A Simulation Study of Selection Methods to Improve ...

A Simulation Study of Selection Methods to Improve Mastitis Resistance of Dairy Cows J. J. COLLEAU lnstitut National de la Recherche Agronomique Quantitative and Applied Genetics Unit 78352 Jouy-en-Josas Cedex. France

E. LE BIHAN-DUVAL lnstitut National de la Recherche Agronomique Poultry Science Unit 37380 Nouzilly, France ABSTRACT

Mastitis problems were assumed to decrease profitability of dairy cows through milk price, treatment cost, and involuntary culling cost. Milk price decreased through a stepwise function of SCC (actual French conditions). A continuous latent variate was supposed to trigger other costs through appropriate thresholds. The relative weights for one genetic standard deviation in the selection objective were 1, -.07, and -.14 for yield, SCC, and mastitis liability, respectively. Annual genetic gains were predicted for a conventional breeding scheme using statistical parameters from the literature. Selection on yield and log SCC, with or without mastitis culling rate, increased genetic gains for the overall profitability of .7 or .9%, respectively, compared with selection on yield only. Increases of log SCC and mastitis problems because of selection were substantially reduced (40 to 60%). Consequences from constraint of the genetic trend for mastitis liability to zero depended on the method used to assess mastitis problems. Use of log SCC had a significant and variable negative impact (-8.9 to -36% according to parameters) on overall efficiency compared with the relevant unconstrained selection. Simultaneous use of log SCC and culling rate had a moderate effect ( 4 . 9 to -7.4%) on

Received January 14, 1994 Accepted July 11. 1994. 1995 J Dairy Sci 78:659-671

overall efficiency compared with that from unconstrained selection. (Key words: mastitis, dairy cattle, selection, threshold variates) Abbreviation key: Y = observed milk yield variate, L = log SCC. M = susceptibility to mastitis variate, H = selection objective. INTRODUCTION

Mastitis is one of the most economically detrimental diseases of dairy cows. Multiple economic losses are incurred through yield losses, decreased milk price and longevity, and increased health care costs. The resulting overall effect is considerable. According to a review by Schepers and Dijkhuizen (52), this overall effect might amount to 40 to 50% of the economic net margin per cow; the largest part of this loss (70 to 80%) comes from yield losses (about 5 to 7% per present cow). Cases of clinical and subclinical mastitis contribute to these losses. Disease detection can be performed directly from milk composition and appearance and body temperature or indirectly from higher milk log SCC (3, 34, 46, 47, 48). Research increasingly demonstrates that selection for mastitis resistance is simultaneously necessary and potentially efficient because the relevant traits (direct or indirect measurements of the disease) are heritable and unfavorably correlated with milk yield, the main trait selected. However, current selection procedures, except those of European Nordic countries (9, 22, 45, 58), generally ignore susceptibility to mastitis. A long-term perspective (56) should include such selection to counteract unfavorable genetic trends and to account for the steady decrease in profitability of selection on yield 659

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COLLEAU AND LE BIHAN-DUVAL

alone, especially when yield quotas are imposed (16, 27, 28, 30, 61). Simulation has been used to attempt to define the relevant breeding schemes for implementation and evaluation of economic responses (21. 41, 50, 54, 59). The objective of this work is to present additional results and conclusions from a simulation using statistical genetic parameters obtained from international literature, but considering French economic data and breeding schemes. The main issues addressed concern the economic weight given to mastitis traits and milk yield, the minimum list of relevant variates to be recorded and included into the estimated breeding values procedures, and the selection responses for the overall economic profitability and for each trait. Because nonlinear methodology is involved for threshold variates, predictions are compared with Monte Carlo results for verification.

and the corresponding within-herd standard deviation is about 1.1. Results obtained by Banos and Shook (4) from about 1 million US Holstein cows and several thousand herds showed that the between-herd variance for this trait corresponded to about 25% of within-herd variance. Thus, increasing penalty would be incurred by 4.4, 4.5, and .5% of herds, respectively. The M variate is supposed to be the real cause of treatment and culling costs specific to mastitis. The literature shows that the mean number of recorded treatments is about 1.2 to 1.3 per lactation (5. 8. 58), that the percentage of treated cows per lactation varies between 10 and 30% (5, 13. 23, 37, 38, 40, 57, 58, 60, 63), and that the percentage of cows culled for mastitis amounts to about 13% of the total disposals per lactation. or about 3% of the whole population [see review (S)]. In France, about 20% of cows have clinical mastitis. and the percentage of cows culled because of MATERIALS AND METHODS mastitis is close to the literature average (5. 7). Consequently, a simple model is proposed to Creating a Functional Model approximate reality: a lower threshold for susThe two purposes of functional modeling ceptibility to mastitis triggers a dummy treatare to assess relevant economic weights and to ment (20% of the cows), the cost of which is define the evaluation procedures to implement. the same as 1.3 treatments and an upper Three functional variates are considered: threshold leads to culling for mastitis (3% of observed milk yield (Y), which includes possi- the cows). Therefore, culling rates are obtained ble losses from clinical or subclinical mastitis; in a rather idealistic situation in which cows with extreme susceptibility to mastitis are althe observed average log SCC (I expressed ,), as the natural logarithm of leukocytes per ways culled, regardless of other traits. This last microliter of milk; and a hypothetical underly- assumption might be at variance with real data ing variable for the susceptibility to mastitis on reasons for disposal (65). This possibility should be kept in mind during discussion of W). results obtained. The functional model describes the analytical links between these three basic variates and the observed components of the economic bal- Derivation of the Corresponding ance, i.e., milk yield, milk price, treatment Economic Weights costs, and costs incurred from early cullings. The economic weight for each unit of milk The log SCC is assumed to influence in- yield is derived from an analysis of cost and dividual milk prices directly through the price income under a quota situation for fat yield system used for herd milk payments in coun- and is drawn from a current work defining the tries such as France. In western France, a current French overall dairy index (16). region with significant milk yield, the average Weights expressed in French francs per kiloprice per kilogram of milk [2 FF (French gram were 45.5, -1.8. and - S O for yields of francs)] is reduced by .02, .06, and .I2 FF if protein, fat, and carrier, respectively. These mean herd SCC is between 250 and 300, 300 three variates are pooled into one variate, Y. and 500, or above 500, respectively @&nard, The economic value of the genetic standard 1993, personal communication). Literature deviation is the same as the counterpart for the parameters for the Holstein breed show that aggregate genotype that combines the three the mean log SCC is about 4.8 (120 cells/pl), original traits. Taking into account the genetic Journal of Dairy Science Vol. 78, No. 3. 1995

