Directory UMM :Data Elmu:jurnal:L:Livestock Production Science:Vol63.Issue2.Apr2000:

www.elsevier.com / locate / livprodsci

Review article

Maintenance of quantitative genetic variation in animal

breeding programmes

*

William G. Hill

Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JT, UK Received 4 November 1998; received in revised form 22 April 1999; accepted 6 May 1999

Abstract

Factors influencing the maintenance of genetic variation in quantitative traits in populations undergoing artificial selection are reviewed. Formulae are given for simple cases, in particular for the infinitesimal model where variation is lost by genetic drift and gained by mutation and therefore the minimum population size to maintain genetic variation is a function of mutation rate. For genes with effects too large for the infinitesimal model assumptions to apply, it is suggested that a criterion for minimum population size is that large enough to give high probabilities of fixation of segregating genes. Those most at risk are at low frequency, and likely to be recent mutations. If the population is subdivided with low rates of migration, variation over the totality of populations may be maintained or increased, but cannot necessarily be readily utilised. For example, if populations are conserved without selection alongside selected populations, variation among the populations rises but is ever harder to utilise as the conserved populations fall behind. With the introduction of new molecular genetic technology, it is likely to be possible to introduce new variation into populations in a number of ways. In view of the large generation interval of some species, the discount rate per generation that should be applied is very high, so long term gains have low net present value.  2000 Elsevier Science B.V. All rights reserved.

Keywords: Animal breeding; Genetic variation; Population size; Selection; Mutation; Genetic conservation

1. Introduction traits of current interest, but will influence the variation present in both these and other traits that If improvement is to be continued in a breeding may in due course become important. Genetic vari-programme, or if there is to be the opportunity to ation is produced by spontaneous mutation, and can redirect the programme to improve different traits or be introduced into the population by immigration, by respond to environmental or production constraints, induced mutation, or by direct genetic manipulation. genetic variability has to be present or generated. There are two quite different topics that have to be Genetic variation is lost as a result of sampling or addressed. The first is essentially a genetic issue: genetic drift, due to finite population size, and as a what factors determine the availability of genetic result of selection. The selection should be on the variation that can be utilised in improvement pro-grammes? The second is essentially an economic, political or cultural issue: what is the importance of

*Tel.: 144-131-650-5705; fax:144-131-650-6564.

E-mail address: w.g.hill@ed.ac.uk (W.G. Hill) such long term response or opportunity. By

defini-0301-6226 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. P I I : S 0 3 0 1 - 6 2 2 6 ( 9 9 ) 0 0 1 1 5 - 3

tion, a population that has undergone genetic im- change in r can be very small (Wei et al., 1996). provement has changed; economic and technical Hence the proportional rate of change in selection circumstances will change. response per generation, (dR /R) / dt, may be little more than one-half of (dV /V ) / dt, i.e. closer toA A

1 / 4N than the more familiar 1 / 2N .e e

If Eq. (1) holds, at steady state V 52N V ,

2. Maintenance of genetic variation in closed A e M

providing the mutational input of variance and the

populations

population structure are constant over time. Despite its many assumptions (1) is a useful base point. 2.1. Additive gene action with the infinitesimal

Estimates of mutational variance are usually

ex-model

pressed in terms of the environmental variance, V ,E 2

as the mutational heritability, h 5V /V . Typical

There are no general formulae for the changes in M M E 2

values of h are of the order of 0.1% of the genetic variance, but results can be given under very M

environmental variance, with much of the infor-restricted assumptions to serve as a reference point.

mation being on bristle number in Drosophila (Fal-Consider the case of additive gene action with no

coner and Mackay, 1996). At this value, for a trait selection, in a population of constant size and

with heritability 1 / 3, so V 52V , a population of breeding structure with effective population size N .e E A

size N 5250 is required to maintain V at its initial Each generation (t), a proportion 1 / 2N of thee e A

value. Although estimates from mammals are scarce, existing variation VAt is lost by genetic drift, and let

mutational variance appears to be higher, up to us assume an amount V is gained by mutation. TheM

2

h 50.5% in mice (Keightley, 1998), so requiring net change is dV / dtA 5 2V / 2NA e1VM or, as a M

N .50 for steady state. In view of their longer proportion of the standing variation, e

generation interval, it seems reasonable to assume (dV /V ) / dtA A 5 21 / 2Ne1V /V .M A that mutation rates for quantitative traits in farm

livestock are at least as high per generation as in Hence _{mice, and certainly no lower. The figure of N .50}

e

could therefore be conservative.

VAt5VA(t21 )(121 / 2N )e 1VM

and, relative to some initial generation 0, 2.2. Effects of natural selection

VAt5V exp(A0 2t / 2N )e 12N V (1e M 2exp(2t / 2N )).e _{There has been much study of the forces that}

(1) maintain variation in natural populations (see, for example, Falconer and Mackay, 1996). It is clear, for This equation also holds for the infinitesimal example, that the neutral model does not hold, model when selection is being practised, where VAt because levels of V maintained are far below 2N VA e M

refers to the genic variance (see Wei et al. (1996), for in very large populations. Clearly many mutations further analysis), although the actual genetic variance are deleterious and removed by natural selection, but is reduced by gametic (linkage) disequilibrium, i.e. predictions of the effects of the natural selection the ‘Bulmer effect’ (Bulmer, 1971). Selection re- depend on how it operates on the trait under artificial sponse per generation is a function of the accuracy of selection and on mutations which affect the trait. In selection, r, and additive genetic standard deviation, the optimum or stabilising selection model due

œ_{V . The proportional change in} œ_{V is approxi- initially to Sewall Wright, body size for example has}

A A

mately half that in V . With index or BLUP selection,A a particular optimum value in some environment, the change in accuracy depends on the amount of fitness is solely a function of the trait value and not a family information used in the index, and on whether property of individual loci. Then for populations near the weights given to its components are properly the optimum, any mutation causing departure one adjusted to take account of the changes in variances. way or the other is deleterious, so predicted values of If family sizes are large and weights are adjusted, the variance maintained are small even in infinitely large

populations. Whilst the optimum model can be used selection also depends on how much genetic vari-to explain why animals are the size they are, it ability is maintained and how much inbreeding implies that all the natural selection acting on the depression occurs over generations, and therefore on genes affecting any trait is due solely to their effects effective population size (Robertson, 1960). These on that trait (Robertson, 1967). An alternative model are conflicting aims. An increase in selection intensi-is the pleiotropic model, in which genes and mutants ty, thereby reducing the number of parents selected are assumed to have a bivariate distribution of effects for given numbers recorded, reduces N . The use ofe

on the trait and on fitness (Robertson, 1967; family information to increase the accuracy of Keightley and Hill, 1990). Then the fate of mutants selection, thereby increasing coselection of relatives depends on their direct effects on fitness, most being within and across generations and variation in family deleterious, and the variation observed in traits such size, also reduces N . There has been extensive worke

as body size therefore reflects the pleiotropic effects on methods to select and mate animals to maximise of these mutants. Theoretical analysis shows, how- the response conditional on effective population size ever, that this model does not satisfactorily explain or rate of inbreeding, and algorithms have been the apparent much lower fitness of extreme indi- developed (e.g. Brisbane and Gibson, 1995; Cabal-viduals (Barton, 1990). With the pleiotropic model, lero et al., 1996; Grundy et al., 1998; Woolliams, the variance maintained is a function of population 1998). These calculations are generally based on the size, mutation rate and the magnitude of the correla- infinitesimal model and do not include mutational tion of effects of mutants on the traits of interest and effects. Whilst it is relatively easy to give figures for fitness. Such calculations have been undertaken by the cost of inbreeding depression, that for the cost of Caballero and Keightley (1994) using data on Dro- reduced variation is much harder to predict. Hence in sophila to relate the variance maintained in bristle all analyses considering short and long-term re-number to population size. sponses some, perhaps rather arbitrary, relationship As we do not fully understand the factors affecting between short and long term benefits has to be variance in natural populations, it is difficult to make specified.

