Optimal Effective Population Size for the Global Population of Black and White Dairy Cattle

Optimal Effective Population Size for the Global Population of Black and White Dairy Cattle M. E. GODDARD Department of Agriculture Melbourne, Australia

inbreeding depression, EBV = estimated breeding values, G x E =genotype by environment interaction, MOET = multiple ovulation and embryo transfer, Ne = effective population size, NPV = net present value of all future genetic gains.

ABSTRACT

The replacement of other black and white cattle strains by the North American Holstein breed, which itself is dominated by a small number of elite sires, has reduced the genetic diversity of the global population. Intense selection on a global basis leads to rapid genetic im~rove~ent but reduces effective populatIOn size. . Th~ optimal global effective populatIOn size was chosen to maximize the net present value of all future benefits from the breeding program. Two separate discount rates were used to reflect concerns about the long-term costs of small effective population size. This led to a higher optimal number of bull-sires than in past analyses. The optimum was sensitive to the magnitude of inbreeding depression and to the discount rates, but not to the variance caused by new mutations and the size of the world population. The genetic correlation between the breeding objectives of different AI studs controls the extent to which they all select the same sires of sons and, hence, affects the global effective population size. The prediction is made that different countries will select partially different sires, but genetically isolated strains will not reemerge. A better global breeding program is likely when selection of s~es takes account of inbreeding depresSIOn and small genotype by environment interactions. (Key words: effective population size, world, black and white cattle, population).

INTRODUCTION

Abbreviation key: 4F =rate of inbreeding per year, aG = annual selection response, D =

Received October 1, 1991. Accepted March 16, 1992. 1992 J Dairy Sci 75:2902-2911

Prior to 1970, several distinct strains of black and white dairy cattle existed around the world. The increased international trade in semen, cattle, and embryos has converted these into a single global population. Comparisons of the black and white strains found that the North American Holstein was superior for milk production (20). Consequently, nearly all other strains of black and white cattle are being replaced by Holsteins. This process has been accelerated in recent years by the export of large numbers of Holstein embryos from North American to become AI bulls in other countries. Consequently, bulls with almost identical pedigrees are being progeny tested simultaneously in several countries. A consequence of this process is a substantial loss of genetic diversity, which is viewed with concern by some people. Intense selection within the AI bull breeding sector means that a few "super sires" dominate the breed worldwide. Likely improvements in reproductive technology could lead to equally intense selection on cows and to a decline in generation interval, causing a further increase in the rate of inbreeding (4F) and the relatedness of all black and white cattle worldwide. Therefore, it seems important to consider the optimal balance between selection intensity and effective population size (Ne) for the world black and white breeding program, and this is the first aim of this paper. However, the world black and white breeding program is not managed by a single person with power to implement an optimal design. The world breeding program is the result of the collective decisions taken by a number of

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SYMPOSIUM: REPRODUCTIVE TECHNOLOGY

AI studs, which are in competition with one another. Therefore, the second aim of this paper is to make a prediction of what will happen in the future as a result of this collective decision-making process.

2903

cause intense selection inevitably reduces Ne , a compromise is needed. DESIGN OF A GLOBAL BREEDING PROGRAM selection

