Estimation of breed contributions to present and future genetic diversity of 44 North Eurasian cattle breeds using core set diversity measures

Gene . Sel. E ol. 38 (2006) 201–220 201 c INRA, EDP Sciences, 2006 DOI: 10.1051/gse:2005036 O iginal a icle Es ima ion o b eed con ibu ions o p esen and u u e gene ic di e si y o 44 No h Eu asian ca le b eeds using co e se di e si y measu es Jö n Bennewi z∗a, Juha Kan anenb,IlmaTapiob, Meng Hua Lib,E ns Kalma, Johanna Vilkkib, Innoken yi Ammoso c,ZoyaI a n o a d, Ta yana Kiselyo ae, Ruslan Popo ,TheoH.E.Meuwisseng aIns i u e o Animal B eeding and Husband y, Ch is ian-Alb ech s-Uni e si y, 24098 Kiel, Ge many bBio echnology and Food Resea ch, MTT Ag i ood Resea ch Finland, 31600 Jokioinen, Finland cBa agay-Aly a, 678580, Sakha, Russia dYaku S a e Ag icul u al Academy, Ul. K asilniko a 15, Yaku sk, 677002, Sakha, Russia eDepa men o Gene ics and Bio echnology, All-Russian Resea ch Ins i u e o Fa m Animal Gene ics and B eeding, Moskowskoye shosse–55a, 189620 S . Pe e sbu g-Pushkin, Russia Depa men o Fa m Animals and B eeding, Minis y o Ag icul u e and Resou ces o Sakha, Yaku sk, 677007, Sakha, Russia gIns i u e o Animal and Aquacul u al Sciences, Ag icul u e Uni e si y o No way, Box 5052, 1432 Ås, No way (Recei ed 13 June 2005; accep ed 26 Oc obe 2005) Abs ac – Ex inc ion o b eeds h ea ens gene ic di e si y o li es ock species. The need o conse e gene ic di e si y is widely accep ed bu in ol es in gene al wo ques ions: (i) is he expec ed loss o di e si y in a se o b eeds wi hin a de ined u u e ime ho izon la ge enough o es ablish a conse a ion plan, and i so (ii) which b eeds should be p io i ised o such a conse - a ion plan? The p esen s udy uses a ma ke assis ed me hodology o add ess hese ques ions. The me hodology combines co e se di e si y measu es wi h a s ochas ic me hod o he es i- ma ion o expec ed u u e di e si y and b eed ma ginal di e si ies. The la e is de ined as he change in he o al di e si y o all b eeds caused by a one uni dec ease in ex inc ion p oba- bili y o a pa icula b eed. The s ochas ic me hod was alida ed by means o simula ions. A la ge ield da a se consis ing o 44 No h Eu asian ca le b eeds was analysed using simpli ied de e mined ex inc ion p obabili ies. The esul s show ha he expec ed loss o di e si y in his se wi hin he nex 20 o 50 yea s is be ween 1 and 3% o he ac ual di e si y, p o ided ha ∗Co esponding au ho : jbennewi z@ ie zuch .uni-kiel.de A icle published by EDP Sciences and a ailable a h p://www.edpsciences.o g/gse o h p://dx.doi.o g/10.1051/gse:2005036 202 J. Bennewi z e al. he ex inc ion p obabili ies which we e used a e app oxima ely alid. I his loss is o be e- duced, i is sufficien o include hose h ee o i e b eeds wi h he highes ma ginal di e si y in a conse a ion scheme. di e si y measu e /ma ginal di e si y /ex inc ion p obabili y /ca le b eeds /gene ic conse a ion 1. INTRODUCTION Ex inc ion o endange ed a m animal b eeds leads o an i e e sible loss o gene ic di e si y. Acco ding o he FAO [8], a ound one hi d o he eco ded li es ock b eeds a e classi ied as ha ing a high isk o ex inc ion and a ound 1000 ha e anished du ing he las 100 yea s. The need o conse e gene ic di- e si y is widely accep ed o biological, economic and cul u al easons [13]. A main eason is ha an abundan esou ce o gene ic di e si y wi hin each li es ock species is he p e equisi e o coping wi h pu a i e u u e changes in li es ock a ming condi ions. Because inancial unds a ailable o conse a- ion o di e si y a e limi ed, i is in gene