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SELECTION FOR MASTITIS RESISTANCE

parameters for pure Holstein bulls in France (12), the equivalent margin per kilogram of milk yield amounts to .74 FF. For threshold variates, calculations are less straightforward, because a threshold model induces nonlinear relationships between the economic merit and the underlying variate. If liability P [either log SCC (L)or mastitis liability (M)] is assumed to be distributed as a standard normal variate and c is the absolute value of the cost incurred if P is larger than a threshold t, the average economic effect of increasing Gp (additive breeding value of P) by one unit = -c4(t), where stands for the probability density of a standard normal variate (17). This reasoning can be readily extended when several thresholds and costs exist. The effect of increasing GL by one unit is therefore

TABLE 1. Statistical parameters used in the present simulation: heritabilities along the diagonal. genetic correlation coefficients above the diagonal, and phenotypic correlation coefficients below the diagonal. Trait

Y

Trait'

Y

.37

L M

L

M

.I5

.30

.I2

.65 .06

-.05

0

lY = Milk yield, L = log SCC. and M = susceptibility to mastitis.

$(e)

where y is the mean milk yield per lactation, tj is a standardized threshold for milk payment standardized for between-herd variation according to L, and pi is the penalty per kilogram of milk when tj L tj+l considering that = a, ti = 1.31, t2 = 1.64, t3 = 2.56, t4 = +oo, and po = 0. Calculations are carried out with the previous distributions and thresholds. The mean milk yield is 9000 kg, the value used for modeling consequences of the quota situation (16) and representing a future situation that European countries are rapidly approaching. Formula [ l ] with these parameters gives mL = -75 FF. The effect of increasing GM by one unit is

problem of evaluating the economic value of longevity when culling is involuntary (1, 6, 11, 51, 61, 62). Another constraint is that these calculated should take into account the existence of a quota situation. Strictly speaking, such a calculation would have needed a specialized work to derive the relevant value for French conditions; instead, reasoning is indirect. The relative weight between milk yield and longevity under a quota situation derived for Australia is assumed to hold for France (6), and then culling probability and longevity are connected using a very simple model (Appendix 1). Such a calculation shows that an approximate value for c2 is 1600 FF. Use of these c1 and c2 values leads to mM = -217 FF. If the relevant genetic standard deviations are taken into account (500 kg for Y, .33 for L, and .24 for M if M is standardized variate) and milk yield is a reference, the aggregate genotype (i.e., selection objective, H) can be defined as follows:

H =

GL GM - - .07 - -.14 -

121

where t; is the first standardized for within-

Statlstical Parameters

herd variation threshold for M, ti is the second one, c1 is the cost of a treatment, and c2 is the cost of a culling. Then c1 is estimated to amount to 300 FF (rounded value), which can be split into discarded milk (126 FF = 4 x 25 kg/d x 1.26 FFkg), medicine (100 FF), and veterinarian service (50 FF = .20 visits per treated case x 250 FF per visit). However, c2 is relatively complex to calculate because of the

Table 1 shows parameters from the literature. The heritability estimate for log SCC is pooled from 39 values (2, 4, 10, 14, 17, 23, 24, 32, 35, 42, 43, 53, 54, 63, The phenotypic and genetic correlation coefficients between milk yield and log SCC are pooled from 25 corresponding values (2, 10, 18, 23, 32, 34, 35, 54, The heritability of clinical mastitis is based on fewer studies (13, 23, 37, 38, 40, 57, Journal of Dairy Science Vol. 78, No. 3, 1995

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COLLEAU AND LE BIHAN-DUVAL

58, 63). Correlation coefficients between clinical mastitis and yield are scarce (13. 23. 40, 57, 60). Correlations between clinical mastitis and log SCC are even scarcer (23, 63). Results involving threshold variables are expressed on the continuous scale by use of transformation formulas (18. 25). Scarcity of some parameters prevented consideration of possible variation according to parity. Therefore, only pooled estimates were considered. For consistency with our method of defining the economic weight for milk yield, the heritability given by Boichard and Bonaiti (12) for this trait was considered.

