Simulation of Genetic Systems.XI. Inversion Polymorphism

ALEX FRASER AND DONALD BURNELL

Genetics Group,University of California,

Davis, California 95616.

FRAsER et al. (1966), working with a six-locus genetic simulation computerprogram, have examined the effects of introduction of inversions into pop-

ulations which were in gametic equilibrium for qj = 0.5. They found that stablepolymorphism can evolve for such inversions if (a) selection strongly favorsa phenotypic intermediate, i.e., is normalizing, (b) the genetic constitution ofthe inversion is only moderately unbalanced, and (c) the initial frequencyof the inversion exceeds a fairly critical value. The frequency dependenceis also a feature of analogous multiple allelic systems. Following a suggestionby Alan Robertson (personal communication), we have found that the effectof normalizing selection on such a genetic system can best be understood byfirst considering a multiple allelic system. Suppose a single locus with threealleles, ao, al, and a2, which form a series in potency. In the absence ofdominance and interaction, the phenotypes of this system can be representedby the following matrix, and double truncation selection for the intermediatephenotype will transform this phenotype matrix into a fitness matrix.

ao al a2 ao al a2

ao0 0 1

a, ° 1 ° (a)

Cl, 1 0 1 01Phenotype Fitness

Although the genetic system is additive on the primary scale of determina-tion of phenotypes, it is marked by complex interactions on the secondary scaleof reproductive fitness.

Supported in part by U. S. Public Health Service research grant GM 11778 from theNational Institutes of Health.

270

AMERICAN JOURNAL OF HUMAN GENETICS, VOL. 19, No. 3, PART I (MAY), 1967

ao

al

a2

0 1 2

1 2 3

2 3 4

FRASER AND BURNELL

In this model, there are two stable equilibria. If the frequencies of the threealleles are q0, ql, and q2, then the equilibria are

(1) qo= 2 = 0; q, = 1.0, w = 1.0 (fixation)(2) qo = q2 = 0.5; q, = 0.0, w = 0.5 (stable polymorphism)

There is a third equilibrium when all three alleles are at equal frequen-cies. This is dependent on the two selected genotypes aoa2 and alai havingdifferent probabilities of producing selected offspring even though they havethe same probability of producing offspring. They have different geneticsurvivals which are markedly frequency dependent.

If the frequencies of aoa2 and alai are x and y, respectively, then the matrixof mating frequencies is

aoa2 alai

a0a2 x2 (b)

alai xy y2

Only two of these matings will produce surviving offspring: aoa2 x aoa2 andala1 x ala1. Half of the progeny of the former type of mating will survive asparents compared to all of the progeny of the latter mating.

Ax 0 when x = 2yThis will only hold for

(3) qo = qi = q2= 0.3, w = 0.3 (unstable polymorphism)A population which contains all three alleles at equal frequency will be in

a state of equilibrium at which any deviation from equality will result in thepopulation shifting to the equilibrium appropriate to the allele with thegreatest frequency. If a population is initiated with all three alleles presentat different frequencies, selection for a phenotypic intermediate will resultin the eventual elimination of the minority allele or alleles. However, if thefrequency of a minority allele is increased sufficiently in some way then theprogression can be reversed.A genotype can be said to have a component of its reproductive fitness which

is independent of its competitive ability to produce functioning gametes. Thiscomponent can be termed its combining ability-the proportion of its gameteswhich combine with the gametic output in general to reproduce the parentalgenotype. Clearly, the combining ability is frequency dependent, increasingwith increase of the frequency of the specific genotype.The same logic developed for the multiple allele case can be applied to a

multigenic system. Suppose a two-locus system with two alleles per locus:anal and bob,. The phenotype matrix will be

271

SIMULATION OF INVERSION POLYMORPHISM

aobo aob1 albo alb1

0 1 1 2

1 2 2 3

1 2 2 3

2 3 3 4

(c)

and, if double truncation selection for the phenotypic intermediate occurs,this phenotype matrix is transformed into a fitness matrix.

aobo aob1 albo aib1

o 0 0 1

o 1 1 0

o 1 1 0

1 0 0 0

(d)

The suppression of recombination

of three alleles at a single locus.

aob0

aob 1

alb,

aobo aob1, albo

will reduce this system to the equivalent

aib1

(e)

