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Selection on testis size as an indicator of maturity in
growing animals. I Direct and correlated responses in
growth
Wg Hill, Pj Marks, Jc Jenkins, Rb Land
To cite this version:
Original
article
Selection
ontestis size
as anindicator
of
maturity
in
growing
animals.
I
Direct and correlated
responses
in
growth
WG
Hill
1
PJ Marks
JC Jenkins
1
RB Land
2
1
Institute
of Animal Genetics, University of Edinburgh,West Mains- Road,
Edinburgh
EH9 3JN;2
AFRC
Instituteof
AnimalPhysiology
and Genetics Research,Edinburgh
ResearchStation,
Roslin, Midlothian EH259PS,
UK*(Received
2 October 1989; accepted 15 February1990)
Summary - Selection was undertaken in mice to test whether
gonad
size,specifically
testisweight,
could be used to indicatedegree
of maturity and producegenetic change
in theshape
of thegrowth
curve from records on young animals only. Selection was practisedfor 11
generations high
and low on 5 wk malebody weight
(lines
HX,LX),
on 5 wk testisweight
(XH, XL)
and on indices with these traits selected in the same(HH,
LL)
and inopposite
(HL,
LH)
directions. There were 2 replicates of each selection line and 4 unselected controls.Divergences
betweenhigh
and low lines withinfamily
standard deviation units for 5 wk bodyweight
and testisweight, respectively,
were: HX-LX: 1.8 and 2.3, XH-XL: 2.2 and 4.2, HH-LL: 1.9 and 3.4, and HL-LH, 2.0 and -2.7. There were minor changesin shape of the growth curve in the direction expected, with those selected for
high
testisweight showing
earlier maturity. A simple measure, 6 wkweight/15
wkweight
(%),
forentire males was: HX 74.3, LX 67.3, XH 71.8, XL 69.6, HH 78.1, LL 72.6, HL 74.2, LH 78.5, averaging 76.1 for lines selected for high testis weight and 72.1 for low, compared to 74.0
for controls. In castrate males, a similar pattern of
changes
ingrowth
curve was observedindicating
that they were not a consequence of testis derived hormones. Mice selected forhigh
testisweight
were leaner than those selected for low testisweight.
Thus,growth
curveschanged
due to selection on testisweight,
but it was not established if this is because testis size is an indicator of sexual maturity.growth / maturity / testis / selection / mouse
Résumé - Sélection par la taille des testicules considérée comme un indicateur de la maturité des animaux en croissance. 1 Réponse directe et réponse corrélée sur les caractères de croissance. Une
expérience
de sélection a été réalisée chez la sourispour déterminer si la taille des gonades, en particulier la masse des testicules, pouvait
indiquer le
degré
de maturité et pouvait modifier l’allure de la courbe de croissance, à partir des seules données recueillies chez de jeunes animaux. La sélection a été conduitependant 11
générations,
vers le haut(H)
et vers le bas(L)
selonplusieurs
critères: masse*
corporelle chez le mâle à 5 semaines
(lignées
HX,LX);
masse testiculaire à 5 semaines(XH,
XL);
indices combinant ces deux caractères, dans le même sens(HH, LL)
ou en sens opposés(HL, LH).
Chaque lignée sélectionnée a été répétée deuxfois,
et .¢ lignéestémoins non sélectionnées ont été élevées. Mesurées en unités d’écart type
intrafamille,
les
divergences
observées entre lignées haute et basse ont été les suivantes, respectivementpour la masse corporelle et la taille des testicules: HX-LX: 1,8 et 2,3; XH-XL: 2,2 et 4,2;
HH-LL: 1,9 et 3,l; HL-LH: 2,0 et -2,7. On a observé de petites
différences
de laforme
des courbes de croissances dans le sens
attendu,
leslignées
sélectionnées pour une massetesticulaire élevée montrant une maturité
plus
précoce. Le rapport de la massecorporelle
à 6 semaines sur celle à 15 semaines était chez les mâles entiers
(en
pourcentage).’
HX:7/,3; LX: 67,3; XH: 71,8; XL: 69,6; HH: 78,1; LL: 72,6; HL: 7.¢,2; LH: 78,5; avec une
moyenne de 76,1 chez les
lignées
sélectionnées pour une masse testiculaire élevée, contre72,1 chez celles sélectionnées pour une masse testiculaire
faible,
et 74,0 chez leslignées
témoins. L’observation chez les mâles castrés de
modifications
similaires des courbes decroissance
indique qu’elles
ne sont pas dues aux hormones sécrétées par les testicules. Lessouris des
lignées
sélectionnées pour une masse testiculaire élevée étaientplus maigres
quecelles sélectionnées pour une masse testiculaire
faible.
