Nonlinear models for describing lettuce growth in autumn-winter

Carini, Fernanda; Cargnelutti Filho, Alberto; Pezzini, Rafael Vieira; Souza, Jéssica Maronez de; Chaves, Gabriela Görgen; Procedi, Andréia

doi:10.1590/0103-8478cr20190534

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CROP PRODUCTION • Cienc. Rural 50 (7) • 2020 • https://doi.org/10.1590/0103-8478cr20190534 copy

Nonlinear models for describing lettuce growth in autumn-winter

Modelos não lineares para descrição do crescimento de cultivares de alface em condições de outono-inverno

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

The objectives of this study were to fit the Gompertz and Logistic models for the fresh and dry matter of leaves and the fresh and dry matter of shoots of three lettuce cultivars and indicate the best model to describe their growth in autumn-winter. The lettuce cultivars Gloriosa, Pira Verde, and Stella were evaluated in the autumn-winter of 2016 and 2017, in soilless in a protected environment. After transplantation, the fresh and dry matter of leaves and shoots were weighed every seven days. These dependent variables were fit using the accumulated thermal sum. The parameters of the Gompertz and Logistic models were estimated, the assumptions of the models were verified, the indicators of fit quality and critical points were calculated and the parametric and intrinsic curvature measures quantified. The Logistic and Gompertz models presented a satisfactory adjustment for the fresh and dry matter of leaves and the fresh and dry matter of shoots, for the lettuce cultivars Gloriosa, Pira Verde and Stella, in autumn-winter. The Logistic model best describes the growth of the lettuce cultivars.

Key words:
dry matter; fresh matter; Gompertz; Lactuca sativa L.; Logistic.

Authorship

Fernanda Carini

Programa de Pós-graduação em Agronomia, Centro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.Universidade Federal de Santa Maria (UFSM)BrazilSanta Maria, RS, BrazilPrograma de Pós-graduação em Agronomia, Centro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.

http://orcid.org/0000-0001-6000-7747

Alberto Cargnelutti Filho^*E-mail: alberto.cargnelutti.filho@gmail.com. *Corresponding author

Departamento de Fitotecnia, Centro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil..Universidade Federal de Santa Maria (UFSM)BrazilSanta Maria, RS, BrazilDepartamento de Fitotecnia, Centro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil..

http://orcid.org/0000-0002-8608-9960

Rafael Vieira Pezzini

http://orcid.org/0000-0003-4134-2499

Jéssica Maronez de Souza

http://orcid.org/0000-0002-0856-9475

Gabriela Görgen Chaves

http://orcid.org/0000-0001-9461-0288

Andréia Procedi

Centro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.Universidade Federal de Santa Maria (UFSM)BrazilSanta Maria, RS, BrazilCentro de Ciências Rurais (CCR), Universidade Federal de Santa Maria (UFSM), Santa Maria, RS, Brasil.

http://orcid.org/0000-0002-3018-2947

E-mail: alberto.cargnelutti.filho@gmail.com. ^*Corresponding author

DECLARATION OF CONFLICT OF INTERESTS

The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

AUTHORS’ CONTRIBUTIONS

The authors contributed equally to the manuscript.

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (1)
Tables (5)

Thumbnail

Figure 1
Logistic model plot for fresh leaf matter (FLM, as g plant-1), dry leaf matter (DLM as g plant-1), fresh shoot matter (FSM, as g plant-1), and dry shoot matter (DSM, as g plant-1) as a function of the accumulated thermal sum (STa, in °C), for the cultivar Gloriosa, in experiment 2.

Thumbnail

Table 1
Estimates of the parameters a, b, and c, lower limit (LL) and upper limit (UL) of the confidence interval (CI 95%) of the Gompertz model for the characters as a function of accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Thumbnail

Table 2
Estimation of the parameters a, b, and c, lower limit (LL) and upper limit (UL) of the confidence interval (CI 95%) of the Logistic model for the characters as a function of accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Thumbnail

Table 3
Comparison of estimates of parameters (a, b and c) in the Gompertz and Logistic models for characters as a function of cumulative thermal sum based on the confidence interval (CI 95%), between lettuce cultivars Gloriosa, Pira Verde, and Stella in two experiments.

