Fat depth-age and fat depth-live weight data were fitted to linear, exponential and power equations and the goodness of fit of these equations evaluated.
Evaluating the R2 values, it was seen that the fitting of the equations to the data was generally satisfactory with values ranging from 0.5 to 0.85. The exponential equation was found to account for the least variation in the data while the linear fitting of fat depth to age had the highest R2 values (> 0.77). Specifically looking at equations with weight as an input factor, it was seen that the linear and power equations had similar R2 and RMSE values, but the linear was found to be marginally better and was therefore selected for further analysis. However, all the equations, with the possible exception of the exponential, appear to be suitable for modelling fat depth.
Since both selected equations were linear, the parameters evaluated were the same for both. The A parameter is the intercept value when the input, weight or age, is zero. All the A values are negative, and thus only mathematical, and not biological, significance can be attached to them. The B parameter, defining the angle of the slope, can however be interpreted biologically, where a higher value would indicate a higher rate of fat deposition and vice versa. The parameter estimates are given as least squares means in Tables 2 and 3.
No differences existed between sexes or genotypes for the A parameter (Table 2), but differences were present between both sex (P = 0.021) and genotype (P = 0.007) groups for the B parameter in the fat depth-age equation. Ewes (0.00440) had a higher value than rams (0.00400), indicating a greater rate of fat deposition while Merino x Dorper was the genotype with the highest value (0.00471). It was not significantly higher than Dohne x Dorper, Dohne x Dormer or Merino x Ile de France crosses. Dohne Merino had the lowest B parameter value of 0.00355, not significantly lower than the Dohne x Ile de France, Merino and Merino x Dormer groups. No differences were found between the Dohne x Dorper, Dohne x Dormer, Dohne x Ile de France, Merino x Dormer and Merino x Ile de France groups. Similarly, no differences between Dohne x Dormer, Dohne x Ile de France, Merino, Merino x Dormer and Merino x Ile de France were present.
Table 2
Least squares means and standard errors for the parameter values of the linear equation fitted to fat depth and age\(\left[{F}{D}={A}+{B}\times {t}\right]\)
Main effects
|
|
Parameter
|
|
|
A
|
B
|
Sex
|
Ram
|
-0.099 ± 0.0187
|
0.00400 ± 0.0001
|
|
Ewe
|
-0.144 ± 0.0187
|
0.00440 ± 0.0001
|
|
P-value
|
0.105
|
0.021
|
Genotype
|
Dohne Merino
|
-0.067 ± 0.0374
|
0.00355d ±0.0002
|
|
Dohne x Dorper
|
-0.138 ± 0.0374
|
0.00468ac ± 0.0002
|
|
Dohne x Dormer
|
-0.131 ± 0.0374
|
0.00449abc ± 0.0002
|
|
Dohne x Ile de France
|
-0.106 ± 0.0374
|
0.00406bcd ± 0.0002
|
|
Merino
|
-0.124 ± 0.0374
|
0.00399bd ± 0.0002
|
|
Merino x Dorper
|
-0.149 ± 0.0374
|
0.00471a ±0.0002
|
|
Merino x Dormer
|
-0.150 ± 0.0374
|
0.00406bcd ± 0.0002
|
|
Merino x Ile de France
|
-0.109 ± 0.0374
|
0.00418abc ± 0.0002
|
|
P-value
|
0.793
|
0.007
|
Means with different superscripts in the same column (a-d) differ significantly (P ≤ 0.05)
FD indicates fat depth in cm and t refers to the age of the animal in days
Table 3