Desmodifications
des courbes decroissance induites par la sélection sur la masse testiculaire ont ainsi pu être observées, mais on n’a pas établi que c’était parce la masse testiculaire est un indicateur
spécifique
de la maturité sexuelle.
croissance / maturité / testicule / sélection / souris
INTRODUCTION
The animal breeders’ aim is to select animals of
high early growth
but low maturesize so as to reduce costs of both the
slaughtered
animal and its dam. Bonegrowth
of animals slows or terminates afterpuberty
under the influence ofgonadal
hormones,
so the
object
of theexperiment
was to test whether selection onbody weight
andtestis
weight
on the immature animal could be used to influence bothearly gains
and matureweights.
This follows results insheep,
where selection on testisweight
of rams with
phenotypic
correction forbody
weight
led to correlatedchanges
inmature
weights
in their femalerelatives,
high
testisweight being
associatedwith
low
body weight,
and vice versa(Land
etal,
1980;
Lee andLand, 1985; Haley
etal,
1989(submitted);
Lee andHaley,
1990).
The present
approach
differs from the more direct method ofselecting
directly
onweight
at different ages which has beenapplied
withvarying
success in differentspecies.
Substantialbending
of thegrowth
curve has been achieved in bothturkeys
(Abplanalp
etal,
1963)
and chickens(Ricard, 1975).
Inmice,
bending
has beeneffected,
but to a lesser extent than inpoultry, by
McCarthy
and Doolittle(1977),
who selected on 5 and 10 wkweight
with theobjective,
interalia,
ofincreasing
5and
holding
10 wkweight
constant,by
Wilson(1973)
who selected on the ratio of3-6 wk
gain
to 3-9 wkgain,
andby
von Butler et al(1980, 1986)
using
3-5 wkgain
and 8 wkweight.
Theseschemes, however,
require
selection decisions to be deferreduntil
animals
approach
their matureweight
which is after the usual age ofslaughter
andoften
after the age of firstmating,
whenculling
decisions have to be made inboth mice and domestic livestock.
In the present
experiment,
mice were selectedhigh
and low forbody
and testisweight
on either trait alone or on indices of the 2 traits in either the same or thesize may also be an indicator of ovulation rate and litter size
(Land 1973),
records
of
reproductive performance
werekept
and will bereported
in asubsequent
paper(Hill
etal,
1990).
Further details of theexperiment
arereported
in PhD thesesby
Jenkins
(n6e
Williams,
1984)
and Marks(1988).
MATERIAL AND METHODS
Mouse stocks and
housing
The mice for
generation
0 of thisexperiment
were crosses atgeneration
3 or 4 betweenpairs
of the unselected control lines of the G strain established from a3-way
cross of 2 inbred and 1 outbred strain(Sharp
etal,
1984).
Four separate setsof crosses were made to establish the different foundation groups. The mouse house
was maintained at 21 f 1°
C,
RH30-40%,
with water and BP’s rat and mouse No1
expanded
maintenance dietprovided
ad libitum. Selection linesTwenty
lines were established as shown in tableI,
with 2replicates
of each of 8 selected lines and 4replicates
of the unselected controls. The lines weremanaged
as4
contemporary
groupsspaced
at 3 wkintervals,
each groupcomprising
4 selected lines(which
were either the 4single
trait lines or the 4 indexlines)
and 1 control.Mice were mated at
approximately
9 wk of age.Eight
pair
matings
per line weremade each
generation, using
the maximum avoidance scheme of Falconer(1973),
together
with 4 reservematings
which wereonly
used if necessary. Atbirth,
litterof males was
practised,
while females were taken at random withinfamilies,
as weremales in the controls. The selection
phase
of theexperiment
was continued for 12generations,
but no selection waspractised
ingeneration
7.A
preliminary study
showed that 5 wk of age was anappropriate
age for selection. Bothbody
and testis are thengrowing rapidly
and there is ahigh
(0.99)
correlation ofright
and left testisweight
to allow hemicastration. The coefficients of variationof
body
weight
and testisweight
were then 0.17 and 0.26respectively
and theirphenotypic
correlation was 0.50.Body
weight
at 5 wk was recorded on all males. Testisweight
at 5 wk wasrecorded every
generation
in lines selected on testisweight,
but not everygeneration
in the others(ie
HX, LX
andCC).