problems, is accessible to observation are abbreviated as YLM and YLMo. These schemes are intended to show the upper limit for consideration of mastitis resistance. A selection method that included treatment rates was not tested, because it would be very difficult to implement in most countries. Prediction of Reliability of Estimated Breeding Values and Direct and Indirect Responses to Selection

Multivariate BLUP are used for calculation of estimated breeding values according to standard theory (31). When continuous and discontinuous data are mixed (method YLC). the Breeding Schemes and Selection Methods relevant multivariate BLUP is that of Foulley et al. (26), which maximizes the a posteriori Selection is assumed to occur along three probability density of the sample, given previgene transmission paths of a conventional ous dispersion parameters. In this case, a diffibreeding scheme: 1) selection of the top 3% of culty arises for calculation of sampling bulls as sires of sons, 2) selection of the top variance-covariances between estimated breed15% of bulls as sires of daughters. and 3) ing values, because the corresponding matrix selection of the top 1% of dams as bull-dams. depends not only on the observed layout but Genetic evaluation for bulls is assumed to also on the true genetic values. For the same be based on 50 daughters and loo0 parternal number of relatives, accuracies of estimated half sisters, which are easily available because breeding values are higher when a higher bull-sires are used extensively. Genetic evalua- proportion of relatives lies beyond the threshtion for dams is assumed to be based on one old. lactation and loo0 paternal half sisters, beThe method presented herein consists of cause bull-dams also are very commonly born calculation of accuracies from an expected layfrom top sires. out given the overall sample size for relatives Essential parameters, such as the number of (daughters, half sisters), the thresholds insampled bulls, selection pressure, and genera- volved, and an assumed null value for every tion intervals, were assumed not to depend on breeding value. The expected layout is thereselection methods. The objective was to test fore the expected distribution of the relatives the efficiency of addition and the use of new of an expected average individual (bull or information in a preexisting structure. Basi- dam); therefore, proportions of relatives becally, the overall efficiency measured in the yond thresholds are assumed to be the same present work is the annual genetic gain for the for each individual. This procedure is as effioverall merit relative to the reference situation cient as a more complex approach, such as a when only yield is selected. Taylor expansion (data not shown), probably Given those assumptions, these ratios were because genetic variance is small for mastitis calculated from the sum of the three selection traits. differentials according to the formula of RenAppendix 2 shows how responses for disdel and Robertson (49). crete categories to selection can be predicted As to selection methods, the true alterna- from accuracies derived as described. tives are selection from yield and log SCC (YL,); selection from yield, log SCC, and cull- Method for Introducing Constraints ing rates for mastitis (YLC); and the homologous selection methods and YLCo) in As stated by Niebel and Van Vleck (44),the which genetic trend for mastitis incidence is unfavorable effect of introducing constraints in constrained to zero. Theoretical schemes in a breeding scheme is minimized when the which M, the underlying variate for mastitis coefficients used to weight each estimated Journal of Dairy Science Vol. 78. No. 3. 1995

SELECTION FOR MASTITIS RESISTANCE

breeding value are not uniform but depend on the accuracies of these estimated breeding values and on their role in gene transmission paths. Specific weights used for sire estimated breeding value and dam estimated breeding value are therefore jointly calculated to maximize the genetic gain for the selection objective, after fulfilment of the constraint. The principles of the algorithm are presented in Appendix 3. In contrast to the method of Niebel and Van Vleck (44), LaGrange multipliers are absorbed during the calculation because this procedure was efficient for other issues with constraints (19). RESULTS AND DISCUSSION

Reliabilities of Estimated Breeding Values

Table 2 shows the reliabilities of estimated breeding values for yield, log SCC, susceptibility to mastitis, and selection objective from multivariate BLUP. Accuracies for log SCC and selection objective do not virtually depend on the selection method, provided that log SCC are directly observed and used. Accuracies for mastitis liability highly depend on the data available for that purpose. Collection of only log SCC would provide a poor predictor because R2 are approximately .30 and .16 for bulls and dams, respectively. Consideration of reasons for disposal also would substantially improve these values, around .42 and .24 for bulls and dams, respectively, i.e., 72 or 79%, respectively, of the values obtained when susceptibility to mastitis can be directly observed.

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Relative Annual Genetic Gains

The order of magnitude of the denominator involved in Rendel and Robertson's formula (49) amounts to 20.1 yr (15). and the reference genetic gains for scheme Y are 88 kglyr of milk, 8.8 x log SCC. and .013 units for susceptibility to mastitis, i.e.. .18, .03, and .05 genetic standard deviations, respectively. Selection based on yield alone leads to increased problems of milk quality and sensitivity to mastitis. The relative genetic gains are shown in Table 3. Selection YL would provide a .7% improvement for the overall economic genetic gains, originating from smaller increases in number of leucocytes and in mastitis problems, by 59 and 32%, respectively. Basically, these results are not far from the ideal situation YLM, in which corresponding values are 1.1, 62. and 46%. respectively. The indirect evaluation of M provided by method YLC gives results halfway between both previous situations. Consequently, reasoning with current economic parameters leads to no possibility of preventing mastitis problems from increasing. When a constraint is imposed, genetic gains for

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COLLEAU AND LE BIHAN-DUVAL log SCC (L), susceptibility to mastitis 0.and aggregate selection

TABLE 3. Relative annual genetic gains for yield objective M according to the selection method. Selection method Y' YL YLC YLM

yLo2

YLCO YLMn

Trait Y

L

100 99.2 99.0 98.8 85.0 89.7

100 41 .O

M

H

100

100 100.7 100.9 101.1 91.8 96.0 98.0

68.1 60.2 53.8

39.8 38.1 -185.0 -100.6 -62.9

0 0

0

'Abbreviated list of variates selected altogether with no constraint. C = Culling rate for mastitis. *Abbreviated list of variates selected altogether. constraining the genetic trend for susceptibility to mastitis to be 0 (subscript 0).