BENEFITS AND DISADVANTAGES OF A GLOBAL BREEDING PROGRAM

The first advantage of selection from a global population is the opportunity for between-strain selection, which is precisely what has led to the replacement of many black and white strains with Holsteins. Consequently, the opportunities for between-strain selection in the future are greatly reduced. The second advantage is that larger populations can make faster genetic gains than smaller populations (7, 17), although this conventional wisdom has been challenged by Franklin (4). This advantage derives largely from the more intense selection of sires of sons that is possible when more bulls are progeny tested. In theory, there is little advantage for a larger population in selection of sires of commercial cows because, although more bulls are tested, more proven sires are needed. However, in practice, dairy farmers vary in their selection objectives and criteria. This means that more bulls than needed are selected to cover a variety of market niches. In a large population, it should be possible to cover all market niches with widely used bulls. To gain these benefits, each country must be able to select from among the world population those bulls that best meet local breeding objectives. To do this, it is necessary to compare all available bulls for traits in the local breeding objective either by equations that convert foreign genetic evaluations to the local scale (5, 19) or by a joint analysis of data from two or more countries (1). In either case, it is important to allow for small genotype x environmental (G x E) interactions, which cause a reranking of sires between countries. This is frequently done in calculating conversion equations but has not yet been done in combined analyses. The disadvantage of intense selection from a global population is reduced Ne . The effects of small Ne are inbreeding depression (D), loss of genetic variance, and a degree of random drift in the mean merit of the population. Be-

Many studies have investigated the optimal design for dairy breeding programs using conventional progeny testing (7, 17) and multiple ovulation and embryo transfer (MOET) schemes (12, 13). These studies usually assumed a closed population, and it is doubtful that their authors intended the conclusions to apply to the world population of the major dairy breed. Intuition suggests that more attention be given to the disadvantages of small Ne when considering the world population. This section interprets this intuition in a rational, quantitative manner. To determine the optimal design, the objective must first be defined. For instance, when the aim is to maximize the total response achieved when a selection plateau is reached, Robertson (15) concluded that the best half of the animals tested should be selected. Similarly, when the objective is to conserve genetic resources or to minimize genetic abnormalities or the probability that a desirable allele is lost, a low selection intensity is optimal. These objectives all emphasize long-term effects that, in cattle, may take many years to eventuate and that lead to recommendation of low selection intensity. Others may wish to emphasize short-term gains by, for instance, maximizing the annual selection response (4G), which leads to very intense selection. This should at least be adjusted for the expected D. On an annual basis, this is ~G - D~ with ~ per year and D per unit of inbreeding. Goddard and Smith (7) called this quantity "net genetic gain". To compare long- and short-term gains, it is conventional to use discounting to assign an equivalent present value to future benefits. Therefore, the objective should be the net present value (NPV) of all future genetic gains from the breeding program. This includes both long- and short-term objectives discussed here. This is the appropriate strategy for the world community, although it is not necessarily one that would be adopted by competing AI studs. To calculate NPV, a discount rate must be chosen. This should be the real rate of return Journal of Dairy Science Vol. 75, No. 10, 1992

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GODDARD

(i.e., adjusted for inflation) on alternative, secure investments. Traditionally, this has been 2 to 5%/yr. However, the price of milk to the farmer has not kept pace with inflation and is unlikely to do so in the future. Therefore, the decline in the real price of milk must be added to the discount rate. In Australia, this has been approximately 2%/yr. The need to allow for the declining real price of milk applies from the viewpoint of both consumers and farmers. Because the real price of milk is dropping, the benefit of a further proportional drop in price, caused by genetic improvement, is also falling. There is also a risk that the expected genetic gain in profitability will not occur. If this risk increases approximately exponentially with time, it can be accommodated by increasing the discount rate (3). One risk is that selection objectives will change such that the value of present genetic improvements is reduced. For instance, past selection for milk fat yield is of less value when milk price is based on protein content; similarly, the value of selection to increase mastitis resistance would be greatly reduced if an effective vaccine were released. This risk might add up to 5% to the discount rate, assuming that the value of a present genetic gain declines by less than 5%/yr. However, future selection decisions will be directed at the selection objectives appropriate at that time. Therefore, this loss of 5%/yr does not apply until the selection decisions have been made. Although selection objectives change, genetic variance is always valuable because improvement is always desirable for some traits. Despite changes in selection objectives, D will continue to be detrimental. Inbreeding depression reduces milk production, fertility, survival, and general hardiness. These effects clearly are always a cost to the dairy farmer and should not be discounted by the additional 5%/yr. These arguments dictate the use of two discount rates: a base rate of approximately 4 to 7% (real return plus declining real milk price) and a higher rate (e.g., 10%) that includes risk. The value of genetic improvement from prior selection decisions is discounted at the higher rate, but the value of future selection decisions and D is discounted at the lower rate. An individual company deciding on its optimal breeding program might include several Journal of Dairy Science Vol. 75. No. 10, 1992

