Genet Res Oamb 1971 16 pp 24125 24With 1 textfigurePrinted in - PDF document

Genet. Res., Oamb. (1971) 16 pp. 241-25 24With 1 text-figurePrinted in Great BritainTh founde effec an respons t artificia selectioB J W JAMESchool of Wool and Pastoral Sciences, The University of New South Wales,Kensington, Australia(Received 2 August 1969SUMMARTh respons t selectio i an lin KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV 24 J W JAMEintroductio ma wel b o onl a smal numbe o individuals I suc circumstance on woul lik t kno ho respons t subsequen selectio wil baffecte b th numbe o foundersTH GENETI MODETh analysi wil b o selectio a a singl locu an mos attentio wil b givet th cas o additiv gen action Fo unlinke loc wit n epistasis thes resultma b applie t polygeni trait i th usua wa b takin th selectio coefficien a a locu a th produc o th standardize selectio differentia an theffec o th locu measure a a proportio o th phenotypi standar deviatio(Falconer 1960 p 206)W conside a ver larg rando matin bas populatio i whic a locu isegregatin fo tw allele A± an A2, th frequenc o th allel A2 bein p. Frothi bas populatio line ar starte b takin a rando sampl o n individualfro whos progen selectio i begun Durin th selectio phas th effectivpopulatio siz i N an th selectiv value o th thre genotype ar\-\s 1 l + £sThi mode shoul giv a reasonabl accurat descriptio o th effec o selectioo a locu wit additiv effect o a quantitativ characterTH RAT O RESPONS I TH FIRS GENERATIOFo th abov mode th rat o respons t selectio i a larg populatio witgen frequenc x i give wit sufficien accurac bAa = \sx(\— x),provide s i no to large I a sampl o n individual fro th bas populatioth numbe o A2 allele wil hav a binomia distributio wit probabilit p

aninde 2n. I w le x b th frequenc o A2 i suc a sample the x wil als bth gen frequenc i a ver larg grou o progen produce b th member oth sample an th respons t selectio i suc a larg progen grou wil bgive b th abov equation W ma find th averag respons ove al suc b usin th moment o th binomia distributio t obtaiThu fo selectio amon larg number o progen produce b sample o siz nth expecte rat o respons i th first generatio i proportiona t ( — [l/2n])Similarl w ma us th moment o th binomia distributio t find thvarianc o th selectio respons betwee initia samples Thi give th resulva KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV Effect and response to artificial selection 24I w writ C2 = va (Ax)/[E(Ax)]2 s tha C i th coefficien o variatio orespons rate2np(l-p) 2n2(l-Th coefficien o variatio i leas whe p = 0- an rise a p depart fro thivalueNex w conside th variatio i rat o respons betwee replicat lines eacwit a effectiv numbe o parent equa t N, take fro th sam initia Kojim (1961 showe tha fo a initia sampl wit gen frequenc x thvarianc o respons wa give b±x(l-Th expecte varianc betwee replicat line withi founde group ma the bfoun b averagin thi expressio ove al initia samples Sinc fo suc binomiaE[x(l-x)(l- 2x)] =3»(lw find th varianc t bvaThi componen o varianc woul usuall b rathe large tha th componeno varianc betwee initia samples especially whe s i small I selectio linear founde fro separat an independen sample th varianc i rat orespons wil b th su o th tw components Th varianc woul b dominateb th withi founde grou componen excep whe loc wit larg s value werinvolved Fo example vrhenp = 0- th rati o th betwee t th withi initiasampl comp

onen i Ns2jl6n2.SELECTIO LIMITO perhap greate interes i th effec o a smal numbe o founder o limitt selectio response Robertso (1960 gav result fo a initia sampl o onpai an als fo thre generation o singl pai mating befor selectio began no conside a arbitrar initia sampl size.I a selectio lin i take fro a initia sampl i whic th favoure allel hafrequenc x then a show b Kimur (1957) th chanc o fixing th desirablallel unde ou mode il_e-2Nsx KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV 24 J W JAMEW mus find th expecte valu o u(x) fo sample o siz n fro a populatiowit gen frequenc p. Denotin thi a un(p) w havun(P) = l_e-2NsNoIn /2«E(e-w*) = 2 \pi(\-p)= (\an consequentl, v i(i + «e«*(!» = 1_e-2iv8 — •Th limi o thi expressio asn- o i Kimura' result a o cours i shoul beFo smal value o Ns a powe serie expansio ishowin tha th tota respons i approximatel 2N time th initia response awa show b Robertso (1960 i th absenc o a founde effect Fo smal valueo Ns th founde effec i t reduc th tota geneti gai b a fractio 1/2% Folarg value o Ns w tak th limi a Ns -* o an obtaiun(P) = l-(l-#)2n-Thi i intuitivel obvious sinc i Ns i larg th favoure allel wil b fixed i ioccur i th initia sample fo whic th probabilit i 1 — ( — p)Zn. I thi casi p i smal an n no larg un{p) ~ 2np. Th selectio limi fo rar allele i thumuc mor strongl influence b numbe o founder whe Ns i larg tha wheNs i smallTh precis treatmen o recessiv gene i muc mor difficult bu a littl mab deduce easily Whe Ns i ver larg th favoure recessiv wil b fixed iinclude i th initia sampl s tha un(p) wil b th sam a fo additiv genesFo a give initia sampl wit frequenc x fo th desirabl re

