Entrevista Nº 1

Complex traits are assumed to be at least oligogenic—under the influence of a few genes of moderate effect—if not polygenic—under the influence of many genes of small effect (Hill, 2010). Interactions between (1) alleles at a locus, (2) alleles at multiple genes throughout the genome (epistasis), and (3) the genes and the environment in which they act (environmental interactions) also contribute to such phenotypes. Measuring phenotypic values in a population provides an estimate of both the overall mean and variation around this mean, which can then be partitioned into the different sources that contribute to phenotypic variance (VP):

!" = !%+ !'+ 2)*+%' + !%' (2.1)

VG includes variation due to: additive gene effects (VA), genetic effects that are not heritable

(VD), and interactions between the two (VI); !' encompasses sources of variation that arise from differences in the environment across the population; 2)*+%' represents any correlation

additive genetic variation (!,), differences in nutrition (!'), correlations between the two (2)*+%'; e.g., children who are judged to be more intelligent are often placed in advanced classes), and interactions between the two (!_%'; e.g., some children perform well on standardized tests used to “measure” intelligence while others are affected negatively by such pressure).

To determine the relative significance of the contributions of VG and VE to a phenotype’s

variance, its heritability is established. In the most basic of terms, this is simply the ratio VG/VP

and it describes the extent to which phenotypic variations are determined by genetic variations (broad-sense heritability, H2) within a generation. Of both greater interest to evolutionary biologists and more importance to this discussion is the narrow-sense heritability (h2), or the proportion of VP that is attributable to gene effects passed from parent to offspring (VA). For the

remainder of this dissertation I will use heritability to mean only narrow-sense heritability.

2.6.1 Basic Quantitative Genetic Parameters

For illustrative purposes I will use B and b to represent the alleles at a single biallelic locus. Three genotypes are observable at this locus in frequencies proportional to the population’s allele frequencies, given Hardy-Weinburg Equilibrium: BB, Bb, and bb. Each genotype is associated with a genotypic value (by convention, BB = +a, bb = -a, and Bb = d) such that the genotype confers a specific value to the individual’s phenotype. The genotypic value halfway between +a and -a is 0 and this is the value you would expect the Bb genotype to confer as the individual has one copy of each allele. If d = 0, the alleles are described as being additive because the relationship among genotypic values is linear and the heterozygote is located at the midpoint between the two homozygote genotypic values. If d ≠ 0 then the locus is said to exhibit dominance because the two alleles interact such that heterozygotes more closely resemble one of the two homozygotes, rather than being exactly intermediate between them (see Panel C, Fig. 2.14). The sign of d determines which allele is the dominant one.

Because dominance deviation is a property of allele combinations, it is not transmissible between generations. Only the effects of individual alleles can be inherited because each parent contributes only half the genotype. The contribution of an individual allele to a phenotype within a population is its average effect (αi) which is a function of a, d, the allele’s frequency in the

population, and the system of mating. The average effects of the alleles within a parent’s

gametes will determine how offspring differ from their population mean. The sum of the average effects of the two gene copies present in the diploid genotype is the breeding value (A), which is evaluated for all genes whose variation contributes to VP. The average squared breeding value

(VA) is the numerator for calculating h2.

Traits with a larger h2 value will have a greater degree of resemblance between parents and offspring. The slope of offspring P on the P of a single parent is ½h2 (one parent provides only half of the offspring’s genetic material) whereas the slope = h2 when the average parental P is the independent variable (Fig. 2.15). Siblings, especially full sibs, share common

environments, thus biasing h2 upward by overestimating familial resemblance. There are methods of accounting for this by including relatives of varying closeness.

2.6.2 The Breeder’s Equation and its Multivariate Equivalent

In addition to its use for evolutionary time scales, heritability is also an important parameter on shorter time scales as knowledge of breeding values can be used to make informed decisions in selective breeding populations. In fact, early 20th century agribusiness brought science to the art of food production by pioneering quantitative genetic methods (e.g., Hanson and Robinson, 1963; Turner and Young, 1969) and continuing to use them today (Miflin, 2000; Andersson and Georges, 2004). Heritability estimation has been an integral part of endeavors to change a population’s characteristics in an efficacious manner. In most cases, this change is to the

Figure 2.15 Ordinary Least Squares Regression of Offspring on Mid-Parent Values for Height at Withers in Horses (Equus caballus). The mean phenotypic value for all offspring of each parental pair is plotted on the Y-axis. The OLS equation is provided and the regression coefficient (b) is indicated in bold, red typeface. It is an estimate of the heritability of withers height in this sample (b = h2). Adapted from Oldenbroeck and van der Waaij (2015).