al only possible o conse e a subse o impo an b eeds a he han all endange ed b eeds. Howe e , o any in- es iga ion ega ding gene ic di e si y wi hin a se o b eeds and subsequen ly o he assessmen o impo ance o pa icula b eeds o di e si y, a sui able di e si y measu e has o be applied. Wei zman [18, 20] desc ibed nice ma hema ical and biological p ope ies o a sui able di e si y measu e ( he so-called Wei zman c i e ia) and de el- oped a di e si y measu e ha ul illed hese c i e ia. Howe e , he Wei zman di e si y measu e was de eloped o assess di e si y ac oss species bu is inap- p op ia e ac oss b eeds [4,5]. Al e na i ely, Eding e al. [7] in oduced a co e se ha is buil by ela i e b eed con ibu ions in o de o maximise gene ic di e si y wi hin he co e se . In hei app oach, di e si y is de ined as he ge- ne ic a iance ha can be ound in pu a i e offsp ing ha a e ob ained om in e b eeding o hose b eeds ha con ibu e o he co e se [7]. A simila ap- p oach was de eloped by Caballe o and To o [4]. A d awback o his app oach migh be ha i gi es no pa icula weigh o he be ween b eed a iance, i.e. o he special allele and geno ype combina ions ha a e p esen wi hin b eeds. The e o e, an al e na i e co e se was ecen ly in oduced by Bennewi z and Meuwissen [2]. Thei co e se algo i hm es ima es ela i e b eed con ibu ions in o de o maximise o al gene ic a iance ha can be ound wi hin and be- ween b eeds. Bo h co e se s ag ee wi h he Wei zman c i e ia o a p ope di e si y measu e [2,7] and addi ionally hey a e less compu a ionally demand- ing e en i a la ge numbe o b eeds is included in he expe imen . B eed con ibu ions o p esen and u u e di e si y 203 Fo quan i ica ion o expec ed u u e di e si y and hence o he expec ed loss o di e si y, ex inc ion p obabili ies o a de ined ime ho izon ha e o be aken in o accoun . Gi en ha ex inc ion p obabili ies a e known (in eal li e hei es- ima ion is no a i ial ask, see [3, 12, 15]), Simiane e al. [17] p esen ed a de e minis ic me hod o he simul aneous calcula ion o expec ed u u e di e - si y and o ma ginal di e si ies o he b eeds. The la e one is de ined as he change in o al di e si y o all b eeds caused by a one uni dec ease in ex inc- ion p obabili y o a pa icula b eed by a conse a ion effo [17]. Howe e , he de e minis ic app oach in ol es 2N imes he compu a ion o he di e si y algo i hm, whe e Nis he numbe o b eeds included in he expe imen . This exponen ial inc ease in compu a ion effo limi s he applica ion o his algo- i hm o smalle da a se s. This is an e en g ea e p oblem when he Wei zman di e si y measu e is used because he Wei zman di e si y algo i hm is i sel compu a ionally e y demanding i many b eeds a e included [18]. This s udy in oduces a s ochas ic me hod o he simul aneous es ima ion o expec ed u u e di e si y and ma ginal di e si ies ha is ailo ed o la ge da a se s. The me hod was alida ed by means o simula ions and was applied o a la ge ield da a se consis ing o 44 No h Eu asian ca le b eeds using he wo co e se di e si y measu es men ioned abo e. The esul s (i) demons a ed he use ulness o he s ochas ic me hod and (ii) o he co e se gene ic di e si y measu es o he ma ke assis ed es ima ion o p esen and expec ed u u e gene ic di e si y and (iii) hey help o iden i y he mos impo an b eeds o he conse a ion o di e si y wi hin his se o No h Eu asian ca le b eeds, p o ided ha he assigned ex inc ion p obabili ies a e app oxima ely alid. 2. MATERIALS AND METHODS 2.1. Expec ed u u e di e si y and ma ginal di e si ies Assume a se o Nb eeds wi h known ex inc ion p