If, as in the simulations discussed by Fraser et al. (1966), the initial popu-lations involve equal allelic frequencies and gametic equilibrium, then thefrequencies of the gametic classes aobo, aob1 + albo, and alb1 are 0.25, 0.50,and 0.25, respectively. Selection will result in the elimination of the a0bo andalb1 classes, with fixation of the (aob1, albo) class. If, however, the frequencyof the a0bo or alb1 class is increased sufficiently, then selection will result ina balanced polymorphism for a0bo//alb1, with elimination of the (aObj, albo)class, since the increased frequency of the a0bo or alb1 class results in an in-

aobo

aob1

alb)

alb1

aobo

albO

alb,

o 0 1

o 1 0

1 0 0

272

FRASER AND BURNELL

creased probability of these combining to produce fit phenotypes. If this in-crease of the combining ability is such as to exceed that of the (aob1, albo)class, then selection will result in a stable polymorphism. Recombination be-tween the a and b loci precludes such a stable polymorphism, and the onlystable end points will be when fixation has occurred for either aobb or albo.The aobi//albo and aobo//a1b1 double heterozygotes will have a recombina-tilonal disadvantage relative to the homozygotes, aobl//aab1 and albo//a1bo,resulting in the latter increasing in frequency. If the two balanced homozygotesoccur at equal frequencies, there are no differences upon which selection canact. Perturbation of the genetic system resulting in one homozygote occurringat a greater frequency than the other will confer an increased combiningability to this class and the population will, eventually, become fixed forthis homozygous combination.

If an inversion is introduced into such a population, then inversion poly-morphism is possible if the inversion has a genetic content of aobo or aibb.The probability that a stable inversion polymorphism will evolve is dependentupon the frequency of the inversion, the conformation of the array of fre-quencies of normal chromosomes, and the intensity of normalizing selection.There will be two trends of change of the conformation of the array of fre-quencies of normal chromosomes. In one trend, towards inversion polymor-phism, the normalizing selection will tend to increase coupling linkages, chang-ing gene frequencies in the noninverted chromosomes to fixation for acomplementary potency to that contained in the inversion. In the other trend,towards fixation of an intermediate, selection will tend to increase repulsionlinkages, changing gene frequencies first to equality (qi = 0.5), followedeventually by fixation of opposite acting alleles at the two loci.

Normalizing selection, in the presence of tight linkage, tends to increasethe frequencies of repulsion types, decreasing the recombinational load(Lewontin, 1965). The advantage of an inversion will, therefore, decrease withtight linkage. Inbreeding will increase the trend to fixation of an intermediatetype, also reducing the fitness of an inversion. Reduction of population size onthe other hand, by causing an increased variation of gametic frequencies, willtend to increase the advantage of an inversion.

Fraser et al. (1966) have shown that the establishment of inversion poly-morphism is possible in a six-locus model if the minimum initial frequencyof an inversion exceeds a value of approximately 10%. They conclude that theestablishment of a stable polymorphism would only be possible from mutationalfrequencies in population structures favoring marked genetic drift, or if theinversion had an inherent advantage independent of the six locus system.The fitness of an inversion is determined to a large degree by the frequency

of the complementary normal chromosome. This will, in its turn, be determinedby the number of loci in the model and by the tightness of their linkage. It ispertinent to expand the earlier study to models involving greater numbers ofloci, over a range of rates of recombination. In this paper, results are detailedand discussed for genetic models of 4, 6, 12, 18, and 30 loci for a range ofrates of recombination and degrees of gametic disequilibrium.

-273

SIMULATION OF INVERSION POLYMORPHISM

GENETIC MODEL

The computer program used in this study is the GSD-2 program run onan IBM 7044 computer. This program allows simulation of multigenic sys-tems of up to 30 loci, in populations of up to 1,024 parents. The number ofprogeny is unrestricted, being defined by the intensity of selection, e.g., ifthe intensity of selection is 25%, then the number of progeny produced, inruns with 1,024 parents, is 4,096.

Selection is based on the additive phenotype which has been illustratedabove for a two-locus model (c). The additive phenotype is transformed intoa probability of selection as a parent (ps) on the following function

n -paPs=1 -

n

where n = number of loci and Pa = additive phenotype.The term 8 is a constant which specifies the intensity of the normalizing

selection. A series of curves of the relation of p8 to pa for different valuesof /8 are shown in Fraser et al. (1966). The notation used below has beendescribed by Fraser et al. (1966).