reliable predictions for experimental and commercial

populations under artificial selection: natural selec- 2.4. Genes of large effect tion must also act, and in an environment alien to

that in which the species evolved. Furthermore, we Such calculations using the neutral or infinitesimal are rather ignorant of the relations between effects model provide a guide to the trade-off between short-and fitness short-and the distribution of mutation effects, and long-term response, but their utility is based on particularly as the mean changes; for example those strong assumptions. Two other considerations whether favourable mutations become a smaller part are important: the consequence of genes of large of the total as the population mean improves. Nor do effect and the potentially deleterious effects of genes, we know the extent to which natural selection is of particularly mutants, on fitness. Whilst we do not stabilising (i.e. mean dependent) or pleiotropic (in- have any general formulae for the rate of change of dividual gene dependent) form. Therefore no un- variance when genes of large effect are taken into equivocal answers can be given as to the size of a account, because the change depends on knowledge population under selection that is sufficiently large to of individual gene effects and frequencies, it may not maintain a constant variance over many generations. matter. What seems more critical is the probability We have two ways to take the argument forward: that they are fixed favourably, rather than lost from theoretical analysis and observations of experiment. the population. A reduction of variance of 1 / 2N pere

generation describes (to good approximation) the 2.3. Short vs. long term response change in variance over a single generation, even for genes of large effect; but it does not describe the loss Response to short term selection of a few genera- in fixation probability.

tions depends on the intensity and accuracy of An additive gene with effect (homozygote differ-selection in these generations. Response to long term ence, assuming there are two alleles) on the trait of a,

or in phenotypic standard deviation (s) units a /s, mutant gene therefore does not depend on the has a selective value equal to s5iar /hs, where i is absolute size of the population (providing its effect is the selection intensity and r is the accuracy of big enough that s.1 /N ), but only on the ratio ofe

selection. The fixation probability of this gene, effective to actual size. Assume the mutation rate to assuming its current frequency is q, is given by favourable mutants of selective value s is equal tom. As the number of such mutants arising in the

u( q)5[12exp(22N sq)] / [1e 2exp(22N s)],e (2) population each generation, 2Nm, is proportional to population size, the rate of fixation is 2Nm 3N s /e

(Robertson, 1960), which reduces to u( q)512 _{N52Nms, i.e. proportional to the effective}

popula-e

exp(22N sq), approximately, for s or a /e s .1 /N .e tion size (Hill, 1982). (This proportionality to N e

As a simple criterion for defining high fixation _{also holds for advantageous dominant mutations; but} probability, let us take u.0.9, i.e. the probability the _{the fixation probability of advantageous recessive} gene is fixed exceeds 90%, which requires N sqe . mutants in a random mating population is equal to

1.15. For example, for a gene with frequency q50.2, œ_{(2N s /p) /N, and therefore their rate of fixation is} e

a value of N se .5.8 is required; and with the further proportional toœN .) Furthermore, if increasing and

e

assumption of ir /h51.9 (e.g. i51.5, r /h51.3), it _{decreasing mutants occur at equal rates and the genes} follows that a value of N a /e s .3 is needed for 90% have relatively small effects on fitness, the steady fixation probability. For a gene of quite large effect, _{state variation maintained under directional selection}

a /s 50.2, an effective population size of only Ne. by additive mutations is equal to 2N V , which

e M

15 would be required. Such a gene would contribute _{applies to genes of large effects as for neutral genes}

2

a heritability of q(12q)(a /s) / 2|0.3%. For each _{(Hill and Keightley, 1988). The variation maintained}

halving of a /s, the required N doubles and con-e is not affected by the selection intensity because, as

tributed heritability is reduced by a factor of 4; and _{selection intensity i is increased, favourable genes} for each halving of q, the required N also doubles,e are more likely to be fixed but contribute variation

but the heritability is halved. For example, with _{for fewer generations as they become fixed more}

a /s 50.1 and q50.1, Ne.60 is required for a gene rapidly. Therefore for genes which are currently which contributes a heritability of only |0.08%, _{segregating in the population there is a diminishing}

several hundred of which would be needed to _{returns relationship between long-term response or} generate a heritability of 25–50% typical for quan- _{variation maintained and population size, whereas} titative traits. _{for new mutations there is a monotonic increasing} relationship. If much of the mutational variance is 2.5. Fate of mutants due to genes of very small effect, the response is achieved over very long time scales, however, The above calculations indicate that the genes because the mutants have such low initial frequency. which have the potential to contribute most to If the mutants increasing the trait under artificial selection response, those of large effect, are at risk selection also have a deleterious pleiotropic effect on only if they are at low frequency or if the population fitness, the variation maintained may exceed 2N V .e M

size is small (i.e. they are present in few copies in The selection response, however, will be less than the population). They are therefore likely to be quite expected from this variance because selection is, in recent mutations if the population has previously essence, on an index of the quantitative trait and been under continuous selection. Arguably, there- fitness (Hill and Mbaga, 1998).

fore, population size has to be considered most

critical when analysing the fate of mutations. An 2.6. Deleterious mutations additive advantageous mutant has initial frequency

1 / 2N, where N is the actual population size, so its In small populations, deleterious mutations are fixation probability (from Eq. (2)) is u(1 / 2N )512 less likely to be eliminated. Each has little chance of exp(2N s /N ), reducing to u(1 / 2N )e 5N s /N, ap-e being fixed, approximately (11N s) / 2N for additivee

21 /Ne,s,0, and zero if more deleterious. The almost 100 years and generations, and in which cumulative consequence of many mutations segregat- responses have continued in the lines selected for ing in the population, however, some of which high oil content or for high protein content in the eventually become fixed, could be a substantial drop kernel plants (Dudley, 1977). The populations are in mean performance, particularly in overall fitness bred with only 30 or so selected plants (maternal for which most mutations are likely to be deleterious. half-sib families). More male parents are likely to be Thus considerable attention has been given to the involved, but the lines are so superior to the natural size of the natural population necessary for the rate base for the selected traits that selection of offspring of elimination of deleterious mutations to be suffi- got by cross pollination outside the selected lines cient that mean fitness does not drop substantially; seems most unlikely to occur. Response in the low or, in the jargon, that the population is large enough lines has attenuated, but they are approaching levels to prevent it going into non-sustainable mutational of zero oil content in the kernels.