obabili ies z o a de- ined ime ho izon . Fu he assume ha he gene ic di e si y Do his se is es ima ed and he applied di e si y measu e ul ils he ollowing Wei zman c i e ia: Mono onici y in species (Dshould no inc ease when a popula ion is emo ed) and win p ope y (addi ion o a b eed ha is a copy o a b eed al- eady p esen in he se should no change D). Fo he es ima ion o expec ed u u e di e si y and o b eed ma ginal di e si ies, he ollowing sampling algo- i hm can be applied. The algo i hm epea edly gene a es a sample s om he b eeds included in he se . I s a s wi h he illing in o an indica o ec o k o dimension N(N=numbe o b eeds). Each elemen kiin kis alloca ed o 204 J. Bennewi z e al. one b eed i, i is ei he se o ze o wi h an ex inc ion p obabili y zi(b eed iis ex inc a ime ) o o one wi h a p obabili y 1 – zi(b eed iis ali e a ime ). The b eeds wi h ki=0 a e emo ed om he cu en sample sand he di e si y es ima ion algo i hm is applied o his sample. The es ima ed di e si y wi hin he sample, Ds, is eco ded. The algo i hm is epea ed S imes (i.e. S diffe en samples s). The expec ed di e si y a he end o he de ined ime ho izon can be es ima ed as: E(D )=1 S S  s=1 Ds,(1) and he a iance o he expec ed di e si y as a (D )=σ2 D =1 S−1 S  s=1 (Ds−E(D ))2.(2) The co a iance s uc u e o kand D is a k D =Qg gσ2 D ,(3) whe e Qis a ma ix o dimension N×Nand con ains he a iance o ki( ha is zi(1 – zi)) on he diagonal elemen s and ze o elsewhe e. σ2 D is a scala and can be ob ained using (2). The ec o g(dimension N) con ains he co a i- ance be ween he kiand D , and hese can be ob ained om he Ssamples. The ma ginal di e si y o b eed i,mi, is hen es ima ed using he ollowing eg ession: mi=bD ,ki×ki=co (D ,ki) a (ki).(4) No e ha he ob ained ma ginal di e si ies will be posi i e due o he eg ession on kiin (4). I is expec ed ha his me hod will yield accu a e es ima es o Sbeing la ge. This s ochas ic app oach was compa ed o he de e minis ic me hod o Simiane e al. [17] ou lined in he ollowing. A he end o he ime ho izon 2Ndiffe en combina ions o kiwi hin ka e possible, hus 2Ndiffe en ec o s migh exis , each wi h p obabili y P(k). Fo a ce ain ec o kj he p obabili y can be es ima ed as ollows: P(kj)= N  i=1ki+(−1)kizi.(5) The mean and a iance o D a e E(D )= 2N  j=1 P(kj)Dj,and a (D )= 2N  j=1 P(kj)D2 j−[E(D )]2,(6) B eed con ibu ions o p esen and u u e di e si y 205 whe e Djis he di e si y acco ding o kj. The ma ginal di e si y o b eed iis calcula ed as he pa ial de i a i e o E(D ) wi h espec o zi: mi=+ ∂E(D ) ∂zi ·(7) The posi i e sign makes i di ec ly compa able wi h he ma ginal di e si ies ob ained om (4) (see [17] o compu a ional de ails). This me hod will p o- duce co ec mies ima es (igno ing e o s in he di e si y measu e). Howe e , i becomes ob ious ha hese o mulae equi e he calcula ion o 2N imes he di e si y measu e, which becomes compu a ionally e y difficul o e en im- possible o la ge N. 2.2. Co e se di e si y measu es Assume a se o Nb eeds wi h a known kinship ma ix Mo dimension N×N. The maximum a iance o al (MVT) me hod o ms a co e se in which he o al gene ic a iance o a hypo he ical quan i a i e ai is maximised [2]. The ela i e con ibu ions o he b eeds o he MVT co e se a e es ima ed as [2] cm =1 4M−1F−1NM−1F−4 1NM−11N ·M−11N,(8) whe e cm is he ela i e con ibu ion ec o o dimension Ncon aining he con ibu ions, Fis a ec o o dimension N ha con ains he wi hin b eed kin- ship, i.e. F=diag(M), and 1Na ec o o dimension Ncon aining ones. The MVT di e si y measu e (Dm ) wi hin he co e se is hen calcula ed as [2] Dm (MVT co e se ) =1+cm F−2cm Mcm .