Proposal for ‘occupancy rate’ of common ancestors, a new selection index to evaluate economical traits in animal genetic resources

Figures & data

Figure 1. Diagrams showing how the occupancy rate (OR) is calculated for a sire. (a) Basic explanation of common ancestor bull OR calculation. Two examples of pedigree are presented. The males and females are represented by squares and circles, respectively. The blue squares indicate ancestral bulls. The red squares represent the sires for which the OR of the ancestral bull was calculated. (b) Practical explanation of common ancestor bull OR calculation. Males and females are represented by squares and circles, respectively. The red squares represent the sires for which the OR of the ancestral bull was calculated. We calculated the ORs of ancestors A, B, and C using Equation (1)(1) $$\mathit{\text{OR}}=\sum \left[{\left(\frac{1}{2}\right)}^n\mathit{\text{CA}}\right]$$(1) in the main text.

Theoretically, the sum of ORs can be between 0 and 0.5. If the sum of the ORs was zero, there were no A, B, or C records in the pedigree. If the OR was 0.5, it meant that A, B, or C occupied every male ancestor in the pedigree.

As the great-grandfather of the sire is ancestor A in the example pedigree, we recognize that the sire (red square) belongs to paternal line A. However, in practice, the OR of A is equal to the OR of C and lower than that of B.

Table 1. Summary of the carcass traits of the 308 sire candidates tested.

Traits	Mean	SD	Median	Minimum	Maximum	First quartile	Third quartile
a. Steer
BMS No.	6.9	1.1	6.9	3.9	9.9	6.2	7.6
CW (kg)	487.8	26.1	487.0	409.0	577.0	471.0	505.0
LMA (cm^2)	60.8	4.8	60.0	49.0	75.0	58.0	63.0
RT (cm)	8.0	0.4	8.0	6.9	9.1	7.7	8.2
SFT (cm)	2.5	0.3	2.5	1.6	3.4	2.3	2.7
YE	74.3	0.7	74.3	72.6	76.2	73.8	74.8
b. Heifer
BMS No.	6.9	1.2	6.8	3.8	10.9	6.1	7.7
CW (kg)	455.1	28.9	456.5	383	545	434.75	476
LMA (cm^2)	60.9	5.8	60	46	86	57	64
RT (cm)	7.9	0.4	7.9	7	9.2	7.7	8.2
SFT (cm)	2.9	0.4	2.8	1.8	3.9	2.6	3.1
YE	74.4	0.8	74.3	72.1	77.7	73.8	74.8

SD, standard deviation; BMS, beef marbling score; CW, carcass weight; LMA, loin muscle area; RT, rib thickness; SFT, subcutaneous fat thickness; YE, carcass yield.

Table 2. Summary of Wright’s F and ORs of Tajiri, Kedaka, and Fujiyoshi in the sire candidates (n = 308) tested.

Traits	Mean	SD	Median	Minimum	Maximum	First quartile	Third quartile
F (%)	–	–	4.330	0	25.773	1.832	7.427
OR of Tajiri	–	–	0.083	0.020	0.221	0.059	0.130
OR of Kedaka	–	–	0.066	0	0.179	0.023	0.101
OR of Fujiyoshi	–	–	0.016	0	0.113	0.003	0.039
Sum of the three ORs	0.188	0.024	0.187	0.100	0.257	0.173	0.205

Since the traits, except the sum of the three occupancy rates (ORs), were not normally distributed, the mean and standard deviation (SD) data are not shown.

Table 3. Pairwise correlations between carcass traits recorded for steers (below diagonal divide) and heifers (above diagonal divide).

	BMS	CW	LMA	RT	SFT	YE
BMS	–	0.3763**	0.7470**	0.3221**	−0.1063	0.6489**
CW	0.2605**	–	0.5709**	0.6355**	0.2267**	0.1874**
LMA	0.6697**	0.5055**	–	0.3958**	−0.1595**	0.8385**
RT	0.1949**	0.6391**	0.3588**	–	0.1701**	0.3202**
SFT	−0.0916	0.1705**	−0.1677**	0.1841**	–	−0.5741**
YE	0.5752**	0.1424*	0.8403**	0.3029**	−0.5464**	–

BMS, beef marbling score; CW, carcass weight; LMA, loin muscle area; RT, rib thickness; SFT, subcutaneous fat thickness; YE, carcass yield. Pearson’s correlations among traits and testing for non-correlation between two traits were performed using the Bell Curve for Excel (Social Survey Research Information Co., Tokyo, Japan).

* p < 0.05; **p < 0.01.

Table 4. Effects of ORs of the most prominent paternal ancestors Tajiri, Kedaka, and Fujiyoshi on BMS in JBK sires.

