RESEARCH ARTICLE Open Access
Can numbe and size o o sp ing inc ease
simul aneously? - a cen al li e-his o y ade-o
econside ed
Ee o Sch ode us
1*
, Minna Koi ula
2
, Esa Koskela
3
, Tapio Mappes
1
, Tuula A Oksanen
1
and Tanja Poikonen
1
Abs ac
Backg ound: To maximize hei i ness, pa en s a e assumed o alloca e hei esou ces op imally be ween numbe
and size o o sp ing. Al hough his undamen al li e-his o y ade-o has been subjec o long s anding in e es , i s
gene ic basis, especially in wild mammals, s ill emains un esol ed. One impo an eason o his p oblem is ha a
la ge mul igene a ional pedig ee is equi ed o conduc a eliable analysis o his ade-o .
Resul s: We used he REML-animal model o es ima e gene ic pa ame e s o li e size and indi idual bi h size o
a common Palea c ic small mammal, he bank ole (Myodes gla eolus). E en hough a pheno ypic ade-o
be ween o sp ing numbe and size was e iden , i was no explained by a gene ic ade-o , bu a he by
nega i e co ela ions in pe manen and empo a y en i onmen al e ec s. In ac , e en posi i e gene ic co ela ions
we e es ima ed be ween di ec gene ic e ec s o o sp ing numbe and size indica ing ha gene ic a ia ion in
hese wo ai s is no necessa ily an agonis ic in mammals.
Conclusions: Ou esul s ha e no able implica ions o he s udy o he li e-his o y ade-o be ween o sp ing
numbe and size in mammals. The es ima ed gene ic co ela ions sugges ha e olu ion o o sp ing numbe and
size in poly ocous mammals is no cons ained by he ade-o caused by an agonis ic selec ion esponses pe se,
bu a he by he opposing co ela i e selec ion esponses in di ec and ma e nal gene ic e ec s o bi h size.
Keywo ds: Myodes gla eolus, Li e size, Bi h size, Gene ic co ela ion, He i abili y
Backg ound
Fi ness is de e mined by he numbe o o sp ing ha
ep oduce success ully. The p obabili y o o sp ing o
ep oduce in ime can be inc eased wi h a la ge in es -
men pe o sp ing, which ine i ably dec eases o sp ing
numbe [1]. This undamen al li e-his o y ade-o
be ween o sp ing numbe and quali y (which is mos
commonly measu ed as body size) is de i ed om he
alloca ion o limi ed pa en al esou ces du ing a single
ep oduc i e a emp , such as ene gy and abdominal
space [2]. Mo eo e , o sp ing size can be cons ained
by pel ic size and shape [3,4]. I is c ucial o ecognize
whe he his pheno ypic ade-o be ween o sp ing
numbe and size is due o a nega i e gene ic co ela ion,
since ha would cons ain he sho e m e olu ion o
hese cen al li e-his o y ai s. In heo y, gene ic co e-
la ions be ween li e-his o y ai s a e expec ed o be
nega i e [5], howe e , hey ha e equen ly been es i-
ma ed as posi i e [6].
A nega i e gene ic co ela ion be ween o sp ing num-
be and size has been epo ed in o ipa ous e eb a es
( ish [7,8], ep iles [9,10] and bi ds [11]). In con as o
hese axa in which o sp ing (egg) size is pu ely a
ma e nal cha ac e , in mammals, he de e mina ion o
he o sp ing size is mo e complica ed. O sp ing bi h
size in mammals is in luenced by bo h he pheno ype o
he mo he (ma e nal e ec s) and genes o he o sp ing.
Ma e nal e ec s o bi h size co e nume ous ac o s
ha in luence nu ien supply o he oe us (such as
u e ine capaci y and blood low) and a e expec ed o
ha e a subs an ial e ec on o sp ing bi h size [12,13].
