Age-related linear and nonlinear modelling of semen quality parameters in Miranda donkeys

Figures & data

Table 1. Models and model syntax.

Model	Initials	Model syntax/equation
Linear	LIN	Y = b0 + (b1 * t)
Logarithmic	LOG	Y = b0 + (b1 * ln(t)
Inverse	INV	Y = b0 + (b1/t)
Quadratic	QUA	Y = b0 + (b1 * t) + (b2 * t**2)
Cubic	CUB	Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3)
Power	POW	Y = b0 * (t**b1) or ln(Y) = ln(b0) + (b1 * ln(t))
Compound	COM	Y = b0 * (b1**t) or ln(Y) = ln(b0) + (ln(b1) * t)
S-curve	SCRV	Y = e**(b0 + (b1/t)) or ln(Y) = b0 + (b1/t)
Logistic	LGI	Y = 1/(1/u + (b0 * (b1**t))) or ln(1/y-1/u) = ln (b0) + (ln(b1) * t)
Growth	GRO	Y = e**(b0 + (b1 * t)) or ln(Y) = b0 + (b1 * t)
Exponential	EXP	Y = b0 * (e**(b1 * t)) or ln(Y) = ln(b0) + (b1 * t)

t represents time expressed in year units. Accessed from IBM Corp (2015).

Table 3. Summary of the measures for model fitness and flexibility criteria of the best fitting linear or nonlinear regression models for each particular trait.

Traits	SS	df	MS	F	Sig.	RSS	MSE	MMSE	AIC	AICc	BIC
Gel-free ejaculate volume (mL)	37553.61	3.00	12517.87	15.96	0.00	28232.33	784.23	3.61	264.37	264.38	10498.64
Ejaculate concentration (× 10^6/mL)	10.73	1.00	10.73	73.64	0.00	5.54	0.15	0.00	−77.08	−77.07	−3159.33
Total sperm number (TSN) (× 10^9)	2617107713.84	3.00	872369237.95	9.71	0.00	3235844535.54	89884570.43	414214.61	730.35	730.35	29137.57
Motility (%)	5886.41	3.00	1962.14	15.17	0.00	4657.97	129.39	0.60	192.30	192.30	7615.62
Normal morphology (%)	2276.62	3.00	758.87	17.11	0.00	1596.48	44.35	0.20	149.47	149.47	5902.37
Abnormal morphology (%)	1966.86	3.00	655.62	14.42	0.00	1636.92	45.47	0.21	150.47	150.47	5942.40
GSI in 1:1	4.69	3.00	1.57	29.97	0.00	1.88	0.05	0.00	−120.30	−120.30	−4888.48
TMS (× 10^9)	1790755678.46	3.00	596918559.49	13.23	0.00	1624416224.92	45122672.91	207938.58	702.78	702.78	28034.94

GSI: gonadosomatic index; TSN: total sperm number; TMS: total motile sperm.

Table 2. Summary of the results for determination coefficients, curve shape parameters, and peak for best fitting models for all the variables in the study.

Traits	Model	R square	F	df1	df2	Sig.	Constant	b1	b2	b3	R/Peak
Gel-free volume (mL)	Cubic	0.571	15.96	3	36	0.000	−29.439	2198.00	−0.013	0.000	0.9365
Sperm concentration (× 10^6/mL)	Exponential	0.660	73.64	1	38	0.000	485.332	−0.01	4560.000	59360.000	0.9232
TSN (× 10^9)	Cubic	0.447	9.71	3	36	0.000	−36037.895	1636.67	−12782.000	0.028	27779.1210
Motility (%)	Cubic	0.558	15.17	3	36	0.000	74.765	0.11	−0.001	0.000	78.0657
Morphologically normal (%)	Cubic	0.588	17.11	3	36	0.000	100.077	−0.35	0.004	0.000	95.6015
Morphologically abnormal (%)	Cubic	0.546	14.42	3	36	0.000	−0.006	0.35	−0.004	0.000	10.4817
GSI	Cubic	0.714	29.97	3	36	0.000	1.817	−0.03	0.000	0.000	1.3009
TMS (× 10^9)	Cubic	0.524	13.23	3	36	0.000	−26411.888	1207.80	−9.346	0.020	21023.5586

GSI: gonadosomatic index; TSN: total sperm number; TMS: total motile sperm.

Figure 1. Gel-free ejaculate volume (mL) modelling using a cubic function.

Figure 2. Ejaculate concentration(×10⁶/mL) modelling using a compound function.

Figure 3. Total Spermatozoa number (TSN) in × 10⁹ modelling using a cubic function.

Figure 4. Sperm motility (%) modelling using a cubic function.

Figure 5. Normal sperm morphology (%) modelling using a cubic function.

Figure 6. Abnormal sperm morphology (%) modelling using a cubic function.

Figure 7. Gonadosomatic Index modelling using a cubic function.

Figure 8. Total motile sperm (× 10⁹) modelling using a cubic function.

Data availability statement

Data will be made available from the corresponding authors F.J.N.G. and A.M.B. upon reasonable request.