Discrete Expressions

77% for culling rates; corresponding values would be only 23% and 40% if selection method YLC is used.

Table 4 shows the phenotypic occurrence of discrete events after a round of selection among daughters of selected bulls (assumed to be mated to average dams) or among bull- Comparison Between Predicted and Simulated Results dams. Mastitis problems incurred with selection Y and even YL are quite apparent, espeMonte Carlo simulation of a population of cially for bull-dams. 4000 independent bulls, each with 50 daughTable 5 shows the general trend for the ters and 1000 half sisters, shows that predicted whole population after 20 yr of selection, as- average reliabilities are quite accurate, even for suming that the genetic trend is asymptotic for mastitis liability for method YLC, despite the continuous variates. Unfavorable genetic approximation previously discussed (Table 6). changes are not dramatic, but over time the The observed incidences of discrete events increase in health problems is considerable. for the daughters, on which estimated breeding Selection Y over 20 yr would lead to relative values for selection were based, correspond to increases of 41% for mastitis treatments and their predicted counterpart. This verifies the

TABLE 4. Predicted treatment and culling rates for mastitis according to the selected group and the selection method. Selected group Daughters of service bulls

Daughters of bull sires

Bull-dms

Selection method'

Treatment2

Culling3

Treatment

Culling

Treatment

Culling

Y YL YLC YLM

21.5 21.2 21.0 20.9

3.4 3.3 3.3 3.2

22.2 21.7 21.6 21.4

3.5 3.4 3.9 3.3

24.0 23.3 22.7 22.9

4.0 3.8 3.7 3.7

'Abbreviated list of variates selected altogether susceptibility to mastitis). 2Baseline: 20%. 3Baseline: 3%. Journal of Dairy Science Vol. 78, No. 3, 1995

= milk yield, L = log SCC. C = culling rate for mastitis, and M =

665

SELECTION RESISTANCE SELECTION FOR MASTITIS RESISTANCE TABLE TABLE 5, 5. Predicted Predicted treatment treatment and culling culling rates for the whole 20 yr of steady-state steady-state selection, selection. whole population population after 20 Selection Selection method method'l

Occurrence Occurrence 2 Treatment Treatment*

Culling Culling33

(%) (96)

(%) (94

YL YL

28.2 28.2 25,3 25.3

YLM YLM

24,6 24.6 24,1 24.1

5.3 4.4 4.4 4.2 4.2 4.1 4.1

y3 Y3

YLC nc

"I

§ '~i:l

.~

~.g

Jl

~

M\Ort"lr-

~

MNNM~rr-)C""'i

'::I

l=

;§00

o

'3 U

=

~~

\0 Q'\ \0 ("f"j MNNN

".g I I Q.co::

II

C""'iM~M

oS i:l

X

'(5]

" Iu

~ oS .!l

=

lAbbreviated 'Abbreviated list of variates variates selected selected altogether altogether (Y ( = I ' milk yield. mastitis, and yield, L = log SCC, SCC, C = culling culling rate for for mastitis, M = = susceptibility susceptibility to mastitis). mastitis). 2Baseline: *Baseline: 20%. 20%. 3Baseline: 3Baseline: 3%, 3%.

..c ..

~cE:

c

"3

il !:!

Q~ J::>

'"

NNNN

'::I '.;:I

~

~

.8 >.

!-

::3 J::>

.,.,,",,oa-

correctness correctness of Appendix Appendix 2, once predicted accuracies curacies of selection selection indexes indexes have been demonstrated demonstrated to be correct. correct.

~

Linear Llnear Versus Versus Nonlinear Nonlinear selection Selection Objective Objective

'(5

~

!f: E U

~

s'"

.g

a j

1 -

i

=>=>=

Journal of 3, 1995 of Dairy Science Vol. 78, No. No.3,

666

COLLEAU AND LE BIHAN-DUVAL

TABLE 7. Relative economic genetic gains for breeding schemes according to the weight given to log SCC in the breeding objective 0.

TABLE 8. Relative economic gains for breeding schemes according to the value of the genetic correlation coefficient between log SCC and mastitis liability. Genetic correlation between L and M

Weight p e n to L in H Selection method

Present weight

No weight

Selection method

.65 (present value)

.50

.30

Y'

100 100.7 100.9 101.1 91.8 96.0 98.0

100 100.2 100.4 100.5 86.8

Y'

100 100.7 100.9 101.1 91.8 96.0 98.0

100 100.5 100.8 100.9 84.6 94.6 97.5

100 100.3 100.6 100.8 64.8 93.2 96.9

YL

nc YLM yLo2 YLCO YLMo

93.9 96.4

IAbbreviated list of variates selected altogether with no constraint (Y = milk yield, L = log SCC, C = culling rate for mastitis. and M = susceptibility to mastitis). 2Abbreviated list of variates selected altogether. constraining the genetic trend or susceptibility to mastitis to be 0 (subscript 0).