cessiv allele, thchanc o fixation give b Kimur (1957 ma b expande i a powe serie fosmal Ns value t givu{x) = x +Averagin thi ove al initia sample o siz n giveFo p = 0- th tota gai i a fractio ( — [1/2%] o tha fro a larg foundegroup fo ver smal p th fractio i ( — [l/4n2]) an fo p nea t 1 th fractioi nearl ( — [3/4%]) Thu fo smal Ns value th founde effec o respons du KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV Effect and response to artificial selection241 r000-0-Al P0-Ns-~ 0- 0-- 0-Ns=0-i i iNs=4I i1 2 4 8 1 3 6 1 2 4 8 1 3 6Numbe o founderFig 1 Tota selectio respons fo a give numbe o founder a a fractio o thafo a infinit number Curve ar draw fo bas populatio gen frequencie o 0-80-5 0-2 0 an 001 KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV 24 J W JAMEt recessiv allele resemble tha fo additiv alleles Th sam i tru fo larg Nsvalues bu n result hav bee foun fo intermediat valuesW retur no t furthe consideratio o th chanc o fixation a a additivlocus I i convenien t wor wit th ratiowhic i th averag tota gai fro a grou o n founder a a fractio o thaexpecte fro a infinitel larg founde grou unde th sam condition oselection I i thu a usefu measur o th limitation o tota gai whic arimpose b a reductio i th initia sampl size an w no conside it behavioua p, Ns an n varyWhe Ns i smalWn{p)^l-±,whil fo larg value o Nswn(p)~ l-(l-p)in-\Fo a rang o value o n, p an Ns th value o wn(p) hav bee calculate anth result ar presente i Fig 1Tabl 1 Total selective gain for a given value o/N as a fractionof that when

N = o(n i th initia sampl size p th gen frequenc i th bas population.nNs p 1 2 4 1 6 o0- 00 0-244 0-134 0-071 0-020 0-008 0-0050- 0-244 0-145 0-091 0156 0-055 0-0560- 0-244 0-210 0-216 0-237 0-243 0-2440- 0-244 0-282 0-319 0-346 0-353 0-3554 0-0 0-964 0-821 0-587 0-220 0-090 0-0670 0-964 0-834 0-653 0-475 0-489 0-5010- 0-964 0-906 0-912 0-953 0-961 0-9640- 0-964 0-964 0-983 0-991 0-993 0-993Fo lo value o Ns, wn(p) i littl affecte b gen frequency Bu whe Nsi hig wn(p) i ver sensitiv t difference i gen frequency th founde effecbein particularl drasti fo allele rar i th bas population Fo allelecommo i th bas populatio (p ^ 0-5 wn(p) i les affecte b numbe ofounder whe Ns i larg tha whe Ns i small whil th opposit i tru whep i smallAnothe wa o lookin a th result i t as ho th fractio o th possibltota advanc varie wit Ns fo a give initia sampl size T d thi w consideth functio KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV Effect and response to artificial selection 24Th possibl advanc i 1 — p excep fo th ( — p)2n case wher th desirablallel i no include i th initia sample henc th denominato o vNs(p).Tabl 1 give th result o a fe calculations I ca b see fro th tabl thavA,s(p) doe no chang ver markedl wit n whe th desirabl allel i commoi th bas population bu decline appreciabl a n increase i th favoureallel i rar i th bas population Th valu o Ns whic i require i orde tobtai a give fractio o th possibl respons i thu greates fo larg initia fro a bas populatio i whic th favoure allel i rareVARIATIO BETWEE LINE A FIXATIOSelectio line obtaine b th sam procedur fro on bas populatio wilvar i tota respons bot becaus differen initia sample ar use

