Estimation of general, specific and maternal combining abilities in crosses among inbred lines of

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Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
1948
Estimation of general, specific and maternal
combining abilities in crosses among inbred lines of
swine
Charles Roy Henderson
Iowa State College
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Recommended Citation
Henderson, Charles Roy, "Estimation of general, specific and maternal combining abilities in crosses among inbred lines of swine "
(1948).Retrospective Theses and Dissertations. 12780.
https://lib.dr.iastate.edu/rtd/12780
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ISTIM&TIOH 0F(G1®E&1., SPICIFIC AHD mTSBML)
CCMBIHIHG ABILITIES IH CSOSSIS momX
IBBEED LIffiS OF SflW
by
Charles Boy Heodersoa
A Bissertation Submitted to the
GradiHite Faoulty is B&rti&I FuXfilli^zit of
The Requirements for «ie Degree of
BOeTOK OF PHIL<^OPffir
Ifaijor Subjects: Animl Breeding
a.,. _
Approveds
Signature was redacted for privacy.
Ijk CChhaarrggee of Major Work
Signature was redacted for privacy.
•ds of ifejor Departments
Signature was redacted for privacy.
Deaa of Sradimte 'College
Iowa State College
1948
UMI Number: DP11842
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TABI^ OF eOMTSIfS
I. INraODUCTOT 1
II. STATISTICAt METHODS 8
A. The Mathsflwtleftl Model .................................. 8
B. Statistical Problems Ih the Analysis of the Single Crose
Data ................................................... 12
C. The li®ast Square# Analysis of Noa-OrthogsnalD ata ...... 14
1. Prineiples of least squares sad the nerml
equations 15 ^
2# Istiwition of fsra«et@rs aod teste of hypotheses * l6
3. Coa^atatioaal shortcat# la the 8®l«tioa of least
squares equfttions 21
4» S®i^li«g errors of least squares estimtes. ...... 27
D. Aijustttent of Ijeast Squares IstiMtes ®teii Iffects .are •
Randoaly Praim fro* Popilatioas with KsBom Variaaees 33
1. fhe aaxisEia likelihood solution 35
2. Co^>utatloaal proeedttre for adjusti»g least
squares estina%i# 33
B. Bstintion of a Faraabter Assumed to he a Lisear
flinotioa of Eandoaly liMtini gffects ..................... 39
F. Sstiimtion of fteo^oBents of Varlaaee int he.Moa-
Orthogo»al <6ase 41
1. Istimtes froB a eoB-reutiosal amlysis of
varianoe 42
2. Sstiaates from least squares sums of squares ....* 44
G. Applieation of the Methods to the Analysis of Siagle
Gross Bata 4$
1. fests of hypotheses $Q
2. Least squares estiaates 54
3. Sampling errors of the least squares estiimtes. .. 5T
4. Adjustment of the least squares estiiBBates •«*....« 61
5< Estimtion of eoi^onests of variaBoe 44
'6. Predietion of line cross perforsMinee ............. 68
ill
P&ge
H. Ixttnsion of the Methois t© Mor® 60)^1® x Tests of
Mnm n
1* Coa8ii«r«ti©Q ©f iiff®r®Be®s aaeag sires 72
2. CoBfliteration @f diiffer®ne«s aaosg dasis 74
3» Br»ei ero8C«B 74
4. fhre®«^a7 Grosses ................................ 75
I. Boim EalaBeed SeaigM for Testily Lines 80
X, SiAgl® erosses 8l
2. Top eross test .................................... 90
3« Baleneod ineos^lete bloek design for f»r»
testing $2
4* Three-nmy erosses 93
5. Appraisal of lines by their own performsAoe ...... 97
6. Relatiw efficiencies of differeat bala&eei
designs 9^
J. lstl«tioa of %tiwa ftiaber of Maes to Test in Single
Crosses 100
III. MAtYSIS BXPffilHENTAI. E1SW.TS ............................... 101
A. Source mnA ieope of the Sata 102 /
1. Methods of jlnnlysis fertaiaiag to the Available Single
Cross Mt« 105
C, Tests of Signifioanee 112
1. Test of hypothesis that rtf "0 113
2. Test ©f hypothesis ttot Sy ® 0 114
3. Test of hypothesis that » 0 115
4. test of hypothesis that gf " 0 ................... Il6
£>. Least Stpares Sstiiaates 117
1. Saapling Irrors of the lieast Squares lstia»tes ......... 124
P. IstiMtes of ¥ariane©s ................................. 126
Cr. MJustBSttBt of Iteast Sfuares Istiaates .................. 132
I¥. DISCBSSIca IMD 1PPLIC4TI01S .................................. I36 '
A. lelatioB of th® Methods of Analysts of Sii^leC rosses
to More Faailiar Methods in Aaiwd Breeding, I36
It
P&ge
B« ©f ijEferiaental levults ................. I38
1» f<^eral eoal>iaiBg uMllty 14©
2. Internal effeets 143
Sfeeifie effeeis 145
4. Sex linkage effeeic 144
0. Wiliaation #f th® lettmtes of tiae aad Cr^ss fcla®
fiharaeteristies 144
1* S«l#etioa of line* for t®p erdsstis^g 144
2» S«leetioB ©f lines for as® a® fewil® parenta ..... 14?
