measuring and managing genetic variability in small

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Measuring and managing genetic variability in smallpopulations

Hubert de Rochambeau, Florence Fournet-Hanocq, Jacqueline Vu Tien Khang

To cite this version:Hubert de Rochambeau, Florence Fournet-Hanocq, Jacqueline Vu Tien Khang. Measuring and man-aging genetic variability in small populations. Annales de zootechnie, INRA/EDP Sciences, 2000, 49(2), pp.77-93. �10.1051/animres:2000109�. �hal-00889883�

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Review article

Measuring and managing genetic variabilityin small populations

Hubert DE ROCHAMBEAU*, Florence FOURNET-HANOCQ,Jacqueline VU TIEN KHANG

Station d’Amélioration Génétique des Animaux, BP 27, 31326 Auzeville Cedex, France

(Received 2 July 1999; accepted 14 January 2000)

Abstract — Genetic variability in small populations is affected by specific phenomena. The jointeffects of genetic drift and selection, in addition to the decrease in genetic variance due to the mereselection (Bulmer effect), enhance the risk of losing alleles at selected or unselected genes andincrease the inbreeding in the population by changing the family structure. Criteria for measuring thischange in genetic variability are derived from the three approaches to describe the genetic variabil-ity. At the genealogical level, the kinship and inbreeding coefficients, or the effective populationsize, can be used. At the trait level, the estimation of its heritability is a good measure of remaininggenetic variance. At the genome level, studying the polymorphism of known genetic markers caninform on the degree of genetic diversity. These criteria are to be integrated in specific tools for themanagement of the genetic variability. After a short introduction on the basic concepts needed for thestudy of genetic variability in small populations, the main criteria available to measure its change inpopulations is exposed and their relative efficiencies discussed. The strategies for monitoring geneticvariability, deriving from the previous criteria, are illustrated through different examples.

small population / genetic variability / genetic drift / genetic management / conservationprogramme

Résumé — Mesure et gestion de la variabilité génétique dans les petites populations. Plusieursphénomènes spécifiques modifient la variabilité génétique dans les petites populations. Les effets com-binés de la dérive génétique et de la sélection, auxquels s’ajoutent la réduction de la variance géné-tique due spécifiquement à la sélection (Effet Bulmer), renforcent le risque de perdre des allèles à desloci sélectionnés et non sélectionnés et augmentent la consanguinité de la population du fait de la modi-fication de la structure familiale. Les critères de mesure de la variabilité génétique dérivent des3 approches utilisées pour la décrire. Les coefficients de consanguinité et de parenté ou l’effectifgénétique résument l’information généalogique. L’estimation de l’héritabilité d’un caractère syn-thétise la variabilité génétique restante. L’étude du polymorphisme pour des marqueurs génétiques

Ann. Zootech. 49 (2000) 77–93 77© INRA, EDP Sciences

* Correspondence and reprintsTel.: 33 (0)5 61 28 51 88; fax: 33 (0)5 61 28 53 53; e-mail: [email protected]

H. de Rochambeau et al.78

1. INTRODUCTION

Genetic variability may be defined as the“genetic ability to vary”, and therefore thecapacity to respond to environmental vari-ations or changes in the selection objectives.Genetic variability is also the basis of anygenetic progress, when a population isundergoing selection. Its maintenance at aconsistent level is then of great concern inany population, selected or not, and what-ever its size. However, the smaller the pop-ulation, the higher the need for conserva-tion, as there are less individuals so less“containers” for genetic variability.

But how can we decide that a populationis “small”? What may be called “small pop-ulation” is a population where the number ofindividuals really contributing to the nextgeneration is restricted, whether the totalpopulation size is really small (up to sev-eral hundreds of individuals) or the use oftechniques allowing a large diffusion ofprogress (artificial insemination, multipleovulation and embryo transfer) reduces thenumber of reproducers in one sex or both, orprovokes a disequilibrium in the reproduc-ers’ contributions to subsequent generations.Some domestic populations may then beconsidered as “small populations” and beconcerned by the following.

This paper aims to present the basic con-cepts and the main tools for the manage-ment of genetic variability in a small popu-lation, with or without selection. After adescription of the phenomena acting ongenetic variability in such a population, thecriteria derived from the different defini-

tions of genetic variability used to measureits evolution will be compared. A presen-tation of more or less complex rules formonitoring small populations will concludethis paper. The concepts developed in thefirst part will concern any kind of small pop-ulation, but the last part of the paper willfocus on populations under conservationprogrammes.

2. BASIC PHENOMENAAND CONCEPTS

2.1. Genetic drift and inbreeding

A restricted number of individuals con-tributing to the next generation in a smallpopulation will have two consequences:genetic drift and inbreeding.

