Quantative Genetics and Evolution

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Quantitative Genetics and Evolution

Abstract

Today,evolution is a unifying concept in biology. A century and halfago,

Darwin developed the theory of natural selection, and proposed it as the main mechanism of evolution. A quantitative approach to the study of evo-lution required new theoretical developments in population and quantita-

tive genetics. Here, I review the basic concepts of quantitative genetics neccessary to understand microevolutionary change. Natural selection is a consequence of differences in fitness (reproductive success) between individ-uals in a population. But natural selection is not equal to evolution. In or-

der to achieve evolutionary change, variation in fitness must be heritable, i. e. it must be transmited by genes from parents to offspring. Besides fitness differences, individuals within a population often differ in many other characters (morphological, physiological and behavioural) which are also genetically transmited from generation to generation. It is crucial to distinguish the process of selection which operates in an existing generation from

the evolutionary change which is visible in the next generation. Most concepts of quantitative genetics centre around variances and covariances, and include the evolutionary potential of a population or heritability (ratio of

additive genetic variance and phenotypic variance), the strength of selectionon a particular trait (covariance of particular trait and fitness), the total

strength of selection (phenotypic variance in fitness) and evolutionary response (phenotypic change in the next generation) which can be predicted by breeder’s equation.

HISTORICAL BACKGROUND

On the 24th of November 1859, Charles Darwin published his fa-mous and most influential book The Origin of Species (1). From that

point on biology was not the same. In The Origin of Species he thor-oughly developed the theory of natural selection providing numerousempirical and experimental examples which support natural selectionas the mechanism of evolution. Natural selection is a consequence of variation in fitness (reproductive success) between individuals in a pop-ulation. The existence of variation in fitness is a prerequisite but notsufficient for evolution to occur. Another essential requirement leading to evolutionary change is that fitness as a trait is inherited throughgenes from parents to offspring. Evolution can be viewed as the changeof allelefrequencies (classical population genetics), as the changeof themean phenotype and variance in a population (quantitative genetics),and as the rate of allele substitutions in a population (molecular popu-lation genetics). The first two aspects concern short-term evolution(microevolution), whereas the latter concerns long-term evolution (ma-croevolution). In this review I will describe the basic concepts of quan-titative genetics required to understand microevolutionary change.

KRUNOSLAVBR^I]-KOSTI]

Laboratory for Evolutionary GeneticsDepartment of Molecular BiologyRu|er Bo{kovi} Institute, Zagreb, CroatiaE-mail: [email protected]

Received January 29, 2010.

PERIODICUM BIOLOGORUM UDC 57:61 VOL. 112, No 4, 395–402, 2010 CODEN PDBIAD

ISSN 0031-5362

Overview



Quantitative genetics was developed as a solution tothe debate between two opposing views on evolution andthe mechanism of inheritance (2). According to salta-tionism evolution was viewed as very fast and an abrupt

process visible through the change of Mendelian (sim-ple) traits. Mendelian traits are determined by a singlegene with large allelic effects on phenotype, and almostno environmental influence. Such phenotypes are quali-tative in nature (they are verbally described), and aresuitable to standard genetic analysis. In contrast, gradu-alism assumed that evolutionary change is gradual, andthat it is a consequence of selection on quantitative traits.Such traits (body size, antipredator behaviour, fitnesscomponents etc.) are expressed as quantities in particu-lar units. At that time, both saltationists and gradualistsbelieved that Mendel’s particulate theory of inheritancecan be applied only to simple traits. The inheritance of

quantitative traits on the other hand, are beleived to fol-low different laws connected with the action of fluids(blending inheritance). In his seminal work Fisher sho-wed that inheritance and variation in quantitative traitscan be explained by simultaneous segregation of manyMendelian factors (genes) (3). Consistant with this, quan-titative (complex) traits are determined by many geneswith very small allelic effects, but with substantial envi-ronmental influence on phenotype. Since inheritanceand variation in quantitative traits are based on the ag-gregate action of many loci, they are described by statisti-cal terms (means and variances) without informationabout the individual effectof anygivenlocus. Phenotypicvalues for most quantitative traits are normaly distrib-uted around a mean, and in theoretical quantitative ge-netics normality is always assumed. Besides its origin inthe field of evolution, the important application of quan-titative genetics is primarily in the field of animal andplant breeding whichgreatly stimulatedits development.

Darwin introduced the verbal concepts of evolution,and he noticed that two visible manifestations of evolu-tion are genetic variation and evolutionary change. Todescribe evolution quantitatively, we must introduce thebasic theoretical concepts of quantitative genetics (4, 5,6) which are incorporated in quantitative genetic equa-tions. From these equations we will understand the rela-

tionships between evolutionary change, genetic varia-tion and the process of selection.