Ma e nal e ec s hemsel es can be he i able o
* Co espondence: [email p o ec ed]i
1
Cen e o Excellence in E olu iona y Resea ch, Depa men o Biological and
En i onmen al Science, Uni e si y o Jy äskylä, P.O. Box 35, FI-40014
Jy äskylä, Finland
Full lis o au ho in o ma ion is a ailable a he end o he a icle
Sch ode us e al.BMC E olu iona y Biology 2012, 12:44
h p://www.biomedcen al.com/1471-2148/12/44
© 2012 Sch ode us e al; licensee BioMed Cen al L d. This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e
Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/2.0), which pe mi s un es ic ed use, dis ibu ion, and
ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
en i onmen ally induced; he la e can ei he in luence
a single ep oduc i e e en o span o e se e al ep o-
duc i e bou s [14]. Fu he mo e, ma e nal gene ic e ec s
can inc ease o dec ease he po en ial o popula ions o
espond o selec ion on o sp ing size depending on he
co ela ion be ween di ec and ma e nal gene ic e ec s
[15,16]. A la ge di ec gene ic e ec (genes in he o -
sp ing) on bi h size would dec ease he ma e nal lex-
ibili y in esou ce alloca ion be ween he numbe and
size o he o sp ing in mammals. Thus, when es ima ing
gene ic pa ame e s i is impo an o use indi idual
eco ds o bi h size ai s, oge he wi h he modelling
o di ec and ma e nal gene ic e ec s [17]. Howe e ,
his causes he ade-o a he gene ic le el o be
di ided in o co ela ions be ween o sp ing numbe and
wo sepa a e gene ic e ec s (di ec and ma e nal) o
bi h size, which makes he es ima ion and in e p e a-
ion o he esul s challenging. Gi en he complexi y o
his o sp ing numbe -o sp ing size ade-o in mam-
mals, i is no su p ising ha only a ew s udies ha e
a emp ed o de e mine he gene ic basis o he num-
be -size ade-o in mammals [14,18,19].
As a li e bea ing small mammal, he bank ole
(Myodes gla eolus) is ideally sui ed o he s udy o he
o sp ing size-numbe ade-o . Bank oles can be b ed
in ensi ely in he labo a o y which allows o he collec-
ion o a deep and la ge pedig ee, which is necessa y o
e icien ly s udy ma e nal gene ic e ec s [20]. A com-
mon ga den expe imen also a oids complica ions in he
es ima ion o he gene ic pa ame e s c ea ed by en i on-
men al he e ogenei y [21,22]. The use o he animal
model ensu es ha es ima ed gene ic pa ame e s e e
o a wild caugh base popula ion. The animal model is a
lexible me hod o es ima e a iance componen s due o
di e en sou ces wi hou he need o complica ed
b eeding designs. I u ilizes all he in o ma ion om he
pedig ee, akes selec ion in o accoun and, unde he
in ini esimal model, gi es unbiased es ima es o he base
popula ion [20].
He e we epo , o he bes o ou knowledge, he i s
es ima ion o he gene ic co ela ion be ween o sp ing
numbe and indi idual o sp ing size in a poly ocous
wild species. Ou analysis is based on a la ge (o e 10
000 animals) pedig eed labo a o y colony ounded by
wild-caugh bank oles. I shows how di ec , ma e nal
gene ic and en i onmen al e ec s con ibu e o he phe-
no ypic ade-o be ween o sp ing numbe and size a
bi h in small mammals.
Me hods
S udy species and da a eco ding
The bank ole is a common mammalian species in he
Palea c ic egion [23]. In cen al Finland, emales p o-
duce up o ou li e s o 1-9 pups du ing he b eeding
season, and he e is subs an ial a ia ion in bo h li e
size and o sp ing size bo h among emales and be ween
li e s o he same emale [24]. Bo h he numbe and he
size o o sp ing a bi h a e impo an i ness compo-
nen s. The size o o sp ing indica es quali y, as i co e-
la es posi i ely wi h su i al and b eeding success
[19,25,26], while li e size is adjus ed o en i onmen al
condi ions and is subjec o balancing selec ion
[25,27,28].
A labo a o y popula ion was es ablished om wild
indi iduals cap u ed in Konne esi, cen al Finland, du -
ing he summe o 2000 and subjec ed o a i icial selec-
ion owa d small and la ge li e sizes. Selec ion lines
we e ounded om 150 emales and 116 males. Bo h
lines we e pooled oge he in he analysis. All ounde
males we e wild-caugh , while some o he “ ounde ”
emales we e labo a o y-bo n o sp ing o wild- apped
indi iduals (and hus had known pa en s). The selec ion
p ocedu e was a combina ion o be ween- and wi hin-
amily selec ions. Li e size eco ds we e collec ed om
gene a ions 1-5 and bi h size eco ds we e aken om
gene a ions 2-6. 1025, 874, 863 and 83 emales had 1, 2,
3 and 4 li e s espec i ely.
