SIMULATION OF GENETIC SYSTEMS BY AUTOMATIC DIGITAL COMPUTERS

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1 SIMULATION OF GENETIC SYSTEMS BY AUTOMATIC DIGITAL COMPUTERS VI. EPISTASIS By A. S. FRASER* [Manuscript received December 3, 1959] Summary Simulatin, by Mnte Carl methds, f the effect n the gentype f seletin against phentypic extremes has shwn that selectin will lead t fixatin f a simple additive genetic system at an extremely slw rate in all but very small ppulatins. In mplex epistati systems, such selectin perates t mdify the relatin f the gentype t the phentype. The relatinship bemes an S shaped functin. The efficieny f seletin is independent f ppulatin size. The deviatin frm initial gene frequencies due t selectin is far less per unit decrease f phentypi variability in the epistatic than in the additive lines. I. INTRODUCTION The wrk f this Labratry n quantitative inheritance has recently centred n the prblems psed by the existence f genetic variability in the absence f phentypic variability (see Rende11959; Fraser and Kindred 1960). Cnsequently, the wrk with simulatin prgrammes n electrnic cmputers has been directed at the prblem f selectin against extreme phentypes. Rbertsn (1956), in a theretical analysis f this prblem, examined tw alternatives: the first, in which extremes are less fit because they are extremes, he fund wuld lead t fixatin; the secnd, in which extremes are less fit nt because they are extremes but because they are hmzygtes, he fund wuld maintain genetic variability. He, thus, clearly supprts Lerner's thesis that heterzygtes have an enhanced fitness per se, i.e. that there is verdminance f fitness (see Lerner 1958). Rbertsn did nt cnsider the effect f such selectin against extreme deviants n epistatic interactins, yet it seems prbable that selectin can mdify such interactins and, cnsequently, reduce the trend twards hmzygsity (RendeI1959). A prgramme written t simulate a genetic system in which bth the dminance and epistatic relatins were under genetic cntrl indicated that fixatin f the basic lci will be cnsiderably reduced by mdificatin f epistatic relatins (Fraser 1959). There were, hwever, several features f this prgramme which might prduce bias, the mst imprtant being an inherent asymmetry. In additin, the prgramme was, by cmputer standards, slw. and it was limited t a maximum ppulatin size f slightly less than 0 prgeny. A new prgramme has been written which, althugh based n a larger number f lci- as against -is faster and puts n limit n the number f prgeny per generatin, the limit being n the number f parents. This prgramme is described belw, and results frm tw sets f its runs discussed. * Divisin f Animal Genetis, C.S.I.R.O., University f Sydney.

2 SIMULATION OF GENETIC SYSTEMS. VI 151 II. STRUCTURE OF THE EPISTASIS PROGRAMME The prgramme has six main sectins: (1) Extract, withut replacement, a pair f parents at randm frm the given set f parents. (2) Frm a set f prgeny frm these parents. (3) Determine the phentypes f the prgeny. (4) Select ptential parents frm the set f prgeny. (5) Repeat (1)-(4) until all parents have prduced the specified number f. prgeny. (6) Print ut any required infrmatin. (7) Repeat (1)-(6) using the selected prgeny as parents. III. SIMULATION OF SEGREGATION Sectin II includes the simulatin f segregatin. The methd initially described by Fraser (1957a, 1957b) is based n a "randm walk" alng the length f the gentype, each lcus being cnsidered separately. Mr. J. B. Butcher, Adlph Basser Cmputing Labratry, has suggested a methd which bviates cnsidering each lcus in sequence, and makes full use f the parallel arithmetic f the SILLIAC cmputer. A single SILLIAC register cntains "bits" f binary infrmatin, and rders in the SILLIAC suppressing carry-ver allw varius peratins f "lgical algebra" t be perfrmed separately, and simultaneusly, fr all bits f a register. Frm such peratins it is pssible t identify the genetic status f lci in a single prcess. Given such identificatin it is then easy t simulate segregatin simultaneusly at lci. This is accmplished by the fllwing sequence, given that register A cntains the "maternal gentype" and register B the "paternal gentype" f a parent which is t prduce gametes: (1) Frm the lgical prduct (L.P.) f A and B 1 A 0 B 0 L.P. (A/B) (2) Frm the lgical nn-equivalent (L.N.E.) f A and B 1 A 0 B 0 L.N.E. (A/B) The L.P. (A/B) identifies the lci hmzygus fr the 1 type alleles; the L.N.E. (A/B) identifies the heterzygus lci.