CONCEPTS

Genetic basis of quantitative trait

If a quantitative trait is transmited by genes from par-ents to offspring, then we expect that parents with highertrait value will give offspring with higher trait value, andvice versa. In contrast, if a trait is not genetically trans-mited, then the offspring of the parents with any traitvalue will have similar (population mean) trait value.The equation which connects the average trait value of particular offspring with the average trait value of theirparents (midparent value) is the regression equation

Y = (1 –h 2) M + h 2 X (1)

Y is the average phenotypic value of offspring from par-ticular parent pair, X is the average phenotypic value of a

parent pair (midparent value), M is the average pheno-typic value of parental population (population mean),and h 2 is heritability of a trait (slope of regression line).Heritability is the ratio of additive genetic variance andtotal phenotypic variance, and its meaning will be fullydescribed later. Phenotypic variances and covariances areessential in quantitative genetics, and before further con-sideration it is useful to define them. From elementarystatistics we know that

V n

x x x x x ii

n

= − = −=

∑1

2

1

2 2( ) ( )

cov ( )( ) ( )( ) xy i ii

n

n x x y y xy x y= − − = −=∑

1

1 (2)

where xi and yi are the phenotypic values of i-th individ-ual, x and y are the mean population values for traits xand y, and n is the number of individuals in a population.The variance of a trait x, V x is a measure of variation in apopulation, andrepresents the mean square deviation, ormean square minus square of the mean. The covariancebetween traits x and y, cov xy is a measure of the linear re-lationship between two traits, and represents the meanproduct deviation, or mean product minus product of themeans. If variance and covariance are estimated from apopulation sample, then in the upper formulas instead of 1/ n we use 1/( n-1).

Decomposition of the phenotype

Each individual in a population has its own pheno-typic value which can be measured. Phenotypic valuecan be decomposed into casual components (5, 6). First,the phenotypic value P isthe sum ofthe effects ofa geno-type andenvironment. In the simplest case, when there isno covariance between genotype and environment, P =G + E, where G is a genotypic value and E is an environ-mental deviation. Since environmental deviation is ran-dom, the mean environmental deviation in a large popu-lation is equal to zero, and the mean phenotypic value isequal to the mean genotypic value. Second, the geno-typic value of a particular individual (or genotype) G isthe sum of different genetic effects. One is transmissionof genes between generations, and the other are allele in-teractions (dominance and epistasis). According to this,we have that G = A + D + I , where A is a breeding value(genic value or additive phenotype), D is a dominancedeviation, and I is an interaction (epistatic) deviation.

Among the components of genotypic value, only thebreeding value is essential for evolution since it measuresthe potential of a particular individual (or genotype) tochange the population mean in the next generation.

In order to understand themeaning of breeding value,we will consider a simple genetic model introduced byFisher (3). It assumes that genotypic value is affected byasingle locus with two alleles. In such a situation there is

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K. Br~i}-Kosti} Quantitative Genetics and Evolution



no effect of epistasis, and contribution of a single locus togenotypic value is G = A + D. The genotypic values forthree genotypes are A1A1 ( a), A1A2 ( d ) and A2A2 (- a),whereas allele frequencies are A1 ( p) and A2 ( q). Let us

assume that the A1 allele increases and A2 allele de-creases the trait value. The genotypic value of a heterozy-gote d reflects the degree of dominance. To clearly distin-guish breeding value from genotypic value let us assumethat in this particular example the A1 allele is dominantover the A2 allele. This means that both the »good«homozygote (A1A1) and the heterozygote (A1A2) havethe same genotypic value equal to a. Before defining thebreeding value, we should introduce the concept of theaverage effect of an allele (Figure 1). Let us assume weperform two crosses. In the first, the male of A1A1 ho-mozygote mates with a random sample of females from apopulation, whereas in the second, the A1A2 heterozy-

gote mates with a random sample of females from a pop-ulation. The mean genotypic value in a population be-fore the cross is M , after the homozygotic cross M’, andafter the heterozygotic cross M’’. The change of the pop-ulation mean in the next generation D M’ = M’ – M islarger than D M’’ = M’’ – M . The reason is obvious be-cause the homozygote always gives a »good« allele (A1)to its progeny, whereas the heterozygote gives a »good«allele (A1) only to half of its progeny. The change in thepopulation mean as a cosequence of transmission of anallele from a particular individual (or genotype) is calledthe average effect of that allele. From the homozygoticcross the average effect of allele A1 is a1 = D M’, whereasthe mean average effect of alleles from the heterozygotic

cross is a12 = D M’’. The breeding value of the individual(or genotype) A1A1 is A11 = 2D M’, whereas the breeding value of the individual (or genotype) A1A2 is A12 =2D M’’. It is twice the average effect of an allele since eachindividual (or genotype) has two alleles, but gives onlyone to its progeny.

