Genetic Response and Inbreeding with Different Selection Methods and Mating Designs for Nucleus Breeding Programs of Dairy Cattle

Genetic Response and Inbreeding with Different Selection Methods and Mating Designs for Nucleus Breeding Programs of Dairy Cattle H. W. LEITCH, C. SMITH, E. B. BURNSIDE, and M. QUINTON Centre for the Genetic Improvement of Livestock University of Guelph Guelph, ON, Canada N1G 2W1 ABSTRACT

,

Stochastic simulation was used to study the effect of selection and mating strategy on rates of genetic response and inbreeding with a closed nucleus breeding program for juvenile and adult schemes with 8 males and 64 females selected to produce 1024 progeny (512 females). Selection strategies considered using all available information or only individual and sibling records. Selection of sires was either unrestricted or restricted to between full-sib families. The effect of avoidance of matings of relatives to limit inbreeding was also evaluated. Four mating designs were examined: each dam was mated to 1, 2 , 4 , or all sires. Mating designs involving one sire per dam and more than one dam per sire were referred to as hierarchical. Use of several mates per dam resulted in a factorial mating design. Selected parents were mated either randomly, best to best, or best to worst. An index based on relative inbreeding to response ratio was used to describe the effectiveness of strategies for reducing inbreeding relative to changes in rates of genetic response. Strategies that lower index values were preferred and include selection on BLUP or approximations of BLUP and factorial mating designs that involve the random mating of dams to several sires. Factorial mating designs were effective for a range of heritabilities. Avoidance of matings of full sibs and restriction of selection of sues to between full-sib families enabled appreciable reductions in the index. Nu-

Received January 26, 1993. Accepted July 23, 1993. 1994 J Dairy Sci 77:1702-1718

cleus breeding programs based entirely on the selection of juveniles were not indicated because they had higher index values than adult schemes. (Key words: inbreeding, mating design, assortative mating, selection)

Abbreviation key: Md = mates per dam, MOET = multiple ovulation and embryo transfer, RIRR = relative inbreeding to response ratio, SI,H = selection index including informaticn on all relatives, SId,, = selection index including information on close relatives, SI,), = selection index including a subset of females selected on phenotype and sires on SIClOse.

INTRODUCTION

Nicholas (10) and Nicholas and Smith (11) introduced the application of a nucleus herd program based on multiple ovulation and embryo transfer (MOET)for increased genetic response to selection in dairy cattle. The nucleus herd concept may be characterized by the selection of juvenile or adult individuals based on records of parents and siblings, respectively. Selection on sib versus progeny test results shortens the generation interval and increases rates of genetic response. A consequence of the nucleus herd concept was that EBV of relatives are more correlated through extensive use of family information; thus, more individuals are selected out of fewer families, thus increasing inbreeding rates. Inbreeding leads to depression in performance traits and a reduction in genetic variance. Inbreeding rates may be reduced by increasing the herd size and the numbers of sires and dams selected. However, increased herd size increases the cost of a nucleus herd program. 1702

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Recent research has focused on ways to obtain maximum genetic response in nucleus herds of small size and to limit inbreeding at the same time. Quinton et al. (13) showed that, when low inbreeding rates are targeted, selection on BLUP of EBV based on an animal model may be inferior to selection on phenotype. Woolliams (19) proposed the use of factorial mating designs for genetic response under constraints of inbreeding. Nicholas and Smith (11) suggested that selection of sires be limited to a maximum of one per full-sib family to limit inbreeding. Because the number of full-sib families increases in proportion to the number of dams and mates per dam (Md), factorial designs offer increased possibilities for restricted selection of sires to limit inbreeding without appreciable reductions of selection response (6, 14, 16, 18, 19). Tor0 and PerezEnciso (17) showed that optimization of selection response under restricted inbreeding was possible with matings of individuals with minimal coancestry. Use of assortative mating, positive (mating of best to best) and negative (corrective), for increased selection response has been the focus of several studies (2, 15). The majority of simulation studies with nucleus breeding programs have assumed random mating of selected parents. Studies are lacking that consider the effect of mating strategy on rates of inbreeding. The objectives of this study were to consider alternative selection and mating strategies and to identify those that offer a balance of genetic response and inbreeding. This study focused on four aspects of selection and mating for both adult and juvenile schemes as follows: 1) selection method (selection index, amount of information on relatives varied); 2) mating design (hierarchical and factorial); 3) mating strategy (random and assortative); and 4) restrictions on selection (unrestricted or restricted selection of sires), mating strategy (matings of close relatives allowed or prohibited), or both. The effect of heritability on comparison of mating designs was also considered.