3 152 A. S. FRASER (3) Frm the L.P. 1 0/1 0/1 f a randm number (C) with the L.N.E. (A/B) L.N.E. (A/B) 0/1 C 0/1 0 L.P. (L.N.E. (A/B)/C) (4) Add the L.P. (A/B) t the L.P. (L.N.E. (A/B)/C) 0/1 0 L.P. (L.N.E. (A/B)/C) L.P. (A/B) 1 0/1 0 Simulated gamete As a result f these peratins 1 is placed in every psitin representing a gene f the 1 type which was hmzygus in the parent and 0 in every psitin representing a hmzygus gene f the 0 type; the heterzygus genes are represented by 1 r 0 at randm. These peratins can be perfrmed simultaneusly fr up t digits. Apart frm the frmatin f a randm number, this sequence takes seven rders, ttalling 395 flsec. IV. DETERMINATION OF THE PHENOTYPE The genetic mdel is f independent lci. The phentype determined by these lci has tw cmpnents, P and PI. each determined similarly by lci. Each grup f lci is cnsidered as fur sets f five lci. The relatinships f these t the phentype are the same as thse in the initial epistasis prgramme (Fraser 1959). These fur subgentypes are termed the A, D, Q, and C gentypes respectively. The A grup f five lci determines a cntributin t the phentype which in the absence f dminance r epistasis is given fr each lcus by Genetic Status Phentypic Cntributin '0 0 The "additive" cntributin f the A subgentype t the phentype is given by summatin ver the five lci. The D grup f five lci determines the degree f dminance at the lci f the A gentype. This gentype simulates a dminance mdifier system affecting identically the five lci f the A gentype. It determines the phentypic cntributin f heterzygtes f the A grup, and has n effect n the phentypic cntributin f the hmzygtes.

4 SIMULATION OF GENETIC SYSTEMS. VI 153 The D lci d nt themselves have any dminance, i.e. ver. the five lci f this gentype there are 11 pssible values cnferring dminance n the A grup. A vectr f pssible dminance values is specified fr a particular run, and remains cnstant fr that run. The value f the D gentype in an individual determines which value f this vectr is apprpriate. If the vectr f pssible dminance cefficients is {dt}, then: Genetic Status Phentypic Cntributin I -1 0 I I dt +1 0 The vectr {dt} has been set, fr the runs which are discussed in this paper, at either zer, r in a linear sequence cvering the range +1 0~di~-1 0, such that a substitutin in the D gentype f a 0 fr a 1 type allele makes a difference f 0 2 in di, which gives a variatin frm cmplete dminance f the I alleles (dt = -1 0) thrugh n dminance (di = 0 0) t cmplete dminance f the 0 alleles (di = +1 0). Summatin ver the five lci f the A gentype then gives the additive + dminance cntributin t the phentype. This is termed (P a + P d). The degree f interactin between the five lci f the A gentype is determined by the Q and C gentypes. Just as a particular D gentype determines a specific value f di, s the Q and 0 gentypes determine specific values f quadratic and cubic interactin cefficients frm the vectrs f such cefficients: {qt} and {Ci}. These have been set fr the runs which are discussed in this paper at either zer, r in linear sequence cvering the fllwing ranges: +0 5~qi~-0 5; ~Ct~ The cefficients qi and Ci, determined by specific Q and C gentypes, give the degree f interactin by P Q = (Pa+Pd)~ qi, and Pc = (Pa+pd)g Ct The cmplete determinatin f the P cmpnent f the phentype is given by P+ (P a+p d)o+qi(p a+p d)~+ci(p a+p d)g. The ther lci similarly determine PI, and the ttal phentype is the simple sum f P and Pl. The subdivisin f the phentype int tw independently determined cmpnents was intrduced t allw independent variatin f the dminance gentypes. Mather (1943) has suggested that the lack f dminance in a quantitative system