Genetic drift has been defined by Wright[51] for a neutral, (i.e. non selected) bi-alleliclocus, as random fluctuations of allelic fre-quencies around their initial value, due tothe sampling of alleles from one generationto the next, finally leading to the fixation ofone of the alleles (and the loss of the other).The higher the number of generations con-sidered and the smaller the population, thegreater the fluctuations. This can beextended to more than one locus, providinga progressive increase of homozygosity overall the genes in the population, due to thesuccessive samplings of alleles over timeand the consecutive random fixations ofsome alleles and losses of others.

The probabilistic approach of inbreed-ing was derived by Malecot [29]. In small

décrit la variabilité existante au niveau du génome. Ces critères servent à construire des outils de ges-tion de la variabilité. Après une brève introduction qui présente les concepts utiles à l’étude de la varia-bilité génétique, les principaux critères utilisés pour suivre son évolution sont décrits, et leur effica-cité est comparée. Les stratégies de gestion qui dérivent de ces critères sont ensuite illustrées à partirde l’étude de quelques exemples.

petites populations / variabilité génétique / dérive génétique / gestion génétique / programme deconservation

Genetic management of small populations

– a dominance effect D, resulting frominteractions between the paternal and mater-nal alleles at a given locus;

– an epistatic effect I, concerning inter-actions between alleles at different loci.

In most cases, only the additive geneticpart of the performance is considered andthe genetic variability of a quantitative traitis approached by its additive genetic vari-ance. Several models, either analytic [6, 49]or stochastic [15], differing by the hypothe-ses they rely on, are available to describeand predict the evolution of additive geneticvariance over generations. The more com-plex the model, the more accurate the pre-diction of genetic variance over time. This isillustrated in Figure 1, where the predictionsprovided by three analytical models basedon Gaussian theory are compared. Wrightmodel [51] and Bulmer model [3] consideronly one effect at a time on genetic vari-ance, either genetic drift (Wright model) orselection (Bulmer model). The Verrier et al.model [49] accounts for genetic drift, selec-tion and interactions between the two fac-tors. The Wright model highlights the effectof genetic drift on genetic variance: theremaining variance after 30 generations is1.4 times higher when the population effec-tive size is 4 times higher. The Bulmermodel evidences the influence of selection,detailed in the next part, on the evolutionof genetic variance.

2.3. Selection in small populations

Selection has a direct effect on geneticvariance:

– Frequencies of “favourable” genes forthe selected trait are increased by selection,modifying the genic variance (i.e. the vari-ance of gene effects), which is one compo-nent of genetic variance. The pattern of evo-lution of the genic variance depends oninitial frequencies of the favourable alleles,but in any case this variance will tend tozero due to the fixation of favourable alleles.

populations, the number of founder ances-tors is restricted (“founder” means an indi-vidual whose parents are unknown). Oversuccessive generations, even if matings arepanmictic, individuals are more likely to berelated, due to one or more common ances-tors, and thereafter, matings between rela-tives produce inbred individuals. As a con-sequence, two homologous genes could be“identical by descent”, i.e. they are bothderiving by copy from the same gene in acommon ancestor.

2.2. Consequences on genetic variability

Genetic drift and inbreeding were twoaspects of a phenomenon which increasesthe rate of homozygous genes in the popu-lation. As the genetic variability of the traitunder study can be characterised by thenumber of different alleles available at theloci controlling the trait in the whole popu-lation, the loss of alleles due to genetic driftor inbreeding consecutively decreases thegenetic variability.

The previous concepts were developedfor one single neutral locus. Most of thetime, geneticists are interested in “quanti-tative” traits, i.e. traits with continuous vari-ation, which they suppose controlled by avery large number of independent genes ofsmall and identical effect [14]. The perfor-mance P of an individual is then split in twoparts, the genetic effect G and the environ-mental effect E:

P = G + E

where G and E are assumed to be indepen-dent and normally distributed with meanzero and variances σ2

G and σ2E respectively.

The genetic effect itself is generally con-sidered as the sum of:

– an additive genetic effect A, which isthe sum of individual gene effects at eachlocus and which constitutes the genetic partexpected to be transmitted from parents tooffspring;

79

H. de Rochambeau et al.

This effect of selection on the genic vari-ance is related to the magnitude of geneeffects on the selected trait and decreasesas the number of loci increases [10].Changes of gene frequencies can beneglected under the infinitesimal hypothesis(i.e. an infinite number of independent genesof small and identical effects controlling theselected trait) but may be significant forother kinds of modelling where the numberof loci is assumed to be finite.

– Genetic disequilibrium between theselected loci is induced by selection. Geneticdisequilibrium consists in an excess of inter-mediate combinations of genes (i.e. as manygenes with favourable effect on the selectedtrait than genes with unfavourable effect)when selection is directional. This leads tonegative covariances between gene effectsand reduces genetic variance in the selected

parents [3, 27]. The genetic variance amongbreeding individuals in a selected popula-tion will then also depend on the selectionintensity and accuracy, decreasing whenselection is more intense and accurate.

