METHODS ARTICLE
published: 14 Decembe 2012
doi: 10.3389/ gene.2012.00262
The gene ic analysis o ole ance o in ec ions: a e iew
An i Kause1*and Jø gen Ødegå d2
1Bio echnology and Food Resea ch, Biome ical Gene ics, MTT Ag i ood Resea ch Finland, Jokioinen, Finland
2No ima, Ås, No way
Edi ed by:
And ea B. Doeschl-Wilson,
The Uni e si y o Edinbu gh, UK
Re iewed by:
Mai ead L. Be mingham,
The Uni e si y o Edinbu gh, UK
Sunday Pe e s, Co nell Uni e si y,
USA
*Co espondence:
An i Kause, Bio echnology
and Food Resea ch, Biome ical
Gene ics, MTT Ag i ood Resea ch
Finland, FI-31600, Jokioinen,
Finland.
e-mail: an i.kause@m . i
Tole ance o in ec ions is de ined as he abili y o a hos o limi he impac o a
gi en pa hogen bu den on hos pe o mance. Uncoupling esis ance and ole ance is a
challenge, and he e is a need o be able o sepa a e hem using speci ic ai eco ding o
s a is ical me hods. We p esen h ee s a is ical me hods ha can be used o in es iga e
gene ics o ole ance- ela ed ai s. Fi s ly, using andom eg essions, ole ance can be
analyzed as a eac ion no m slope in which hos pe o mance (y-axis) is eg essed agains
an inc easing pa hogen bu den (x-axis). Gene ic a iance in ole ance slopes is he gene ic
a iance o ole ance. Va ia ion in ole ance can induce geno ype e- anking and changes
in gene ic and pheno ypic a ia ion in hos pe o mance along he pa hogen bu den
ajec o y, con ibu ing o en i onmen -dependen gene ic esponses o selec ion. Such
geno ype-by-en i onmen in e ac ions can be quan i ied by combining andom eg essions
and co a iance unc ions. To apply andom eg essions, pa hogen bu den o indi iduals
needs o be eco ded. Secondly, when pa hogen bu den is no eco ded, he cu e
model o ime-un il-dea h da a allows sepa a ing wo ai s, suscep ibili y and endu ance.
Suscep ibili y is whe he o no an indi idual was suscep ible o an in ec ion, whe eas
endu ance deno es how long ime i ook un il he in ec ion killed a suscep ible animal
(in luenced by ole ance). Thi dly, he no mal mix u e model can be used o classi y
con inuously dis ibu ed hos pe o mance, such as g ow h a e, in o di e en sub-classes
(e.g., non-in ec ed and in ec ed), which allows es ima ion o hos pe o mance educ ion
speci ic o in ec ed indi iduals. Mo eo e , gene ics o hos pe o mance can be analyzed
sepa a ely in heal hy and a ec ed animals, e en in he absence o pa hogen bu den and
su i al da a. These me hods p o ide no el ools o inc ease ou unde s anding on he
impac o pa asi es, pa hogens, and p oduc ion diseases on hos ai s.
Keywo ds: cu e model, geno ype-by-en i onmen in e ac ion, mix u e model, quan i a i e gene ics, andom
eg ession, esis ance, s a is ical me hods, ole ance
INTRODUCTION
Tole ance and esis ance a e wo di e en de ense mechanisms
o de end agains pa hogens and pa asi es. Resis ance is he abil-
i y o a hos o p e en pa hogen en y and o con ol pa hogen
li ecycleinaway o educepa hogenbu denwi hinahos indi-
idual. Tole ance o in ec ions, in u n, is de ined as he abili y
o he hos o limi he impac o a gi en pa hogen bu den on
hos heal h, pe o mance, and ul ima ely on hos i ness (Clunies-
Ross, 1932; Pain e , 1958; Albe s e al., 1987; Simms and T iple ,
1994; Simms, 2000)(Figu e 1).
Being able o uncouple esis ance and ole ance is essen-
ial o se e al easons. Fi s ly, hey ha e di e en impac
on he a ms- ace co-e olu ion be ween he hos and he
pa hogen (Mau icio e al., 1997; Raushe , 2001; Bishop and
MacKenzie, 2003; Bes e al., 2008). Mo eo e , bo h in ani-
mals and plan s, ole ance and esis ance a e weakly gene i-
cally co ela ed, and hus hey a e gene ically di e en ai s
(Leimu and Ko iche a, 2006; Ødegå d e al., 2011b; Kause
e al., 2012). Finally, animal and plan b eede s should exploi
bo h inc eased esis ance and ole ance o ensu e global ood
secu i y.
In addi ion o pa hogens, ole ance can be assessed agains
abio ic ac o s such as empe a u e, hea y me als, o agains
p oduc ion diseases causing damage o body issues (Ra agnolo
and Misz al, 2000a,b; Scha e al., 2002; Bloemho e al., 2012;
Kause e al., 2012). Na u ally, p oduc ion diseases, such as asci es,
a e no s anda d disease ai s caused by a pa hogen o pa asi e
in ec ion. Thus, he e is no co-e olu ion be ween a hos and a
p oduc ion disease, and he p oduc ion disease does no e ol e
in esponse o he e olu ion o he hos . Ne e heless, imp o ed
esis ance and ole ance can be bo h used o educe he ha m ul
e ec s o p oduc ion diseases on a med animals, mo i a ing hei
ole ance analysis (Kause e al., 2012). F om he eon in his pape ,
pa hogen bu den is used as a gene al e m o e e o a pa hogen
load o an indi idual, o ins ance, numbe o biomass o ec o-
and endopa asi es, numbe o pa hogens in a blood sample, o
se e i y o a p oduc ion disease. In plan s, pa hogen bu den may
e e o he biomass o numbe o he bi o es, o pe cen age o lea
a ea los o he bi o es.