If we know the average effects of both alleles in thege-notype, then thebreedingvalueof this genotype is simplythe sum of the average effects of its alleles (5). It is impor-tant to note that genotypic value is a constant quantity(for particular environment), whereas the average effectof allele and the breeding value are relative quantitieswhich are dependent on the referent population, i. e. on

its allele frequency. This means that a particular individ-ual (or genotype) always has the same genotypic value,but has different breeding values in different popula-tions. Also, from the above example it is obvious that in

the case of complete dominance, the dominant homozy-gote and heterozygote have the same genotypic values,butdifferent breeding values. It canbe shown that the av-erage effects of alleles A1 and A2 expressed as deviationsfrom the population mean are

a1 = q [ a + d ( q – p)]

a2 = – p [ a + d ( q – p)] (3)

The corresponding breeding values of the three geno-types A1A1, A1A2 and A2A2 are

A11 = 2a1 = 2 q[ a + d ( q – p)]

A12 = a1 + a2 = ( q – p)[ a + d ( q – p)]

A22 = 2a2 = –2 p[ a + d ( q – p)] (4)

In all of theabove formulas, there is a common factor(insquare brackets) which is called the average effect of allelesubstitution a. Its meaning is a = a1 – a2 = a + d(q–p).

After defining the breeding value, we can understand the meaning of the dominance deviation. It is the difference between genotypic value and breeding value D = G – A. Ac-cording to the above model, the dominance deviations of the three genotypes are

D11 = –2 q2 d

D12 = 2 pqd

D22 = –2 p2 d (5)

It is important to note that breeding value and domi-nance deviation are statistical descriptions, and that bothare dependent on allele frequencies. In addition, thebreeding value depends on the genotypic values a (ho-mozygote) and d (heterozygote), whereas dominancedeviationdepends only on d (heterozygote). If there is nointeraction (dominance) between alleles, then genotypicvalue is equal to breeding value.

Partitioning the variance

After decomposition of the phenotype, we can pro-ceed with the study of phenotypic variation and the vari-ation in its components. If we know the phenotypic val-ues of individuals in a population, we can estimate thephenotypic variance V P. Phenotypic variance is the totalvariance in a population, andas with phenotypic value, itcan be partitioned into casual components (5, 6). A par-ticular theorem of random variables states that varianceof the sum is equal to the sum of variances. Since phe-notypic value is thesum of its components, it follows thatV P = V G + V E, where V G is genotypic variance (total ge-netic variance) and V E is environmental variance. Simi-larly, genotypic variance can be further partitioned, andwe have V G = V A +V D + V I . These components are thevariance of breeding value V A, the variance of dominancedeviation V D and the variance of epistatic deviation V I .

Period biol, Vol 112, No 4, 2010. 397

Quantitative Genetics and Evolution K. Br~i}-Kosti}

Figure 1. Average effect of allele – Two individuals (genotypes A1A1 and A1A2) with the same genotypic value (a) have different poten-

tial to change population mean genotypic value (M). The mean progeny genotypic value of the homozygotic cross is M’ and of heterozygotic cross is M’’. For details see the text.



Evolutionary significancelies with the variance of breed-ing value V A, andit is called the additive genetic variance.

Additive genetic variance is part of the phenotypic vari-ance caused by transmission of genes to the next genera-

tion. According to the above model, in the absence of epi-stasis, we have V G = V A + V D. It can be shown that addi-tive genetic variance anddominancevariance are equal to

V A = 2 pq [ a + d(q – p) ] 2=2pqa 2

V D = (2 pqd) 2 (6)

Both variances are dependent on 2 pq which repre-sents the equilibrium heterozygosity, and is a measure of genetic variation in classical population genetics. Addi-tive variance depends on both genotypic values (homo-zygotes and heterozygotes), whereas dominance varian-ce depends only on thegenotypic value of heterozygotes.