Selection has also an indirect effecton genetic variance:

– Selection modifies the family structureof the population whatever its size. Thiseffect is enhanced when the population issmall because it increases inbreeding overtime. The chance of two related individu-als being selected or rejected together ishigher than for two unrelated ones. The rela-tionship between selected individuals thenbecomes closer and closer over generationsof selection. This effect can be partly con-sidered in the computation of the inbreedingcoefficient [49]. This effect will be enhanced

80

Figure 1. Evolution of genetic variance in three models, depending on effective population size Ne,with a proportion of selected males p (the proportion of females being 50%), for a trait with heritability0.25 – W for Wright [53], with Ne = 120 (h) or Ne = 31 (■), B for Bulmer [3], withp = 50% (e) or p = 6.25% (r), and V for Verrier et al. [49], with Ne= 120 and p = 6.25% (n) orNe= 31 and p = 6.25% (m).


founders, have been largely used for a longtime (see Vu Tien Khang, [50] for a review;see also [13, 17, 32]). More recently, variouscriteria derived from probabilities of geneorigin have been proposed. Boichard et al.[2] presented an overview of these methodsand developed an original one. Many of thefollowing considerations, as well as nota-tions, originate from their work.

3.1.1. Coefficients of kinshipand inbreeding [29, 52, 53]

Two related figures are used to measureinbreeding in a population: the coefficientsof kinship and inbreeding. The coefficient ofkinship ΦXY of two individuals X and Y isdefined as the probability that two homolo-gous genes, one chosen at random from eachof these individuals, are “identical bydescent” [29]. The inbreeding coefficientFI of an individual I is defined as the prob-ability that the two genes present at oneautosomal locus are identical by descent: itis equal to the coefficient of kinship of itsparents. Inbreeding will then also increasethe total homozygosity in the population bythe appearance of these identical genes inthe individuals. The mean kinship coeffi-cient, defined as the mean of the N(N-1)/2coefficients of kinship in a population of Nindividuals, is an alternative way to char-acterise the level of inbreeding.

Coefficients of kinship and inbreedingresult from pathways connecting two indi-viduals through common ancestors. There-fore, these criteria depend strongly on theextent and quality of pedigree information:missing or unreliable data may lead to largebiases in their calculation. Several authorspresented methods to compute them quickly,even in large populations [30, 47]. The maindrawback of the average coefficient ofinbreeding is its inability to reflect recentchanges, such as bottlenecks in the numberof parents. Another drawback is its sensi-tivity to the mating system used to procreateanimals included in the set under study. Away to take this effect into account is to split

in a small population as the inbreedingincreases to the population size, to the selec-tion and to interactions between selectionand genetic drift.

– Moreover, when the number of candi-dates is finite, the expected selection dif-ferential is smaller compared with an infinitepopulation. For normally distributed traits,the selection intensity must be calculated orapproximated using order statistics theory[4, 21].

The response to selection in a small pop-ulation will then differ from the classicalexpected response in an infinite population,due to the decrease in genetic variance. Theratio between the observed response in aselection experiment and the expectedresponse provides an estimate of the realisedheritability and therefore of the remaininggenetic variance in the population.

2.4. Conclusion

Various phenomena influence the evo-lution of genetic variability in a small pop-ulation, selected or not. Several approachesare available to study this evolution and tomanage the population in order to obtainthe optimum compromise between actualbreeding objectives and conservation ofgenetic variability. The effectiveness of thedifferent criteria derived from theseapproaches are compared and the main rulesfor monitoring small populations are devel-oped.

3. CRITERIA FOR ASSESSINGGENETIC VARIABILITY:A COMPARATIVE APPROACH

3.1. Criteria based on pedigreeinformation

Analysis of genetic variability of a pop-ulation is frequently based on genealogicaldata. Coefficients of inbreeding and kin-ship, as well as genetic contributions of

81


total inbreeding into ‘close inbreeding’(which result from matings between closerelatives) and ‘remote inbreeding’ (whichfollows mainly from cumulative effects ofgenetic drift). The mean coefficient of kin-ship is less affected by these drawbacks thanthe mean coefficient of inbreeding, but itrequires more calculation: N(N-1)/2 coeffi-cients of kinship instead of N coefficientsof inbreeding in a sample of N animals.Moreover, the average coefficient of kin-ship between animals kept for mating givesan indication about future trends of inbreed-ing under random mating.

3.1.2. Realised effective populationsize Ne

To illustrate the evolution of meaninbreeding over generations, Crow andKimura [10] consider an idealised popula-tion in the sense of Wright [53], i.e. a closedmonoecious population of N diploïd indi-viduals mating randomly (self-fertilisationincluded), with non-overlapping generationsand all individuals contributing equally toa large pool of gametes. The probability ofdrawing the same parental gene twice whenproducing an offspring is 1/2N and the prob-ability of drawing two different genes is1 – 1/2N. However, the probability that thesetwo different genes are in fact identical bydescent is the mean kinship coefficient atthe parental generation (or the inbreedingcoefficient of an individual in the parentalgeneration, as mating is at random). F(t) isthe coefficient of inbreeding at generation(t). Then the coefficient of inbreeding in thepopulation can be written as:

(1)

(2)

Recalling that (1 – F[t]) is proportional tothe rate of heterozygosity, the formula (1)allows expressing the decrease in heterozy-gosity H from generation t-1 to generationt as:

The increase in inbreeding coefficient andthe consecutive decrease in heterozygosityis then higher as the population size issmaller.