The objec i e o his pape is o p esen ecen s a is ical
ad ances in he gene ic analysis o ole ance- ela ed ai s.
Fi s ly, andom eg ession models ha e been applied o
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Kause and Ødegå d Gene ic analysis o ole ance
FIGURE 1 | Tole ance o in ec ions. Tole ance is he eac ion no m slope
o hos pe o mance eg essed agains indi idual’s pa hogen bu den. The
lines ep esen pe o mance o h ee geno ypes wi h a di e en deg ee o
ole ance.
ole ance analysis. They allow a sophis ica ed gene ic analysis
o ai s de ined as unc ions as well as he quan i ica ion o
geno ype-by-en i onmen in e ac ions (G ×E) induced by in ec-
ions (Kause, 2011; Kause e al., 2012). Secondly, Ødegå d e al.
(2011b,c) in oduced a cu e model o sepa a e “suscep ibili y”
and “endu ance” om challenge es da a wi h ime-un il-dea h
obse a ions (wi hou ha ing any knowledge abou in ec ion s a-
us o he animals). The i s ai is compa able o esis ance,
while endu ance may be in luenced by ole ance. “Suscep ibili y”
can be de ined as whe he o no he animal is liable o die as a
esul o an in ec ion (i.e., long- e m su i al, which is likely asso-
cia ed wi h esis ance), while “endu ance” is de ined as how long
ime i akes be o e a po en ial in ec ion kills he animal (which
is likely associa ed wi h ole ance). Bo h endu ance and suscep i-
bili y may show gene ic a ia ion, and may be iewed as di e en
gene ic ac o s a ec ing su i al unde an in ec ion. Finally, no -
mal mix u e models can be ex ended o in ol e esponses in
hos pe o mance ai s (e.g., g ow h cu es) speci ic o heal hy
and a ec ed indi iduals (Wang and Bodne , 2007; Madsen e al.,
2008).
RANDOM REGRESSION MODELS
Tole ance is by de ini ion he change in hos pe o mance as a
unc ion o pa hogen bu den (Simms, 2000), and hence, i is
na u al o apply andom eg ession models o es ima e gene ic
pa ame e s and b eeding alues o ole ance (Kause, 2011).
Using andom eg essions, ole ance can be analyzed as a eac ion
no m in which hos pe o mance (on y-axis) is eg essed agains
pa hogen bu den o indi iduals (on x-axis) (Box 1). I is impo -
an o no e ha pa hogen bu den is measu ed sepa a ely om
each indi idual, and i is no a gene al en i onmen al cha ac e is-
ic. The slope o such a eg ession is consis en wi h he de ini ion
o ole ance (Figu e 1), and hence gene ic a iance in eg ession
slopes is he gene ic a iance o ole ance (Kause, 2011).
The in e cep o he ole ance eg ession is in e p e ed as
he hos pe o mance in a pa hogen- ee en i onmen , and he
gene ic co ela ion be ween he slope and he in e cep quan i ies
he deg ee o which hos pe o mance unde no in ec ion is
Box 1 | A andom eg ession model.
An animal model andom eg ession model is o he o m:
yi=b0+b1PBu den +b0i+b1iPBu deni+i, whe e yiis
hos pe o mance o an indi idual ia i s pa hogen bu den
PBu den,b0is he ixed popula ion mean in e cep , b1PBu den
is he ixed popula ion mean ole ance slope, b0iis he andom
gene ic e ec o in e cep o an indi idual i,b1iPBu deniis he
andom gene ic e ec o ole ance slope o an indi idual i,and
iis he andom e o e m. Bo h b0iand b1ia e modeled wi h a
pedig ee, allowing he es ima ion o hei gene ic a iance.
Co a iance unc ions. Gene ic a iance o hos pe o mance
as a unc ion o pa hogen bu den can be calcula ed: as
x’PBu denGxPBu den, whe e G=σ2
b0σb0b1
σb0b1σ2
b1,σ2
b0and σ2
b1a e
gene ic a iances o in e cep and slope, espec i ely, and σb0b1
is co a iance be ween he wo e ms (Kolmodin and Bijma, 2004).
The e m xPBu den isa ec o [1PBu den]in which PBu den
e e s o a pa hogen bu den alue on he x-axis. A gene ic co ela-
ion be ween he pe o mance o non-in ec ed (PBu den =0) and
in ec ed indi iduals a a ce ain PBu den alue can be calcula ed
as: G=x
0GxPBu den
x
0Gx0×x
PBu denGxPBu den
, whe e Gis he gene ic
(co) a iance ma ix o slope and in e cep , x0isa ec o o [10]
,
and xPBu den is as desc ibed ea lie (Calus e al., 2004).
gene ically aded o wi h ole ance. Mo eo e , gene ic co ela-
ions o he slope and in e cep wi h hi d-pa y ai s can be
es ima ed by ex ending he andom eg ession model o mul i ai
animal o si e model (Kause e al., 2012).
