Rxy
=(�)n
(l+Fx) (l+Fy)
(where, as indicated on Page 18, Fx and Fy are the coefficients of
inbreeding of two individuals
Xand
Y;FA is that of common ancestor
and n refers to the total number of Mendelian segregations in the path
of descent through which
Xand Y are related )
Since
Ycould have 2n ancestors in the generation in which A appears,
the contribution of a single random line must be multiplied by 2n to
obtain an estimate of relationship between A and Y.
Thus, RAY is estimated by
if a
tie is present between single random lines back of the two animals
considered (A, Y). In the case of four-line pedigrees, R is
estimated by
and so on.
In so far as Y is a sample of the population, an estimate of the
22 .
coeff icient . By taking a large sample o f Y' s the sampling errors are reduced and a reliable estimate of the relationship between a par t icular individual and the population (RA . POP) is obtained .
When asses s ing the relationship o f a large group to a par t icular animal the inbreed ing ceoffieient (FA) of that animal should b e
calculated accura t ely . Unless these inbreeding coeff icients are o f reasonable dimensions , however , l i t tle error i s introduced i f they are neg1ec ted . For example , if FA = 10% and Fpop = 5% then the
expression reduce to ( l +FA) ( l +Fy) 1+0 . 10 ( 1+0 . 10) ( 1+0 . 05) = 1 . 10 1 . 15 1 . 0 2
Clearly the error introduced by neglecting
wil l b e ( l +Fpop)
would
smal l if inbr eeding coeff icients are low . As Wright and McPhee ( 1925) pointed ou t , the method can be extended t o determine the relationship b e tween random individual s of the popula t ion or within a specia l ly chosen sec tion of the breed , or between two sec t ions o f a breed .
The above m ethod of Wr ight and McPhee was applied by Lush ( 1932) to a s tudy of the Rambouillet breed o f s heep . H� concluded that the met hod is about as accurate as its theore tical s tandard errors i nd ica t e , i f a l l sources o f sys tematic errors which might prevent the l ines f rom being truly random are carefully avoided . He further caut ioned that one mus t be on guard agains t sys t ematic errors which at f irst thought appear
cer tain circums tances , may creep into the supposedly random tracing o f the lines .
Fowler (1932) , in a s tudy of the Ayr shire br eed , concluded tha t Wrigh t ' s "Long Method", in compar ison wi th h i s "Shor t Method", gave far mor e reliable results especially when applied to breeds of rela tively recent origin .
V . THE EFFECTS OF INBREEDING
The primary g ene t ic effect of inbr eeding is to increase the propo r t ion of the loci in the population which are homo zygous . This results f rom the f ac t that rela ted ma tes are mor e alike in their genetic constitu t ion than are ma tes which are chosen at random .
Cons equently , the unit ing gametes will b e a l ike in more g enes and the result ing offspring more homo zygous than if the par ents were unrelated . All the o ther effec t s of inbr eeding , such as the uncovering of recessives and the f ormation of d is tinc t families f o l low from this primary ef f ec t .
S ome mention should b e mad e a t this junc ture o f the phenomenon commonly referred to as inbreeding depr ess ion. It is well known tha t close inbreeding is nearly always accompanied by lowered f er tility , reduc tion of libido , an increase in gametic s terility and embryonic mor tality, as wel l as a reduc tion in the v iability of newborn animals . Product ion is also advers ely affec ted .
Wright (1922) explained this d ec line in vigour on the premis e that Mendelain factors unfavourabl e to vigour in any respec t are mor e
frequently recessiv e than dominant . This s i tuation is a logical consequence o f the two ideas that
24.
(i) mu tations are mor e likely t o inj ure than improve the complex adj u s tments wi thin an organism and that
( ii) harmful dominant mutations will be weeded out relatively q uickly , leaving the rece s s ive ones to accumulate , espec ially if they happen to be l inked wi th f avourable d ominant fac trs.
Knowledg e of the eff ec ts of inbreeding on productivity is useful for two purposes . Firstly , the accuracy of s elec tion can be improved by c orrec ting for any dif f erences between ind ividuals which resul t f rom variation in their degree o f inbreeding . S econdly , in compar ing breeding p lans , allowance needs to be made for any differences in the rate at wh ich they increase inbreed ing .
A . Evidence o f in farm animals
There is a cons iderabl e amount o f informa t ion on this subj ec t . Evid ence pre s ented here , mainly f rom American s tudies , will b e conf ined to d airy ca ttle . In mos t cases , the aim has been to try a comb inat ion of r ela tively mild inbreeding and s election as a method o f br eed ing in dairy cows ra ther than to produce inbred lines for cross ing wi th each o ther .
One such s tudy was tha t by Swe t t , Ma t thews and Fohrman
(1949).
