TABLE 1. Expectations for genetic effects in a
diallel crossbreeeding system
|
Breed of sire (j) |
Breed of
dam (i) |
||
|
A |
B |
C |
|
|
A |
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
B |
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
C |
|
|
|
|
|
|
|
|
|
|
|
0 |
|
where:
and 
are breed
average individual and maternal effects, and 
, is the mean heterosis effect for a two-breed reciprocal
cross
, is mean phenotype for one purebred 
Xij, is mean
phenotype for a two-breed-cross 
breed maternal less
paternal effect, because
breed mean individual
effect
mean heterosis for
reciprocal cross.
specific reciprocal
effect
breed mean heterosis 
Table 2. Second phase of diallel mating design to estimate heterosis for maternal effects on progeny performance (hM)a.
|
Breed of dams |
Breed of
sires |
|||
|
A |
B |
C |
D |
|
|
A |
|
B•A |
C•A |
D•A |
|
B |
A•B |
|
C•B |
D•B |
|
C |
A•C |
B•C |
|
D•C |
|
D |
A•D |
B•D |
C•D |
|
|
AB+BA |
|
|
C(AB+BA) |
D(AB+BA) |
|
AC+CA |
|
B(AC+CA) |
|
D(AC+CA) |
|
AD+DA |
|
B(AD+DA) |
C(AD+DA) |
|
|
BC+CB |
A(BC+CB) |
|
|
D(BC+CB) |
|
BD+DB |
A(BD+DB) |
|
C(BD+DB) |
|
|
CD+DC |
A(CD+DC) |
B(CD+DC) |
|
|
|
|
||||
aSampling
error for estimates of 
will be minimum, for
any total scale of experiment, when equal
numbers of contemporary progeny are produced for each mating combination,
i.e. DA, DB, D(A•B) and D(B•A), and when each sire of a breed produces the same
proportion of progeny in each cross.
Table 3.
Expected fraction of defined genetic components in deviations of alternative
crossbreeding categories from weighted
mean of parental breeds relative to
Ft
heterosis, h = d + l/2gg.
|
generationa |
Heterosis |
|
|
Recombinationb |
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
1/2 |
1 |
1 |
1/4 |
1/2 |
0 |
0 |
0 |
0 |
0 |
0 |
|
A(A●B)
AB×A AB×B Composite |
1/2 |
1/2 |
1/2 |
1/4 |
1/2 |
1/4 |
1/2 |
1/4 |
1/2 |
0 |
0 |
|
1/2 |
1 |
0 |
|
|
|
|
|
|
|
|
|
|
SCALESYM32} |
1/8 |
1/2 |
0 |
0 |
0 |
0 |
0 |
0 |
|||
|
1/2 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
––– |
> |
|
|
|
|
|
|
|
|
|
|
n=2 |
1/2 |
1/2 |
1/2 |
1/4 |
1/2 |
1/4 |
1/2 |
1/4 |
1/2 |
0 |
0 |
|
n=3 |
2/3 |
2/3 |
2/3 |
1/3 |
2/3 |
1/3 |
2/3 |
1/3 |
2/3 |
0 |
0 |
|
n=4 |
3/4 |
3/4 |
3/4 |
3/8 |
3/4 |
3/8 |
3/4 |
3/8 |
3/4 |
0 |
0 |
|
Rotation |
|
–––> |
0 |
|
|
|
|
0 |
0 |
|
|
|
n=2 |
2/3 |
–––> |
0 |
1/9 |
4/9 |
1/9 |
4/9 |
0 |
0 |
0 |
0 |
|
n=3 |
6/7 |
–––> |
0 |
1/7 |
4/7 |
1/7 |
4/7 |
0 |
0 |
0 |
0 |
|
n=4 |
14/15 |
–––> |
0 |
7/45 |
28/45 |
7/45 |
28/45 |
0 |
0 |
0 |
0 |
|
C♂ Rotation♀ |
|
|
|
|
|
|
|
|
|
|
|
|
n=2 |
1 |
2/3 |
0 |
1/9 |
4/9 |
1/9 |
4/9 |
0 |
0 |
0 |
0 |
|
n=3 |
1 |
6/7 |
0 |
1/7 |
4/7 |
1/7 |
4/7 |
0 |
0 |
0 |
0 |
|
n=4 |
1 |
14/15 |
0 |
1/45 |
28/45 |
7/45 |
28/45 |
0 |
0 |
0 |
0 |
|
3-breed Cross |
|
|
|
|
|
|
|
|
|
|
|
|
C♂ × A ● B♀ |
1 |
1 |
0 |
1/8 |
1/4 |
0 |
0 |
0 |
|
|
|
|
a ● b♂ × C♀ |
1 |
0 |
1 |
1/8 |
1/4 |
0 |
0 |
0 |
|
|
|
|
4 Breed Cross CD♂ × AB♀ |
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
1/4 |
1/2 |
0 |
0 |
0 |
|
|
||
aMean of reciprocal
crosses, equilibrium for n sire breed rotation, or for qi,
fractions of n breeds in a composite at F3 or later
generation.