In animals, pa hogen bu den is ypically a con inuously dis-
ibu ed ai , especially when a popula ion is unde a na u al
pa hogen in ec ion (S ea e al., 1995; Kuukka-An ila e al.,
2010). E en in a challenge es in which all indi iduals a e exposed
o he same ini ial pa hogen load, a ia ion among indi iduals
in esis ance c ea es con inuous a ia ion in pa hogen bu den.
Random eg ession models allow gene ic analysis o ole ance
along a con inuous pa hogen bu den ajec o y. In animal b eed-
ing, andom eg ession models ha e been commonly applied o
he eac ion no m analysis o G ×E(Hende son, 1982; Meye
and Hill, 1997; Calus e al., 2004; Schae e , 2004; Lillehamme
e al., 2009).
TOLERANCE-INDUCED VARIATION IN HOST PERFORMANCE
Gene ic a ia ion in ole ance may induce G ×Einhos pe -
o mance, leading o changes in gene ic a ia ion o hos pe -
o mance along an inc easing pa hogen bu den ajec o y. Fo
ins ance, in Figu e 1, gene ic a iance in hos pe o mance is
ele a ed along inc eased pa hogen bu den due o di e ging ol-
e ance eac ion no ms. In poul y, pigs, and aquacul u e species,
b eeding nucleuses may be held in ec ion- ee due o biosecu i y
easons, whe eas comme cial p oduc ion and/o collec ion o sib
and p ogeny in o ma ion o b eeding alue es ima ion occu s
a ield a ms wi h di e se diseases p esen . Such a design may
induce G ×Edue o a ia ionin hele elo ole ance,which
should be accoun ed o in b eeding alue e alua ions.
In an in ec ion- ee en i onmen , indi idual a ia ion in hos
pe o mance, e.g., in g ow h a e, is due o a ia ion in gene ic
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Kause and Ødegå d Gene ic analysis o ole ance
po en ial o g ow h and unexplained en i onmen al a ia ion.
Unde in ec ion, in u n, indi idual a ia ion in bo h esis ance
and ole ance induce addi ional a ia ion in o hos pe o mance.
Some indi iduals a e ully esis an o a e no exposed o an
in ec ion, and hus hei g ow h is no in luenced by he in ec-
ion. Some indi iduals a e in ec ed, and he deg ee o which
hei g ow h a e is educed depends on hei pa hogen bu den
and he le el o ole ance. G ow h o ully ole an indi iduals
is no a ec ed, whe eas g ow h o e y sensi i e ones is g ea ly
educed.
Despi e he la ge numbe o s udies dealing wi h he changes
induced by bio ic (e.g., die ) and abio ic ac o s in gen-
e al (Ho mann and Me ilä, 1999; Kause and Mo in, 2001;
Cha man ie and Ga an , 2005), he e has been only a limi ed
ocus on in ec ion-induced changes in gene ic pa ame e s and he
consequen en i onmen -speci ic gene ic esponses o selec ion
( an de Waaij e al., 2000). In ec ions a e indeed known o induce
changes in he i abili y o hos pe o mance ai s (Cha man ie
e al., 2004; Pakdel e al., 2005; Ze ehda an e al., 2006; Kause
e al., 2007, 2012; Veh iläinen e al., 2008; Lewis e al., 2009).
Ye , cu en ly we do no know how much o he pheno ypic a i-
a ion in hos pe o mance is in ac c ea ed by in ec ions and
he associa ed ole ance. A s udy by Kause e al. (2012)showed
ha coe icien o pheno ypic a ia ion in b oile body weigh
was ele a ed om 11.5% when bi ds we e heal hy, o 19.1%
when bi ds we e se e ely a ec ed by asci es. Simila ly, coe icien
o gene ic a ia ion was inc eased om 4.9% o 7.9%, imply-
ing he changes in a iance can be ex ensi e (Figu e 2). I is
hypo hesized ha in popula ions exposed o in ec ions, a la ge
p opo ion o pheno ypic a iance in hos ai s is induced by
in ec ions and he associa ed indi idual a ia ion in esis ance
and ole ance.
Random eg ession models combined wi h co a iance unc-
ions (Ki kpa ick e al., 1990; Meye and Hill, 1997)p o ide
means o quan i y he changes in pheno ypic and gene ic a i-
ances in hos ai s along a con inuous pa hogen bu den a-
jec o y (Kause, 2011; Kause e al., 2012). Gi en he gene ic
(co) a iance es ima es o ole ance slope and in e cep es ima ed
using andom eg essions, he changes in gene ic a iance in hos
pe o mance can be calcula ed using o mulas (Box 1;Figu e 2).
FIGURE 2 | Tole ance analysis using andom eg essions and co a iance
unc ions illus a ed using da a on 7-week body weigh and hea a io
o b oile s [ ep oduced om Kause e al. (2012); h p://c ea i e
commons.o g/licenses/by/3.0/]. Hea a io, he a io o igh en icula
weigh o o al hea weigh , is an indica o o asci es esis ance, he bi ds
wi h highe han 27–30% hea a io ypically being asci ic (Wideman e al.,
1998). Tole ance is he change in body weigh as a unc ion o inc easing
asci es se e i y, measu ed as he hea h a io. (A) Popula ion a e age
ole ance cu e wi h body weigh on y-axis and asci es se e i y on x-axis.