other sources of risk, e.g., the risk that a more successful competitor may force it out of business. These risks do not apply to the world black and white cattle population. The main additional risk from this global perspective is that the world dairy industry would decline in importance. However, an increase in importance with the increasing world population is also possible. For any specified breeding program, the genetic merit of commercial dairy cows in all future years can be predicted, the discount rates chosen can be applied, and an NPV for that program can be calculated. By using a few simplifying assumptions, relatively simple expressions for NPV can be derived. Derivation of an Expression for NPV

Let (I - a)/a = 1 - a = base discount rate, (I - b)/b = 1 - b =risk discount rate, and ~Gj genetic response in dol1ars because of selection in year j, Then ai~Gj = NPV of this gain

=

co

in year j, and

L

ai~Gj(ab)k

= NPV

of this

k=O

gain in al1 future years = ai~G/(l - ab). (For simplicity, this ignores the lag between selection decisions and genetic improvement.) The NPV of al1 future gains is then

i '=0

J-

ai~Gj

.

1 - ab

[ 1]

N ow ~Gj depends on the genetic variance (Vgj) present in year j. Assume that

[2]

(This underestimates the response to selection in future years.) The genetic variance declines because of inbreeding but increases because of mutation, which have long-term importance (9). That is,

= V gj-l

(l - ~) + V m . - V n/~)(I - ~)l Vn/~

= (Vgo +

[3]

where V m

= mutational

variance per year.

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SYMPOSIUM: REPRODUcrIVE TECHNOLOGY

Substituting Equation [3] into Equation [2] 'C' 7 into Equation [1] yields NPV of all future ~ c:i 6 gains in additive genetic merit:

-----~-------

.s

"'0 Ql

Ql

Q) C/)

NPV

--------------- ---

~

_________________ J

5

4 3

[(Vgo - Vn/aF)(1 - aF~ + Vn/aF] ..!!! "5 2

t..G - Dt..F

m

liS 1 '0 I-

0

500 1000 1500 2000 Total Bulls Tested (no';yr)

0

I - V~/M' + V~/M'] [ I-a(l-M) I-a

Figure I. Effect of total number of bulls tested on optimal number to select. NPV = Net present value; ~G and ~ are annual rates of selection response and inbreeding, respectively, and D is the inbreeding depression per unit inbreeding coefficient.

[4]

• where Vm = VmN go' From this must be subtracted the cost of O. If in year j the inbreeding coefficient is the cost of 0 is 0[1 - (1 - aF~],

Optimal Selection Intensity

When bull-dams are selected on estimated breeding values (EBV), they are often the daughters of the bull-sires of the previous generation. Thus, the bull breeding part of the population tends to become a dispersed nucleus; the same elite sires are used to breed sons and daughters, as discussed by Goddard and Smith (7). In this case, aF is

and the discounted value of this is aiO[1 - (l -

m].

where Nm

The sum of these losses over all years is

L

L 8.G

aiO[1 - (1 - aF~]

j=O

D

= 'l"=a

-

D I - a(l - M)

[5]

The NPV of all genetic gains is Equation [4] minus Equation [5]. For any particular breeding program, equilibrium values of 8.G and aF can be calculated and substituted into Equation [4] minus Equation [5].

= effective number of new year used in the nucleus, = generation length, and = imrmO"g + iffJg

bulls per

Lm + Lr where i = standardized selection differential, r = accuracy of selection, L = generation length, and subscripts refer to male (m) or female (t). The standard parameters used in evaluating = .85, rf = .5, if = .8, Lm =6 yr, Lf =3.5 yr, O'g =7%, 0 =.5, Vm = .000Vgo and 1 - a = .03, and I - b = .07. Figure 1 shows how the optimal number of bulls to select as bull-sires from each year's

NPV, aF and ~G, were rm

Journal of Dairy Science Vol. 75, No. 10, 1992

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GODDARD

TABLE 1. TIle effect of discount rates on optimal number of bulls to select to maximize net present value.