bFrom Dickerson
(1973) and Hill (1982).
Table 4.
Expected fraction of defined genetic components in linear contrasts between
means for alternative matinga
|
Code |
Linear
Contrast |
|
|
|
|
|
|
|
1 |
BA–AA |
(B–A)/2 |
BA |
0 |
0 |
0 |
0 |
|
2 |
BA–CA |
(B–C)/2 |
BA–CA |
0 |
0 |
0 |
0 |
|
3 |
A(BA)–AA |
(B–A)/4 |
BA/2 |
BA/8 |
(B–A)/2 |
BA |
0 |
|
4 |
(BA)2–AA |
(B–A)/2 |
BA/2 |
BA/4 |
(B–A)/2 |
BA |
0 |
|
5 |
B(BA)–AA |
3(B–A)/4 |
BA/2 |
BA/8 |
(B–A)/2 |
BA |
0 |
|
5–3 |
|
(B–A)/2 |
0 |
0 |
0 |
0 |
0 |
|
4–(3+5)/2 |
|
0 |
0 |
BA/8 |
0 |
0 |
0 |
|
6 |
A(BA)–A(CA) |
(B–C)/4 |
(BA–CA)/2 |
(BA–CA)/8 |
(B–C)/2 |
BA–CA |
0 |
|
7 |
(BA)2–(CA)2 |
(B–C)/2 |
(BA–CA)/2 |
(BA–CA)/4 |
(B–C)/2 |
BA–CA |
0 |
|
8 |
B(BA)–C(CA) |
3(B–C)/4 |
(BA–CA)/2 |
(BA–CA)/8 |
(B–C)/2 |
BA–CA |
0 |
|
8–6 |
|
(B–C)/2 |
0 |
0 |
0 |
0 |
0 |
|
7–(8+6)/2 |
|
0 |
0 |
(BA–CA)/8 |
0 |
0 |
0 |
|
9 |
D(BA)–AA |
|
(DB+DA)/2 |
BA/8 |
(B–A)/2 |
BA |
0 |
|
10 |
D(A·BA)–AA |
|
|
3BA/32 |
(B–A)/4 |
BA/2 |
BA/8 |
|
11 |
D(BA)2–AA |
|
(DB+DA)/2 |
4BA/32 |
(B–A)/2 |
BA/2 |
BA/4 |
|
12 |
D(B·BA)–AA |
|
|
3BA/32 |
3(B–A)/4 |
BA/2 |
BA/8 |
|
12–10 |
|
(B–A)/4 |
(DB–DA)/2 |
0 |
(B–A)/2 |
0 |
0 |
|
9–11 |
|
0 |
0 |
0 |
0 |
BA/2 |
–BA/4 |
|
13 |
D(BA–D(CA) |
(B–C)/4 |
(DB–DC)/2 |
(BA–CA)/8 |
(B–C)/2 |
BA–CA |
0 |
|
14 |
D(A·BA)–D(A·CA) |
(B–C)/8 |
(DB–DC)/4 |
3(BA–CA)/32 |
(B–C)/4 |
(BA–CA)/2 |
(BA–CA)/8 |
|
15 |
D(BA)2 –D(CA)2 |
(B–C)/4 |
(DB–DC)/2 |
(BA–CA)/8 |
(B–C)/2 |
(BA–CA)/2 |
(BA–CA)/4 |
|
16 |
D(B·BA)–D(C·CA) |
3(B–C)/8 |
3(DB–DC)/4 |
3(BA–CA)/32 |
(B–C)/4 |
(BA–CA)/2 |
(BA–CA)/8 |
|
13–15 |
|
0 |
0 |
0 |
0 |
(BA–CA)/2 |
–(BA–CA)/4 |
|
15–(14+16)/2 |
|
|
|
|
|
|
|
|
11–(10+12)/2 |
0 |
0 |
(BA–CA)/32 |
0 |
0 |
(BA–CA)/8 |
a"Individual
(I) and maternal (M) additive (gI and gM), heterosis hI
and hM and non-allelic gene interaction (rI and rM)
effects on performance traits.
