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).
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APPENDIX
In o ma ion abou he b eeds included in he ield da a se .
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.