Cows of mixed ances try wer e used as f oundat ion f emales and they were ma t ed to a proven Holstein bull . Their exper iment was designed to lookinto the pos s ib ilities of building up a high-produc ing herd by us ing a prov en bull and h
�
s sons, on cows o f average produc t ion. Daughters , and in s ome cases even grandd aughters , were back-cro ssed to the same bull , s o25.
that the progeny ob tained car r ied 7 5 and 8 7 . 5 percen t , respec t ively , of the genic cons titution of their paternal ances tor .
This intens iv e linebr eeding was accompanied by ra ther pronounced inbreeding depres sion symp toms . The number of services required per concept ion incr eas ed from 2 . 0 for non-inbred cows to 3 . 6 when the inbreeding coefficient of the calves reached 0 . 5 . The mor tal i ty o f inbred calves less than one mon th old was 1 5 percent . However , when the same bull was ma ted with unrela ted cows , there were no deaths among the 43 c alves born; but , in the ' purebr ed ' Hols tein herd served at the same t ime , 29 calves died out o f the 300 born (9 . 7 p ercent) . The effect of inbreeding on body-weight and produc t ion is illus tra ted by the
rela t iv e figures shown below :
Degree o f inbreed ing non-inbred F : 0 . 1 0-0 . 29 0 . 30-0 . 4 9 0 . 5 0-0 . 69 TABLE 3 . 3 The Effect of on
and Milk Yield ( af ter Swe t t e t . al. 1949)
Bir th Weigh t o f Cows which
Weight heifers Lac tation
o f a t 18 No . of Weigh t o f
a t
Calves months ' Cows Pit- Udder *
u itary 100 100 22 1 00 100 1 00 . 1 9 2 . 5 15 96 . 7 9 5 . 1 9 5 . 9 89 . 6 27 9 2 . 2 8 3 . 8 8 3 . 7 87 . 3 7 80 . 2 5 4 . 1 leas t one Yield of Butterfat 100 101 . 5 9 3 . 0 8 2 . 6
* The rela tive f igures for the udder weigh ts refer to full udders of lactating cows which were s laugh tered.
26.
The inb red animal s were smaller a t b ir th and grew mor e slowly than the non-inb r eds ; they were also lis t less and had coarse coa t s , which is indicativ e o f lowered condition .. The pituitary glands were also smaller . Milk and b u t terfat yield decl ined with increased inb reeding ; the butter fat content of the milk decreased during the first g enerations of
inbreeding but the reason for this would appear to b e tha t the original cow popula t ion had a rela tively h igh butterfat content ( 4 . 4 3 percent) and the ma ting took p lace with Hols tein bulls .
Other s tudies of a s imilar nature have been reported by o ther w or kers (Tyler e t . al . 1949 ; Rober tson , 1954 ; Von Kros igk and Lush , 195 8 ; Hans son e t . al . 1961 and Mi e t . aZ. 1965) . Therefor e , from the evidence presented , there is hardly any doub t that inbreed ing carries· wi th i t r educed f er t ility , lowered viability in the offspring , especially
in the f ir s t few weeks af ter bir th , as wel l as decreased produc tion. I t is reasonab le to expect the resu l t s t o vary from case t o case , depending on the gene tic cons t i tution of the animals used for inbreeding . Various studies have also cl early shown tha t crosses between d i f f erent inbred lines , wi thin which d egeneratio n symptoms have been evident , result in increas ed f er tili ty and viability of the progeny . Indeed , such increases in vitality (heteros is) are o f ten seen in crosses between d ifferent
pedigree l ines or between breeds, even if no inbreeding o f impor tance has taken place previous ly .
B . of and
27.
From s tudies on mai ze, i t was believ ed tha t the increase in vigour , which always accompanied crosses between two inbred lines , was due to hetero zygos i ty per se . S o , in a locus with two alleles say A1 and A2 , the heterozygous combina tion A1A2 is superior to either o f the possib l e homo zygo tes , A1A1 or A2A2 . I t is thought that the alleles A1 and A2 have separate ef f ec t s (which in this case , may be respons ible for crucial s teps in a biochemical pa thway) and the sum of their different produc ts , or some interac t ion product between them , is superio r , in terms of
their effects o n heterosis than tha t produced by ei ther allele in the homo zygous s ta t e .
I t has also been sugges ted that heterosis may be explained in terms of ordinary dominance of genes relatively favourable for vigour and the correspond ing recessiveness of genes unfavourable for vigour . This implies that in crosses between highly homo zygous inbred lines the d ominant and recessive alleles were brought together and the lat ter could no t then exert their effec t . East and Jones ( 1919) have also s ta ted tha t homo zygos i ty for all advantageous genes cons tituted the
mos t favourab le conditions for growth and reproduc t ion . On the contrary ,
Srb ,
Owen and Edgar ( 1965) pointed out that no one has succeeded in producing , even in maize , a homo zygous ·line which exhibi t s the same viability as the heterozygous crossbreds . I t was then though t thatthis might b e due to l inkage b e tween favourab le and unfavourable genes , whereby the union of ent irely f avourable genes was prevented ; but t his explana t ion may be somewha t s imp l i s t i c .