To dothis,
mice were anaesthetisedby
Sagatal
andhemicastrated,
and 1 testis was excised andweighed.
The indices used were7 == ± t!/o-! ± T/o-r = ! 0.54 tV ± 0.112 T
where W and T denote
body weight
(g)
and testisweight
(mg);
and Uw and err denote their within
family
phenotypic
standard deviations ingeneration
0,
estimated at 1.82 g and 8.9 mg
respectively.
In lineHL,
forexample,
mice wereselected for
high
values of I = 0.54 W — 0.112 T eachgeneration.
Data recorded
Analyses
ofgrowth
curves were made atgenerations
7 and13,
after 6 and 11generations
ofselection, respectively.
Atgeneration
13,
litters were standardizedto 7 young at
birth,
and at 19 d half the male mice were castrated anddummy
operations
were undertaken on the rest.Eight
entire and 8 castrated mice of each line wereweighed,
at leastweekly
fromweaning
at 3 wk untilthey
were 17 wk old. Food intake was recorded atgeneration
13 on the samemice,
who werecaged
inpairs
and fed ad libitum. Gonadal fatpads
and hind limb fatpads
were dissected on11 wk old entire males of
generation
11,
and chemicalanalysis
of the whole minced carcass was undertaken on the mice ofgeneration
13.Statistical
analysis
The
experiment
wasbasically
apartial
blockdesign,
with each blockcomprising
5lines,
each linereplicated
over 2 blocks.Apart
from the block(group)
effects whichwere taken as
fixed,
there were 2 other sources of error associated with a line mean:genetic
drift accumulated over the selection and error due torecording
limited numbers. This combined error variance was estimated as the interaction variancebetween selection line and
replicate. Thus,
the model used for observations takenonly
on males waswhere:
Yg
hij
is an observation onindividual j
inreplicate
h of line i within thetype of selection g; u is the overall mean;
Tg
is the effect of type of selection(g
= 1for
single trait, g
= 2 forindex;
Rg
h
(h
=1, 2)
is the effect of the hthreplicate
nested within the
gth
type ofselection;
Lg
i
(i
=1, ... , 5)
is the effect of the linealthough
withonly
8df;
and e9hz! is theremainder,
which in someanalyses
waspartitioned
to include a litter effect.RESULTS ‘
Responses
in 5 weekbody
weight
and testisweight
Generation means for
body
weight
and testisweight
of 5 wk old males are shownin
figures
1-5. Forclarity,
results forpooled replicates
are shown in thegraphs,
butin table
II,
differences betweenpairs
of selected lines at the end of selection(means
ofgenerations 10,
11 and12)
are shown for eachreplicate.
In the
single
trait lines there were direct responses(as
divergence
betweenhigh
and low
lines)
of the order of 2 sd(within
family
standarddeviations)
forbody
weight
and 4 sd for testisweight,
and similarpositive
correlated responses of about 2 sd in testisweight
andbody weight respectively. Thus,
there were substantialpositive
correlated responses in index1,
wherebody weight
and testisweight
have the samesign,
andnegative
correlated responses in index2,
albeit very small inthe
body weight
lines. There was,however,
substantial variation betweenreplicates
(table II),
and,
although
selection differentials were similar inhigh
and lowlines,
some asymmetry of response
(figs 1-5).
Thereplicate
linescomprised only
8mating
pairs
and so betweenreplicate
anddirection,
variation would beexpected
fromgenetic
sampling.
Theanalyses
havetherefore,
to minimise theirnumber,
beenbased on
divergence
betweenhigh
and low lines.There were responses of the same order in the index 1
lines,
ie about 3 sd in theindex
itself,
withpositive
correlated responses of 2 and over 3 sd inbody weight
and testis
weight
respectively,
andthus,
since testisweight
hadchanged relatively
single
trait selection indicate apositive
genetic
correlation between thetraits,
with index 2 there was a substantial direct response of 4 sd in the index and correlatedresponses of the order of 2 sd of
increasing
body
weight
anddecreasing
testisweight.