Additive genetic variance is often expressed as he-ritability, or the ratio of additive genetic variance and to -tal phenotypic variance

hV

V

A

P

2 = (7)

Heritability represents a proportion of total phenoty-pic variance attributable to the transmission of genesfrom parents to offspring. It is a measure of the evolu-tionary potential of a population. The reason for this liesin the fact that genes are inherited between generations,whereas gene interactions are not. Gene interactions areproperties of genotypes which are de novo formed in each

generation. Heritability is sometimes called narrow sen-se heritability to distinguish it from the so called broadsense heritability (degree of genetic determination of atrait) which is the ratio of genotypic variance and phe-notypic variance, H 2 = V G / V P.

Breeder’s equation

As we mentioned earlier, two essential requirementsfor evolutionary change to occur are the presence of ge-netic variation in a population and the action of evolu-tionary force, i. e. natural selection or genetic drift. Wewill here consider Darwinian evolution by natural selec-tion. More precisely, we will deal with a particular type of

natural selection called directional selection (Figure 2).Directional selection operates on fitness itself and itscomponents (life history traits), as well as on other quan-titative traits which are (in a particular environment)positively correlated with fitness. Under the term fitness

we assume standardized fitness which is called relativefitness. Onetype of directional selectionis artificial selec-tion where the breeder wants to increase (or decrease) thepopulation mean of a particular quantitative trait. To

achieve this, the breeder in each generation selects indi-viduals with high (or low) trait value as parents for thenext generation. Thefinal consequence of directional se-lection is fixation of the »best« allele of the locus, and thestable equlibrium allele frequency is p = 1 and q = 0 (or

p = 0 and q = 1) (7). At the level of change of allele fre-quency the general selection equation is

∆ p pq p w w q w w

w=

− + −[ ]( ) ( )11 12 12 22(8)

This equation describes the unit change of allele fre-quency D p (between two successive generations) due toselection. The w11, w12 and w22 are the fitnesses of A1A1,

A1A2 and A2A2 genotypes respectively, whereas w is themean fitness of a population. Two important inferencescan be drawn from this equation. First, it is visible thatselection is based on fitness diferences between individu-als (genotypes), and second, that evolutionary change isfaster when genetic variation in a population is larger, i.e. when p and q tend to have intermediate values.

To derive an analogous equation which shows theunit change of mean phenotype (between two successivegenerations) in a population dueto selection, we must goback to the regression equation. In its original sense, itrelates the mean phenotype of particular offspring withthe mean phenotype of their parents (midparent value).

It can also relate the mean phenotype of all individuals inthe offspring generation (all offspring of all parents) andthe mean phenotype of all parents (8, 9). Now we have

Y h Y h X t t t+ = − +1

2 21( ) (9)

where Y t + 1 is the mean phenotype of offspring genera-

tion, Y t is the mean phenotype of parent generation (allindividuals) and X

tis the mean phenotype of the indi-

viduals selected as parents. To obtain the breeder’s equa-tion in its recognizableform, the upper equation must berearranged

Y Y h X Y

Y Y h X Y

R h S

t t t t

t t t t

+

+

= + −

− = −

=

1

2

1

2

2

( )

( ) (10)

In the breeder’s equation, S is the strength of selectioncalled selection differential which is the difference be-tween the mean phenotype of selected individuals (par-ents) and the mean phenotype of the population beforeselection (all individuals) (5, 6). Heritability h2 is the ge-netic variation attributable to the additive effects of ge-nes. Finally, R is the evolutionary change called the re-sponse of the population to selection, or evolutionaryresponse. It represents the difference between the meanphenotype of offspring of the selected parents and themean phenotypeof thepopulation beforeselection (5, 6).The above description gives us one meaning of the selec-



Figure 2. Relationship between trait and fitness reflects the type of natural selection – On the left, there is a linear relationship between

trait and fitness (directional selection), in the middle (stabilizing se-lection) and on the right (disruptive selection) the relationship between trait and fitness is nonlinear (quadratic).



tion differential. It does not tell us anything about the re-lation of a particular trait and fitness. It is intuitive for ar-tificial selection (truncation selection) when individualsare selected if their phenotypic value is equal or higher

than the determined value (truncation point). It is alsointuitive for strong natural selection which acts at thelevel of viability, i. e. when the population experiences ahigh mortality rate due to environmental factors. In thisscenario, the selection differential can be estimated as thedifference between the mean phenotype of survivors andthe mean phenotype of all individuals (before selection).In most real situations natural selection is not so strong,andis manifested through the actionof both viability andfertility. When differences in fertility are more importantfor fitness, the above meaning of selection differential isnot so intuitive although it is correct. For such a scenario,we will apply a different definition for selection differen-

tial, and will arrive at a simple and intuitive expressionwhich relates a particular trait with fitness.

