Characterizing land-use change over space and time: applying principal components analysis in the Brazilian Legal Amazon

Figures & data

Table 1. Derivation of municipal-level variables included

Variable	Calculation
Average property size
Property GINI^a
Crop/animal production ratio
Total production intensity
Crop production intensity
Animal production intensity
Rate of tractor use^b
Rate of contract labor use^b
Fraction of land in pasture^b
Fraction of land in forest^b
Fraction of land in crops^b
Fraction of land abandoned or unused^b

Notes: ^aProperty sizes are reported as the number of properties and total area falling in a particular size class j. In the case of the Property GINI, individual areas A_i are calculated as the average area in the size class. Bounds for class sizes differ between the 1996 and 2006 census, so there is some error associated with this differing resolution. ^bProportion variables are arcsine transformed.

Table 2. Descriptive statistics for municipal-level variables included

		Tocantins		Maranhão		Acre		Pará		Rondônia		Mato Grosso		Amapá		Amazonas		Roraima
		1996	2006	1996	2006	1996	2006	1996	2006	1996	2006	1996	2006	1996	2006	1996	2006	1996	2006
Average property size (ha)	Mean	281	263	40	61	152	116	133	144	139	119	615	613	252	253	42	52	387	239
	SD	217	254	56	68	121	74	203	228	129	107	612	701	270	363	56	49	305	199
Property GINI	Mean	0.73	0.65	0.83	0.40	0.63	0.51	0.69	0.61	0.66	0.63	0.82	0.76	0.73	0.45	0.62	0.49	0.67	0.45
	SD	0.10	0.13	0.12	0.35	0.13	0.21	0.15	0.24	0.14	0.12	0.07	0.09	0.16	0.37	0.20	0.32	0.19	0.25
Crop/animal production ratio	Mean	0.50	3.94	2.87	8.96	4.05	4.06	5.67	17.78	1.07	1.29	2.83	40.91	49.68	12.96	283.25	25.04	1.62	15.03
	SD	0.65	10.52	3.56	16.32	7.13	2.90	11.22	40.97	0.68	1.17	7.24	180.00	126.53	31.70	1983.31	58.79	1.48	43.92
Total production intensity ($R/ha)	Mean	55	80	496	511	130	133	248	342	92	114	110	220	180	208	617	290	53	118
	SD	43	100	2024	2046	181	106	441	483	55	65	117	368	149	368	798	280	22	245
Crop production intensity ($R/ha)	Mean	40	30	179	127	29	26	78	78	47	57	45	23	30	25	39	33	23	15
	SD	34	45	796	877	18	22	183	263	29	39	46	27	24	20	49	67	13	15
Animal production intensity ($R/ha)	Mean	14	49	317	336	100	92	169	220	44	54	64	194	150	152	578	226	30	102
	SD	16	82	1340	1190	174	75	357	331	32	43	104	355	162	307	792	246	18	246
Rate of tractor use	Mean	0.14	0.19	0.01	0.04	0.02	0.02	0.04	0.08	0.04	0.08	0.43	0.64	0.04	0.03	0.01	0.01	0.04	0.16
	SD	0.14	0.15	0.03	0.06	0.02	0.02	0.05	0.12	0.03	0.07	0.51	1.01	0.06	0.07	0.03	0.03	0.04	0.44
Rate of contract labor Use	Mean	0.21	0.22	0.09	0.19	0.12	0.13	0.11	0.19	0.15	0.19	0.23	0.30	0.05	0.25	0.05	0.10	0.17	0.10
	SD	0.16	0.14	0.10	0.12	0.11	0.09	0.11	0.15	0.10	0.08	0.10	0.23	0.04	0.16	0.10	0.09	0.17	0.08
Fraction of Land in Pasture	Mean	0.68	0.57	0.39	0.47	0.20	0.29	0.30	0.40	0.37	0.60	0.52	0.50	0.37	0.35	0.13	0.18	0.41	0.44
	SD	0.11	0.16	0.21	0.24	0.10	0.15	0.22	0.25	0.15	0.13	0.21	0.21	0.27	0.18	0.12	0.18	0.23	0.22
Fraction of land in forest	Mean	0.19	0.34	0.20	0.25	0.70	0.61	0.43	0.40	0.53	0.32	0.37	0.35	0.53	0.49	0.55	0.41	0.49	0.44
	SD	0.08	0.14	0.14	0.16	0.19	0.18	0.23	0.18	0.17	0.13	0.22	0.16	0.23	0.17	0.21	0.25	0.24	0.26
Fraction of land in crops	Mean	0.02	0.06	0.14	0.23	0.04	0.07	0.08	0.15	0.07	0.06	0.07	0.13	0.05	0.11	0.20	0.37	0.04	0.08
	SD	0.02	0.09	0.16	0.26	0.04	0.08	0.09	0.15	0.04	0.03	0.10	0.18	0.04	0.09	0.21	0.31	0.03	0.10
Fraction of land abandoned or unused	Mean	0.11	0.03	0.27	0.02	0.06	0.02	0.19	0.03	0.04	0.01	0.04	0.02	0.06	0.01	0.12	0.02	0.06	0.02
	SD	0.08	0.03	0.14	0.03	0.10	0.02	0.19	0.04	0.03	0.01	0.03	0.03	0.04	0.02	0.13	0.02	0.03	0.01

Figure 1. Variable loadings in the first four PCs for the combined 1996–2006 agricultural census dataset. Shade intensity represents the strength of the PC loadings, with bolder shades representing stronger loadings. Loadings to the left of the central axis in each PC are negative; loadings to the right of the central axis are positive.

Figure 2. Changes in the first four PCs for conserved municipalities from 1996 to 2006.

Figure 3. Changes in first four PCs in municipalities, organized by state. In each graph, a municipality’s PC score in 1996 is represented as a small circle, with the 2006 score represented by a large circle, connected to the 1996 score by a black vertical line. Municipalities are ordered from lowest to greatest 1996 PC score.

Figure 4. Fuzzy c-means clusters for n = 4 for the PC scores resulting from the combined 1996–2006 dataset, with clustering applied separátely to the 1996 and 2006 subsets. Each municipality has a fractional membership in each of the four clusters, with a fraction near 1 indicating near-complete membership in the cluster, a fraction near 0 indicating near-complete membership in other clusters, and fractions near 0.5 indicating weak membership in the cluster. PC loading fractions for each cluster are identified as BR (‘Big Ranching’), PF (‘Pre-frontier’), SF (‘Small Farming’), and MF (‘Mechanized Farming’).

Map 1. Municipalities in the Brazilian Legal Amazon Region. Note that the Legal Amazon is bounded to the east by the 44th Meridian; our analysis includes municipalities in their entirety that have some share to the west of this line, and are included in the set of IBGE-defined Legal Amazon municipalities.