‘meltdown’. Conclusions depend on assumptions of Continued selection has been practised in Dum-the rate of occurrence and size of effects of deleteri- merstorf for increased body weight in mice, with 160 ous mutations: for a given input of variance, the animals selected each generation, a relatively large smaller their mean effect, the harder the mutants are size for a selection experiment in laboratory animals

¨

to eliminate and the greater their cumulative in- (Bunger et al., 1990). Selection has now been fluence on mean fitness. Some theoretical arguments continued for over 90 generations. At 6 weeks the indicate that populations as small as 100 could be at high line mice average |65 g and the unselected

risk (Lynch et al., 1995); whereas experimental controls 30 g, a response of about 12 phenotypic checks suggest that smaller populations are expected standard deviations. Response continues, albeit at a

¨

to be safe for very long periods (Gilligan et al., reduced rate (L. Bunger, personal communication). 1997). For populations under artificial selection, In a review of mouse selection experiments to that fitness is also likely to fall as a consequence of date, Eisen (1980) showed that long-term responses pleiotropic effects of genes affecting the trait under increased with population size and Jones et al. selection that have increased in frequency or become (1968) showed similar relationships in Drosophila. fixed by artificial selection. Laboratory or domestic Selection experiments in animals with the largest livestock populations are, however, protected against populations have been carried out by Weber (1990), extinction by careful and good management, for who got 30% higher responses over 55 generations example by giving many opportunities to breed and of selection for wing-tip height in Drosophila with by health control. 1000 than with 200 selected parents.

The effect of population size on maintaining variation and selection response is confounded with

3. Selection experiments its effect on inbreeding depression, particularly on fitness associated traits not necessarily under direct 3.1. Effect of population size selection. A contributing factor to the greater re-sponses in populations of larger size may have been The many laboratory selection experiments con- reductions in deleterious inbreeding associated ef-ducted over the years give us much information on fects (except in many Drosophila experiments where what can be achieved by continual selection, indeed fixed numbers of animals are sampled to be recorded whether variation and thus response is sustainable. as candidates for selection). Rapid inbreeding can be Although there is not a uniform outcome, it is very hard to sustain in livestock populations in which possible to draw some inferences from them to the it has been attempted (for review see e.g. Wright, design of animal improvement programmes. 1977, ch. 3). The effects of inbreeding over the long It is clear that some long-term experiments have term in selected lines cannot be simply predicted given continued responses over very many genera- from data on close matings in non-inbred base tions, without obvious limits. The classical example populations, however. Natural selection or artificial is the Illinois corn experiment that has now run for selection on fitness associated traits may reduce the

effects, and also (see Section 4) because pleiotropic In summary, the selection experiments in labora-or stabilising selection effects confound the picture. tory species show that substantial progress can be maintained for very many generations, even with 3.2. Contribution of mutations populations of effective size well under 100, but that responses increase with population size. Mutation Observations such as regression of performance on contributes to response, but it is clearly demonstrated relaxation or reversal of selection, and statistical only in populations selected from an inbred base. analyses undertaken within selected lines indicate

that there is substantial genetic variation present, for

example in lines of mice divergently selected for 4. Correlated traits

high and low body weight in our laboratory (Hill and

Mbaga, 1998). In such experiments started from We have considered here only variation main-outbred or crossbred base populations, in principle it tained in the trait under selection. For a completely is possible to disentangle the relative contribution uncorrelated trait, neutral arguments apply, i.e. a loss being made to long-term response and standing of variation at 1 / 2N and gain of Ve M by mutation. variation by genetic variation present in the base Selection will then act solely through its impact on population and by mutation after selection began. effective population size, whereas for traits that are Although we have tried to use maximum likelihood correlated with those under selection variation is (REML) to partition these sources of variance, the likely to be lost as the loci with pleiotropic effects power to separate them is low, and dependent on become fixed. Predictions over several generations assumptions of the infinitesimal model. are simple under the infinitesimal model, in which Direct evidence of the role of mutations in case variances, covariances and correlations do not generating, and thus by inference maintaining, vari- change with selection (other than due to the Bulmer ation comes from selection experiments started from effect). More generally, however, simple theory an inbred or isogenic base population, most of which shows that the correlation between the traits may have been undertaken in Drosophila. Responses to change substantially, even in sign, depending on the selection have been obtained, which give estimates sizes of gene effects leading to positive and negative of mutational heritability of about 0.1% as already covariances (Bohren et al., 1966). Only by making noted. There are some other features of these experi- assumptions about the distribution of frequencies and

´ ´

ments (e.g. Lopez and Lopez-Fanjul, 1993; Mackay pleiotropic effects of genes can predictions over et al., 1994). Importantly, analyses show that much several generations be made. Information is needed of the variation comes from mutations of large on genetic variances in traits other than those under effects, and many of these mutations are deleterious selection in long-term selected lines, in order to with respect to fitness. There may also be substantial indicate the potential for changes in the direction of asymmetry of response, for example in Mackay’s selection. (No selection experiments come to mind in experiment the response in abdominal bristle number which selection for many generations has been was much higher in the down than up direction, followed by selection for a very different trait). whereas in a separate set of lines response in Research in this area would be useful.

sternopleural bristle number was much greater in the It was noted previously that the genetic variance up direction. The only equivalent experiment in maintained by additive mutants on a trait unrelated to mammals was of smaller scale and by the standard of fitness is independent of the selection intensity on the other selection experiments the response was unim- trait. Therefore the genetic variation in other traits pressive. Even so, the divergence in body weight, the and covariation of these with each other and with the selected trait, between high and low lines maintained selected trait is also unaffected by the amount of with only 12 pairs a generation and weak selection selection, assuming each of the other traits is also (30%) was about 30% of the mean. Responses were independent of fitness. As fitness itself can be erratic over generations, and it appears that much of regarded as a quantitative trait that is always under the divergence was due to a single mutation direct selection, whatever other traits are being (Keightley, 1998). selected, the same simplifications do not hold.

Whereas mean fitness is likely to drop due to overall effective size isSN , where the effective sizeej

directional selection on other traits, whether stabilis- of subpopulation j is N . If there is limited migrationej

ing or pleiotropic effects apply, variation in fitness is among them and contributions to the pool do not likely to rise because genes that are deleterious with differ greatly, the effective size increases; indeed if respect to fitness are maintained segregating by the there is no migration at all, variation is maintained artificial selection. Furthermore, the observed selec- indefinitely in the set of populations as a whole, even tion response in the trait under selection is likely to if individual populations become fixed. These calcu-be less than expected from the standing genetic lations in terms of effective size are probably of variation, because of the negative correlated response limited relevance to the case of animal breeding, for from natural selection (Hill and Mbaga, 1998). they refer to asymptotic changes in unselected populations over what may be very long time scales.