population’s mean phenotype, which is symbolized as R, the response to selection. As A is a major determinant of P, the equation describing the impact VA has on R is defined in the

Breeder’s Equation:

R = h

_S

where S is the force of selection applied to the phenotype in question. This means that, for example, the increase in milk yield (R) a dairy farmer is hoping to achieve in his/her next generation of Holsteins by selectively breeding high-yield cows (S) is a factor of the magnitude of heritable variation in milk yield. The difference in mean phenotype between the high-yield cows selected for breeding and that of unselected individuals (S) and knowledge of a trait’s h2 provides a way to estimate R. In an evolutionary sense, this is a valuable attribute of Equation 2.2 if formulating hypotheses about the potential selective forces applied is the goal.

The example used above describes the case in which selection acts upon a single trait. However, the reality is that traits co-vary because their function and developmental pathways are interrelated (see 2.5.2 Morphological Integration in the Cranium) and are co-inherited

because of linkage disequilibrium and pleiotropy (see 2.6.5 Methods for Conducting Quantitative Genetic Research). The implication of this covariance is that change in one trait will almost always produce a concomitant change in the traits phenotypically and genetically correlated with the true target of selection. To reflect this trait inter-relationship, Lande (1979) proposed a multivariate version of the Breeder’s Equation:

01 = 23 (2.3)

where Δz is a vector of changes in mean trait values, G is the additive genetic covariance matrix (explained in greater detail in 2.6.3 The G-matrix and What It’s Good For), and β is a vector of selection gradients, or the regression of relative fitness on the phenotype: 3 = 4567 . Taking the case of two traits, 1₆ and 1₈:

019 01: = 299 29: 2:9 2:: 39 3_: (2.4)

and multiplying through the multivariate Breeder’s Equation demonstrates how important genetic covariance is to trait evolution:

01

= 2

3

+ 2

3

01

= 2

3

+ 2

3

Any evolutionary change in a phenotype is the result of both direct selection on that trait—the first term in each equation—as well as indirect selection on any correlated traits—the second term. For this reason, understanding how individual components are correlated with one another, both at the phenotypic and the genetic level, is important to model complex trait evolution (e.g., Mezey et al., 2000; Wagner et al., 2008; Wagner and Zhang, 2011). That is a

create hypotheses about the significance of this covariation for craniofacial evolution in papionins.

2.6.3 The G-matrix and What It’s Good For

The G-matrix is a symmetric matrix with VA for each trait on the diagonal and additive genetic

covariance between traits ; and < on the off-diagonal (cov(=>=?)). Estimates of G are obtained by measuring phenotypic covariance (cov(@_>@_?)) in large populations of individuals of known

genealogical relationship and comparing the observed value to that expected based on amount of co-ancestry among individuals (Lynch and Walsh, 1998; Falconer and Mackay, 1996). This has been accomplished in a wide variety of animal taxa, ranging from frogs to sheep to guppies (e.g., Lofsvold, 1986; Brodie, 1993; Shaw et al., 1995; Vaez et al., 1996; Reznick et al., 1997; Arnold and Phillips, 1999; Roff and Mousseau, 1999; Cano et al., 2004; Sigurdsson et al., 2009). However, these conditions are rarely met in primates due to relatively long interbirth interval, gestation, and maturation and to reduction in the number of offspring produced per parturition. Hence, the more readily estimated matrix of phenotypic variances and covariances (P) is often used as a proxy for G (Cheverud, 1988; Roff, 1995, 1996; Waitt & Levin, 1998; Reusch & Blanckenhorn, 1998).

Cheverud and various coauthors estimated both P and G for the cranium in macaques (Cheverud and Buikstra, 1981; Cheverud 1982) and tamarins (Cheverud, 1996b). These were the first attempts at understanding whether most phenotypic variance is genetic. Resolution for Cheverud’s analyses was reduced because sample sizes (both census and effective, see 4.2.4 Sample Size Verus Effective Sample Size (Ne)) were relatively small and, in the case of the Rhesus macaques (Macaca mulatta) on Cayo Santiago, Puerto Rico, only matrilineal heritage was established. This increases standard errors for estimates of h2, limiting power and efficiency of the estimate. The extended pedigree research design used in this dissertation provides an

opportunity to estimate both G and P for a primate taxon’s craniofacial complex to unprecedented levels of precision. First, all genealogical relationships are known, which provides twice the information about co-inheritance patterns than would be true if only one parent were identifiable. Secondly, the census population size is large enough to ensure that power is sufficiently large to estimate quantitative genetic parameters. Consequently, I have the ability to answer questions about the genetic makeup and evolutionary history of the cranium in a species more closely related to humans than traditional biomedical mouse models.