(9) The co e se o Eding e al. [7] is buil by ela i e b eed con ibu ions in o - de o maximise he gene ic a iance in he po en ial offsp ing o a conse ed popula ion ha is ob ained by in e b eeding he conse ed b eeds. I will be e med maximum a iance offsp ing (MVO) co e se in he ollowing. The el- a i e b eed con ibu ions o he MVO co e se (s o ed in he ec o cm o)a e es ima ed as [7] cm o =M−11N 1NM−11N ·(10) The MVO di e si y measu e (Dm o) wi hin he co e se can be es ima ed as [7] Dm o(MVO co e se ) =1−cm oMcm o.(11) 206 J. Bennewi z e al. Bo h con ibu ion ec o s, cm and cm o, a e es ima ed unde he es ic ion ha he con ibu ions a e ze o o posi i e and ha hey sum up o one. I he b eeds showed nega i e con ibu ions, he mos nega i e con ibu ion was se o ze o and he con ibu ion ec o was ecalcula ed wi hou he co espond- ing b eed. This is epea ed un il no u he nega i e con ibu ion es ima es a e obse ed. In p ac ice he a e age kinship ma ix Mis gene ally unknown, bu can be es ima ed om molecula ma ke in o ma ion [6], esul ing in ˆ M.ˆ Mcan hen be used in he equa ions (8)–(11). Howe e , mo e accu a e con ibu ion ec- o s a e ob ained i his me hod is ex ended wi h boo s apping [2]. B ie ly, a boo s ap sample bis gene a ed by sampling he indi iduals wi hin b eed and he ma ke loci ac oss b eeds simul aneously wi h eplacemen . Fo each b, he kinship ma ix is es ima ed by a log-linea model [6] and subsequen ly he co esponding con ibu ion ec o s (cm band cm ob) a e es ima ed using equa- ions (8) and (10). Addi ionally he wo di e si y measu es Dm band Dm ob a e calcula ed o each busing (9) and (11). A o al o Bboo s ap samples a e gene a ed. The inal boo s ap es ima es o he con ibu ion ec o s a e he ollowing: cm =1 B B  b=1 cm b,and cm o =1 B B  b=1 cm ob.(12) The inal boo s ap es ima es o Dm and Dm oa e he ollowing: Dm =1 B B  b=1 Dm b,and Dm o=1 B B  b=1 Dm ob.(13) 2.3. Simula ion To es he pe o mance o he p oposed sampling app oach o i s abili y o es ima e accu a e expec ed u u e di e si y and ma ginal di e si ies, i was compa ed by means o simula ions wi h he de e minis ic app oach. Nb eeds (N=10, 20, espec i ely) we e simula ed o each eplica e, one base b eed (consis ed o 50 indi iduals) and N−1 b eeds ha we e o med by ission om he base b eed. The numbe o gene a ions conside ed was 50. Fo each indi- idual a numbe o 20 unlinked gene ic ma ke loci we e assumed. Fo each b eed an ex inc ion p obabili y was sampled om he in e al 0.1/0.9. Because some cons ella ions we e compu a ionally e y demanding o simula e and analyse, he numbe o eplica es was es ic ed o 10. Fo de ails o he simu- la ion p o ocol see [2]. B eed con ibu ions o p esen and u u e di e si y 207 The pedig ee in o ma ion was eco ded du ing he simula ion and was used o calcula e he ue a e age kinship ma ix M. I was used o calcula e he ue ac ual di e si ies using equa ions (8)–(11) and o calcula e he ue expec ed u u e di e si ies and he ue ma ginal di e si ies by he de e minis ic o mu- lae (Eqs. (5)–(7)). The geno ypes o gene a ion 50 we e used o es ima e he ma ke es ima ed kinship ma ix ˆ Mby a weigh ed log-linea model [6]. The ac- ual di e si y was es ima ed by wo diffe en me hods. Fi s by he use o ˆ Min equa ions (8)–(11) and second by he boo s ap app oach (Eqs. (12) and (13)). The expec ed u u e di e si y as well as he ma ginal di e si ies o he b eeds we e es ima ed using he ollowing h ee app oaches. Fi s by he use o ˆ M in equa ions (8)–(11) and he de e minis ic o mulae (5)–(7), second by he boo s ap app oach (Eqs. (12) and (13), B=100) and he de e minis ic o mu- lae (5)–(7), and hi d by he boo s ap app oach (Eqs. (12) and (13), B=100) and he sampling algo i hm (Eq. (1)–(4)), b eeds wi h ki=0 we e emo ed om all boo s ap samples). Fo he las app oach he numbe o samples was a ied (S=10, 100, 1000, 10000). 