5. Utilisation of different populations 5.3. Selection in sub-populations

5.1. Multiple objectives Selection within sub-populations, whether a breed-er’s nucleus herd or a whole breed, has the effect of The discussion has been restricted to single closed reducing the effective size of each. The amount of populations, but applies to any populations that are variability retained in this set of populations will currently of commercial importance in satisfying depend on the extent to which the same selection demand for a particular product or in utilising a criteria apply in each. It is obvious that variation is particular environment. There is clearly then justifi- maintained if, for example, both selected and un-cation in retaining and improving those populations selected populations are kept. The question is then where the market share justifies doing so. Maintain- whether such variation can be utilised. This depends ing populations in anticipation of long-term commer- on critical assumptions, among which is the extent cial need requires good luck or insight, however. A that selection objectives may change — essentially separate consideration is how to make best use of an unknowable. If selection objectives are assumed resources in maintaining long term response for any to remain constant, issues that affect the value of single population and objective, options for which maintaining subpopulations with different sizes / could involve population subdivision with selection selection intensities include the following.

or conservation, which impacts on effective

popula-tion size and useful variability. 1. Useful genes in any subpopulation are more likely to be retained and fixed favourably if selection is 5.2. Effective population size practised, although the optimum may be at rather weak selection because of the trade-off between Firstly consider the case of no selection. Then, selection intensity and effective population size. while migration generally increases the variation 2. The rate of response in the population as a whole present in any single population, providing there are is generally maximised if it is kept as a single not big differences in the contributions of individual population. This is because subdivision and re-populations to the pool, genetic variation in the crossing in the absence of between line selection population as a whole is retained longest if there is leads to lower mean responses at any time as Ne

no migration. The population dispersion can be and thus genetic variance are lower in each described in terms of variance in gene frequencies, subpopulation (Robertson, 1960). There are ex-summarised by Wright’s F-statistics, specifically ceptions to this general result, however. If there is

F . The asymptotic change in variance in the totalST recessive gene action or particular forms of population can be described by its effective popula- epistasis in which variation rises when the popu-tion size, N (see Wang and Caballero (1999) for ae lation undergoes a bottleneck in size, then in-recent review of the effective size of a subdivided creased rates can be achieved. Also, if between population). At its simplest, providing there is sub- line (subpopulation) selection is practised, there stantial migration among a set of subpopulations, the are transient situations whereby the performance

of the best of a group of small lines is expected to knowledge and technology. There are other possi-be greater than that of one large population. This bilities.

is, of course, the main function of

inbreeding-selection schemes. 1. Marker assisted introgression is essentially a way 3. It is important to distinguish between the total of backcrossing in a particular region (QTL) or amount of variation present within and among a gene, whereby performance of the recipient popu-set of populations and that utilisable by selection lation is increased whilst retaining most of its in finite time. Thus if unselected populations are previous variability. The problem is to locate the maintained alongside selected populations to con- QTL, and then to do the backcrossing with the serve variation, the total variation in the set of recipient population of sufficient effective size populations is increased, but it may not be that substantial background variation is not lost, possible to utilise the conserved variation in an except in the region very close to the introgressed effective and timely way as the unselected popu- QTL. A first and major problem is to identify the lations lag further behind. If an unselected or QTL to introgress. These are likely only to be backward population is to be used, the loss of found by intensive study of well-recorded popula-performance from bringing in inferior genes has tions or of crosses between populations. Detailed to be made up quite quickly, either by backcros- QTL mapping in large numbers of populations sing out all but specified loci, which requires would be a major undertaking.

information on relevant marker genes, or because 2. Induced mutagenesis of unspecified quantitative genetic variation is much higher. Assuming the variation is an old idea that seems still to be used

infinitesimal model, the increment in additive in a limited way in plant breeding, but has not variance is proportional to the genetic distance been applied successfully in animals. The reasons between the populations (which is proportional to are not entirely clear, but traditionally X-rays the sum of their inbreeding coefficients sub- have been used; they cause chromosomal damage, sequent to derivation from the same source). With so mutations are ‘unfit’. Chemical mutagenesis is accurate selection, such that response is nearly being widely used to screen for mutants in mice proportional to standard deviation, the propor- to serve as models for particular diseases in man. tional increment inœV , about half that in V , isA A For quantitative traits, because mutants are at low relevant. These issues need further consideration frequency, those of small effect take a long time in design of conservation programmes. to become useful; and laboratory experiments 4. A more interesting and difficult case is where have typically been too short. Experiments using selection objectives change in the medium or long mutagenesis have in fact indicated an increase in term. If these go through a process of gradual genetic variance, but these have not been regarded evolution rather than revolution, variation present in most cases as large enough to be worthwhile. in current commercial populations can be utilised. Spectacular changes have, however, been found Populations maintained just to increase the total in some cases, for example from mobile P-ele-variation present among and within populations ment mutagenesis in Drosophila by Mackay remain unlikely to be able to contribute usefully (1985), and smaller responses using retroviral unless relevant QTL have been identified. insertions in mice (Keightley et al., 1993). Per-haps the subject needs revisiting, if only to provide a better understanding of how to

in-6. Other sources of variation fluence the generation of variability.

3. Site directed mutagenesis is a technique that has In the previous discussion we have considered been limited by two restrictions: an inability to solely classical sources of variation, namely that perform the technique except in a specific line of present initially in populations and that arising by mice using embryo stem (ES) cells, and a lack of mutation. This is a very restricted viewpoint in light knowledge as to which genes to mutate. A of new developments in genetic and reproductive solution to the former seems likely through the

use of the nuclear transfer (‘Dolly’) techniques of of such long term response or opportunity in terms of Wilmut and co-workers (Schnieke et al., 1997). potential economic benefit and / or political oppor-The second will take some time while information tunity from having unique material, and cultural accumulates, but already there are candidates for benefit from maintaining our heritage? The other is knockouts or partial change in function. For essentially a genetic issue and the subject of the example, null mutations of the myostatin gene previous discussion: what factors determine the lead to muscular hypertrophy in mice and double availability of useful genetic variation?

muscling in cattle (Grobet et al., 1997), with The long term selection experiments undertaken in several independent mutants identified in cattle; laboratory animals have spanned many tens of an obvious experiment is therefore to manipulate generations, equivalent to many centuries in cattle the gene or its promoter in these and other species terms, which is well beyond the time horizon where to modify its effects. consumer demands and resource supplies can be 4. Gene transfer through addition experiments has predicted. In order to assess the value of retained not yet been successful in livestock improvement, variation in enabling selection response, the formal, perhaps mainly because expression of the trans- hard-line, approach is to discount returns from future genes such as for growth hormone could not be years to the present in order to assess opportunity controlled. It has, however, enabled new functions costs properly. Even if discount rates as low as 3% such as the expression of human proteins in the per year are taken, which is well below the level milk to be incorporated. With the opportunity for which a business would use for investment, this specific gene modification, however, rather than translates in typical breeding programmes to a gene insertion via traditional transgenic technolo- discount rate of almost 5% per generation in pigs and gy, gene transfer is likely to use the same 15% per generation in cattle. Thus, with cattle, processes as site directed mutagenesis so as to improvements five or more generations later become make a single copy of a complete gene from rather economically unimportant when viewed from another species. the present day. Consider the simple trade-off be-tween short and long term improvements (as func-These routes whereby individual genes can be tions of selection intensity and effective population constructed and incorporated have unlimited poten- size). As James (1972) showed, with high per tial, although they are obviously expensive compared generation discount rates, selecting very intensively

with traditional selection. Whilst there are obviously at the expense of population size best uses fixed ethical and public acceptance issues which arise with resources.

