It is possible to describe a realized selection by means of an indicator, f(x): probability for an individual of value x to be selected.  Various models for this indicator are proposed, in the univariate case, and on the assumption that individuals are ranked on a linear index of measured variables.  Estimators are defined on the basis of these models for rating traits controlled during selection.  A numeric example with ewes is given

Bodin, L.

Elsen, J. M.

Ricordeau, G.

English

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University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln 3rd World Congress on Genetics Applied to Livestock Production Animal Science Department 1986 CRITERIA FOR EVALUATING A SELECTION SCRENE: SOME PROPOSALS J. M. Elsen I.N.R.A. L. Bodin I.N.R.A. G. Ricordeau I.N.R.A. Follow this and additional works at: https://digitalcommons.unl.edu/wcgalp  Part of the Animal Sciences Commons Elsen, J. M.; Bodin, L.; and Ricordeau, G., "CRITERIA FOR EVALUATING A SELECTION SCRENE: SOME PROPOSALS" (1986). 3rd World Congress on Genetics Applied to Livestock Production. 13. https://digitalcommons.unl.edu/wcgalp/13 This Article is brought to you for free and open access by the Animal Science Department at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in 3rd World Congress on Genetics Applied to Livestock Production by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. CRITERIA FOR EVALUATING A SELECTION SCRENE: SOl>!E PR,OPOSALS J.l>!. ELSEN, L. BODIN, G. RICORDEAU, FRANCE Station d'Amelioration Genetique des Animaux, I.N.R.A. Toulouse, B.P. 27, 31326 CASTANET-TOLOSAN CEDEX, FRANCE SUM MAR Y It is possible to describe a realized selection by ~eans of an "dleator, fix): probability for an individual of value x to be selected. I dOUS I'lodeh for this indicator are proposed, in the univariate case, and ~ the assul'lption that individuals are ranked on a linear index of ~easured 0" ' -bles . Estil'lators are defined on the basis of these ~odels for rating •• rl g Ir. lt5 controlled during selection. A nu~eric exa~ple with ewes is given. KEY WORDS : Selection sche~e, selection index, selection differential, realized selection. INTRODUCTION In neceuary ."II'Ial5 . order to ~easure the efficiency of a selection schefte, it is to esti"ate how breeders rate the various traits when choosing Only those traits that have been controlled can be . taken into • ccount, and one ftust exa~ine not only their relative i~portance (each in relation to the other), but also the role of a "deviation" representing all Ihe selection criteria that are used without being known. Several studies hive been published on this topic concerning dairy cattle (ROBERTSON, 1966; HINKS, 1966, 1975; SCHAEI;f'ER and BURNSIDE, 1974; BERGER et al., 1973; WHITE a"d NICHOLS, 19G5; ROBERTSON and BARKER, 1966; ALLAIRE and HENDERSON, 1966a, 1966b, 1966cl. Hore recently, ELSEN et al. (1985) have extended these Mthods to an exa~ple of a selection sche~e for suckling ewes. I . METHODS A - Univariate Models - Notation Pj anil'lel populations: tested (Pt), retained (Pr) and eli~inated (Pe) Nj Ihe nUI'lber in each category. XI ~andol'l variable: value of the ith trad . Xi can be divided In lo elk classes of stock Nij~ (Nitk for tested, etc.). rlk • Nirk NiH : intra-class selection rate. ri-r-Nr Nt ~Ij and v\j : averages and variance!'