Fundamental theorem of naturalselection

Let us assume that selection on a trait x operates dueto differences in fertility. Since the contribution to thenext generation will vary among individuals, the differ-ence between the phenotypic value of a particular indi-vidual and the population mean must be weighted by thefitness of this individual. Then, the selection differentialis defined as

Sw x x

n x

i ii

n

= −=∑ ( )1(11)

where wi is the fitness of i-th individual, xi is the pheno-typic value of i-th individual, x is the mean phenotypicvalue of a population, and n is the number of individualsin a population (5). The upper expression can be rear-ranged in the following way

S

w x

n

w x

n

w x

nx

w

n

S wx

x

i ii

n

ii

n

i ii

n

ii

n

x

= − = −

= −

= = = =∑ ∑ ∑ ∑

1 1 1 1

( )( ) covw x wx=

(12)

It implies that selection differential operating on atrait x is equal to the phenotypic covariance between trait

x and fitness (10, 11, 12). This is intuitive and logicalconclusion since the primary target for natural selectionare fitness differences. It is important to note that bothmeanings of selection differential are mathematicallyequivalent (13), and that they only refer to differentpoints of view. The strength of selection is sometimes ex-pressed as the intensity of selection which is the stan-dardized selection differential scaled by phenotypic stan-dard deviation (5, 7) or by phenotypic variance (9). Selec-tion intensity is useful for comparing the strength of se-lection between different traits.

Since the primary target of selection is fitness, it is im-portant to describe the selection differential for fitness it-

self, andthe rate of change in population mean fitness. Inorder to define selection differential for fitness, we canapply the same logic. We have

S

w w w

n

w

n

w w

n

S

w

n

w

i ii

n

ii

n

ii

n

w

ii

n

=−

= −

= −

= = =

=

∑ ∑ ∑

∑

( )1

2

1 1

2

1w

w

nw w

S V

ii

n

w Pw

=∑

= −

=

1 2 2( ) (13)

The selection differential for fitness is equal to thephenotypic variance of fitness in a population. It is alsoknown as the opportunity for selection (14). To expressthe change of mean fitness between two successive gen-erations as a result of natural selection, we will apply the

breeder’s equation to fitness as a trait (5). We have there-fore that

Rw = h 2wSw = h 2

wV Pw

Rw = V Aw (14)

This expression is called the fundamental theorem of natural selection, and was discovered by Fisher (4). Thechange of mean fitness in a population due to natural se-lection between two successive generations is equal tothe additive genetic variance of fitness in previous gener-ation. Fisher’s original statement was slightly differentand somewhat obscure (4).

Multivariate evolutionThe breeder’s equation concerns selection of a single

trait. In reality there are many traits which are under nat-ural selection. Some of these traits are correlated. Onecan distinguish genetic correlation (correlation betweenbreeding values) from phenotypic correlation (correla-tion between phenotypic values). There are two causes of genetic correlations. The first and most common cause ispleiotropy which means that the same locus determinestwo (or more) traits. The second is linkage disequilib-rium which is a consequence of selection for particularallelic combinations of two (or more) loci which affectdifferent traits. If two traits ( x and y) are genetically cor-

related andnatural selectionacts on trait x, weexpect twoconsequences. Oneis a direct evolutionary response on atrait x, and the second is an indirect (correlated) evolu-tionary response on trait y. The selection differential of aparticular trait measures the net effect of selection causedby different factors (direct and indirect). An importantquestion is how to distinguish the direct strength of se-lection on a particular trait from indirect (correlated)strength of selection on the same trait. Based on Pear-son’s regression theory, Lande and Arnold showed thatthe partial regression coefficient of fitness on any traitvalue is a measure of the strength of direct selection onthis trait. This measure is called the selection gradient,and is designated as b (15). Avoiding details, we will justsummarize the most important equations concerning multivariate evolution, and their meanings (6, 7, 8, 15).





First, we will write the breeder’s equation on a singletraitemphasizing that heritability is the ratio of additive vari-ance and phenotypic variance

R=V AV P –1

S (15)

The multivariate analogue of the breeder’s equationcan be written in matrix algebra as

R

R

V

V

V x

y

Ax Axy

Axy Ay

Px Pxy

Pxy

=

cov

cov

cov

cov V

S

S Py

x

y

−1

(16)

The left side term is called the vector of selection re-sponses, and is designated as R . On the right side, thefirst term is the matrix of genetic variances and covarian-ces, or G matrix; thesecond is the inverse of the matrix of phenotypic variances and covariances, or P–1 matrix; andthird is the vector of selection diferentials, or S. Equation