germ-line manipulation, opinions can change with Such arguments do not accord with what is time and barriers should not be put up to the considered socially acceptable, in relation to our acquisition of knowledge. As genes can be changed, descendants’ benefits and opportunities. Even so, the transferred between species, and presumably ‘in- issues of maintenance of genetic variation in lives-vented’ with defined expression patterns, it does not tock and of conservation in general cannot be seem sensible to ignore them in any discussion of rationally discussed without a consideration of the long-term maintenance and generation of genetic time horizon. We do not know how demands for variation and constrain discussion solely to retaining animal products will change, and we do not know what is currently present. what new technologies will come along. For exam-ple, genetic conservation programmes in cart-horses would have had no impact in the tractor age;

7. Time horizons technologies such as blood typing of livestock have been replaced by molecular methods; and whole There are two quite different issues that have to be industries, such as coal mining and rabbit meat addressed when assessing the importance of retaining production in the UK, have almost disappeared. It genetic variation. One is essentially an economic, seems reasonable to assume that the rate of change in political or cultural question: what is the importance technology and demands is likely to be greater than

Eisen, E.J., 1980. Conclusions from long-term selection

experi-the rate of loss of variation from all but experi-the smallest

¨

ments with mice. Z. Tierz. Zuchtungsbiol. 97, 305–323.

programmes. In the face of the unknowable, how

Falconer, D.S., Mackay, T.F.C., 1996. In: 4th ed, Introduction To

should resources be devoted to short-term, known, _{Quantitative Genetics, Longman, Harlow, Essex.}

benefits in contrast to long term, perhaps negligible Gilligan, D.M., Woodworth, L.M., Montgomery, M.E., Briscoe, D.A., Frankham, R., 1997. Is mutation accumulation a threat to

benefits because they are unknown? This is primarily

the survival of endangered populations? Conserv. Biol. 11,

a political and not genetic question, but actions,

1235–1241.

including deliberate conservation of genetic variation _{Grobet, L., Martin, L.J.R., Poncelet, D., Pirottin, D., Brouwers, B.,} incur substantial cost. The clearest arguments for Riquet, J., Schoerbelein, A., Dunner, S., Menissier, F., Mas-sabanda, J., Fries, R., Hanset, R., Georges, M., 1997. A

conservation of existing breeds and populations are

deletion in the bovine myostatin gene causes the

double-cultural: so we and then our descendants can

con-muscled phenotype in cattle. Nature Genet. 17, 71–74.

tinue to observe the variety of nature. _{Grundy, B., Villanueva, B., Woolliams, J.A., 1998. Dynamic}

selection procedures for constrained inbreeding and their consequences for pedigree development. Genet. Res. 72, 159– 168.

Acknowledgements Hill, W.G., 1982. Predictions of response to artificial selection from new mutations. Genet. Res. 40, 255–278.

Hill, W.G., Keightley, P.D., 1988. Interrelations of mutation,

This paper is based on a presentation to the

population size, artificial and natural selection. In: Weir, B.S.,

Genetics Commission at the EAAP meeting in

Eisen, E.J., Goodman, M.M., Namkoong, G. (Eds.),

Proceed-¨

Warsaw, 1998, in a session organised by Asko Maki- _{ings of the Second International Conference On Quantitative} Tanila on ‘Sustainable breeding — a challenge?’. I Genetics, Sinauer, Sunderland, MA, pp. 57–70.

am grateful to Armando Caballero, Peter Keightley, Hill, W.G., Mbaga, S.H., 1998. Mutation and conflicts between artificial and natural selection for quantitative traits. Genetica

¨

Asko Maki-Tanila, Jinliang Wang and John

Wool-102 / 103, 171–181.

liams for helpful comments on the paper.

James, J.W., 1972. Optimum selection intensity in breeding programmes. Anim. Prod. 14, 1–9.

Jones, L.P., Frankham, R., Barker, J.S.F., 1968. The effects of population size and selection intensity for a quantitative trait in References _{Drosophila. II. Long-term response to selection. Genet. Res.}

12, 249–266.

Barton, N., 1990. Pleiotropic models of quantitative variation. Keightley, P.D., 1998. Genetic basis of response to 50 generations Genetics 124, 773–782. of selection on body weight in inbred mice. Genetics 148, Bohren, B.B., Hill, W.G., Robertson, A., 1966. Some observations 1931–1939.

on asymmetrical correlated responses to selection. Genet. Res. Keightley, P.D., Evans, M.J., Hill, W.G., 1993. Effects of multiple 7, 44–57. retrovirus insertions on quantitative traits of mice. Genetics Brisbane, J.R., Gibson, J.P., 1995. Balancing selection response 135, 1099–1106.

and rate of inbreeding by including genetic relationships in Keightley, P.D., Hill, W.G., 1990. Variation maintained in quantita-selection decisions. Theor. Appl. Genet. 91, 421–431. tive traits with mutation-selection balance: pleiotropic side-Bulmer, M.G., 1971. The effect of selection on genetic variability. effects on fitness traits. Proc. R. Soc. Lond. B242, 95–100.

´ ´

Am. Nat. 105, 201–211. Lopez, M.A., Lopez-Fanjul, C., 1993. Spontaneous mutations for

¨ ¨

Bunger, L., Herrendorfer, G., Renne, U., 1990. Results of long a quantitative trait in Drosophila melanogaster. II. Distribution term selection for growth traits in laboratory mice. In: Proceed- of mutant effects on the trait and fitness. Genet. Res. 61, ings 4th World Congress On Genetic Applications in Livestock 117–126.

¨

Production, Vol. 13, pp. 321–324. Lynch, M., Conery, J., Burger, R., 1995. Mutation accumulation Caballero, A., Keightley, P.D., 1994. A pleiotropic nonadditive and the extinction of small populations. Am. Nat. 146, 489–

model of variation in quantitative traits. Genetics 138, 883– 518.

900. Mackay, T.F.C., 1985. Transposable element-induced response to

Caballero, A., Santiago, E., Toro, M.A., 1996. Systems of mating artificial selection in Drosophila melanogaster. Genetics 111, to reduce inbreeding in selected populations. Anim. Sci. 62, 351–374.

431–442. Mackay, T.F.C., Fry, R.F., Lyman, R.F., Nuzhdin, S.V., 1994. Dudley, J.W., 1977. 76 generations of selection for oil and protein Polygenic mutation in Drosophila melanogaster: estimates percentage in maize. In: Pollak, E., Kempthorne, O., Bailey, Jr. from response to selection of inbred strains. Genetics 136, T.B. (Eds.), Proceedings of the International Conference On 937–951.