Animals we e housed in s anda d mouse cages and
main ained in a 16 L:8D pho ope iod a 20 ± 2°C.
Wood sha ings and hay we e p o ided as bedding, while
ood (lab o 36, Lac amin AB, S ockholm, Sweden) and
wa e we e a ailable ad libi um. P egnan emales we e
checked once a day o pa u i ion. A e pa u i ion,
he bi h size was measu ed using an elec onic scale (±
0.01 g) and head wid h wi h a s e eomic oscope.
The use o he animals adhe ed o e hical guidelines
o animal esea ch in Finland (The Finnish Ac on Ani-
mal Expe imen a ion, 62/2006) as well as he ins i u-
ional guidelines. The s udy was conduc ed unde
pe missions om he Na ional Animal Expe imen
Boa d.
S a is ical analysis
S a is ical signi icance o ixed ac o s was ini ially s u-
died wi h uni a ia e models using SPSS s a is ical so -
wa e ( e sion 18.0). All andom e ec s we e excluded
excep o he esidual and ‘indi idual’ o he li e size.
Fixed e ec s i ed o he bi h mass we e he numbe
o pa i y ( ou classes) and sex ( wo classes); o head
wid h, he ac o s we e sex and measu e ( en classes);
o li e size, he ac o s we e pa i y, age (in days)
nes ed as a linea co a ia e wi hin he pa i y. Al e na-
i elyin heuni a ia eanalysis, hesizeo hebi hli -
e was used as a co a ia e o bi h mass and head
wid h o es ima e a iance componen s a e he e ec
o li e size was emo ed. The e ec o inb eeding on
he s udied ai s was ound o be s a is ically non-
signi ican .
Sch ode us e al.BMC E olu iona y Biology 2012, 12:44
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Page 2 o 7
The (co) a iance componen s we e es ima ed wi h he
a e age in o ma ion Res ic ed Maximum Likelihood
(REML) -p ocedu e using ASReml e sion 2.0 [29,30].
The ollowing linea models we e used:
Bi h mass and head wid h:
y1=X1b1+Z1a1+Mm +Nn +Lc +e1
Li e size:
y2=X2b2+Z2a2+Qq +e2
In which y
1
and y
2
a e he ec o s o pheno ypic
obse a ions o bi h mass/head wid h and li e size;
b
1
and b
2
a e he ec o s o ixed e ec s o bi h size
and li e size; a
1
,a
2
and ma e he ec o s o di ec
addi i e gene ic e ec s o bi h size, li e size and
ma e nal addi i e gene ic e ec s o bi h size; nand q
a e he ec o s o ma e nal pe manen e ec s o bi h
size (non-gene ically de e mined e ec s ha he mo he
has on all he o sp ing in all li e s) and pe manen
indi idual e ec s o li e size (non-gene ic e ec on
sizes o all li e s o one emale); cand ka e he ec o s
o li e e ec s o bi h size (en i onmen al e ec com-
mon o all he o sp ing in one li e ) and empo a y
en i onmen al e ec o li e size (desc ibed la e );
inally, e
1
and e
2
a e he ec o s o esiduals o bi h
size and li e size espec i ely. Fixed and andom e ec s
a e i ed o indi idual eco ds by incidence ma ices X
1
,
X
2
,Z
1,
Z
2,
M, N, Q,Land K.
Ey1
y2=X1b1
X2b2and he expec a ions o andom
e ec s a e ze o.