All runs were based on a genetic system of two alleles at n loci, locatedalong a single chromosome with a rate of recombination of r between adjacentloci. The initial population was specified as being in gametic equilibrium forgene frequencies of 0.5, over all loci. The population size was set at 256 par-ents. Inversion chromosomes were substituted for normal chromosomes with adefined probability. Only one type of inversion was introduced into a particularpopulation. Recombination was completely suppressed in inversion heterozy-gotes. The program contained a test for establishment of inversion poly-morphism. The frequency of the inversion was tested to determine whetherit lay within the bounds, 0.45-0.55. If such a test was successful for four suc-cessive generations, the run was terminated. Runs were otherwise continuedto 50 generations. In some runs, the frequency of the inversion had increasedover the initial frequency but had not reached the stable frequency of 0.50 bythe 50th generation. A judgment of whether inversion polymorphism wouldhave been established if selection were continued was made. This source ofmisclassification was of minor importance.

RESULTS AND DISCUSSION

The number of possible types of chromosomes is 2n where n is the numberof loci. The genetic model is based on all loci having equal effects, and it is,therefore, possible to group the types of chromosomes into classes in whichthe criterion is the number of 0 and 1 alleles, i.e., chromosomes of equalpotency are grouped. The formula 1i On-i can signify chromosomes with i locihaving 1 allele, and n - i loci having 0 alleles. The number of classes is n + 1,ranging from lon through ln/20n/2 to Inoo classes. Comparisons of potency forsystems involving different number of loci where selection is normalizing canbe based on the degree of balance where ln/20n/2 has a balance of unity, and

274

FRASER AND BURNELL

1Oo0, 1P00 have a balance of zero. This is illustrated in Table 1 for geneticsystems of 4, 6, 18, and 30 loci.The initiation of populations with equal allelic frequencies at gametic phase

balance results in the classes of chromosomes occurring in binominal propor-tions. This is illustrated in Table 1 for 4, 6, 18, and 30-locus models. Thesefrequencies apply to the noninverted chromosomes. Introduction of inversionchromosomes results in gametic disequilibrium, but the relative proportionsof the classes of noninverted chromosomes will still be in binominal proportionsas in Table 1.

Sets of replicate runs were made for inversions differing in their potency,introduced at a range of frequencies, for multigenic systems of 2, 4, 6, 12, 18,and 30 loci. The number of runs in which polymorphism was established iscompared in Table 2 with the number of runs in which the inversion was lost.These data are shown as percentages in Fig. 1.A feature of these runs is the lack of consistent differences between the runs

made at recombination rates of 0.25 and 0.50. Figure 2 shows the correlationbetween analogous runs made at these two recombination rates. This com-parison excludes runs in which the probability of polymorphism was 0.0 or1.0. It is possible that a more extensive comparison would demonstrate aneffect of this difference of recombination rate, but it is apparent that anysuch difference will be small and the data can be grouped to simplify thisstudy.Grouping the data from runs made with recombination set at 0.25 and 0.50

allows a comparison between analogous runs with (a) effectively free re-combination (0.25 + 0.50) and (b) fairly tight linkage (0.025). This is shownin Fig. 3 for the runs involving the least unbalanced types of chromosomes,e.g., 114016, 18010, etc. There is an interaction between the number of loci inthe model and the effect of the difference of recombination. The effect of thedifference of recombination is at a maximum for the 12-locus model, decreasingwith increase or decrease of the number of loci.A set of runs were made for the 6, 12, 18, and 30-locus models and the 1204,

1507 18010, and 114016 inversions, in which the rates of recombination were setto equalize the recombinational lengths of the inversions, i.e., at 0.145 forthe six-locus model, 0.0659 for the 12-locus model, 0.0426 for the 18-locus mod-el, and 0.025 for the 30-locus model, each specifying a total recombinationlength of 0.725. The results of these runs are shown in Fig. 4. There is a pro-gression, from the six to the 30-locus model, of decrease of the minimum fre-quency at which inversion polymorphism will evolve.