2.4. No h Eu asian ca le b eeds A da a se o 44 diffe en na i e and comme cial ca le b eeds o igina ing om a la ge geog aphic egion (i.e. om he Scandina ian and he Bal ic coun ies, Finland, Russia, Byelo ussia, Uk aine and Poland) was examined. The Russian b eeds included in he s udy we e om he Eu opean pa o he Russian Fede a ion excep he Yaku ian ca le, which o igina e om Asia. The Yaku ian ca le make he da a se o pa icula in e es because his b eed is classi ied as a Tu ano-Mongolicus ype o ca le [1, 9]. This ca le b eed is an endange ed na i e b eed in he Sakha Republic ( o me ly he Yaku ia Republic) in he no heas o Sibe ia in Russia. The da a se includes bo h in ensi ely selec ed comme cial b eeds and less selec ed land aces. Fu he in o ma ion o he b eeds can be ound a h p://neu ocad.l a.l /. The b eed samples we e geno yped a he ollowing 20 mic osa elli e ma ke s: BM1824, BM2113, ETH10, ETH225, ETH3, HEL5, ILSTS005, INRA023, INRA035, INRA005, BM1818, CSSM66, ETH152, HEL1, HEL13, HEL9, ILSTS006, INRA032, INRA037 and INRA063. A mo e de ailed desc ip ion o he b eed geno ype da a se will be published elsewhe e. I was analysed by he wo co e se algo i hms using he boo s ap app oach as desc ibed abo e. A o al o 100 (B=100) boo s ap samples we e gene a ed and hese we e s o ed o he ma ginal di e si y es ima ion. The ela i e b eed con ibu ion ec o s as well as he conse ed di e si y we e es ima ed using he equa ions (8)–(13). Gene ic 208 J. Bennewi z e al. dis ances we e ob ained om he ma ke es ima ed kinships as desc ibed in [5] and hey we e isualised in a dend og am using he PHYLIP so wa e [10]. Expec ed u u e di e si y as well as ma ginal di e si ies we e es ima ed using he sampling algo i hm (Eqs. (1)–(4)) applied o he s o ed 100 boo - s ap samples and using he di e si y measu es ob ained om equa ions (12) and (13). A o al o wen y housand samples we e pe o med (S=20000). The es ima ion o ex inc ion p obabili ies needs a subs an ial amoun o da a [3,15]. These we e no a ailable o he majo i y o he 44 b eeds. The e- o e, he b eeds we e classi ied in o i e diffe en isk classes acco ding o hei numbe o b eeding emales. Simpli ied ex inc ion p obabili ies o he b eeds we e hen ob ained by assigning ex inc ion p obabili ies o he co esponding isk class. I was assumed ha hese a e alid o a ime ho izon be ween 20 and50yea sin o he u u e.The i ediffe en isk classes and he assigned ex inc ion p obabili ies za e he ollowing: class one (less han 100 b eeding emales) z=0.8; class wo (be ween 100 and 1000 b eeding emales) z=0.6; class h ee (be ween 1000 and 5000 b eeding emales) z=0.4; class ou (be- ween 5000 and 10000 b eeding emales) z=0.2; and class i e (mo e han 10000 b eeding emales) z=0.02. An ex inc ion p obabili y abo e ze o was assigned o he i e, because a comple ely sa e b eed is no alid [15]. Fo he isk class o he b eeds in his s udy as well as o o he b eed in o ma ion see he Appendix. Fo each b eed, he conse a ion po en ial (CP) was es ima ed as CPi=zi×mi. The conse a ion po en ial quan i ies how bene icial i would be in e ms o di e si y o make a b eed comple ely sa e. 3. RESULTS 3.1. Resul s om he simula ions The esul s om he expec ed u u e di e si y es ima ion a e p esen ed in Table I. I