5 154 A. S. FRASER may be due t individual lci f the system having dminance values in ppsite directins. The average value f dminance ver all the lci can then be zer, and variatin still have a dminance cmpnent. In ur mdel, tw values f dminance are pssible, ne fr each set f A lci, and it was riginally cnsidered that this culd prvide data n the feasibility f Mather's suggestin. Latter (persnal cmmunicatin) has made the pint that each D gentype sets a dminance value fr five A lci, and, cnsequently. any trends twards different dminance values between these lci wuld average ut t zer. An adequate test f Mather's hypthesis requires an individual dminance mdifier system fr each A lcus. The separatin f the phentype int tw cmpnents is therefre nly f value in indicating the cnsistency f any trends. V. METHOD OF SELECTION In this prgramme, each prgeny as it is frmed is tested against fixed phentypic limits which are specified at the beginning f the run, and remain cnstant fr the duratin f the run. Since the number f individuals required as parents (n) may be less than the number f individuals with phentypes within limits, the first n acceptable parents are prvisinally accepted and placed in the "parent" stre. Thereafter each acceptable parent is tested fr substitutin in that stre against a randm number, with a prbability f nji, where i is the ttal number f acceptable parents which have s far been tested. This ensures that all ptential parents have an equal prbability f being accepted as parents. The selectin limits set fr the runs discussed in this paper are ±1 0, i.e. the effect f a single gene substitutin n the simple additive scale. This methd f simulating selectin, althugh fast, has the disadvantage that the selectin limits cannt be easily varied during a run. Anther methd, which will be used in a mdificatin f this prgramme, des nt have this disadvantage. It is based n the sequence f pseud-randm numbers being cmpletely determined. Given the values f the randm numbers at a specific pint in a run, it is pssible, by substituting these values, t repeat any particular sequence f the peratins f the prgramme. This ability t repeat a sequence can be used t determine selectin limits. At the beginning f the frmatin f prgeny the values f the randm number generatr are stred. Then all, r a sample, f the prgeny are frmed and their phentypes cmputed. Only sufficient infrmatin is retained t describe the frequency distributin f phentypes. Frm this, selectin limits are cmputed which will cntain a specified fractin f the prgeny. Given such limits, the riginal values f the randm number generatr are substituted, and the generatin f prgeny restarted. Each prgeny as frmed is then tested fr acceptance against the selectin limits. VI. PRE-SET PARAMETERS Althugh the "epistasis" prgramme has been cnstructed t mllllmlze the number f parameters initially specified, and thereafter, maintained cnstant, sme must be specified and these are:

6 SIMULATION OF GENETIC SYSTEMS. VI 155 (1) Whether randm mating r self-fertilizatin is t ccur. (2) The number f parents. (3) The number f prgeny per mating. (4) The maximum and minimum limits f eligible phentypes. (5) The identificatin number f the run. (6) The vectrs f dminance and interactin cefficients. (7) The gentypes f the initial set f parents. Sixteen runs f the prgramme have been made: eight in the absence f any dminance r epistasis, and eight in the presence f such effects. These runs were made at fur ppulatin sizes:,, 80, and 160 parents, tw runs at each ppulatin size. The number f prgeny per mating was set at fr all runs, making the ttal numbers f prgeny 0, 00, 00, and 00. Tw independent runs were made fr each set f parameters. '*- ~ ~1 ;--.J ~ ::i ~~ > f Z 01, ~ 0~ -----L----~----L----.! a. z ~ ;;: >- z 01 80r-----L-----L-----L-----L----. ~ a. ~ GENERATION OF SELECTION Fig. I.-Percentage f prgeny within the phentypic limits pltted against generatin f selectin. Runs made in the absence f dminance and epistasis n the left. Runs made in the presence f dminance and epistasis n the right. The absence f dminance and epistasis was prduced in the first eight runs by setting {dt}, {qt}, and {cd at zer. These gentypes cnsequently have n effect n the phentype, and selectin is directed slely at the A gentype, i.e. selectin is perating n a simple additive system f lci. The D, Q, and C lci, ttalling, are, in these runs, nt under selectin and changes f their frequencies can be taken as the basis fr cmparisn with the A lci t determine the changes prduced by selectin. All parents at the beginning f all runs were heterzygus at all lci.

7 156 A. S. FRASER... r 0 (01 0 (bl ~0 0 0 g -' ~g -----~ 0 0 i;: l) d Z I 1'~ GENERATION OF SELECTION ".r-" " 0 Fig. 2.-(a) Genetic fixatin in the absence f selectin. The percentage f D, Q, and 0 lci which have becme fixed is pltted against generatin fr the eight runs in which these lci have n phentypic effect. (b) Genetic fixatin f a simple additive system. The percentage f A lci which have becme fixed, pltted against generatin f selectin fr the first eight runs. (0) Genetic fixatin f the A lci in runs which include selectin fr mdifiers f dminance and epistasis. PARENTS /../~,.... ~.,.... -, "... " i " ~ z ~ ;; w 0 w (!) 0( It: W > 0( 80 PARENTS 160 PARENTS!S l.. :~.~.,""""~ 0 (,:ENERATION OF SELECTION Fig. a.-average deviatin f the frequencies f the A lci frm the initial value f 0 5 is shwn pltted against generatin fr (a) unselected lci ( ); (b) simple additive system (-); (0) epistatic system (-).