Fifty repetitions of the breeding program were carried out. Offspring were generated as a single cohort, and generations were assumed to be discrete. Eight sires and 64 dams were selected to breed each generation. Each dam was required to produce 16 offspring. The effect of variation in reproductive rate was ignored in this study, and large numbers of offspring were assumed to be obtained with use of reproductive technologies such as MOET or in vitro embryo production. Genetic Evaluation and Selection

Selection was for a total merit index with heritabilities in the base population of .lo, .25, or SO. Records were available only on adult females. An infinitesimal additive genetic model was assumed. Genotypic values (G) for base population (generation 0) animals are simulated as G =

VU,^,

where v is a random normal deviate sampled from N(0, l), and a,o is the additive genetic standard deviation equal to the square root of the base population heritability. The phenotypic standard deviation was assumed to be 1.0. Progeny genotypic values (Gp) were simulated as G, = .%,

+

+

.5Gd

V$

where G, and Gd are the additive genetic values for the sire and dam,and vlp represents the Mendelian sampling of gametes from the sire and dam. The latter was randomly sampled where F was the from N(0, .5 (1 average inbreeding coefficient of the sire and dam derived from the additive relationship matrix (12). The phenotypic value (P) of each female progeny, ignoring fixed e&ects, was generated by

No),

P, = Gp + w

u,

where w is a random normal deviate sampled from N(0, 1) and a, is the environmental stanAny effect A closed nucleus breeding program of herd dard deviation equal to T(1 size of 1024 offspring per generation (one-half of inbreeding depression on phenotypic perforwere female) was stochastically simulated. mance was ignored. MATERIALS AND METHODS

do).

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LElTCH ET AL.

Genetic Evaluation. Parents of the next generation were selected on EBV. Three different methods for the calculation of EBV were considered: 1) selection index including information on all relatives available (!3I,U> (4); 2) selection index including information on close relatives only: full and half sibs and the individual (female) @Ic],-,& and 3) selection of females on the basis of phenotype and selection of sires was on SIclose @ I d ) . Because fixed effects were ignored in the simulation, SId1 was equivalent to selection on BLUP (4). Selection. Juveniles were selected at 15 mo on the basis of pedqree index, the average of EBV of sires and dams. Adults were selected at 34 mo based on their EBV. Three selection strategies were considered: 1) strategy A, no restrictions on the selection of sires were imposed, and mating of full sibs was allowed; 2) strategy B, no restrictions on the selection of sires were imposed and mating of full sibs was prohibited; and 3) strategy C, selection of sires was restricted to between full-sib families, and mating of full sibs was prohibited. Assuming a 15-yr planning horizon, which was a reasonable planning period for dauy cattle breeding programs, the simulation was carried out for 7.5 and 4 generations of selection for juvenile and adult schemes, respec-

tively. Table 1 shows the timetable for the juvenile and adult schemes. Meting Strategy

Muting Designs. Four mating designs, distinguished by the Md, were considered: 1) design 1, each dam was mated to 1 sire (Md = 1); 2) design 2, each dam was mated to 2 sires (Md = 2); 3) design 3, each dam was mated to 4 sires (Md = 4); and 4) design 4, each dam was mated to all sires @id = 8). Design 1 was referred to as hierarchical, and designs 2, 3, and 4 were factorial. Selection of Mutes. Three approaches for mating selected sires and dams were considered: 1) sires and dams were randomly mated; 2) best sires were mated to the best dams (Le., positive assortative); or 3) corrective mating (i.e., negative assortative) was carried out. These approaches were modified according to strategies B and C described herein, which excluded matings of full sibs. Table 2 provides a summary of the methods used in this study. Genetic Response and Inbreeding

Genetic Response. The response to selection in generation t (Rt) was the mean genotypic value for offspring born in generation t.

TABLE 1. Timetable of events for juvenile and adult schemes. Time

Time

Juvenile'

(mol

(mol 15 24 34 39

S i s and dams mated Generation 1 born Complete first lactation record Sires and dams selected

48 58

Generation 2 born Complete first lactation record

63

Sires and dams selected

72

Generation 3 born

96 120

I44 168 192

Adult*

Generation Generation Generation Generation Generation

4 5 6 7 8

born born born born born

45

Sires and dams mated Calving Complete first lactation record Sis and dams selected Generation 1 born

60

Mate generation I offspring

69

Generation 1 offspring calve

79 81

Complete first lactation record Sires and dams selected

15 24 34

90 135 180

Generation 2 born Generation 3 born Generation 4 born

'Generation interval was 24 mo (2 yr); generations were based on a 15-yr (180 mo) planning horizon: 180/24 = 7.5. weneration interval was 45 mo (3.8 yr); generations were based on a 15-yr (180 mo) planning horizon: 180/45 = 4.

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Presentation of results for genetic response and inbreeding as annual rates facilitated comparison with other studies. AR = (Rt - Rt -

l ) L

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terval &), namely, 2 and 3.8 yr for juvenile and adult schemes, respectively. Inbreeding. Rates of inbreeding (m expressed as a proportionate increase from generation t - 1, were calculated for each generation using the equation (3),

Rates of genetic response were averaged over generations 2 to 7.5 (inclusive) and 2 to 4 AF = (Ft - F' - 'y(1 - F - 1)L, (inclusive) for juvenile and adult schemes, respectively. Rates of genetic response for divided by the appropriate generation interval generation 7.5 were obtained from S(R8 - R7). to obtain annual rates of inbreeding for juveAnnual rates of genetic response were obtained nile and adult schemes. Rates of inbreeding by dividing by the appropriate generation in- were averaged over generations, which is simi-