seems ha i is sligh ly easie o es ima e he expec ed u u e di e - si y i he numbe o b eeds included is low. No subs an ial diffe ences be ween he esul s ob ained om he diffe en me hods we e obse ed. E en he sam- pling app oach wi h a low numbe o samples p oduced eliable u u e di e - si y es ima es. The co ela ion be ween he es ima ed a iances o he expec ed u u e di e si ies we e on a simila ly high le el (no shown) indica ing ha he second momen can also be es ima ed accu a ely by he sampling app oach. The a e age co ela ion be ween ue and es ima ed ma ginal di e si ies is shown in Table II. The de e minis ic app oach p oduced mo e accu a e es ima es when applied o he boo s ap ma ke es ima ed kinship ma ices. B eed con ibu ions o p esen and u u e di e si y 209 Table I. A e age co ela ion be ween es ima ed and ue expec ed u u e di e si y o he diffe en me hods and numbe o b eeds (N), esul s om he simula ions. Me hodaMVT co e se MVO co e se N=10 N=20 N=10 N=20 11111 2 0.918 0.794 0.923 0.903 3 0.930 –b0.921 –b 4(S=10) 0.888 0.561 0.763 0.938 4(S=100) 0.932 0.911 0.921 0.889 4(S=1000) 0.924 0.887 0.910 0.899 4(S=10000) 0.931 0.901 0.915 0.903 aMe hod 1: Use o Mma ix in equa ions (8)–(11) and de e minis ic app oach (Eqs. (5)–(7)), ue scena io. Me hod 2: Use o ˆ Mma ix in equa ions (8)–(11) and de e minis ic app oach (Eqs. (5)–(7)). Me hod 3: Use o boo s ap ˆ Mma ices and de e minis ic app oach (Eqs. (5)–(7)). Me hod 4: Use o boo s ap ˆ Mma ices and s ochas ic app oach (Eqs. (1)–(4)), Sdeno es he numbe o samples. bCompu a ionally oo demanding o es ima ion. Table II. A e age co ela ion be ween es ima ed and ue ma ginal di e si y o he diffe en me hods and numbe o b eeds (N), esul s om he simula ions. Me hodaMVT co e se MVO co e se N=10 N=20 N=10 N=20 11111 2 0.871 0.812 0.856 0.821 3 0.921 –b0.843 –b 4(S=10) 0.489 0.493 0.410 0.236 4(S=100) 0.833 0.688 0.807 0.736 4(S=1000) 0.908 0.853 0.874 0.825 4(S=10000) 0.916 0.858 0.891 0.843 a,bSee Table I. Fu he mo e, he de e minis ic app oach always p oduced mo e accu a e es- ima es han he s ochas ic app oach (Tab. II). Hence, i is ad isable o apply he de e minis ic app oach i possible (small/mode a e N) and o apply he boo s ap s a egy. O he wise, i he de e minis ic app oach is eplaced by he s ochas ic sampling algo i hm, he educ ion in accu acy is only small i a ea- sonably high numbe o samples a e pe o med. In gene al, o a gi en Si is easie o ob ain accu a e es ima es o a se wi h small N. Some o he es ima es o he ma ginal di e si ies we e nega i e due o es ima ion e o . These es i- ma es we e se o ze o. 216 J. Bennewi z e al. As al eady men ioned, he es ima ion o ex inc ion p obabili ies is a diffi- cul ask [3, 12, 15]. The e o e, in his s udy hey we e de e mined by simply assigning p obabili ies o he de ined i e isk classes o endange men . In o - de o es he sensi i i y o he somewha a bi a y alues, wo diffe en se s o assigned ex inc ion p obabili ies we e used. The i s se was as desc ibed abo e and he ex inc ion p obabili ies o he second se we e exac ly he hal om hose o he i s se . Consequen ly, wo ma ginal di e si y es ima es o each b eed we e es ima ed. A linea model was applied ha included he b eed and he se o ex inc ion p obabili ies (ei he se one o se wo) as ixed e - ec s. The null hypo hesis was ha bo h ma ginal di e si ies wi hin a b eed we e he same, he al e na i e hypo hesis was ha a leas o one b eed he ma ginal di e si ies we e no he same. The esul s o his model sugges ed o ejec he null hypo hesis (P<0.01 o bo h di e si y measu es). In