Quantitative Genetics, Iowa State University Press, Ames, pp. Robertson, A., 1960. A theory of limits in artificial selection. Proc.

Robertson, A., 1967. The nature of quantitative genetic variation. tions. I. Selection for wing-tip height in Drosophila melano-In: Brink, A. (Ed.), Heritage From Mendel, University of gaster at three population sizes. Genetics 125, 579–584. Wisconsin Press, Madison, pp. 265–280. Wei, M., Caballero, A., Hill, W.G., 1996. Selection response in Schnieke, A.E., Kind, A.J., Ritchie, W.A., Mycock, K., Scott, finite populations. Genetics 144, 1959–1973.

A.R., Ritchie, M., Wilmut, I., Colman, A., Campbell, K.H.S., Woolliams, J.A., 1998. A recipe for the design of breeding 1997. Human factor IX transgenic sheep produced by nuclei schemes. In: Proceedings 6th World Congress On Genetic from transfected fetal fibroblasts. Science 278, 2130–2133. Applications in Livestock Production, Vol. 25, pp. 427–430. Wang, J., Caballero, A., 1999. Developments in predicting the Wright, S., 1977. In: Evolution and the Genetics of Populations.

effective size of subdivided populations. Heredity 82, 212–226. Experimental Results and Evolutionary Deductions, Vol. 3, Weber, K.E., 1990. Increased selection response in large popula- University of Chicago Press, Chicago.

effects, and also (see Section 4) because pleiotropic In summary, the selection experiments in labora-or stabilising selection effects confound the picture. tory species show that substantial progress can be maintained for very many generations, even with 3.2. Contribution of mutations populations of effective size well under 100, but that responses increase with population size. Mutation Observations such as regression of performance on contributes to response, but it is clearly demonstrated relaxation or reversal of selection, and statistical only in populations selected from an inbred base. analyses undertaken within selected lines indicate

that there is substantial genetic variation present, for

example in lines of mice divergently selected for 4. Correlated traits

high and low body weight in our laboratory (Hill and

Mbaga, 1998). In such experiments started from We have considered here only variation main-outbred or crossbred base populations, in principle it tained in the trait under selection. For a completely is possible to disentangle the relative contribution uncorrelated trait, neutral arguments apply, i.e. a loss being made to long-term response and standing of variation at 1 / 2N and gain of Ve M by mutation. variation by genetic variation present in the base Selection will then act solely through its impact on population and by mutation after selection began. effective population size, whereas for traits that are Although we have tried to use maximum likelihood correlated with those under selection variation is (REML) to partition these sources of variance, the likely to be lost as the loci with pleiotropic effects power to separate them is low, and dependent on become fixed. Predictions over several generations assumptions of the infinitesimal model. are simple under the infinitesimal model, in which Direct evidence of the role of mutations in case variances, covariances and correlations do not generating, and thus by inference maintaining, vari- change with selection (other than due to the Bulmer ation comes from selection experiments started from effect). More generally, however, simple theory an inbred or isogenic base population, most of which shows that the correlation between the traits may have been undertaken in Drosophila. Responses to change substantially, even in sign, depending on the selection have been obtained, which give estimates sizes of gene effects leading to positive and negative of mutational heritability of about 0.1% as already covariances (Bohren et al., 1966). Only by making noted. There are some other features of these experi- assumptions about the distribution of frequencies and

´ ´

ments (e.g. Lopez and Lopez-Fanjul, 1993; Mackay pleiotropic effects of genes can predictions over et al., 1994). Importantly, analyses show that much several generations be made. Information is needed of the variation comes from mutations of large on genetic variances in traits other than those under effects, and many of these mutations are deleterious selection in long-term selected lines, in order to with respect to fitness. There may also be substantial indicate the potential for changes in the direction of asymmetry of response, for example in Mackay’s selection. (No selection experiments come to mind in experiment the response in abdominal bristle number which selection for many generations has been was much higher in the down than up direction, followed by selection for a very different trait). whereas in a separate set of lines response in Research in this area would be useful.

sternopleural bristle number was much greater in the It was noted previously that the genetic variance up direction. The only equivalent experiment in maintained by additive mutants on a trait unrelated to mammals was of smaller scale and by the standard of fitness is independent of the selection intensity on the other selection experiments the response was unim- trait. Therefore the genetic variation in other traits pressive. Even so, the divergence in body weight, the and covariation of these with each other and with the selected trait, between high and low lines maintained selected trait is also unaffected by the amount of with only 12 pairs a generation and weak selection selection, assuming each of the other traits is also (30%) was about 30% of the mean. Responses were independent of fitness. As fitness itself can be erratic over generations, and it appears that much of regarded as a quantitative trait that is always under the divergence was due to a single mutation direct selection, whatever other traits are being

Whereas mean fitness is likely to drop due to overall effective size isSN , where the effective sizeej

directional selection on other traits, whether stabilis- of subpopulation j is N . If there is limited migrationej

ing or pleiotropic effects apply, variation in fitness is among them and contributions to the pool do not likely to rise because genes that are deleterious with differ greatly, the effective size increases; indeed if respect to fitness are maintained segregating by the there is no migration at all, variation is maintained artificial selection. Furthermore, the observed selec- indefinitely in the set of populations as a whole, even tion response in the trait under selection is likely to if individual populations become fixed. These calcu-be less than expected from the standing genetic lations in terms of effective size are probably of variation, because of the negative correlated response limited relevance to the case of animal breeding, for from natural selection (Hill and Mbaga, 1998). they refer to asymptotic changes in unselected populations over what may be very long time scales.

5. Utilisation of different populations 5.3. Selection in sub-populations

5.1. Multiple objectives Selection within sub-populations, whether a breed-er’s nucleus herd or a whole breed, has the effect of The discussion has been restricted to single closed reducing the effective size of each. The amount of populations, but applies to any populations that are variability retained in this set of populations will currently of commercial importance in satisfying depend on the extent to which the same selection demand for a particular product or in utilising a criteria apply in each. It is obvious that variation is particular environment. There is clearly then justifi- maintained if, for example, both selected and un-cation in retaining and improving those populations selected populations are kept. The question is then where the market share justifies doing so. Maintain- whether such variation can be utilised. This depends ing populations in anticipation of long-term commer- on critical assumptions, among which is the extent cial need requires good luck or insight, however. A that selection objectives may change — essentially separate consideration is how to make best use of an unknowable. If selection objectives are assumed resources in maintaining long term response for any to remain constant, issues that affect the value of single population and objective, options for which maintaining subpopulations with different sizes / could involve population subdivision with selection selection intensities include the following.