These formulae were obtained for an ide-alised population, in which each parent isexpected to contribute equally to the poolof gametes. The rate of increase in inbreed-ing, ∆F, is:

(3)

Most populations depart from this ideal, asthey are dioecious and as parents producemore or less offspring depending on theirsex and even in the same sex, according totheir fertility or their genetic value. To studythe evolution of inbreeding in these popu-lations, N is replaced by Ne, called the“effective population size”, and defined asthe number of individuals in an idealisedpopulation in the sense of Wright [53] char-acterised by the same increase of inbreedingrate or the same decrease in genetic vari-ance as observed in the studied bisexualpopulation. The effective population sizeNe can be calculated from the formula(3) as function of the rate of increase ininbreeding:

The effective population size Ne can alsobe calculated from the variance of change ofgene frequency observed in the actual popu-lation under consideration [10, 42].

The effective population size Neof a popu-lation can be estimated from the rate ofincrease in inbreeding (calculated frompedigrees) during a given lapse of time. In apopulation with stable size and breeding

82

1

2NF[t] = F[t–1]+ (1– )1

2N

⇔ 1– F[t] = (1–F[t–1])(1– )1

2N

⇔ 1– F[t] = (1– )t.1

2N

H[t] = (1– )H[t–1].1

2N

∆F = .1

2N

Ne = .1

2∆F


tive, and is efficient for describing recentevolutions in a population structure.

As this concept did not account for thepossible bottlenecks in the population,another criterion was proposed by Boichardet al. [2], the effective number of ancestorsfa, i.e. the minimum number of individuals(founders or not) required to explain thecomplete genetic diversity in the studiedpopulation. It is defined by analogy withthe effective number of founders but usingthe marginal contributions of the individu-als pk, i.e. the contributions not yet explainedby the other ancestors:

Ancestors (founders or not) are successivelydesignated, according to an iterative proce-dure, on the basis of their marginal contri-butions. The number of ancestors with anon-zero marginal contribution is less thanor equal to the number of founders and thesum of their marginal contributions is equalto 1. Consequently, fa is always less than orequal to fe. In large populations, identificationof every contributing ancestor may requirevery long computations, so the iterative pro-cedure could be stopped according to a pre-determined rule. Upper and lower boundsof the true value of fa are then calculated.

Under steady conditions, the effectivenumber of ancestors decreases slightly withthe number of generations. This parameter,which reflects shorter ascent lines than theothers, shows a noteworthy robustness topartial lack of genealogical data [2].

A third concept derived from the proba-bilities of gene origin is the effective num-ber of founder genomes [8, 26, 28]. It con-sists in calculating the probability xk for agiven autosomal gene among the 2f presentin the founders to be drawn at random inthe population under study. The effectivenumber of founder genes is then:

characteristics, Ne is constant and presents apredictive value as long as conditions donot change. Like the mean inbreeding ratefrom which it is derived, the realised effec-tive size is very sensitive to pedigree infor-mation: Ne may be overestimated whengenealogical data are missing, particularlywhen a long time period is considered [2].

3.1.3. Probability of gene origin[12, 23, 26, 40, 41]

A complementary approach to measurethe level of genetic drift in a population isderived from the probabilities of gene origin.This concept relies on the principle that agene drawn randomly in an individual at anautosomal locus has a 1/2 probability ofcoming from each of its parents, a 1/4 prob-ability of originating from each of its4 grandparents, and so on. Applying thisrule to the complete pedigree allows calcu-lating the probability for one gene randomlydrawn to originate from any of the knownfounders of the population [23]. Eachfounder k can then be characterised by itsexpected contribution qk to the genetic poolof the population under study. By defini-tion, the genetic contributions of all founderssum up to 1. The concept of “effective num-ber of founders”fe then corresponds to thenumber of equally contributing founders,and allows to measure the balance of geneticcontributions among real founders. If f isthe real number of founders, the effectivenumber of founders is calculated as:

fe is equal to the actual number of foundersif they contribute equally. If not, it is smaller:the more unbalanced their contributions, thesmaller the effective number of founders.As shown by Boichard et al. [2], fe is verystable across generations as long as condi-tions do not change. Unlike the effectivepopulation size, the effective number offounders is more descriptive than predic-

83

1fe = ∑k = 1 qk

f 2

1fa = .

∑k = 1 pkf 2

1Na = .