TABLE 2. Summary of parameters, genetic evaluation, selection, and mating strategies considered. Parameters Heritability in base population .lo, .25, S O Herd size 1024 per generation (one-half are female) Breeding population 8 sires and 64 dams 15 Yr Planning horizon Genetic evaluation and selection strategy Selection scheme Adult Selection on EBV Selection at 3 yr after first lactation Generation interval 3.8 yr 4 generations of selection Selection on mean of pamtal EBV Juvenile Selection at 15 rno Generation interval of 2 yr 7.5 generations of selection Evaluation methodl Based on performance information on individual (for females) and SIdl all relatives Based on performance information on individual (for females) and SIClOse full and half sibs Females selected on own performance and males selected on SI,lose Stsub. Selection strategy A No restriction on selection of sires or matings of full sibs B No restriction on selection of sires and no matings of full sibs allowed C Sire selection restricted to a maximum of 1 per full-sib family and no matings of full sibs allowed Mating strategy Mating design 1 Each dam mated to 1 sire 2 Each darn mated to 2 sires 3 Each dam mated to 4 sires 4 Each dam mated to all sires Selection of mates Random Mating of selected individuals at random Assortative mating and best sires mated to best dams Positive Assortative mating and best sires mated to worst of the selected dams Negative Wall = Selection index including information on all relatives; = selection index including information on close relatives; sISub = selection of females on phenotype and sires selected on Sl,lose.

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1 Iuo

U I 1 L I - l c1 liL.

TABLE 3. Comparison of average annual rates of genetic response (AR) in standard deviation units and percentage of inbreeding (AF) and the relative i n b d i n g to response ratio (RIRR) for juvenile and adult schemes with different selection methods based on index Heritability of .25. Juvenile scheme Selection index

Design 4 (Md = sires)

Design 1 (MB = 1) AR

AF Sbl

RIRR AR

AF %ub

AR

AF RlRR

.I04 4.20 1.w

.005

.125 3.45 1.09 ,137 3.50 ,113 2.91 1.02

,056

.IO8

.005

4.18 .094 3.60 .98

.047

Design 1 (Md = 1)

SE

SE4 SIclose

Adult scheme

,005 ,045 ~

.004

.036 .004 .030 .004

.030

Design 4 (Md = sires)

SE

SE ,104 2.17 .97

,003 .029

.lo7 ,006 2.24 ,099 1.99 .97

.030 .003 .029

.lo4 2.11 1.04 .lo8 2.11 .092 1.89 1.06

.002

.030 ,002

,022 .002 .018

~

Wall = Selection index including information on all relatives; SIclosc = selection index including information on close

relatives; sIs,,f, = selection of females on phenotyp and sires selected on SIc]=. *Rates were averaged over the 15-yr planning horizon, excluding the fust generation of selection. No restrictions on sire selection, and mating of full-sibs was allowed (strategy A). 3Mates per dam. Mating of selected sires and dams was random. 4Averaged over 50 replications. sRIRR = [(4.2/4.18)~[(.104/.108)] = 1.04.

lar to the approach described for calculating SIclw, or sIs"b selection indices are presented in Table 3. Selection was for a trait with average rates of genetic response. heritability of .25. Results are shown for the hierarchical (design 1) and the complete facRelative inbreeding to Responru, Ratio torial mating design (design 4)for juvenile and An index called the relative inbreeding to adult schemes. No restrictions were imposed response ratio (RIRR)was used to evaluate on the selection of sires or on matings of full strategies for their ability to effect changes in sibs (strategy A). Matings of selected sires and rate of inbreeding relative to changes in rate of dams were carried out at random. Rates of genetic response and was determined from genetic response and inbreeding with selection on S&lOse and SI,&, were expressed as percenRIRR = (AFi/AFjr(ARi/ARj> tages of rates with selection on SId1. This expression gave an indication of the relative where j is the standard strategy used, and i was efficiency of the selection methods for increasthe strategy examined. For example, for com- ing rates of response or decreasing rates of parison of the effects of mating design on inbreeding. selection response and inbreeding, j denotes Genetic Response. The relative efficiency of hierarchical design 1, and i refers to factorial selection on S I d for increased rates of genetic designs 2, 3, or, 4. Low index values were response was similar to that with Sklose, but preferred. The RIRR was used to simplify appreciably higher than that with SIsub (Table comparison of strategies. 3). Mating designs considered in this study resulted in contributions of large numbers of full and half sibs (up to 8 full sibs and 70 half RESULTS AND DISCUSSION sibs, depending on the mating design) to the genetic evaluation of sires and dams with Genetic Evaluation Method Sklw and for selection of males with SI,&,. Average rates of genetic response and in- Correlation between the EBV and true breeding values (indicative of accuracy of selection) breeding with genetic evaluation using SI,, Journal of Dairy Science Vol. 77, No. 6, 1994