Least squares means and standard errors for the parameter values of the linear equation fitted to fat depth and live weight\(\left[{F}{D}={A}+{B}\times {W}\right]\)
Main effects
|
|
Parameter
|
|
|
A
|
B
|
Sex
|
Ram
|
-0.339 ± 0.0316
|
0.0167 ± 0.006
|
|
Ewe
|
-0.526 ± 0.0316
|
0.0236 ± 0.006
|
|
P-value
|
< 0.001
|
< 0.001
|
Genotype
|
Dohne Merino
|
-0.404ab ± 0.0633
|
0.0187bc ± 0.001
|
|
Dohne x Dorper
|
-0.578bc ± 0.0633
|
0.0218ab ± 0.001
|
|
Dohne x Dormer
|
-0.369a ± 0.0633
|
0.0181c ± 0.001
|
|
Dohne x Ile de France
|
-0.336a ± 0.0633
|
0.0177c ± 0.001
|
|
Merino
|
-0.559bc ± 0.0633
|
0.0231a ± 0.001
|
|
Merino x Dorper
|
-0.591c ± 0.0633
|
0.0240a ± 0.001
|
|
Merino x Dormer
|
-0.290a ± 0.0633
|
0.0188bc ± 0.001
|
|
Merino x Ile de France
|
-0.353a ± 0.0633
|
0.0189bc ± 0.001
|
|
P-value
|
0.004
|
0.002
|
Means with different superscripts in the same column (a-c) differ significantly (P ≤ 0.05)
FD indicates fat depth in cm and W represents live weight in kilogram
For the fat depth-live weight equation parameters (Table 3), differences were present for both parameters. Rams had a significantly higher A parameter value than ewes (-0.339 vs -0.526) while genotypes also differed (P = 0.004). The Merino x Dormer, Dohne x Ile de France, Merino x Ile de France and Merino x Dormer crosses had the highest values and were not significantly higher than Dohne Merino. Dohne Merino, in turn did not differ from Dohne x Dorper and Merino. Merino x Dorper had the lowest value (-0.591), significantly lower than all groups except Dohne x Dorper and Merino.
Ewes had a higher B value than rams (0.0236 vs. 0.0167). The highest B parameters were found for Merino (0.0231) and Merino x Dorper (0.024), significantly higher than the other groups except for Dohne x Dorper. No differences were present between Dohne Merino, Merino x Dormer and Merino x Ile de France who were not significantly different from the lowest groups, Dohne x Dormer and Dohne x Ile de France.
Linear, exponential and power equations using age and live weight as inputs were once again compared to find the most suitable equation to model loin muscle growth between 100 and 220 days. The power equation with live weight as an input was deemed to provide the best fit, but still did not account for more than approximately 40% of the variation in the data and will therefore not be very accurate in predicting loin muscle depth. Results from the parameter analysis are given in Table 4 below. No significant differences were observed between sexes or genotypes for either parameter.
Table 4
Least squares means and standard errors for the parameter values of the power equation fitted to muscle depth and live weight\(\left[{M}{D}={A}\times {{W}}^{{B}}\right]\)
Main effects
|
|
Parameter
|
|
|
A
|
B
|
Sex
|
Ram
|
0.535 ± 0.072
|
0.490 ± 0.034
|
|
Ewe
|
0.396 ± 0.072
|
0.552 ± 0.034
|
|
P-value
|
0.175
|
0.207
|
Genotype
|
Dohne Merino
|
0.404 ± 0.143
|
0.530 ± 0.068
|
|
Dohne x Dorper
|
0.401 ± 0.143
|
0.515 ± 0.068
|
|
Dohne x Dormer
|
0.341 ± 0.143
|
0.573 ± 0.068
|
|
Dohne x Ile de France
|
0.448 ± 0.143
|
0.584 ± 0.068
|
|
Merino
|
0.621 ± 0.143
|
0.503 ± 0.068
|
|
Merino x Dorper
|
0.527 ± 0.143
|
0.489 ± 0.068
|
|
Merino x Dormer
|
0.598 ± 0.143
|
0.424 ± 0.068
|
|
Merino x Ile de France
|
0.386 ± 0.143
|
0.552 ± 0.068
|
|
P-value
|
0.809
|
0.778
|
MD indicates muscle depth in cm and W represents live weight in kilogram.