∑k = 1 xk

2f 2


As each individual is carrying two genes,the effective number of founder genomesis defined as:

The concept of effective number of foundergenomes Ng is based on the probabilitiesthat 2f genes carried by f founders at a givenautosomal locus are still present in the pop-ulation under investigation. These proba-bilities can be calculated by an analyticalderivation (not feasible in large pedigrees),or estimated by Monte-Carlo simulation.

The main property of Ng is to account,not only for unbalanced contributions ofparents to the next generation (as fa and fe)and for bottlenecks in pedigrees (as fa), butalso for random loss of genes from parentsto their offspring: therefore, Ng is alwayssmaller than fa and fe, and decreases morequickly over time. However, it should bekept in mind that the number of alleles car-ried by f founders is lower than 2f ‘foundergenes’: as a consequence, loss of alleles isusually much slower than loss of foundergenes.

While coefficients of kinship and inbreed-ing reflect pathways connecting two indi-viduals through common ancestors, proba-bilities of gene origin depend only on ascentlines up to the founders. Therefore, proba-bilities of gene origin are easier to calcu-late. Moreover, they are less affected bymissing data in pedigrees, as well as the var-ious criteria originating from them.

3.2. Criteria derived from demographicanalysis

Genetic variability of a populationreflects the fate of its genetic stock, which isstrongly dependent on the history of theindividuals carrying the genes. It is there-fore useful to carry out a demographicdescription of the population under inves-tigation. As a matter of fact, genetic analy-ses are often accompanied by a demographic

approach (see examples reviewed by VuTien Khang [50]). Describing the structureand dynamics of a population considered asa set of individuals gives keys to interpretgenetic criteria (see [18]). For instance,demographic analysis provides informationon crucial aspects such as functional struc-ture of the population of herds (or flocks),circulation of breeding material amongthem, numbers of male and female parents,distribution of the size of their progeny, gen-eration length... Demographic parameterscan be used to infer evolution of geneticvariability, either by simulation [7] or byestimating the effective population size Ne.

Assume that the number of sires (Nm) isdifferent from that of dams (Nf) and thatthese are constant over generations. There-fore without other deviation from the ide-alised population [51]:

Assume now that the number of sires issmaller than that of dams and each sire ismated to Nf /Nm dams. Afterwards, onechoose as parents one male and Nf /Nmfemales from each sire’s progeny and onefemale and Nm/Nf males from each dame’sprogeny. In this situation, we obtain[35, 42]:

A more general formula was derived for theeffective size of random mating populationsof constant size and sex ratio with overlap-ping generations [20, 22]. The effective sizeis equal to the effective size of a populationwith discrete generations which have thesame number of individuals entering thepopulation at each generation and the samevariance of lifetime family number. Eachyear, M sires and F dams are taken forbreeding. Vmm is the variance of the num-ber of male progeny of one sire and Vmf isthe variance of the number of female

84

1

2

1Ng = Na = .

2∑k = 1 xk

2f 2

1

Ne

1

4Nm

1

4Nf

= + .

1

Ne

3

16Nm

1

16Nf

= + .


ing to the number of loci and the number ofindividuals per locus. They concluded that alarge number of loci rather than a large num-ber of individuals should be used. Nei [33]presented statistical methods to obtain unbi-ased estimates of this parameter.

Loci currently used are among those cod-ing for visible features, enzymes or anti-genic factors (e.g. blood groups, MajorComplex of Histocompatibility). In farmanimals, blood typing, which has achievedwidespread application in detecting wrongparentages, constitutes the main source ofdata. In the future, molecular genetics toolswill provide a rising amount of information.Statistical methods intended to assessgenetic variability of populations on thebasis of DNA polymorphisms (e.g. micro-satellites) will have to be improved to takeinto account the specificities of both DNApolymorphisms and structure of farm ani-mals populations. An important issue is howmany markers should be used and how theyshould be distributed along the chromo-somes.

3.4. Criteria derived from quantitativegenetics

A classical approach is based on the esti-mation of realised genetic parameters byregression of selection responses on selec-tion differentials. On the other hand,Restricted Maximum Likelihood fitting an‘animal’ model is being increasingly used:under the ‘infinitesimal model’, it providesestimates of parameters (heritabilities, addi-tive genetic variances) in the base popula-tion, before it is submitted to drift and selec-tion [44]. In order to assess changes inadditive genetic variance over time, Meyerand Hill [31] applied this method to vari-ous segments of data and relationship infor-mation corresponding to a small number ofconsecutive generations: parents of the old-est generation considered in each segmentare treated as unrelated base animals, omit-ting data available about earlier generations.

progeny of one sire. Vfm and Vff are the cor-responding variances for one dam. Let thecovariance of the number of male andfemale progeny from each sire be Cmmmf andfrom each dam be Cmmmf. Hill [20] hasshown that:

where L is the generation interval.