SELECTION RESPONSE AND INBREEDING

with SIclose was comparable with that with SId1 BLUP, and rates of genetic response with Siclose were from 91 to 97% of those with SIdl. Selection of dams on the basis of phenotype with SISub resulted in loss of accuracy of selection, which was reflected by the reduction in the relative efficiency of selection. Rates of genetic response were from 83 to 90% of those with selection on SId. Differences in the relative efficiency of SId compared with SElose or SISub were similar for designs 1 and 4. Inbreeding. Rates of inbreeding with S&lose were generally similar to those with SId. This result supported those of Quinton et al. (13), who reported almost identical genetic response and inbreeding with index selection compared with selection on BLUP for different heritabilities. The BLUP model considered in the study by Quinton et al. (13) is equivalent to SId when fixed effects are ignored. Substantial reductions in inbreeding rates were realized with SISub; inbreeding rates were 85 to 90% of those with SId1 (Table 3). Higher inbreeding with selection on S I d or Sblosewas due to higher accuracy of selection (based on increased numbers of relatives contributing information) and to the emphasis on information from relatives rather than on the individual. Correlations among EBV of relatives were increased, resulting in an increased probability of selection of related individuals. Quinton et al. (13) suggested that selection on animal model BLUP may not lead to optimal selection response under constraints of inbreeding. The use of BLUP for genetic evaluation of dairy cattle is widely accepted and is an effective selection tool. A preferred approach is to use BLUP, or approximations of BLUP, in conjunction with selection and mating strategies designed to limit inbreeding. This study focused on alternatives to balance selection response and inbreeding. The EBV calculated using SI,.lose was the selection criterion applied herein because this method provided a very good approximation to S I d and was easier to apply. RZRR. Generally, evaluation methods which ignore information on relatives (&lose and sI,,b) resulted in larger percentages of reduction in genetic response relative to reductions in inbreeding. However, ratios were close to 1. Quinton et al. (13) showed that the relative advantage of selection on animal model BLUP

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(equivalent to SId in this study) for increased rates of genetic response decreased with declining herd size when methods of evaluation were compared at same levels of inbreeding. Thus, with larger herd sizes than considered in this study (1024 herds), SI, might be even more superior in RIRR. Studies comparing selection on BLUP versus selection on phenotype (1, 13) have shown that differences in selection response with BLUP were greatest for traits with low heritability. The BLUP model considered information on relatives other than full and half sibs, which was particularly important at lower heritabilities, when more emphasis was on information on relatives. However, results by Quinton et a]. (13) indicated that, as heritability declines, selection on phenotype was relatively more efficient for decreasing inbreeding relative to reductions in rates of genetic response that were due to reduced accuracy of selection. Mating Designs

Rates of genetic response and inbreeding for the four mating designs are presented in Table 4. Results are shown for juvenile and adult schemes at three heritabilities. No restrictions were imposed on selection of sires, and matings of full sibs were allowed (strategy A). Matings of selected individuals were carried out at random. Details of genetic parameters are provided in Tables 5 and 6 for juvenile and adult schemes. Generic Response. Factorial designs 2, 3, and 4 gave higher rates of genetic response than hierarchical design 1 for juvenile schemes for all heritabilities studied. For juvenile schemes, rates of response increased as Md increased @om design 1 to 4). Factorial designs had little effect on rates of genetic response with adult schemes. For juvenile schemes, rates of genetic response with factorial designs were from 110 to 145% of the rates with the hierarchical design. Rates of genetic response for adult schemes were from 96 to 109% of the rates with the hierarchical design. With the same selection strategy (strategy A), Woolliams (19), using a semistochastic simulation, observed small increases in rates of genetic response for juvenile and adult schemes, when the Md increased from 1 to 4. Lack of agreement with juvenile results Journal of Dauy Science Vol. 77, No. 6, 1994

LEITCH ET AL.

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0

1

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3

0

Y

SELECTION RESPONSE AND INBREEDING

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Journal of Dairy Science Vol. 77, No. 6 , 1994

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LEITCH ET AL.

i

A

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SELECTION RESPONSE AND INBREEDING

of Woolliams (19) may be due to the increased number of generations of selection considered herein. Increased number of generations of selection resulted in greater losses of genetic variance because of increased inbreeding with the hierarchical design than with the factorial design. This effect was most pronounced with low heritabilities (h2 = .IO) when correlation among EBV of relatives was highest. Although not shown, factorial designs had no clear advantage over hierarchical designs for the first generation of selection for juvenile or adult schemes. For subsequent generations, rates of genetic response were highest with the factorial designs because genetic variance from which to select was greater because of the slower accumulation of inbreeding. As shown in Tables 5 and 6, average genetic variance was lowest with the hierarchical designs. For all designs, rates of genetic response were generally highest after the first generation of selection and subsequently declined. The decline in rates of genetic response was due to the continual buildup of inbreeding. Except for additive genetic variance, few consistent differences existed among designs for the other genetic parameters considered (Tables 5 and 6). Replacement of full sibs with increasing numbers of paternal and maternal half sibs (from designs 1 to 4) had little effect on accuracy of selection. With strategy A, sues and dams were selected with equal selection pressure across mating designs, and differences in intensity of selection of sues or dams were not appreciable (maximum difference in selection intensity of designs was 7.2%). Assuming the use of MOET, Woolliams (19) and Stranden et al. (16), using a stochastic simulation, showed that, when the additional time to carry out matings with factorial designs was considered, mating each dam to 24 sires reduced rates of genetic response compared with mating each dam to 2 sires. The effect of reproductive rate was excluded in the present study; Leitch et al. (1994, unpublished data) provided a comprehensive analysis of the effect of reproductive rate on selection response for different mating designs. Inbreeding. Inbreeding rates with factorial designs were from 70 to 99% of rates with hierarchical designs (Table 4). Woolliams (19), using deterministic methods, predicted significant reductions in inbreeding rates when the