(B) F equency dis ibu ion o es ima ed b eeding alues o ole ance slopes
o indi iduals, showing sensi i e (s eep nega i e slope) and mo e ole an
(weak nega i e slope) geno ypes. (C) Inc eased coe icien s o pheno ypic
and gene ic a ia ion in body weigh as a unc ion o asci es se e i y,
showing asci es molds ai a ia ion. (D) Gene ic co ela ion be ween
heal hy bi ds and bi ds wi h di e en deg ee o asci es se e i y, showing
asci es c ea es geno ype e- anking (Kause e al., 2012).
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Kause and Ødegå d Gene ic analysis o ole ance
The same logic can be applied o he ma e nal and en i onmen al
componen s o (co) a iance.
TOLERANCE-INDUCED GENOTYPE RE-RANKING IN HOST
PERFORMANCE
C ossing ole ance eac ion no ms c ea e geno ype e- anking in
hos pe o mance ai s ac oss pa hogen bu den ajec o y. This
is simila o any geno ype e- anking ac oss en i onmen al g a-
dien s (Via and Lande, 1985), wi h he di e ence ha now he
en i onmen is pa hogen bu den o indi iduals (Kause e al.,
2012). The wo o ms o G ×E, scaling e ec and geno ype e-
anking, acili a e en i onmen -dependen gene ic esponses, ye
he e- anking is mo e se e e issue o selec i e b eeding because
geno ypes in one en i onmen a e no necessa ily he bes ones in
he o he en i onmen s. Re- anking ac oss en i onmen s can be
quan i ied by a gene ic co ela ion be ween measu emen s in wo
en i onmen s o a gi en ai (Falcone , 1952).
The deg ee o e- anking be ween any wo pa hogen bu den
le els can be calcula ed by combining andom eg ession esul s
wi h co a iance unc ions (Box 1). Fo ins ance, asci es induced
mode a e geno ype e- anking in b oile body weigh , he gene ic
co ela ion o heal hy bi ds wi h weakly a ec ed bi ds being
uni y bu wi h se e ely a ec ed bi ds 0.45 (Kause e al., 2012;
Figu e 2). In ield da a se s wi h mul iple en i onmen s, in ec ion
p essu e is ypically no he only en i onmen al ac o a ying
ac oss en i onmen s, ye he e ec o pa hogen bu den on G ×E
could be e ealed using a combined eac ion no m and mul i-
ai model (Windig e al., 2011), in which pa hogen bu den is
modeled as a con inuous eac ion no m and he disc e e en i-
onmen s cap u ing o he en i onmen al ac o s a e modeled as
sepa a e disc e e ai s. Pe o ming ex ensi e in ec ion-challenge
es s is imp ac ical in many a m animal species, bu he com-
bined eac ion no m and mul i- ai model may be an e ec i e
addi ional me hod o e ealing he deg ee o G ×Einducedby
in ec ions.
In ec ions do no induce only geno ype e- anking and a
change in a iance bu also changes in he co ela ion s uc u e o
esis ance, g ow h, and ep oduc ion ai s (de G ee e al., 2001;
Kause e al., 2005, 2012; Ze ehda an e al., 2006; Kuukka-An ila
e al., 2010). The modi ica ion o gene ic a chi ec u e o hos ai s
by pa hogens, pa asi es, and p oduc ion diseases, media ed by
ole ance gene ics, may play a mo e undamen al ole in animal
b eeding and mic oe olu ion han has been p e iously hough .
DATA REQUIREMENTS FOR RANDOM REGRESSION
Ob aining a solid x-axis is a majo challenge o he ole -
ance analysis in animals because he x-axis should consis s o
indi idual-le el quan i a i e da a on pa hogen bu den (e.g., num-
be o pa asi es, pa hogen biomass). Quali a i e da a on bu den
(in ec ed s. non-in ec ed indi iduals) c ea es biased es ima es
o gene ic a iance o ole ance (Kause, 2011). Mo eo e , i he
x-axis consis s o he a e age bu dens o each en i onmen , a he
han indi idual-le el bu den measu emen s, hen high hos pe -
o mance o a geno ype a a gi en pa hogen bu den can be a
esul o high esis ance and/o high ole ance, impeding a p ope
ole ance analysis. The analyzed hos pe o mance ai , in u n,
can be eed in ake, g ow h, ep oduc ion, su i al o a physio-
logical ai , which oge he can be used o e eal mechanisms
con ibu ing o a ia ion among geno ypes in ole ance.
A spli - amily design wi h bo h an in ec ion- ee con ol and
an expe imen al challenge es is he mos e ec i e design o
ole ance analysis. In his way, in ec ed animals a e a andom
sample o hei amily and hus he e will be a eal causal ela-
ionship be ween hos pe o mance and pa hogen bu den (Ti in
and Inouye, 2000; Kause, 2011). This equi es, howe e , ha all
he challenged indi iduals ge he same pa hogen bu den le el.
This a ely is he case because indi iduals ha e inna e indi id-
ual a ia ion in esis ance, c ea ing a ia ion in pa hogen bu den
e en in a challenge es . Va ia ion in esis ance can be po en ially
ela ed o he hos pe o mance ai s used on he y-axis in he
ole ance eg ession, biasing he es ima e o gene ic a ia ion o
ole ance (Ti in and Inouye, 2000; Kause, 2011). As an al e na-
i e o he con ol-and-challenge es design, all indi iduals can
be i s eco ded unde in ec ion- ee condi ions (e.g., o ma u e
body weigh ), and hen e- eco ded a e expe imen al exposi-
ion o equal pa hogen bu den le el. Howe e , such an analysis
is unjus i ied in cases in which hos pe o mance shows na u-
al empo al a ia ion (e.g., a ia ion in g ow h cu es), which
is hus con ounded wi h ole ance (Albe s e al., 1987; Bisse and
Mo is, 1996; Woolas on and Windon, 2001). T ypano ole ance
o A ican ca le has been analyzed as a change in body weigh in
esponse o an expe imen al in ec ion by T ypanosoma congolense,
bu al hough he numbe o pa asi es in he blood o indi iduals
was eco ded, i was no used o s anda dize he hos pe o mance
changes o indi iduals (Hano e e al., 2003; an de Waaij e al.,
2003).