Thumbnail

Table 4
Coefficient of determination (R²), Akaike information criterion (AIC), residual standard deviation (RSD), intrinsic curvature measures (ICM), curvature measures of the parameter effect (PE), inflection point (IP), maximum acceleration point (MAP), and maximum deceleration point (MDP) of the Gompertz model for characters ⁽¹⁾ as a function of the accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Thumbnail

Table 5
Coefficient of determination (R²), Akaike information criterion (AIC), residual standard deviation (RSD), intrinsic curvature measures (ICM), curvature measures of the parameter effect (PE), inflection point (IP), maximum acceleration point (MAP), and maximum deceleration point (MDP) of the Logistc model for characters ⁽¹⁾ as a function of the accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Figure 1 Logistic model plot for fresh leaf matter (FLM, as g plant-1), dry leaf matter (DLM as g plant-1), fresh shoot matter (FSM, as g plant-1), and dry shoot matter (DSM, as g plant-1) as a function of the accumulated thermal sum (STa, in °C), for the cultivar Gloriosa, in experiment 2.

Table 1 Estimates of the parameters a, b, and c, lower limit (LL) and upper limit (UL) of the confidence interval (CI 95%) of the Gompertz model for the characters as a function of accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Character ⁽¹⁾	Parameter	Estimates	CI 95%			Estimates
			LL	UL		LL	UL
		------------------------Experiment 1------------------------			-----------------------Experiment 2----------------------
-------------------------------------------------------------------------------------Gloriosa------------------------------------------------------------------------------------------
FLM	a ^*(2)	929.8712	597.8730	1261.8694	455.6514	370.6086	540.6942
	b ^ns	2.3061	1.8969	2.7154	2.4371	2.0036	2.8707
	c ^ns	0.0076	0.0049	0.0102	0.0082	0.0061	0.0102
DLM	a ^*	16.7031	15.3232	18.0831	25.3207	17.9166	32.7249
	b ^*	4.2032	2.9665	5.4398	2.3264	1.8240	2.8288
	c ^*	0.0198	0.0138	0.0258	0.0073	0.0048	0.0098
FSM	a ^*	984.0988	617.5294	1350.6682	535.0355	420.6123	649.4587
	b ^ns	2.2898	1.8898	2.6897	2.3731	1.9682	2.7780
	c ^ns	0.0074	0.0048	0.0100	0.0076	0.0056	0.0095
DSM	a ^*	17.8364	16.2972	19.3755	30.4005	19.9823	40.8187
	b ^*	4.0599	2.8834	5.2364	2.2844	1.8061	2.7627
	c ^*	0.0189	0.0132	0.0246	0.0068	0.0043	0.0092
-------------------------------------------------------------------------------------Pira Verde----------------------------------------------------------------------------------------
FLM	a ^ns	1234.9167	-921.8006	3391.6340	396.8462	344.1902	449.5022
	b ^ns	2.4801	1.9083	3.0518	2.8152	2.2292	3.4012
	c ^*	0.0072	0.0013	0.0130	0.0105	0.0079	0.0132
DLM	a ^ns	16.1548	10.3930	21.9166	14.3685	12.1452	16.5917
	b ^ns	3.9116	2.2996	5.5236	2.9788	2.0259	3.9317
	c ^ns	0.0179	0.0088	0.0271	0.0120	0.0076	0.0164
FSM	a ^ns	1334.4813	-1078.0040	3746.9667	417.3858	359.6425	475.1292
	b ^ns	2.4846	1.9148	3.0543	2.7758	2.2012	3.3503
	c ^ns	0.0071	0.0012	0.0130	0.0103	0.0077	0.0129
DSM	a ^ns	17.0319	10.9575	23.1063	15.3914	12.8463	17.9365
	b ^ns	3.9517	2.3272	5.5762	2.8810	1.9750	3.7870
	c ^ns	0.0181	0.0089	0.0273	0.0114	0.0073	0.0156
-------------------------------------------------------------------------------------Stella----------------------------------------------------------------------------------------------
FLM	a ^ns	331.9249	222.8545	440.9954	302.7635	242.6119	362.9151
	b ^ns	4.5969	2.7416	6.4522	3.9793	2.0114	5.9472
	c ^ns	0.0207	0.0107	0.0306	0.0151	0.0072	0.0231
DLM	a ^ns	11.4854	9.7928	13.1781	12.6652	9.4969	15.8334
	b ^*	6.3329	4.1776	8.4882	3.4840	1.5131	5.4548
	c ^*	0.0306	0.0197	0.0416	0.0136	0.0051	0.0221
FSM	a ^ns	350.0046	228.7424	471.2668	329.2424	258.0313	400.4536
	b ^ns	4.5261	2.6718	6.3805	3.8011	1.9389	5.6633
	c ^ns	0.0202	0.0102	0.0302	0.0142	0.0067	0.0217
DSM	a ^ns	12.2469	10.3352	14.1586	14.1283	10.1332	18.1234
	b ^*	6.2374	4.0542	8.4205	3.3240	1.4419	5.2061
	c ^*	0.0300	0.0189	0.0411	0.0127	0.0046	0.0207