1711

number of sires per dam increased from 1 to 2 or 4 sires; rates of inbreeding with juvenile and adult schemes were 76 to 85% of the rates with 1 Md. In the present study, rates of inbreeding generally decreased as number of Md increased up to 4 (design 3). Higher inbreeding was associated with designs that resulted in large full-sib families. Because the full-sib family structure was highly correlated for juvenile and adult schemes, selection favored entire families of males and females. The probability of coselecting full sibs and of matings of full sibs was diminished as the size of the full-sib family decreased and as selection involved more families. However, when dams were mated to all sires (design 4), a proportion of the matings was guaranteed to be between full sibs unless restrictions were imposed. The probability of full-sib matings also decreased by increasing the number of mates. Although the probability of coselecting fullsibs was diminished by the smaller number available, the completely crossclassified structure of design 4 ensured a larger number of related individuals with a higher average degree of relationship. Inbreeding decreased the Mendelian sampling variance within families, thus reducing additive genetic variance. Lower rates of inbreeding with factorial designs increased additive genetic variance, which contributed to increased rates of genetic response (Tables 5 and 6). RIRR. Generally, factorial designs resulted in FURR <1.0 because inbreeding rates with factorial designs decreased, and rates of genetic response tended to increase, compared with the hierarchical design. Effect of Varying Heritability

Genetic Response. As expected, rates of response increased with heritability. Comparison of designs at each heritability showed that the advantage of factorial designs over hierarchical diminished as heritability increased (Table 4). This observation was the case for juvenile schemes. No clear trend emerges for adult schemes. In contrast, Stranden et al. (16) observed that, for adult schemes, the advantage of factorial designs was greatest with high = .50). The main effect of heritabilities (l? changing heritability was the weight of inforJournal of Dairy Science Vol. 77, No. 6, 1994

I I l L

us.-.*

-1

.-.

TABLE 7. Annual rates of genetic response (AR) and inbreeding (AF) with juvenile schemes expressed as percentages of rates with adult schemes, and the relative inbreeding to response ratio (RIRR). h* .10

AR

AF .25

RIRR AR

AF SO

RIRR AR

AF RRR

Design 1 (Mdl = 1)

Design 2 (Md = 2)

Design 3 (Md = 4)

Design 4 (Md = sires)

84 192 2.292 100 194 1.94 105 206 1.96

82 202 2.46 107 219 2.05 119 235 1.97

100

205 2.05 117 204 1.74 120 217 1.81

113 147 1.30 I20 164

1.37 124 185 I .49

‘Mates per dam. Matings of selected sires and dams were random. ZRIRR = (AFj,,,nile/hF,dul,y(ARj~”~~l~AR~~l,) = 192/84 = 2.29.

mation on the individual compared with that of records on relatives. The amount of pedigree information did not change with mating design. Furthermore, as shown by Woolliams (19), differences in correlations among EBV that were due to mating design were similar for different heritabilities. Thus, differences in the relative advantage in response of factorial designs over hierarchical were not expected by changing heritability. A possible reason for the advantage of factorial mating designs with heritability of .10 for juvenile schemes may have been related to the higher correlation among EBV of relatives. Inbreeding. Rates of inbreeding decreased as heritability increased because of the reduced weight on pedigree information. The relative reduction in inbreeding rates with factorial designs compared with hierarchical designs was not much affected by heritability. These results conflicted with those of Stranden et al. (16). who showed that opportunities for reduced inbreeding with factorial designs were greatest for traits with high heritability @ = SO). An explanation for these differences was not apparent. RIRR. Generally, heritability made little difference to RIRR for overall effectiveness of factorial designs for decreasing inbreeding rates relative to opportunities for increasing rates of genetic response.

schemes relative to adult schemes for the three heritabilities considered. These relative rates were based on the figures provided in Table 4. Genetic Response. Annual rates of response with juvenile schemes were generally greater than those with adult schemes, especially for higher heritability. Woolliams (19) compared juvenile and adult schemes at heritability equal to .25 and found that rates of genetic response with juvenile schemes were, on average, 146% of those with adult schemes. Accuracy of selection for adult schemes (Table 6) was higher than accuracy of selection of juveniles (Table 5). Selection differentials were slightly higher with adult schemes because the population structure was less correlated. With juvenile schemes, the generation interval was, however, nearly one-half that of adult schemes (2 vs. 3.8 yr). However, when heritability was low and hierarchical mating designs were used, potentially higher rates of genetic progress with juvenile schemes were eroded by higher inbreeding rates. Generation interval for adult schemes assumed that selection followed the completion of one lactation record. Selection on the basis of records in progress or test day yields could have shortened the generation interval, which could have decreased the relative advantage of juvenile schemes for increased annual rates of genetic response. Inbreeding. Annual rates of inbreeding with Juvenile Versus Adult Schemes juvenile schemes were from 147 to 235% of Table 7 provides a summary of rates of those with adult schemes. Woolliams (19) genetic response and inbreeding for juvenile found that annual rates of inbreeding with Journal of Dairy Science Vol. 77, No. 6, 1994