Unde na u ally occu ing in ec ion, i is possible ha ei he
high (o low) pe o ming indi iduals a e in ec ed, leading o
biased es ima es o gene ic a ia ion o ole ance (Ti in and
Inouye, 2000; Kause, 2011). This is a majo weakness o ield
da a se s, because i is well es ablished ha indi iduals wi h
ini ially di e en g ow h o li e-his o y ai le els may be di -
e en ly exposed o in ec ions, pa asi es and p oduc ion diseases
(A end , 1997; Rauw e al., 1998), con ounding he cause-and-
e ec ela ion be ween pa hogen bu den and educ ion in hos
pe o mance.
Random eg ession models equi e la ge sample sizes, e.g.,
wi hin si e amilies. Dec ease in amily size leads o upwa d-
biased gene ic a iance es ima es o ole ance slope (Kause,
2011).Thiscanbeillus a edinasi emodelse up.Whenasmall
numbe o indi iduals a e sampled o each si e amily, he sam-
ple is no longe ep esen a i e o he ue dis ibu ion and single
obse a ions ha e s ong impac on he slope es ima e. Fo some
amilies he slope is unde es ima ed, o o he s o e es ima ed, and
hus gene ic a iance es ima e o slope is a i icially inc eased.
Wi h he i abili y o 0.3 o ole ance slope, mo e han 50 sibs pe
amily a e equi ed o ob ain unbiased es ima es o slope a i-
ance using a si e model analysis (Kause, 2011). Mo eo e , gene ic
co ela ion be ween ole ance slope and in e cep is easily biased
downwa d when amily size is low. An upwa d (downwa d) bias
in he slope o a amily pushes he in e cep downwa d (upwa d),
c ea ing an a i icial nega i e gene ic ade-o when i does no
exis in eali y. This can be a oided by using high amily sizes and
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Kause and Ødegå d Gene ic analysis o ole ance
high numbe o non-in ec ed indi iduals ha o ce he in e cep
o a geno ype o be placed close o he eal alue (Mau icio e al.,
1997; Kause, 2011).
When each hos indi idual has only a single pe o mance
eco d, i is possible o es ima e gene ic a iance and b eeding al-
ues o ole ance slope, bu no i s esidual a iance. He i abili ies
o ole ance slope can be es ima ed when each indi idual has se -
e al pe o mance obse a ions, e.g., he ini ial pe o mance unde
condi ions o no in ec ion and he ea e he pe o mance a e an
in ec ion. By using eg ession slopes o indi iduals as aw obse -
a ions in he gene ic analysis, bo h en i onmen al and gene ic
componen s o slope a iance and he i abili y can be es ima ed
(Schae e , 2004).
Random eg ession can be applied o non-linea eac ion
no ms (Ki kpa ick e al., 1990; Meye and Hill, 1997; Schae e ,
2004) and pla eau-linea eg ession models (Ra agnolo and
Misz al, 2000a,b; Kause e al., 2012), and hus he impac o
pa hogens on hos pe o mance does no need o be analyzed as a
linea ela ionship.
A CURE MODEL FOR TIME-UNTIL-DEATH DATA
The andom eg ession app oach equi es indi idual-le el da a
on pa hogen bu den which may be challenging o eco d. The
cu e model o ime-un il-dea h da a p o ides a possibili y o
analyze gene ics o esis ance (o suscep ibili y) and endu ance
wi hou a need o pa hogen bu den eco ding.
Many s udies, especially on aquacul u e species, ha e analyzed
su i al o ime-un il-dea h in a challenge es in which indi idu-
als a e expe imen ally exposed o a speci ic pa hogen (Ødegå d
e al., 2011a). Mo eo e , su i al analysis has been applied o
ime-un il-dea h da a when mo ali y ac o s emain unknown
(e.g., Duc ocq and Casella, 1996; Se enius and S alde , 2004;
Veh iläinen e al., 2010). A ypical assump ion in such analyses
is ha indi iduals wi h high p obabili y o su i al a e esis an .
Howe e , an indi idual can su i e i i has ei he high esis-
ance, o low esis ance bu high ole ance (Figu e 3), o was
ne e exposed o a pa hogen. The cu e su i al models a e used
o modeling o ime-un il-dea h da a which include a ac ion o
non-suscep ible animals, i.e., animals ha a e no liable o die as
a esul o he in ec ion (Fa ewell, 1982). Ødegå d e al. (2011c)
de eloped a cu e model aiming o dis inguish wo ai s, “suscep-
ibili y” and “endu ance,” om ime-un il-dea h da a. These wo
concep s may be compa able wi h esis ance and ole ance.