Base

Risk discount rate

TABLE 2. The effect of inbreeding depression and mutation variance on the optimal number of buns to select to maximize net present value. Inbreeding depression2

0

Mutation variance l

0

.50

1.50

3

2

0

2

6

3

6 6

13 12

discount rate

.20

.00

.10 .03

4 10

.004

2

'Mutation variance variance.

as a proportion of initial genetic

2Decline in objective per unit inbreeding coefficient.

progeny test team is affected by the number of bulls tested. The optimum is shown for both NPV and the more short-term criterion net genetic gain (~G - D AF). Even as the number of bulls tested approaches the world population of AI progeny-tested Holsteins, the optimal number to select remains at only 6. The optimum is very flat; > 90% (95%) of the maximum NPV is obtained from 2 (3) to 34 (19) bulls selected. Maximizing NPV results in substantially more bulls selected and, hence, lower inbreeding than maximizing net genetic gain. Table 1 shows the effect of choice of the two discount rates on the optimal number of bulls selected for maximum NPV. Increasing the base discount rate (1 - a) leads to more intense selection (Le., lower Ne and higher AF). This is expected because a higher discount rate gives less emphasis to long-term returns. However, increasing the risk discount rate (1 - b) leads to less intense selection, higher Ne, and lower AF. This occurs because b affects gains from selection, but not D. Thus, when the risk discount rate is high, the future benefits of additive genetic gains are discounted more severely, so the cost of D becomes proportionately greater. Table 2 shows the effect of mutation variance (VrJ and severity of D on the optimal number of bulls selected for maximum NPV. Increasing D markedly increases the optimal 0, the number of bulls selected. When D optimal number is only 2. This demonstrates that preserving genetic variance to increase future genetic gains has little effect on the optimum, even at a base discount rate of only 3%. Typical estimates of mutation variance are approximately .001 Ve per generation (11) where Ve = envirollIDental variance. For a trait with heritability of .25, this is .003 V per generation. If generation length is 5 yr, ~m

=

=

Joumal of Dairy Science Vol. 75. No. 10, 1992

.0006 Vg' Table 2 shows that even a value of Vm more than six times this level has a negligible effect on the optimal number of bulls to select. As an alternative to conventional progeny testing, a juvenile MOET breeding program was briefly examined. The purpose was not to predict the genetic gain accurately from such a scheme but, rather, to examine the effect of the NPY criterion on the optimal selection intensity. For simplicity, 1000 yearling males and females were assumed to be available for .5 in both sexes. selection with accuracy r The family structure of this population was ignored, and reproductive technology was assumed to allow an unlimited number of offspring per cow. The optimal designs to maximize NPV and ~G - DAF are in Table 3. Although not intended to be accurate, the rates of genetic gain calculated are comparable with those of Kinghorn et al. (10) for a similar scheme. As expected from the assumptions, the same number of bulls and cows is selected. When NPV is maximized, AF is higher !han for progeny

=

TABLE 3. Optimal number of bulls (NB) and cows (Nc) to select in a juvenile multiple ovulation and embryo transfer scheme with unlimited female reproduction rate.• Criterion

maximized

NB

Nc

NPV aG - D6F

24

24

4.1

6

6

5.0

aG -

=

6F (%/yr)-

=

.26 1.04

lNPV Net present value; aG and 6F annual rate of selection response and inbreeding, respectively; D = inbreeding depression per unit of inbreeding coefficient.