Comparison between my results and corresponding ones for other taxa may provide insight into the general genetic makeup of the mammalian cranium as well as fodder for the development of more targeted research questions about our own evolutionary history.

2.6.4 Genotype-Phenotype Maps

As population-level variation is essential to evolution, understanding the evolutionary history of and potential for future change in a complex structure involves bridging the gap between developmental genetic mechanisms working at the individual level during ontogeny to produce adult phenotypes and the population-level variation in those phenotypes (Hlusko, 2004;

Hallgrímsson et al., 2007, 2009; Hlusko and Mahaney, 2009). Quantitative genetics provides a tool for statistically bridging genotype and phenotype, providing a method for both identifying the genes that underlie variation in complex traits and defining the GP-map. This “map” describes how genetic variation at each genomic locus is translated at the phenotypic level through the lenses of development and plasticity. Characteristics of the GP-map include descriptions of:

• pleiotropy: a single gene affecting multiple traits,

• epistasis: genetic variation in one gene influencing the phenotypic effects of other genes, • polygeny: many genes contributing to a single trait, and

• genetic modularity: non-overlapping suites of genes underlying different trait sets (Zeng et al., 1999; Shao et al., 2008; see Fig. 2.14).

The GP-map details how genetic variation influences phenotypic variation (Debat and David, 2001), how genetic correlations (i.e., the G-matrix) have evolved (Phillips and Arnold, 1999; Steppan et al., 2002), and the potential for genetic variation to yield adaptive change (Altenberg, 1995). For example, traits that are strongly genetically correlated will respond to indirect selection on each other (Lande, 1979; although see Gromko, 1995). If this response by both traits is adaptive, morphological change can occur more quickly than if the traits were uncorrelated and being selected for independently. However, the necessity of maintaining emergent functions of trait complexes means that evolution may be constrained if selection for one trait produces negative effects on a correlated trait. One way to circumvent this antagonism is through morphological redundancy, which may explain the evolution of the complex four-bar linkage system of wrasse (family, Labridae) jaws (Alfaro et al., 2005). Another way would be to develop genetic modularity whereby a set of genes has effects concentrated within a functional complex of characters more so than by chance. Mezey et al. (2000) found evidence for this in the ascending ramus of the mouse mandible—and that this region is independent from the alveolar region—which comprises half of the masticatory system.

2.6.5 Methods for Conducting Quantitative Genetic Research

Genes underlying variation within a complex trait can be identified by: (1) testing candidate genes that have been previously implicated in the etiology of the trait because of knowledge of developmental processes, metabolic pathways, and/or functional analyses or (2) scanning the genomes of a large number of individuals who demonstrate a range of phenotypic variation in the trait. Because the first approach starts with a proposed candidate gene(s), it is considered hypothesis testing. In systems where the anatomy and physiology are well studied, this is an appropriate and preferred approach because power is greater when testing smaller genomic stretches and powerful haplotype tree approaches can be utilized (e.g., Templeton et al., 2005).

In contrast, the second approach makes no assumptions about putative involved biological processes and is hypothesis-generating. The benefit of such an approach is that it identifies previously unidentified genomic loci that can then be tested with more targeted, candidate gene- based approaches (Borecki and Suarez, 2001).

Regardless of methodological specifics, the basic premise underlying all methods of dissecting the genetic basis of complex traits involves demonstrating an association between a locus and the trait. Both linkage and association can be used to test candidate genes and perform genome scans. The available data will determine the type of analysis conducted: association studies identify relevant genetic variants using population data while pedigree studies identify loci that co-segregate with phenotypes within families. If the data and resources are available, both can be used in conjunction to clarify the genetic basis of a trait, as the methods will likely produce complementary, rather than identical, results.

When a pair of alleles appears together more often than expected based on random assortment, given the degree of relatedness among individuals, they are in linkage

disequilibrium (LD). Linkage disequilibrium is a violation of Mendel’s Law of Independent Assortment, which states that both genes and alleles are split between germ cells at random (i.e., probability = 0.5) during meiosis. The research sample used in my dissertation was derived from a colony of baboons with a unique population history that lends itself well to linkage

analysis. Two loci can demonstrate LD if they are physically close on a chromosome—the likelihood of a recombination event splitting a chromosome between loci during meiosis increases with increasing distance between a pair of loci. In other words, recombination is a function of distance between loci. In fact, the unit of measure for recombination is the centiMorgan (cM), which is defined as the distance between two loci for which the expected

Production of LD depends on a population’s history of mutation, and it is destroyed by recombination. The founder population was a hybrid population of Anubis and yellow baboons, which would produce high levels of LD among genetic loci. Parental type gametes for a pair of genetic loci would contain anubis alleles at both loci (AA) or yellow alleles at both loci (YY), giving complete LD. Independent assortment of the loci would produce the two contrasting gamete types in equal number (AY or YA), destroying the LD. If the loci in LD are genetically closely linked, they will remain in LD for many generations because recombination between them is low. A locus used as a molecular marker will retain LD with a linked locus that effects the phenotypic variation of interest.