an becauso differen samplin accident durin selection Fo independen line th varianc line a th limi i give b th binomia samplin variancThi varianc i greates whe un(p) = 0-5 On resul o thi i tha unde somcondition replicat selectio line founde b fairl larg group ma responmor variabl tha similarl selecte line founde b onl a fe individuals Foexample whe p = 0-0 an Ns i larg th betwee lin varianc i greates whe = 34 Thu i selectio fo a trai whos respons depend mainl o loc o largeffec wher th desirabl allel i rare th result ma b mor variabl i linefounde b a moderat numbe o individual tha i line founde b ver feo ver many Th reaso i simpl tha i initia sample o moderat sizappreciabl proportion woul includ an fai t includ th favoure allelesVirtuall al ver smal sample woul fai t includ the whil virtuall al verlarg sample woul includ themA EXAMPLD D E Robertso ha kindl allowe m t quot som o hi dat whic arrelevan t th abov considerations A ful accoun o th experimen i t bpublishe later Fro th Canberr bas populatio (Latter 1964 a numbe o sample wer taken som consistin o on pai (n = 2) som o five pair(n = 10 an som 2 pair (n = 40) Fro eac founde grou tw sample oprogen wer taken On wa a onc subjecte t selection an th othe wakep fo five generation o rando matin wit 4 pair o parent an theselecte i th sam wa a th first sample Al line wer selecte fo hig sternopleura bristl numbe o th lef sid a a intensit o 2 % Som line ha five o parent pe generatio (N = 10 an som 2 pair (N = 40) Th numbe replicat line varie betwee treatments Afte 3 generation o selectio (i.eafte generatio 3 i th line wit a la period selectio wa discontinuedalthoug som line appeare t b stil responding I Tabl 2 th mea increas KWWSVGRLRUJ6 3XEOLV

KHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV 1414148664642-8-4-3-6-2-5-4-6-62-7-4-7-4-6-24 J W JAMBi bristl number average ove bot sexes i give fo eac treatment I shaltak thes value a approximatin t relativ value o selectio limits Th laperio ha n consisten effec s I shal discus average ove la an direcselectio linesClearl N ha ha a marke effec o th limits Bu th numbe o founderseem t hav ha a appreciabl influenc onl whe N = 1 an no wheN = 40 Alternatively w migh sa a reductio i N ha ha mor seriou consequence fo smal tha fo larg founde groups Ca suc result b explainei term o th theor give aboveTabl 2 Gains in sternopleural bristle number from 3 generations of selection(n i th numbe o founders N th numbe o selecte parents Direc line werselecte a once la line afte five generation o rando mating.n N Replicate Direc La Averag14Fro Fig 1 w se tha fo loc wit hig value o p, th proportio o possiblrespons whic i achieve i les sensitiv t numbe o founder a hig Ns values a lo Ns values Thi suggest a a interpretatio tha mos o th responswa obtaine fro loc a whic th desirabl allele wer commo i th baspopulation Fo exampl i w tak p = 0- w ca calculat selectio gain awn(0-8)-0-8 Fo n = 2 an 1 an Ns = 1 an 4 th gain arn = 2 n = 1Ns = 1 0-101 0-120Ns = 4 0-191 0-198Withou pressin th compariso to fa w ma not tha i relativ valu thesar somewha simila t th observe pattern A explanatio alon thes line ithu possible However M Robertso tell m ther i evidenc tha a goo deao th respons i du t allele rar i th bas population I i therefor no cleatha th theor presente her ca provid a vali explanationDISCUSSIOPerhap th mos strikin featur o th theor i th wa i whic th foundeeffec varie wit th subsequen leve o selectio pressur a measure b Ns.Thi i especiall marke fo rar d