8 SIMULATION OF GENETIC SYSTEMS. VI 157 VII. RESULTS AND DISOUSSION (a) Phentypic Variability The percentage f prgeny prduced each generatin which have phentypes within the specified phentypic limits is a measure f the effectiveness f selectin against the extreme phentypes. These percentages are shwn pltted against generatin f selectin in Figure l. In cnsidering the eight runs made in the absence f dminance and epistasis, there is a marked effect f ppulatin size. In small ppulatins, selectin causes, r- SO PARENTS Z 0 ;: " ~ 0 Cl "' "' > [/ 0 SO 0 ~ r- 80 PARENTS I 160 PARENTS " [ ;/ r /~ s s 0 GENERATION OF SELECTION Fig. 4.-As fr Figure 3, but the tw replicate runs have been averaged. at the small ppulatin sizes, a marked increase f the percentage f prgeny with phentypes within the selectin limits. In large ppulatins the percentage f acceptable prgeny increases mre slwly. This cntrasts very markedly with the eight runs made in the presence f dminance and epistasis; the percentage f "acceptable" prgeny increases rapidly ver the initial generatins f selectin, and then mre slwly as selectin prceeds. The effect f ppulatin size is slight, being mst apparent in a lwer variatin frm generatin t generatin in larger ppulatins (see Fig. 1). The effect f selectin n phentypic variability in the tw sets f ppulatins. is sufficiently different t suggest that different mechanisms are perating. This is shwn by the gentypes which the machine recrded each generatin.

9 158 A. S. FRASER The effect f selectin and ppulatin size n the distributin f gene frequencies is shwn in Figure 2 in which the percentage f lci which have becme fixed is pltted against generatin f selectin and in Figure 3 in which the average deviatin f gene frequencies frm the initial value f 0 5 is shwn pltted against generatin f selectin. The incidence f genetic fixatin shws that there is a marked effect f ppulatin size and that there is little if any effect f selectin. The deviatins frm the riginal gene frequency shw similarly that there is a marked 'effect f ppulatin size. Selectin is ineffective in smaller ppulatins f and parents but in nes Z ~ s PARENTS r JY :/ : :' ~. ~:'., ~ 0 ~I.L._-";L I W C W Cl «s a: w > «s... :1' i.(\"' fl"" e PARENTS,--.'~.....,.. /:)9 /~I/ s.:i.. f.., loa 0 NO. OF "ACCEPTABLE" PROGENY (~) PARENTS ("-(:{ /.. ~:,/ r':"'"... ;;JJl' \./,"'J PARENTS ;',./ / J {7 (.. /...,J l~. ~.' : Fig. 5.-Average deviatin f the frequencies f the A lci frm initial value f 0 5 pltted against the percentage f "acceptable" prgeny. -- Additive system; epistatic system. f 80 and markedly in nes f 160 parents there is a real difference between the changes f gene frequency f unselected and selected lci. This is shwn mre clearly in Figure 4, in which the tw replicate runs have been averaged. Figure 4 indicates that selectin f an epistatic system prduces a greater change f gene frequency than selectin f a simple additive system. Hwever, n accunt has been taken f the effectiveness f selectin in reducing phentypic variability. This is particularly evident in large ppulatins. In large ppulatins withut dminance r epistasis, i.e. a simple additive system, selectin fr ver generatins has prduced nly a slight reductin f phentypic variability whereas with dminance r epistasis, i.e. fr the epistatic system, selectin has