Sensitivity of Results to Assumptions

n YLC YLM

no2 YLCO

n M o

'Abbreviated list of variates selected altogether with no constraint (Y = milk yield, L = log SCC, C = culling rate for mastitis. and M = susceptibility to mastitis). 2Abbreviated list of vanates selected altogether, constraining the genetic trend or susceptibility to mastitis to be 0 (subscript 0).

Introduction of the constraint that the genetic trend should be 0 for mastitis led to an overall economic decrease of 17 or 7%, respectively, when estimated breeding values for log SCC or for occurrence of mastitis were taken into account. These results were more pessimistic than ours, even though the economic value of mastitis was higher than in the present work. Reliabilities of estimated breeding values for susceptibility to mastitis for bulls and dams were substantially lower than ours, especially because we considered half sisters of bulls, which could explain the observed discrepancy. To summarize, results of Strandberg and Shook (59) very much resemble those shown in Table 7, for which no weight is given to log SCC. In contrast with results of Stranberg and Shook (59), Sender et al. (55) found that simultaneous increases of the economic value of a Comparison with the Literature breeding scheme (4%) and decreases of clinical Strandberg and Shook (59) created a selec- mastitis and log SCC were quite achievable. tion objective in which the economic value of This finding is in partial disagreement with our one genetic standard deviation for clinical work; Table 3 shows that negative trend for mastitis was .3 times its counterpart for an occurrence of mastitis would be difficult to aggregate dairy trait (milk yield plus fat yield). obtain without damaging the overall economic They gave no weight to log SCC. Introduction value; maintenance of a zero trend is demandof additional separate evaluation for log SCC ing. Examination of the parameters given by or mastitis liability increased the genetic gain Sender et al. (55) shows that the economic for the overall economic value by .4 or .8%, weights of one genetic standard deviation relarespectively, compared with a reference tive to its counterpart for dairy traits was .45 scheme, in which only yield was selected. and .15, respectively, for log SCC and for

Most simulations do not give any economic weight to log SCC. Table 7 shows the potential impact of such a procedure: a slight increase of overall merit and, most of all, a larger economic cost of constraints, especially for method YLo. The value of the genetic correlation between log SCC and mastitis liability is not yet known with sufficient accuracy. References are scarce and variable. The relevant range is .30 (63) to .80(23). Table 8 shows that when the true correlation is equal to the lowest value, the increase of overall merit through the YL and YLC methods is slightly reduced. The most dramatic impact is the economic cost of introducing a constraint, especially for the YLo method.

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SELECTION FOR MASTITIS RESISTANCE

occurrence of mastitis. An important weight was given to log SCC because it included yield losses (predicted from regression coefficients). This procedure was not at all comparable with ours. which took into account that yield losses were already included in observed yields. Madsen (41) found that constraining the bull selection differential for clinical mastitis to be 0 would cost 34 or 7% of the overall economic selection differential, depending on the absence or presence of recording of clinical mastitis, to complement recording of log SCC. In the present study, the genetic correlation coefficient between log SCC and occurrence of mastitis was assumed to be high, .8. Consequently, such a high cost of the constraint might be caused by the economic weight chosen, .33 vs. 1. when genetic standard deviation for occurrence of mastitis and yield, respectively. were compared. CONCLUSIONS

As in previous simulations. the results of the present work show that introduction of new variates, such as log SCC or susceptibility to mastitis, do not lead to dramatic increases of genetic gain for the overall economic profitability. These increases correspond to about 1%. Therefore, corresponding modifications of breeding schemes should be considered to ensure against future economic conditions under which health costs might be more expensive. Our data show that some positive alterations might be already envisioned, even when present health costs and modest accuracies of estimated breeding values are considered for these new variates (a major constraint is that the organization for bull sampling and selection is unchanged). Recording of log SCC can be considered to be a good start. However, this procedure might be not sufficient for the long term, because increases of mastitis problems are reduced or resolved at too high of an overall economic cost. Also, the efficiency of this procedure is highly dependent on the genetic correlation between log SCC and susceptibility to mastitis, which is not well known. In contrast with this selection procedure, introduction of culling rates for mastitis in data and estimated breeding value procedures theoretically appears to be the most robust and efficient solution for

667

preventing steady increases in mastitis problems, provided culling decisions are really objective, a requisite that is probably very hard to meet in practice, especially when the relevant genetic parameters are considered (65). Of course, the solution implemented by European Nordic countries, i.e., recording treatments. would be even better but could be difficult to put into practice. The long-term search for major susceptibility genes, some of which already apparently exist in the major histocompatibility complex (39), could provide new solutions. The perspectives given by markerassisted selection are most favorable for traits of low heritability (36). i.e., mastitis traits and other traits such as reproduction performance (11) and general longevity (20). ACKNOWLEDGMENTS

The reviewers are thanked for their careful examination of the manuscript and their suggestions. REFERENCES 1 Allaire, F. R., and J. P. Gibson. 1992. Genetic value of herd life adjusted for milk production. J. Dairy Sci.