> of trai t 1 in populat Ion P j. 2 - S tudIed Mo del> 0) - Generalities The Model, ,n all cases, is a descr'ption of probability for an Individual of value xl to be retained. COMpare the Models by evaluating their likelihood (or Measured giving paraMeters the values that MaxiMize it. indicator fe It· ~t I · '5 pOUlbl . th e to e Ir logar U .. -..... , Table 1 sketches a few possible hypothese.s. Other exaMples are foun Elsen et al. (19851. Note that selection hypotheses for high (reap. d til values follow frOM Table 1 aSSUMing: for Model 2, very high (resp. 10W~~' for Models 3 and 4, very SMail (resp. biglAi · I' b) - SuppleMentary Criteria In addition to their likel,hood and the optiMal values of the para"ater that characterize ModelsJthere are other criteria that can give Indications Oil the realized selection. - Model 4 goes .back to those of ROBERTSON (1966) and ALLAIRE and HENOER~ C(rI916te6railo·n. TThehsi: ai~thora use the pi correlation between Xi and Hi-Xi+ EI a. a ~ ~ a non-Measurable variable that the breeder uses to select aMong his aniMals p05slbly by a truncation procedure (a tested anhlal ta retained If Ih hi value is greater than a 'Yi threshold). This correlation can be estiMated loll th Pi - «;:;:r i -jiCi )//iic )1 o5i ~ Oil o5t where 051 i5 the MaxiMUM value of the di fference between retained and tested anll'lal5, therefore for HI-Xi. In the case where Xi obeY5 a nor"al law we have i-drl.uic, where ·.the selection intensity Hr) is exp(-'Yi1/2IM ... r • - in this context, we define : • the Q1 realized selection rate, .............. r-ql.pi --- ........ Oi-i!qi I. We wi II have such that a new way of Measuring the il'lportance of XI, ?i:( I-Qi )/( I-r). that varies between O(Xi play~ no role ,n selection) and I(only Xi plays a rolel • finally, I-pi can be interpreted as a lack of benefit due to select,~ on Ei. B - Multivariate ModelS - Notation and Hypotheses We will exal'line here only the case that ALLAIRE and HENDERSON (1966b.c) and BERGER et 01. (1973) studied . This is a selection favoring individuals with a high linear index H for the I'leasured var,ables. It applies to the Multivariate case our continuous selectlon Model (Model 4). H-~bi xlt E where E ,s a non-I'leasured "deviat,on" var,able, that covers all non-controlled traits and randol'lness in selection. Since b, are defined to wit.hin one proportionality coefficient, it is always possible to a~su .. e th.t E. is independent frOM the Xi, and of unit variance. By hypothesiS. the H index of retained reproducers goes beyond a threshold. We also asSU"1 MultinorMality of the Xi, Vc being the I'latr1)( of variances and covarlances of these variables In Pc. /ILL! . e prj t",een ~e.e sh ' "rlbe Ir (e S realIZe t /' b • Thi · the re ,elect 10 re,ul t i • the se • the r ")f{ I-r) · 1-; is ;01 (q )1 i · fiM11 correillt ~,-c'l-I • Elsen .f H .nalY~l~ .h.lanc corre I II I ~" X IMU'" • we ct , ,,\Obit ecof'le 5 II - API A . EII( Cooperll l be proll( ' arlebl( ror 19B( that .h, _ Weighting Coefficients a l - Generalities LAIRE and HENDERSON (1966b), restated later on by BERGER et 151. (1973) ALresented their solution as the result of I'Iaxil'lizing the correlation . e P H-b'xtE and a I'Ieasurable index J-2:[Ji Xi-~'X. Elsen et 151. (19B5) :etweenhOwn that it is not necessary to define this J index in order to ... e "b' selection. Following our hypotheses, E(dJ.l)-i(r).Vc.b/Vb'.Vc..btl and crt e . s ALLAIRE and HENDERSON do) we rep lace expectat ions E (dJ.l ) wi th their ( (as " ations , .lhe result is ,e,llz yj.l .il/l: I" _I .I ....... .1 b ." i< r) -0 where b) - Criteria for Rating the II'Iportance of Traits in Selection This is an extent ion of the criteria proposed in the univariate case : · the realized selection rate q is the rate that would have given the £;.i if 1 Ctlon had been carried out on J (or on the I-b'.x part of Ih. The te e ".. ;'II. result is 1< q )-0. · t~ .elaction rate on the other criteria i5 i-r/i · the relative il'lportance of controlled traits can be I'Ieasured with (;-( 1-Qlf( l-rl. The result · I-P i. the lack of benefit due to selecting on E. ;.dq 1/ i< r) - vvarcT )/va;::o:n-:-· flnally, the il'lportance of the ith X variable