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SYMPOSIUM: REPRODUCTIVE TECHNOLOGY

testing programs but, perhaps, still acceptable. When ~G - D6F is maximized, 6F of I%/yr appears to be dangerously high. Expected Future Ne

The future world breeding program will not be planned by a single individual or institution but will result from the collective decisions of the AI studs. As competing commercial organizations, AI studs are likely to give more emphasis to short-term returns than has been advocated as optimal from a global perspective. For instance, if AI studs maximized ~G D6F, they would select far fewer bulls (Figure I and Table 3) than needed to maximize NPV. If they all select the same bulls, the world black and white population will be genetically less diverse than is desirable. However, if they have different selection objectives, they will not select exactly the same bulls; hence, the total number of bullsires used will increase. If the commercial herds served by an AI stud are considered as an "environment", then different selection objectives can be considered as a G x E for profitability; Le., the bulls do not rank in the same order for profitability in all environments. A G x E for profitability can occur for two reasons. First, there may be different selection objectives in different environments. For instance, some countries pay farmers for milk on the basis of volume, but other countries pay for milk fat and protein but penalize milk volume. In Norway, but not in most countries, a large economic weight is given to mastitis resistance (18). Second, a G x E may exist for individual traits. For instance, bulls rank differently for milk production in Canada and New Zealand (14), probably because of the marked difference in feeding systems in the two countries. Small changes of ranking probably also occur between other countries, but they are usually not large (6). The degree of reranking for profitability can be expressed as a genetic correlation between profitability in the two environments. Because milk production traits are important everywhere and generally show only minor G x E, the genetic correlation for profitability will be high, although less than 1.0, between most environments.

If the genetic correlation between profitability in country A and profitability in the rest of the world is sufficiently low, then country A will make more genetic progress by closing its population and not selecting from the global population. In this way, separate strains of black and white might reemerge in different countries, although the global population would have passed through a bottleneck as other countries converted to American Holsteins. Will isolated strains reemerge? The net genetic gain in an isolated strain is ~Ga D~a where ~Ga - D~a is optimized for the number of bulls progeny tested in that country. Genetic isolation will be better than some continued importation if ~Ga - D~a is greater than rg&Gr , where ~Gr is the genetic progress in the rest of the world, and rg is the genetic correlation between profitability in country A and in the rest of the world. No ~r term is included because, when country A is almost isolated, bulls from other countries will not be increasing in their relatedness to country A cows; i.e., they have an advantage over country A bulls because they produce calves with a lower average inbreeding coefficient. Figure 2 shows the value of genetic correlation at which ~Ga - D~a rg&G r assuming that 2000 bulls are progeny tested per year in the rest of the world. As the number of bulls progeny tested per year in country A increases, the breakeven value of the genetic correlation increases. For situations below the curve in Figure 2, country A would benefit from eventually stopping the import of genes from the rest of the world. This need not be a deliberate policy. As a result of selection based on appropriate EBV, all of the best bulls will eventually be in country A. Although no formal analysis has been done, the situation in most countries will probably lie above the curve in Figure 2, and some continued importation will be desirable. 1berefore, most local black and white populations will probably not become isolated from the global population. Even if all countries continue to import genes from the global population, this does not imply that they all select exactly the same bulls. Again, the degree of overlap in their selections depends on the genetic correlation between the objectives. Consider two countries that each progeny tested 1000 bulls of equal

=

Journal of Dairy Science Vol. 75, No. 10, 1992

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GODDARD

c:

o

~ ~

(;

.9

(J

o ~ c:

<3

.8

c: ~

W

~

.7

~

a:l

i

a

I

500

1,000

1.500

2,000

Bulls Tested Locally (no.) Figure 2. Genetic correlation between local and outside selection objectives below which local net selection response is greater without importation.

