Weibull distribution and dynamics of germination of Rangpur lime seeds at different temperatures

Rangpur lime is the most commonly used rootstock in Brazil, and its propagation occurs through seeds. Currently, no methodology is described in the prescriptions of the Rules for Seed Testing to perform the germination test of Rangpur lime. Thus, this research aimed to study the dynamics of germination in Rangpur lime seeds according to the Weibull distribution under the effect of different temperatures and lots. The experiment was conducted in a completely randomized design, with treatments arranged in a 3 × 5 factorial scheme (temperatures of 25, 30 and 35 °C for the germination test and five seed lots, respectively) and four replications. The percentage of germination, the number of days required obtaining 50% of germination, and the parameters of the Weibull equation were determined. The optimum temperature for germination of Rangpur lime seeds was 30 °C, with the first and last counts at 21 and 30 days after test installation, respectively. The germination process can be described by the three-parameter Weibull cumulative distribution function.

Index terms:
Citrus limonia Osbeck; germination curves; rootstock; viability

Authorship

Marizangela Rizzatti Ávila

IAPAR. Instituto Agronômico do Paraná, 86047-902 - Londrina, PR, Brasil.IAPAR. Instituto Agronômico do ParanáBrazilLondrina, PR, BrazilIAPAR. Instituto Agronômico do Paraná, 86047-902 - Londrina, PR, Brasil.

Juliana Barbosa

Nelson da Silva Fonseca Júnior

Getúlio Takashi Nagashima

Carolina Maria Gaspar de Oliveira ^**Corresponding author <carolina@iapar.br>

http://orcid.org/0000-0001-6908-1601

*Corresponding author <carolina@iapar.br>

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (4)
Tables (2)
Formulas (18)

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Figure 1
Seedlings and seeds of Rangpur lime observed in the germination test evaluation: dead seeds [A], normal seedlings [B], abnormal seedlings [C], and polyembryonic seedlings [D]. IAPAR, Londrina, PR (Photos: Willian Cason, 2014).

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Figure 2
Abnormal seedlings of Rangpur lime: root thickening and shortening. IAPAR, Londrina, PR (Photo: Juliana Barbosa, 2016).

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Figure 3
Regression curves by the three-parameter Weibull model of the accumulated germination (%) as a function of time of Rangpur lime seeds of the lot 5 submitted to temperatures of 25, 30 and 35 °C.

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Figure 4
Regression curves by the three-parameter Weibull model of the accumulated germination (%) of five lots of Rangpur lime seeds as a function of time (days) submitted to a temperature of 30 °C.

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Table 1
Germination, parameters a, b, and c of the Weibull regression, and T50W for five lots of Rangpur lime seeds obtained in the germination test conducted at different temperatures.

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Table 2
Regression equations of the three-parameter Weibull model for five lots of Rangpur lime seeds obtained in the germination test conducted at different temperatures.

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Figure 1 Seedlings and seeds of Rangpur lime observed in the germination test evaluation: dead seeds [A], normal seedlings [B], abnormal seedlings [C], and polyembryonic seedlings [D]. IAPAR, Londrina, PR (Photos: Willian Cason, 2014).

Figure 2 Abnormal seedlings of Rangpur lime: root thickening and shortening. IAPAR, Londrina, PR (Photo: Juliana Barbosa, 2016).

Figure 3 Regression curves by the three-parameter Weibull model of the accumulated germination (%) as a function of time of Rangpur lime seeds of the lot 5 submitted to temperatures of 25, 30 and 35 °C.

Figure 4 Regression curves by the three-parameter Weibull model of the accumulated germination (%) of five lots of Rangpur lime seeds as a function of time (days) submitted to a temperature of 30 °C.

Table 1 Germination, parameters a, b, and c of the Weibull regression, and T50W for five lots of Rangpur lime seeds obtained in the germination test conducted at different temperatures.