3» Selecti©n #f sfscifie ereases 148
B. Ghole« «f m Ifficieat fssting Profraa ................. 149
1. Valme of further testing of existiag llaas 150
2. D«t®riBiHing the optimum aaafcer of lines to test .. 152
3. T&p eross •8* single cr&sa taat 154
4. Sarly culling ©f lines f©il@*ed by further
tasting 155
!• farther Apflioatioag of the lathefl of Saleeting Sifflal-
tanaottsly f#r I®th Qmmml ani gpeeifi® Iff acts ........ 154
T. SWMbM 159
?I. I.im4TWl CI® 143
Til. ACKIOfUTOMSlf 144
APPSMSIX I. IXAMPI^ m AiAtisis m swui
CROSSIS ........................................................ 14T
A. Taats of i^STpothasas 148
1. Test of hypothasis that rjj « 0 l48
2* f«#t »f hypatheais that S|j * 0 assoaiBg r^i • 0 . 1T4
3. Teat ©f hypethasia that a.. * 0 aaauaing a, »
. r^j • 0 175
4. fast of hypethasia that a* « 0a aaasing rjj " 0 .. 1??
5. Ttst «f hypathasla that mi• 0 aaaaadsg a,* •
r^. « 0. ...............177
4, Telt of hypathaaia that g£ * 0 aasusiiig a^j »
HS " 0
7. taat @f hypathaaia that gi.« 0 as8imisg_r4i »
®14 » » 0. ........... 178
V
F»g#
B. %mms% Sqtmr#® Estimtes 17®
1. l«ttaat®s @f gj,. ffli, Bjf, ITS
t» Istiaaies ®f au, Sjj a»#aiBdng r^« « 0 ........ 181
3. Istiatttes ©f jtt, gj, aj iss«ainf By • • 0 lS2
§, Sasi>liag Irrera l8|
S. 60a|»#ssnts Ii6
1. ef l8t
2m Xetimtim l8f
3* 108
4. IsiteiiM ef 1^
APPENDIX II. NUMERicAi. mm^m m amauub GT MUMcm
SIKGLS CROSS DESIGN IfO
4. Sq^ttares Isiimies 190
B« of Ryfot}i«ees 1ft
Im Teat of th« hypothesis ttet ry • 0 asaaaiag
2. list of the hypothasie that • 0 assumiag
/ 0 m
3« l^st of the hypothesis that * 0 .•.*.••••••«««. 193
4m f®8t of tha hffothesia that gt * 0 assaaiRg that
^ 194
&• IstiMtioB of fcriaaee !€ oni)on@iits 194
latimtion of 195
1# tonstmetioa ©f Isiexes for 8®l««ti»g Llaes aai
Groasas 195
I, lifEODUGTIOM
Bueeessful «f iafer#Ming by the founders of »ur present
day livestock breeds and the eowiereial saeee»0 of hybrid eorn hmr@ lei t®
83^ intenaive investigations lat® the posaibilities ef utilizing these
methods to improve 8*1«®». Three i^ortantp robleas hsve arisen in eonnee**
tion with these stadiee. (W&ml and lash, 1948.)
I. low best to »JEe inbred lines. This problem is closely re­
lated to the question of the effeeta of inbreeding*
2* How .best to test inbred lines. For exanspl©, ean liaes be
Jttdfed on their em. perforaane© or aast they be tested in
Htttinge with other line# or with non-iabredaf If own per-
forsmaee i# an iaadeqtiat© te®t, what type of tester stoek
should b® aeedt
3. Ho* bfgt t© utilise Inbred lines in eo»ereial porit: produc­
tion.
The effeeta of inbreeding have been investigated very extensivel#: by
several of the experiaent stations of the Morth CentmlS tates in coopera­
tion with the tJnited.S tates Department of Igriealture.' The data from these
exferiaents deaonstrate that inbreeding is aceo^anied by tmrk04 loss of
sow frodttotivlty* , ^e namber of pigs weaned,' 'per litter has deereased
• >
linearly with increase in coefficient of inbfeediaf. (Oiekerson et
194?.) ae effect of inbreeding on the weight of the individual fig Ms been
less pronoaneed than the effect on litter nttmber. It appears pj^bable fro*
these studies that the mst efficient way to ^ke inbred lines is to sake
ffiany swill lines and to inbreed rapidly,r ather than to Mke fewer large