(16) can be written as

R = G P–1 S (17)

Conveniently the product of the inverse of the P ma-trix (P–1) and S is called the vector of selection gradients,andis designated asb. According to this, the multivariateselection equation is often written as

R = G b (18)

If the covariance term in the G matrix is equal to zero,then the two traits evolve independently and evolution of each trait canbe described by thesingle trait breeder’s equa-tion(Figure 3). The multivariate breeder’s equation for two

traits can be written by using the ordinary algebra as

R x = V Ax b x + cov Axy b y

R y = V Ay b y + cov Axy b x (19)

The selection gradient b for a particular trait is

b

b

x

Py x Pxy y

Px Py Pxy

y

Px y Pxy x

P

V S S

V V

V S S

V

=−

−

=−

cov

cov

cov

2

x Py PxyV − cov2

(20)

We must again emphasize that selection diferential S

measures the net effect of selection (all factors, i. e. directand indirect), whereas the selection gradient b measuresonly the direct effect of selection on particular trait. In or-der to estimate b, we need to have estimates of selectiondiferentials (S x and S y), phenotypic variances (V Px andV Py), and phenotypic covariance cov Pxy. Natural selectioncan be visualized by individual fitness surface (selectionsurface) which represents the relationship between phe-notypic values and corresponding individual fitness (16).Hypothetical individual fitness surface for two traits ispresented in Figure 4. The empirical shape of the fitnesssurface, i. e. local average slopes (linear or directional se-lection) and local average curvatures (nonlinear selec-tion – stabilizing or disruptive selection) can be studiedby the multiple regression approach in order to estimatepartial regression coefficients (selection gradients) (16).

EVOLUTION IN THE REAL WORLD

In order to predict the evolutionary response accord-ing to breeder’s equation, one should have an estimate of heritability. After many generations under directional se-lection, heritability is no longer constant since selectionerodes the additive variance and the heritability of a trait.For a certain number of generations (15–20 generationsfor a typical artificial selection experiment) there is nochange in heritability, and the response is relatively con-stant (short-term response) (5). For further prediction of the response (long-term response), a new estimate of heritability is required. For the prediction of a multiva-riate evolutionary response it is necessary to have esti-mates of genetic variances and covariances, as well as se-

lection gradients. Empirical results from selection of asingle trait imply that the breeder’s equation correctlypredicts the response to selection. In contrast, the re-sponses to selection on multiple traits are less consistentwith the current theor y. A possible explanation for this isthat the multivariate model assumes multivariate nor-mality which is often biologically inconsistent (9). Herewe will briefly consider some examples of evolution innatural populations, as well as experimental evolutiondriven by artificial selection on quantitative traits.



Figure 3. Relationship between breeding values of trait x and y – On the left, there is no covariance between two breeding values (each trait evolves independently); on the right, there is positive covariancebetween two breeding values (correlated evolution). Spots represents

hypothetical individual breeding values of traits x and y.

Figure 4.Hypothetical individual fitness surface – The individual fitness value in a populationis a function of the phenotypicvalues for

traits x and y.



Evolution by natural selection

Lande and Arnold studied the effects of natural selec-tion on morphological characters in the pentatomid bug

Euschistus variolarius. They collected 94 bugs after a storm(39 survived and 55 died), and measured four morpho-logical traits on all bugs (15). From this data they esti-mated phenotypic variances and covariances according to equation 2. The selection differential for a particulartrait was estimated as the difference between the meantrait value of surviving bugs and the mean trait value of allbugs,whereas theselection gradient was estimatedac-cording to equation 20. They found no significant chan-ge in thorax width as indicated by selection differential.In contrast, the selection gradient indicated strong directselection for increased thorax width. The thorax width ishighly positively correlated with another trait, wing length.The selection gradient for wing length indicated strong

direct selection for decreased wing length. Therefore, theabsence of significant change in thorax width representsthe net effect of a strong direct increase in thorax widthand strong indirect (correlated) decrease in thorax widthdue to strong direct selection for decreased wing length.They also noticed that scutellum length decreased signif-icantly as indicated by the selection differential while theselectiongradient wasnot significant. From this, it canbeconcluded that a significant selection differential on scu-tellumlenght is a consequence of the correlated selectionon scutellum length due to direct selection on other traits(thorax width and/or wing length).