3.3. Criteria based on observed geneticpolymorphisms

Tests of departure from Hardy-Weinbergproportions are frequently made to checkon random mating in a population (see [32]),and excess of homozygotes above expecta-tions may be used to estimate the inbreedingcoefficient, defined here in terms of corre-lation between uniting gametes relative tothe gamete pool of the present population.Robertson and Hill [36] analysed distribu-tion of the deviations from Hardy-Weinbergproportions and of the estimates of inbreed-ing coefficient obtained from these devia-tions, according to the structure of the pop-ulation under study.

Allelic diversity of a population at a givenautosomal locus may be measured by theeffective number of alleles [10]:

where pi is the estimated frequency of theallele i.

This parameter is related to the Hardy-Weinberg heterozygosity H observed at thislocus:

Nei and Roychoudhury [34] gave samplingvariance of average heterozygosity accord-

85

1

Ne[2+V

mm+2( M )Cmmmf

+( M )2Vmf]1

16ML=

F F

1

16FL [2+( F )2V

fm+2( F )Cfmff

+Vff]+

M M

1na =

∑ pii

2

1H = 1 – ∑ pi

= 1 – .nai

2


Although one of the major reasons forpreserving the genetic diversity of the popu-lations is to maintain their ability to respondto artificial selection, the quantitative genet-ics approach has not been fully used, untilnow, to measure genetic variability. Unlikecriteria based on pedigree information(which refer to any neutral autosomal locus)or criteria based on observed genetic poly-morphisms (which refer to genes often con-sidered as neutral or to non-coding regions),criteria derived from quantitative geneticsmirror phenomena affecting the only genesinvolved in genetic variation of traits underconsideration. Consequently, a critical aspectof this approach lies in the choice of thesetraits. In addition to the classical ones relatedto production, traits associated to adapta-tion (e.g. behaviour, stress resistance, dis-ease resistance) should draw particularattention on breeds considered as adaptedto rigorous and changing environments: fur-ther studies are needed to find reliable meth-ods for measuring such characters.

4. GENERAL RULES FOR MANAGINGGENETIC VARIABILITY

4.1. Simple rules

The effective population size Ne high-lights a first rule: the distribution of the fam-

ily size should be as uniform as possible.Table I (from [35]) analyses fluctuations ofNe depending on the variance of the familysize along the 4 paths (male-male, male-female, female-male, female-female). Solu-tion 3 is unrealistic; in practice it is not pos-sible to completely fix the number ofoffspring for each parent. Solution 2 is oftena good compromise; each sire has a son andonly one, the number of offspring is at ran-dom for each other path.

Furthermore, Table I points out the con-sequences of an increase in numbers ofmales (Nm) and females (Nf). In most ani-mal domestic populations the sex ratio isunbalanced; Nf is greater than Nm. The sec-ond rule is to increase the number of malesin order to reduce the sex ratio imbalance.Nevertheless, from an economical point ofview, it is difficult to increase too much thenumber of males used for breeding. Con-servation programmes generally lead to anextra-cost related to the rearing and the useof a greater number of reproducing males.

4.2. More complex methods

4.2.1. Rotational schemes

Since the famous paper of Wright [51],systems of mating to avoid inbreeding werestudied in detail (see for example [9, 10,

86

Table I. Effective size according to the rule applied on the various parent-offspring path (from [35]).(Solution 1: choice at random for each path; Solution 2: each sire has one and only one son, choiceat random for each other path; Solution 3: the numbers of offspring are completely fixed).

Number of parents Effective size Coefficient of inbreeding (%)after 10 generations

Nm NfSolution Solution

1 2 3 1 2 3

18 500 31 42 63 15 11 8 16 500 62 82 124 8 6 4 32 500 120 157 241 4 3 2 18 250 31 41 62 15 12 8 18 1 000 32 42 63 15 11 8


of inbreeding coefficients, and induce agenetic structure independent of the initialrelationships between founders animals.

Hall [19] points out that the success ofgenetic conservation can be assessed bypedigree analysis. Djellali et al. [13] evalu-ate the conservation programmes of twosheep breeds, managed with circular mat-ing systems. Demographic analysis indi-cates that both the number of males and theirreplacement rate are high in accordance withthe management rules. Although progenysizes are not always balanced, the variousfounder animals, as well as the reproduc-tion groups from which they originate, con-tribute to the gene pool in a balanced way(Fig. 2). The genetic conservation pro-grammes prevent close inbreeding andrestrict total inbreeding.

The genetic conservation programmesare well implemented and effective. Onepractical problem deserves some comments.The splitting up of the population may bemade on the basis of the observed kinshipcoefficients. Groups are then called fami-lies, i.e. groups of animals more relatedbetween them than with other animals.Ascending hierarchical classification, fac-torial analysis of a distance table or cluster-ing analysis are used to split up a set of ani-mals using information from a table ofkinship coefficient. Probabilities of geneorigin in relation to founders or to majorancestors provide another description of thesample [37, 38]. Unfortunately when the

25]). Inbreeding would be kept at a mini-mum if the least related individuals aremated. A system involving the creation ofseparate groups which exchange individuals,allows to minimise inbreeding.