It is apparent from these various sets of runs that the initial frequencyof an inversion from which a stable polymorphism will occur with a reason-able probability rapidly decreases with increase of the number of loci, reach-ing mutational frequencies in the 18 and 30-locus models. (Mutational fre-quency is specified as 1/2N, 2/2N, etc., rather than the frequency at whichchromosomes mutate to an inverted form.) This aspect has been investi-gated in more detail for the 114016 inversion in the 30-locus model. Runs weremade in which the inversion was introduced at frequencies of 1/2N, 2/2N,and 3/2N, over a range of rates of recombination.

275

O

st 1~ ^10o IiIi III

f~~~~~~ l10Seo Ol liIIHeQl

0 -4

11 C, 10o ~ OO 1111° 11s

- ~00CO~t ¢ U tet 1° I°~HHZ N u ~~~~~~~~~~~~~~~~~~~~~~~~~~I o[H|co

LO CD C> to OO* M t- M0t)10°0°- 001000

°O00 D> Z° 5 U5 oo

01

000 H 0 10 i 0 J1 0

0-oO<> I rOII I =o:=. E: 1 top^^ller-lollllI0

¢- 0 L Lo | ,° CD 00 EM|

0100~^ 000 001000100001

CO COCOCOCOCOO -~~~~~~~~~~~~~~~~~~~~~iCl iC

000- ~~~~~~6100001c> 000-O 0000

;T-4~OOO0 10 ~ H0101C00~00O

CO -~~~~~~~~~~~~~-C ~ ~ ~ ~ 0~o o o o o 5

0-4

00 0COO C O

10 C/~~ ~~~~~~~~~~~~~~~ 0410 W00C =H ~~~~~~~~o 0100 ~~~~~~~~~~~~~~~~~~~~ ~~~~L 00 41000111

00 0..~~~~~

z CO 00L .. ot- m CD 0

r-((=; cII CO CO r- 4l4l: 0C

0

CO0CO COOo O0CCCOOOO

H COO 1~~~~~ ~ ~ ~ ~~-4 4

U~~~~~~~~~~~~~~~~~CH--

CO0 ~~~~~~COOSH CO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C

H Q,

Q) Cd EH 000 000 00

276

l Il

°-I-

"q00eq - 00Oj2 I

00000'O 0

0q v 10 CO O

0010 10

01 CO

Ieq 00101I101I

00 tD" 1O

I0

IN

Q"mION CZmp1-

C> 00 t- N I" CN _4 _-

° - qN X

M m14 -

coNT N

0 CD CD

km, t-

N Ce N=CON N N ~ _ _ o c c: O c Q NN N0000101010100000000

IX. eq

o C)

O

1toIO I. to

a4

z,.

a,

II

IU:l l

ID- OD

0 0~Io t-

OZ O to M< N N -4N eN 10

0-01I I 00l I II

11!I110I lII IItI 10 0

II

o Z2; 00 0 0O -4O

I 0*0000>-

N, 10 0 00o

0 X 0toO _

0

00 0

_j °La

0)

U:1ND

CoLo

(D

'ns

IR=

za4

1Q

%

:2;Z.

N T0 C 1t 0 0 0

000 t- 10 4 N

00q - 10000I

000 Cq 10 t- 0

t- t- 0 0100104 _4

Q 4=

= O_1 el

I1 1°°

1 -

'11

II aa ull

-4CO

-4 _- w ew1-

= cn -"_- _- 1

La U O

01 J" 10 11It0 L1-0 CO4 1- I" -N

O w O

O 00

1101IC C5t N t c

t 0oo

", a C N N to

°= = w = _4 lt. m er w m t- _ cOo 2; % 2U1 X L t V N -4_ ;

I OO= O O O OO= O OCO O O OC> M N -4

277

0UiC)

I

2

O 2;Om

0

-4

-4I

CH I. el!CINP0

LO

-4

LO

N- :2UmNlOC

toC1

20 I.

N0 %

o 4

C>

Lo

SIMULATION OF INVERSION POLYMORPHISM

> ~~~~~~~\\ 2.\s

X 2 4X \ A

ID~~~ \/ i

INITIAL FREQUENCY OF INVERSIONFIG. LA. The probability of establishment of stable polymorphism is shown against the

initial frequency of inversion for a series of inversions. Results are shown for 6, 12, 18,and 30-locus models. Selection was maintained at 13 = 0.1, in populations of 256 parents.Runs were made at three rates of recombination in homomorphic individuals: x-x = 0.5,

---- =0.25, and 0-0 = 0.025.