75:1349. 2 Bahr, T., R. Priesinger, and E. Kalm. 1993. Genetic parameters of cell count in consecutive lactations. Page 83 in Proc. 44th Annu. Mtg. Eur. Assoc. Anim. Prod.. Aarhus, Denmark. 3 Bakken, G. 1981. Relationships between udder and teat morphology, mastitis and milk production in Norwegian Red cattle. Acta Agric. Scand. 31:28. 4Banos. G., and G . E. Shook. 1990. Genotype by environment interaction and genetic correlations among paxities for somatic cell count and milk yield. J. Dairy Sci. 73:2563. 5 Barnouin, J., J. C. Fayet, M. Brochart, A. Bouvier, and P. Paccard. 1983. Enquete kco-pathologique continue: 1. Hitrarchie de la pathologie observQ en tlevage bovin laitier. Ann. V6t. 14:247. 6 Beard, K. T., and J. W. James. 1993. Including the involuntary component of longevity in a breeding objective. Page 75 in Proc. 44th Annu. Mtg. Eur. Assoc. Anim. Prod., Aarhus, Denmark. 7 Beaudeau. F. 1992. La &forme sous toutes ses formes. French Holstein Breed Association Bull. 161. Prim 'Holstein Assoc., St. Sylvain d' Anjou, France. 8 Beaudeau, F., A. Henken, C. Fourichon, K. Frankema, and H. Seegers. 1993. Associations between health disorders and culling of dairy cows: a review. Livest. Prod. Sci. 35:213. 9 Bech Andersen, B., T. Steine, and G. A. Pedersen. 1993. Economic consequences of including health and fertility traits in dairy cattle breeding. Page 11 in Proc. 44th Annu. Mtg. Eur. Assoc. Anim. Prod., Aarhus, Denmark. Journal of Dairy Science Vol. 78, No. 3, 1995

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10 Boettcher. P. J.. L. B. Hansen. P. M. Van Raden, and C. A. Emst. 1992. Genetic evaluation of Holstein bulls for somatic cells in milk of daughters. J. Dairy Sci. 75:1127. 11 Boichard, D. 1990. Estimation of the economic value of conception rate in dairy cattle. Livest. Prod. Sci. 24:187. 12 Boichard, D., and B. Bonati. 1987. Genetic parameters for first lactation dairy traits in Friesian. Montbeliarde and Normande breeds. Genet. Sel. Evol. 19:337. 13 Bunch, K. J., D.J.S. Heneghan, K. G. Hibbitt. and J. Rowlands. 1984. Genetic influences on clinical mastitis and its relationship with milk yield, season and stage of lactation. Livest. Prod. Sci. 11:91. 14 Coffey, E. M., W. E. Vinson, and R. E. Pearson. 1985. Heritabilities for lactation average of somatic cell counts in first. second. and thrd or later parities. J. Dary Sci. 68:3360. 15 Colleau, J. J. 1985. Genetic efficiency of embryo transfer within selection nuclei in dairy cattle. Genet. Sel. Evol. 17:499. 16 Colleau, J. J., D. Regaldo, and P. L. Gastinel. 1994. Adapting the French INEL to milk quotas. Int. Natl. Rech. Agron. Prod. Anim. 7:151. 17 Da, Y., M. Grossman, I. Misztal, and G. R. Wiggans. 1992. Estimation of genetic parameters for somatic cell score in Holsteins. J. Dairy Sci. 75:2265. 18 Dempster, E. R., and I. M. Lerner. 1950. Heritability of threshold characters. Genetics 35:212. 19 Ducrocq, V., and J. J. Colleau. 1989. Optimum truncation points for independent culling level selection on a multivariate normal distribution, with an application to dairy cattle selection. Genet. Sel. Evol. 21:185. 20 Ducrocq, V., R. L. Quaas, E. J. Poll&, and G. Casella. 1988. Length of production life of dairy cows. 2. Variance component estimation and sire evaluation. J. Dairy Sci. 71:3071. 21 Emanuelson, U. 1985. Usefulness of somatic cell counts in breeding for mastitis resistance. Kiel. Milchwirtsch. Forschungsber. 37:497. 22 Emanuelson, U. 1988. Recording of production diseases in cattle and possib es for genetic improvement: a review. Livest. Prod. Sci. 2089. 23 Emanuelson, U,,B. Danell. and J. Philipsson. 1988. Genetic parameters for clinical mastitis, somatic cell counts and milk production estimated by multiple-trait restricted maximum likelihood. J. Dairy Sci. 71:467. 24 Emanuelson, U.L.F.. and J. Philipsson. 1984. Studies on somatic cell counts in milk from Swedish dairy cows. Acta Agric. Scand. 34:45. 25 Foulley, J. L. 1992. Prediction of selection response for threshold dichotomous traits. Genetics 132:1187. 26 Foulley. J. L.. D. Gianola, and R. Thompson. 1983. Prediction of genetic merit from data on binary and quantitative variates with an application to calving difficulty, birth weight and pelvic opening. Genetic. Sel. Evol. 15401. 27 Gibson, J. P. 1989. Economic weights and index selection of milk production traits when multiple production quotas apply. Anim. Prod. 49:171. 28 Groen, A. F. 1989. Economic values in cattle breeding. 11. Influences of production circumstances in situations with output limitations. Livest. Prod. Sci. 22:17. Journal of Dairy Science Vol. 78, No. 3, 1995