Va iances and co a iances:
Va
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
a1
a2
m
n
q
c
k
e1
e2
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
Aσ2
a1Aσa2Aσa1m0 0 0000
Aσa1a2Aσ2
a2Aσa2m0 0 0000
Aσa1mAσa2mAσ2
m0 0 0000
000Iσ2
nIσnq 0000
000Iσnq Iσ2
q0000
00000Iσ2
cIσck 00
00000Iσck Iσ2
k00
0000000Iσ2
e10
0 0 0 0 0 000Iσ2
e2
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
In which Aand Ia e he nume a o ela ionship
ma ix and iden i y ma ix espec i ely. s
2a1
,s
2a2
and
s
2m
a e he di ec addi i e gene ic a iance o bi h
size and li e size and ma e nal addi i e gene ic a -
iance o bi h size; s
2n
and s
2q
a e he pe manen
en i onmen al ma e nal a iance o bi h size and pe -
manen indi idual a iance o li e size; s
2c
and s
2k
a e he common li e a iance o bi h size and em-
po a y en i onmen al a iance o li e size; s
2e1
and
s
2e2
a e he esidual a iances o he bi h size ai
and li e size. s
a1a2
,s
a1m
and s
a2m
a e he addi i e
gene ic co a iances be ween co esponding gene ic
e ec s; s
nq
is he co a iance be ween pe manen ma e -
nal e ec s o bi h size and pe manen indi idual
e ec s o li e size; s
ck
is he co a iance be ween com-
mon li e e ec s o bi h size and he empo a y en i -
onmen al e ec o li e size. In he uni a ia e models,
di ec -ma e nal gene ic co a iance o bi h size ai s
was se o ze o because models including co a iance did
no con e ge. In he bi a ia e analysis, he esidual co -
a iance was se o ze o because he da ase was com-
posed o wo sepa a e pa s: one con aining eco ds o
li e size and he o he o bi h mass and head wid h.
Howe e , due o he unc ional ela ionship be ween li -
e size and o sp ing size, esidual a ia ion in he o -
me is p esumably co ela ed wi h he common li e
en i onmen o he la e . Fo ha eason, ac ual esi-
dual a iance o li e size was ixed o 0.01, and a
dummy ‘ empo a y en i onmen al e ec ’was i ed o
li e size in he bi a ia e models which was hen
allowed o co ela e wi h he i ed li e e ec o o -
sp ing. Wi hou his empo a y en i onmen al e ec o
li e size, he co ela ion be ween pe manen en i on-
men al e ec s ended o con e ge ou side he pa ame e
space.
Es ima es o he a ios o a iance componen s o he
o al pheno ypic a iance we e calcula ed as: (he i abil-
i y) h
2
= Va/Vp; (ma e nal he i abili y) m
2
=Vm/Vp;
(ma e nal pe manen en i onmen al e ec ) n
2
= Vn/Vp;
(common li e e ec ) c
2
= Vc/Vp; (pe manen indi i-
dual e ec ) q
2
= Vq/Vp, in which he o al pheno ypic
a iance (Vp) was de e mined as a sum o he app op i-
a e (co) a iance componen s.
S a is ical signi icance o he gene ic and en i onmen-
al co a iances was assessed wi h Log Likelihood a io
es sbycompa inga ullmodelwi hamodelinwhich
es ed co a iance was cons ained o ze o.
Resul s
The e was la ge a ia ion in bo h o sp ing numbe and
o sp ing size (body mass and head wid h) a bi h. The
coe icien o a ia ion was la ges in he li e size and
lowes in he head wid h a bi h (Table 1). The a e age
li e size and o sp ing bi h mass o he s udy popula-
ion we e close o alues we ha e ea lie obse ed in
na u e (5.3 pups, 1.76 g) [24]. Pheno ypic co ela ions
be ween li e size and mean o sp ing bi h size we e
Table 1 Numbe o obse a ions (n), ai means (± SD),
coe icien s o a ia ion (CV) and ange
T ai n Mean CV Range
Bi h mass (g) 10986 1.89 ± 0.22 0.11 0.84-3.28
Head wid h (mm) 10971 8.22 ± 0.38 0.05 5.78-10.56
Li e size 2665 4.48 ± 1.53 0.34 1-9
Sch ode us e al.BMC E olu iona y Biology 2012, 12:44
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Page 3 o 7
mode a ely nega i e (bi h mass = -0.46, P< 0.001;
bi h head wid h = -0.35, P< 0.001) and simila o
es ima es om a na u al popula ion (-0.41 and -0.38
espec i ely) [19].