Estimates of realized
heritability
from withinfamily
selection(h!)
obtained fromregression
ofdivergence
of response( eg HX-LX)
on cumulative withinfamily
sectiondifferential each
generation
aregiven
in table III.Using
the intra-class correlation estimate(t)
from the basepopulation,
estimates ofheritability
were obtained ash
2
=2(1-
t)hw
(Falconer, 1989).
Bothhw
and h
2
estimates werehigher
for testisweight
and index2,
whereantagonistic
selection waspractised,
than forbody
weight
and index 1.Heritability
estimates were lower thanpreviously
obtained forbody weight
in thispopulation
(Sharp
etal,
1984)
and testisweight
on a differentFrom the
pairs
ofsingle
trait selection lines an estimate ofgenetic
correlation isreadily
obtained asw
l/2
)J
R
T
)/(R
w
C
T
[(C
where,
forexample,
R
w
,C
T
denote the direct response inbody
weight
and correlated response in testisweight
from selection onbody
weight
(Falconer, 1989).
From tableII,
the estimates of correlationare
0.85,0.49
and 0.80 fromreplicates
1,
2 andpooled, respectively.
An estimate ofthe
genetic
correlation from the index lines can also beobtained,
and the method ofcalculation is
given
in theAppendix.
This estimate was 0.17 forreplicates
pooled.
It is clear that the index selection was more effective inproducing divergence
ofheritability
of index 2 than of index 1 would be if the environmental correlation were muchhigher
than thegenetic
correlation.Analysis
ofgrowth
The selected lines did not differ
greatly
from each other or from the controls in thegeneral shape
of theirgrowth
curves atgeneration
13. There were however somethese.
Therefore,
in order to show thedifferences,
meanweights
of males of the selected lines aregiven
infigures
6 and 7 for entire and castratemales,
respectively,
as a percentage of the
weights
of thecorresponding
controls at the same age. The control means aregiven
in table IV. Forexample,
both the entire and castrate males of the LL index line are about 10% smaller than those of its control at 21d,
butonly
2% smaller at 119
d;
whereas those of the LH line are also smaller than thecontrols,
but
relatively
less so at 21 than 119 d. Even at 17 wk whenrecording
ceased,
miceAn alternative to
expressing
body weights
of 1 line as a ratio of those in anotheris to use
logarithms,
andparticularly
naturallogs
because when ratiosy/x)
are nearunity,
y/x -1 ;zt; In y -in x.
Some contrasts between relevantpairs
of lines aregiven
in table IV(scaled
up x 100 to removeleading
decimalzeros),
and some data are included from thestudy
ofbody weight
taken atgeneration
7,
midway
through
the
experiment.
Apart
from 6 wk(strictly
41d)
when LX mice wereatypically
small,
thedivergence
inbody weight
between lines HX andLX,
selected forbody
weight,
was similar at different ages in the entiremales,
but tended to increase inthe castrates. The
divergence
inbody
weight
between XH andXL,
the testisweight
selectedlines, consistently
decreased with age, as was the case between the indexlines HH and
LL,
mostnotably
atgeneration 13;
these results could beexpected
ifhigh
testisweight
lines matured earlier. In contrast, thedivergence
between the other indexlines,
HL andLH,
remained more constant,tending
to increase withestimated from differences between
replicates
with 8degrees
offreedom, only
a small number ofcomparisons
ofweights
weresignificant.
Relative
maturity
wascomputed
as the ratio ofbody weight
at 6 wk to that at15 wk for data from both
generations
7 and 13.(Records
ceased at 15 w ingeneration
7. In
generation
13,
records at 41 and 107 d wereused).
At 6 wk the mice had achieved about 70% of their 15-wkweight
(table V).
The lines selected forhigh
testis
weight,
ieXH, HH
andLH,
were allrelatively
earliermaturing
than thecorresponding
lines selected for low testisweight,
ieXL, LL
andHL,
the differencebeing
about4%
on average.Analyses
of the records on food intake taken ingeneration
13 showed that the responses ingain
weregenerally
accompanied
by
similarproportional
changes
in food
intake,
so there wereonly
trivial differences between the lines in food conversionefficiency
(results
notshown).
Body composition
Body
composition
was assessed from the ratio of fatpad
weights
(gonadal
plus
hind limb
depots)
tobody weight
on entire males of 11 wk of age ingeneration
10,
and from total chemical fat as aproportion
of(wet)
body
weight
on entire andcastrate males of 5 and 17 wk at
generation
13(table
VI).
