TECHNOLOGY REPORT
published: 20 Ma ch 2015
doi: 10.3389/ gene.2015.00109
F on ie s in Gene ics | www. on ie sin.o g 1Ma ch 2015 | Volume 6 | A icle 109
Edi ed by:
Paolo Ajmone Ma san,
Uni e si à Ca olica del Sac o Cuo e,
I aly
Re iewed by:
Da id MacHugh,
Uni e si y College Dublin, I eland
Yu i Tani U sunomiya,
Uni e sidade Es adual
Paulis a(UNESP), B azil
*Co espondence:
Ma io Ba ba o,
School o Biosciences, Ca di
Uni e si y, Si Ma in E ans Building,
Museum A enue CF10 3AX Ca di ,
UK
[email p o ec ed]
Special y sec ion:
This a icle was submi ed o
Li es ock Genomics, a sec ion o he
jou nal F on ie s in Gene ics
Recei ed: 15 No embe 2014
Accep ed: 03 Ma ch 2015
Published: 20 Ma ch 2015
Ci a ion:
Ba ba o M, O ozco- e Wengel P,
Tapio M and B u o d MW (2015)
SNeP: a ool o es ima e ends in
ecen e ec i e popula ion size
ajec o ies using genome-wide SNP
da a. F on . Gene . 6:109.
doi: 10.3389/ gene.2015.00109
SNeP: a ool o es ima e ends in
ecen e ec i e popula ion size
ajec o ies using genome-wide SNP
da a
Ma io Ba ba o1*, Pablo O ozco- e Wengel1,Miika Tapio2and Michael W. B u o d1
1School o Biosciences, Ca di Uni e si y, Ca di , UK, 2MTT Ag i ood Resea ch Finland, Bio echnology and Food Resea ch,
Jokioinen, Finland
E ec i e popula ion size (Ne) is a key popula ion gene ic pa ame e ha desc ibes he
amoun o gene ic d i in a popula ion. Es ima ing Nehas been subjec o much esea ch
o e he las 80 yea s. Me hods o es ima e Ne om linkage disequilib ium (LD) we e
de eloped ∼40 yea s ago bu depend on he a ailabili y o la ge amoun s o gene ic
ma ke da a ha only he mos ecen ad ances in DNA echnology ha e made a ailable.
He e we in oduce SNeP, a mul i h eaded ool o pe o m he es ima e o Neusing LD
using he s anda d PLINK inpu ile o ma (.ped and.map iles) o by using LD alues
calcula ed using o he so wa e. Th ough SNeP he use can apply se e al co ec ions o
ake accoun o sample size, mu a ion, phasing, and ecombina ion a e. Each a iable
in ol ed in he compu a ion such as he binning pa ame e s o he ch omosomes o
include in he analysis can be modi ied. When applied o published da ase s, SNeP
p oduced esul s closely compa able wi h hose ob ained in he o iginal s udies. The use
o SNeP o es ima e Ne ends can imp o e unde s anding o popula ion demog aphy in
he ecen pas , p o ided a su icien numbe o SNPs and hei physical posi ion in he
genome a e a ailable. Bina ies o he mos common ope a ing sys ems a e a ailable a
h ps://sou ce o ge.ne /p ojec s/snepne ends/.
Keywo ds: e ec i e popula ion size, linkage disequilib ium, SNPChip, demog aphy, la ge scale geno yping
In oduc ion
E ec i e popula ion size (Ne) is an impo an gene ic pa ame e ha es ima es he amoun o
gene ic d i in a popula ion, and has been desc ibed as he size o an idealized W igh –Fishe pop-
ula ion expec ed o yield he same alue o a gi en gene ic pa ame e as in he popula ion unde
s udy (C ow and Kimu a, 1970). Nesizes can be in luenced by luc ua ions in census popula ion
size (Nc), by he b eeding sex a io and he a iance in ep oduc i e success.