29 Goddard, M. E. 1983. Selection indices for non linear profit functions. Theor. Appl. Genet. 64:339. 30Harris. B. L., and A. E. Freeman, 1993. Economic weights for milk yield traits and herd life under various economic conditions and production quotas. J. Dairy Sci. 76:868. 31 Henderson, C. R. 1973. Sire evaluation and genetic Proc. Anim. Breeding. Genetic. trends. Page 10 Symp. in Honor of Dr. J. L. Lush, Am. Soc. Anim. Sci. Assoc., Champaign. IL. 32Heuven, H.C.M.. H Bovenhuis. and R. D. Politiek 1988. Inheritance of somatic cell count and its genetic relationship with milk yield in different panties. Livest. Prod. Sci. 18:115. 33 Itoh, Y.. and Y. Yamada. 1988. Linear selection indices for nonlinear profit functions. Theor. Appl. Genet. 75553. 34 Jones, G. M., R. E. Pearson, G. A. Clabaugh, and C. W. Heald. 1984. Relationships between somatic cell counts and milk production. J. Dairy Sci. 67:1823. 35 Kennedy, B. W.. M. S. Sethar. J. E. Moxley, and B. R. Downey 1982. Hentability of somatic cell count and its relationship with milk yield and composition in Holsteins. J. Dairy Sci. 65:843. 36Lande. R., and R Thompson. 1990. Efficiency of marker-assisted selection In the improvement of quantitative traits. Genetics 124:743. 37 Lin, H. K., P. A. Oltenacu, L. D. Van Vleck, H. N. Erb, and R. D. Smith. 1989. Heritabilities and genetic correlation among six health problems in Holstein cows. J. Dairy Sci. 72:180. 38 Lindstrom, U. B., and J. S y v a j b i . 1978. Use of field records in breeding for mastitis resistance in dairy cattle. Livest. Prod. Sci. 5:29. 39 Lunden, A.. S. Sigurdardottir, I. Edfors-Lilja, B . Danell, J. Rendel, and L. Andersson. 1990. The relationship between bovine major histocompatibility complex class I1 polymorphism and disease studied by use of bull breeding values. Anim. Genet. 21:221. 40 Lyons, D. T., A. E. Freeman, and A. L. Kuck. 1991. Genetics of health traits in Holstein cattle. J. Dairy Sci. 74:1092. 41 Madsen. P. 1989. Genetic resistance to bovine mastitis. Cum. Top. Vet. Med. Anim. Sci. 52:169. 42 Monardes, H. G., and J. F. Hayes. 1985. Genetic and phenotypic statistics of lactation cell counts in different lactations of Holstein cows. J. Dairy Sci. 68:1449. 43 Monardes, H. J. F. Hayes. and J. E. Moxley. 1984. Heritability of lactation cell count measures and their relationships with milk yield and composition in Ayrshire cows. J. Dairy Sci. 67:2429. 44 Niebel, E., and L. D. Van Vleck. 1982. Selection with restriction in cattle. J. Anim. Sci. 55:439. 45 Philipsson, 3.. G. Ral. and B. Berglund. 1993. Somatic cell count as a selection criterion for mastitis research. Page 21 Proc. 44th Annu. Mtg., Eur. Assoc. Anim. Prod.. Aarhus, Denmark. 46 Philpot, W. N. 1967. Influence of subclinical mastitis on milk production and milk composition. J. Dairy Sci. 50:978. 47 Poutrel, B. 1982. Susceptibility to mastitis: a review of factors related to the cow. Ann. Rech. Vet. 13:85. 48 Raubertas, R. F.. and G. E. Shook. 1982. Relationship between lactation measures of somatic cell concentra-