Table 5. Level of significance (P) for a 5% mean difference (+ or -) between two strains in traits with differing Coefficient Variation (CV) and heritability (h2).
|
No progeny
per |
No. sires
/strain Ns |
SEa
|
t = |
Minimum t
forc |
|||
|
strain |
sire |
P05 |
P01 |
||||
|
a. CV = 20%; h2 = 10% |
|
|
|
|
|||
|
280 |
28 |
|
10 |
1.95 |
2.57 |
2.10 |
2.88 |
|
|
20 |
|
14 |
1.87 |
2.67 |
2.06 |
2.78 |
|
|
14 |
|
20 |
1.81 |
2.76 |
2.02 |
2.71 |
|
|
10 |
|
28 |
1.77 |
2.82 |
2.01 |
2.67 |
|
|
5 |
|
56 |
1.72 |
2.90 |
1.98 |
2.62 |
|
220 |
20 |
|
11 |
2.11 |
2.37 |
2.09 |
2.85 |
|
|
10 |
|
22 |
2.00 |
2.50 |
2.02 |
2.71 |
|
|
5 |
|
44 |
1.94 |
2.57 |
1.99 |
2.63 |
|
b. CV = 10%; h2 = 10% |
|
|
|
|
|||
|
140 |
20 |
|
7 |
1.45 |
3.44 |
2.18 |
3.06 |
|
|
10 |
|
14 |
1.32 |
3.78 |
2.06 |
2.78 |
|
|
5 |
|
28 |
1.25 |
3.99 |
2.01 |
2.67 |
|
100 |
20 |
|
5 |
1.72 |
2.91 |
2.31 |
3.36 |
|
|
10 |
|
10 |
1.56 |
3.20 |
2.10 |
2.88 |
|
|
5 |
|
20 |
1.48 |
3.37 |
2.02 |
2.71 |
|
80 |
20 |
|
4 |
1.92 |
2.60 |
2.45 |
3.71 |
|
|
10 |
|
8 |
1.75 |
2.85 |
2.14 |
2.98 |
|
|
5 |
|
16 |
1.66 |
3.02 |
2.04 |
2.75 |
|
60 |
20 |
|
3 |
2.22 |
2.25 |
2.78 |
4.60 |
|
|
10 |
|
6 |
2.02 |
2.47 |
2.23 |
3.17 |
|
|
5 |
|
12 |
1.92 |
2.60 |
2.07 |
2.82 |
|
40 |
20 |
|
2 |
2.72 |
1.84 |
4.30 |
9.92 |
|
|
10 |
|
4 |
2.48 |
2.02 |
2.45 |
3.71 |
|
|
5 |
|
8 |
2.34 |
2.13 |
2.14 |
2.98 |
with 
Total phenotypic
variance are expressed as the squared coefficient of variation (%), assuming
one (1) progeny per dam.
cSee Table A.3
in Steele and Torrie (1960) or any other source of probability values for t-ratio, plus or minus mean difference (i.e.