								ORs				Residual variance	Variance (%)
Traits		Gender	CW	LMA	RT	SFT	F (%)	Tajiri	Kedaka	Fujiyoshi
Coefficients	μ	b0	b2	b3	b4	b5	b6	b7	b8	b9	R^2 (%)
BMS
Full GLM model	−2.864	0.286	−0.0076	0.1713	0.171	0.186	−0.0241	4.82	5.65	7.53	53.75	391.11	3.11
SE of coefficients	0.803	0.105	0.0019	0.0077	0.109	0.106	0.0078	1.66	1.39	2.19
p value	< 0.01	< 0.01	< 0.01	< 0.01	0.117	0.078	< 0.01	< 0.01	< 0.01	< 0.01
Model omitting ORs	−2.41	0.213	--0.00546	0.16782	0.149	0.178	--0.01716	–	–	–	52.26	378.94
SE of coefficients	0.717	0.102	0.00174	0.00771	0.110	0.106	0.00739
p value	< 0.01	< 0.05	< 0.01	< 0.01	0.177	0.094	< 0.05

JBK, Japanese black cattle; BMS, beef marbling score; CW, carcass weight; LMA, loin muscle area; RT, rib thickness; SFT, subcutaneous fat thickness; F (%), Wright’s inbreeding coefficient; ORs, occupancy rates; GLM, generalized linear model; μ, model intercept; SE, standard error.

Table 5. Effects of ORs of the most prominent paternal ancestors Tajiri, Kedaka, and Fujiyoshi on CW in JBK sires.

								ORs				Residual variance	Variance (%)
traits		Gender	BMS	LMA	RT	SFT	F (%)	Tajiri	Kedaka	Fujiyoshi
Coefficients	μ	b0	b1	b3	b4	b5	b6	b7	b8	b9	R^2 (%)
CW
Full model	52.4	38.47	−3.470	2.514	28.13	14.92	−0.255	−26.8	136.7	85.1	72.33	174191	16.28
SE of coefficients	17.3	1.63	0.860	0.197	2.05	2.19	0.169	35.8	29.7	47.2
p value	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	0.131	0.454	< 0.01	0.072
Model omitting ORs	18.3	38.68	−2.904	2.546	32.21	15.52	0.227	–	–	–	66.98	208065
SE of coefficients	16.7	1.770	0.927	0.213	2.19	2.37	0.171
p value	0.272	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	0.185

JBK, Japanese black cattle; BMS, beef marbling score; CW, carcass weight; LMA, loin muscle area; RT, rib thickness; SFT, subcutaneous fat thickness; F (%), Wright’s inbreeding coefficient; ORs, occupancy rates; GLM, generalized linear model; μ, model intercept; SE, standard error.

Figure 2. Simulation data of the relationship between beef marbling score (BMS) and carcass weight (CW) vs. Fujiyoshi occupancy rate (OR) (x-axis) and Kedaka OR (y-axis), respectively, when the sum of the three ORs ≤ 0.180, 0.185, 0.190, 0.195, and 0.200.

Table 6. Comparative analysis of carcass traits among Tajiri, Kedaka, and Fujiyoshi paternal lines.

Paternal line	n	BMS (No.)	CW (kg)	LMA (cm^2)	RT (cm)	SFT (cm)	YE
Steer
Tajiri	124	6.7 ± 1.1 ^b	476.8 ± 23.6 ^b	59.7 ± 4.2 ^b	7.9 ± 0.4 ^b	2.5 ± 0.3 ^a	74.2 ± 0.7 ^a
Kedaka	99	7.0 ± 1.0 ^ab	495.3 ± 25.7 ^a	61.9 ± 4.7 ^a	8.0 ± 0.4 ^a	2.4 ± 0.3 ^a	74.4 ± 0.7 ^a
Fujiyoshi	85	7.1 ± 1.2 ^a	495.3 ± 24.8 ^a	61.0 ± 5.4 ^ab	8.1 ± 0.4 ^a	2.5 ± 0.3 ^a	74.2 ± 0.8 ^a
Heifer
Tajiri	124	6.7 ± 1.2 ^b	440.9 ± 23.5 ^b	59.6 ± 5.2 ^b	7.8 ± 0.3 ^b	2.9 ± 0.4 ^a	74.3 ± 0.8 ^a
Kedaka	99	7.0 ± 1.2 ^ab	467.4 ± 26.7 ^a	61.9 ± 5.3 ^a	8.0 ± 0.4 ^a	2.9 ± 0.4 ^a	74.4 ± 0.8 ^a
Fujiyoshi	85	7.2 ± 1.3 ^a	461.6 ± 29.7 ^a	61.8 ± 6.8 ^a	8.0 ± 0.4 ^a	2.9 ± 0.3 ^a	74.4 ± 0.9 ^a

BMS, beef marbling score; CW, carcass weight; LMA, loin muscle area; RT, rib thickness; SFT, subcutaneous fat thickness; YE, carcass yield. ^a,b Within a column for steers and heifers, means without a common superscript were significantly different (p < 0.05).

Data availability statement

The data that support the findings of this study are available from the corresponding author, HT, upon reasonable request.