Es ima es o di ec he i abili y (h
2
) om he uni a ia e
models we e low: 0.10 ± 0.03 o li e size, 0.08 ± 0.03
o bi h mass and 0.07 ± 0.03 o bi h head wid h
(Tables 2, 3 and 4 espec i ely). The pe manen indi i-
dual e ec (q
2
) o li e size was 0.14 ± 0.03. The li e
e ec (c
2
) explained app oxima ely hal o he pheno y-
pic a iance in he bi h size. Ma e nal he i abili ies
(m
2
) we e 0.09 ± 0.03 o bi h mass and 0.03 ± 0.02 o
bi h head wid h. Pe manen ma e nal e ec s (n
2
)we e
0.08 ± 0.03 o bi h mass and 0.06 ± 0.02 o bi h
head wid h, while li e e ec s we e 0.45 ± 0.02 and 0.49
± 0.02, espec i ely. Adjus ing he bi h mass and head
wid h o size o he bi h li e dec eased o al pheno y-
pic a iance by 19% in he bi h mass and 13% in he
bi h head wid h. The a iance due o a common li e
and ma e nal pe manen en i onmen dec eased wi h
he adjus men , whe eas di ec gene ic a iance
inc eased. When bi h mass and head wid h we e ana-
lyzed in bi a ia e models wi h li e size, he e we e only
mino di e ences in a iance componen s compa ed o
hose de i ed om uni a ia e models.
Di ec gene ic co ela ions be ween li e size and
bi h size ai s we e posi i e (bi h mass 0.54 ± 0.23;
bi h head wid h 0.47 ± 0.26), whe eas he co ela ions
be ween di ec gene ic e ec s o li e size and ma e nal
gene ic e ec s o bi h size we e nega i e (bi h mass
-0.30 ± 0.23; bi h head wid h -0.47 ± 0.38) (Table 5).
The la e we e s a is ically non-signi ican . Co ela ions
be ween di ec and ma e nal gene ic e ec s in bo h he
bi h mass and head wid h we e weakly posi i e (0.04 ±
0.32 and 0.34 ± 0.76) bu s a is ically non-signi ican .
In bo h bi h size ai s, he empo a y en i onmen al
co ela ions be ween li e size and bi h size ai s we e
signi ican ly nega i e (Table 5). The co ela ion be ween
pe manen indi idual and ma e nal e ec s was -0.35 ±
0.17 be ween li e size and bi h mass and -0.44 ± 0.17
be ween li e size and bi h head wid h. The co ela-
ions be ween he empo a y en i onmen al e ec o
li e size and li e e ec s o bi h size we e -0.67 ±
0.02 and -0.52 ± 0.02 espec i ely.
Discussion
In his s udy, we quan i ied he gene ic basis o a unda-
men al li e-his o y ade-o be ween o sp ing numbe
and size. This is essen ial, as unde s anding he ela i e
in luence o gene ic e sus en i onmen al causes behind
his impo an pheno ypic ade-o is necessa y o p e-
dic ing he s eng h and di ec ion o e olu ion. By using
a su icien ly deep pedig ee, we ound ha he
Table 2 Es ima ed a iance componen s, he i abili ies
(h
2
) and pe manen animal e ec s (q
2
) o li e size
(S anda d e o )
Uni a ia e Bi a ia e
Wi h bi h mass Wi h bi h head wid h
Vp 2.011 (0.059) 2.013 (0.059) 2.011 (0.059)
Va 0.193 (0.055) 0.194 (0.054) 0.194 (0.054)
Vq 0.279 (0.062) 0.274 (0.061) 0.270 (0.061)
h
2
0.10 (0.03) 0.10 (0.03) 0.10 (0.03)
q
2
0.14 (0.03) 0.14 (0.03) 0.13 (0.03)
Vp = pheno ypic a iance; Va = addi i e gene ic a iance; Vq = pe manen
indi idual e ec a iance
Table 3 Es ima ed a iance componen s, he i abili ies
(h
2
), common li e e ec s (c
2
), ma e nal he i abili ies
(m
2
) and pe manen ma e nal e ec s (n
2
) o bi h mass
(S anda d e o )
Uni a ia e Bi a ia e
No adjus ed o li e size Adjus ed o
li e size
(wi h li e size)
Vp 0.054 (0.001) 0.044 (0.001) 0.055 (0.001)
Va 0.004 (0.002) 0.005 (0.002) 0.005 (0.002)
Vm 0.005 (0.002) 0.005 (0.001) 0.004 (0.002)
Vc 0.024 (0.001) 0.014 (0.001) 0.025 (0.001)
Vn 0.004 (0.001) 0.004 (0.001) 0.004 (0.001)
h
2
0.08 (0.03) 0.11 (0.03) 0.09 (0.03)
c
2
0.45 (0.02) 0.32 (0.02) 0.44 (0.02)
m
2
0.09 (0.03) 0.11 (0.03) 0.08 (0.03)
n
2
0.08 (0.03) 0.08 (0.03) 0.08 (0.03)
Vp = pheno ypic a iance; Va = addi i e gene ic a iance; Vc = common li e
a iance; Vm = ma e nal gene ic a iance; Vn = ma e nal pe manen
en i onmen al a iance
Table 4 Es ima ed a iance componen s, he i abili ies
(h
2
), common li e e ec s (c
2
), ma e nal he i abili ies
(m
2
) and pe manen ma e nal e ec s (n
2
) o head wid h
a bi h (S anda d e o ).