or conservation, which impacts on effective

popula-tion size and useful variability. 1. Useful genes in any subpopulation are more likely to be retained and fixed favourably if selection is 5.2. Effective population size practised, although the optimum may be at rather weak selection because of the trade-off between Firstly consider the case of no selection. Then, selection intensity and effective population size. while migration generally increases the variation 2. The rate of response in the population as a whole present in any single population, providing there are is generally maximised if it is kept as a single not big differences in the contributions of individual population. This is because subdivision and re-populations to the pool, genetic variation in the crossing in the absence of between line selection population as a whole is retained longest if there is leads to lower mean responses at any time as Ne

no migration. The population dispersion can be and thus genetic variance are lower in each described in terms of variance in gene frequencies, subpopulation (Robertson, 1960). There are ex-summarised by Wright’s F-statistics, specifically ceptions to this general result, however. If there is F . The asymptotic change in variance in the totalST recessive gene action or particular forms of population can be described by its effective popula- epistasis in which variation rises when the popu-tion size, N (see Wang and Caballero (1999) for ae lation undergoes a bottleneck in size, then in-recent review of the effective size of a subdivided creased rates can be achieved. Also, if between population). At its simplest, providing there is sub- line (subpopulation) selection is practised, there stantial migration among a set of subpopulations, the are transient situations whereby the performance

of the best of a group of small lines is expected to knowledge and technology. There are other possi-be greater than that of one large population. This bilities.

is, of course, the main function of

inbreeding-selection schemes. 1. Marker assisted introgression is essentially a way 3. It is important to distinguish between the total of backcrossing in a particular region (QTL) or amount of variation present within and among a gene, whereby performance of the recipient popu-set of populations and that utilisable by selection lation is increased whilst retaining most of its in finite time. Thus if unselected populations are previous variability. The problem is to locate the maintained alongside selected populations to con- QTL, and then to do the backcrossing with the serve variation, the total variation in the set of recipient population of sufficient effective size populations is increased, but it may not be that substantial background variation is not lost, possible to utilise the conserved variation in an except in the region very close to the introgressed effective and timely way as the unselected popu- QTL. A first and major problem is to identify the lations lag further behind. If an unselected or QTL to introgress. These are likely only to be backward population is to be used, the loss of found by intensive study of well-recorded popula-performance from bringing in inferior genes has tions or of crosses between populations. Detailed to be made up quite quickly, either by backcros- QTL mapping in large numbers of populations sing out all but specified loci, which requires would be a major undertaking.

information on relevant marker genes, or because 2. Induced mutagenesis of unspecified quantitative genetic variation is much higher. Assuming the variation is an old idea that seems still to be used infinitesimal model, the increment in additive in a limited way in plant breeding, but has not variance is proportional to the genetic distance been applied successfully in animals. The reasons between the populations (which is proportional to are not entirely clear, but traditionally X-rays the sum of their inbreeding coefficients sub- have been used; they cause chromosomal damage, sequent to derivation from the same source). With so mutations are ‘unfit’. Chemical mutagenesis is accurate selection, such that response is nearly being widely used to screen for mutants in mice proportional to standard deviation, the propor- to serve as models for particular diseases in man. tional increment inœV , about half that in V , isA A For quantitative traits, because mutants are at low relevant. These issues need further consideration frequency, those of small effect take a long time in design of conservation programmes. to become useful; and laboratory experiments 4. A more interesting and difficult case is where have typically been too short. Experiments using selection objectives change in the medium or long mutagenesis have in fact indicated an increase in term. If these go through a process of gradual genetic variance, but these have not been regarded evolution rather than revolution, variation present in most cases as large enough to be worthwhile. in current commercial populations can be utilised. Spectacular changes have, however, been found Populations maintained just to increase the total in some cases, for example from mobile P-ele-variation present among and within populations ment mutagenesis in Drosophila by Mackay remain unlikely to be able to contribute usefully (1985), and smaller responses using retroviral unless relevant QTL have been identified. insertions in mice (Keightley et al., 1993). Per-haps the subject needs revisiting, if only to provide a better understanding of how to

in-6. Other sources of variation fluence the generation of variability.

3. Site directed mutagenesis is a technique that has In the previous discussion we have considered been limited by two restrictions: an inability to solely classical sources of variation, namely that perform the technique except in a specific line of present initially in populations and that arising by mice using embryo stem (ES) cells, and a lack of mutation. This is a very restricted viewpoint in light knowledge as to which genes to mutate. A of new developments in genetic and reproductive solution to the former seems likely through the

use of the nuclear transfer (‘Dolly’) techniques of of such long term response or opportunity in terms of Wilmut and co-workers (Schnieke et al., 1997). potential economic benefit and / or political oppor-The second will take some time while information tunity from having unique material, and cultural accumulates, but already there are candidates for benefit from maintaining our heritage? The other is knockouts or partial change in function. For essentially a genetic issue and the subject of the example, null mutations of the myostatin gene previous discussion: what factors determine the lead to muscular hypertrophy in mice and double availability of useful genetic variation?

muscling in cattle (Grobet et al., 1997), with The long term selection experiments undertaken in several independent mutants identified in cattle; laboratory animals have spanned many tens of an obvious experiment is therefore to manipulate generations, equivalent to many centuries in cattle the gene or its promoter in these and other species terms, which is well beyond the time horizon where

to modify its effects. consumer demands and resource supplies can be

4. Gene transfer through addition experiments has predicted. In order to assess the value of retained not yet been successful in livestock improvement, variation in enabling selection response, the formal, perhaps mainly because expression of the trans- hard-line, approach is to discount returns from future genes such as for growth hormone could not be years to the present in order to assess opportunity controlled. It has, however, enabled new functions costs properly. Even if discount rates as low as 3% such as the expression of human proteins in the per year are taken, which is well below the level milk to be incorporated. With the opportunity for which a business would use for investment, this specific gene modification, however, rather than translates in typical breeding programmes to a gene insertion via traditional transgenic technolo- discount rate of almost 5% per generation in pigs and gy, gene transfer is likely to use the same 15% per generation in cattle. Thus, with cattle, processes as site directed mutagenesis so as to improvements five or more generations later become make a single copy of a complete gene from rather economically unimportant when viewed from

another species. the present day. Consider the simple trade-off

be-tween short and long term improvements (as func-These routes whereby individual genes can be tions of selection intensity and effective population constructed and incorporated have unlimited poten- size). As James (1972) showed, with high per tial, although they are obviously expensive compared generation discount rates, selecting very intensively with traditional selection. Whilst there are obviously at the expense of population size best uses fixed ethical and public acceptance issues which arise with resources.

germ-line manipulation, opinions can change with Such arguments do not accord with what is time and barriers should not be put up to the considered socially acceptable, in relation to our acquisition of knowledge. As genes can be changed, descendants’ benefits and opportunities. Even so, the transferred between species, and presumably ‘in- issues of maintenance of genetic variation in lives-vented’ with defined expression patterns, it does not tock and of conservation in general cannot be seem sensible to ignore them in any discussion of rationally discussed without a consideration of the long-term maintenance and generation of genetic time horizon. We do not know how demands for variation and constrain discussion solely to retaining animal products will change, and we do not know what is currently present. what new technologies will come along. For exam-ple, genetic conservation programmes in cart-horses would have had no impact in the tractor age;

7. Time horizons technologies such as blood typing of livestock have

been replaced by molecular methods; and whole There are two quite different issues that have to be industries, such as coal mining and rabbit meat addressed when assessing the importance of retaining production in the UK, have almost disappeared. It genetic variation. One is essentially an economic, seems reasonable to assume that the rate of change in political or cultural question: what is the importance technology and demands is likely to be greater than