In a su i al analysis he in ec ion s a us o each animal is
ypically unknown. Unde pa hogen a ack, some animals may
be ully capable o a oiding dea h (non-suscep ible), ei he by
esis ing he in ec ion, o by a success ul eco e y a e he ini-
ial in ec ion due o high ole ance (Figu e 3). Fu he mo e, he
deg ee o ole ance may also a y among he suscep ible indi id-
uals, po en ially causing a ia ion in hei expec ed ime-un il-
dea h. As mo ali y is usually eco ded o e a limi ed ollow-up
pe iod, a ac ion o suscep ible animals a e also likely o be ali e
a he ime o eco ding. Fo suscep ible animals, he abili y o
su i e depends on he expec ed ime-un il-dea h o he animal,
which may show gene ic a ia ion. Hence, analogy o he e ms
“endu ance” and “suscep ibili y” wi h ole ance and esis ance a e
no necessa ily clea -cu in a su i al analysis, due o he ac ha
FIGURE 3 | Con ibu ion o esis ance and ole ance o mo ali y due
o a speci ic pa hogen. Only indi iduals wi hou esis ance and ole ance
will e en ually die gi en a su icien ly long ollow-up pe iod. When ha ing a
limi ed ollow-up pe iod, indi iduals wi h high ole ance may s ill be ali e a
he end o an expe imen .
one only obse es he ex eme ou comes o an in ec ion (whe he
o no an animal dies). Al hough “endu ance” and “suscep ibil-
i y” a e impossible o sepa a e on indi idual su i o s, hese wo
ac o s may s ill be dis inguished on a amily le el using longi udi-
nal su i al analysis (i.e., sho - e m mo ali y a es s. long- e m
su i al).
A classical su i al analysis o ime-un il-dea h assumes ha
all indi iduals a e a isk and ha all will e en ually die gi en
a su icien ly long ollow-up pe iod. When s udying li espan in
gene al his is necessa ily ue, bu may no hold when es ing
o mo ali y due o a speci ic pa hogen. Fo non-suscep ible ani-
mals ime-un il-dea h will necessa ily be censo ed, i espec i e
o he ollow-up ime, and su i al ime may hus be a poo
indica o o speci ic pa hogen esis ance. The endu ance e lec s
he expec ed mo ali y pe ime-uni among suscep ible indi id-
uals, bu will ha e no e ec on su i al o he non-suscep ible
indi iduals (Fa ewell, 1982).
The su i o s a e likely a mix u e o non-suscep ible long-
e m su i o s and a ac ion o suscep ible (bu highly endu e)
animals being s ill ali e, and he ue condi ion o each animal
is unknown (unless he animal dies). In he cu e model, p oba-
bili ies o he al e na i e se ings (non-suscep ible o suscep ible
bu s ill ali e) can be es ima ed while simul aneously aking in o
accoun a ia ion in endu ance among he su i ing animals
(Ødegå d e al., 2011c;Box 2).
The cu e model has been applied o ime-un il-dea h da a in
a med sh imp challenge- es ed wi h he Tau a synd ome i us
(Ødegå d e al., 2011b). I was es ima ed ha al hough 72%
o he sh imp su i ed, only 62% could be conside ed non-
suscep ible. The unde lying he i abili y (±SE) o suscep ibili y
was high (0.41 ±0.07), while he he i abili y o endu ance was
low, albei signi ican (0.07 ±0.03). The mos s iking esul
was ha endu ance and suscep ibili y we e seemingly dis inc
gene ic ai s ( G=0.22 ±0.25). The low gene ic a ia ion o
endu ance and he gene ic independency o endu ance and sus-
cep ibili y a e in line wi h he esul s on o he animal species
(Kause e al., 2012). These esul s ha e subs an ial impac on
how disease challenge- es ing should be pe o med. I he aim
is o imp o e long- e m su i al unde an in ec ion p essu e,
www. on ie sin.o g Decembe 2012 | Volume 3 | A icle 262 |5

Kause and Ødegå d Gene ic analysis o ole ance
Box 2 | A cu e model.
In a mixed popula ion o suscep ible (z=1) and non-suscep ible
(z=0) animals he p obabili y o an indi idual being s ill ali e
(censo ed) (c=0) a ime is:
P (c=0| )=P (c=0| ,z=1)P (z=1)
+P (c=0| ,z=0)P (z=0)
=P (c=0| ,z=1)P (z=1)+1−P (z=1),
whe e P (z=1)is he p io p obabili y o being suscep ible and
P (c=0| ,z=0)=1. The p obabili y o being s ill ali e o sus-
cep ible animals, P (c=0| ,z=1), is a unc ion o he endu ance
o he animal. Fu he mo e, i su i al ime is spli in o a se ies o
bina y su i al sco es (e.g., s1 o s , whe e 0 indica es su i al),
his p obabili y is:
P (c=0| ,z=1)=

j=1
P (sj=0|z=1),
whe e P (sj=0|z=1)is he p obabili y o su i ing a pe iod j,
gi en ha he animal is suscep ible. Highly endu e animals will
ha e highe p obabili ies o su i ing each sub-pe iod and hus
also highe p obabili y o su i ing un il end o ollow-up pe iod.
Pu a i e non-suscep ible animals will always su i e.
Fo animals ha die du ing he ollow up pe iod, suscep ibili y
s a us is known (z=1), while o su i ing animals he ue sus-
cep ibili y s a us is no obse able. S ill, o hese indi iduals he
p obabili y o being suscep ible can be calcula ed as:
P (z=1|c=0, )=P (c=0| ,z=1)P (z=1)
P (c=0| )
The p oposed cu e model allows o indi idual a ia ion in
bo h p io p obabili y o being suscep ible as well as in he
endu ance o suscep ible animals (Ødegå d e al., 2011b,c). A
de ailed desc ip ion o he cu e model is gi en in Ødegå d e al.