Nees ima ion can be achie ed using app oaches ha all in o h ee me hodological ca ego ies:
demog aphic, pedig ee-based, o ma ke -based (Flu y e al., 2010). Pedig ee da a ha e been a-
di ionally used o ob ain Nees ima es in li es ock. Howe e , eliable es ima es o Nedepend on
he pedig ee being comple e. This s a e o knowledge is easible in some domes ic popula ions,
he demog aphic pa ame e s o which ha e been accu a ely moni o ed o a su icien ly la ge
numbe o gene a ions. Howe e , in p ac ice, he applicabili y o his app oach emains limi ed
o a ew cases in ol ing highly managed b eeds (Flu y e al., 2010; Uima i and Tapio, 2011).
Ba ba o e al. SNeP: a ool o es ima e Ne
One solu ion o o e come he limi a ion o an incomple e
pedig ee is o es ima e he ecen end in Neusing genomic da a.
Se e al au ho s ha e ecognized ha Necould be es ima ed om
in o ma ion on linkage disequilib ium (LD) (S ed, 1971; Hill,
1981). LD desc ibes he non- andom associa ion o alleles in di -
e en loci as a unc ion o he ecombina ion a e be ween he
physical posi ions o he loci in he genome. Howe e , LD signa-
u es can also esul om demog aphic p ocesses such as admix-
u e and gene ic d i (W igh , 1943; Wang, 2005), o h ough
p ocesses such as “hi chhiking” du ing selec i e sweeps (Smi h
and Haigh, 1974) o backg ound selec ion (Cha leswo h e al.,
1997). In such scena ios alleles a di e en loci become associ-
a ed independen ly o hei p oximi y in he genome. Assuming
ha a popula ion is closed and panmic ic, he LD alue calcula ed
be ween neu al unlinked loci depends exclusi ely on gene ic
d i (S ed, 1971; Hill, 1981). This occu ence can be used o p e-
dic Nedue o he known ela ionship be ween he a iance in LD
(calcula ed using allele equencies) and e ec i e popula ion size
(Hill, 1981).
Recen ad ances in geno yping echnology (e.g., using SNP
bead a ays wi h ens o housands o DNA p obes) ha e enabled
he collec ion o as amoun s o genome-wide linkage da a ideal
o es ima ing Nein li es ock and humans among o he s (e.g.,
Tenesa e al., 2007; de Roos e al., 2008; Co bin e al., 2010; Uima i
and Tapio, 2011; Kijas e al., 2012). Howe e , a so wa e ool ha
enables es ima ion o Ne om LD is lacking, and esea che s cu -
en ly ely on a combina ion o ools o manipula e da a, in e
LD, and end o use bespoke sc ip s o pe o m he app op ia e
calcula ions and es ima e Ne.
He e we desc ibe SNeP, a so wa e ool ha allows he es ima-
ion o Ne ends ac oss gene a ion using SNP da a ha co ec s
o sample size, phasing and ecombina ion a e.
Ma e ials and Me hods
The me hod SNeP uses o calcula e LD depends on he a ailabil-
i y o phased da a. When he phase is known he use can selec
Hill and Robe son (1968) squa ed co ela ion coe icien ha
makes use o haplo ype equencies o de ine LD be ween each
pai o loci (Equa ion 1). Howe e , in he absence o a known
phase, squa ed Pea son’s p oduc -momen co ela ion coe icien
be ween pai s o loci can be selec ed. While hese wo app oaches
a e no he same, hey a e highly compa able (McE oy e al.,
2011):
2=pAB−pApB2
pA1−pApB1−pB(1)
2
X,Y=Pn
i=1Xi−XYi−Y2
Pn
i=1Xi−X2Pn
i=1Yi−Y2(2)
whe e pAand pBa e espec i ely he equencies o alleles A and
B a wo sepa a e loci (X,Y) measu ed o nindi iduals, pAB is he
equency o he haplo ype wi h alleles A and B in he popula ion
s udied, Xand Ya e he mean geno ype equencies o he i s
and second locus espec i ely, Xiis he geno ype o indi idual ia
he i s locus and Yiis he geno ype o indi idual ia he second
locus. Equa ion (2) co ela es he geno ypic allele coun s ins ead
o he haplo ype equencies and is no in luenced by double he -
e ozygo es ( his app oach esul s in he same es ima es as he -- 2
op ion in PLINK).