Grant and Grant studied the evolution of morpholog-ical traits in Darwin’s medium ground finch Geospiza

fortis from the Galapagos islands (17, 18). Several speciesof Galapagos finches have been the research subject of Charles Darwin, and inspired him in the development of his ideas about evolutionary change. The normal diet of Galapagos finches includes various types of seeds, fromlarge hard seeds to small soft seeds. The type of availableseeds is determined by the amount of rainfall. The abilityof a bird to handle a particular type of seed depends onthe characteristics of its bill. Two periods, 1976 – 1977and 1984 – 1986, were characterized by a severe drought,and the Grants measured the survival of G. fortis overthese periods. During the first period only 15% of birds

survived, and the survivors were larger birds. During thesecond period 32% of birds survived, and the surviving birds were slightly smaller. The selection differential forbody weight during the first period was larger than theselection gradient, although both tended to increase bodyweight. The difference between them represents the stren-ght of correlated selection since body weight is positivelycorrelated with several other morphological traits whichwere directly selected to increase their phenotypic values.Interesting behaviour during the first period showed se-lection for bill width. The selection differential tended toincrease the bill width whereas the selection gradienttended to decrease it. This can be explained by correlatedselection which tended to increase bill width due to di-rect selection on other morphological traits (bill depth,wing length and weight). During the second period the

selection differential for bill length was weak and nega-tive (statistically not significant) whereas the selectiongradient was strong and positive. The selection differen-tial for bill length can be explained by correlated selec-

tion on other traits which had small and weak selectiongradients. TheGrants also predicted the evolutionary re-sponses for several traits (equation 16 or 19), and com-pared them with the observed responses (difference be-tween the mean phenotypic value of the progeny of surviving birds and the mean phenotypic value before se-lection). Theobserved selectionresponseswere in a goodagreement with theoretical predictions, especially for thefirst period (1976 – 1977) when natural selection wasstronger (18).

Evolution by artificial selection

Finally, I will mention two examples of experimentalphenotypicevolution driven by artificial selection. One isthe artificial evolution of behaviour in silver fox, a rarenaturallyoccuringvariety of red fox Vulpes vulpes,andtheother is artificial evolution of oil content in the maize Zea

mays. Selection experiments with silver foxes started in1959, and were led by the Russian geneticist Dmitry K.Belyaev. In addition to its scientific purpose, the experi-ment was also motivated by the Russian fur industrywhich prefered tame animals for routine handling. The-refore the target for selection was tameness, a behavioraltrait which is normally present in juvenile animals. Inthe original (wild) population, the vast majority of foxesshowed fear and/or aggresion towards humans, whereas

a small fraction was more or less tolerant to humans.These tolerant animals were selected as parents of thenext generation. The fox behaviour was quantified ac-cording to the degree of tameness, and in each genera-tion animals with higher degreeof tameness were furtherselected. The response to selection was very strong in theearly generations, and after several decades of selectionthe end product was a unique population of domesti-cated foxes which are fundamentally different in manyaspects from their wild counterparts. They are devoted,affectionate and capable of forming strong social bondswith people. In addition to large changes in behaviour,the domesticated foxesevolved many new characteristics,i. e. piebald coat colour, rolled tails, floppy ears andchanges in reproductive cycle accompanied by changesin hormone levels. It follows that direct selection on a be-havioural trait caused correlated selection responses tovarious morphological, physiological and life history traits(19, 20). The fur industry was not satisfied with these re-sults since the fur of domesticated foxes was in many as-pects different from the fur of wild silver foxes, and wascommercially useless. Most important were the scientificimplications of the results. This experiment showed thatthe process of domestication could be much faster thanwas previously thought with obvious implications to thedomestication of dogs.

The last example includes the selection of a trait of ag-ronomic importance, the oil content in maize kernels.This experiment started in 1896, and is the longest selec-





tion experiment ever performed. Geneticists from theUniversity of Illinois continuously selected maize tochange its oil content in both directions, i. e. to increaseand to decrease the oil level in kernels. The base popula-

tion had about 5%oil in thekernel, and after more than acentury of selection the high oil-producing line hasabout 20% of oil in kernels, whereas the low oil-produc-ing line has almost none (21). Subsequent analysis hasshown that the number of quantitative trait loci (QTLs)which can account for half of the divergence betweenhigh and low oil producing lines is about 50 (22). All de-tected QTLs show a small effect, and the rest (still unde-tected QTLs) should have even smaller effects. This pic-ture places the oil content in a typical quantitative traitcharacterized by many genes with small allelic effects.Consistant with this is the observed continuous responseto artificial selection.