Uni a ia e Bi a ia e
No adjus ed o li e
size
Adjus ed o li e
size
(wi h li e
size)
Vp 0.134 (0.003) 0.117 (0.003) 0.137 (0.003)
Va 0.010 (0.004) 0.013 (0.004) 0.010 (0.005)
Vm 0.005 (0.003) 0.005 (0.003) 0.003 (0.004)
Vc 0.066 (0.003) 0.050 (0.002) 0.068 (0.003)
Vn 0.008 (0.003) 0.005 (0.003) 0.009 (0.003)
h
2
0.07 (0.03) 0.11 (0.03) 0.07 (0.03)
c
2
0.49 (0.02) 0.43 (0.02) 0.49 (0.02)
m
2
0.03 (0.02) 0.04 (0.02) 0.02 (0.03)
n
2
0.06 (0.02) 0.04 (0.02) 0.06 (0.02)
Vp = pheno ypic a iance; Va = addi i e gene ic a iance; Vc = common li e
a iance; Vm = ma e nal gene ic a iance; Vn = ma e nal pe manen
en i onmen al a iance
Sch ode us e al.BMC E olu iona y Biology 2012, 12:44
h p://www.biomedcen al.com/1471-2148/12/44
Page 4 o 7
pheno ypic ade-o be ween o sp ing numbe and size
in he bank ole was due o en i onmen al e ec s a he
han addi i e gene ic e ec s. Ou esul s emphasize ha
despi e being unc ionally bound o a pheno ypic ade-
o , he common gene ic basis o li e size and bi h
size is comp ised o an agonis ic as well as pa allel
gene ic a ia ion.
He i abili y o li e size
The he i abili y o li e size was low, bu simila o es i-
ma es o h
2
in o he poly ocous mammals [31-35]. This
is expec ed since li e size is a composi e ai , wi h
o ula ion a e se ing he maximum alue, while he
numbe o o sp ing is u he in luenced by e iliza ion,
implan a ion and emb yonic mo ali y. I espec i e o
he unde lying gene ic componen o li e size, hese
e ec s add en i onmen al a ia ion o he o al pheno y-
pic a ia ion in li e size. Indeed, he he i abili y o he
o ula ion a e is g ea e han he he i abili y o li e
size in se e al e eb a es (swine [36] and mice [37]).
P e ious es ima es o li e size he i abili y in bank oles
we e subs an ially o e es ima ed [19], mos likely
because o he smalle sample size and me hods used (i.
e. mo he -daugh e eg ession). He i abili y es ima es
based on mo he -daugh e eg ession can be ou imes
la ge han animal model es ima es o h
2
[33].
Sou ces o a ia ion in o sp ing size a bi h
Di ec gene ic e ec s ha desc ibe he gene ic po en ial
o a oe us o g ow and abso b nu ien s h ough he
placen a explained 7-8% o he pheno ypic a ia ion in
bo h bi h size ai s. These alues a e compa able o
es ima es o h
2
epo ed o bi h size in o he mammals
[14,17,38]. Bi h size is expec ed o be la gely de e -
mined by ma e nal e ec s, and, including a li e e ec ,
he o e all combina ion o ma e nal e ec s accoun ed
o 58-62% o pheno ypic a ia ion. Howe e , only a
small p opo ion o ma e nal e ec s was explained by
addi i e gene ic e ec s, since he ma e nal he i abili y
was only 9% in bi h mass and 3% in bi h head wid h.