Rochambeau and Chevalet [39] have pro-posed a method taking account of usualbreeding constraints (generations overlap,demographic parameters change amongfarm and among year, founders animals arerelated, the distribution of the populationbetween various herds avoids random mat-ing...). Table II refers to the French Poitevinegoat population [39]. It deals with theresearch of an optimal strategy to minimisethe drift over a period of 15 years. Threenumbers of groups (5, 11 or 23) and 2 mat-ing schemes are compared. The populationis split in various reproduction groups. Maleand female offspring are assigned to thegroup of their dam. Males of a given groupnever mate to the group of their dam. In thefixed scheme, males of group (i) are alwaysmated with the females of group (j). In thecircular one, a periodic function gives thecorrespondence between (i) and (j). Chang-ing the number of reproduction groups orthe mating scheme turn out to have verysmall effects, if we consider the effectivenumber of founder genomes (Ng) or themean kinship coefficient (Φ). Regarding themean inbreeding coefficient (F), the bestsolution is a circular mating scheme with23 groups. Moreover, circular matingschemes lead to a reduction in the variance

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Table II. Effective number of founder genomes (Ng), mean individual inbreeding coefficient (F)and mean kinship coefficient (Φ) in relation with the number of reproduction groups and the matingscheme after 15 years in a model goat population (from [40]).

Criteria 5 Groups 11 Groups 23 Groups

Fixed Circular Fixed Circular Fixed Circular

Ng 38.5 37.5 43.5 44 52 51.5F 0.63 1.18 1.49 0.64 1.70 0.44Φ 1.24 1.24 1.06 1.07 0.88 0.89


reproducing females are distributed into dif-ferent farms, splitting up the population onthe basis of pedigree may lead to manage-ment difficulties [48]. Therefore, the split-ting up of the population is now made onthe basis of the distribution of females intofarms: each group includes the whole or apart of the females from a given farm only.

Artificial insemination with frozen semenappears to be a useful aid in various domes-tic species like cattle. It can be used toimprove the management of the males. Mat-ing rules can be more easily applied: phys-ical exchanges of males are not needed, andtheir number per breeding group can be keptto a minimum. Chevalet and Rochambeau[7] discuss the conservation programme ofthe French Bretonne Pie Noire dairy cattlepopulation. The programme was initiatedseveral years ago according to a scheme thatlengthens the generation interval and makesuse of artificial insemination with frozensemen. Table III summarises the mainresults. The population is split into 8 groupsof about 40 cows. Only cows more than5-year-old are used for the renewal of thebreed. In Scheme 1, 8 apparently unrelatedbulls were chosen among offspring of old

cows. Each bull, whose semen is frozen, isused to inseminate females from othergroups. It is mated during 2 consecutiveyears with cows of one group, and thentransferred to another group. When the bullhas been used over all groups it is replacedby one son. In Scheme 2, old females aremated to 8 chosen males at the beginningof the programme. Male offspring are kept,and their semen frozen. This provides for8 “replacement males”, whose use isdeferred until the first bulls are withdrawn.The circulation of males over femalesremains the same, but at the time a bull isreplaced, one of his sons is kept as a new“replacement male”. In the last scheme, bullsare used during 2 years, instead of 16 inSchemes 1 and 2. Scheme 3 is a basis forcomparison with the methods developed forpopulations reared under natural mating. Asexpected, Scheme 2 is generally better thanScheme 1, and Scheme 3 is the best. Thepercentage of genes originating from the8 initial bulls provides a clear separationbetween the third scheme and the first two.The rapid renewal of bulls enables the pop-ulation to keep genes from the femalesfounders, their contribution being 80%instead of about 40%, after 40 years.

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Figure 2. Cumulatedgenetic contributions ofthe families or the repro-duction groups in twosheep breeds. Total num-ber of groups is 11 forSolognote (r) and 16 forMérinos précoce (■).


Hall [18, 19] proposes the following defi-nition of successful genetic conservation:“the continuing representation of a high pro-portion of animals registered as foundationsstocks, in pedigrees of recent generations”.Alderson [1] develops a similar idea: “theideal animal would receive equal contribu-tions from all the founder ancestors in thebreed. This is likely to represent the bestopportunity to maximise the retention offounder alleles”. Then Alderson measuresthe value of an animal by calculating fe, theeffective numbers of founders in its pedi-gree.

For such a purpose, Hall [18] points outthat the gene flow among farms is the statis-tics of most value for monitoring breeds.One practical conservation method, withgreat opportunities for development of pub-lic relations, is the organisation of saleswhich facilitate gene flow within breeds.The structure of the population should showno hierarchy between farms, and the geneflow between farms should be as large aspossible. Criteria like percentage of farmswhich supply males and percentage ofbreeding males born in the same farm areuseful to characterise the population. Onecan also draw a matrix describing exchangeof males between farms. Kennedy and Trus[24] develop a method that measures theexchange of genes between herds.