There is a marked decrease of the probability of polymorphism with decreaseof the recombination rate below a few per cent (Fig. 5). It would appearthat the suppression of recombination in heteromorphic individuals only con-fers an effective advantage when the rate of recombination between adjacentloci in homomorphic standard chromosomes exceeds a fairly critical value of 1%to 2%. It would appear that the multigenic system becomes essentially a mul-tiple allelic system when the rate of recombination drops below this value.

278

FRASER AND BURNELL

010 N.

0

0~

0 140151

FIG. 13Seleedo pag 278)

Frse(95)ond intensity of slation s-j~~~~~~~%

m~~~~~~~~~~~~~~~~~~

0

\wadjacn 9\caI 0~~~0

INITIAL FREQUENCY OF INVERSIONFIG.lB. (See legend on page 278).

Fraser (1958) found that the interaction of intensity of selection with popu-lation size to produce discontinuities in the effectiveness of directional selec-tion is not manifest at rates of recombination of more than a few perccnt.Lewontin (1964), in a study of the effects of normalizing selection, found thatsuch selection can result in gametic disequilibrium if the rates of recombinationbetween adjacent loci are small.The above runs were all based on the noninverted chromosomes occurring

in gametic equilibrium which specifies that the frequency distribution of poten-cy classes has binominal proportions. (See Table 1.) The degree of potencyof a chromosome is, therefore, confounded with its frequency, and it is not

279

SIMULATION OF INVERSION POLYMORPHISM

r6.25 o051 0//O ~~/ /00

0 /'/

0/ 0

00,''00,0~

A// Q 01-0O5 10

r0-50

FIG. 2. Comparison between the r = 0.5 and r = 0.25 rates of recombination of theprobability of establishment of stable polymorphism. The comparison excludes runs inwhich the probability of polymorphism was 0 or 1.

possible to determine whether differences of fitness between inversions are dueto their differing in potency or to their complementary normal chromosomesdiffering in frequency. Runs were made, therefore, for populations in whichthe array of normal chromosomes did not occur in gametic equilibrium.Gametic disequilibrium can be introduced by initiating each population in

full coupling and interpolating a generation without selection at some specificrate of recombination. With the rate of recombination for this interpolatedgeneration set at 0.50, gametic equilibrium will result, whereas if it is set at0.00 then the original coupling disequilibrium will be maintained, and if itis set at 1.00 then a repulsion disequilibrium will be generated. A series ofdistributions of gametic classes produced in this way are shown in Fig. 6 forthe 30-locus model.Runs were made at various degrees of disequilibrium from full coupling

to full repulsion for the 113017 inversion. The results are given in Fig. 7.The fitness of an inversion appears, as would be expected, to be minimal

when the gametic phase is in strong repulsion disequilibrium; it increasesto a maximum when the gametic phase is in intermediate coupling dis-

280

FRASER AND BURNELL

FREE RECOMBINATION

TIGHT LINKAGE

INITIAL FREQUENCY OF INVERSIONFIG. 3. The probability of establishment of polymorphism is shown against the initial

frequency of the inversion for free recombination (0.25 and 0.5) and tight linkage (0.025)in homomorphic individuals.

equilibrium and decreases for strong coupling disequilibrium. It is pertinentto consider the change from gametic phase balance which would occur undernormalizing selection in the absence of an inversion. This is illustrated in Fig. 8for two runs of the 112017 inversion in populations with an initial disequilibrium

0:2

LL0lo

-i

co0cx-

281

SIMULATION OF INVERSION POLYMORPHISM

EQUAL LENGTH (72ScM),I.

Lfl

0a0~IL 00

F-I

m

Q C

FIG. 4.morgans).

INITIAL FREQUENCY OF INVERSIONAs in Fig. 3 for inversions of the same recombinational length (72.5 centi-

of 0.4375, i.e., in coupling disequilibrium. In one of these runs, the populationbecame established in inversion polymorphism; in the other, the inversion de-creased in frequency and the gametic phase changed to a repulsion dis-equilibrium. Lewontin (1965), Gill (1965), and Fraser et al. (1966) haveshown that normalizing selection results in repulsion imbalance for multigenicsystems involving tight linkage, and, consequently, any consideration of theprobability of establishment of inversion polymorphism for a multigenic systemunder normalizing selection needs to be based on estimates of the degree ofrepulsion imbalance which would be expected to occur.