'
28.
Inbreeding depr e s s ion and i t s mirror image ' hybrid vigour ' (he terosis) probably have several causes . Rei terating commen ts mad e earlier , i t i s c er ta in that the inbreeding t ends t o increase the homozygos i ty of the o f f spring , with the following consequences :
(1 ) Segregation of recessive genes which of ten have unfavourab le effects in the homo zygous cond i t io n .
( 2 } Reduced frequency of heterozygous g ene pairs . In so f a r a s favourable interac tion of alleles a t the same locus ( over dominance) o ccurs , reduced hetero zygosity is associa ted wi t h lowered viab ility .
(_3 )
Al teration in the gene combina t ions which , in turn , al ters the interac tion between genes a t different loci (ep i s tatic effect) .All three of these changes probably con tribute to the dec line in fertil i ty and general vigour which invar iab ly fo llows intense inbreeding when it is prac tised for several generations . Breeding popula t ions o f farm animals are highly hetero zygous and , as such , are balanced f o r a more favourab le interac tion be tween the majo ri ty of geno types and t heir environment . Increased homo zygos ity would d is turb this equilibr ium . On the o t her hand , one may expect that in many cases , a favourab le e f f e c t should result from fur ther increasing the he tero zygosity b y crosses between populations which have been bred a s separate units for many
generations .
To sum up , inb r eeding depression and hybrid vigour have , in t he main , the same bas ic causes. The heterozygosity and gene interact ion
'
29.
whi ch was lo s t by inbreeding can be restored by sui table crosses . Ind eed , even as early as 1 8 6 8 , when animal b reeding may be regard ed as s till in i t s infancy , Charles Darwin pointed out tha t inbreeding operates gradually but with accumulated eff ec t , whereas cross ing usually exhib its full e f f e c t in the first generation . To this day , this s t ill r e tains its validity .
VI STUDIES OF GENETIC CHANGES IN LIVESTOCK POPULATION$
S tudies concerned wi th the changes in the g ene tic makeup of
par ticular b reeds wi th t ime have been numerous . One mus t , however , b e cau tious about comparing r esults from var ious s tudies sinc e the genetic s i tuation in a par ticular set of c ircums tances may be qui te different f rom ano ther . This is true between and within b reeds , a t different t imes , and a t d ifferent locations . A summary o f these s tud ies is shown in Table 3 . 4 .
Insp ection of Table 3 . 4 shows that the increase in inbreeding seems qui te uniform in view of the diversity o f spec ies . Great
var iability exists , however , b e tween s tud ies for to tal inbreeding and this arises par tly from p edigrees being traced to more remo te dates in some breeds than in o ther s .
Thes e s tudies of b reed his tor ies may b e viewed from the s tandpoint of how much they indica te gene frequency to change merely f rom chance in the Mendel ian sampling which takes place when o ne genera tion replaces ano ther . Mos t of the s t udies show tha t the pure breeds lose something of the order of 0 . 5% of their heterozygos i ty per genera tion from this
TABLE :
I
nbreetling- a:nd:· -subdi.vision of the :pure breeds of livestock . :Breeds Studied Ca ttle : Shorthorns(
Gt.
:Britain)
Jerseys ( Gt . :Britain) Ayrshires�
Gt.
Britain)
��iesians Gt . Britain)
Shorthorns ( Gt . Britain) Holstein-Friesi�ns(
U . S . A .)
:Brawn Swiss(
U. S . A .)
HeTefords (U . S . A. ) Abe rdeen-��g�s(
U . S . A.)
Brown Siviss
(
Sivi tzerland)
TeleQ�rk(
Norway)
Red Danish
(
Denmark)Jersey
(
Aus tralia)
Polled Hereford (Australia)
Hereford
Jersey
(
New Sivim:J :Polard-Chi.na
(
U.
S.A. )
LanQ�ace
(
Denmark)
:Border Leicester ( Gt . :Bri t )
Rambouillet
(
U. S. A.)
Hampshire(
U. S. A .)
Horses : Clydesdale(
Scotland)
Thoroughbreds) (
U. S. A.)
}
Standardbred�
Saddle horse Author McPhee ��d Wright( 1925)
Smi th(
1928)
· Fo v1ler( 19 32)
Robertson and Asker
( 1951)
Clayton( 1956)
Lush , Halbert and Wil lham