can be I'Ieasured with the corr~lation be.!.ween X and H (which equals (dltilcT1c );0), or with the quant ity ~i -ci-l )/( l-ci-l) c) - Other Approaches "' .... · Elsen et a1. (1985) have shown that the previously defined b,lJcoefficients .f Hand J indexes are proportional to the coefficients of dj,scril'linant , .,ly.,s between Pr and Pe. On the other hand, the quant Ity o:z. is the ~~Ianobis distance between tested and retained, and the square of correlation p~ can be" interpreted as the ra,tio of this distance to the -i1 X 1 MUI"I distance. · we can also use the continuous selection I'Iodeling presented above. Here, " n.ble Xi is replaced with I - b'.X, Hi with Hand Ei with E. The I'Iodel b.co~es f( I I - n( A -I) and it 15 necessary to adjust for A and b II - APPLICATION TO A EWE SELECTION SCHEME A - Presentation of the Analyzed Case Each year, breeders of Lacaune ewes who practice the OVitest Cooperative's selection schel'le on prol1 ficacy, collectively choose I'Iales to eprogeny tested. We have analyzed this chOice and considered 8 controlled ;ert.bles (see Table 2). The true selection rate is r-O 23 on the average thor 'tl980 and 1981. Table 2 presents sOl'le basic statistic~ on these B traits • show: I - few differences between retained and tested for NC and P2 - a higher average a~ong the retained for IL, PI, DT, NA and Ip With increase In variance for the last two variables ~ - a preference for extre~es for MN. RESULTS I - Univariate Analyses Table 3 shows the values of the various para~eters proposed In order rate selection . The lost four pertain to Model 4. Probabilities o'.a to of distributions (X 1 0f ho~ogeneity) verify the interest breeders h ... "", ~aternal traits (MN, NA, IL, IP) and to a lesser extent In DT. aYe 111 Para~eters in Model 4 have the sa~e tendency as the X 1 of ho~ogene1ty r .. last seven traits but suggest no particular ra~ choice on MN. Th1s r ~ . e, .. lt can be explained .by the afore~entioned breeders' preference, regard1ng th variable, for extre~e anl~a15. Thi.s preference will be conf1r~ed further ,:,.' Co~parlng likelihoods Ll (no selection) and L2 (general ~odel) shows on • hand, that NC and PI are of Ilttle 1~portance for breeders, and on the ot:: hand, that IP and NA range first . We found a sub-~odel of the "'" explanatory value as the general ~odel for only three variables : - MN : continuous selection for extre~es (Model 4). The optl",al 1nd1cator is f(MN)-1-0(.83 MN - . 522>+0(1.033 MN-3.93) NA and IP : selection .ai·~ed at greater values. In effect, the ophllel value of para",eter Xi for these two variables is very high. 2 - Multivariate Analysis 2 to 8 variables can be taken into account si~ultaneously in the 11~ index. For each i nu~ber of variables, Table 3 gives the characteristic. 0' the ~ost explanatory J index. COMpared with results of univariate analysl., conclu·sions regarding trait ratings are siMilar : Maternal aspects (Nil, IL, IP) co~e first, then co~es weight Pl. The last 4 traits have a neglig1ble role in the description ot the real ized select ion (nei ther bi nor (YoI, J) correlations are Modified between J4 and J81 . Finally, Elsen et al. (1985 ) show that the optiMality criterion for linear COMbinations (discrl"inent analysis or Ma x i~u~ likelihood of f(A -I I indicator has little effect on the nUMeric result). Expressed in standard deviation unit of traits, the optiNI weights are about I for NA, . 67 for IL, . 6 for IP, . 45 for PI. The index II first correlated with NA and IP, and then with IL. CONCLUSION Teste I : no II : sel II : sel ch' II : sel cor The ~ethods described here should clardy how select ion sche~e5 operate nlS an and consequently help decide whether to Modify the~ or not. Nevertheless, they have liMits : only controlled traits can be analyzed ; other ~odel5 are conceivable ; their results regard only one stage in selectlon and will have to be supple~ented by COMbining analysis of the various stages in each path of genetiC IMproveMent . REFERENCES F.R. and HENDERSON, C.R. 1966a. J . Dairy Sci . 