(2011c).
selec i e b eeding should ocus on suscep ibili y. This implies ha
he ollow-up pe iod should con inue un il he as majo i y o
suscep ible animals ha e died, ensu ing ha he obse ed end-
su i al la gely esembles he ac ion o non-suscep ible animals
in he popula ion.
NORMAL MIXTURE MODELS
No mal mix u e models can be used o analyze gene ics o hos
pe o mance, e.g., g ow h a e, wi hin a popula ion consis ing o
indi iduals a ec ed and una ec ed by a pa hogen, e en in he
absence o pa hogen bu den and ime-un il-dea h da a.
Fini e no mal mix u e models ha e ea lie been p oposed o
analysis o in ec ion-a ec ed, con inuously dis ibu ed pheno-
ypes, assuming ha he ue in ec ion s a uses o indi iduals
a e unknown (De illeux and Le oy, 2000; Ødegå d e al., 2003,
2005; Gianola e al., 2004). The mix u e model a emp s o iden-
i y hidden ca ego ies (e.g., non-in ec ed and in ec ed) among he
obse a ions, assuming ha he con inuous scale obse a ions
o igina e om wo no mal dis ibu ions di e ing in mean and
Box 3 | A no mal mix u e model.
In a mixed popula ion o in ec ed (z=1) and heal hy (z=0)
animals, he densi y o an obse a ion ycan be w i en as:
P(y)=P(y|z=0)P (z=0)+P(y|z=1)P (z=1).
The p obabili y o an animal being in ec ed is hus:
P (z=1|y)=P(y|z=1)P (z=1)
P(y|z=0)P (z=0)+P(y|z=1)P (z=1)·
A de ailed desc ip ion o he no mal mix u e model is gi en in
Ødegå d e al. (2003, 2005).
FIGURE 4 | An example o a wo-componen mix u e dis ibu ion.
The do ed lines a e he unobse ed dis ibu ions o non-in ec ed “heal hy”
indi iduals (70% o he obse a ion) wi h ∼N(−1.0, 1.0) and in ec ed
“diseased” indi iduals (30%) wi h ∼N(1.0, 1.0). The solid line ep esen s
he esul ing dis ibu ion o he obse ed pheno ypes. T ai alues a e gi en
on x-axis and he equencies o obse a ions on y-axis.
(po en ially) a iance (Box 3;Figu e 4). Fo ins ance, he b oile
asci es example gi en in Figu e 2 can be analyzed using a mix u e
model analysis assuming ha he hea a io has wo unde ly-
ing dis ibu ions, one o non-in ec ed and one o asci ic bi ds
(Ze ehda an e al., 2006). Ano he example o a mix u e ai is
soma ic cell sco es in milk o dai y ca le (Madsen e al., 2008).
Soma ic cell sco e is a low le el in non-in ec ed cows, bu inc ease
o high le els in cases o (unobse ed) subclinical mas i is. Hence,
he obse ed soma ic cell sco es may be iewed as a mix u e o
wo no mal dis ibu ions (non-in ec ed and mas i ic). In A lan ic
salmon Salmo sala L., diseases such as in ec ious panc eas nec o-
sis and panc eas disease can kill a ac ion o he animals, bu
may also educe subsequen g ow h o a ec ed su i o s. Hence,
a e an ou b eak, obse ed g ow h o su i o s may be iewed
as a mix u e ai depending on he indi iduals’ p e ious heal h
s a us.
Classical selec ion aims a changing a ai in he desi ed di ec-
ion. Howe e , o mix u e ai s he a ia ion is pa ly explained
by mixing o he wo (o mo e) sub-dis ibu ions wi h di e -
en means, and pa ly by a ia ion wi hin each sub-dis ibu ion
(Figu e 4). Hence, i he aim is o educe he incidence o he
in ec ion a he han al e ing he obse ed con inuous hos ai
F on ie s in Gene ics | Li es ock Genomics Decembe 2012 | Volume 3 | A icle 262 |6
Kause and Ødegå d Gene ic analysis o ole ance
i sel , simple di ec ional selec ion o he la e (e.g., o soma ic
cell sco e) may no be op imal. The mix u e model opens new
possibili ies o selec ion, and can be used o di ec ly selec o
educed in ec ion isk. Addi ionally, he ai eco ded on in ec ed
and non-in ec ed animals may be iewed as wo dis inc sub- ai s
whose gene ic a iances and hei gene ic co ela ion can be es i-
ma ed. This esembles he G ×E analysis pe o med wi h andom
eg ession models (Figu e 2) wi h he di e ence ha he mix u e
model does no ake in o accoun ha in ec ed indi iduals may
ha e di e en pa hogen bu dens.
No mal mix u e models ypically assume ha an indi id-
ual is ei he in ec ed o no , and ha in ec ion has a ce ain
e ec on he pheno ype (Figu e 4). Howe e , a ia ion in en i-
onmen al pa hogen load and in indi idual ole ance o he
in ec ion imply ha he e ec o an in ec ion may a y sub-
s an ially among indi iduals and en i onmen s. The p oposed
mix u e models may be ex ended o allow o indi idual esponses
o in ec ion (Madsen e al., 2008). Al e na i ely, he model may
be ex ended o a g ow h mix u e model (Wang and Bodne ,
2007). The g ow h mix u e models assume ha he obse a-
ions come om di e en la en ajec o ies, i.e., heal h s a us
does no only a ec he expec a ion o indi idual obse a ions,
bu also he slope o a pheno ypic ajec o y (g ow h cu es).