Eisen, E.J., 1980. Conclusions from long-term selection experi-the rate of loss of variation from all but experi-the smallest

¨

ments with mice. Z. Tierz. Zuchtungsbiol. 97, 305–323. programmes. In the face of the unknowable, how

Falconer, D.S., Mackay, T.F.C., 1996. In: 4th ed, Introduction To should resources be devoted to short-term, known, _{Quantitative Genetics, Longman, Harlow, Essex.}

benefits in contrast to long term, perhaps negligible Gilligan, D.M., Woodworth, L.M., Montgomery, M.E., Briscoe, D.A., Frankham, R., 1997. Is mutation accumulation a threat to benefits because they are unknown? This is primarily

the survival of endangered populations? Conserv. Biol. 11, a political and not genetic question, but actions,

1235–1241.

including deliberate conservation of genetic variation _{Grobet, L., Martin, L.J.R., Poncelet, D., Pirottin, D., Brouwers, B.,} incur substantial cost. The clearest arguments for Riquet, J., Schoerbelein, A., Dunner, S., Menissier, F., Mas-sabanda, J., Fries, R., Hanset, R., Georges, M., 1997. A conservation of existing breeds and populations are

deletion in the bovine myostatin gene causes the double-cultural: so we and then our descendants can

con-muscled phenotype in cattle. Nature Genet. 17, 71–74. tinue to observe the variety of nature. _{Grundy, B., Villanueva, B., Woolliams, J.A., 1998. Dynamic}

selection procedures for constrained inbreeding and their consequences for pedigree development. Genet. Res. 72, 159– 168.

Acknowledgements Hill, W.G., 1982. Predictions of response to artificial selection from new mutations. Genet. Res. 40, 255–278.

Hill, W.G., Keightley, P.D., 1988. Interrelations of mutation, This paper is based on a presentation to the

population size, artificial and natural selection. In: Weir, B.S., Genetics Commission at the EAAP meeting in

Eisen, E.J., Goodman, M.M., Namkoong, G. (Eds.), Proceed-¨

Warsaw, 1998, in a session organised by Asko Maki- _{ings of the Second International Conference On Quantitative} Tanila on ‘Sustainable breeding — a challenge?’. I Genetics, Sinauer, Sunderland, MA, pp. 57–70.

am grateful to Armando Caballero, Peter Keightley, Hill, W.G., Mbaga, S.H., 1998. Mutation and conflicts between artificial and natural selection for quantitative traits. Genetica ¨

Asko Maki-Tanila, Jinliang Wang and John

Wool-102 / 103, 171–181. liams for helpful comments on the paper.

James, J.W., 1972. Optimum selection intensity in breeding programmes. Anim. Prod. 14, 1–9.

Jones, L.P., Frankham, R., Barker, J.S.F., 1968. The effects of population size and selection intensity for a quantitative trait in

References _{Drosophila. II. Long-term response to selection. Genet. Res.}

12, 249–266.

Barton, N., 1990. Pleiotropic models of quantitative variation. Keightley, P.D., 1998. Genetic basis of response to 50 generations Genetics 124, 773–782. of selection on body weight in inbred mice. Genetics 148, Bohren, B.B., Hill, W.G., Robertson, A., 1966. Some observations 1931–1939.

on asymmetrical correlated responses to selection. Genet. Res. Keightley, P.D., Evans, M.J., Hill, W.G., 1993. Effects of multiple 7, 44–57. retrovirus insertions on quantitative traits of mice. Genetics Brisbane, J.R., Gibson, J.P., 1995. Balancing selection response 135, 1099–1106.

and rate of inbreeding by including genetic relationships in Keightley, P.D., Hill, W.G., 1990. Variation maintained in quantita-selection decisions. Theor. Appl. Genet. 91, 421–431. tive traits with mutation-selection balance: pleiotropic side-Bulmer, M.G., 1971. The effect of selection on genetic variability. effects on fitness traits. Proc. R. Soc. Lond. B242, 95–100.

´ ´

Am. Nat. 105, 201–211. Lopez, M.A., Lopez-Fanjul, C., 1993. Spontaneous mutations for

¨ ¨

Bunger, L., Herrendorfer, G., Renne, U., 1990. Results of long a quantitative trait in Drosophila melanogaster. II. Distribution term selection for growth traits in laboratory mice. In: Proceed- of mutant effects on the trait and fitness. Genet. Res. 61, ings 4th World Congress On Genetic Applications in Livestock 117–126.

¨

Production, Vol. 13, pp. 321–324. Lynch, M., Conery, J., Burger, R., 1995. Mutation accumulation Caballero, A., Keightley, P.D., 1994. A pleiotropic nonadditive and the extinction of small populations. Am. Nat. 146, 489–

model of variation in quantitative traits. Genetics 138, 883– 518.

900. Mackay, T.F.C., 1985. Transposable element-induced response to

Caballero, A., Santiago, E., Toro, M.A., 1996. Systems of mating artificial selection in Drosophila melanogaster. Genetics 111, to reduce inbreeding in selected populations. Anim. Sci. 62, 351–374.

431–442. Mackay, T.F.C., Fry, R.F., Lyman, R.F., Nuzhdin, S.V., 1994. Dudley, J.W., 1977. 76 generations of selection for oil and protein Polygenic mutation in Drosophila melanogaster: estimates percentage in maize. In: Pollak, E., Kempthorne, O., Bailey, Jr. from response to selection of inbred strains. Genetics 136, T.B. (Eds.), Proceedings of the International Conference On 937–951.

Quantitative Genetics, Iowa State University Press, Ames, pp. Robertson, A., 1960. A theory of limits in artificial selection. Proc.

Robertson, A., 1967. The nature of quantitative genetic variation. tions. I. Selection for wing-tip height in Drosophila melano-In: Brink, A. (Ed.), Heritage From Mendel, University of gaster at three population sizes. Genetics 125, 579–584.

Wisconsin Press, Madison, pp. 265–280. Wei, M., Caballero, A., Hill, W.G., 1996. Selection response in Schnieke, A.E., Kind, A.J., Ritchie, W.A., Mycock, K., Scott, finite populations. Genetics 144, 1959–1973.

A.R., Ritchie, M., Wilmut, I., Colman, A., Campbell, K.H.S., Woolliams, J.A., 1998. A recipe for the design of breeding 1997. Human factor IX transgenic sheep produced by nuclei schemes. In: Proceedings 6th World Congress On Genetic from transfected fetal fibroblasts. Science 278, 2130–2133. Applications in Livestock Production, Vol. 25, pp. 427–430. Wang, J., Caballero, A., 1999. Developments in predicting the Wright, S., 1977. In: Evolution and the Genetics of Populations.

effective size of subdivided populations. Heredity 82, 212–226. Experimental Results and Evolutionary Deductions, Vol. 3, Weber, K.E., 1990. Increased selection response in large popula- University of Chicago Press, Chicago.