SELECTION RESPONSE AND INBREEDING

juvenile schemes were about 190% of those with adult schemes but that rates of inbreeding per generation were similar to those for adult schemes. Higher rates of inbreeding per year with juvenile schemes were due to the higher correlation of EBV of relatives and because of shorter generation intervals. Opportunities exist with the use of in vitro embryo production to utilize prepubertal and even fetal female donors, thus further decreasing the generation interval. However, nucleus programs based entirely on such schemes may not be practical because of associated high inbreeding rates. RZRR. The RIRR for juvenile versus adult schemes exceeded 1.0 for all designs and heritabilities. Thus, potential for increased rates of genetic response with juvenile schemes was more than offset by increased inbreeding rates because small increases in rates of genetic response led to large increases in inbreeding rates. In practice, however, generations will overlap and optimal nucleus herd programs will involve selection across age groups to maximize genetic merit (7, 8). Selection Strategies and Mating Restrlctlons

Table 8 compares the effect of imposing restrictions on selection of sires and matings of full sibs on rates of genetic response and inbreeding. Rates of genetic response and inbreeding with strategy B (no restrictions on selection of sires, but matings of full sibs were not allowed) and strategy C (selection of sires restricted to between full sibships, and matings of full sibs were not allowed) were expressed as percentages of rates with strategy A (no restrictions on sire selection or matings of full sibs). Matings of selected sires and dams were carried out randomly, except with strategies B and C, in which matings of full sibs were prohibited. Results for juvenile and adult schemes for the four mating designs compared are for selection on a trait with heritability of .25. Generic Response. Imposing restrictions on matings of full sibs and restricting selection of sires had little effect on rates of genetic response. Tables 5 and 6 compare genetic parameters for strategies A and C.Limiting the selection of sires to no more than one per fullsib family with strategy C resulted in a decline

1713

in sire selection pressure and, thus, selection intensity, compared with strategies A or B. Pairwise correlation of EBV among relatives was similar across the different selection strategies, and, therefore, reductions in selection intensity that were due to population structure were also similar. Selection intensities of dams were unaffected. Reduction in selection intensities of sires with strategy C was, however, counterbalanced by higher additive genetic variance, and, thus, rates of genetic response remained fairly constant across designs. These results contrast with those of Meuwissen (9), who showed that restricting selection to 1 sire per full-sib family led to lower rates of genetic response at the same rate of drift variance (which was related to inbreeding) or to more drift at the same rate of genetic response. However, in his study (S), when no restriction on sire selection was imposed and selection was of entire male full-sib families, the number of sires selected was increased in order to decrease rates of inbreeding. Accuracy of selection across mating designs does not follow any consistent pattern (Table 5 and 6). Accuracy of selection was expected to be similar across mating designs because, as Md increase, the number of full sibs contributing information decline but are replaced by increasing numbers of half sibs. Woolliams (19) observed that accuracy decreased slightly with increasing Md and related this trend to the redistribution of information as animals contributing information were simultaneously both maternal and paternal half sibs. Inbreeding. Imposing restriction on matings of full sibs with strategy B resulted in inbreeding rates that were 84 to 97% of inbreeding rates with strategy A. Percentages of reduction in rates of inbreeding were largest with large full-sib families (design 1) and declined with the size of the full-sib family. This decline occurred because the more full sibs that existed per family, the higher was the probability of matings between them under random mating. Toro and Perez-Enciso (17) also showed that substantial reductions in inbreeding were possible with matings of minimal coancestry. In the majority of studies reviewed, full-sib matings were not prohibited. If the planning horizon was sufficiently long, negligible reductions of rates of inbreeding were expected Journal of Dairy Science Vol. 77, No. 6, 1994

Journal of Dairy Science Vol. 77, No. 6, 1994

SELECTION RESPONSE AND INBREEDING

compared with breeding programs that did not prohibit full-sib matings. However, the main effects of avoidance of matings of full sibs with strategy B were that initial rates of inbreeding were reduced by exclusion of matings of full sibs, and subsequent rates of inbreeding became more constant over generations. These two effects caused a delay in the buildup of inbreeding. Restriction of mating of full sibs is useful, for example, when reproductive fitness in the nucleus herd is not to be threatened in the long term by high initial rates of inbreeding or when the planning horizon is short. Rates of inbreeding were further reduced for designs 1, 2, and 3 by restriction of selection of sues to no more than one per full-sib family, as with strategy C. Rates of inbreeding with strategy C were 70 to 97% of those with strategy A. If no restriction on sire selection was imposed, all full brothers within a family were selected. Thus, reductions in inbreeding rates were largest with design 1, for which the number of full sibs was largest. The relative advantages of factorial over hierarchical designs for reducing rates of inbreeding were unaffected by selection restrictions (Table 8). Several studies (14, 16, 18, 19) have compared factorial with hierarchical designs based on a strategy that restricts selection of sires to between full-sib families. For designs for which direct comparisons were possible, inbreeding rates in this study were, on average, 10% higher than stochastic results by Tor0 and Silio (18) and 3 to 20% lower than predictions by Woolliams (19) for juvenile and adult schemes, respectively. Disagreement with Woolliams (19) may be explained because his study involved deterministic predictions of rates of inbreeding, which may have suffered from prediction biases, and he also simulated breeding programs involving the selection of fewer sires and dams than were considered herein. Differences in the magnitude of the estimates of inbreeding rate and opportunity for reduced rates of inbreeding with factorial designs were significant compared with results by Ruane (14) and Stranden et al. (16). Rates of inbreeding shown by Ruane (14), for a breeding program involving selection of 4 sires and 32 dams, showed no clear trend when Md increased from 1 to 4. However, with 8 sires selected, rates of inbreeding increased significantly. The same trend was observed by Stran-