SUMMARY

The simulations of inversion polymorphism with a six-locus model by Fraseret al. (1966) showed that the model of additivity on the phenotypic scale withinteraction imposed by a normalizing mode of selection can only account forthe establishment of inversion polymorphism in a fairly restricted set of cir-cumstances. The present extension of this model to a larger number of locihas shown that the restrictions decrease with increase of the number of loci.In models of 18 and 30 loci, the establishment of inversion polymorphismwould appear to be adequately explicable without reference to inversionshaving specific advantages outside the framework of the basic model. A majordeficiency of this work is that it is based on the existence of a multigenic

282

FRASER AND BURNELL

PROBABILITY

OF

POLYMORPHISM

N = 256B = 0-05

RECOMBINATION RATEFIG. 5. The probability of establishing stable polymorphism of the 114016 inversion

from initial frequencies of 1/2N, 2/2N, and 3/2N is shown for different rates of recombina-tion in homomorphic individuals.

polymorphism at intermediate allelic frequencies. So far, there has not beenany adequate demonstration that such a multigenic polymorphism can bemaintained in the absence of generalized overdominance, i.e., an advantageof heterozygosity per se in Lerner's (1954) terms. It is, therefore, pertinentto examine our model in terms of the existence of such overdominance todetermine, firstly, the minimal degree of such overdominance necessary tomaintain intermediate gene frequencies and, secondly, to determine the effectsof introducing inversions into such populations. This will be the next step inour investigation of this model.

283

6ADN3n0t3U

284

Uz

LU

Cc

"0 C

C K~

"0 C)

uO Cd:

C-

UtC)

0)W

0.42

0 3~

CT_

V "0

_ *ZC .0

C)

FRASER AND BURNELL

0o--- _- 0

X

_ . .asm

10

05

0*

0'1250-0940-0630-0470-031

0 05S

coupling balance repulsionFIG. 7. The probability of establishing stable polymorphism for the 113017 inversion

introduced at a series of frequencies into populations with various degrees of gameticdisequilibrium of the noninverted chromosomes.

I0n

0-J

0

0~L~.0

I

0cr

Q.

285

1 0

SIMULATION OF INVERSION POLYMORPHISM

N-256Rs025Q: .5

GENERATION0

10 1---O10 12 14 15 16 17 IS 20

POTENCY

w0 4

___ -4

xI

0 0-1 0-2 03

TNVERSION

FIG. 8A. The frequency distributions of potency classes for the noninverted chromosomesare shown for two runs in which the 113017 inversion was introduced at an initial frequencyof 0.0625. The population of noninverted chromosomes had an initial gametic dis-equilibrium of 0.4375. The frequency of the inversion and the fitness of the populationare also shown.

286

,80e 05R Ia*4375INV2 1131o7

0

.1

G0

uzLLJ

LuJ

IL0o

.1

0

*t

III

c

,8=o005RIa4375INV2 1'307'

w

x

I

I'

I'

I

x

14 15 16 17 18 20 0 0 1 0-2 03

POTENCY

FIG. 8B.

INVERSION

(See legend on page 286).

REFERENCESFRASER, A. S. 1958. Monte Carlo analyses of genetic models. Nature 181: 208-209.FRASER, A. S., BURNELL, D., AND MILLER, D. 1966. Simulation of genetic systems. X. Inver-

sion polymorphism. J. Theor. Biol. (in press).GILL, J. L. 1965. Selection and linkage in simulated genetic populations. Austral. J. Biol.

Sci. 18: 1171-1187.LERNER, I. M. 1954. Genetic Homeostasis. New York: John Wiley.LEWONTIN, R. C. 1964. The interaction of selection and linkage. I. General considerations;

heterotic models. Genetics 49: 49-67.LEWONTIN, R. C. 1965. Selection in and of populations. In Ideas in Modern Biology.

Proceedings, XVI Internat. Congr. Zool., Vol. 6.

287

NRO256RQ:025Q's.5

QzLIJ:D

U-

6

9

12

Is

18

10 12