Multifractal analysis of weeds in a no-tillage system in the Pre-Amazon region

Silva, Daniel M. da; Silva, Guimarães V. da; Siqueira, Glécio M.

doi:10.1590/1807-1929/agriambi.v28n1e273778

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Original Article • Rev. bras. eng. agríc. ambient. 28 (1) • Jan 2024 • https://doi.org/10.1590/1807-1929/agriambi.v28n1e273778 copy

Multifractal analysis of weeds in a no-tillage system in the Pre-Amazon region¹ 1 Research developed at Unha de Gato Farming, Mata Roma, MA, Brazil

Análise multifractal das plantas-daninhas em sistema de semeadura direta na região Pré-Amazônia

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS:

Weeds present varying spatial variability scales.

Euphorbia hirta L. exhibited high density and abundance.

Commelina benghalensis L. exhibited the greatest heterogeneity among the evaluated weeds.

ABSTRACT

Weeds have several mechanisms of dispersal and reproduction, resulting high spatial variability. The objective of this study was to assess the scale and spatial heterogeneity of weeds using multifractal analysis in a no-tillage system in the Pre-Amazon region. Sampling was conducted in a commercial soybean (Glycine max) production plot in the Mata Roma, Maranhão, Brazil, comprising 1,071 points marked on a 10 × 10 m grid. Data were analyzed using descriptive statistics and multifractal analysis through the box-counting method. Weeds showed varying degrees of multifractality, resulting in different scales and spatial heterogeneity in the study area. Euphorbia hirta and Turnera subulata exhibited asymmetry of branches to the left in the singularity spectrum, indicating dominance of high measurement values.

Key words:
spontaneous plants; degree of multifractality; generalized dimension; singularity spectrum

Variable	D	RD	F	RF	A	RA	IVI
Cenchrus echinatus L.	1.84	9.28	0.97	17.08	1.89	7.65	34.00
Commelina benghalensis L.	0.86	4.36	0.81	14.23	1.06	4.31	22.90
Desmodium tortuosum (Sw.) DC.	0.08	0.39	0.05	0.80	1.69	6.87	8.06
Euphorbia hirta L.	9.36	47.23	1	17.54	9.36	37.92	102.69
Scoparia dulcis L.	0.06	0.30	0.06	1.05	1	4.05	5.40
Sida rhombifolia L.	0.14	0.69	0.10	1.69	1.43	5.78	8.16
Spermacoce verticillata L.	1.89	9.54	1	17.54	1.89	7.66	34.74
Spigelia anthelmia L.	4.11	20.73	0.91	15.95	4.52	18.31	54.99
Turnera subulata Sm.	1.48	7.48	0.81	14.13	1.84	7.45	29.05
Total	19.81	100	5.70	100	24.67	100	300

Weeds	$\bar{x}$	Variance	SD	CV (%)	Skew	Kurtosis	D-KS
Cenchrus echinatus L.	1.89	0.21	0.46	24.00	-0.44	1.32	0.05 Ln
Commelina benghalensis L.	1.06	0.06	0.25	23.00	3.55	10.66	0.06 Ln
Euphorbia hirta L.	9.36	20.03	4.48	48.00	1.64	6.43	0.05 Ln
Spermacoce verticillata L.	1.89	0.20	0.45	24.00	-0.45	1.40	0.05 Ln
Spigelia anthelmia L.	4.52	4.28	2.07	46.00	0.49	-0.50	0.05 Ln
Turnera subulata Sm.	1.84	1.08	1.04	57.00	1.66	5.13	0.06 Ln
OW	2.85	5.38	2.32	81.00	3.76	15.65	0.16 Ln

Weeds	q_-	q₊	Δ	D₀	D₁	D₂	α_-5	α₅	α₀	AI
Cenchrus echinatus L.	-5	5	0.255	1.995	1.986	1.980	2.532	1.953	2.007	0.102
Commelina benghalensis L.	-5	5	0.388	1.995	1.913	1.818	2.227	1.657	2.055	2.324
Euphorbia hirta L.	-5	5	0.124	1.995	1.984	1.971	2.118	1.845	2.005	1.401
Spermacoce verticillata L.	-5	5	0.191	1.995	1.986	1.981	2.319	1.955	2.006	0.164
Spigelia anthelmia L.	-5	5	0.094	1.995	1.988	1.980	2.151	1.935	2.002	0.448
Turnera subulata Sm.	-5	5	0.219	1.995	1.967	1.942	2.167	1.805	2.024	1.529
Richness	-5	5	0.071	1.995	1.992	1.988	2.163	1.969	1.998	0.172
Abundance	-5	5	0.086	1.995	1.988	1.980	2.122	1.907	2.001	0.780
OW	monofractal

Unidade Acadêmica de Engenharia Agrícola Unidade Acadêmica de Engenharia Agrícola, UFCG, Av. Aprígio Veloso 882, Bodocongó, Bloco CM, 1º andar, CEP 58429-140, Campina Grande, PB, Brasil, Tel. +55 83 2101 1056 - Campina Grande - PB - Brazil
E-mail: revistagriambi@gmail.com

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[1] * Corresponding author - E-mail: danielmartins@uft.edu.br

Partition function	$P_{i} (ε) ~ ε^{α_{i}}$	(1)
	$μ (q, ε) = \sum_{i = 1}^{N (ε)} P_{i}^{q} (ε)$	(2)
	$μ (q, ε) ~ ε^{τ (q)}$	(3)
Generalized dimension	$D_{q = \lim_{ε \to 0}} (\frac{1}{q - 1} \frac{\log \sum_{i = 1}^{N (ε)} P_{i}^{q} (ε)}{\log (ε)})$	(4)
	$D_{0 = \lim_{ε \to 0}} \frac{\log (N (ε))}{\log (ε)}$	(5)
	$D_{1 = \lim_{ε \to 0}} \frac{\sum_{i = 1}^{N (ε)} μ_{i} (ε) \log (μ_{i} (ε))}{\log (ε)}$	(6)
	$D_{2 = \lim_{ε \to 0}} \frac{\log (C (ε))}{\log (ε)}$	(7)
Spectrum of singularities	$f (q) = \lim_{ε \to \infty} \frac{1}{\log (ε)} \sum_{i = 1}^{N (ε)} μ_{i} (q, ε) \log [μ_{i} (q, ε)]$	(8)
Spectrum of singularities	$α (q) = \lim_{ε \to \infty} \frac{1}{\log (ε)} \sum_{i = 1}^{N (ε)} μ_{i} (q, ε) \log [P_{i} (ε)]$	(9)
Degree of multifractality (Δ) and asymmetry (AI)	$Δ = D_{- 5} - D_{5}$	(10)
Degree of multifractality (Δ) and asymmetry (AI)	$A I = \frac{α_{0} - α_{5}}{α_{- 5} - α_{0}}$	(11)

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Multifractal analysis of weeds in a no-tillage system in the Pre-Amazon region1 1 Research developed at Unha de Gato Farming, Mata Roma, MA, Brazil

Análise multifractal das plantas-daninhas em sistema de semeadura direta na região Pré-Amazônia

HIGHLIGHTS:

ABSTRACT

Multifractal analysis of weeds in a no-tillage system in the Pre-Amazon region¹ 1 Research developed at Unha de Gato Farming, Mata Roma, MA, Brazil