SNeP es ima es he his o ic e ec i e popula ion size based
on he ela ionship be ween 2,Ne, and c( ecombina ion a e),
(Equa ion 3—S ed, 1971), and enabling use s o include co -
ec ions o sample size and unce ain y o he game ic phase
(Equa ion 4—Wei and Hill, 1980):
E 2=(1+4Nec)−1(3)
2
adj = 2−(βn)−1(4)
whe e nis he numbe o indi idual sampled, β=2 when he
game ic phase is known and β=1 i ins ead he phase is no
known.
Se e al app oxima ions a e used o in e he ecombina ion
a e using he physical dis ance (δ) be ween wo loci as a e e -
ence and ansla ing i in o linkage dis ance (d), which is usually
desc ibed as Mb(δ)≈cM(d). Fo small alues o d he la e
app oxima ion is alid, bu o la ge alues o d he p obabili y o
mul iple ecombina ion e en s and in e e ence inc eases, mo e-
o e he ela ionship be ween map dis ance and ecombina ion
a e is no linea , as he maximum ecombina ion a e possible
is 0.5. Thus, unless using e y sho δ, he app oxima ion d≈
cis no ideal (Co bin e al., 2012). We he e o e implemen ed
mapping unc ions o ansla e he es ima ed din o c, ollow-
ing Haldane (1919),Kosambi (1943),S ed (1971), and S ed and
Feldman (1973). Ini ially SNeP in e s d o each pai o SNPs
as di ec ly p opo ional o δacco ding o d=kδwhe e kis a
use de ined ecombina ion a e alue (de aul alue is 10−8as in
Mb =cM). The in e ed alue o δcan hen be subjec ed o one
o he a ailable mapping unc ions i equi ed by he use .
Sol ing Equa ion (3) o Neand including all he co ec-
ions desc ibed, allows he p edic ion o Ne om LD da a using
(Co bin e al., 2012):
NT( )=4 (c )−1Eh 2
adj|c i−1−α(5)
whe e N is he e ec i e popula ion size gene a ions ago
calcula ed as =(2 (c ))−1(Hayes e al., 2003), c is he
ecombina ion a e de ined o a speci ic physical dis ance
be ween ma ke s and op ionally adjus ed wi h he mapping unc-
ions men ioned abo e, 2
adj is he LD alue adjus ed o sam-
ple size and α:={1, 2, 2.2} is a co ec ion o he occu ence o
mu a ions (Oh a and Kimu a, 1971). The e o e, LD o e g ea e
ecombinan dis ances is in o ma i e on ecen Newhile sho e
dis ances p o ide in o ma ion on mo e dis an imes in he pas .
A binning sys em is implemen ed in o de o ob ain a e aged 2
alues ha e lec LD o speci ic in e -locus dis ances. The bin-
ning sys em implemen ed uses he ollowing o mula o de ine
he minimum and maximum alues o each bin:
bmin
i=minD +(maxD −minD)bi−1
o Binsx
(6a)
bmax
i=minD +(maxD −minD)bi
o Binsx
(6b)
F on ie s in Gene ics | www. on ie sin.o g 2Ma ch 2015 | Volume 6 | A icle 109
Ba ba o e al. SNeP: a ool o es ima e Ne
Whe e bi(N1) is he i h bin o he o al numbe o bins ( o Bins),
minD, and maxD a e espec i ely he minimum and he maxi-
mum dis ance be ween SNPs and xis a posi i e eal numbe (R0)
When xequals 1, he dis ibu ion o dis ances be ween he bins is
linea and each bin has he same dis ance ange. Fo la ge alues
o x he dis ibu ion o dis ances changes allowing a la ge ange
on he las bins and a smalle ange on he i s bins. Va ying his
pa ame e allows he use o ha e a su icien numbe o pai wise
compa isons o con ibu e o he inal Nees ima e o each bin.