In ec ed and non-in ec ed animals could show di e en a-
jec o ies, wi h he non-in ec ed ones being una ec ed by he
pa hogen, while he in ec ed indi iduals being a iably a ec ed
by he pa hogen bu den. Such models may be use ul o ana-
lyze esis ance and in ec ion-a ec ed ai s obse ed on animals
wi h unknown in ec ion s a us and in en i onmen s wi h a iable
pa hogen loads.
APPLICATION OF THE METHODS IN BREEDING PROGRAMMES
Random eg ession models a e ou inely applied in a m ani-
mal b eeding p og ams, e.g., o milk es -day models in dai y
cows and o g ow h cu es (Schae e , 2004). Simila ly, andom
eg ession models can be implemen ed o selec o ole ance,
gi en sui able da a a e a ailable. The cu e model app oach o he
analysis o ime-un il-dea h da a (Vee kamp e al., 2001; Ødegå d
e al., 2011a) ha e been implemen ed in he DMU so wa e,
allowing he es ima ion o gene ic pa ame e s and b eeding al-
ues o p ac ical b eeding (Madsen and Jensen, 2010). To ou
knowledge, he cu e model has no been implemen ed in ou ine
gene ic e alua ions in any b eeding p og am. Á nason (1999)and
U ios e e al. (2007) ha e p oposed a bi a ia e linea - h eshold
model which can be used o analyze whe he an animal su -
i ed (a h eshold ai ) and how long i ook un il dea h (a
linea ai ). Such a model esembles he cu e model and is
s aigh o wa d o apply in mul i- ai b eeding alue e alua-
ions. Also he no mal mix u e model has been implemen ed
in he DMU so wa e (Madsen and Jensen, 2010), and is he e-
o e a ailable o mul i- ai gene ic e alua ions, bu o ou
knowledge, has no ye been implemen ed in ou ine gene ic
e alua ions.
The cu e model has been applied o su i al da a in aqua-
cul u e species, leading o al e ed ecommenda ions o ou ine
disease-challenge es ing (Ødegå d e al., 2011b). His o ically,
challenge es s in aquacul u e species ha e been e mina ed a
in e media e cumula i e mo ali ies o ensu e maximum a i-
a ion in bina y su i al da a. Howe e , his app oach is only
p ope gi en ha endu ance and suscep ibili y a e equi alen
ai s, which is no necessa ily he case. The cu en ad ice is o
con inue es ing un il mo ali y na u ally ceases, e en a le els
abo e 50% mo ali y (Ødegå d e al., 2011a).
So a , only a limi ed numbe o b eeding p og ams ha e con-
side ed selec ing o ole ance. Some A ican ca le b eeding p o-
g ams a e speci ically selec ing o ypano ole ance- ela ed ai s,
he ole ance being a majo b eeding objec i e ai (Hano e
e al., 2003; an de Waaij e al., 2003). In con as , ega dless
o he ex ensi e s udies conduc ed in Aus alia and New Zealand
on nema ode ole ance in sheep, a decision has been made no
o eco d and selec o ole ance because o he need o le
animals o su e and p oduc ion o be educed o ole ance
o be exp essed (Albe s e al., 1987; Bisse and Mo is, 1996;
Woolas on and Windon, 2001). The no el s a is ical me hods
and he inc easing awa eness o he de ailed physiological mech-
anisms o ole ance (Medzhi o e al., 2012)mayp o idemo e
oppo uni ies o ole ance selec ion in a m animals.
CONCLUSIONS
The ecen s a is ical de elopmen s p o ide ools o inc ease
ou unde s anding o gene ics o al e na i e s a egies o de end
agains pa asi es, pa hogens, and p oduc ion diseases. Mos o he
s a is ical me hods can be applied in b eeding alue e alua ions o
b eed o ole ance. Mo eo e , he me hods p esen ed he e p o-
ide ools o quan i y geno ype-by-pa hogen bu den in e ac ions
ha may explain a signi ican p opo ion o pheno ypic a ia ion
in ai s wi hin popula ions ha a e exposed o a ious in ec ions
and p oduc ion diseases. The ai s whose a ia ion is a ec ed
a e ypically p oduc ion ai s ha a e selec ed o in b eeding
p og ams.Tobeable ounambiguouslyselec o hegene ic
po en ial o a p oduc ion ai , he e ec s o esis ance and ol-
e ance should be sepa a ed om i . The me hods p esen ed in
his pape p o ide po en ial o cons uc mo e e ec i e b eeding
p og ams o inc ease bo h p oduc i i y and animal heal h.
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Con lic o In e es S a emen : The
au ho s decla e ha he esea ch
was conduc ed in he absence o any
comme cial o inancial ela ionships
ha could be cons ued as a po en ial
con lic o in e es .
Recei ed: 29 Ma ch 2012; accep ed: 05
No embe 2012; published online: 14
Decembe 2012.
Ci a ion: Kause A and Ødegå d J (2012)
The gene ic analysis o ole ance o in ec-
ions: a e iew. F on . Gene. 3:262. doi:
10.3389/ gene.2012.00262
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in Li es ock Genomics, a special y o
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