asymmetrical effects ofcomplex developmental entanglement, make it


clear that a body of theory based on partition-ing phenotypic variance is inadequate for cap-turing the complexity of developmental evo-lution. We thus face the task of building acoherent and widely applicable mathematicalevolutionary theory that does not discount thecomplexity that we now know to underlie es-sentially all phenotypic traits.

Conflicts of Interest

The author declares no conflicts of interest.

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Theoretical Approaches to the Evolution of Development and Genetic · PDF file · 2012-06-01Theoretical Approaches to the Evolution ... evolution of genetic architecture. ... type