The lines differed littlein fat content at 5 wk. At later ages there was no very consistent pattern among
those selected on
body weight,
but the lines selected forhigh
testisweight
were,DISCUSSION AND CONCLUSION
The
objective
of thisexperiment
was to check thehypothesis
which arose fromthe
experiment
withsheep
(Land
etal,
1980)
that the pattern ofgrowth
could be alteredby using
a measure ofmaturity
such as testis size on immature animals.Undoubtedly
such achange
waseffected,
perhaps
seen mostclearly by
the ratio of 6-15 wks in table V for the meancomparisons
ofmaturity
ofhigh
and low testisweight lines,
which differedby
about 4% around a mean of 70%.Nevertheless,
the results were not&dquo;spectacular&dquo;: they
are notclearly
seen insimple plots
ofbody
weight against
age, so the derived results shown infigures
6-7 were necessary.One of the more
striking
aspects of thegrowth
curveanalyses
is that very similarchanges
were effected in both entire and castrated males(see
tableV),
andanalyses
(Williams,
1984,
nottabulated)
atgeneration
7yielded
similar results for females as for males. Thisimplies
that the presence of the testis after 19d,
the age of castrationat
generation
13,
andcirculating
testosterone are notrequired
for thegrowth
curvesto
change.
Estimates of testosterone levels were made on 5 and 10-wk-old miceby
the method of radioimmune assay of Webb et al(1985).
Differences between lines were,however,
smallcompared
to error from natural and assayvariation,
forcorrelations of line means on successive
samplings
were low(<
0.5),
and no clear differences were found(results
notshown).
Inaddition,
age at sexualmaturity
of males was assessed inreplicate
1(there
was not time torepeat
inreplicate
2)
the
day
of firstcopulatory plug.
The control mean was 43.5d,
and the contrastswere HX-LX =
-2.0,
XH-XL =4.4,
HH-LL =-1.2,
HL-LH =4.7,
each with SEof 1.1
including
only
withinreplicate
error. In summary, the mean forhigh
testisweight
lines was 0.5 d less than for low testisweight lines,
a trivial difference(a
fewmice did not
plug
by
49d,
whenrecording ceased,
butaccounting
for them wouldnot influence this
conclusion).
It is therefore unclear from thisexperiment
that thechange
in testisweight
inducedchanges
ingrowth
rate as aspecific
indicator ofsexual
maturity
ordirectly through
its hormonal action.Alternatively,
testisweight
in relation tobody
weight might
simply
be an indicator of allometricgrowth
of internal organs, and thathigh
ratios ofweights
of several organs tobody weight
are an indicator of
approaching
maturity.
In the
experiment
withsheep
(Land
etal,
1980),
the selection criterion was testisweight averaged
over 3 ages,6,
10 and 14wk,
adjusted by phenotypic regression
onbody
weight
at these ages(Haley
etal,
1989).
Thusthey
were, ineffect,
selected on an index ofhigh
testisweight
and lowbody weight
at these ages and thechanges
inbody weight
couldlargely
be due to selection onbody weight. Haley
et al(1990)
calculatehowever,
that thegenetic
correlation between their selection criterion inmales and
body weight
in females becameincreasingly negative
with successive years of age of thefemale,
whereassimple negative
selection onbody weight might
beexpected
togive
a different trend.Correlated responses in
reproductive performance
are described in asubsequent
paper
(Hill
etal,
1990),
but these are relevant to the discussion of what influencesmature size.
Briefly,
positive
correlated responses in litter size were obtained withselection on
body weight
alone,
testisweight
alone,
and on the index of the traits in the same direction(HH-LL),
but not when selected inopposite
directions(HL-LH).
The
analyses
undertaken on those results indicate that selection on testisweight
influenced litter
size,
even after correction forbody weight,
inaccordance
with the results of Eisen and Johnson(1981)
andsuggesting
that testis size is indeed an indicator ofdevelopment
in somespecific
way, as Land(1973)
proposed.