This is a bi su p ising as selec ion is less e icien on
ma e nal gene ic e ec s compa ed o di ec gene ic
e ec s [39]. Adjus ing bi h size o na al li e size
educed he a iance explained by he li e e ec and
pe manen ma e nal e ec . This esul was expec ed
since he low he i abili y o li e size indica es ha he
a ia ion in li e size was mainly due o en i onmen al
ac o s; emo ing he e ec o li e size on bi h size
should he e o e dec ease he amoun o en i onmen al
a ia ion in bi h size. Mo eo e , when adjus ed o
na al li e size, mo e a ia ion was emo ed om bi h
mass han om bi h head wid h. This demons a es he
mo e subs an ial ade-o be ween li e size and bi h
mass as was obse ed al eady om he pheno ypic
co ela ions.
Gene ic basis o esou ce alloca ion be ween o sp ing
numbe and size
Ou es ima ion o co- a ia ion be ween di e en gene ic
and en i onmen al e ec s showed only weak suppo o
a gene ic ade-o be ween li e size and o sp ing size.
The gene ic co ela ion be ween li e size and di ec
gene ic e ec s o bi h size was posi i e, which indi-
ca es ha he genes ha inc ease emale li e size end
o also enhance ha indi idual’s size a bi h. P e ious
epo s o a nega i e gene ic co ela ion be ween li e
size and mean o sp ing bi h size in a bank ole [19] do
no disag ee wi h he p esen esul s (see Table 5). The
p e ious s udy es ima ed he co ela ion only be ween
he li e size and ma e nal gene ic e ec s o bi h size
(he e p o en o be nega i e) and igno ed he posi i e
co ela ion be ween li e size and di ec gene ic e ec s
o bi h size.
O he s udies ha e epo ed bo h nega i e [14] and
posi i e [38] es ima es o he ma e nal en i onmen al
co ela ion be ween li e size and bi h size. A posi i e
en i onmen al co ela ion could a ise i he en i onmen
a ec s he ai s h ough esou ce acquisi ion [40]. Fo
example, in he case o o sp ing numbe and size, abun-
dan nu i ion ha causes o ula ion o ex a eggs allows
mo he s o suppo he g ow h o la ge oe uses. Con-
e sely, a nega i e en i onmen al co ela ion is expec ed
i he en i onmen al sou ce o a ia ion in li e size
does no a ec o al ma e nal ep oduc i e esou ces.
The la e case is likely o happen in he bank ole, in
which pe manen and empo a y en i onmen al co ela-
ions be ween li e size and o sp ing size we e s ongly
nega i e. The bank ole has an ex emely a iable li e
size [19,24], and la ge en i onmen al a ia ion in he li -
e size demons a ed by a low he i abili y ( his s udy).
Table 5 Gene ic and en i onmen al co ela ions be ween
li e size and bi h size ai s (s anda d e o )
Bi h mass c
2
Bi h head
wid h
c
2
Gene ic co ela ions
LS di ec - BS di ec 0.54 (0.23)* 5.00 0.47 (0.26)* 3.34
LS di ec - BS ma e nal -0.30 (0.23) 1.20 -0.47 (0.38) 0.30
BS di ec - BS ma e nal 0.04 (0.32) 0.00 0.34 (0.76) 1.26
En i onmen al
co ela ions
Pe manen
en i onmen al
-0.35 (0.17)* 3.00 -0.44 (0.17)* 4.32
LS esidual - BS li e -0.67 (0.02)
***
635.40 -0.52 (0.02)*** 345.22
LS li e size; BS bi h size (mass o head wid h)
S a is ical signi icance: * P< 0.1; **P< 0.01;***P< 0.001
c
2
Chi squa e es s a is ic o loglikelihood- a io es o he co a iance
Sch ode us e al.BMC E olu iona y Biology 2012, 12:44
h p://www.biomedcen al.com/1471-2148/12/44
Page 5 o 7

As a small mammal, he bank ole is an income b eede
whose capaci y o suppo g ow h o he oe uses du ing
la e p egnancy is no likely o be connec ed wi h en i -
onmen al a ia ion a ec ing o sp ing numbe , which is
al eady de e mined ea ly in p egnancy.
Selec ion o o sp ing numbe and size
In gene al, selec ion on o sp ing size a bi h and li e
size ac s an agonis ically on he mo he and o sp ing
[19,25,41-43]. This combined wi h a p esumed nega i e
gene ic co ela ion be ween o sp ing numbe and size is
hough o cons ain he e olu ion o hese ai s [44].