gene al, he ma ginal di e si ies we e somewha highe o he highe ex inc ion p ob- abili ies, howe e , wi hou changing he anking o de o he b eed ma ginal di e si ies (no shown). The expec ed loss o di e si y was a ound 50% lowe o he se o lowe ex inc ion p obabili ies. Based on hese esul s, i is ben- e icial o ha e mo e accu a e ex inc ion p obabili y es ima es because mo e p ecise conclusions could be d awn om he esul s ob ained. An al e na i e o he applied combina ion o ex inc ion p obabili ies and di e si y measu es is he so-called ‘sa e se sa e se +1’ app oach as used in [7]. By using his app oach, he anking o endange ed b eeds o conse a ion p io i y is done acco ding o hei con ibu ion o he di e si y o a sa e (i.e. no endange ed) se o b eeds. The ad an age is ha no ex inc ion p obabili ies a e needed, i only has o be decided which b eeds o m he sa e se . 4.3. Conse a ion o he No h Eu asian ca le b eed gene ic di e si y As men ioned abo e, e en wi hou any conse a ion effo he expec ed loss o di e si y wi hin his se o b eeds is low, ega dless o he applied di e si y measu e. I , howe e , e en his small loss is o be educed, i is no help ul o educe he ex inc ion p obabili ies o he mos endange ed b eeds wi hou conside ing he ma ginal di e si ies because he e is i ually no ela ionship be ween he ex inc ion p obabili y on he one hand and he ela i e b eed con ibu ion and ma ginal di e si y on he o he hand as shown in Table IV. Simila esul s ound in a diffe en da a se we e epo ed by [17]. Assume a conse a ion scheme in which he cos o make a b eed sa e (i.e. b inging i s ex inc ion p obabili y close o ze o) is independen om i s ex inc- ion p obabili y and mo e o less equal o all b eeds. Unde hese condi ions, B eed con ibu ions o p esen and u u e di e si y 217 he b eeds wi h he highes conse a ion po en ial would ecei e he highes p io i y o he inclusion in he conse a ion p og amme. In he p esen s udy he i e b eeds wi h he highes conse a ion po en ial o he MVT di e si y measu e a e Yaku ian ca le, Bohus Poll, Ringamala ca le, Red Danish 1970 and Väne ca le. Fo he MVO, hese b eeds a e he Ringamala ca le, Bohus Poll, Doela ca le, La ian Blue and Swedish Moun ain ca le. I by including hem in a conse a ion plan he ex inc ion p obabili y o hese b eeds would be close o ze o, he e would be almos no expec ed loss o di e si y a he end o he ime ho izon (no shown). Howe e , hese assump ions migh only be alid in ex-si u conse a ion schemes (e.g. ans e ing a deposi o gene ic ma- e ial om endange ed b eeds o a genebank), bu no in in-si u conse a ion schemes, whe e he b eeds a e conse ed wi hin he p oduc ion sys em. Fo he la e si ua ion, Simiane e al. [17] p oposed a mo e sophis ica ed amewo k o iden i y he mos efficien conse a ion plan. The cu en s udy p o ides he p e equisi e o apply he me hods o [17], gi en ha he unknowns in he me hod can be eplaced by eliable es ima es. Howe e , i is easonable o as- sume ha hose h ee o i e b eeds wi h high conse a ion po en ial will also be ecommended o a conse a ion plan by he algo i hms o [17]. Th oughou his s udy he ocus was based exclusi ely on gene ic di e si y as a c i e ion o he conse a ion o a b eed. O he conse a ion c i e ia such as adap a ion o a speci ic en i onmen , special ai s o economic in e es o his o ical o cul u al alue a e discussed by e.g. [11,13,16]. 