10 SIMULATION OF GENETIC SYSTEMS. VI 159 prduced a very marked reductin f variability. Cnsequently, the percentage f prgeny within limits is shwn pltted against deviatins frm the initial gene frequency in Figure 5. These graphs shw that selectin against extreme phentypes prduces a much greater reductin f variability fr a specified deviatin frm the initial gene frequency in the "epistatic" runs than in the "additive" runs. The dminance and epistasis runs were made with {di}, {qt}, and {Ci} set t the ranges specified in Sectin IV. Variatin f the D, Q, and C gentypes due t segregatin will therefre prduce variatin f di, qi, and Ci. This will affect Pi and cnsequently selectin can affect the D, Q, and C gentypes. The mean values '00 D PARENTS PARENTS '~ '~' ~ D~ ~ ~O =.!t!O I I d '00 '00 ~ '00 ~ 0 I :::1:=:; 5: bs Q Q 5: 0 0 ~ ~L "' c c c c!;aj I!!! I ~ ""' 8 II: I.L... 0 ~~ ~5:~ '00 9 LI --'---'---'-~~ ~ D Q c 80 PARENTS 0 I D ~~ g'~ ~ a ~ _0 c '00 1 D a 0~Q 160 PARENTS '00 ~ J,g~ Q D Q 0 ~~ ~ ~ -L ~I,~LI -L J- L- L-~ 'DO I--- ~ "'" c c I L---.J GENERATION OF SELECTION Fig. 6.-Average gene frequencies f the lci f the D, Q, and C subgentypes, shwn separately fr the fur ppulatin sizes. There are tw D, Q, and C subgentypes fr each run, and tw runs were made at each ppulatin size. f the gene frequencies f the D, Q, and C gentypes are given in Figure 6, pltted against generatin f selectin fr the tw runs made at each f the fur sizes f ppulatin. The dminance gentypes shw n cnsistent changes frm the riginal frequencies except in small ppulatins where such deviatin are prbably due t randm sampling effects. The effect f selectin n the percentage f prgeny with phentype within limits cannt be ascribed t mdificatin f the dminance system. The epistasis gentypes shw cnsistent changes such that the relatinship f gentype t phentype deviates cnsiderably frm a linear functin. In the runs at smaller ppulatin sizes the high incidence f genetic fixatin interacts with the selectin fr epistasis. This is nt evident at larger ppulatin sizes. There is a trend twards a gene frequency f 0 8 """ 0. 9 in the Q gentypes and f

11 160 A. S. FRASER 0 5 ~ 0 7 in the C gentypes, which crrespnd t a range f -(0 3 ~ 0 4) fr qi and f 0 ~ -0 5 fr Ci. These ranges f qi and Ci crrespnd t a set f curves f the type shwn in Figure 7. Clearly the increased percentage f individuals with phentypes within the selectin limits has been prduced by changes in frequency f the Q and C gentypes; these have brught abut a relatinship f phentype t gentype such that the majrity f A gentypes have phentypes within the selectin limits f ±1 0. t w,. a. z w 1: a GENOTYPIC SCALE Fig. 7.-Relatinship f gentype t phentype fr qi = , 0 0, , -0 05, and Ci (b) Cnclusin The runs made with this prgramme have shwn that selectin f an additive genetic system will in the absence f epistasis lead t an increased degree f genetic fixatin, as shwn by the straightfrward mathematical analysis (see Rbertsn 1956). This is especially marked in runs made at small ppulatin sizes. Inclusin f a variable degree f epistasis, under genetic cntrl, causes a marked reductin f the rate f genetic fixatin fr any given degree f phentypic unifrmity. Selectin f the epistasis gentypes causes a change f the gentype-phentype relatinship frm the linear, additive frm, t a cmplex frm which is such that

12 SIMULATION OF GENETIC SYSTEMS. VI 161 the majrity f the A gentypes have the same phentype. The effect f this n the frequency distributin f phentype is shwn in Figure 8. Selectin against extreme phentypes can, in ur genetic mdel, affect either the genetic system determining the gentype-phentype relatinship f the A lci r the degree f fixatin f the A lci. It is clear that the frmer effect predminates. Sme phentypic variability still des ccur even after r mre generatins f selectin. This is due predminantly t segregatin f the Q and C gentypes, rather than f the A gentypes. Cnsequently, lng cntinued selectin shuld, eventually, result in the fixatin f the epistasis gentypes. Selectin f a cmplex genetic system, althugh decreasing the rate f fixatin f the additive lci, results in fixatin f the epistasis-determining lci, i.e. selectin against extremes results in fixatin, but in a cmplex system this fixatin is restricted t a specific part f the gentype. II~li[~1 ~ III r-m~i,.otype w " >- b I 7/ / z I'\: 7 "I '''"""7, I '..." W I "- GENOTYPE Fig. 8.-Frequency distributin f phentypes when the frequency distributin f gentypes crrespnds t an F2 frm cmpletely heterzygus parents. This is shwn fr several gentype-phentype relatinships. An intriguing feature f these runs has been the frm f the gentypephentype relatinship which has been prduced. Such a relatinship, if genetically fixed, will have unexpected effects n the prgress f selectin twards an extreme phentype. Suppse that selectin against extreme phentypes has caused the fixatin f such a relatinship, and that the gene frequencies f the additive lci are distributed t frm a nrmal distributin centred n a "zer" phentype. Then selectin twards either an extreme psitive r an extreme negative phentype will initially cause a straightfrward shift f the distributin. Hwever, as selectin prceeds the distributin will be mved twards the inflexin pint f the gentypephentype relatinship, and this will prduce a marked decrease f the phentypic variance, due t an increase in the prprtin f gentypes having the same phentype. The phentypic distributin will becme skewed against a selectin limit, and further selectin fr the extreme phentype will be against the genetic extremes, resulting in fixatin f the additive lci. It wuld seem that n further advance culd be achieved. Hwever, if the extreme gentypes f the psitive-selected