⁽¹⁾FLM: fresh leaf matter, as g plant^-1; DLM: dry leaf matter, as g plant^-1; FSM: fresh shoot matter, as g plant^-1; and DSM: dry shoot matter, as g plant^-1. ⁽²⁾Comparison of the parameters estimates (a, b and c) between the experiments: ^* Significant effect at 0.05 probability of error. ^ns Non-significant.

Table 2 Estimation of the parameters a, b, and c, lower limit (LL) and upper limit (UL) of the confidence interval (CI 95%) of the Logistic model for the characters as a function of accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Character ⁽¹⁾	Parameter	Estimates	CI 95%		Estimates	CI 95%
			LL	UL		LL	UL
		-------------------------Experiment 1------------------------			------------------------Experiment 2-------------------------
---------------------------------------------------------------------------------------Gloriosa------------------------------------------------------------------------------------------
FLM	a ^*(2)	644.5429	548.4506	740.6351	374.9478	336.2122	413.6834
	b ^ns	-5.1549	-5.8057	-4.5041	-5.0146	-5.7298	-4.2994
	c ^ns	0.0174	0.0140	0.0208	0.0159	0.0131	0.0187
DLM	a ^*	16.1507	15.1791	17.1223	19.8721	16.8842	22.8600
	b ^*	-6.9451	-8.6093	-5.2809	-4.9363	-5.7612	-4.1114
	c ^*	0.0301	0.0224	0.0378	0.0149	0.0117	0.0182
FSM	a ^*	671.9417	568.1495	775.7339	423.4933	375.6487	471.3380
	b ^ns	-5.1427	-5.7829	-4.5026	-5.0110	-5.6958	-4.3261
	c ^ns	0.0172	0.0139	0.0206	0.0154	0.0127	0.0181
DSM	a ^*	17.1579	16.1129	18.2030	22.6678	18.9117	26.4239
	b ^*	-6.7920	-8.3663	-5.2178	-4.9890	-5.7998	-4.1783
	c ^*	0.0291	0.0219	0.0364	0.0146	0.0114	0.0179
------------------------------------------------------------------------------------Pira Verde-----------------------------------------------------------------------------------------
FLM	a ^ns	354.7561	225.9895	483.5227	357.4533	329.5156	385.3911
	b ^*	-6.9162	-8.2985	-5.5339	-5.4368	-6.3065	-4.5671
	c ^*	0.0275	0.0189	0.0361	0.0185	0.0151	0.0219
DLM	a ^ns	12.9143	10.9345	14.8941	13.4350	12.0807	14.7892
	b ^*	-8.1440	-10.4198	-5.8683	-5.3736	-6.7002	-4.0469
	c ^*	0.0366	0.0249	0.0483	0.0194	0.0141	0.0248
FSM	a ^ns	371.9859	233.7199	510.2519	373.1430	343.2436	403.0423
	b ^*	-6.9521	-8.3426	-5.5615	-5.4148	-6.2733	-4.5563
	c ^*	0.0276	0.0189	0.0362	0.0183	0.0150	0.0216
DSM	a ^ns	13.5725	11.5050	15.6401	14.2652	12.7645	15.7659
	b ^*	-8.2774	-10.6061	-5.9486	-5.2873	-6.5615	-4.0131
	c ^*	0.0371	0.0252	0.0490	0.0189	0.0137	0.0240
--------------------------------------------------------------------------------------Stella----------------------------------------------------------------------------------------------
FLM	a ^ns	267.4332	225.5213	309.3451	284.7468	246.6736	322.8200
	b ^ns	-9.5607	-12.5727	-6.5486	-7.2670	-10.4551	-4.0790
	c ^*	0.0421	0.0273	0.0570	0.0253	0.0138	0.0367
DLM	a ^ns	10.4087	9.5845	11.2329	11.9094	9.8986	13.9203
	b ^*	-12.9179	-16.8192	-9.0166	-6.2848	-9.2759	-3.2937
	c ^*	0.0599	0.0415	0.0783	0.0222	0.0109	0.0335
FSM	a ^ns	279.2195	233.6137	324.8253	305.9605	262.6841	349.2370
	b ^ns	-9.4826	-12.4910	-6.4743	-7.0754	-10.1261	-4.0247
	c ^*	0.0417	0.0268	0.0566	0.0243	0.0133	0.0352
DSM	a ^ns	11.0147	10.1213	11.9081	13.0975	10.6849	15.5101
	b ^*	-12.9199	-16.9054	-8.9345	-6.1507	-9.0592	-3.2421
	c ^*	0.0597	0.0409	0.0785	0.0213	0.0104	0.0321