Reduction of inbreeding levels between thefirst scheme and the second, is primarilydue to the longer generation interval, ratherthan to an enlarged genetic background.However artificial insemination with frozensemen is still a useful tool, but it is necessaryto keep the second rule in mind: the numberof males should be as high as possible inorder to reduce the sex ratio imbalance.

Storage of frozen semen and embryosare suggested also for conservation ofgenetic variability of endangered livestockpopulations, as an alternative to living ani-mals. In that case, sample size must be con-sidered to minimise genetic drift in sam-pling [43]. Gandini et al. [16] analyse theprobability distribution of founder genes ina semen storage of a small cattle popula-tion. In both cases, we have to manage apopulation made up of a small number ofanimals before and after obtaining frozenmaterial.

4.2.2. Schemes based on probabilitiesof gene origin

Circular mating schemes are effective tomaintain genetic variability. However, it isnot possible to use them in many situations(for example when the population size istoo large to manage the reproduction groups,or when the number of females in each farmis too small to make reproduction groups).

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Table III. Mean individual inbreeding coefficient (F), mean kinship coefficient (Φ), percentage ofgenes originating from the initial males (M), and percentage of original genes still present (S) inrelation to the management rule. (Scheme 1: frozen semen from 8 old bulls; Scheme 2: frozen semenfrom 8 offspring; Scheme 3: natural mating. See text for more details).

CriteriaAfter 20 years After 40 years

Scheme 1 Scheme 2 Scheme 3 Scheme 1 Scheme 2 Scheme 3

F 1.4 0.78 0.26 5.5 2.3 1.8Φ 4.0 3.0 1.2 7.4 4.0 2.5M 59 52 20 62 56 20S 13 15 21 5 7 11


Giraudeau et al. [17] provide a descrip-tion of an example of the ideas discussedby Alderson and Hall. The Parthenaise breedis a multiple-purpose breed of the west ofFrance. Giraudeau et al. compute the matrixof coefficients of kinship between the 135natural service bulls used in 1988 / 1989.Then a procedure of automatic classifica-tion is used for pooling these bulls into fam-ilies. Later, they choose 10 famous ArtificialInsemination (AI) bulls, which have largenumbers of offspring; these bulls are similarto the major ancestors defined by Boichardet al. [2]. A given family of natural servicebull is characterised by the average values ofcoefficients of kinship between the mem-bers of this family and the 10 famous AIbulls (Fig. 3). In this example, kinship coef-ficients and probabilities of gene origin aresimilar.

Figure 3 underlines the distinction ofthree kinds of families: families muchrelated to the AI bulls, showing a pro-nounced kinship with one or two famousAI bulls, as family “B” ; families relativelyrelated to the AI bulls, with more balancedcoefficients of kinship with the famous AIbulls, as family “E” ; families slightly relatedto the AI bulls, as family “K” . For Alder-son and Hall, family “E” has the best profile.However, family “B” deserves some

consideration: the strategy could be to lookat a balanced contribution not at an indi-vidual level but at a higher level like thesample of renewal bulls chosen on year.Finally, if family “K” has a genetic infor-mation as good as the other two families,family “K” deserves also some considera-tion because it enlarges the available geneticvariability. Further work is needed to definemanagement strategies on the basis of geneorigin probabilities related to major ances-tors.

4.2.3. “Marker Assisted Conservation”

The genetic variability of a populationmay be defined by lists of alleles and theirfrequencies at many loci in the various sub-sets of the population (herd, age classes,sex...). In the former paragraphs, pedigreeinformation was used to infer the change ingenetic variability. This probabilisticapproach will be supplemented by a morebiological approach. Molecular geneticstechniques make it possible to consider theallelic frequencies for many loci in domes-tic animals species. It will be possible toprovide a better description of the geneticvariability. One will be able to control theefficiency of a conservation programme.The choice of genotypes to conserve will

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Figure 3. Average coefficientof kinship (Φ) between 3 fam-ilies of natural service bulls and10 famous Parthenais AI bulls.( for family “B” , for fam-ily “ E ” and for family “K” ).


5. CONCLUSION

To assess genetic variability, variouscomplementary criteria are available, deri-ving from demographic analysis, pedigreeinformation, genetic polymorphisms andquantitative genetics. Some of them, likeinbreeding and kinship coefficients or effec-tive population size, are concepts originatingfrom the beginning of population genetics.They remain operational and are widelyused. The improvement of computers (mem-ory capacity and computing speed) evenextended their scope of application. There-fore, their limit is related to their definition,with respect to a “neutral autosomal locus”,which is quite an abstract concept, inde-pendent from a specified trait. The improve-ment in genome analysis of domesticlivestock might allow to identify the chro-mosomic areas involved in genetic vari-ability of traits (“classical” traits in animalproduction or “adaptation” traits). This evo-lution of knowledge might induce, in a nearfuture, a change in the methods of descrip-tion and management of the genetic vari-ability, by focusing more specifically ongenes (or chromosomic areas) involved inthe genetic variability of the populationsconsidered.

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