Description of the peach fruit growth curve by diphasic sigmoidal nonlinear models

Fernandes, Jaqueline Gonçalves; Silva, Édipo Menezes da; Ribeiro, Thais Destefani; Silva, Edilson Marcelino; Fernandes, Tales Jesus; Muniz, Joel Augusto

doi:10.1590/0100-29452022875

Abstract

The aim of this study was to describe the growth curve of “Aurora 1” peaches using fruit height and diameter data over time through diphasic sigmoidal models constructed from eight combinations of the following models: Brody, Gompertz and Logistic. Data were obtained from an experiment carried out in 2005 in the municipality of Vista Alegre do Alto, São Paulo, Brazil. The parameters of models were adjusted by the least squares method using the Gauss-Newton algorithm implemented in the R software. Assumptions of normality, homogeneity and independence of residues were verified based on Shapiro-Wilk, Breush and Pagan and Durbin-Watson tests, respectively. The goodness of fit of models was verified according to the corrected Akaike information criterion (AICc), residual standard deviation (RSD), asymptote adjustment index (AI) and nonlinearity measures. All models adjusted for both fruit height and diameter variables met the assumptions of normality, independence and homoscedasticity of errors. In addition, all of them present good quality of fit to fruit height and diameter data, since they presented AI values close to one and low RSD values and non-linearity measures. However, the double Gompertz (GG) and the Logistic + Gompertz (LG) models presented, respectively, the best quality of fit to fruit height and diameter data in relation to the other models. It could be concluded that all diphasic sigmoidal models evaluated showed good fit to height and diameter data and can be used to describe the growth curve of “Aurora-1” peaches, according to goodness of fit criteria. However, it is important to highlight that GG and LG models presented the best quality of fit and can be selected to describe the height and diameter growth of “Aurora 1” peach fruits, respectively, with maximum expected growth close to 63 mm in height and 48 mm in diameter.

Index terms
Peach Growth; Double Gompertz Model; Logistics + Gompertz Model; Double Sigmoidal Model

[TFN0201] ¹
BG = Brody + Gompertz; BL = Brody + Logistic; GG = Gompertz + Gompertz; GB = Gompertz + Brody; GL = Gompertz + Logistic; LL = Logistic + Logistic; LB = Logistic + Brody; LG = Logistic + Gompertz.

Variables	Number of collections	Minimum	Maximum	Mean	Median
Height (mm)	14	9.53	57.36	38.57	37.89
Diameter (mm)	14	4.83	50.31	29.50	26.85

Variable	Model¹	Parameters
	Model¹	A₁	A₂	B₁	B₂	K₁	K₂
	BG	36,32	61,55	16,82	82,73	0,0943	0,0529
	BL	34,68	59,26	17,00	86,02	0,1036	0,0819
	GG	35,03	62,43	21,81	81,79	0,1444	0,0485
	GB	25,24	61,55	82,73	16,82	0,0529	0,0943
	GL	33,35	59,76	21,57	85,12	0,1559	0,0754
	LL	32,35	60,37	24,09	84,65	0,2170	0,0690
	LB	24,58	59,26	86,02	17,00	0,0819	0,1036
	LG	34,10	63,79	24,43	81,56	0,2041	0,0436
	BG	27,78	48,06	17,90	81,69	0,0728	0,1448
	BL	27,53	47,55	17,93	84,55	0,0743	0,2217
	GG	26,70	48,08	25,07	81,20	0,1263	0,1397
	GB	20,28	48,06	81,69	17,90	0,1448	0,0728
	GL	26,42	47,57	24,97	84,12	0,1294	0,2103
	LL	25,91	47,62	28,17	83,85	0,1923	0,2023
	LB	20,02	47,55	84,55	17,93	0,2217	0,0743
	LG	26,22	48,12	28,35	80,90	0,1868	0,1367

Variable	Model ¹	Shapiro-Wilk	Durbin-Watson	Breusch-Pagan
Height	BG	0.26	0.88	0.17
	BL	0.45	0.66	0.15
	GG	0.14	0.95	0.18
	GB	0.26	0.95	0.17
	GL	0.25	0.88	0.15
	LL	0.38	0.93	0.16
	LB	0.45	0.68	0.15
	LG	0.33	0.85	0.21
Diameter	BG	0.17	0.47	0.28
	BL	0.20	0.22	0.19
	GG	0.45	0.77	0.09
	GB	0.17	0.65	0.21
	GL	0.45	0.75	0.16
	LL	0.48	0.71	0.12
	LB	0.20	0.59	0.36
	LG	0.23	0.67	0.08
¹BG = Brody + Gompertz; BL = Brody + Logistic; GG = Gompertz + Gompertz; GB = Gompertz + Brody; GL = Gompertz + Logistic; LL = Logistic + Logistic; LB = Logistic + Brody; LG = Logistic + Gompertz.

Variable	Model ¹	Quality measures ²
Variable	Model ¹	AICc	RSD	AI	K^T	K^N
Height	BG	56.39	1.46	0.88	4.7	0.61
	BL	57.26	1.5	0.92	5.04	0.45
	GG	55.85	1.43	0.87	4.46	0.52
	GB	56.39	1.46	0.88	5.04	0.45
	GL	56.37	1.45	0.91	4.77	0.39
	LL	75.13	1.46	0.9	5.05	0.38
	LB	57.26	1.5	0.92	5.04	0.45
	LG	56.44	1.46	0.85	5.03	0.48
Diameter	BG	64.09	1.92	0.98	2.13	0.5
	BL	65.04	1.98	0.99	2.23	0.59
	GG	60.07	1.66	0.98	1.31	0.46
	GB	64.09	1.92	0.98	2.23	0.59
	GL	61.09	1.72	0.99	1.28	0.47
	LL	78.22	1.63	0.99	1.12	0.44
	LB	65.04	1.98	0.99	2.23	0.59
	LG	58.82	1.59	0.98	1.18	0.48

Brasil

Brasil

Description of the peach fruit growth curve by diphasic sigmoidal nonlinear models

Descrição da curva de crescimento do fruto do pessegueiro via modelos não lineares sigmoidais difásicos

Abstract