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APPENDIX 1 tion and milk yield. J. Dairy Sci. 65:419. 49 Rendel, J. M.. and A. Robertson. 1950. Estimation of genetic gain in milk yield by selection in a close herd Culling Cost Estimation in a Quota of dairy cattle. I. Genet. 50:l. 50 Rogers. W. 1993. Index selection using milk yield, Beard and James (6) found that, when a somatic cell score, udder depth, teat placement, and quota prevails, the economic value of one foot angle. J. Dairy Sci. 76664. 51 Rogers, W., J.A.M. Van Arendonk, and B. T. genetic standard deviation for “involuntary” McDaniel. 1988. Influence of involuntary culling on longevity (IL) amounts to .26 times the coroptimum culling rates and annualized net revenues. J. responding value for yield Dairy Sci. 71:3463. The cumulated probability of presence, ex52Schepers. J. A.. and A. A. Dijkhuizen. 1991. The economics of mastitis and mastitis control in dairy cluding voluntary cullings. IL, is cattle: a critical analysis of estimates published since x 1970. Prev. Vet. Med. 10:213. IL= 1 + c p i 53 Schutz, M. M.. L. B. Hansen. G. R. Steuernagel, and J. K. Reneau. 1990. Genetic parameters for somatic i=2 cells, protein, and fat in milk of Holsteins. I. Dairy Sci. 73:494. where pi stands for the probability of presence 54 Schutz, M. M., P. M. Van Raden, P. J. Boettcher, and at lactation i, and X is the last possible lactaL. B. Hansen. 1993. Relationship of somatic cell score and linear type trait evaluations of Holstein sires. J. tion. The genetic standard deviations gY and Dairy Sci. 76:658. U were 330 kg for milk yield and .70 for IL. 55 Sender, G.. J. Juga, T. Hellman, and H. Saloniemi. gu 1992. Selection against mastitis and cell count in dairy Assuming that the involuntary culling rate cattle breeding programs. Acta Agric. Scand. 42:205. (IC) is constant then 56 Shook, G. E. 1989. Selection for disease resistance. J. Dairy Sci. 721349. IL = 1 (1 . .+(l 57 Simianer, H., and L. R. Schaeffer. 1989. Estimation of covariance components between one continuous and one binary trait. Genet. Sel. Evol. 21:303. - 1 - (1 58 Solbu, H. 1984. Disease recording in Norwegian dairy (Y cattle. 11. Heritability estimates and progeny testing Tierz. for mastitis, ketosis and “all diseases”. so that Zuechtungsbiol. 101:51. 59 Strandberg, E..and E. Shook. 1989. Genetic and economic responses to breeding programs that consider mastitis. I. Dairy Sci. 72:2136. 60SyvajW. J., H. Saloniemi, and Y. Grtjhn. 1986. An epidemiological and genetic study on registered dis- with the values proposed by Beard and James eases in Finnish Ayrshire cattle. Acta Vet. Scand. 27: = .18; X = lo), 6IL/6a = -17.9. (6) 223. If my is the margin per unit of Y, the 61 Van Arendonk, J.A.M. 1991. Use of profit functions to determine the relative economic value of dairy selection objective is cattle herd life and production from field data. J . Dairy Sci. 74:1491. U gY 62 Van Arendonk. J.A.M.. and E. W. Brascamp. 1990. H = my g, .26 m y agL Economic considerations in dairy cattle breeding. &L Proc. 4th World Congr. Genet. Appl. Livest. Prod., Edinburgh, Scotland XIV:78. 63 Weller, J. I.. A. Saran, and Y. Zeliger. 1992. Genetic or, equivalently, and environmental relationships among somatic cell count, bacterial infection and clinical mastitis. J. Dairy Sci. 75:2532. 64Welper. R. D.. and A. E. Freeman. 1992. Genetic parameters for yield traits of Holsteins including lac- where c is the cost of one involuntary culling. Therefore. tose and somatic cell score. J. Dairy Sci. 75:1342. 65 Westell, R. A., E. B. Burnside, and L. R. Schaeffer. 1982. Evaluation of Canadian Holstein-Friesian sires on disposal reasons of their daughters. J. Dairy Sci. c = = 6W6IL x 65:2366.

.

+

(Yp

+

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330 = .26 x m x - x (-17.9). Y .7

If my is .74 FF as here, then c = 1623 FF.

= Ci mi AGi

APPENDIX 2

where j is a subscript for the gene transmission paths (1 for elite bull selection, 2 for regular Calculation of the Discrete Responses bull selection, and 3 for bull-dam selection), to Selection where di, is the genetic selection differential Let us suppose two normal variates: an for trait i along the path j and where the 0, are estimated breeding value I for an aggregate constants. Let b, be the vector of the estimated genotype H, with standard deviation and breeding values used in path j. In presence of accuracy rI, and a liability continuous variate constraints such as AGi = 0 for the first q traits, the vector of coefficients to be used is M with heritability hL and unit phenotypic no longer vector m. but a vector w,, possibly depending on j. Let V, and C, be, respectively, variance. Correlation between I amd M is r IM‘ the variance-covariance matrix of bJ and the A proportion PI of the candidates is covariance matrix between b, and g, the vector selected, corresponding to I > t1 The pheno- of breeding values. type corresponding to M is either 0 or l, If additionally the variance of aggregate according to the position of M below or above estimated breeding values (w, bj) is cona threshold tM. The overall proportion of strained to be 1, then phenotypes 1 is p ~ . p , Foulley (25) shows that the proportion of AH = 0.w.C.m. phenotypes 1 among selected candidates is J J J j=l equal to Therefore, we have to maximize * I p h q = - L 2(tI’ tM; ‘IM ’M) PI

where L2 0;y) is the probability that two standardized normal variates with correlation coefficient y lie simultaneously above thresholds (Y and 0.Response to selection is therefore p; - pM.

and 0, are LaGrange’s multipliers, where and where sj = wj Vj w.. J

APPENDIX 3 Maximization of Annual Genetic Gains with Constraints

The selection objective is

AG =

n

H =

I:mi gi I=

1

where the mi are the economic margins, and g, are the selected traits. The annual genetic gain for H can be written as Journal of Dairy Science Vol. 78. No. 3. 1995

t =

(“s“) ,

U

=

(t)

SELECTION FOR MASTITIS RESISTANCE

W

x =

q

w, W2n

,

67 1

If z = z is forced to be 0. which gives U = K-'z where K = (6t/6x)'. Finally, it necesto find the zeros of the functions corresponding to the elements o f t and z* = 6W6y - (6t/6yYu. The corresponding Newton-Raphson algorithm is therefore

W

The first and second derivatives involved are straightforward because the original functions H, s,, and AGi are linear or quadratic functions of the unknowns. Starting from the unconstrained solutions, convergence is obtained after about five iterations.

Journal of Dairy Science Vol. 78, No.

1995