genetic merit per year. Both countries select the best two as bull-sires from the complete 2000 bulls tested. Will they select the same two bulls? Two situations can be distinguished. In the first situation, economic weights differ between the two countries, but there is no G x E for individual traits, and all bulls are evaluated with equal accuracy for all traits. This means that selection for the objective of country A is equally accurate, regardless of the country in which a bull was progeny tested. In the second situation, the economic weights are the same, but there is a G x E for the individual traits. This means that an EBV based on a progeny test in country A must be "regressed toward the mean" when it is converted to an EBV in country B (i.e., EBVB r g EBVA). The true situation is likely to lie between these extremes and is due in part to traits evaluated only in the country that includes them in its objective. Computer simulation was used to calculate the total number of bulls selected, assuming that each country selects the best two for its own objective out of the 2000 tested (Figure 3). Naturally, when their objectives are the same (rg = 1.0), both countries select the same bulls, and the total number selected is 2. As the correlation between their objectives fall, they tend to select different bulls, and, when rg = .6, the total number selected approaches 4 (the maximum possible under these assump-

=

Journal of Dairy Science Vol. 75. No. 10, 1992

.6

.7

.8

.9

Genetic correlation Figure 3. The total number of bulls selected from two populations and the genetic correlation between selection objectives in the two environments: situation 1, all bulls evaluated for both objectives (- - -); situation 2, bulls only evaluated for local objective (-); 1000 bulls are tested in each environment.

tions). The results for the two situations just described differ, but not greatly. Simulations were also carried out for more than two countries. In this case, the total number of bulls tested was assumed to be 2000, divided equaJly among the countries, and the correlation between the objectives of any pair of countries was assumed to be .9. The mean breeding value of bulls tested in each country was assumed to be the same. Figure 4 shows that, as the number of countries increases, the total number of bulls selected increases. If there is a G x E for individual traits (the second situation), the number of bulls selected reaches a maximum of 5. To understand this, consider two countries, A and B, out of 10 countries that each test 200 bulls. For the objective of country A, the bulls tested in country A are evaluated more accurately than other bulls and so are more likely to be selected. On average, .47 bulls are selected from country A and 1.53 from all other countries. Any bulls from country B will also be selected for use there, and the majority of bulls, which come from neither A nor B, will rank in the same order in both countries, so the same ones will be selected. As the number of countries increases, the proportion of all bulls tested in country A decreases, and fewer country A bulls are selected. This balances the

SYMPOSIUM: REPRODUCTIVE TECHNOLOGY

8

~J "0

~ 6 OJ

0:;

(/)5 !!l "3

C04

(ij

~3 2

0

5

10

15

20

Populations (no.) Figure 4. The total number of bulls selected from 2000 bulls tested. The best two for each objective area selected. The genetic correlation between any pair of objectives is .9. Situation I, all bulls evaluated for all objectives (- - -); situation 2, bulls only evaluated for local objective (-).

increasing number of countries so that the total number selected remains about 5. If the countries differ in economic weights (the first situation), the total number of bulls selected continues to increase as the number of countries increases to at least 10 (Figure 4). This occurs because countries A and B now rank the bulls tested in third countries differently and so select different bulls. DISCUSSION

The optimal design for two populations has been investigated by Banos and Smith (2). They use a criterion similar to AG - DAF and found that each country should select approximately 7 to 10 bulls per generation. If the two populations had the same breeding objectives, they both selected the same 7 to 10 bulls, which is comparable with the results given in Figure 1 of 1 to 2 bulls selected per year. The NPV criterion with its two separate discount rates was an attempt to provide a logical interpretation of the intuition of many people that the disadvantages of low Ne merit greater consideration when dealing with the world population of the major dairy breed. The NPV includes the long-term effects of loss of genetic variance, mutation, and D. Perhaps surprisingly, maintaining genetic variance and capturing new favorable mutations have little

