MIXED MODELS FOR NUTRIENTS PREDICTION IN SPECIES OF THE BRAZILIAN CAATINGA BIOME

Abreu, Jadson Coelho de; Silva, José Antônio Aleixo da; Ferreira, Rinaldo Luiz Caraciolo; Rocha, Samuel José Silva Soares da; Tavares Júnior, Ivaldo da Silva; Farias, Aline Araújo; Villanova, Paulo Henrique; Viana, Aguida Beatriz Travaglia; Schettini, Bruno Leão Said; Telles, Lucas Arthur de Almeida; Silva, Arthur Araújo

doi:10.1590/1806-908820230000012

Jadson Coelho de Abreu ^**Corresponding author.

Conceptualization

Experimental testing

Statistical analysis

Results analysis

Writing, review, and editing

Research supervision and coordination

Universidade do Estado do Amapá, Departamento de Engenharia Florestal, Macapá, AP - Brasil. E-mail: <jadsoncoelhoabreu@hotmail.com>

https://orcid.org/0000-0001-9273-7533

José Antônio Aleixo da Silva

Conceptualization

Statistical analysis

Results analysis

Research supervision and coordination

Universidade Federal Rural de Pernambuco, Departamento de Ciência Florestal, Recife, PE - Brasil. E-mail: <jaaleixo@uol.com.br> and <rinaldo.ferreira@ufrpe.br>

https://orcid.org/0000-0003-0675-3524

Rinaldo Luiz Caraciolo Ferreira

Conceptualization

Statistical analysis

Results analysis

Writing, review, and editing

Research supervision and coordination

Universidade Federal Rural de Pernambuco, Departamento de Ciência Florestal, Recife, PE - Brasil. E-mail: <jaaleixo@uol.com.br> and <rinaldo.ferreira@ufrpe.br>

https://orcid.org/0000-0001-7349-6041

Samuel José Silva Soares da Rocha

Conceptualization

Experimental testing

Statistical analysis

Results analysis

Writing, review, and editing

Universidade Federal de Lavras, Departamento de Ciências Florestais, Lavras, MG - Brasil. E-mail: <samuel.rocha@ufla.br>

https://orcid.org/0000-0001-6686-1936

Ivaldo da Silva Tavares Júnior

Conceptualization

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Programa de Pós-Graduação em Ciência Florestal, Viçosa, MG - Brasil. E-mail: <ivaldojunior@ufv.br> , <aline.a.araujo@ufv.br> , <paulo.villanova@ufv.br> , <aguida.vianaufv@gmail.com> and <lucasarthur36@gmail.com>

https://orcid.org/0000-0001-5226-0638

Aline Araújo Farias

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Programa de Pós-Graduação em Ciência Florestal, Viçosa, MG - Brasil. E-mail: <ivaldojunior@ufv.br> , <aline.a.araujo@ufv.br> , <paulo.villanova@ufv.br> , <aguida.vianaufv@gmail.com> and <lucasarthur36@gmail.com>

https://orcid.org/0000-0002-5462-1406

Paulo Henrique Villanova

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Programa de Pós-Graduação em Ciência Florestal, Viçosa, MG - Brasil. E-mail: <ivaldojunior@ufv.br> , <aline.a.araujo@ufv.br> , <paulo.villanova@ufv.br> , <aguida.vianaufv@gmail.com> and <lucasarthur36@gmail.com>

https://orcid.org/0000-0002-4187-2740

Aguida Beatriz Travaglia Viana

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Programa de Pós-Graduação em Ciência Florestal, Viçosa, MG - Brasil. E-mail: <ivaldojunior@ufv.br> , <aline.a.araujo@ufv.br> , <paulo.villanova@ufv.br> , <aguida.vianaufv@gmail.com> and <lucasarthur36@gmail.com>

https://orcid.org/0000-0001-6779-2661

Bruno Leão Said Schettini

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Departamento de Engenharia Florestal, Viçosa, MG - Brasil. E-mail: <blsschettini@gmail.com> and <arthur.araujo@ufv.br>

https://orcid.org/0000-0001-6510-4511

Lucas Arthur de Almeida Telles

Experimental testing

Results analysis

Writing, review, and editing

Universidade Federal de Viçosa, Programa de Pós-Graduação em Ciência Florestal, Viçosa, MG - Brasil. E-mail: <ivaldojunior@ufv.br> , <aline.a.araujo@ufv.br> , <paulo.villanova@ufv.br> , <aguida.vianaufv@gmail.com> and <lucasarthur36@gmail.com>

https://orcid.org/0000-0002-5310-5442

Arthur Araújo Silva

Writing, review, and editing

Universidade Federal de Viçosa, Departamento de Engenharia Florestal, Viçosa, MG - Brasil. E-mail: <blsschettini@gmail.com> and <arthur.araujo@ufv.br>

https://orcid.org/0000-0002-7342-6163

*Corresponding author.

Table 1 Estimates of fixed-effects parameters for the Spurr model to predict native species NPK content regarding trees located in Floresta municipality, Pernambuco State, Brazil.