13 162 A. S. FRASER ppulatin culd be identified, they culd act as a basis fr a negative selectin line in which there wuld be n epistasis restrictins n the effectiveness f selectin. The examinatin f epistatic relatinships has rarely been taken past the identificatin f a term in the analysis f variance. This is due t the attitude that selectin can nly act n additive variance. If the mre general view is adptedthat epistatic systems can, as has been shwn fr dminance systems, be affected by selectin-then it is pertinent nt nly t determine the existence f epistasis, but als t measure the pattern f its effect. The results f Waddingtn (1957), Dun and Fraser (1959), and Rendel and Sheldn (1960) have demnstrated that knwledge f the pattern f epistasis is useful in the design and interpretatin f artificial selectin experiments. Many f the ambiguities fund in selectin experiments when selectin pressures are reduced r reversed suggest that mechanisms f this type may perate and are certainly wrth cnsidering as a basis fr experiment. Simulatin f genetic systems by prgramming an electrnic cmputer is a research activity readily available t the experimenter fr the small expenditure f time taken t learn the techniques f prgramming. As a cncmitant t actual experiments it will allw the gap between the theretical and experimental geneticists t be bridged almst effrtlessly. Genetic mdels can be devised, prgrammed, and tested within weeks r mnths; certainly with sufficient speed fr an experimenter t examine many f the theretical cnsequences f his ideas befre he devises experiments with live rganisms. This wuld seem t be the field in which this methd can be used t the greatest value, thugh its use in the methdical examinatin f the imprtance f variables determining the effectiveness f selectin is undeniable. Hwever, it is mre ecnmical t restrict such extensive studies t prgrammes fr extremely fast machines with very large memries allwing maximum efficiency, a very necessary feature when time n a machine may ttal several hundred hurs. VIII. REFERENCES DUN, R. B., and FRASER, A. S. (1959).-Selectin fr an invariant character, vibrissa number, in the huse muse. Aust. J. Bil. Sci. 12: FRASER, A. S. (1957a).-Simulatin f genetic systems by autmatic digital cmputers. I. Intrductin. Aust. J. Bil. Sci. : FRASER, A. S. (1957b).-Simulatin f genetic systems by autmatic digital cmputers. II. Effects f linkage n rates f advance under selectin. Aust. J. Bil. Sci. : FRASER, A. S. (1959).-Simulatin f genetic systems by autmatic digital cmputers. V. Linkage, dminance, and epistasis. Prc. Int. Symp. Bimet. Genet. (In press.) FRASER, A. S., and KINDRED, B. M. (1960).-Selectin fr an invariant character, vibrissa number, in the huse muse. II. Limits t variability. Aust. J. Bil. Sci. 13: LERNER, M. (1958).-"The Genetic Basis f Selectin." (J. Wiley & Sns, Inc.: New Yrk.) MATHER, K. (1943).-Plygenic inheritance and natural selectin. Bil. Rev. 18: RENDEL, J. M. (1959).-Canalizatin f the scute phentype f Drsphila. Evlutin 13: RENDEL, J. M., and SHELDON, B. L. (1960).-Selectin fr canalizatin f the scute phentype in D. melangaster. Aust. J. Bil. Sci. 13: ROBERTSON, A. (1956).-Effect f selectin against extreme deviants. J. Genet. 54: WADDINGTON, C. H. (1957).-"Strategy f the Genes." (Allen and Unwin: Lndn.)