G (%)	Temperature (°C)²			Mean
Lot¹	25	30	35
1	75 Ab	74 Ab	34 Bc	61
2	90 Aa	90 Aa	45 Bbc	75
3	72 Ab	75 Ab	46 Bb	64
4	86 Aa	89 Aa	61 Ba	79
5	89 Aa	91 Aa	66 Ba	82
Mean	82	84	50
LSD of lots: 10.53; LSD of temperatures: 8.96; Coefficient of variation (%): 7.16
a (% of germination)	Temperature (°C)²			Mean
Lot¹	25	30	35
1	71 Ab	68 Ab	35 Bb	58
2	88 Aa	87 Aa	36 Bb	70
3	71 Ab	70 Ab	40 Bb	60
4	83 Aa	85 Aa	62 Ba	77
5	85 Aa	87 Aa	68 Ba	80
Mean	80	79	48
LSD of lots: 10.97; LSD of temperatures: 11.58; Coefficient of variation (%): 7.83
b ³	Temperature (°C)²			Mean
Lot¹	25	30	35
1	25.82 Aa	21.77 Ba	22.26 Bb	23.29
2	22.63 Ab	19.54 Bb	15.40 Cc	19.19
3	25.79 Aa	21.77 Ba	20.54 Bb	22.70
4	26.88 Aa	21.98 Ba	26.33 Aa	25.06
5	27.04 Aa	22.26 Ba	25.68 Aa	24.99
Mean	25.63	21.46	22.04
LSD of lots: 2.11; LSD of temperatures: 1.80; Coefficient of variation (%): 4.53
c ⁴	Temperature (°C)²			Mean
Lot¹	25	30	35
1	7.88 Aa	6.52 Ba	3.62 Cb	6.01
2	6.83 Aa	5.72 ABa	5.10 Ba	5.88
3	6.81 Aa	6.66 Aa	4.86 Bab	6.11
4	8.13 Aa	6.75 Ba	4.59 Cab	6.49
5	7.89 Aa	6.40 Ba	4.14 Cab	6.14
Mean	7.51	6.41	4.46
LSD of lots: 1.43; LSD of temperatures: 1.22; Coefficient of variation (%): 11.58
T50W⁵	Temperature (°C)²			Mean
Lot¹	25	30	35
1	26.7	22.9	-	24.8 a
2	22.1	19.1	-	20.6 b
3	26.8	22.6	-	24.7 a
4	26.6	21.6	-	24.1 a
5	26.6	21.7	-	24.2 a
Mean	25.7 A	21.6 B	-
LSD of lots: 1.83; LSD of temperatures: 1.28; Coefficient of variation (%): 3.70

¹Means followed by the same uppercase letter in the row do not differ from each other by the Tukey’s test at 5% probability. ²Means followed by the same lowercase letter in the column do not differ from each other by the Tukey’s test at 5% probability. ³Estimated time (days) to obtain 63.21% of the maximum germination estimated by the regression (parameter a). ⁴Germination progression rate as a function of time b (percentage of germination at day b). ⁵Time required to reach 50% of germination.

Table 2 Regression equations of the three-parameter Weibull model for five lots of Rangpur lime seeds obtained in the germination test conducted at different temperatures.