From the results of this
experiment
it is notpossible
todirectly
compare theaccuracy of selection
including
records on testisweight
of immature animals to thatincluding body weight
on matureanimals,
without estimates ofgenetic
variances and covariances ofweights
except at 5 wks. If the intention were to increase anearly
weight
and hold a laterweight
constant, the response would then be a little less than(1-rG)
1/z
of that with selection for theearly weight alone,
where rG is thegenetic
correlation. For 5 and 10 wk
body
weight, Hayes
andMcCarthy
(1976)
obtainedr
G =
0.8,
for which(1 —
T
&)
1/2
= 0.6.Nevertheless,
lines selected on testisweight
and on the indices of 5 wk
body
weight
and testisweight
gave similar responses in5 wk
body weight
as did the lines selectedsolely
for that trait and lower but notzero responses at later ages. Five-wk
body weight
had a rather lowheritability,
bothto within
family
selection and also when converted to massselection, substantially
lower than for testisweight;
therefore testisweight
was a betterpredictor
ofbody
weight
than vice versa. This may notapply
to otherspecies.
The index ofpractical
interest,
ieincreasing
body
weight
and testisweight
(HH),
similarly
had a lowheritability,
particularly
for mass selection because the intra-class correlation of sibsin the correlated responses of the index lines and apparent
discrepancies
betweengenetic
correlations ofbody
weight
and testisweight
among the sets of lines.Whilst there was
reasonably
good
evidence tosuggest
that matureweights
werereduced
by
selection on testisweight
relative tobody
weight, indicating
that such animals maturedearlier,
thefairly
clear observation thatthey
were also leaner was rathersurprising because,
in farmanimals,
early maturity
isusually
associated withhigher degrees
of fatness whencomparisons
are made at constant age. There is no evidence that thehigh
testisweight
selection led to any restriction ofappetite
whichmight
have effectedthis;
nor is there any obvious mechanism.In
conclusion selection on testisweight
led to somechanges
in theshape
of thegrowth
curve. That these were not marked is notsurprising
in view of thehigh
correlation betweenweights
at different ages. At thisstage
we would not,however,
advocate selection to bepractised
on testisweight
tochange
degree
ofmaturity.
It tislikely
to be safer to selectdirectly
onweights
at different ages; and if selection decisions need to be madeearly
in the animal’slife,
records of older relatives suchas parents and uncles can be used.
ACKNOWLEDGMENTS
This work was
supported by
agrant
from theAgricultural
and Food Research Council. We are verygrateful
to RobertaWallace,
Ann Walker and staff of the mouse house for technical assistance and to GeneEisen,
Douglas
Falconer and ChrisHaley
for comments on a draft of the paper.Roger
Land initiated theexperiment
reported
here and died after lab work had beencompleted.
He isgreatly
missed.REFERENCES
Abplanalp
H,
Ogasawara
FX,
Asmundson VS(1963)
Influence of selection forbody
weight
at different ages ongrowth
ofturkeys.
Br Poult Sci4,
71-82von Butler
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1098-1103APPENDIX
Estimates of
genetic
correlationestimates of
genetic
variances(V
A
),
genetic
covariances(Cov
A
)
andgenetic
cor-relations(r
A
)
wereobtained,
where W =body weight
(g)
and T = testisweight
(mg),
and the units of the indices arearbitrary.
From thesingle
traitlines, V,qyy
=2
(
0
.
26
)(
1
.
82
)
2
= 1.72 andV
AT
=76
,
and thusCov
AWT
=(C
T/
Rw)V
AW
= 10.1 orC
OV
,g
WT
=(CW !RT)vAT
=8.2,
with a mean of9.1,
corresponding
to r AWT =0.80,
as in the text. From the index
lines,
V
AIl
= 1.69 andV
A12
=
1.24 and thusCOV
AIII2
=
(C
I2/
R
Il
)V
AIl
= -0.52 OrOVAI112
C
=(C
Il/
R
I2
)V
AI2
=W
.18,
with mean-0.35,
giving
rAIlI2 = -0.24.Predictions of index variances and covariances from the
single
trait lines and vicevers d
can also be made.
Letting
b
l
= 0.54and b
2
= 0.112 be the indexweights,
then:Y
All
=b2V
AW
+2bib2 COV
AWT
+b22VAT, VA12 blV
-
AW
2b
1
b
2
COV
AWT
+b2V
AT
and
Cov
AI1I2
=b1 V
AW
-
b’
2
V
AT
andthus,
forexample,
V
AW
=(V
A
n
+V
A12
+2
COV,q1112)!(4b1)·
Predicting
from thesingle
trait lines: VAn =2.56, V
Arz
=0.35,
CO
VAIlI2
= -0.45 and rAll12= 0.48;
andpredicting
from the indexlines,
using
the mean estimate ofCov
All
1
2
= -0.35 :V
AW
=1.90, V
AT
=73,
C
OVAWT
=1.90