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den et al. (16). These researchers speculated that higher rates of inbreeding with factorial designs were due to a more complex pedigree structure, which resulted in relation of selected individuals through the paternal and maternal sides. This explanation, although plausible, does not account for the larger numbers of full-sib females that are selected from hierarchical designs, which, in subsequent generations of selection, ensures maternal relationship of selected individuals. RIRR. With one exception, the RIRR with strategies B and C for juvenile and adult schemes relative to strategy A were 4 . 0 . Generally, RIRR were lowest with strategy C. The low RIRR were due to the substantial reductions in rates of inbreeding by imposing selection and mating restrictions with little reduction in rates of genetic response. Alternative Strategies. Only three selection strategies were compared herein, but many other possibilities for selection exist. No attempt was made in this study to identify strategies that optimize selection response. Studies by Ruane (14) and Stranden et al. (16) have shown that response was maximized when 2 sires per full-sib family were selected. Woolliams (19) showed that further reduction in inbreeding may be achieved by limiting selection of sires to between paternal half-sib families. Kinghorn et al. (5) showed that selection response may be maximized with factorial designs with restricted selection of both sires and dams to between full-sib families. Larger nucleus herd sizes or several nucleus herds, involving selection of increased numbers of sires and dams, further limit inbreeding. Studies have considered the application of indicator traits for increased rates of genetic response when selection was from families of full sibs (5, 20). When indicator trait selection was used, increased rates of genetic response that were due to increased accuracy of selection were provided for and correlation among EBV of full sibs was reduced; thus, this method can also be applied to reduce rates of inbreeding with juvenile and adult schemes. Furthermore, selection on indicator traits or markers potentially enables early identification of superior genotypes, thus reducing the generation interval. Journal of Dairy Science Vol. 77, No. 6 , 1994

Journal of Dairy Science Vol. 77, No. 6, 1994

Selectlon of Mates

hgher rates of inbreeding. Higher rates of inbreeding with positive assortative mating Table 9 compares the effect on rates of may be due to increased variance of family genetic response and inbreeding for three matsize and the inheritance of selective advantage, ing strategies: matings selected parents at ranwhich significantly reduces genetic variance dom, mating best to the best (positive assorta- over time. With random mating, buildup of tive), or mating correctively (negative inbreeding was slower because, even when assortative). Rates of genetic response and in- mating is between closely related individuals, breeding with the two assortative mating resulting progeny will be randomly mated to strategies were expressed as percentages of less closely related individuals. rates with the random mating program. No MRR. The use of assortative mating, either restrictions were made on selection of sires, positive or corrective, was not effective to and matings of full sibs were allowed (strategy reduce inbreeding rates or to effect large inA). Results are shown for juvenile and adult creases in rates of genetic response in relation schemes for the three mating designs for which to inbreeding rates, and RIRR exceeded 1.O for consideration of alternative strategies for mate the majority of designs. selection was feasible (designs 1, 2, and 3). Genetic Response. Rates of genetic reCONCLUSIONS sponse with corrective mating were 84 to 102% of those with random mating of selected Selection should be based on methods of sires and dams. When rates of genetic response animal model BLUP or approximations of differed, they were not appreciable because of BLUP that lead to the highest degree of acthe high selection intensity considered. A curacy of selection and, thus, selection rereduction in rates of response can be explained sponse. Selection methods based largely on by the reduction in additive genetic variance, phenotype lower inbreeding, but at the expense resulting from the introduction of a negative of reduced genetic response. Inbreeding may covariance between mates (2). Conversely, a be effectively reduced with selection and matpositive covariance between mates was in- ing strategies. Selection and mating strategies troduced when the best individuals were mated should be judged on the basis of opportunities to each other, generally increasing response, of their genetic response relative to their inwhich was due to an increase in additive breeding. Breeding strategies based on adult genetic variance. Increases in rates of genetic schemes are then favored over schemes based response were small for juvenile and adult only on selection of juveniles. Opportunities schemes. Smith and Hammond (15) showed for increased rates of genetic response with that positive assortative mating is only useful juvenile schemes that are due to shorter generas a means to increase rates of genetic re- ation intervals are potentially offset by their sponse temporarily, when heritability was high higher rates of inbreeding. Mating strategies that lead to maximum selection response inand selection intensity was low. Inbreeding. Corrective and positive assorta- volve random mating of selected dams to tive mating strategies generally increased in- several of the sires selected. Imposition of breeding rates for juvenile schemes. Except for restrictions on selection of sires and matings of design 3 for the adult scheme, rates of inbreed- full sibs effectively reduces inbreeding without ing with corrective and positive mating in- loss of selection response. Finally, better detercreased, respectively, from 101 to 137% and mination of the appropriate criteria for optimi102 to 137% of those with random mating. zation of breeding strategies constrained by Increased rates of inbreeding with corrective inbreeding requires knowledge of the tradeoff mating were due to the reduction of between between selection response and inbreeding. family variance resulting from negative covariances between mates. When selection was enREFERENCES tirely on variance between families, as in juve1 Belonsky, G.M., and B. W. Kennedy. 1988. Selection nile schemes and selection of sues in adult on individual phenotype and best linear unbiased schemes, reduced variances led to increased predictor of breeding value in a closed swine herd. J. h i m . Sci. 66:1124. correlations among EBV of relatives and Journal of Dairy Science Vol. 77, No. 6, 1994