Temperature 25 °C	Weibull regression parameters			Weibull equation	R²
Lot¹	a	b	c	$G (%) = a (1 - e x p (- ((x / b)^c)))$	-
1	71.00±2.07	25.82±0.44	7.88±0.84	$G (%) = 71 (1 - e x p (- ((x / 25.82)^7.88)))$	0.99
2	88.00±2.69	22.63±0.50	6.83±0.41	$G (%) = 88 (1 - e x p (- ((x / 22.63)^6.83)))$	0.99
3	71.00±0.40	25.79±0.33	6.81±1.42	$G (%) = 71 (1 - e x p (- ((x / 25.79)^6.81)))$	0.99
4	83.00±1.66	26.88±0.32	8.13±0.71	$G (%) = 83 (1 - e x p (- ((x / 26.88)^8.13)))$	0.99
5	85.00±2.20	27.04±0.31	7.89±0.97	$G (%) = 85 (1 - e x p (- ((x / 27.04)^7.89)))$	0.99
Temperature 30 °C	Weibull regression parameters			Weibull equation	R²
Lot¹	a	b	c	$G (%) = a (1 - e x p (- ((x / b)^c)))$	-
1	68.00±2.93	21.77±0.51	6.52±1.08	$G (%) = 68 (1 - e x p (- ((x / 21.77)^6.52)))$	0.99
2	87.00±0.86	19.54±0.03	5.72±1.06	$G (%) = 87 (1 - e x p (- ((x / 19.54)^5.72)))$	0.99
3	70.00±2.20	21.77±0.45	6.66±0.67	$G (%) = 70 (1 - e x p (- ((x / 21.77)^6.66)))$	0.99
4	85.00±3.55	21.98±0.52	6.75±0.57	$G (%) = 85 (1 - e x p (- ((x / 21.98)^6.75)))$	0.99
5	87.00±3.38	22.26±0.44	6.40±0.85	$G (%) = 87 (1 - e x p (- ((x / 22.26)^6.40)))$	0.99
Temperature 35 °C	Weibull regression parameters			Weibull equation	R²
Lot¹	a	b	c	$G (%) = a (1 - e x p (- ((x / b)^c)))$	-
1	35.00±6.93	22.26±2.70	3.62±1.43	$G (%) = 35 (1 - e x p (- ((x / 22.26)^3.62)))$	0.99
2	36.00±1.02	15.40±0.67	5.10±1.34	$G (%) = 36 (1 - e x p (- ((x / 15.40)^5.10)))$	0.99
3	40.00±2.24	20.54±0.58	4.86±0.93	$G (%) = 40 (1 - e x p (- ((x / 20.54)^4.86)))$	0.99
4	62.00±16.41	26.33±3.10	4.59±1.23	$G (%) = 62 (1 - e x p (- ((x / 26.33)^4.59)))$	0.99
5	68.00±13.69	25.68±2.48	4.14±0.62	$G (%) = 68 (1 - e x p (- ((x / 25.68)^4.14)))$	0.99

G (%) = a (1 - e x p (- ((x / b)^c)))

G (%) = 71 (1 - e x p (- ((x / 25.82)^7.88)))

G (%) = 88 (1 - e x p (- ((x / 22.63)^6.83)))

G (%) = 71 (1 - e x p (- ((x / 25.79)^6.81)))

G (%) = 83 (1 - e x p (- ((x / 26.88)^8.13)))

G (%) = 85 (1 - e x p (- ((x / 27.04)^7.89)))

G (%) = a (1 - e x p (- ((x / b)^c)))

G (%) = 68 (1 - e x p (- ((x / 21.77)^6.52)))

G (%) = 87 (1 - e x p (- ((x / 19.54)^5.72)))

G (%) = 70 (1 - e x p (- ((x / 21.77)^6.66)))

G (%) = 85 (1 - e x p (- ((x / 21.98)^6.75)))

G (%) = 87 (1 - e x p (- ((x / 22.26)^6.40)))

G (%) = a (1 - e x p (- ((x / b)^c)))

G (%) = 35 (1 - e x p (- ((x / 22.26)^3.62)))

G (%) = 36 (1 - e x p (- ((x / 15.40)^5.10)))

G (%) = 40 (1 - e x p (- ((x / 20.54)^4.86)))

G (%) = 62 (1 - e x p (- ((x / 26.33)^4.59)))

G (%) = 68 (1 - e x p (- ((x / 25.68)^4.14)))

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Weibull distribution and dynamics of germination of Rangpur lime seeds at different temperatures

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[1] *Corresponding author <carolina@iapar.br>