⁽¹⁾FLM: fresh leaf matter, as g plant^-1; DLM: dry leaf matter, as g plant^-1; FSM: fresh shoot matter, as g plant^-1; and DSM: dry shoot matter, as g plant^-1. ⁽²⁾Comparison of the parameters estimates (a, b and c) between the experiments: ^* Significant effect at 0.05 probability of error. ^ns Non-significant.

Table 3 Comparison of estimates of parameters (a, b and c) in the Gompertz and Logistic models for characters as a function of cumulative thermal sum based on the confidence interval (CI 95%), between lettuce cultivars Gloriosa, Pira Verde, and Stella in two experiments.

Cultivars	Cultivars	FLM⁽¹⁾	DLM	FSM	DSM	FLM	DLM	FSM	DSM
		--------------------------Experiment 1-------------------------			--------------------------Experiment 2-------------------------
------------------------------------------------------------------------------------Gompertz-------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------a----------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	ns⁽²⁾	ns	ns	ns	ns	^*	^*	^*
Gloriosa	Stella	^*	^*	^*	^*	^*	^*	^*	^*
Pira Verde	Stella	ns	ns	ns	^*	^*	ns	^*	ns
--------------------------------------------------------------------------------------------b---------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	ns	ns	ns	ns	ns	ns	ns	ns
Gloriosa	Stella	^*	ns	^*	ns	ns	ns	ns	ns
Pira Verde	Stella	^*	^*	^*	^*	ns	ns	ns	ns
--------------------------------------------------------------------------------------------c---------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	ns	ns	ns	ns	ns	^*	^*	^*
Gloriosa	Stella	^*	ns	^*	ns	ns	ns	ns	^*
Pira Verde	Stella	^*	^*	^*	^*	ns	ns	ns	ns
----------------------------------------------------------------------------------------Logistic-----------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------a-----------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	^*	^*	^*	^*	ns	^*	^*	*
Gloriosa	Stella	^*	^*	^*	^*	^*	^*	^*	*
Pira Verde	Stella	^*	^*	ns	^*	^*	ns	^*	ns
--------------------------------------------------------------------------------------------b---------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	^*	ns	^*	^*	ns	ns	ns	ns
Gloriosa	Stella	^*	^*	^*	^*	^*	ns	ns	ns
Pira Verde	Stella	ns	^*	ns	ns	ns	ns	ns	ns
--------------------------------------------------------------------------------------------c----------------------------------------------------------------------------------------------
Gloriosa	Pira Verde	^*	ns	^*	ns	ns	ns	ns	ns
Gloriosa	Stella	^*	^*	^*	^*	ns	ns	ns	ns
Pira Verde	Stella	ns	^*	ns	ns	ns	ns	ns	ns

⁽¹⁾FLM = fresh leaf matter, as g plant^-1; DLM = dry leaf matter, as g plant^-1; FSM = fresh shoot matter, as g plant^-1; and DSM = dry shoot matter, as g plant^-1. ⁽²⁾Comparison of the parameters estimates (a, b and c) between the cultivars: * = Significant effect at 0.05 probability of error. ns = Non-significant.