Ou esul s indica e ha gene ic a ia ion in o sp ing
iabili y and o sp ing numbe a e no necessa ily an ag-
onis ic in mammals. A posi i e gene ic co ela ion
be ween di ec gene ic e ec s o li e size and o sp ing
bi h size can educe pa en -o sp ing con lic in o -
sp ing size as he same genes inc ease i ness a bo h
le els. Also, an e ec i ely null co ela ion be ween di ec
and ma e nal gene ic e ec s o bi h size implies a low
le el o pa en -o sp ing con lic in he bank ole.
Gene ic co ela ions in na u al popula ions o bank
oles should be s onge han hose es ima ed he e,
since gene ic co ela ions a e ypically weake in good
en i onmen s such as labo a o y condi ions [22,45].
These da a we e ob ained using a popula ion ha has
been subjec o sho - e m, wo-way selec ion o li e
size. Unde an in ini esimal model and wi h comple e
pedig ee in o ma ion, he animal model akes selec ion
in o accoun when he selec i e e en s a e included in
he da a se [20]. The in ini esimal model, whe eby
quan i a i e gene ic a ia ion is explained wi h a la ge
numbe o unlinked genes o small e ec , is no a ealis-
ic assump ion bu i does wo k easonably well o
sho - e m selec ion expe imen s [46]. In ou selec ion
expe imen , li e size in he wo lines ( owa ds small
and la ge) has di e ged. Howe e , di e gence in o -
sp ing size has no been so s aigh o wa d, hus
demons a ing he complex na u e o his impo an
li e-his o y ade-o . (Sch ode us, Koi ula, Koskela,
Mappes, Oksanen and Poikonen; Unpublished da a).
Conclusions
We ha e shown ha he pheno ypic ade-o obse ed
be ween o sp ing numbe and size in a poly ocous
small mammal was due o en i onmen al e ec s a he
han addi i e gene ic e ec s. Ou esul s indica e ha
gene ic a ia ion in o sp ing numbe and size a e no
necessa ily an agonis ic in mammals. This inding is in
line wi h he many posi i e es ima es o gene ic co ela-
ions epo ed be ween li e-his o y ai s [6]. Ou esul s
emphasize he complex na u e o o sp ing numbe -
size ade-o in mammals in e ms o bo h en i onmen-
al and gene ic a ia ion. The s uc u e o he addi i e
gene ic co a iance ma ix sugges s ha e olu ion o o -
sp ing numbe and size in poly ocous mammals may
no be cons ained by he ade-o pe se caused by
an agonis ic selec ion esponses, bu a he by he
opposing co ela i e selec ion esponses in di ec and
ma e nal gene ic e ec s o bi h size.
Acknowledgemen s
We hank Ma i Ojala o commen s on he s a is ical models and he esul s
and wo anonymous e iewe s o commen s on he ea lie e sion o he
manusc ip . Phill Wa s and Mikael Mokkonen commen ed and checked he
English o his manusc ip . We hank he Academy o Finland o inancial
suppo (g an no. 132190 o T.M.; 218107, 119200, 115961 o E.K.) and he
Cen e o Excellence in E olu iona y Resea ch o he Academy o Finland.
Au ho de ails
1
Cen e o Excellence in E olu iona y Resea ch, Depa men o Biological and
En i onmen al Science, Uni e si y o Jy äskylä, P.O. Box 35, FI-40014
Jy äskylä, Finland.
2
MTT, Bio echnology and Food Resea ch, Biome ical
Gene ics, FI-31600 Jokioinen, Finland.
3
Depa men o Biological and
En i onmen al Science, Uni e si y o Jy äskylä, P.O. Box 35, FI-40014
Jy äskylä, Finland.
Au ho s’con ibu ions
ES pa icipa ed in he collec ion o he da a, pe o med s a is ical analysis
and w o e he manusc ip . All o he au ho s pa icipa ed in he collec ion o
he da a, and con ibu ed and app o ed he inal manusc ip .
Compe ing in e es s
The au ho s decla e ha hey ha e no compe ing in e es s.
Recei ed: 23 Ma ch 2011 Accep ed: 31 Ma ch 2012
Published: 31 Ma ch 2012
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doi:10.1186/1471-2148-12-44
Ci e his a icle as: Sch ode us e al.: Can numbe and size o o sp ing
inc ease simul aneously? - a cen al li e-his o y ade-o econside ed.
BMC E olu iona y Biology 2012 12:44.
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