2909

effect on the optimal Ne , even when a discount rate of only 3% is used. The value of future gains is eroded by both discounting and by loss of genetic variance. However, the loss from inbreeding and the gain from mutation are an order of magnitude less than the discount rate and so do not greatly affect the optimal design. Inbreeding depression largely determines the optimal Ne . The value of D chosen should reflect the total costs of D (e.g., on fertility), not just those on traits for which EBV are calculated. Goddard and Smith (7) suggested that every 1% inbreeding costs as much as a .25 to .5% decrease in milk production (i.e., D =25 to 50). The NPV gives more weight to D because it discounts future costs at a slower rate than the future benefits from additive genetic gains. A similar result might be obtained with the net genetic gain (AG - DAF) criterion by increasing the value of D used. The importance of using a criterion such as NPV is emphasized by considering likely advances in reproductive physiology. Follicle aspiration and cloning could result in breeding programs with intense female selection and short generation intervals. In this situation, a conventional AG - DAF criterion leads to AF at approximately 1%/yr. Breeding the entire world's population of black and white cattle from 6 bulls and 6 cows each year seems to be too extreme. The formula used to calculate AF ignores the tendency of selection to increase inbreeding. If this were allowed for the optimum, Ne would increase somewhat. Alternatively, the optimal number of selected bulls and cows given in the results can be considered as the effective numbers calculated retrospectively after several generations of selection. The effect of low Ne on genetic drift has not been considered in deriving the optimum. A common mechanism to account for drift is to maximize a utility function (16), m - kv, where m is the expected value of the criterion (e.g., NPV), v is the variance of this criterion over conceptual repetitions of the selection program, and k is a constant. If the accuracy of selection is fixed, var(AG) is proportional to 11 Ne. Therefore the -kv term has approximately the same effect as an increase in D. The optimal design will only be realized if commercial signals lead individual decision Journal of Dairy Science Vol. 75, No. 10, 1992

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GODDARD

markers to the same decisions as would be made by implementation of an optimal design. Because of its importance in determining the optimum, this is most likely to happen if individual decision markers consider 0 in their decisions. Goddard and Smith (8) suggested that farmers select AI sires to maximize EBV - OF of the resulting calf (where F is the inbreeding coefficient of the calf). If farmers do this, then AI studs will have to consider the relatedness of their bulls to one another and to the cow population. Goddard and Smith (8) suggested that AI studs choose their young and proven bull teams to maximize EBV - ORl2, where EBV is the mean EBV of the team, and R is the mean relatedness of the bulls. Farmers and AI studs alteady consider relatedness of bulls and cows in making decisions. Advisers should show how this can be done in a systematic way. In doing this, a higher rather than lower 0 value would benefit the individual because a higher 0 value acknowledges the discount rate arguments used to derive NPV and because it allows for a weighting for drift. Avoiding inbreeding may also have noneconomic benefits. Recessive genes for genetic abnonnalities are individually rare, but, when all abnormalities are combined, recessive genes are quite common. Avoiding known genetic abnonnalities is given far greater weight than their economic value justifies. The most effective way to avoid abnormal homozygote calves is to avoid inbreeding. Use of a high 0 value will also be of benefit to the industry as a whole because it will cause the outcome of collective decisions to approach the optimal design more closely. Even when 0 is taken into account by individual decision makers, they will likely put more emphasis on short-term gains and low Ne than desirable for the world black and white population. However, Figures 3 and 4 show that, if selection objectives differ, the world Ne will increase. Genuine difference in objectives will be recognized by considering all traits, not just milk production, and by allowing for even small G x E. As Figure 4 shows, even a genetic correlation between environments of .9 causes different bulls to be selected in different places and the total Ne to increase. Thus, formulas to convert EBV between countries and joint analyses of data from several countries should recognize these G x E. Journal of Dairy Science Vol. 75, No. 10, 1992

If the genetic correlations between objectives in different countries were sufficiently low, all of the best bulls in a country would eventually be progeny tested locally, and a genetically isolated population would reemerge. Banos and Smith (2) investigated the time course of this process in two populations that each tested 1000 bulls per generation. They (2) found that, if the genetic correlation between their objectives was .7, each country stopped selecting bulls from the other country after three generations. However, inbreeding effects and the large size of the world population work to prevent complete isolation. A possible future course is one in which, following a bottleneck, some differences between local population reemerge, but these local populations continue to exchange genes and do not become isolated strains.