Example Applica ion
We es ed SNeP wi h wo published da ase s ha had been
p e iously used o desc ibe ends in Neo e ime using LD,
Bos indicus [54,436 SNPs o 423 Eas A ican Sho ho n Zebu
(SHZ)–Mbole-Ka iuki e al., 2014, da a a ailable a D yad Dig-
i al Reposi o y: doi:10.5061/d yad.bc598.] and O is a ies [49,034
SNPs geno yped in 24 Swiss Whi e Alpine (SWA), 24 Swiss Black-
B own Moun ain sheep (SBS), 24 Valais Blacknose sheep (VBS),
23 Valais Red sheep (VRS), 24 Swiss Mi o sheep (SMS) and
24 Bundne Obe lände sheep (BOS)–Bu en e al., 2014]. The
2es ima es o he ca le da ase s we e ob ained by he au ho s
using GenABLE (Aulchenko e al., 2007) using a minimum allele
equency (MAF) <0.01 and adjus ing he ecombina ion a e
using Haldane’s mapping unc ion (Haldane, 1919). The 2es i-
ma es o he sheep da a we e calcula ed by he au ho s using
PLINK-1.07 (Pu cell e al., 2007), wi h a MAF <0.05 and no u -
he co ec ions. Fo bo h au osomal da ase s 2es ima es whe e
co ec ed o sample size using equa ion (4) wi h β=2. Fo hese
compa a i e analyses he SNeP command line included he same
pa ame e s used o he published da a apa om he 2es i-
ma es, calcula ed h ough geno ype coun and he use o SNeP’s
no el binning s a egy.
Resul s
SNeP is a mul i h eaded applica ion de eloped in C++ and
bina ies o he mos common ope a ing sys ems (Windows,
OSX, and Linux) can be downloaded om h ps://sou ce
o ge.ne /p ojec s/snepne ends/. The bina ies a e accompanied
by a manual desc ibing he s ep-by-s ep use o SNeP o in e
ends in Neas desc ibed he e. SNeP p oduces an ou pu ile wi h
ab delimi ed columns showing he ollowing o each bin ha
was used o es ima e Ne: he numbe o gene a ions in he pas
ha he bin co esponds o (e.g., 50 gene a ions ago), he co e-
sponding Nees ima e, he a e age dis ance be ween each pai o
SNPs in he bin, he a e age 2and he s anda d de ia ion o 2in
he bin, and he numbe o SNPs used o calcula e 2in he bin.
This ile can be easily impo ed in Mic oso Excel, R o o he
so wa e o plo he esul s. The plo s shown he e (Figu es 1,3)
co espond o he columns o gene a ions ago and Ne om he
ou pu ile. The column wi h he 2s anda d de ia ion is p o-
ided o use s o inspec he a iance in he Nees ima e in each
bin, pa icula ly o hose bins e lec ing olde ime es ima es and
which a e less eliable as he numbe o SNPs used o es ima e 2
becomes smalle .
The o ma equi ed o he inpu iles is he s anda d PLINK
o ma (ped and map iles) (Pu cell e al., 2007). SNeP allows
he use s o ei he calcula e LD on he da a as desc ibed abo e,
o use a cus om p ecalcula ed LD ma ix o es ima e Neusing
Equa ion (5).