2-tailed distributions).
|
FAO TECHNICAL PAPERS |
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|
FAO ANIMAL PRODUCTION AND HEALTH
PAPERS |
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1 |
Animal breeding: selected articles
from the World Animal Review, 1977 (C E F S) |
37 |
African animal trypanosomiasis:
selected articles from the World Animal Review, 1983 (E F) |
|
2 |
Eradication of hog cholera and
African swine fever, 1976 (E FS) |
38 |
Diagnosis and vaccination for the
control of brucellosis in the Near East, 1982 (Ar E) |
|
3 |
Insecticides and application
equipment for tsetse control, 1977 (E F) |
39 |
Solar energy in small-scale milk
collection and processing, 1983 (E F) |
|
4 |
New feed resources, 1977 (E/F/S) |
40 |
Intensive sheep production in the
Near East, 1983 (Ar E) |
|
5 |
Bibliography of the criollo cattle
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41 |
Integrating crops and livestock in
West Africa, 1983 (E F) |
|
6 |
Mediterranean cattle and sheep in
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42 |
Animal energy in agriculture in
Africa and Asia, 1984 (E/FS) |
|
7 |
The environmental impact of tsetse
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43 |
Olive by-products for animal feed,
1985 (Ar E F S) |
|
7 Rev. |
1. The environmental impact of
tsetse control operations, 1980 (E F) |
44/1 |
Animal genetic resources
conservation by management, data banks and training, 1984 (E) |
|
8 |
Declining breeds of Mediterranean
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44/2 |
Animal genetic resources:
cryogenic storage of germplasm and molecular engineering, 1984 (E) |
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9 |
Slaughterhouse and slaughterslab
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43 |
Olive by-products for animal feed,
1985 (Ar E F S) |
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10 |
Treating straw for animal feeding,
1978 (C E F S) |
44/1 |
Animal genetic resources
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11 |
Packaging, storage and
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44/2 |
Animal genetic resources:
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12 |
Ruminant nutrition: selected
articles from the World Animal Review, 1 978 (C E F S) |
45 |
Maintenance systems for the dairy
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|
13 |
Buffalo reproduction and
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46 |
Livestock breeds of China, 1984 (E
F S) |
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14 |
The African trypanosomiases, 1979
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47 |
Réfrigération du lait à
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des transports, 1985 (F) |
|
15 |
Establishment of dairy training
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48 |
La fromagerie
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|
16 |
Open yard housing for young
cattle, 1981 (Ar E F S) |
49 |
Manual for the slaughter of small
ruminants in developing countries, 1985 (E) |
|
17 |
Prolific tropical sheep, 1980 (E F
S) |
50 |
Better utilization of crop
residues and by-products in animal feeding: research guidelines - 1. State of
knowledge, 1985 (E) |
|
18 |
Feed from animal wastes: state of
knowledge, 1980 (C E) |
50/2 |
Better utilization of crop
residues and by-products in animal feeding: research guidelines - 2. A practical
manual for research workers, 1986 (E) |
|
19 |
East Coast fever and related
tick-borne diseases. 1980 (E ) |
51 |
Dried salted meats: charque and carne-de-sol, 1985 (E) |
|
20/1 |
Trypanotolerant livestock in West
and Central Africa – Vol. 1. General study, 1980 (E F) |
52 |
Small-scale sausage production,
1985 (E) |
|
20/2 |