Table 4 Coefficient of determination (R²), Akaike information criterion (AIC), residual standard deviation (RSD), intrinsic curvature measures (ICM), curvature measures of the parameter effect (PE), inflection point (IP), maximum acceleration point (MAP), and maximum deceleration point (MDP) of the Gompertz model for characters ⁽¹⁾ as a function of the accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Statistic		FLM	DLM	FSM	DSM	FLM	DLM	FSM	DSM
		----------------------------Experiment 1------------------------------			-------------------------------Experiment 2---------------------------------
----------------------------------------------------------------------------------------Gloriosa----------------------------------------------------------------------------------------
R²		0.968	0.918	0.968	0.922	0.969	0.952	0.970	0.952
AIC		7.243	1.309	7.296	1.371	6.334	0.786	6.453	0.953
RSD		35.802	1.851	36.758	1.909	22.596	1.410	23.982	1.533
ICM		0.165	0.128	0.164	0.134	0.147	0.191	0.146	0.192
PE		6.975	0.787	7.448	0.851	2.575	4.373	3.111	5.477
IP	x	305.065	212.742	309.348	214.657	298.835	319.371	314.040	337.689
IP	y	342.080	6.145	362.030	6.562	167.625	9.315	196.829	11.184
MAP	x	177.750	164.029	179.324	163.771	180.824	187.248	186.681	195.418
MAP	y	67.831	1.218	71.786	1.301	33.238	1.847	39.029	2.218
MDP	x	432.380	261.455	439.372	265.543	416.846	451.494	441.398	479.961
MDP	y	634.654	11.400	671.665	12.174	310.990	17.282	365.171	20.749
--------------------------------------------------------------------------------------Pira Verde----------------------------------------------------------------------------------------
R²		0.964	0.935	0.964	0.935	0.960	0.913	0.961	0.915
AIC		5.769	0.335	5.846	0.442	6.665	0.998	6.727	1.066
RSD		16.940	1.126	17.608	1.188	26.674	1.569	27.519	1.623
ICM		0.324	0.229	0.327	0.207	0.141	0.213	0.143	0.220
PE		87.261	5.582	92.807	5.552	1.627	1.904	1.708	2.043
IP	x	345.989	217.964	349.716	218.552	266.933	247.837	269.886	251.721
IP	y	454.300	5.943	490.928	6.266	145.992	5.286	153.548	5.662
MAP	x	211.724	164.335	214.251	165.325	175.678	167.763	176.310	167.631
MAP	y	90.082	1.178	97.345	1.242	28.948	1.048	30.447	1.123
MDP	x	480.254	271.592	485.181	271.780	358.189	327.910	363.462	335.811
MDP	y	842.853	11.026	910.808	11.625	270.855	9.807	284.873	10.505
---------------------------------------------------------------------------------------------Stella---------------------------------------------------------------------------------------
R²		0.935	0.925	0.935	0.923	0.821	0.769	0.824	0.769
AIC		6.474	0.359	6.552	0.489	8.090	1.997	8.185	2.151
RSD		24.130	1.139	25.093	1.215	54.362	2.583	57.029	2.791
ICM		0.057	0.065	0.060	0.067	0.360	0.311	0.340	0.312
PE		4.705	1.388	5.087	1.506	2.182	2.860	2.371	3.232
IP	x	222.486	206.749	223.651	207.711	262.976	255.899	267.333	262.513
IP	y	122.108	4.225	128.759	4.505	111.380	4.659	121.122	5.198
MAP	x	175.906	175.329	176.094	175.661	199.373	185.208	199.646	186.506
MAP	y	24.213	0.838	25.531	0.893	22.085	0.924	24.017	1.031
MDP	x	269.067	238.169	271.208	239.760	326.578	326.589	335.020	338.519
MDP	y	226.545	7.839	238.885	8.359	206.642	8.644	224.714	9.643

⁽¹⁾ FLM: fresh leaf matter, as g plant^-1; DLM: dry leaf matter, as g plant^-1; FSM: fresh shoot matter, as g plant^-1; and DSM: dry shoot matter, as g plant^-1.

Table 5 Coefficient of determination (R²), Akaike information criterion (AIC), residual standard deviation (RSD), intrinsic curvature measures (ICM), curvature measures of the parameter effect (PE), inflection point (IP), maximum acceleration point (MAP), and maximum deceleration point (MDP) of the Logistc model for characters ⁽¹⁾ as a function of the accumulated thermal sum (in °C) of lettuce cultivars (Gloriosa, Pira Verde, and Stella) in two experiments.