The so wa e in e ace allows he use o con ol all pa am-
e e s o he analysis, e.g., he dis ance ange be ween SNPs in
bp, and he se o ch omosomes used in he analysis (e.g., 20–
23). Addi ionally, SNeP includes he op ion o choose a MAF
h eshold (de aul 0.05), as i has been shown ha accoun ing o
MAF esul s in unbiased 2es ima es i espec i e o sample size
FIGURE 1 | Compa ison o Ne ends o six Swiss sheep b eeds acco ding o Bu en e al. (2014) (dashed lines) and his wo k (solid lines).
F on ie s in Gene ics | www. on ie sin.o g 3Ma ch 2015 | Volume 6 | A icle 109
Ba ba o e al. SNeP: a ool o es ima e Ne
(S ed e al., 2008). SNeP’s mul i h eaded a chi ec u e allows as
compu a ion o la ge da ase s (we es ed up o ∼100K SNPs o
a single ch omosome), o example he BOS da a desc ibed he e
was analyzed wi h one p ocesso in 2′43′′, he use o wo p o-
cesso s educed he ime o 1′43′′, ou p ocesso s educed he
analysis ime o 1′05′′.
Zebu Example
Fo he zebu analysis, he shapes o he Necu es ob ained wi h
SNeP and hei published da a ends showed he same ajec-
o y wi h a smoo h decline un il a ound 150 gene a ions ago,
ollowed by an expansion wi h a peak a ound 40 gene a ions ago
and ending in a s eep decline on he mos ecen gene a ions
(Figu e 1). Howe e , while he ends in bo h cu es we e he
same, he wo app oaches esul ed in di e en Nees ima es, wi h
SNeP’s alues being app oxima ely h ee- old la ge han hose
in he o iginal pape . While we a emp ed o use he au ho s’
pa ame e s in ou analyses, some di e ences we e ine i able, i.e.,
he o iginal publica ion o he ca le da a es ima ed 2wi h a
di e en app oach o ha implemen ed in SNeP. Analyses wi h
SNeP we e based on geno ypes, while he o iginal analysis was
based on in e ed wo locus haplo ypes, which esul s in he
published da a showing an expec ed 2o 0.32 a he minimum
dis ance, while ou es ima es was 0.23. Simila ly, Mbole-Ka iuki
e al. (2014) ob ained a backg ound le el 2=0.013 a ound 2
Mb, while ou es ima e a he same dis ance was 0.0035 (da a no
shown). Consequen ly, as ou es ima es o LD we e consis en ly
smalle han Mbole-Ka iuki e al. (2014) i is expec ed ha ou
Nees ima es should be la ge . While his obse a ion highligh s
he impo ance o a ca e ul choice o he pa ame e s and hei
h esholds, i is impo an o highligh ha al hough he abso-
lu e magni ude o he Ne alues is di e en , he ends a e almos
iden ical.
Swiss Sheep Example
The six Swiss sheep b eeds analyzed wi h SNeP p oduced compa-
able esul s wi h hose om he o iginal pape (Figu e 2), wi h
mos ly o e lapping Ne end cu es (Figu e 3). Howe e , he
gene al end in Neshowed a decline owa d he p esen . SNeP
p oduced sligh ly la ge alues o Ne o he mo e dis an pas
(700–800 gene a ions). This is due o he di e en binning sys em
FIGURE 2 | Compa ison be ween ecen Ne alues calcula ed a he
29 h gene a ion in his wo k and Bu en e al. (2014) o six Swiss
sheep b eeds.
used in SNeP, which allows he use o ob ain a mo e e en dis i-
bu ion o pai wise compa isons wi hin each bin (i.e., he numbe
o SNP pai wise compa isons wi hin each bin is compa able). Fo
he ime span ex ending beyond 400 gene a ions ago, Bu en e al.