Trypanotolerant livestock in West
and Central Africa – Vol. 2. Country studies, 1980 (E F) |
53 |
Slaughterhouse cleaning and
sanitation, 1985 (E) |
|
20/3 |
Le bétail
trypanotolérant en Afrique occidentale et centrale – Vol. 3. Bilan d'une décennie, 1988 (F) |
54 |
Small ruminants in the Near East -
Vol. I. Selected papers presented for the Expert Consultation on Small
Ruminant Research and Development in the Near East (Tunis, 1985), 1987 (E) |
|
21 |
Guideline for dairy accounting,
1980 (E) |
55 |
Small ruminants in the Near East -
Vol. II. Selected articles from World Animal Review 1972-1986, 1987
(Ar E) |
|
22 |
Recursos
genéticos animales en América Latina, 1981 (S) |
56 |
Sheep and goats in Pakistan, 1985
(E) |
|
23 |
Disease control in semen and
embryos, 1981 (C E F S) |
57 |
The Awassi sheep with special
reference to the improved dairy type, 1985 (E) |
|
24 |
Animal genetic resources -
conservation and management, 1981 (C E) |
58 |
Small ruminant production in the
developing countries, 1986 (E) |
|
25 |
Reproductive efficiency in cattle,
1982 (C E F S) |
59/1 |
Animal genetic resources data
banks - 1. Computer systems study for regional data banks, 1986 (E) |
|
26 |
Camels and camel milk, 1982 (E) |
59/2 |
Animal genetic resources data
banks - 2. Descriptor lists for cattle, buffalo, pigs, sheep and goats, 1986
(E F S) |
|
27 |
Deer farming, 1982 (E) |
59/3 |
Animal genetic resources data
banks - 3. Descriptor lists for poultry, 1986 (E F S) |
|
28 |
Feed from animal wastes: feeding
manual, 1982 (C E) |
60 |
Sheep and goats in Turkey, 1986
(E) |
|
29 |
Echinococcosis/hydatidosis
surveillance, prevention and control: FAO/UNEP/WHO
guidelines, 1982 (E) |
61 |
The Przewalski horse and
restoration to its natural habitat in Mongolia, 1986 (E) |
|
30 |
Sheep and goat breeds of India,
1982 (E) |
62 |
Milk and dairy products:
production and processing costs, 1988 (E FS) |
|
31 |
Hormones in animal production,
1982 (E) |
63 |
Proceedings of the FAO expert
consultation on the substitution of imported concentrate feeds in animal
production systems in developing countries, 1987 (C E) |
|
32 |
Crop residues and agro-industrial
by-products in animal feeding, 1982 (E/F) |
64 |
Poultry management and diseases in
the Near East, 1987 (Ar) |
|
33 |
Haemorrhagic septicaemia, 1982 (E
F) |
65 |
Animal genetic resources of the
USSR, 1989 (E) |
|
34 |
Breeding plans for ruminant
livestock in the tropics, 1982 (E FS) |
|
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35 |
Off-tastes in raw and
reconstituted milk, 1983 (Ar E F S) |
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36 |
Ticks and tick-borne diseases:
selected articles from the World Animal Review, 1983 (E F S) |
|
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66 |
Animal genetic resources - strategies
for improved use and conservation, 1987 (E) |
100 |
Programme for the control of
African animal trypanosomiasis and related development, 1992 (E) |
|||||
|
67/1 |
Trypanotolerant cattle and
livestock development in West and Central Africa - Vol I, 1987 (E) |
101 |
Genetic improvement of hair sheep
in the tropics, 1992 (E) |
|||||
|
67/2 |
Trypanotolerant cattle and
livestock development in West and Central Africa - Vol II, 1987 (E) |
102 |
Legume trees and other fodder
trees as protein sources for livestock, 1992 (E) |
|||||
|
68 |
Crossbreeding Bos indicus and
Bos taurus for milk production in the tropics, 1987 (E) |
103 |
Improving sheep reproduction in
the Near East, 1992 (Ar) |
|||||
|
69 |
Village milk processing, 1988 (E F
S) |
104 |
The management of global animal
genetic resources, 1992 (E) |
|||||
|
70 |
Sheep and goat meat production in
the humid tropics of West Africa, 1989 (E/F) |
105 |
Sustainable livestock production
in the mountain agro-ecosystem of Nepal, 1992 (E) |