esirabl alleles Fo suc alleles especiall aloc o larg effect a bottlenec wil hav drasti effect o th limit i thereafte KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV Effect and response to artificial selection 24selectio line hav man parent whic hav bee intensel selected Th effecwil b muc les drasti i selecte line ar maintaine b onl a fe parentunde mil selection O th othe hand whe th favoure allele ar common abottlenec wil affec limit les i larg intensel selecte line tha i smalmildl selecte onesRobertso (1960 wrote 'Highl selecte population o thos whic havpasse throug a sever "bottleneck i populatio siz wil b toleran o anfurthe siz restriction i th sens tha th desirabl allele wil b harde t losbecause i the ar presen a all the wil hav a reasonabl frequency. Thi icertainl s i on i thinkin o favourabl allele whic ar rar i th baspopulation Bu i th statemen i interprete a suggestin tha onc a lin ha throug a bottlenec subsequen selectio ma safel b don wit smalnumbers ou theor show thi interpretatio t b incorrect sinc i a leas case a lin woul b mor sensitiv t suc a reduce Ns valu tha i wabefor th bottleneckTh reaso fo thi i no har t see I a allel i ver commo befor thbottlenec the i wil probabl b include i al samples eve smal ones selectio i larg population thereafte shoul fix th favoure allel i al cases Mil selectio i smal population thereafte ha a hig proba o fixing th desirabl allel i sample i whic it frequenc i high buno i sample i whic it frequenc is b chance low Onl i smal sample wilth frequenc b likel t fal sharply s the wil b mor seriousl affecte tha samples I a sens thi i Robertson' argumen looke a fro th otheside wit th rar allel bein

no th unfavourabl oneLeavin th subjec o bottleneck fo th moment le u suppos a lin habee selecte fo som tim an tha th frequenc o a desirabl allel ha reache0- i th line I a thi poin th lin i subdivide an on replicat i continuewit Ns = 4 whil a secon i ru wit Ns = 1 th respectiv probabilitie o ar 0-998 an 0-9230 Th relativ furthe gain ar thu 0-198 an0-123 s tha th lin wit smalle Ns valu achieve onl 60 o th furtherespons o tha wit Ns = 4 Thi ma b relevan t th interpretatio o result b Jones Frankha & Barke (1968) Fro line whic ha bee selectefo 1 generation wit 4 pair o parent the too line wit 1 pair o parentselecte a th sam intensit whil continuin th 40-pai lines I al thre caseth 10-pai line gav a goo dea les furthe respons tha th 40-pai line oveth nex 3 generations Discussin this th author wrote 'Robertso als tha restrictin populatio siz afte a numbe o generation oselectio woul hav littl effec o th tota response.. Thu ther wer desirablgene stil a lo frequencies. Thoug thi conclusio ma wel b tru i doe no follo fro th observationsA alternativ explanatio woul b tha al loc o larg effec ha becomfixed, an onl loc o smal effec remaine segregating Subsequen responsfro suc loc woul b highl susceptibl t reductio i th valu o Ns.I i o cours possibl i suc a situatio tha a hig proportio o th tota KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3UHVV 25 J W JAMErespons obtainabl fro th foundatio sampl ha bee achieve whe threstrictio i imposed an tha th los o respons du t th reductio i numbeo parent i a smal fractio o thi tota response However i anima breedinpractic th importan questio i no 'ho fa hav w come? bu rathe 'hofa ca w go?Th presen theor suggest tha th

effec o a bottlenec o limit t selectioma b sever o mild dependin o gen frequenc an o th subsequenselectio programme I is moreover a singl locu theory an i i important kno th exten t whic th result ar affecte whe selectio act o linkesystem o genes A genera analysi o thi proble raise ver considerabldifficultie whic wil probabl requir extensiv simulatio studie fo theielucidationREFERENCEFALCONEB D S (1960) An Introduction to Quantitative Genetics. Edinburgh Olive an BoydHILL W G & ROBERTSON A (1966) Th effec o linkag o limit t artificia selectionOenetical Research 8 269-294JONES L P. FBANKHAM R & BABKER J S F (1968) Th effect o populatio siz anselectio intensit i selectio fo a quantitativ characte i Drosophila. II Long-terrespons t selection Oenetical Research 12 249-266KIMURA M (1957) Som problem o stochasti processe i genetics Annals of Mathe-matical Statistics 28 882-901KOJIMA K (1961) Effect o dominanc an siz o populatio o respons t mas selectionOenetical Research 2 177-188LATTEB B D H (1964) Selectio fo a threshol characte i Drosophila. I A analysi oth phenotypi varianc o th underlyin scale Oenetical Research 5 198-210LATTEB B D H (1965) Respons t artificia selectio du t autosoma gene o largeffect II Th effect o linkag o limit t selectio i finit populations AustralianJournal of Biological Sciences 18 1009-1023ROBERTSON A (1960) A theor o limit i artificia selection Proceedings of the RoyalSociety, London, B 153 234-249ROBEBTSON A (1966) Artificia selectio i plant an animals Proceedings of the RoyalSociety, London, B 164 341-349WBIGHT S (1931) Evolutio i Mendelia populations Genetics 16 97-159 KWWSVGRLRUJ6 3XEOLVKHGRQOLQHE\&DPEULGJH8QLYHUVLW\3U