Recombination frequency varies across an individual’s genome (Sturtevant and Beadle, 1936), between sexes (Morgan, 1914), and among species (e.g., Ptak et al., 2005) so genetic map distances are not equivalent to physical map distances, or the actual number of base pairs along a chromosome. Linkage analysis is performed by measuring phenotypes within families, typically parent-offspring trios but complex pedigrees with many different types of familial relationships can be used as well (Elston and Stewart, 1971), and scanning the species genetic map of marker loci to calculate a LOD score at each locus (Morton, 1955). A LOD score is the logarithm of an odds ratio, the ratio of:

the probability of observing the specific genotypes in the family given linkage at a particular recombination fraction versus the same probability computed conditional on independent assortment. Thus, high values of the odds ratio would favor the linkage hypothesis, while values close to 1 provide evidence against linkage.

-Borecki and Suarez (2001, p 50) The control predctions of independent assortment are a function of relatedness and

6, in which methods and results are given that describe how I applied linkage mapping to the questions posed in my research.

Whereas linkage mapping is based on the notion of recombination at a more individual level, association analysis relies on the population-level concept of linkage disequilibrium. If two loci are not linked, and thus are following Mendel’s Law of Independent Assortment by randomly assorting into gametes, the frequency of each possible pair of alleles at two or more loci (a haplotype) should be a function of the allele frequencies at each locus. For example, for loci X and Y with allele frequencies p and q at each, the population should contain the following nine genotypes: 1. XXYY = pX2pY2 2. XXYy, XXyY = 2pX2pYqy 3. XxYY, xXYY = 2pXqxpY2 4. XXyy = pX2qy2 6. xxYY = qx2pY2 7. Xxyy, xXyy = 2pXqxqy2 8. xxYy, xxyY = 2qx2pYqy 9. xxyy = qx2qy2

5. XxYy, xXYy, xYyY, XxyY = 4pXqxpYqy

If the observed frequency of genotypes is greater than expected, the two loci are in LD and, thus, recombination has not yet disassociated the two. The stronger the linkage (i.e., the closer two loci are on a chromosome) the longer LD will persist in a population. Genetic drift, migration, admixture, and rapid population expansion can all affect patterns of LD. Marker loci that

demonstrate evidence for linkage/association are not necessarily, and indeed are rarely, the genetic variants that contribute to trait variation. They simply bookmark the stretch of DNA in which this contributory variant (or variants) can be found, meaning the list of genes and regulatory sequences between the linked marker loci is a list of candidate genes to be further tested directly for association with the phenotypic variation.

2.6.6 Going a Step Further: Identifying Quantitative Trait Loci (QTLs)

Advances in next generation sequencing technology since the publication of the draft human genome sequence in 2001 have made it possible to obtain large amounts of genetic data for both non-model organisms and wild populations (Rogers et al., 1999; Joly and Faure, 2015). With the ability to sequence many individuals, we have produced genetic linkage maps for multiple taxa (e.g., O’Brien, 1990; Auton et al., 2012; Liu et al., 2014; Van Oers et al., 2014), providing a key component in the identification of genetic variants responsible for morphological variation. Using these genetic maps and the methods described in 2.6.5 Methods for

Conducting Quantitative Genetic Research, quantitative trait loci (QTLs)—regions containing genetic variation that is correlated with variation in the measured trait of interest—can be located within the genomes of a study population (Lynch and Walsh, 1998). One of the greatest benefits of using a quantitative genetics approach in this manner is that it allows us to work backward from population-level cranial variation to the responsible genetic loci (see discussion on top-down approaches in 2.2.5 The Role of Continuous Variation in Evolutionary Process). Hypotheses about the evolutionary importance of these genetic variants can then be formulated and subsequently tested in other populations and taxa.

Quantitative genetic methods have identified QTLs affecting craniofacial, mandibular, and dental morphology in the commonly used mammal model, the house mouse (Cheverud et al., 1997; Leamy et al., 1999, 2008; Workman et al., 2002; Ehrich et al., 2003; Cheverud et al., 2004; Klingenberg et al., 2004). Pleiotropic QTLs, a large number of QTLs, variable

environmental effects, and a generally small effect size for each QTL are common findings, all