(2014) used only h ee bins in hei analysis (cen e ed a 400, 667,
and 2000 gene a ions ago) while o he same ime span SNeP
used 5 bins wi h a numbe o pai wise compa isons dependen o
he ange de ined wi h o mulae 6a,b. Consequen ly, Bu en and
colleagues’ app oach ends wi h a highe densi y o da a desc ib-
ing he mos ecen gene a ions han desc ibing he oldes gen-
e a ions. The e o e, he use o ewe bins ends o inc ease he
p esence o smalle alues o Nein each bin, consequen ly lowe -
ing he a e age Ne alue o each bin. The Ne alues o he ecen
pas , compa ed a he 29 h gene a ion in he pas , ga e e y sim-
ila esul s. The la ges di e ence (50) was ob ained o he SBS
b eed.
Discussion
Analysis o Neusing LD da a was i s demons a ed 40 yea s ago,
and has been applied, de eloped and imp o ed since (S ed, 1971;
Hayes e al., 2003; Tenesa e al., 2007; de Roos e al., 2008; Co bin
e al., 2012; S ed e al., 2013). The adi ionally small numbe o
SNPs analyzed is no longe a limi a ion, since SNP Chips com-
p ise an ex emely la ge numbe o SNPs, a ailable in a sho
ime and a a easonable p ice. This has boos ed he use o he
me hod, which has been applied o humans (Tenesa e al., 2007;
McE oy e al., 2011) as well as o se e al domes ica ed species
(England e al., 2006; Uima i and Tapio, 2011; Co bin e al., 2012;
Kijas e al., 2012). Along wi h hese imp o emen s, me hodolog-
ical limi a ions ha e become appa en and ha e been add essed
he e, wi h he majo i y o he e o s poin ing o he co ec es i-
ma ion o ecen Ne. Ye , he quan i a i e alue o he es ima e
is highly dependen on sample size, he ype o LD es ima ion
and he binning p ocess (Waples and Do, 2008; Co bin e al.,
2012), while i s quali a i e pa e n depends mo e on he gene ic
in o ma ion han on da a manipula ion.
So a his me hod has been applied using a a ie y o so wa e,
no s anda dized app oach exis s o bin he esul s and each s udy
has applied a mo e o less a bi a y app oach, e.g., binning o
gene a ion classes in he pas (Co bin e al., 2012), binning o
dis ance classes wi h a cons an ange o each bin (Kijas e al.,
2012) o binning pe dis ance classes in a linea ashion bu wi h
la ge bins o he mo e ecen ime poin s (Bu en e al., 2014).
To ou knowledge he only so wa e a ailable ha es ima e Ne
h ough LD is NeEs ima o (Do e al., 2014), an upg aded e -
sion o he o me LDNE (Waples and Do, 2008) allowing he
analysis o la ge da ase (as 50k SNPChip). Impo an ly, while
SNeP ocuses on es ima ing his o ical Ne ends, NeEs ima o ’s
aim is o p oduce con empo a y unbiased Nees ima es, he la -
e should he e o e be conside ed as a complemen a y ool while
in es iga ing demog aphy h ough LD.
We used SNeP o analyze wo da ase s whe e he me hod
was p e iously applied. The esul s we ob ained o he sheep
da a we e bo h quan i a i ely and quali a i ely compa able wi h
hose ob ained by Bu en e al. (2014), while o he Zebu da a
we ob ained a Ne end es ima e ha closely ma ched ha o
F on ie s in Gene ics | www. on ie sin.o g 4Ma ch 2015 | Volume 6 | A icle 109
Ba ba o e al. SNeP: a ool o es ima e Ne
FIGURE 3 | Compa ison o Ne ends o he las 250 gene a ions in he SHZ da a ob ained by Mbole-Ka iuki e al. (2014) (dashed line) and using SNeP
(solid line).