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LEITCH ET AL.

2Bulmer. M. G. 1980. The Mathematical Theory of Quantitative Genetics. Clarendon Press, Oxford, Engl. 3Falconer, D. S. 1989. Introduction to Quantitative Genetics. 3rd ed. Longman, London, England. 4Henderson, C. R. 1984. Applications of Linear Models in Animal Breeding. Univ. Guelph, ON, Canada. 5 Kinghorn, B. P., C. Smith, and J.C.M. Dekkers. 1991. Potential genetic gains in dairy cattle with gamete harvesting and in vitro fertilization. 1. Dairy Sci. 7 4 611.

6Leitch, H. W., C. Smith and E. B. Bumside. 1990. Implications of in vitro feailization technology on genetic response in dairy cattle. Proc. 4th World Congr. Genet. Appl. Livest. Prod., Edinburgh, Scotland XIV:279. 7 Lohuis, M. M. 1993. Strategies to improve efficiency and genetic response of progeny test programs in dairy cattle. Ph.D. Diss., Univ. Guelph, Guelph, ON, Can. 8 Meuwissen, T.H.E. 1989. A determinastic model for the optimization of dairy d e breeding based on BLUP breeding value estimates. Anim. Prod. 49:193. 9 Meuwissen, T.H.E. 1990. The effect of the size of the MOET nucleus dairy cattle breeding plans on the genetic gain and its variance. Roc. 4th World Coagr. Genet. Appl. Livest. Prod., Edinburgh, Scotland XIV: 271. 10Nicholas. F. W. 1979. The genetic implications of multiple ovulation and embryo transfer in small dairy herds. 30th Ann. Mtg. Eur. Assoc. Anim. Prod., Harrogate, England. 11 Nicholas, E W., and C. Smith. 1983. Increased rates of genetic change in dairy cattle by embryo transfer and splitting. Anim. Prod. 36:341. 12 Quaas, R. L. 1976. Computing the diagonal elements and inverse of a large numerator relationship matrix. Biometrics 32:949.

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13 Quinton, M., C. Smith, and M. E. Goddard. 1992. Comparison of selection methods at the same level of inbreeding. 1. Anim. Sci. 70:1060. 14Ruane, J. 1991. The effect of alternative mating designs and selection strategies on adult multiple ovulation and embryo transfer (MOEI7 nucleus breeding schemes in dairy cattle. Genet. Sel. Evol. 23:47. 15 Smith, S. P., and K. Hammond. 1987. Assortative mating and artificial selection: a second appraisal. Genet. Sel. Evol. 19:181. 16Stranden. I., A. Maki-Tanila and E. A. M a n t y s h . 1991. Genetic progress and rate of inbreeding in a closed adult MOET nucleus under different mating strategies and heritabilities. 1. Anim. Breed. Genet. 108:401. 17 Toro, M. A,, and M. Perez-Enciso. 1990. Optimization of selection response under restricted inbreeding. Genet. Sel. Evol. 22:93. 18Toro. M., and L. Silio. 1989. Genetic simulation of juvenile MOET breeding schemes in dairy cattle. Page 64 in New Selection Schemes in Cattle: Nucleus P r o m . Publ. No. 44.E. Kalm and T. Libonussen, ed. Eur. Assoc. Anim. Prod., Wageningen, Neth. 19Woolliams, J. A. 1989. Modifications to MOET nucleus breeding schemes to improve rates of genetic progress and decrease rates of inbreeding in dairy cattle. Anim. Prod. 49:l. 2OWoolliams, J. A., and C. Smith. 1988. The value of indicator traits in the genetic improvement of dairy cattle. Anim. Prod. 46:333. 21 Wray, N. R., and W. G. Hill. 1989. Asymptotic rates of response from index selection. Anim. Prod. 49:217. 22 Wray, N. R.,and G. Simm. 1990. The use of embryo transfer to accelerated genetic improvement in beef cattle. Proc. 4th World Congr. Genet. Appl. Livest. Prod., Edinburgh, Scotland XV:315.