REFERENCES 1 Banos, G., L. R. Schaeffer, and E. B. Burnside. 1990. North American genetic evaluation of Ayrshire bulls with a linear model. Proc. 4th World Congr. Genet. AppI. Livest. Prod., Edinburgh, Scotland. XIV:62. 2 Banos. G., and C. Smith. 1991. Selecting buIls across countries to maximize genetic improvement in dairy cattle. J. Anim. Breed. Genet. 108:174. 3 Bird, PJ.W.N., and G. MitcheIl. 1980. The choice of discount rate in animal breeding investment appraisal. Anim. Breed. Abstr. 48:499. 4 Franklin. I. R. 1982. Population size and the genetic improvement of animals. Page 181 in Future Developments in the Genetic Improvement of Animals. J.S.F. Barker, K. Hammond, and A. E. McClintock, ed. Academic Press, Sydney, Aust. 5 Goddard, M. E. 1985. A method of comparing sires evaluated in different countries. Livest. Prod. Sci. 13: 321. 6 Goddard, M. E. 1985. Genotype x environment interactions in dairy cattle. Proc. Aust. Assoc. Anim. Breed. Genet. 5:52. 7 Goddard, M. E., and C. Smith. 1990. Optimum number of bull sires in dairy cattle breeding. 1. Dairy Sci. 73:1113. 8 Goddard, M. E., and C. Smith. 1990. Adjustment of sire EBV for their prospective inbreeding impact on the breed. J. Dairy Sci. 73(SuppI. 1):233.(Abstr.) 9 Hill, W. G. 1989. Mutation and maintenance of quantitative genetic variation. Page 105 in Evolution and Animal Breeding. W. G. Hill and T.F.C. Mackay, ed. Commonw. Agric. Bur. Int., Wallingford, EngI. 10 Kinghorn, B. P., C. Smith, and J.C.M. Dellers. 1991. Potential genetic gains in dairy cattle with gamete harvesting and in vitro fertilization. J. Dairy Sci. 74: 611. 11 Lynch, M. 1988. The rate of polygenic mutation. Genet. Res. 51:137.

SYMPOSIUM: REPRODUCTIVE TECHNOLOGY 12 Meuwissen, T.H.E. 1990. The use of increased female reproductive rates in dairy cattle breeding schemes. Anim. Prod. 52:21. 13 Nicholas, F. W., and C. Smith. 1983. Increased rates of genetic change in dairy cattle by embryo transfer and splitting. Anim. Prod. 26:341. 14 Peterson, R. 1988. Comparison of Canadian and New Zealand sires in New Zealand for production, weight and conformation traits. Res. BuD. No.5. Livest. Improvement Corp., Hamilton, N.Z. 15 Robertson, A. 1960. On the theory of limits in artificial selection. Proc. R. Soc. Lond. Ser. B BioI. Sci. 153:234. 16 Schneekerger, M., A. E. Freeman, and M. D. Boehlje. 1981. Estimation of a utility function from semen purchases from Holstein sires. 1. Dairy Sci. 64:1713.

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17 Skjervo1d, H., and H. J. Langholtz. 1964. Factors affecting the optimum structure of AI breeding in dairy cattle. Z. Tierz. Zuechtungsbiol. 80:25. 18 Steine, T. 1991. Recording and utilisation of health and reproduction information in dairy cattle. Page 171 in Performance Recording of Animals: State of the Art 1990. P. Gallion and Y. Chabert. ed. Pudoc, Wageningen, Neth. 19 Wilmink, J.B.M., A. Meijering, and B. Engel. 1986. Conversion of breeding values for milk from foreign populations. Livest. Prod. Sci. 14:223. 20 Zameki, A., and M. Sto1zman. 1986. A preliminary comparison of later lactation productions of different Friesian strains in Poland. Proc. 3rd World Congr. Genet. Appl. Livest. Prod., Lincoln, NE XII: 112.

Journal of Dairy Science Vol. 75, No. 10, 1992