Mbole-Ka iuki e al. (2014) al hough ou poin es ima es o Ne
we e la ge han hose desc ibed o he da a (Mbole-Ka iuki
e al., 2014). The disc epancy be ween hese wo esul s e lec s
ha Bu en and colleagues p oduced hei 2es ima es using
PLINK ( he s anda d so wa e o la ge scale SNP da a manip-
ula ion) which uses he same app oach used o es ima e 2by
SNeP, while Mbole-Ka iuki e al. ollowed Hao e al. (2007) o
2es ima ion. The use o di e en es ima es o LD is c i ical
o he quan i a i e aspec o he Necu e, whe e due o he
hype bolic co ela ion be ween Neand 2, a dec ease in 2on
i s ange close o 0 can lead o a e y la ge change in Nees i-
ma es, while di e ences in es ima es a e less signi ican when
he 2 alue is high, i.e., close o 1. The e o e, al hough in
one o he da ase s he Ne alues whe e subs an ially di e en ,
in bo h cases he Necu es o e lapped wi h hose o iginally
published.
As al eady sugges ed by o he au ho s, he eliabili y o he
quan i a i e es ima es ob ained wi h his me hod mus be aken
wi h cau ion, especially o Ne alues ela ed o he mos ecen
and he oldes gene a ions (Co bin e al., 2012) because o ecen
gene a ions, la ge alues o ca e in ol ed, no i ing he heo-
e ical implica ions ha Hayes p oposed o es ima e a a iable
Neo e ime (Hayes e al., 2003). Es ima es o he oldes gen-
e a ions migh also be un eliable as coalescen heo y shows ha
no SNP can be eliably sampled a e 4Negene a ions in he pas
(Co bin e al., 2012). Fu he , Nees ima es, and especially hose
ela ed o gene a ions u he in he pas , a e s ongly a ec ed by
da a manipula ion ac o s, such as he choice o MAF and alpha
alues. Addi ionally, he binning s a egy applied can in e e e
wi h he gene al p ecision o he me hod, o example whe e an
insu icien numbe o pai wise compa isons a e used o popula e
each bin.
One o he applica ions o me hod is o compa e b eed
demog aphies. In his case he shape o he Necu es would be
he op imal ool o di e en ia e di e en demog aphic his o ies,
mo e han hei nume ical alues, by using hem as a po en ial
demog aphic inge p in o ha b eed o species, ye aking in o
conside a ion ha mu a ion, mig a ion, and selec ion can in lu-
ence he Nees ima ion h ough LD (Waples and Do, 2010). Addi-
ionally, ca e ul conside a ion o he da a analyzed wi h SNeP
(and o he so wa e o es ima e Ne) is e y impo an , as he p es-
ence o con ounding ac o s such as admix u e, may esul in
biased es ima es o Ne(O ozco- e Wengel and B u o d, 2014).
The aim o SNeP is he e o e o p o ide a as and eliable ool
o apply LD me hods o es ima e Neusing high h oughpu geno-
ypic da a in a mo e consis en way. I allows wo di e en 2
es ima ion app oaches plus he op ion o using 2es ima es om
ex e nal so wa e. The use o SNeP does no o e come he limi s
o he me hod and he heo y behind i , ye i allows he use o
apply he heo y using all co ec ions sugges ed o da e.
F on ie s in Gene ics | www. on ie sin.o g 5Ma ch 2015 | Volume 6 | A icle 109

Ba ba o e al. SNeP: a ool o es ima e Ne
Au ho Con ibu ions
MB concei ed and w o e he so wa e and he manusc ip . MB,
MT, and PO W es ed he so wa e and pe o med he analy-
ses. MT, PO W, and MWB e ised he manusc ip . All au ho s
app o ed he inal manusc ip .
Acknowledgmen s
We hank Ch is ine Flu y o p o iding he sheep da a and o
use ul discussion. We also hank he wo e iewe s o use ul
sugges ions o imp o e his pape . MB was suppo ed by he
p og am Mas e and Back (Regione Sa degna).
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Con lic o In e es S a emen : The au ho s decla e ha he esea ch was con-
duc 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 .
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