49(11),1426-1434. ,lj.LMRE, F.R . and HENDERSON, C.R. 1966b. J. Dairy Sci. 49(11),1435-1440. L~ ::~' F.R . and HENDERSON, C.R. 1966c. J. Dairy Sci. 50(2), 194-200. LA 'p J HARVEY, !.I.R. and RADER, E.R. 1973. J. Dairy Sci. 56, 805-811. e£R6ER'J M' "80DIN, L. and GOUPILLON, C. 1985. Sub",itted to Genet. Sel. Evol. EN, . ., . ~S C.J.M. 1966. An1",. Prod. 8, 467-480. I~~S, C J M. 1975. Ani",. Prod. 20, 337-343. ~S , .' . I ERTSON, A. 1966 An1",. Prod. 8, 95-108. ?Q6 TSON A and BARKER, J .S.F. 1966. Ani",. Prod. 8, -""ER ' . . ::AEFFER, L.R. and BURNSIDE E.B. 1974. J. Dairy Sci. 241-252 . 11, 1394-1400. 468-474. ,.... J M and NICHOLS, J.R. 1965. J. Dairy Sci. 48, ITE, . . rested hypothe sis I : no selection on Xi II : selection for extremes general case I : selection for extremes choosing by truncation , : selection fo r extremes cont i nuous cho i ce -TABlEl-Compared univariate models Corresponding model f(x i )=l- Qi ifxiE [Ail ' Xi2 ) = Qi el sewhere [I(~_--.l ) Uti + n(~:....l) 0"£ i Parameters to be estimated set of the f(X i ) Method used Dynamic programming Xi1 • Xi2 andQi Trial and error Ail' A i 2 and 0" Ei Newton - Raphson nlS an ascending functio n of xi' We choose for II the distribution function of the standardized normal distribution T A B L E Analysed variables Averages Standard devht lo. Variables rega rd I ng the dam tested selected tested MN birth type 2.044 2.021 't1tcttt . 65 <:: ( 11) .11 NC lambing sequence number of the dam 4 .79 4.78 1. 57 NA mean number of lambs per year of the dam 2.45 < 2.70 .39 '.SI ( 11) <: ( 11) .4, lL milk production Index of the dam .35 < .62 . 91 ( 11) ·Il I P prolificacy index of the dam 1.45 < 1. 49 .08 < ( 11) ( 11) ·'1 Variables regarding the individual '" ...PI weight on day 40 224.54 < 230.13 29.92 " 30.1\ .. P2 weight on day 140 480 .24 486.44 49 . 11 ... SS.13 .. OT testis diameter 59.17 < 60.40 6.29 0 (51) '.1' .. GI D e " c GI &: ... 0 ... 0> C T A 8 L E " .. 0 Unlvarlable selection parameters u u " '" Tra I t MN NC NA IL IP PI P2 OT GI " " " Sameness probabl- < >Iity of dlstrlbu- .67 a a a .42 .86 .07 .. GI tl ons +' GI e Models likelihoOd '" .. -L 1 227 227 227 227 227 227 227 227 '" 0. -L2 215 223 196 212 206 221 215 ~ -L3 224 226 215 229 219 228 225 228 '" -l4 215 227 202 221 212 224 226 224 ... '" >, Real ized selec- '" .99 .995 .59 .83 .68 .90 .94 .90 c tion rate ~ '" GI Rate O"r/~ .22 .22 . 37 .26 .32 .24 .23 .24 +' '" L Coefficient '" 1 - ~ >e .02 .01 .53 .22 . 40 . 12 . 08 .13 " -,--:-,:- +' " Lack of ~gain :.: 100(1-0/g) 97 100 51 78 63 86 91 86 , A tl L. L Multivariate analysis parameter values according to the number of traits Number of Discriminant variables Realized Relative Good ranking Possible Maximum variables MN NC NA I L IP P 1 P2 DT selection importance probability gain Li ke I I hood studied rate e 1 - ~ -l X .586 .529 .66 .51 196.4 2 X X .541 .585 .68 .46 194.8 X X X .516 .618 .69 .43 191. 4 4 X X X X .489 .652 .7D .40 186.7 8 X X X .487 .655 .70 .35 186. , TAB L 5 Characteristics of the 4 variable selection indexes Variables MN NC NA IL IP P 1 P2 DT J4 coefficients discriminant analysis 1. .26 3.01 .006 maximum likelihood 1. .30 3.06 .007 Cor relations (X, J4) -.026 -.035 .817 .371 .632 .229 .093 .174 ~ parameter of the optimal indicator Is -10.07 

CRITERIA FOR EVALUATING A SELECTION SCRENE: SOME PROPOSALS

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CRITERIA FOR EVALUATING A SELECTION SCRENE: SOME PROPOSALS

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