5. CONCLUSION I was shown ha he sampling algo i hm in combina ion wi h he wo co e se gene ic di e si y measu es p o ides a sui able s a is ical ool o he ma ke assis ed es ima ion o p esen and expec ed u u e di e si y and o b eed ma ginal di e si ies, gi en ha ex inc ion p obabili ies o he b eeds a e known. The analysis o he No h Eu asian ca le b eeds e ealed ha wi h- ou any conse a ion effo s he expec ed loss o di e si y du ing he nex 20 o 50 yea s is be ween 1 and 3% om ac ual di e si y, p o ided ha he sim- pli ied de e mined ex inc ion p obabili ies a e app oxima ely alid. I his loss was o be educed o e en s opped by a limi ed conse a ion und, i seems o be sufficien o in es he a ailable money in he educ ion o he ex inc ion p obabili y o hose h ee o i e b eeds wi h he highes ma ginal di e si y and he highes conse a ion po en ial. These a e no necessa ily he mos endan- ge ed b eeds. 218 J. Bennewi z e al. ACKNOWLEDGEMENTS Jö n Bennewi z was suppo ed by a g an om he Ge man Academic Exchange Se ice (Deu sche Akademische Aus auschdiens , DAAD). REFERENCES [1] Banniko a L.V., Zuba e a L.A., Gene ic s uc u e o some na i e and comme - cial b eeds o ca le (Bos au us) om Eu asia, Russian J. Gene . 31 (1995) 597–607. [2] Bennewi z J., Meuwissen T.H.E., A no el me hod o he es ima ion o he ela- i e impo ance o b eeds in o de o conse e he o al gene ic a iance, Gene . Sel. E ol. 37 (2005) 315–337. [3] Bennewi z J., Meuwissen T.H.E., Es ima ion o ex inc ion p obabili ies o i e Ge man ca le b eeds by popula ion iabili y analysis, J. Dai y Sci. 88 (2005) 2949–2961. [4] Caballe o A., To o M.A., Analysis o gene ic di e si y o he managemen o conse ed subdi ided popula ions, Conse . Gene . 3 (2002) 289–299. [5] Eding J.H., Meuwissen T.H.E., Ma ke based es ima es o be ween and wi hin popula ion kinships o he conse a ion o gene ic di e si y, J. Anim. B eed. Gene . 118 (2001) 141–159. 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B eed Sample size Sample o igin Risk classa Byelo ussian Red 23 Byelo ussia Fi e Danish Je sey 41 Denma k Fi e Es onian Red 40 Es onia Fi e Finnish Ay shi e 46 Finland Fi e Finnish Hols ein-F iesian 43 Finland Fi e Icelandic ca le 44 Iceland Fi e Kholmogo y 42 Russia Fi e La ian B own 40 La ia Fi e Li huanian Black and Whi e 41 Li huania Fi e Li huanian Red 40 Li huania Fi e No wegian Dai y ca le 38 No way Fi e Polish Black and Whi e 30 Poland Fi e Swedish Hols ein-F iesian 44 Sweden Fi e Swedish Red and Whi e 39 Sweden Fi e Ya osla l 44 Russia Fi e Is oben 49 Russia Fou Suksun 40 Russia Fou Blacksided T oende 34 No way Th ee Es onian Na i e 40 Es onia Th ee Swedish Moun ain ca le 41 Sweden Th ee Telema k ca le 46 No way Th ee Uk ainian Whi eheaded 11 Uk aine Th ee Wes e n Finnca le 41 Finland Th ee Doela ca le 35 No way Two Eas e n Finnca le 31 Finland Two Eas e n Red Polled 11 No way Two Ju land b eed 49 Denma k Two La ian Blue 40 La ia Two La ian Danish Red 40 La ia Two Li huanian Ligh G ey 41 Li huania Two Li huanian Whi e Backed 40 Li huania Two No h Finnca le 26 Finland Two Pecho a 33 Russia Two Red Danish 1970 39 Denma k Two Swedish Red Polled 34 Sweden Two Uk ainian G ey 30 Uk aine Two Väne ca le 18 Sweden Two Wes e n Fjo d ca le 41 No way Two Wes e n Red Polled 36 No way Two Yaku ian ca le 54 Russia Two Bohus Poll 14 Sweden One Danish Black-Pied 1965 27 Denma k One Fjällnä a ca le 15 Sweden One Ringamala ca le 20 Sweden One aClassi ica ion done acco ding o he numbe o b eeding emales as ollows: class one (less han 100 e- males), class wo (be ween 100 and 1000 emales), class h ee (be ween 1000 and 5000 emales), class ou (be ween 5000 and 10000 emales), class i e (mo e han 10000 emales). F om his, class one is c i ically endange ed and class i e no endange ed.