|||||
|
71 |
The development of village based
sheep production in West Africa, 1988 (Ar E F S) |
106 |
Sustainable animal production from
small farm systems in South-East Asia, 1993 (E) |
|||||
|
|
(Published as Training manual for
extension workers, IWS5840E) |
107 |
Strategies for sustainable animal
agriculture in developing countries, 1993 (E) |
|||||
|
72 |
Sugarcane as feed, 1988 (E/S) |
108 |
Evaluation of breeds and crosses
of domestic animals, 1993 (E) |
|||||
|
73 |
Standard design for small scale
modular slaughterhouses, 1988 (E) |
109 |
Bovine spongiform encephalopathy,
1993 (E) |
|||||
|
74 |
Small ruminants in the Near East -
Vol III North Africa, 1989 (E) |
110 |
L'amélioration génétique des
bovins en Afrique de I'Ouest, 1993 (F) |
|||||
|
75 |
The eradication of ticks, 1989
(E/S) |
Availability: Avril 1993 |
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|
76 |
Ex situ cryoconservation
of genomes and genes of endangered cattle breeds by means of modern
biotechnological methods, 1989 (E) |
Ar |
- |
Arabic |
Multil |
- |
Multilingual |
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C |
- |
Chinese |
* |
|
Out of print |
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|
77 |
Training manual for embryo
transfer in cattle, 1991 (E) |
E |
- |
English |
** |
|
In preparation |
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|
78 |
Milking, milk production hygiene
and udder health, 1989 (E) |
F |
- |
French |
|
|
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|
79 |
Manual of simple methods of meat
preservation, 1990 (E) |
P |
- |
Portuguese |
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|
80 |
Animal genetic resources - a
global programme for sustainable development, 1990 (E) |
S |
- |
Spanish |
|
|
|
|
|
81 |
Veterinary diagnostic bacteriology
- a manual of laboratory procedures of selected diseases of livestock, 1990
(E F) |
|
||||||
|
82 |
Reproduction in camels - a review,
1990 (E) |
The FAO
Technical Papers are available through the authorized |
||||||
|
83 |
Training manual on artificial
insemination in sheep and goats, 1991 (E) |
FAO Sales
Agents or directly from Distribution and Sales Section, |
||||||
|
84 |
Training manual for embryo
transfer in water buffaloes, 1991 (E) |
FAO, Viale delle Terme di Caracalla, 00100 Rome, Italy |
||||||
|
85 |
The technology of traditional milk
products in developing countries, 1990 (E) |
|
||||||
|
86 |
Feeding dairy cows in the tropics,
1991 (E) |
|||||||
|
87 |
Manual for the production of
anthrax and blackleg vaccines, 1991 (E F) |
|||||||
|
88 |
Small ruminant production and the
small ruminant genetic resource in tropical Africa, 1991 (E) |
|||||||
|
89 |
Manual for the production of
Marek's disease, Gumboro disease and inactivated Newcastle disease vaccines,
1991 (E F) |
|||||||
|
90 |
Application of biotechnology to
nutrition of animals in developing countries, 1991 (E F) |
|||||||
|
91 |
Guidelines for slaughtering, meat
cutting and further processing, 1991 (E) |
|||||||
|
92 |
Manual on meat cold store
operation and management, 1991 (E S) |
|||||||
|
93 |
Utilization of renewable energy
sources and energy saving technologies by small scale milk plants and
collection centres, 1992 (E) |
|||||||
|
94 |
Proceedings of the FAO expert
consultation on the genetic aspects of trypanotolerance, 1992 (E) |
|||||||
|
95 |
Roots, tubers, plantains and
bananas in animal feeding, 1992 (E) |
|||||||
|
96 |
Distribution and impact of
helminth diseases of livestock in developing countries, 1992 (E) |
|||||||
|
97 |
Construction and operation of
medium-sized abattoirs in developing countries, 1992 (E) |
|||||||
|
98 |
Small scale poultry processing,
1992 (E) |
|||||||
|
99 |
In situ conservation
of livestock and poultry, 1992 (E) |
|||||||
B(A