Model	Nutrient	Model	Effect	β₀	β₁	p-valor
1	Nitrogen	$L n N = β_{0} + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Fixed	2.85399	0.35005	<0.0001
2	Phosphorous	$L n P = β_{0} + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Fixed	0.88364	0.31707	<0.0001
3	Potassium	$L n K = β_{0} + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Fixed	2.08847	0.23923	<0.0001
4	Nitrogen	$L n N = (β_{0} + a_{i}) + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mxed	2.88710	0.34353	<0.0001
5	Nitrogen	$L n N = (β_{0} + a_{i}) + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Mixed	2.87613	0.34589	<0.0001
6	Nitrogen	$L n N = β_{0} + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mxed	2.88710	0.34353	<0.0001
7	Phosphorous	$L n P = (β_{0} + a_{i}) + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mxed	1.08482	0.27727	<0.0001
8	Phosphorous	$L n P = (β_{0} + a_{i}) + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Mixed	1.07884	0.28038	<0.0001
9	Phosphorous	$L n P = β_{0} + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mixed	1.08482	0.27727	<0.0001
10	Potassium	$L n K = (β_{0} + a_{i}) + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mxed	1.86127	0.28221	<0.0001
11	Potassium	$L n K = (β_{0} + a_{i}) + β_{1} \times L n (d b h^{2} \times H t) + ε_{i}$	Mixed	1.88175	0.27809	<0.0001
12	Potassium	$L n K = β_{0} + (β_{1} + b_{l i}) \times L n (d b h^{2} \times H t) + ε_{i}$	Mxed	1.89594	0.27718	<0.0001

Table 2 Random effects estimates regarding the Spurr equation to predict NPK content in native species located in Floresta municipality, Pernambuco State, Brazil.

Species	Parameters
	β0	β1	β0	β1	β0	β1
	Model 4		Model 5		Model 6
1	1.12×10^-09	4.82×10^-02	2.35×10^-02	-	-	4.83×10^-02
2	-7.05×10^-10	1.96×10^-03	-1.56×10^-02	-	-	1.96×10^-03
3	-1.19×10^-10	-2.05×10^-02	-8.52×10^-02	-	-	-2.06×10^-02
4	-2.86×10^-10	-2.00×10^-02	-8.89×10^-02	-	-	-2.00×10^-02
5	3.69×10^-12	-9.65×10^-03	-4.49×10^-02	-	-	-9.65×10^-03

	Model 7		Model 8		Model 9
1	3.35×10^-02	9.46×10^-02	5.31×10^-01	-	-	1.00×10^-01
2	-2.59×10^-02	3.64×10^-02	1.36×10^-01	-	-	3.20×10^-02
3	8.39×10^-03	-9.44×10^-02	-4.52×10^-01	-	-	-9.29×10^-02
4	-2.71×10^-02	-5.11×10^-02	-3.02×10^-01	-	-	-5.57×10^-02
5	1.11×10^-02	1.44×10^-02	8.63×10^-02	-	-	1.64×10^-02

	Model 10		Model 11		Model 12
1	1.66×10^-01	4.84×10^-02	4.20×10^-01	-	-	7.62×10^-02
2	-3.58×10^-01	4.62×10^-02	-1.14×10^-01	-	-	-1.72×10^-02
3	8.54×10^-02	-6.15×10^-02	-2.17×10^-01	-	-	-4.81×10^-02
4	3.62×10^-01	1.90×10^-02	4.57×10^-01	-	-	8.36×10^-02
5	-2.55×10^-01	-5.21×10^-02	-5.45×10^-01	-	-	-9.45×10^-02

Table 3 Maximum likelihood ratio test for equations that predict NPK in native species in Floresta municipality, Pernambuco State, Brazil.

Model	Effect	MLE	Test	Ratio MLE
4	Mixed	-4.55232	1 vs 4	7.88577
5	Mixed	-5.81343	1 vs 5	5.36355
6	Mixed	-4.55232	1 vs 6	7.88577
1	Fixed	-8.49521
7	Mixed	-6.28711	2 vs 7	45.55119
8	Mixed	-9.93831	2 vs 8	38.24879
9	Mixed	-6.28711	2 vs 9	45.55119
2	Fixed	-29.06271
10	Mixed	-2.20533	3 vs 10	56.29369
11	Mixed	-3.68907	3 vs 11	53.32622
12	Mixed	-3.53774	3 vs 12	53.62888
3	Fixed	-30.35218

Table 4 Precision statistics of the Spurr model in its fixed and mixed forms in Floresta municipality, Pernambuco State, Brazil.

Model	AIC	BIC	r_yŷ	RSME%
1	22.99	28.72	0.8614	42.64
4	19.1	28.66	0.8982	30.96
5	19.62	27.27	0.8973	33.61
6	17.1	24.75	0.8982	30.96
2	64.12	69.86	0.6688	7.07
7	22.57	32.13	0.9126	3.01
8	27.87	35.52	0.9115	3.29
9	20.57	28.22	0.9126	3.01
3	66.7	72.44	0.5412	16.13
10	14.41	23.97	0.9379	6.81
11	15.37	23.07	0.9311	7.19
12	15.07	22.72	0.9319	7.28

[1] *Corresponding author.

Brasil

Brasil

MIXED MODELS FOR NUTRIENTS PREDICTION IN SPECIES OF THE BRAZILIAN CAATINGA BIOME

MODELOS MISTOS PARA PREDIÇÃO DE NUTRIENTES EM ESPÉCIES DO BIOMA CAATINGA, BRASIL

ABSTRACT