Statistic		FLM	DLM	FSM	DMS	FLM	DLM	FSM	DMS
		--------------------------------Experiment 1--------------------------------			---------------------------------Experiment 2--------------------------------
--------------------------------------------------------------------------------------Gloriosa------------------------------------------------------------------------------------------
R²		0.966	0.924	0.966	0.928	0.966	0.950	0.967	0.951
AIC		7.287	1.234	7.342	1.301	6.427	0.825	6.546	0.984
RSD		36.621	1.777	37.635	1.838	23.708	1.439	25.157	1.558
ICM		0.109	0.163	0.108	0.158	0.109	0.129	0.105	0.127
PE		1.817	0.479	1.901	0.494	0.985	1.461	1.085	1.634
IP	x	296.197	230.903	298.366	233.091	315.854	330.376	325.917	340.785
IP	y	322.271	8.075	335.971	8.579	187.474	9.936	211.747	11.334
MAP	x	220.526	187.118	221.960	187.895	232.902	242.235	240.261	250.828
MAP	y	136.208	3.413	141.998	3.626	79.236	4.199	89.495	4.790
MDP	x	371.869	274.688	374.773	278.287	398.806	418.517	411.573	430.742
MDP	y	508.335	12.738	529.944	13.532	295.712	15.673	333.999	17.878
------------------------------------------------------------------------------------------Pira Verde------------------------------------------------------------------------------------
R²		0.965	0.940	0.966	0.940	0.962	0.916	0.963	0.918
AIC		5.731	0.264	5.809	0.372	6.614	0.971	6.674	1.039
RSD		16.605	1.083	17.267	1.144	25.990	1.546	26.785	1.600
ICM		0.197	0.188	0.198	0.184	0.121	0.192	0.119	0.187
PE		6.247	1.674	6.484	1.665	0.742	1.004	0.758	1.036
IP	x	251.318	222.612	252.083	222.943	293.726	276.446	296.137	280.373
IP	y	177.378	6.457	185.993	6.786	178.727	6.717	186.571	7.133
MAP	x	203.463	186.614	204.330	187.472	222.577	208.694	224.112	210.537
MAP	y	74.969	2.729	78.610	2.868	75.539	2.839	78.854	3.015
MDP	x	299.173	258.610	299.836	258.414	364.876	344.198	368.162	350.208
MDP	y	279.787	10.185	293.376	10.704	281.915	10.596	294.289	11.251
-------------------------------------------------------------------------------------------Stella-----------------------------------------------------------------------------------------
R²		0.936	0.930	0.936	0.929	0.824	0.772	0.826	0.771
AIC		6.467	0.279	6.546	0.409	8.072	1.987	8.171	2.143
RSD		24.014	1.096	24.968	1.170	53.860	2.570	56.593	2.778
ICM		0.169	0.153	0.172	0.160	0.316	0.354	0.310	0.349
PE		1.810	0.596	1.918	0.624	1.284	1.623	1.342	1.741
IP	x	226.871	215.800	227.530	216.468	287.776	282.866	291.759	289.191
IP	y	133.717	5.204	139.610	5.507	142.373	5.955	152.980	6.549
MAP	x	195.620	193.800	195.930	194.403	235.624	223.593	237.453	227.270
MAP	y	56.515	2.200	59.006	2.328	60.174	2.517	64.657	2.768
MDP	x	258.122	237.801	259.129	238.533	339.928	342.140	346.065	351.112
	y	210.918	8.209	220.213	8.687	224.573	9.393	241.303	10.330

⁽¹⁾ FLM: fresh leaf matter, as g plant^-1; DLM: dry leaf matter, as g plant^-1; FSM: fresh shoot matter, as g plant^-1; and DSM: dry shoot matter, as g plant^-1.

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Universidade Federal de Santa Maria Universidade Federal de Santa Maria, Centro de Ciências Rurais , 97105-900 Santa Maria RS Brazil , Tel.: +55 55 3220-8698 , Fax: +55 55 3220-8695 - Santa Maria - RS - Brazil
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[1] E-mail: alberto.cargnelutti.filho@gmail.com. ^*Corresponding author