CONCLUSION

Today, more than 150 years after the release of The Or-igin of Species, evolutionary theory is a unifying force forall biology. Following Darwin, new theoretical develop-ments led to the quantitative genetic approach in thestudy of evolution. Most concepts of quantitative genet-ics centre around variances and covariances. According to the breeder’s equation, the response to selection (evo-lutionary change) is equal to the product of heritability(genetic variation) and selection differential (strength of selection). Heritability represents the evolutionary po-

tential of a population. Selection differential for a partic-ular trait is equal to the phenotypic covariance of thistrait and fitness. Selection differential for fitness itself measures total opportunity for selection, and is equal tothe phenotypic variance of fitness. The change of meanfitness in a population between two successive genera-tions due to natural selection is equal to the additive ge-netic variance of fitness in the previous generation. Thisstatement is called Fisher’s fundamental theorem of nat-ural selection. The multivariate breeder’s equation showsthat the vector of selection responses is equal to the prod-uct of the genetic variance – covariance matrix (geneticvariation) and vector of selection gradients (strength of selection). From the vector of selection gradients one can

distinguish direct selection on a particular trait from in-direct (correlated) selection on the same trait.

The mechanisms of evolution described by quantita-tive genetics is just one aspect of studying evolution.Other questions in evolution are studied by different ap-proaches (paleontology, ecology, developmental biology,

bioinformatics etc.). Simultaneous achievements in all of these approaches paint a more complete pictureof reality.

Acknowledgments: I thank Ignacija Vla{i} and Vedran

Dunjko for the help in preparation of figures. This work is supported by the Croatian Ministry of Science, Education and Sport (grant 098-0982913-2867).

REFERENCES

1. DARWINC 1859On theOriginof Species byMeans of NaturalSe-lection, or the Preservation of Favoured Races in the Struggle forLife. Murray, London.

2. PROVINE W B 1971 The Originsof TheoreticalPopulationGenet-ics. University of Chicago Press, Chicago.

3. FISHERR A 1918 The correlationbetweenrelativeson thesupposi-tionof mendelianinheritance.TransRoyalSoc Edinburgh 52:399–433

4. FISHER R A 1930 The Genetical Theory of Natural Selection.Clarendon Press, Oxford.

5. FALCONER D S, MACKAY T F C 1996 Introduction to Quantita-tive Genetics. Longman, Essex.

6. LYNCH M, WALSH B 1998 Genetics and Analysis of QuantitativeTraits. Sinauer Associates Inc, Sunderland, MA.

7. HALLIBURTON R 2004Introductionto PopulationGenetics. Pear-son Education Inc.

8. ROFF D A 1997 Evolutionary Quantitative Genetics. Chapman &Hall, New York.

9. ROFF D A 2006 Evolutionary quantitative genetics. In: Fox C W, Wolf J B (ed) Evolutionary Genetics: Concepts and Case Studies.Oxford University Press, Oxford, p 267

10. ROBERTSON A 1966 A mathematical model of the cullingprocessin dairy cattle. Anim Prod 8: 95–108

11. PRICE G 1970 Selection and covariance. Nature 227: 520–521

12. PRICE G 1972 Extension of covariance selection mathematics. Ann Hum Genet 35: 485–490

13. WADEM J 2006 Natural selection In: FoxC W, WolfJ B (ed) Evolu-tionary Genetics: Concepts and Case Studies. Oxford UniversityPress, Oxford, p 49

14. CROW J F 1958 Some possibilities for measuring selection intensi-ties in man. Hum Biol 30: 1–13

15. LANDE R, ARNOLD S J 1983 The measurement of selection oncorrelated characters. Evolution 37: 1210–1226

16. BRODIEE D III, MOORE A J, JANZEN F J 1995 Visualizingandquantifying natural selection. Trends Ecol Evol 10: 313–318

17. GRANT B R, GRANT P R 1989Evolutionary Dynamics of a Natu-ral Population. University of Chicago Press, Chicago.

18. GRANT P R, GRANT B R 1995 Predicting microevolutionary re-sponses to directional selection on heritable variation. Evolution 49:241–251

19. BELYAEV D K 1979 Destabilizing selection as a factor in domesti-cation. J Hered 70: 301–308

20. TRUT L N 1999 Early canid domestication: The farm-fox experi-ment. Amer Scient 87: 160–169

21. HILL W G 2005 A century of corn selection. Science 307: 683–684

22. LAURIEC C, CHASALOW SD,LEDEAUX J R, MCCAROLL R,BUSH D, HAUGE B, LAI C, CLARK D, ROCHEFORD T R,DUDLEY J W 2004 The genetic architecture of response to long--term artificial selection for oil concentration in the maize kernel.Genetics 168: 2141–2155



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Quantative Genetics and Evolution